TSTP Solution File: SYN482-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN482-1 : TPTP v8.1.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.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 23:55:49 EDT 2022
% Result : Unsatisfiable 1.38s 1.16s
% Output : Proof 1.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYN482-1 : TPTP v8.1.0. Released v2.1.0.
% 0.07/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n017.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Sep 5 03:46:40 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.36 Usage: tptp [options] [-file:]file
% 0.13/0.36 -h, -? prints this message.
% 0.13/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.36 -m, -model generate model.
% 0.13/0.36 -p, -proof generate proof.
% 0.13/0.36 -c, -core generate unsat core of named formulas.
% 0.13/0.36 -st, -statistics display statistics.
% 0.13/0.36 -t:timeout set timeout (in second).
% 0.13/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.36 -<param>:<value> configuration parameter and value.
% 0.13/0.36 -o:<output-file> file to place output in.
% 1.38/1.16 % SZS status Unsatisfiable
% 1.38/1.16 % SZS output start Proof
% 1.38/1.16 tff(c1_1_type, type, (
% 1.38/1.16 c1_1: $i > $o)).
% 1.38/1.16 tff(a1758_type, type, (
% 1.38/1.16 a1758: $i)).
% 1.38/1.16 tff(hskp3_type, type, (
% 1.38/1.16 hskp3: $o)).
% 1.38/1.16 tff(c0_1_type, type, (
% 1.38/1.16 c0_1: $i > $o)).
% 1.38/1.16 tff(a1780_type, type, (
% 1.38/1.16 a1780: $i)).
% 1.38/1.16 tff(a1781_type, type, (
% 1.38/1.16 a1781: $i)).
% 1.38/1.16 tff(c2_1_type, type, (
% 1.38/1.16 c2_1: $i > $o)).
% 1.38/1.16 tff(a1783_type, type, (
% 1.38/1.16 a1783: $i)).
% 1.38/1.16 tff(c3_1_type, type, (
% 1.38/1.16 c3_1: $i > $o)).
% 1.38/1.16 tff(ndr1_0_type, type, (
% 1.38/1.16 ndr1_0: $o)).
% 1.38/1.16 tff(hskp19_type, type, (
% 1.38/1.16 hskp19: $o)).
% 1.38/1.16 tff(a1765_type, type, (
% 1.38/1.16 a1765: $i)).
% 1.38/1.16 tff(a1762_type, type, (
% 1.38/1.16 a1762: $i)).
% 1.38/1.16 tff(a1771_type, type, (
% 1.38/1.16 a1771: $i)).
% 1.38/1.16 tff(hskp13_type, type, (
% 1.38/1.16 hskp13: $o)).
% 1.38/1.16 tff(hskp6_type, type, (
% 1.38/1.16 hskp6: $o)).
% 1.38/1.16 tff(a1768_type, type, (
% 1.38/1.16 a1768: $i)).
% 1.38/1.16 tff(hskp11_type, type, (
% 1.38/1.16 hskp11: $o)).
% 1.38/1.16 tff(a1827_type, type, (
% 1.38/1.16 a1827: $i)).
% 1.38/1.16 tff(hskp0_type, type, (
% 1.38/1.16 hskp0: $o)).
% 1.38/1.16 tff(hskp4_type, type, (
% 1.38/1.16 hskp4: $o)).
% 1.38/1.16 tff(a1759_type, type, (
% 1.38/1.16 a1759: $i)).
% 1.38/1.16 tff(a1788_type, type, (
% 1.38/1.16 a1788: $i)).
% 1.38/1.16 tff(a1756_type, type, (
% 1.38/1.16 a1756: $i)).
% 1.38/1.16 tff(hskp27_type, type, (
% 1.38/1.16 hskp27: $o)).
% 1.38/1.16 tff(hskp2_type, type, (
% 1.38/1.16 hskp2: $o)).
% 1.38/1.16 tff(a1757_type, type, (
% 1.38/1.16 a1757: $i)).
% 1.38/1.16 tff(hskp1_type, type, (
% 1.38/1.16 hskp1: $o)).
% 1.38/1.16 tff(hskp28_type, type, (
% 1.38/1.16 hskp28: $o)).
% 1.38/1.16 tff(hskp8_type, type, (
% 1.38/1.16 hskp8: $o)).
% 1.38/1.16 tff(hskp25_type, type, (
% 1.38/1.16 hskp25: $o)).
% 1.38/1.16 tff(a1767_type, type, (
% 1.38/1.16 a1767: $i)).
% 1.38/1.16 tff(hskp10_type, type, (
% 1.38/1.16 hskp10: $o)).
% 1.38/1.16 tff(a1799_type, type, (
% 1.38/1.16 a1799: $i)).
% 1.38/1.16 tff(hskp22_type, type, (
% 1.38/1.16 hskp22: $o)).
% 1.38/1.16 tff(hskp16_type, type, (
% 1.38/1.16 hskp16: $o)).
% 1.38/1.16 tff(hskp21_type, type, (
% 1.38/1.16 hskp21: $o)).
% 1.38/1.16 tff(a1809_type, type, (
% 1.38/1.16 a1809: $i)).
% 1.38/1.16 tff(hskp24_type, type, (
% 1.38/1.16 hskp24: $o)).
% 1.38/1.16 tff(a1763_type, type, (
% 1.38/1.16 a1763: $i)).
% 1.38/1.16 tff(hskp7_type, type, (
% 1.38/1.16 hskp7: $o)).
% 1.38/1.16 tff(a1805_type, type, (
% 1.38/1.16 a1805: $i)).
% 1.38/1.16 tff(hskp29_type, type, (
% 1.38/1.16 hskp29: $o)).
% 1.38/1.16 tff(hskp17_type, type, (
% 1.38/1.16 hskp17: $o)).
% 1.38/1.16 tff(a1823_type, type, (
% 1.38/1.16 a1823: $i)).
% 1.38/1.16 tff(hskp30_type, type, (
% 1.38/1.16 hskp30: $o)).
% 1.38/1.16 tff(a1754_type, type, (
% 1.38/1.16 a1754: $i)).
% 1.38/1.16 tff(a1807_type, type, (
% 1.38/1.16 a1807: $i)).
% 1.38/1.16 tff(a1779_type, type, (
% 1.38/1.16 a1779: $i)).
% 1.38/1.16 tff(hskp15_type, type, (
% 1.38/1.16 hskp15: $o)).
% 1.38/1.16 tff(a1777_type, type, (
% 1.38/1.16 a1777: $i)).
% 1.38/1.16 tff(hskp14_type, type, (
% 1.38/1.16 hskp14: $o)).
% 1.38/1.16 tff(hskp23_type, type, (
% 1.38/1.16 hskp23: $o)).
% 1.38/1.16 tff(a1760_type, type, (
% 1.38/1.16 a1760: $i)).
% 1.38/1.16 tff(a1786_type, type, (
% 1.38/1.16 a1786: $i)).
% 1.38/1.16 tff(hskp20_type, type, (
% 1.38/1.16 hskp20: $o)).
% 1.38/1.16 tff(hskp12_type, type, (
% 1.38/1.16 hskp12: $o)).
% 1.38/1.16 tff(a1770_type, type, (
% 1.38/1.16 a1770: $i)).
% 1.38/1.16 tff(hskp18_type, type, (
% 1.38/1.16 hskp18: $o)).
% 1.38/1.16 tff(a1782_type, type, (
% 1.38/1.16 a1782: $i)).
% 1.38/1.16 tff(a1795_type, type, (
% 1.38/1.16 a1795: $i)).
% 1.38/1.16 tff(hskp5_type, type, (
% 1.38/1.16 hskp5: $o)).
% 1.38/1.16 tff(1,assumption,(~c2_1(a1783)), introduced(assumption)).
% 1.38/1.16 tff(2,plain,
% 1.38/1.16 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.38/1.16 inference(bind,[status(th)],[])).
% 1.38/1.16 tff(3,plain,
% 1.38/1.16 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.38/1.16 inference(quant_intro,[status(thm)],[2])).
% 1.38/1.16 tff(4,plain,
% 1.38/1.16 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.38/1.16 inference(rewrite,[status(thm)],[])).
% 1.38/1.16 tff(5,plain,
% 1.38/1.16 (^[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)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~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)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~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)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | 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)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | hskp3) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp3))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp3) <=> (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.38/1.16 inference(bind,[status(th)],[])).
% 1.38/1.16 tff(6,plain,
% 1.38/1.16 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.38/1.16 inference(quant_intro,[status(thm)],[5])).
% 1.38/1.16 tff(7,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c2_1(V)) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause178')).
% 1.38/1.16 tff(8,plain,
% 1.38/1.16 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[7, 6])).
% 1.38/1.16 tff(9,plain,
% 1.38/1.16 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[8, 4])).
% 1.38/1.16 tff(10,plain,(
% 1.38/1.16 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.38/1.16 inference(skolemize,[status(sab)],[9])).
% 1.38/1.16 tff(11,plain,
% 1.38/1.16 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[10, 3])).
% 1.38/1.16 tff(12,assumption,(~hskp19), introduced(assumption)).
% 1.38/1.16 tff(13,plain,
% 1.38/1.16 (^[U: $i] : refl((hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))),
% 1.38/1.16 inference(bind,[status(th)],[])).
% 1.38/1.16 tff(14,plain,
% 1.38/1.16 (![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.38/1.16 inference(quant_intro,[status(thm)],[13])).
% 1.38/1.16 tff(15,plain,
% 1.38/1.16 (![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.38/1.16 inference(rewrite,[status(thm)],[])).
% 1.38/1.16 tff(16,plain,
% 1.38/1.16 (^[U: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp13) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp13))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp13) <=> (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp13) <=> (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))))),
% 1.38/1.16 inference(bind,[status(th)],[])).
% 1.38/1.16 tff(17,plain,
% 1.38/1.16 (![U: $i] : (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp13) <=> ![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.38/1.16 inference(quant_intro,[status(thm)],[16])).
% 1.38/1.16 tff(18,axiom,(![U: $i] : (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause140')).
% 1.38/1.16 tff(19,plain,
% 1.38/1.16 (![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[18, 17])).
% 1.38/1.16 tff(20,plain,
% 1.38/1.16 (![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[19, 15])).
% 1.38/1.16 tff(21,plain,(
% 1.38/1.16 ![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.38/1.16 inference(skolemize,[status(sab)],[20])).
% 1.38/1.16 tff(22,plain,
% 1.38/1.16 (![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[21, 14])).
% 1.38/1.16 tff(23,assumption,(~hskp13), introduced(assumption)).
% 1.38/1.16 tff(24,plain,
% 1.38/1.16 (^[U: $i] : refl((hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 1.38/1.16 inference(bind,[status(th)],[])).
% 1.38/1.16 tff(25,plain,
% 1.38/1.16 (![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.38/1.16 inference(quant_intro,[status(thm)],[24])).
% 1.38/1.16 tff(26,plain,
% 1.38/1.16 (![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.38/1.16 inference(rewrite,[status(thm)],[])).
% 1.38/1.16 tff(27,plain,
% 1.38/1.16 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp13) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp13))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp13) <=> (hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp13) <=> (hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp13) | hskp19) <=> ((hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp19))), rewrite(((hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp19) <=> (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp13) | hskp19) <=> (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 1.38/1.16 inference(bind,[status(th)],[])).
% 1.38/1.16 tff(28,plain,
% 1.38/1.16 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp13) | hskp19) <=> ![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.38/1.16 inference(quant_intro,[status(thm)],[27])).
% 1.38/1.16 tff(29,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp13) | hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause147')).
% 1.38/1.16 tff(30,plain,
% 1.38/1.16 (![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[29, 28])).
% 1.38/1.16 tff(31,plain,
% 1.38/1.16 (![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[30, 26])).
% 1.38/1.16 tff(32,plain,(
% 1.38/1.16 ![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.38/1.16 inference(skolemize,[status(sab)],[31])).
% 1.38/1.16 tff(33,plain,
% 1.38/1.16 (![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[32, 25])).
% 1.38/1.16 tff(34,assumption,(~c3_1(a1759)), introduced(assumption)).
% 1.38/1.16 tff(35,assumption,(~hskp3), introduced(assumption)).
% 1.38/1.16 tff(36,assumption,(~c2_1(a1759)), introduced(assumption)).
% 1.38/1.16 tff(37,plain,
% 1.38/1.16 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W))))),
% 1.38/1.16 inference(bind,[status(th)],[])).
% 1.38/1.16 tff(38,plain,
% 1.38/1.16 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.38/1.16 inference(quant_intro,[status(thm)],[37])).
% 1.38/1.16 tff(39,plain,
% 1.38/1.16 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.38/1.16 inference(rewrite,[status(thm)],[])).
% 1.38/1.16 tff(40,plain,
% 1.38/1.16 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))))),
% 1.38/1.16 inference(bind,[status(th)],[])).
% 1.38/1.16 tff(41,plain,
% 1.38/1.16 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.38/1.16 inference(quant_intro,[status(thm)],[40])).
% 1.38/1.16 tff(42,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | (~c3_1(W))) | c1_1(U)) | c0_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause192')).
% 1.38/1.16 tff(43,plain,
% 1.38/1.16 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[42, 41])).
% 1.38/1.16 tff(44,plain,
% 1.38/1.16 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[43, 39])).
% 1.38/1.16 tff(45,plain,(
% 1.38/1.16 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.38/1.16 inference(skolemize,[status(sab)],[44])).
% 1.38/1.16 tff(46,plain,
% 1.38/1.16 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.38/1.16 inference(modus_ponens,[status(thm)],[45, 38])).
% 1.38/1.16 tff(47,assumption,(~c1_1(a1759)), introduced(assumption)).
% 1.38/1.16 tff(48,assumption,(hskp2), introduced(assumption)).
% 1.38/1.16 tff(49,plain,
% 1.38/1.16 (((~hskp2) | (~c2_1(a1757))) <=> ((~hskp2) | (~c2_1(a1757)))),
% 1.38/1.16 inference(rewrite,[status(thm)],[])).
% 1.38/1.16 tff(50,plain,
% 1.38/1.16 (((~c2_1(a1757)) | (~hskp2)) <=> ((~hskp2) | (~c2_1(a1757)))),
% 1.38/1.16 inference(rewrite,[status(thm)],[])).
% 1.38/1.16 tff(51,axiom,((~c2_1(a1757)) | (~hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause126')).
% 1.38/1.17 tff(52,plain,
% 1.38/1.17 ((~hskp2) | (~c2_1(a1757))),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[51, 50])).
% 1.38/1.17 tff(53,plain,
% 1.38/1.17 ((~hskp2) | (~c2_1(a1757))),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[52, 49])).
% 1.38/1.17 tff(54,plain,
% 1.38/1.17 (~c2_1(a1757)),
% 1.38/1.17 inference(unit_resolution,[status(thm)],[53, 48])).
% 1.38/1.17 tff(55,plain,
% 1.38/1.17 (((~hskp2) | c1_1(a1757)) <=> ((~hskp2) | c1_1(a1757))),
% 1.38/1.17 inference(rewrite,[status(thm)],[])).
% 1.38/1.17 tff(56,axiom,((~hskp2) | c1_1(a1757)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause82')).
% 1.38/1.17 tff(57,plain,
% 1.38/1.17 ((~hskp2) | c1_1(a1757)),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[56, 55])).
% 1.38/1.17 tff(58,plain,
% 1.38/1.17 ((~hskp2) | c1_1(a1757)),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[57, 55])).
% 1.38/1.17 tff(59,plain,
% 1.38/1.17 ((~hskp2) | c1_1(a1757)),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[58, 55])).
% 1.38/1.17 tff(60,plain,
% 1.38/1.17 ((~hskp2) | c1_1(a1757)),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[59, 55])).
% 1.38/1.17 tff(61,plain,
% 1.38/1.17 ((~hskp2) | c1_1(a1757)),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[60, 55])).
% 1.38/1.17 tff(62,plain,
% 1.38/1.17 ((~hskp2) | c1_1(a1757)),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[61, 55])).
% 1.38/1.17 tff(63,plain,
% 1.38/1.17 ((~hskp2) | c1_1(a1757)),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[62, 55])).
% 1.38/1.17 tff(64,plain,
% 1.38/1.17 ((~hskp2) | c1_1(a1757)),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[63, 55])).
% 1.38/1.17 tff(65,plain,
% 1.38/1.17 (c1_1(a1757)),
% 1.38/1.17 inference(unit_resolution,[status(thm)],[64, 48])).
% 1.38/1.17 tff(66,plain,
% 1.38/1.17 (((~hskp2) | c0_1(a1757)) <=> ((~hskp2) | c0_1(a1757))),
% 1.38/1.17 inference(rewrite,[status(thm)],[])).
% 1.38/1.17 tff(67,axiom,((~hskp2) | c0_1(a1757)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause81')).
% 1.38/1.17 tff(68,plain,
% 1.38/1.17 ((~hskp2) | c0_1(a1757)),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[67, 66])).
% 1.38/1.17 tff(69,plain,
% 1.38/1.17 ((~hskp2) | c0_1(a1757)),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[68, 66])).
% 1.38/1.17 tff(70,plain,
% 1.38/1.17 ((~hskp2) | c0_1(a1757)),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[69, 66])).
% 1.38/1.17 tff(71,plain,
% 1.38/1.17 ((~hskp2) | c0_1(a1757)),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[70, 66])).
% 1.38/1.17 tff(72,plain,
% 1.38/1.17 ((~hskp2) | c0_1(a1757)),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[71, 66])).
% 1.38/1.17 tff(73,plain,
% 1.38/1.17 ((~hskp2) | c0_1(a1757)),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[72, 66])).
% 1.38/1.17 tff(74,plain,
% 1.38/1.17 ((~hskp2) | c0_1(a1757)),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[73, 66])).
% 1.38/1.17 tff(75,plain,
% 1.38/1.17 ((~hskp2) | c0_1(a1757)),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[74, 66])).
% 1.38/1.17 tff(76,plain,
% 1.38/1.17 (c0_1(a1757)),
% 1.38/1.17 inference(unit_resolution,[status(thm)],[75, 48])).
% 1.38/1.17 tff(77,assumption,(~ndr1_0), introduced(assumption)).
% 1.38/1.17 tff(78,plain,
% 1.38/1.17 ((ndr1_0 | (~hskp1)) <=> (ndr1_0 | (~hskp1))),
% 1.38/1.17 inference(rewrite,[status(thm)],[])).
% 1.38/1.17 tff(79,plain,
% 1.38/1.17 (((~hskp1) | ndr1_0) <=> (ndr1_0 | (~hskp1))),
% 1.38/1.17 inference(rewrite,[status(thm)],[])).
% 1.38/1.17 tff(80,axiom,((~hskp1) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause30')).
% 1.38/1.17 tff(81,plain,
% 1.38/1.17 (ndr1_0 | (~hskp1)),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[80, 79])).
% 1.38/1.17 tff(82,plain,
% 1.38/1.17 (ndr1_0 | (~hskp1)),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[81, 78])).
% 1.38/1.17 tff(83,plain,
% 1.38/1.17 (~hskp1),
% 1.38/1.17 inference(unit_resolution,[status(thm)],[82, 77])).
% 1.38/1.17 tff(84,plain,
% 1.38/1.17 ((ndr1_0 | (~hskp28)) <=> (ndr1_0 | (~hskp28))),
% 1.38/1.17 inference(rewrite,[status(thm)],[])).
% 1.38/1.17 tff(85,plain,
% 1.38/1.17 (((~hskp28) | ndr1_0) <=> (ndr1_0 | (~hskp28))),
% 1.38/1.17 inference(rewrite,[status(thm)],[])).
% 1.38/1.17 tff(86,axiom,((~hskp28) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause3')).
% 1.38/1.17 tff(87,plain,
% 1.38/1.17 (ndr1_0 | (~hskp28)),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[86, 85])).
% 1.38/1.17 tff(88,plain,
% 1.38/1.17 (ndr1_0 | (~hskp28)),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[87, 84])).
% 1.38/1.17 tff(89,plain,
% 1.38/1.17 (~hskp28),
% 1.38/1.17 inference(unit_resolution,[status(thm)],[88, 77])).
% 1.38/1.17 tff(90,plain,
% 1.38/1.17 ((ndr1_0 | (~hskp4)) <=> (ndr1_0 | (~hskp4))),
% 1.38/1.17 inference(rewrite,[status(thm)],[])).
% 1.38/1.17 tff(91,plain,
% 1.38/1.17 (((~hskp4) | ndr1_0) <=> (ndr1_0 | (~hskp4))),
% 1.38/1.17 inference(rewrite,[status(thm)],[])).
% 1.38/1.17 tff(92,axiom,((~hskp4) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause27')).
% 1.38/1.17 tff(93,plain,
% 1.38/1.17 (ndr1_0 | (~hskp4)),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[92, 91])).
% 1.38/1.17 tff(94,plain,
% 1.38/1.17 (ndr1_0 | (~hskp4)),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[93, 90])).
% 1.38/1.17 tff(95,plain,
% 1.38/1.17 (~hskp4),
% 1.38/1.17 inference(unit_resolution,[status(thm)],[94, 77])).
% 1.38/1.17 tff(96,plain,
% 1.38/1.17 ((hskp28 | hskp4 | hskp1) <=> (hskp28 | hskp4 | hskp1)),
% 1.38/1.17 inference(rewrite,[status(thm)],[])).
% 1.38/1.17 tff(97,plain,
% 1.38/1.17 (((hskp28 | hskp1) | hskp4) <=> (hskp28 | hskp4 | hskp1)),
% 1.38/1.17 inference(rewrite,[status(thm)],[])).
% 1.38/1.17 tff(98,plain,
% 1.38/1.17 ((hskp28 | hskp1) <=> (hskp28 | hskp1)),
% 1.38/1.17 inference(rewrite,[status(thm)],[])).
% 1.38/1.17 tff(99,plain,
% 1.38/1.17 (((hskp28 | hskp1) | hskp4) <=> ((hskp28 | hskp1) | hskp4)),
% 1.38/1.17 inference(monotonicity,[status(thm)],[98])).
% 1.38/1.17 tff(100,plain,
% 1.38/1.17 (((hskp28 | hskp1) | hskp4) <=> (hskp28 | hskp4 | hskp1)),
% 1.38/1.17 inference(transitivity,[status(thm)],[99, 97])).
% 1.38/1.17 tff(101,axiom,((hskp28 | hskp1) | hskp4), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause32')).
% 1.38/1.17 tff(102,plain,
% 1.38/1.17 (hskp28 | hskp4 | hskp1),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[101, 100])).
% 1.38/1.17 tff(103,plain,
% 1.38/1.17 (hskp28 | hskp4 | hskp1),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[102, 96])).
% 1.38/1.17 tff(104,plain,
% 1.38/1.17 (hskp28 | hskp4 | hskp1),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[103, 96])).
% 1.38/1.17 tff(105,plain,
% 1.38/1.17 (hskp28 | hskp4 | hskp1),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[104, 96])).
% 1.38/1.17 tff(106,plain,
% 1.38/1.17 (hskp28 | hskp4 | hskp1),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[105, 96])).
% 1.38/1.17 tff(107,plain,
% 1.38/1.17 (hskp28 | hskp4 | hskp1),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[106, 96])).
% 1.38/1.17 tff(108,plain,
% 1.38/1.17 (hskp28 | hskp4 | hskp1),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[107, 96])).
% 1.38/1.17 tff(109,plain,
% 1.38/1.17 (hskp28 | hskp4 | hskp1),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[108, 96])).
% 1.38/1.17 tff(110,plain,
% 1.38/1.17 ($false),
% 1.38/1.17 inference(unit_resolution,[status(thm)],[109, 95, 89, 83])).
% 1.38/1.17 tff(111,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 1.38/1.17 tff(112,plain,
% 1.38/1.17 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp13 | c2_1(a1757) | (~ndr1_0) | (~c1_1(a1757)) | (~c0_1(a1757)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp19 | hskp13 | c2_1(a1757) | (~ndr1_0) | (~c1_1(a1757)) | (~c0_1(a1757)))),
% 1.38/1.17 inference(rewrite,[status(thm)],[])).
% 1.38/1.17 tff(113,plain,
% 1.38/1.17 ((hskp19 | hskp13 | (~ndr1_0) | c2_1(a1757) | (~c1_1(a1757)) | (~c0_1(a1757))) <=> (hskp19 | hskp13 | c2_1(a1757) | (~ndr1_0) | (~c1_1(a1757)) | (~c0_1(a1757)))),
% 1.38/1.17 inference(rewrite,[status(thm)],[])).
% 1.38/1.17 tff(114,plain,
% 1.38/1.17 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | c2_1(a1757) | (~c1_1(a1757)) | (~c0_1(a1757)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp13 | c2_1(a1757) | (~ndr1_0) | (~c1_1(a1757)) | (~c0_1(a1757))))),
% 1.38/1.17 inference(monotonicity,[status(thm)],[113])).
% 1.38/1.17 tff(115,plain,
% 1.38/1.17 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | c2_1(a1757) | (~c1_1(a1757)) | (~c0_1(a1757)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp19 | hskp13 | c2_1(a1757) | (~ndr1_0) | (~c1_1(a1757)) | (~c0_1(a1757)))),
% 1.38/1.17 inference(transitivity,[status(thm)],[114, 112])).
% 1.38/1.17 tff(116,plain,
% 1.38/1.17 ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | c2_1(a1757) | (~c1_1(a1757)) | (~c0_1(a1757)))),
% 1.38/1.17 inference(quant_inst,[status(thm)],[])).
% 1.38/1.17 tff(117,plain,
% 1.38/1.17 ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp19 | hskp13 | c2_1(a1757) | (~ndr1_0) | (~c1_1(a1757)) | (~c0_1(a1757))),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[116, 115])).
% 1.38/1.17 tff(118,plain,
% 1.38/1.17 ($false),
% 1.38/1.17 inference(unit_resolution,[status(thm)],[117, 111, 12, 23, 76, 65, 54, 33])).
% 1.38/1.17 tff(119,plain,((~hskp2) | hskp19 | hskp13), inference(lemma,lemma(discharge,[]))).
% 1.38/1.17 tff(120,plain,
% 1.38/1.17 (~hskp2),
% 1.38/1.17 inference(unit_resolution,[status(thm)],[119, 23, 12])).
% 1.38/1.17 tff(121,plain,
% 1.38/1.17 (^[U: $i] : refl((hskp8 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> (hskp8 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))))),
% 1.38/1.17 inference(bind,[status(th)],[])).
% 1.38/1.17 tff(122,plain,
% 1.38/1.17 (![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.38/1.17 inference(quant_intro,[status(thm)],[121])).
% 1.38/1.17 tff(123,plain,
% 1.38/1.17 (![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.38/1.17 inference(rewrite,[status(thm)],[])).
% 1.38/1.17 tff(124,plain,
% 1.38/1.17 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp8) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp8))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp8) <=> (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp8) | hskp4) <=> ((hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp4))), rewrite(((hskp8 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp4) <=> (hskp8 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp8) | hskp4) <=> (hskp8 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))))),
% 1.38/1.17 inference(bind,[status(th)],[])).
% 1.38/1.17 tff(125,plain,
% 1.38/1.17 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp8) | hskp4) <=> ![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.38/1.17 inference(quant_intro,[status(thm)],[124])).
% 1.38/1.17 tff(126,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp8) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause146')).
% 1.38/1.17 tff(127,plain,
% 1.38/1.17 (![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[126, 125])).
% 1.38/1.17 tff(128,plain,
% 1.38/1.17 (![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[127, 123])).
% 1.38/1.17 tff(129,plain,(
% 1.38/1.17 ![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.38/1.17 inference(skolemize,[status(sab)],[128])).
% 1.38/1.17 tff(130,plain,
% 1.38/1.17 (![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[129, 122])).
% 1.38/1.17 tff(131,plain,
% 1.38/1.17 (^[U: $i] : refl((hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))),
% 1.38/1.17 inference(bind,[status(th)],[])).
% 1.38/1.17 tff(132,plain,
% 1.38/1.17 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.38/1.17 inference(quant_intro,[status(thm)],[131])).
% 1.38/1.17 tff(133,plain,
% 1.38/1.17 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.38/1.17 inference(rewrite,[status(thm)],[])).
% 1.38/1.17 tff(134,plain,
% 1.38/1.17 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | 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))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp3) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp3))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp3) | hskp4) <=> ((hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp4))), rewrite(((hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp4) <=> (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp3) | hskp4) <=> (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))))),
% 1.38/1.17 inference(bind,[status(th)],[])).
% 1.38/1.17 tff(135,plain,
% 1.38/1.17 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp3) | hskp4) <=> ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.38/1.17 inference(quant_intro,[status(thm)],[134])).
% 1.38/1.17 tff(136,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp3) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause133')).
% 1.38/1.17 tff(137,plain,
% 1.38/1.17 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[136, 135])).
% 1.38/1.17 tff(138,plain,
% 1.38/1.17 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[137, 133])).
% 1.38/1.17 tff(139,plain,(
% 1.38/1.17 ![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.38/1.17 inference(skolemize,[status(sab)],[138])).
% 1.38/1.17 tff(140,plain,
% 1.38/1.17 (![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[139, 132])).
% 1.38/1.17 tff(141,plain,
% 1.38/1.17 (((~hskp4) | c1_1(a1759)) <=> ((~hskp4) | c1_1(a1759))),
% 1.38/1.17 inference(rewrite,[status(thm)],[])).
% 1.38/1.17 tff(142,axiom,((~hskp4) | c1_1(a1759)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause78')).
% 1.38/1.17 tff(143,plain,
% 1.38/1.17 ((~hskp4) | c1_1(a1759)),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[142, 141])).
% 1.38/1.17 tff(144,plain,
% 1.38/1.17 ((~hskp4) | c1_1(a1759)),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[143, 141])).
% 1.38/1.17 tff(145,plain,
% 1.38/1.17 ((~hskp4) | c1_1(a1759)),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[144, 141])).
% 1.38/1.17 tff(146,plain,
% 1.38/1.17 ((~hskp4) | c1_1(a1759)),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[145, 141])).
% 1.38/1.17 tff(147,plain,
% 1.38/1.17 ((~hskp4) | c1_1(a1759)),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[146, 141])).
% 1.38/1.17 tff(148,plain,
% 1.38/1.17 ((~hskp4) | c1_1(a1759)),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[147, 141])).
% 1.38/1.17 tff(149,plain,
% 1.38/1.17 ((~hskp4) | c1_1(a1759)),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[148, 141])).
% 1.38/1.17 tff(150,plain,
% 1.38/1.17 ((~hskp4) | c1_1(a1759)),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[149, 141])).
% 1.38/1.17 tff(151,plain,
% 1.38/1.17 (~hskp4),
% 1.38/1.17 inference(unit_resolution,[status(thm)],[150, 47])).
% 1.38/1.17 tff(152,plain,
% 1.38/1.17 ((hskp25 | hskp4 | hskp2) <=> (hskp25 | hskp4 | hskp2)),
% 1.38/1.17 inference(rewrite,[status(thm)],[])).
% 1.38/1.17 tff(153,plain,
% 1.38/1.17 (((hskp2 | hskp4) | hskp25) <=> (hskp25 | hskp4 | hskp2)),
% 1.38/1.17 inference(rewrite,[status(thm)],[])).
% 1.38/1.17 tff(154,axiom,((hskp2 | hskp4) | hskp25), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause34')).
% 1.38/1.17 tff(155,plain,
% 1.38/1.17 (hskp25 | hskp4 | hskp2),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[154, 153])).
% 1.38/1.17 tff(156,plain,
% 1.38/1.17 (hskp25 | hskp4 | hskp2),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[155, 152])).
% 1.38/1.17 tff(157,plain,
% 1.38/1.17 (hskp25 | hskp4 | hskp2),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[156, 152])).
% 1.38/1.17 tff(158,plain,
% 1.38/1.17 (hskp25 | hskp4 | hskp2),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[157, 152])).
% 1.38/1.17 tff(159,plain,
% 1.38/1.17 (hskp25 | hskp4 | hskp2),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[158, 152])).
% 1.38/1.17 tff(160,plain,
% 1.38/1.17 (hskp25 | hskp4 | hskp2),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[159, 152])).
% 1.38/1.17 tff(161,plain,
% 1.38/1.17 (hskp25 | hskp4 | hskp2),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[160, 152])).
% 1.38/1.17 tff(162,plain,
% 1.38/1.17 (hskp25 | hskp4 | hskp2),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[161, 152])).
% 1.38/1.17 tff(163,plain,
% 1.38/1.17 (hskp25),
% 1.38/1.17 inference(unit_resolution,[status(thm)],[162, 120, 151])).
% 1.38/1.17 tff(164,plain,
% 1.38/1.17 (((~hskp25) | (~c1_1(a1827))) <=> ((~hskp25) | (~c1_1(a1827)))),
% 1.38/1.17 inference(rewrite,[status(thm)],[])).
% 1.38/1.17 tff(165,plain,
% 1.38/1.17 (((~c1_1(a1827)) | (~hskp25)) <=> ((~hskp25) | (~c1_1(a1827)))),
% 1.38/1.17 inference(rewrite,[status(thm)],[])).
% 1.38/1.17 tff(166,axiom,((~c1_1(a1827)) | (~hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause88')).
% 1.38/1.17 tff(167,plain,
% 1.38/1.17 ((~hskp25) | (~c1_1(a1827))),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[166, 165])).
% 1.38/1.17 tff(168,plain,
% 1.38/1.17 ((~hskp25) | (~c1_1(a1827))),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[167, 164])).
% 1.38/1.17 tff(169,plain,
% 1.38/1.17 (~c1_1(a1827)),
% 1.38/1.17 inference(unit_resolution,[status(thm)],[168, 163])).
% 1.38/1.17 tff(170,plain,
% 1.38/1.17 (((~hskp25) | (~c0_1(a1827))) <=> ((~hskp25) | (~c0_1(a1827)))),
% 1.38/1.17 inference(rewrite,[status(thm)],[])).
% 1.38/1.17 tff(171,plain,
% 1.38/1.17 (((~c0_1(a1827)) | (~hskp25)) <=> ((~hskp25) | (~c0_1(a1827)))),
% 1.38/1.17 inference(rewrite,[status(thm)],[])).
% 1.38/1.17 tff(172,axiom,((~c0_1(a1827)) | (~hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause87')).
% 1.38/1.17 tff(173,plain,
% 1.38/1.17 ((~hskp25) | (~c0_1(a1827))),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[172, 171])).
% 1.38/1.17 tff(174,plain,
% 1.38/1.17 ((~hskp25) | (~c0_1(a1827))),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[173, 170])).
% 1.38/1.17 tff(175,plain,
% 1.38/1.17 (~c0_1(a1827)),
% 1.38/1.17 inference(unit_resolution,[status(thm)],[174, 163])).
% 1.38/1.17 tff(176,plain,
% 1.38/1.17 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | c0_1(a1827) | c1_1(a1827) | (~ndr1_0) | c3_1(a1827))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp4 | hskp3 | c0_1(a1827) | c1_1(a1827) | (~ndr1_0) | c3_1(a1827))),
% 1.38/1.17 inference(rewrite,[status(thm)],[])).
% 1.38/1.17 tff(177,plain,
% 1.38/1.17 ((hskp4 | hskp3 | (~ndr1_0) | c3_1(a1827) | c1_1(a1827) | c0_1(a1827)) <=> (hskp4 | hskp3 | c0_1(a1827) | c1_1(a1827) | (~ndr1_0) | c3_1(a1827))),
% 1.38/1.17 inference(rewrite,[status(thm)],[])).
% 1.38/1.17 tff(178,plain,
% 1.38/1.17 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | (~ndr1_0) | c3_1(a1827) | c1_1(a1827) | c0_1(a1827))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | c0_1(a1827) | c1_1(a1827) | (~ndr1_0) | c3_1(a1827)))),
% 1.38/1.17 inference(monotonicity,[status(thm)],[177])).
% 1.38/1.17 tff(179,plain,
% 1.38/1.17 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | (~ndr1_0) | c3_1(a1827) | c1_1(a1827) | c0_1(a1827))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp4 | hskp3 | c0_1(a1827) | c1_1(a1827) | (~ndr1_0) | c3_1(a1827))),
% 1.38/1.17 inference(transitivity,[status(thm)],[178, 176])).
% 1.38/1.17 tff(180,plain,
% 1.38/1.17 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | (~ndr1_0) | c3_1(a1827) | c1_1(a1827) | c0_1(a1827))),
% 1.38/1.17 inference(quant_inst,[status(thm)],[])).
% 1.38/1.17 tff(181,plain,
% 1.38/1.17 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp4 | hskp3 | c0_1(a1827) | c1_1(a1827) | (~ndr1_0) | c3_1(a1827)),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[180, 179])).
% 1.38/1.17 tff(182,plain,
% 1.38/1.17 (c3_1(a1827)),
% 1.38/1.17 inference(unit_resolution,[status(thm)],[181, 111, 151, 35, 175, 169, 140])).
% 1.38/1.17 tff(183,plain,
% 1.38/1.17 (^[V: $i, U: $i] : refl((hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))),
% 1.38/1.17 inference(bind,[status(th)],[])).
% 1.38/1.17 tff(184,plain,
% 1.38/1.17 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.38/1.17 inference(quant_intro,[status(thm)],[183])).
% 1.38/1.17 tff(185,plain,
% 1.38/1.17 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.38/1.17 inference(rewrite,[status(thm)],[])).
% 1.38/1.17 tff(186,plain,
% 1.38/1.17 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c1_1(V))), (((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(V) | c1_1(V))), (((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(V) | c1_1(V)))), ((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), (((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), ((((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), (((((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | hskp13) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp13))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | hskp13) <=> (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), (((((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | hskp13) <=> (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))))),
% 1.38/1.17 inference(bind,[status(th)],[])).
% 1.38/1.17 tff(187,plain,
% 1.38/1.17 (![V: $i, U: $i] : ((((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | hskp13) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.38/1.17 inference(quant_intro,[status(thm)],[186])).
% 1.38/1.17 tff(188,axiom,(![V: $i, U: $i] : ((((((((~ndr1_0) | (~c3_1(U))) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(U)) | c2_1(U)) | hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause157')).
% 1.38/1.17 tff(189,plain,
% 1.38/1.17 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[188, 187])).
% 1.38/1.17 tff(190,plain,
% 1.38/1.17 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[189, 185])).
% 1.38/1.17 tff(191,plain,(
% 1.38/1.17 ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.38/1.17 inference(skolemize,[status(sab)],[190])).
% 1.38/1.17 tff(192,plain,
% 1.38/1.17 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[191, 184])).
% 1.38/1.17 tff(193,plain,
% 1.38/1.17 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | c1_1(a1759) | c3_1(a1759) | (~ndr1_0) | c0_1(a1759))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp4 | hskp3 | c1_1(a1759) | c3_1(a1759) | (~ndr1_0) | c0_1(a1759))),
% 1.38/1.17 inference(rewrite,[status(thm)],[])).
% 1.38/1.17 tff(194,plain,
% 1.38/1.17 ((hskp4 | hskp3 | (~ndr1_0) | c3_1(a1759) | c1_1(a1759) | c0_1(a1759)) <=> (hskp4 | hskp3 | c1_1(a1759) | c3_1(a1759) | (~ndr1_0) | c0_1(a1759))),
% 1.38/1.17 inference(rewrite,[status(thm)],[])).
% 1.38/1.17 tff(195,plain,
% 1.38/1.17 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | (~ndr1_0) | c3_1(a1759) | c1_1(a1759) | c0_1(a1759))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | c1_1(a1759) | c3_1(a1759) | (~ndr1_0) | c0_1(a1759)))),
% 1.38/1.17 inference(monotonicity,[status(thm)],[194])).
% 1.38/1.17 tff(196,plain,
% 1.38/1.17 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | (~ndr1_0) | c3_1(a1759) | c1_1(a1759) | c0_1(a1759))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp4 | hskp3 | c1_1(a1759) | c3_1(a1759) | (~ndr1_0) | c0_1(a1759))),
% 1.38/1.17 inference(transitivity,[status(thm)],[195, 193])).
% 1.38/1.17 tff(197,plain,
% 1.38/1.17 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | (~ndr1_0) | c3_1(a1759) | c1_1(a1759) | c0_1(a1759))),
% 1.38/1.17 inference(quant_inst,[status(thm)],[])).
% 1.38/1.17 tff(198,plain,
% 1.38/1.17 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp4 | hskp3 | c1_1(a1759) | c3_1(a1759) | (~ndr1_0) | c0_1(a1759)),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[197, 196])).
% 1.38/1.17 tff(199,plain,
% 1.38/1.17 (hskp4 | hskp3 | c1_1(a1759) | c0_1(a1759)),
% 1.38/1.17 inference(unit_resolution,[status(thm)],[198, 111, 34, 140])).
% 1.38/1.17 tff(200,plain,
% 1.38/1.17 (c0_1(a1759)),
% 1.38/1.17 inference(unit_resolution,[status(thm)],[199, 35, 47, 151])).
% 1.38/1.17 tff(201,plain,
% 1.38/1.17 (^[V: $i, U: $i] : refl((hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))))),
% 1.38/1.17 inference(bind,[status(th)],[])).
% 1.38/1.17 tff(202,plain,
% 1.38/1.17 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.38/1.17 inference(quant_intro,[status(thm)],[201])).
% 1.38/1.17 tff(203,plain,
% 1.38/1.17 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.38/1.17 inference(rewrite,[status(thm)],[])).
% 1.38/1.17 tff(204,plain,
% 1.38/1.17 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | 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))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | 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))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | 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))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | 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))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp2) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp2))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp2) <=> (hskp2 | (~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))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp2) <=> (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))))),
% 1.38/1.17 inference(bind,[status(th)],[])).
% 1.38/1.17 tff(205,plain,
% 1.38/1.17 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp2) <=> ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.38/1.17 inference(quant_intro,[status(thm)],[204])).
% 1.38/1.17 tff(206,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause172')).
% 1.38/1.17 tff(207,plain,
% 1.38/1.17 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[206, 205])).
% 1.38/1.17 tff(208,plain,
% 1.38/1.17 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[207, 203])).
% 1.38/1.17 tff(209,plain,(
% 1.38/1.17 ![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.38/1.17 inference(skolemize,[status(sab)],[208])).
% 1.38/1.17 tff(210,plain,
% 1.38/1.17 (![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.38/1.17 inference(modus_ponens,[status(thm)],[209, 202])).
% 1.38/1.17 tff(211,plain,
% 1.38/1.17 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp2 | c1_1(a1759) | (~c2_1(a1759)) | c3_1(a1759) | (~ndr1_0) | (~c0_1(a1759)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp2 | c1_1(a1759) | (~c2_1(a1759)) | c3_1(a1759) | (~ndr1_0) | (~c0_1(a1759)))),
% 1.38/1.17 inference(rewrite,[status(thm)],[])).
% 1.38/1.17 tff(212,plain,
% 1.38/1.17 ((hskp2 | (~ndr1_0) | c3_1(a1759) | (~c2_1(a1759)) | (~c0_1(a1759)) | c1_1(a1759) | c3_1(a1759) | (~c0_1(a1759))) <=> (hskp2 | c1_1(a1759) | (~c2_1(a1759)) | c3_1(a1759) | (~ndr1_0) | (~c0_1(a1759)))),
% 1.38/1.17 inference(rewrite,[status(thm)],[])).
% 1.38/1.17 tff(213,plain,
% 1.38/1.17 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a1759) | (~c2_1(a1759)) | (~c0_1(a1759)) | c1_1(a1759) | c3_1(a1759) | (~c0_1(a1759)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp2 | c1_1(a1759) | (~c2_1(a1759)) | c3_1(a1759) | (~ndr1_0) | (~c0_1(a1759))))),
% 1.38/1.17 inference(monotonicity,[status(thm)],[212])).
% 1.38/1.17 tff(214,plain,
% 1.38/1.17 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a1759) | (~c2_1(a1759)) | (~c0_1(a1759)) | c1_1(a1759) | c3_1(a1759) | (~c0_1(a1759)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp2 | c1_1(a1759) | (~c2_1(a1759)) | c3_1(a1759) | (~ndr1_0) | (~c0_1(a1759)))),
% 1.38/1.17 inference(transitivity,[status(thm)],[213, 211])).
% 1.38/1.17 tff(215,plain,
% 1.38/1.17 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a1759) | (~c2_1(a1759)) | (~c0_1(a1759)) | c1_1(a1759) | c3_1(a1759) | (~c0_1(a1759)))),
% 1.38/1.18 inference(quant_inst,[status(thm)],[])).
% 1.38/1.18 tff(216,plain,
% 1.38/1.18 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp2 | c1_1(a1759) | (~c2_1(a1759)) | c3_1(a1759) | (~ndr1_0) | (~c0_1(a1759))),
% 1.38/1.18 inference(modus_ponens,[status(thm)],[215, 214])).
% 1.38/1.18 tff(217,plain,
% 1.38/1.18 (hskp2 | (~c2_1(a1759)) | (~c0_1(a1759))),
% 1.38/1.18 inference(unit_resolution,[status(thm)],[216, 111, 47, 34, 210])).
% 1.38/1.18 tff(218,plain,
% 1.38/1.18 (~c2_1(a1759)),
% 1.38/1.18 inference(unit_resolution,[status(thm)],[217, 120, 200])).
% 1.38/1.18 tff(219,plain,
% 1.38/1.18 (((~hskp25) | (~c2_1(a1827))) <=> ((~hskp25) | (~c2_1(a1827)))),
% 1.38/1.18 inference(rewrite,[status(thm)],[])).
% 1.38/1.18 tff(220,plain,
% 1.38/1.18 (((~c2_1(a1827)) | (~hskp25)) <=> ((~hskp25) | (~c2_1(a1827)))),
% 1.38/1.18 inference(rewrite,[status(thm)],[])).
% 1.38/1.18 tff(221,axiom,((~c2_1(a1827)) | (~hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause89')).
% 1.38/1.18 tff(222,plain,
% 1.38/1.18 ((~hskp25) | (~c2_1(a1827))),
% 1.38/1.18 inference(modus_ponens,[status(thm)],[221, 220])).
% 1.38/1.18 tff(223,plain,
% 1.38/1.18 ((~hskp25) | (~c2_1(a1827))),
% 1.38/1.18 inference(modus_ponens,[status(thm)],[222, 219])).
% 1.38/1.18 tff(224,plain,
% 1.38/1.18 (~c2_1(a1827)),
% 1.38/1.18 inference(unit_resolution,[status(thm)],[223, 163])).
% 1.38/1.18 tff(225,plain,
% 1.38/1.18 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp13 | c1_1(a1759) | c0_1(a1827) | c2_1(a1827) | c2_1(a1759) | c3_1(a1759) | (~ndr1_0) | (~c3_1(a1827)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp13 | c1_1(a1759) | c0_1(a1827) | c2_1(a1827) | c2_1(a1759) | c3_1(a1759) | (~ndr1_0) | (~c3_1(a1827)))),
% 1.38/1.18 inference(rewrite,[status(thm)],[])).
% 1.38/1.18 tff(226,plain,
% 1.38/1.18 ((hskp13 | (~ndr1_0) | c2_1(a1827) | c0_1(a1827) | (~c3_1(a1827)) | c2_1(a1759) | c1_1(a1759) | c3_1(a1759)) <=> (hskp13 | c1_1(a1759) | c0_1(a1827) | c2_1(a1827) | c2_1(a1759) | c3_1(a1759) | (~ndr1_0) | (~c3_1(a1827)))),
% 1.38/1.18 inference(rewrite,[status(thm)],[])).
% 1.38/1.18 tff(227,plain,
% 1.38/1.18 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | c2_1(a1827) | c0_1(a1827) | (~c3_1(a1827)) | c2_1(a1759) | c1_1(a1759) | c3_1(a1759))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp13 | c1_1(a1759) | c0_1(a1827) | c2_1(a1827) | c2_1(a1759) | c3_1(a1759) | (~ndr1_0) | (~c3_1(a1827))))),
% 1.38/1.18 inference(monotonicity,[status(thm)],[226])).
% 1.38/1.18 tff(228,plain,
% 1.38/1.18 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | c2_1(a1827) | c0_1(a1827) | (~c3_1(a1827)) | c2_1(a1759) | c1_1(a1759) | c3_1(a1759))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp13 | c1_1(a1759) | c0_1(a1827) | c2_1(a1827) | c2_1(a1759) | c3_1(a1759) | (~ndr1_0) | (~c3_1(a1827)))),
% 1.38/1.18 inference(transitivity,[status(thm)],[227, 225])).
% 1.38/1.18 tff(229,plain,
% 1.38/1.18 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | c2_1(a1827) | c0_1(a1827) | (~c3_1(a1827)) | c2_1(a1759) | c1_1(a1759) | c3_1(a1759))),
% 1.38/1.18 inference(quant_inst,[status(thm)],[])).
% 1.38/1.18 tff(230,plain,
% 1.38/1.18 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp13 | c1_1(a1759) | c0_1(a1827) | c2_1(a1827) | c2_1(a1759) | c3_1(a1759) | (~ndr1_0) | (~c3_1(a1827))),
% 1.38/1.18 inference(modus_ponens,[status(thm)],[229, 228])).
% 1.38/1.18 tff(231,plain,
% 1.38/1.18 ($false),
% 1.38/1.18 inference(unit_resolution,[status(thm)],[230, 111, 23, 47, 175, 224, 218, 34, 192, 182])).
% 1.38/1.18 tff(232,plain,(hskp13 | c1_1(a1759) | c3_1(a1759) | hskp3 | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.38/1.18 tff(233,plain,
% 1.38/1.18 (hskp13),
% 1.38/1.18 inference(unit_resolution,[status(thm)],[232, 35, 34, 47, 12])).
% 1.38/1.18 tff(234,plain,
% 1.38/1.18 (((~hskp13) | (~c0_1(a1771))) <=> ((~hskp13) | (~c0_1(a1771)))),
% 1.38/1.18 inference(rewrite,[status(thm)],[])).
% 1.38/1.18 tff(235,plain,
% 1.38/1.18 (((~c0_1(a1771)) | (~hskp13)) <=> ((~hskp13) | (~c0_1(a1771)))),
% 1.38/1.18 inference(rewrite,[status(thm)],[])).
% 1.38/1.18 tff(236,axiom,((~c0_1(a1771)) | (~hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause109')).
% 1.38/1.18 tff(237,plain,
% 1.38/1.18 ((~hskp13) | (~c0_1(a1771))),
% 1.38/1.18 inference(modus_ponens,[status(thm)],[236, 235])).
% 1.38/1.18 tff(238,plain,
% 1.38/1.18 ((~hskp13) | (~c0_1(a1771))),
% 1.38/1.18 inference(modus_ponens,[status(thm)],[237, 234])).
% 1.38/1.18 tff(239,plain,
% 1.38/1.18 (~c0_1(a1771)),
% 1.38/1.18 inference(unit_resolution,[status(thm)],[238, 233])).
% 1.38/1.18 tff(240,assumption,(~hskp6), introduced(assumption)).
% 1.38/1.18 tff(241,assumption,(ndr1_0), introduced(assumption)).
% 1.38/1.18 tff(242,assumption,(hskp13), introduced(assumption)).
% 1.38/1.18 tff(243,plain,
% 1.38/1.18 (((~hskp13) | c1_1(a1771)) <=> ((~hskp13) | c1_1(a1771))),
% 1.38/1.18 inference(rewrite,[status(thm)],[])).
% 1.38/1.18 tff(244,axiom,((~hskp13) | c1_1(a1771)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause65')).
% 1.38/1.18 tff(245,plain,
% 1.38/1.18 ((~hskp13) | c1_1(a1771)),
% 1.38/1.18 inference(modus_ponens,[status(thm)],[244, 243])).
% 1.38/1.18 tff(246,plain,
% 1.38/1.18 ((~hskp13) | c1_1(a1771)),
% 1.38/1.18 inference(modus_ponens,[status(thm)],[245, 243])).
% 1.38/1.18 tff(247,plain,
% 1.38/1.18 ((~hskp13) | c1_1(a1771)),
% 1.38/1.18 inference(modus_ponens,[status(thm)],[246, 243])).
% 1.38/1.18 tff(248,plain,
% 1.38/1.18 ((~hskp13) | c1_1(a1771)),
% 1.38/1.18 inference(modus_ponens,[status(thm)],[247, 243])).
% 1.38/1.18 tff(249,plain,
% 1.38/1.18 ((~hskp13) | c1_1(a1771)),
% 1.38/1.18 inference(modus_ponens,[status(thm)],[248, 243])).
% 1.38/1.18 tff(250,plain,
% 1.38/1.18 ((~hskp13) | c1_1(a1771)),
% 1.38/1.18 inference(modus_ponens,[status(thm)],[249, 243])).
% 1.38/1.18 tff(251,plain,
% 1.38/1.18 ((~hskp13) | c1_1(a1771)),
% 1.38/1.18 inference(modus_ponens,[status(thm)],[250, 243])).
% 1.38/1.18 tff(252,plain,
% 1.38/1.18 ((~hskp13) | c1_1(a1771)),
% 1.38/1.18 inference(modus_ponens,[status(thm)],[251, 243])).
% 1.38/1.18 tff(253,plain,
% 1.38/1.18 (c1_1(a1771)),
% 1.38/1.18 inference(unit_resolution,[status(thm)],[252, 242])).
% 1.38/1.18 tff(254,plain,
% 1.38/1.18 (((~hskp13) | c2_1(a1771)) <=> ((~hskp13) | c2_1(a1771))),
% 1.38/1.18 inference(rewrite,[status(thm)],[])).
% 1.38/1.18 tff(255,axiom,((~hskp13) | c2_1(a1771)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause66')).
% 1.38/1.18 tff(256,plain,
% 1.38/1.18 ((~hskp13) | c2_1(a1771)),
% 1.38/1.18 inference(modus_ponens,[status(thm)],[255, 254])).
% 1.38/1.18 tff(257,plain,
% 1.38/1.18 ((~hskp13) | c2_1(a1771)),
% 1.38/1.18 inference(modus_ponens,[status(thm)],[256, 254])).
% 1.38/1.18 tff(258,plain,
% 1.38/1.18 ((~hskp13) | c2_1(a1771)),
% 1.38/1.18 inference(modus_ponens,[status(thm)],[257, 254])).
% 1.38/1.18 tff(259,plain,
% 1.38/1.18 ((~hskp13) | c2_1(a1771)),
% 1.38/1.18 inference(modus_ponens,[status(thm)],[258, 254])).
% 1.38/1.18 tff(260,plain,
% 1.38/1.18 ((~hskp13) | c2_1(a1771)),
% 1.38/1.18 inference(modus_ponens,[status(thm)],[259, 254])).
% 1.38/1.18 tff(261,plain,
% 1.38/1.18 ((~hskp13) | c2_1(a1771)),
% 1.38/1.18 inference(modus_ponens,[status(thm)],[260, 254])).
% 1.38/1.18 tff(262,plain,
% 1.38/1.18 ((~hskp13) | c2_1(a1771)),
% 1.38/1.18 inference(modus_ponens,[status(thm)],[261, 254])).
% 1.38/1.18 tff(263,plain,
% 1.38/1.18 ((~hskp13) | c2_1(a1771)),
% 1.38/1.18 inference(modus_ponens,[status(thm)],[262, 254])).
% 1.38/1.18 tff(264,plain,
% 1.38/1.18 (c2_1(a1771)),
% 1.38/1.18 inference(unit_resolution,[status(thm)],[263, 242])).
% 1.38/1.18 tff(265,plain,
% 1.38/1.18 (^[U: $i] : refl((hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))),
% 1.38/1.18 inference(bind,[status(th)],[])).
% 1.38/1.18 tff(266,plain,
% 1.38/1.18 (![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.38/1.18 inference(quant_intro,[status(thm)],[265])).
% 1.38/1.18 tff(267,plain,
% 1.38/1.18 (![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.38/1.18 inference(rewrite,[status(thm)],[])).
% 1.38/1.18 tff(268,plain,
% 1.38/1.18 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp3) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp3))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp3) <=> (hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp3) | hskp6) <=> ((hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp6))), rewrite(((hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp6) <=> (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp3) | hskp6) <=> (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))))),
% 1.38/1.18 inference(bind,[status(th)],[])).
% 1.38/1.18 tff(269,plain,
% 1.38/1.18 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp3) | hskp6) <=> ![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.38/1.18 inference(quant_intro,[status(thm)],[268])).
% 1.38/1.18 tff(270,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp3) | hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause142')).
% 1.38/1.18 tff(271,plain,
% 1.38/1.18 (![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.38/1.18 inference(modus_ponens,[status(thm)],[270, 269])).
% 1.38/1.18 tff(272,plain,
% 1.38/1.18 (![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.38/1.18 inference(modus_ponens,[status(thm)],[271, 267])).
% 1.38/1.18 tff(273,plain,(
% 1.38/1.18 ![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.38/1.18 inference(skolemize,[status(sab)],[272])).
% 1.38/1.18 tff(274,plain,
% 1.38/1.18 (![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.38/1.18 inference(modus_ponens,[status(thm)],[273, 266])).
% 1.38/1.18 tff(275,assumption,(~c0_1(a1771)), introduced(assumption)).
% 1.38/1.18 tff(276,plain,
% 1.38/1.18 (((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp6 | hskp3 | c0_1(a1771) | (~ndr1_0) | (~c1_1(a1771)) | (~c2_1(a1771)))) <=> ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp6 | hskp3 | c0_1(a1771) | (~ndr1_0) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 1.38/1.18 inference(rewrite,[status(thm)],[])).
% 1.38/1.18 tff(277,plain,
% 1.38/1.18 ((hskp6 | hskp3 | (~ndr1_0) | c0_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771))) <=> (hskp6 | hskp3 | c0_1(a1771) | (~ndr1_0) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 1.38/1.18 inference(rewrite,[status(thm)],[])).
% 1.38/1.18 tff(278,plain,
% 1.38/1.18 (((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp6 | hskp3 | (~ndr1_0) | c0_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)))) <=> ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp6 | hskp3 | c0_1(a1771) | (~ndr1_0) | (~c1_1(a1771)) | (~c2_1(a1771))))),
% 1.38/1.18 inference(monotonicity,[status(thm)],[277])).
% 1.38/1.18 tff(279,plain,
% 1.38/1.18 (((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp6 | hskp3 | (~ndr1_0) | c0_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)))) <=> ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp6 | hskp3 | c0_1(a1771) | (~ndr1_0) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 1.38/1.18 inference(transitivity,[status(thm)],[278, 276])).
% 1.38/1.18 tff(280,plain,
% 1.38/1.18 ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp6 | hskp3 | (~ndr1_0) | c0_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)))),
% 1.38/1.18 inference(quant_inst,[status(thm)],[])).
% 1.38/1.18 tff(281,plain,
% 1.38/1.18 ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp6 | hskp3 | c0_1(a1771) | (~ndr1_0) | (~c1_1(a1771)) | (~c2_1(a1771))),
% 1.38/1.18 inference(modus_ponens,[status(thm)],[280, 279])).
% 1.38/1.18 tff(282,plain,
% 1.38/1.18 (hskp6 | (~ndr1_0) | (~c1_1(a1771)) | (~c2_1(a1771))),
% 1.38/1.18 inference(unit_resolution,[status(thm)],[281, 35, 275, 274])).
% 1.38/1.18 tff(283,plain,
% 1.38/1.18 ($false),
% 1.38/1.18 inference(unit_resolution,[status(thm)],[282, 264, 253, 241, 240])).
% 1.38/1.18 tff(284,plain,((~hskp13) | (~ndr1_0) | hskp6 | hskp3 | c0_1(a1771)), inference(lemma,lemma(discharge,[]))).
% 1.38/1.18 tff(285,plain,
% 1.38/1.18 ((~hskp13) | hskp6 | hskp3 | c0_1(a1771)),
% 1.38/1.18 inference(unit_resolution,[status(thm)],[284, 111])).
% 1.38/1.18 tff(286,plain,
% 1.38/1.18 (hskp6),
% 1.38/1.18 inference(unit_resolution,[status(thm)],[285, 239, 35, 233])).
% 1.38/1.18 tff(287,plain,
% 1.38/1.18 (((~hskp6) | (~c0_1(a1762))) <=> ((~hskp6) | (~c0_1(a1762)))),
% 1.38/1.18 inference(rewrite,[status(thm)],[])).
% 1.38/1.18 tff(288,plain,
% 1.38/1.18 (((~c0_1(a1762)) | (~hskp6)) <=> ((~hskp6) | (~c0_1(a1762)))),
% 1.38/1.18 inference(rewrite,[status(thm)],[])).
% 1.38/1.18 tff(289,axiom,((~c0_1(a1762)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause119')).
% 1.38/1.18 tff(290,plain,
% 1.38/1.18 ((~hskp6) | (~c0_1(a1762))),
% 1.38/1.18 inference(modus_ponens,[status(thm)],[289, 288])).
% 1.38/1.18 tff(291,plain,
% 1.38/1.18 ((~hskp6) | (~c0_1(a1762))),
% 1.38/1.18 inference(modus_ponens,[status(thm)],[290, 287])).
% 1.38/1.18 tff(292,plain,
% 1.38/1.18 (~c0_1(a1762)),
% 1.38/1.18 inference(unit_resolution,[status(thm)],[291, 286])).
% 1.38/1.18 tff(293,plain,
% 1.38/1.18 (((~hskp6) | c3_1(a1762)) <=> ((~hskp6) | c3_1(a1762))),
% 1.38/1.18 inference(rewrite,[status(thm)],[])).
% 1.38/1.18 tff(294,axiom,((~hskp6) | c3_1(a1762)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause77')).
% 1.38/1.18 tff(295,plain,
% 1.38/1.18 ((~hskp6) | c3_1(a1762)),
% 1.38/1.18 inference(modus_ponens,[status(thm)],[294, 293])).
% 1.38/1.18 tff(296,plain,
% 1.38/1.18 ((~hskp6) | c3_1(a1762)),
% 1.38/1.18 inference(modus_ponens,[status(thm)],[295, 293])).
% 1.38/1.18 tff(297,plain,
% 1.38/1.18 ((~hskp6) | c3_1(a1762)),
% 1.38/1.18 inference(modus_ponens,[status(thm)],[296, 293])).
% 1.38/1.18 tff(298,plain,
% 1.38/1.18 ((~hskp6) | c3_1(a1762)),
% 1.38/1.18 inference(modus_ponens,[status(thm)],[297, 293])).
% 1.38/1.18 tff(299,plain,
% 1.38/1.18 ((~hskp6) | c3_1(a1762)),
% 1.38/1.18 inference(modus_ponens,[status(thm)],[298, 293])).
% 1.38/1.18 tff(300,plain,
% 1.38/1.18 ((~hskp6) | c3_1(a1762)),
% 1.38/1.18 inference(modus_ponens,[status(thm)],[299, 293])).
% 1.38/1.18 tff(301,plain,
% 1.38/1.18 ((~hskp6) | c3_1(a1762)),
% 1.38/1.18 inference(modus_ponens,[status(thm)],[300, 293])).
% 1.38/1.18 tff(302,plain,
% 1.38/1.18 ((~hskp6) | c3_1(a1762)),
% 1.38/1.18 inference(modus_ponens,[status(thm)],[301, 293])).
% 1.38/1.18 tff(303,plain,
% 1.38/1.18 (c3_1(a1762)),
% 1.38/1.18 inference(unit_resolution,[status(thm)],[302, 286])).
% 1.38/1.18 tff(304,plain,
% 1.38/1.18 (((~hskp6) | c2_1(a1762)) <=> ((~hskp6) | c2_1(a1762))),
% 1.38/1.18 inference(rewrite,[status(thm)],[])).
% 1.38/1.18 tff(305,axiom,((~hskp6) | c2_1(a1762)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause76')).
% 1.38/1.18 tff(306,plain,
% 1.38/1.18 ((~hskp6) | c2_1(a1762)),
% 1.38/1.18 inference(modus_ponens,[status(thm)],[305, 304])).
% 1.38/1.18 tff(307,plain,
% 1.38/1.18 ((~hskp6) | c2_1(a1762)),
% 1.38/1.18 inference(modus_ponens,[status(thm)],[306, 304])).
% 1.38/1.18 tff(308,plain,
% 1.38/1.18 ((~hskp6) | c2_1(a1762)),
% 1.38/1.18 inference(modus_ponens,[status(thm)],[307, 304])).
% 1.38/1.18 tff(309,plain,
% 1.38/1.18 ((~hskp6) | c2_1(a1762)),
% 1.38/1.18 inference(modus_ponens,[status(thm)],[308, 304])).
% 1.38/1.18 tff(310,plain,
% 1.38/1.18 ((~hskp6) | c2_1(a1762)),
% 1.38/1.18 inference(modus_ponens,[status(thm)],[309, 304])).
% 1.38/1.18 tff(311,plain,
% 1.38/1.18 ((~hskp6) | c2_1(a1762)),
% 1.38/1.18 inference(modus_ponens,[status(thm)],[310, 304])).
% 1.38/1.18 tff(312,plain,
% 1.38/1.18 ((~hskp6) | c2_1(a1762)),
% 1.38/1.18 inference(modus_ponens,[status(thm)],[311, 304])).
% 1.38/1.18 tff(313,plain,
% 1.38/1.18 ((~hskp6) | c2_1(a1762)),
% 1.38/1.18 inference(modus_ponens,[status(thm)],[312, 304])).
% 1.38/1.18 tff(314,plain,
% 1.38/1.18 (c2_1(a1762)),
% 1.38/1.18 inference(unit_resolution,[status(thm)],[313, 286])).
% 1.38/1.18 tff(315,plain,
% 1.38/1.18 (((~![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp8 | hskp4 | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)))) <=> ((~![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp8 | hskp4 | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)))),
% 1.38/1.18 inference(rewrite,[status(thm)],[])).
% 1.38/1.18 tff(316,plain,
% 1.38/1.18 ((hskp8 | hskp4 | (~ndr1_0) | c0_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762))) <=> (hskp8 | hskp4 | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)))),
% 1.38/1.18 inference(rewrite,[status(thm)],[])).
% 1.38/1.18 tff(317,plain,
% 1.38/1.18 (((~![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp8 | hskp4 | (~ndr1_0) | c0_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)))) <=> ((~![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp8 | hskp4 | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762))))),
% 1.38/1.18 inference(monotonicity,[status(thm)],[316])).
% 1.38/1.18 tff(318,plain,
% 1.38/1.18 (((~![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp8 | hskp4 | (~ndr1_0) | c0_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)))) <=> ((~![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp8 | hskp4 | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)))),
% 1.38/1.18 inference(transitivity,[status(thm)],[317, 315])).
% 1.38/1.18 tff(319,plain,
% 1.38/1.18 ((~![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp8 | hskp4 | (~ndr1_0) | c0_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)))),
% 1.38/1.18 inference(quant_inst,[status(thm)],[])).
% 1.38/1.18 tff(320,plain,
% 1.38/1.18 ((~![U: $i] : (hskp8 | hskp4 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp8 | hskp4 | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762))),
% 1.38/1.18 inference(modus_ponens,[status(thm)],[319, 318])).
% 1.38/1.18 tff(321,plain,
% 1.38/1.18 (hskp8),
% 1.38/1.18 inference(unit_resolution,[status(thm)],[320, 111, 151, 314, 303, 292, 130])).
% 1.38/1.18 tff(322,plain,
% 1.38/1.18 (((~hskp8) | (~c1_1(a1765))) <=> ((~hskp8) | (~c1_1(a1765)))),
% 1.38/1.18 inference(rewrite,[status(thm)],[])).
% 1.38/1.18 tff(323,plain,
% 1.38/1.18 (((~c1_1(a1765)) | (~hskp8)) <=> ((~hskp8) | (~c1_1(a1765)))),
% 1.38/1.18 inference(rewrite,[status(thm)],[])).
% 1.38/1.18 tff(324,axiom,((~c1_1(a1765)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause117')).
% 1.38/1.18 tff(325,plain,
% 1.38/1.18 ((~hskp8) | (~c1_1(a1765))),
% 1.38/1.18 inference(modus_ponens,[status(thm)],[324, 323])).
% 1.38/1.18 tff(326,plain,
% 1.38/1.18 ((~hskp8) | (~c1_1(a1765))),
% 1.38/1.18 inference(modus_ponens,[status(thm)],[325, 322])).
% 1.38/1.18 tff(327,plain,
% 1.38/1.18 (~c1_1(a1765)),
% 1.38/1.18 inference(unit_resolution,[status(thm)],[326, 321])).
% 1.38/1.18 tff(328,plain,
% 1.38/1.18 (^[V: $i, U: $i] : refl((hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.38/1.18 inference(bind,[status(th)],[])).
% 1.38/1.18 tff(329,plain,
% 1.38/1.18 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.38/1.18 inference(quant_intro,[status(thm)],[328])).
% 1.38/1.18 tff(330,plain,
% 1.38/1.18 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.38/1.18 inference(rewrite,[status(thm)],[])).
% 1.38/1.18 tff(331,plain,
% 1.38/1.18 (^[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) | c3_1(U) | 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) | c3_1(U) | c1_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) | 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)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | 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)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | 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)) | hskp10) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp10))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp10) <=> (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | 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)) | hskp10) <=> (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.51/1.18 inference(bind,[status(th)],[])).
% 1.51/1.18 tff(332,plain,
% 1.51/1.18 (![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) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.51/1.18 inference(quant_intro,[status(thm)],[331])).
% 1.51/1.18 tff(333,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','clause162')).
% 1.51/1.18 tff(334,plain,
% 1.51/1.18 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.51/1.18 inference(modus_ponens,[status(thm)],[333, 332])).
% 1.51/1.18 tff(335,plain,
% 1.51/1.18 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.51/1.18 inference(modus_ponens,[status(thm)],[334, 330])).
% 1.51/1.18 tff(336,plain,(
% 1.51/1.18 ![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.51/1.18 inference(skolemize,[status(sab)],[335])).
% 1.51/1.18 tff(337,plain,
% 1.51/1.18 (![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.51/1.18 inference(modus_ponens,[status(thm)],[336, 329])).
% 1.51/1.18 tff(338,assumption,(hskp6), introduced(assumption)).
% 1.51/1.18 tff(339,plain,
% 1.51/1.18 (~c0_1(a1762)),
% 1.51/1.18 inference(unit_resolution,[status(thm)],[291, 338])).
% 1.51/1.18 tff(340,plain,
% 1.51/1.18 (c3_1(a1762)),
% 1.51/1.18 inference(unit_resolution,[status(thm)],[302, 338])).
% 1.51/1.18 tff(341,plain,
% 1.51/1.18 (c2_1(a1762)),
% 1.51/1.18 inference(unit_resolution,[status(thm)],[313, 338])).
% 1.51/1.18 tff(342,assumption,(~hskp4), introduced(assumption)).
% 1.51/1.18 tff(343,plain,
% 1.51/1.18 (hskp8),
% 1.51/1.18 inference(unit_resolution,[status(thm)],[320, 111, 342, 341, 340, 339, 130])).
% 1.51/1.18 tff(344,plain,
% 1.51/1.18 (~c1_1(a1765)),
% 1.51/1.18 inference(unit_resolution,[status(thm)],[326, 343])).
% 1.51/1.18 tff(345,plain,
% 1.51/1.18 (^[U: $i] : refl((hskp27 | hskp22 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> (hskp27 | hskp22 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))))),
% 1.51/1.18 inference(bind,[status(th)],[])).
% 1.51/1.18 tff(346,plain,
% 1.51/1.18 (![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.51/1.18 inference(quant_intro,[status(thm)],[345])).
% 1.51/1.18 tff(347,plain,
% 1.51/1.18 (![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.51/1.18 inference(rewrite,[status(thm)],[])).
% 1.51/1.18 tff(348,plain,
% 1.51/1.18 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp27))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp27) <=> (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) | hskp22) <=> ((hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp22))), rewrite(((hskp27 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U))) | hskp22) <=> (hskp27 | hskp22 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) | hskp22) <=> (hskp27 | hskp22 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))))),
% 1.51/1.18 inference(bind,[status(th)],[])).
% 1.51/1.18 tff(349,plain,
% 1.51/1.18 (![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) | hskp22) <=> ![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.51/1.18 inference(quant_intro,[status(thm)],[348])).
% 1.51/1.18 tff(350,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | hskp27) | hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause144')).
% 1.51/1.18 tff(351,plain,
% 1.51/1.18 (![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.51/1.18 inference(modus_ponens,[status(thm)],[350, 349])).
% 1.51/1.18 tff(352,plain,
% 1.51/1.18 (![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.51/1.18 inference(modus_ponens,[status(thm)],[351, 347])).
% 1.51/1.18 tff(353,plain,(
% 1.51/1.18 ![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.51/1.18 inference(skolemize,[status(sab)],[352])).
% 1.51/1.18 tff(354,plain,
% 1.51/1.18 (![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))),
% 1.51/1.18 inference(modus_ponens,[status(thm)],[353, 346])).
% 1.51/1.18 tff(355,assumption,(~hskp22), introduced(assumption)).
% 1.51/1.18 tff(356,plain,
% 1.51/1.18 (((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp27 | hskp22 | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)))) <=> ((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp27 | hskp22 | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)))),
% 1.51/1.18 inference(rewrite,[status(thm)],[])).
% 1.51/1.18 tff(357,plain,
% 1.51/1.18 ((hskp27 | hskp22 | (~ndr1_0) | c0_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762))) <=> (hskp27 | hskp22 | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)))),
% 1.51/1.18 inference(rewrite,[status(thm)],[])).
% 1.51/1.18 tff(358,plain,
% 1.51/1.18 (((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp27 | hskp22 | (~ndr1_0) | c0_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)))) <=> ((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp27 | hskp22 | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762))))),
% 1.51/1.18 inference(monotonicity,[status(thm)],[357])).
% 1.51/1.18 tff(359,plain,
% 1.51/1.18 (((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp27 | hskp22 | (~ndr1_0) | c0_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)))) <=> ((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp27 | hskp22 | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)))),
% 1.51/1.18 inference(transitivity,[status(thm)],[358, 356])).
% 1.51/1.18 tff(360,plain,
% 1.51/1.18 ((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | (hskp27 | hskp22 | (~ndr1_0) | c0_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)))),
% 1.51/1.18 inference(quant_inst,[status(thm)],[])).
% 1.51/1.18 tff(361,plain,
% 1.51/1.18 ((~![U: $i] : (hskp27 | hskp22 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c3_1(U)))) | hskp27 | hskp22 | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762))),
% 1.51/1.18 inference(modus_ponens,[status(thm)],[360, 359])).
% 1.51/1.18 tff(362,plain,
% 1.51/1.18 (hskp27),
% 1.51/1.18 inference(unit_resolution,[status(thm)],[361, 111, 355, 341, 340, 339, 354])).
% 1.51/1.18 tff(363,plain,
% 1.51/1.18 (((~hskp27) | c3_1(a1756)) <=> ((~hskp27) | c3_1(a1756))),
% 1.51/1.18 inference(rewrite,[status(thm)],[])).
% 1.51/1.18 tff(364,axiom,((~hskp27) | c3_1(a1756)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause49')).
% 1.51/1.18 tff(365,plain,
% 1.51/1.18 ((~hskp27) | c3_1(a1756)),
% 1.51/1.18 inference(modus_ponens,[status(thm)],[364, 363])).
% 1.51/1.18 tff(366,plain,
% 1.51/1.18 ((~hskp27) | c3_1(a1756)),
% 1.51/1.18 inference(modus_ponens,[status(thm)],[365, 363])).
% 1.51/1.18 tff(367,plain,
% 1.51/1.18 ((~hskp27) | c3_1(a1756)),
% 1.51/1.18 inference(modus_ponens,[status(thm)],[366, 363])).
% 1.51/1.18 tff(368,plain,
% 1.51/1.18 ((~hskp27) | c3_1(a1756)),
% 1.51/1.18 inference(modus_ponens,[status(thm)],[367, 363])).
% 1.51/1.18 tff(369,plain,
% 1.51/1.18 ((~hskp27) | c3_1(a1756)),
% 1.51/1.18 inference(modus_ponens,[status(thm)],[368, 363])).
% 1.51/1.18 tff(370,plain,
% 1.51/1.18 ((~hskp27) | c3_1(a1756)),
% 1.51/1.18 inference(modus_ponens,[status(thm)],[369, 363])).
% 1.51/1.18 tff(371,plain,
% 1.51/1.18 ((~hskp27) | c3_1(a1756)),
% 1.51/1.18 inference(modus_ponens,[status(thm)],[370, 363])).
% 1.51/1.18 tff(372,plain,
% 1.51/1.18 ((~hskp27) | c3_1(a1756)),
% 1.51/1.18 inference(modus_ponens,[status(thm)],[371, 363])).
% 1.51/1.18 tff(373,plain,
% 1.51/1.18 (c3_1(a1756)),
% 1.51/1.18 inference(unit_resolution,[status(thm)],[372, 362])).
% 1.51/1.18 tff(374,plain,
% 1.51/1.18 (((~hskp27) | c1_1(a1756)) <=> ((~hskp27) | c1_1(a1756))),
% 1.51/1.18 inference(rewrite,[status(thm)],[])).
% 1.51/1.18 tff(375,axiom,((~hskp27) | c1_1(a1756)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause48')).
% 1.51/1.18 tff(376,plain,
% 1.51/1.18 ((~hskp27) | c1_1(a1756)),
% 1.51/1.18 inference(modus_ponens,[status(thm)],[375, 374])).
% 1.51/1.18 tff(377,plain,
% 1.51/1.18 ((~hskp27) | c1_1(a1756)),
% 1.51/1.18 inference(modus_ponens,[status(thm)],[376, 374])).
% 1.51/1.18 tff(378,plain,
% 1.51/1.18 ((~hskp27) | c1_1(a1756)),
% 1.51/1.18 inference(modus_ponens,[status(thm)],[377, 374])).
% 1.51/1.18 tff(379,plain,
% 1.51/1.18 ((~hskp27) | c1_1(a1756)),
% 1.51/1.18 inference(modus_ponens,[status(thm)],[378, 374])).
% 1.51/1.18 tff(380,plain,
% 1.51/1.18 ((~hskp27) | c1_1(a1756)),
% 1.51/1.18 inference(modus_ponens,[status(thm)],[379, 374])).
% 1.51/1.18 tff(381,plain,
% 1.51/1.18 ((~hskp27) | c1_1(a1756)),
% 1.51/1.18 inference(modus_ponens,[status(thm)],[380, 374])).
% 1.51/1.18 tff(382,plain,
% 1.51/1.18 ((~hskp27) | c1_1(a1756)),
% 1.51/1.18 inference(modus_ponens,[status(thm)],[381, 374])).
% 1.51/1.18 tff(383,plain,
% 1.51/1.18 ((~hskp27) | c1_1(a1756)),
% 1.51/1.18 inference(modus_ponens,[status(thm)],[382, 374])).
% 1.51/1.18 tff(384,plain,
% 1.51/1.18 (c1_1(a1756)),
% 1.51/1.18 inference(unit_resolution,[status(thm)],[383, 362])).
% 1.51/1.18 tff(385,plain,
% 1.51/1.18 (((~hskp27) | c0_1(a1756)) <=> ((~hskp27) | c0_1(a1756))),
% 1.51/1.18 inference(rewrite,[status(thm)],[])).
% 1.51/1.18 tff(386,axiom,((~hskp27) | c0_1(a1756)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause47')).
% 1.51/1.18 tff(387,plain,
% 1.51/1.18 ((~hskp27) | c0_1(a1756)),
% 1.51/1.18 inference(modus_ponens,[status(thm)],[386, 385])).
% 1.51/1.18 tff(388,plain,
% 1.51/1.18 ((~hskp27) | c0_1(a1756)),
% 1.51/1.18 inference(modus_ponens,[status(thm)],[387, 385])).
% 1.51/1.18 tff(389,plain,
% 1.51/1.18 ((~hskp27) | c0_1(a1756)),
% 1.51/1.18 inference(modus_ponens,[status(thm)],[388, 385])).
% 1.51/1.18 tff(390,plain,
% 1.51/1.18 ((~hskp27) | c0_1(a1756)),
% 1.51/1.18 inference(modus_ponens,[status(thm)],[389, 385])).
% 1.51/1.18 tff(391,plain,
% 1.51/1.18 ((~hskp27) | c0_1(a1756)),
% 1.51/1.18 inference(modus_ponens,[status(thm)],[390, 385])).
% 1.51/1.18 tff(392,plain,
% 1.51/1.18 ((~hskp27) | c0_1(a1756)),
% 1.51/1.18 inference(modus_ponens,[status(thm)],[391, 385])).
% 1.51/1.18 tff(393,plain,
% 1.51/1.18 ((~hskp27) | c0_1(a1756)),
% 1.51/1.18 inference(modus_ponens,[status(thm)],[392, 385])).
% 1.51/1.18 tff(394,plain,
% 1.51/1.18 ((~hskp27) | c0_1(a1756)),
% 1.51/1.18 inference(modus_ponens,[status(thm)],[393, 385])).
% 1.51/1.18 tff(395,plain,
% 1.51/1.18 (c0_1(a1756)),
% 1.51/1.18 inference(unit_resolution,[status(thm)],[394, 362])).
% 1.51/1.18 tff(396,assumption,(c1_1(a1756)), introduced(assumption)).
% 1.51/1.18 tff(397,assumption,(c0_1(a1756)), introduced(assumption)).
% 1.51/1.18 tff(398,plain,
% 1.51/1.18 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | c2_1(a1756) | (~c1_1(a1756)) | (~c0_1(a1756)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp19 | hskp13 | (~ndr1_0) | c2_1(a1756) | (~c1_1(a1756)) | (~c0_1(a1756)))),
% 1.51/1.18 inference(rewrite,[status(thm)],[])).
% 1.51/1.18 tff(399,plain,
% 1.51/1.18 ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | c2_1(a1756) | (~c1_1(a1756)) | (~c0_1(a1756)))),
% 1.51/1.18 inference(quant_inst,[status(thm)],[])).
% 1.51/1.19 tff(400,plain,
% 1.51/1.19 ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp19 | hskp13 | (~ndr1_0) | c2_1(a1756) | (~c1_1(a1756)) | (~c0_1(a1756))),
% 1.51/1.19 inference(modus_ponens,[status(thm)],[399, 398])).
% 1.51/1.19 tff(401,plain,
% 1.51/1.19 (hskp13 | c2_1(a1756)),
% 1.51/1.19 inference(unit_resolution,[status(thm)],[400, 111, 12, 397, 396, 33])).
% 1.51/1.19 tff(402,plain,
% 1.51/1.19 (c2_1(a1756)),
% 1.51/1.19 inference(unit_resolution,[status(thm)],[401, 23])).
% 1.51/1.19 tff(403,assumption,(~c0_1(a1762)), introduced(assumption)).
% 1.51/1.19 tff(404,assumption,(c2_1(a1762)), introduced(assumption)).
% 1.51/1.19 tff(405,plain,
% 1.51/1.19 (((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | c0_1(a1762) | (~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp13 | c0_1(a1762) | (~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)))),
% 1.51/1.19 inference(rewrite,[status(thm)],[])).
% 1.51/1.19 tff(406,plain,
% 1.51/1.19 ((hskp13 | (~ndr1_0) | c0_1(a1762) | (~c2_1(a1762)) | (~c1_1(a1762))) <=> (hskp13 | c0_1(a1762) | (~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)))),
% 1.51/1.19 inference(rewrite,[status(thm)],[])).
% 1.51/1.19 tff(407,plain,
% 1.51/1.19 (((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | (~ndr1_0) | c0_1(a1762) | (~c2_1(a1762)) | (~c1_1(a1762)))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | c0_1(a1762) | (~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762))))),
% 1.51/1.19 inference(monotonicity,[status(thm)],[406])).
% 1.51/1.19 tff(408,plain,
% 1.51/1.19 (((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | (~ndr1_0) | c0_1(a1762) | (~c2_1(a1762)) | (~c1_1(a1762)))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp13 | c0_1(a1762) | (~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)))),
% 1.51/1.19 inference(transitivity,[status(thm)],[407, 405])).
% 1.51/1.19 tff(409,plain,
% 1.51/1.19 ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | (~ndr1_0) | c0_1(a1762) | (~c2_1(a1762)) | (~c1_1(a1762)))),
% 1.51/1.19 inference(quant_inst,[status(thm)],[])).
% 1.51/1.19 tff(410,plain,
% 1.51/1.19 ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp13 | c0_1(a1762) | (~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762))),
% 1.51/1.19 inference(modus_ponens,[status(thm)],[409, 408])).
% 1.51/1.19 tff(411,plain,
% 1.51/1.19 (hskp13 | (~c1_1(a1762))),
% 1.51/1.19 inference(unit_resolution,[status(thm)],[410, 111, 404, 403, 22])).
% 1.51/1.19 tff(412,plain,
% 1.51/1.19 (~c1_1(a1762)),
% 1.51/1.19 inference(unit_resolution,[status(thm)],[411, 23])).
% 1.51/1.19 tff(413,plain,
% 1.51/1.19 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W))))),
% 1.51/1.19 inference(bind,[status(th)],[])).
% 1.51/1.19 tff(414,plain,
% 1.51/1.19 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.51/1.19 inference(quant_intro,[status(thm)],[413])).
% 1.51/1.19 tff(415,plain,
% 1.51/1.19 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.51/1.19 inference(rewrite,[status(thm)],[])).
% 1.51/1.19 tff(416,plain,
% 1.51/1.19 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))))),
% 1.51/1.19 inference(bind,[status(th)],[])).
% 1.51/1.19 tff(417,plain,
% 1.51/1.19 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.51/1.19 inference(quant_intro,[status(thm)],[416])).
% 1.51/1.19 tff(418,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause198')).
% 1.51/1.19 tff(419,plain,
% 1.51/1.19 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.51/1.19 inference(modus_ponens,[status(thm)],[418, 417])).
% 1.51/1.19 tff(420,plain,
% 1.51/1.19 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.51/1.19 inference(modus_ponens,[status(thm)],[419, 415])).
% 1.51/1.19 tff(421,plain,(
% 1.51/1.19 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.51/1.19 inference(skolemize,[status(sab)],[420])).
% 1.51/1.19 tff(422,plain,
% 1.51/1.19 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.51/1.19 inference(modus_ponens,[status(thm)],[421, 414])).
% 1.51/1.19 tff(423,assumption,(c3_1(a1762)), introduced(assumption)).
% 1.51/1.19 tff(424,assumption,(c3_1(a1756)), introduced(assumption)).
% 1.51/1.19 tff(425,plain,
% 1.51/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c2_1(a1756)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c2_1(a1756)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))),
% 1.51/1.19 inference(rewrite,[status(thm)],[])).
% 1.51/1.19 tff(426,plain,
% 1.51/1.19 (((~ndr1_0) | (~c2_1(a1756)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c2_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)) | c0_1(a1762) | c1_1(a1762) | (~c3_1(a1762))) <=> (c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c2_1(a1756)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))),
% 1.51/1.19 inference(rewrite,[status(thm)],[])).
% 1.51/1.19 tff(427,plain,
% 1.51/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1756)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c2_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)) | c0_1(a1762) | c1_1(a1762) | (~c3_1(a1762)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c2_1(a1756)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756))))),
% 1.51/1.19 inference(monotonicity,[status(thm)],[426])).
% 1.51/1.19 tff(428,plain,
% 1.51/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1756)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c2_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)) | c0_1(a1762) | c1_1(a1762) | (~c3_1(a1762)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c2_1(a1756)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))),
% 1.51/1.19 inference(transitivity,[status(thm)],[427, 425])).
% 1.51/1.19 tff(429,plain,
% 1.51/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1756)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c2_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)) | c0_1(a1762) | c1_1(a1762) | (~c3_1(a1762)))),
% 1.51/1.19 inference(quant_inst,[status(thm)],[])).
% 1.51/1.19 tff(430,plain,
% 1.51/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c2_1(a1756)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756))),
% 1.51/1.19 inference(modus_ponens,[status(thm)],[429, 428])).
% 1.51/1.19 tff(431,plain,
% 1.51/1.19 ($false),
% 1.51/1.19 inference(unit_resolution,[status(thm)],[430, 111, 397, 396, 424, 423, 403, 422, 412, 402])).
% 1.51/1.19 tff(432,plain,(hskp13 | (~c0_1(a1756)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c3_1(a1762)) | c0_1(a1762) | hskp19 | (~c2_1(a1762))), inference(lemma,lemma(discharge,[]))).
% 1.51/1.19 tff(433,plain,
% 1.51/1.19 (hskp13),
% 1.51/1.19 inference(unit_resolution,[status(thm)],[432, 395, 384, 373, 340, 339, 12, 341])).
% 1.51/1.19 tff(434,plain,
% 1.51/1.19 (~c0_1(a1771)),
% 1.51/1.19 inference(unit_resolution,[status(thm)],[238, 433])).
% 1.51/1.19 tff(435,plain,
% 1.51/1.19 (((~hskp8) | c2_1(a1765)) <=> ((~hskp8) | c2_1(a1765))),
% 1.51/1.19 inference(rewrite,[status(thm)],[])).
% 1.51/1.19 tff(436,axiom,((~hskp8) | c2_1(a1765)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause73')).
% 1.51/1.19 tff(437,plain,
% 1.51/1.19 ((~hskp8) | c2_1(a1765)),
% 1.51/1.19 inference(modus_ponens,[status(thm)],[436, 435])).
% 1.51/1.19 tff(438,plain,
% 1.51/1.19 ((~hskp8) | c2_1(a1765)),
% 1.51/1.19 inference(modus_ponens,[status(thm)],[437, 435])).
% 1.51/1.19 tff(439,plain,
% 1.51/1.19 ((~hskp8) | c2_1(a1765)),
% 1.51/1.19 inference(modus_ponens,[status(thm)],[438, 435])).
% 1.51/1.19 tff(440,plain,
% 1.51/1.19 ((~hskp8) | c2_1(a1765)),
% 1.51/1.19 inference(modus_ponens,[status(thm)],[439, 435])).
% 1.51/1.19 tff(441,plain,
% 1.51/1.19 ((~hskp8) | c2_1(a1765)),
% 1.51/1.19 inference(modus_ponens,[status(thm)],[440, 435])).
% 1.51/1.19 tff(442,plain,
% 1.51/1.19 ((~hskp8) | c2_1(a1765)),
% 1.51/1.19 inference(modus_ponens,[status(thm)],[441, 435])).
% 1.51/1.19 tff(443,plain,
% 1.51/1.19 ((~hskp8) | c2_1(a1765)),
% 1.51/1.19 inference(modus_ponens,[status(thm)],[442, 435])).
% 1.51/1.19 tff(444,plain,
% 1.51/1.19 ((~hskp8) | c2_1(a1765)),
% 1.51/1.19 inference(modus_ponens,[status(thm)],[443, 435])).
% 1.51/1.19 tff(445,plain,
% 1.51/1.19 (c2_1(a1765)),
% 1.51/1.19 inference(unit_resolution,[status(thm)],[444, 343])).
% 1.51/1.19 tff(446,plain,
% 1.51/1.19 (((~hskp8) | c0_1(a1765)) <=> ((~hskp8) | c0_1(a1765))),
% 1.51/1.19 inference(rewrite,[status(thm)],[])).
% 1.51/1.19 tff(447,axiom,((~hskp8) | c0_1(a1765)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause72')).
% 1.51/1.19 tff(448,plain,
% 1.51/1.19 ((~hskp8) | c0_1(a1765)),
% 1.51/1.19 inference(modus_ponens,[status(thm)],[447, 446])).
% 1.51/1.19 tff(449,plain,
% 1.51/1.19 ((~hskp8) | c0_1(a1765)),
% 1.51/1.19 inference(modus_ponens,[status(thm)],[448, 446])).
% 1.51/1.19 tff(450,plain,
% 1.51/1.19 ((~hskp8) | c0_1(a1765)),
% 1.51/1.19 inference(modus_ponens,[status(thm)],[449, 446])).
% 1.51/1.19 tff(451,plain,
% 1.51/1.19 ((~hskp8) | c0_1(a1765)),
% 1.51/1.19 inference(modus_ponens,[status(thm)],[450, 446])).
% 1.51/1.19 tff(452,plain,
% 1.51/1.19 ((~hskp8) | c0_1(a1765)),
% 1.51/1.19 inference(modus_ponens,[status(thm)],[451, 446])).
% 1.51/1.19 tff(453,plain,
% 1.51/1.19 ((~hskp8) | c0_1(a1765)),
% 1.51/1.19 inference(modus_ponens,[status(thm)],[452, 446])).
% 1.51/1.19 tff(454,plain,
% 1.51/1.19 ((~hskp8) | c0_1(a1765)),
% 1.51/1.19 inference(modus_ponens,[status(thm)],[453, 446])).
% 1.51/1.19 tff(455,plain,
% 1.51/1.19 ((~hskp8) | c0_1(a1765)),
% 1.51/1.19 inference(modus_ponens,[status(thm)],[454, 446])).
% 1.51/1.19 tff(456,plain,
% 1.51/1.19 (c0_1(a1765)),
% 1.51/1.19 inference(unit_resolution,[status(thm)],[455, 343])).
% 1.51/1.19 tff(457,plain,
% 1.51/1.19 (c2_1(a1771)),
% 1.51/1.19 inference(unit_resolution,[status(thm)],[263, 433])).
% 1.51/1.19 tff(458,plain,
% 1.51/1.19 (c1_1(a1771)),
% 1.51/1.19 inference(unit_resolution,[status(thm)],[252, 433])).
% 1.51/1.19 tff(459,plain,
% 1.51/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c0_1(a1771) | c1_1(a1765) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c1_1(a1771)) | (~c2_1(a1771)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1771) | c1_1(a1765) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 1.51/1.19 inference(rewrite,[status(thm)],[])).
% 1.51/1.19 tff(460,plain,
% 1.51/1.19 (((~ndr1_0) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)) | c0_1(a1762) | c1_1(a1762) | (~c3_1(a1762))) <=> (c0_1(a1771) | c1_1(a1765) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 1.51/1.19 inference(rewrite,[status(thm)],[])).
% 1.51/1.19 tff(461,plain,
% 1.51/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)) | c0_1(a1762) | c1_1(a1762) | (~c3_1(a1762)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c0_1(a1771) | c1_1(a1765) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c1_1(a1771)) | (~c2_1(a1771))))),
% 1.51/1.19 inference(monotonicity,[status(thm)],[460])).
% 1.51/1.19 tff(462,plain,
% 1.51/1.19 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)) | c0_1(a1762) | c1_1(a1762) | (~c3_1(a1762)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1771) | c1_1(a1765) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 1.51/1.19 inference(transitivity,[status(thm)],[461, 459])).
% 1.51/1.19 tff(463,plain,
% 1.51/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)) | c0_1(a1762) | c1_1(a1762) | (~c3_1(a1762)))),
% 1.51/1.19 inference(quant_inst,[status(thm)],[])).
% 1.51/1.19 tff(464,plain,
% 1.51/1.19 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1771) | c1_1(a1765) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c1_1(a1771)) | (~c2_1(a1771))),
% 1.51/1.19 inference(modus_ponens,[status(thm)],[463, 462])).
% 1.51/1.19 tff(465,plain,
% 1.51/1.19 (c1_1(a1762)),
% 1.51/1.19 inference(unit_resolution,[status(thm)],[464, 111, 458, 457, 456, 445, 340, 434, 344, 339, 46])).
% 1.51/1.19 tff(466,plain,
% 1.51/1.19 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W))))),
% 1.51/1.19 inference(bind,[status(th)],[])).
% 1.51/1.19 tff(467,plain,
% 1.51/1.19 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 1.51/1.19 inference(quant_intro,[status(thm)],[466])).
% 1.51/1.19 tff(468,plain,
% 1.51/1.19 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 1.51/1.19 inference(rewrite,[status(thm)],[])).
% 1.51/1.19 tff(469,plain,
% 1.51/1.19 (^[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(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(W)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(W))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c1_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)) | (~c1_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))))),
% 1.51/1.19 inference(bind,[status(th)],[])).
% 1.51/1.19 tff(470,plain,
% 1.51/1.19 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 1.51/1.19 inference(quant_intro,[status(thm)],[469])).
% 1.51/1.19 tff(471,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | (~c1_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause196')).
% 1.51/1.19 tff(472,plain,
% 1.51/1.19 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 1.51/1.19 inference(modus_ponens,[status(thm)],[471, 470])).
% 1.51/1.19 tff(473,plain,
% 1.51/1.19 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 1.51/1.19 inference(modus_ponens,[status(thm)],[472, 468])).
% 1.51/1.19 tff(474,plain,(
% 1.51/1.19 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 1.51/1.19 inference(skolemize,[status(sab)],[473])).
% 1.51/1.19 tff(475,plain,
% 1.51/1.19 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))),
% 1.51/1.19 inference(modus_ponens,[status(thm)],[474, 467])).
% 1.51/1.19 tff(476,plain,
% 1.51/1.19 (^[U: $i] : refl((hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) <=> (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))))),
% 1.51/1.19 inference(bind,[status(th)],[])).
% 1.51/1.19 tff(477,plain,
% 1.51/1.19 (![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))),
% 1.51/1.19 inference(quant_intro,[status(thm)],[476])).
% 1.51/1.19 tff(478,plain,
% 1.51/1.19 (![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) <=> ![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))),
% 1.51/1.19 inference(rewrite,[status(thm)],[])).
% 1.51/1.19 tff(479,plain,
% 1.51/1.19 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | 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)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp16) <=> (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp16) | hskp22) <=> ((hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | hskp22))), rewrite(((hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | hskp22) <=> (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp16) | hskp22) <=> (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))))),
% 1.51/1.19 inference(bind,[status(th)],[])).
% 1.51/1.19 tff(480,plain,
% 1.51/1.19 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp16) | hskp22) <=> ![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))),
% 1.51/1.19 inference(quant_intro,[status(thm)],[479])).
% 1.51/1.19 tff(481,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp16) | hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause153')).
% 1.51/1.19 tff(482,plain,
% 1.51/1.19 (![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))),
% 1.51/1.19 inference(modus_ponens,[status(thm)],[481, 480])).
% 1.51/1.19 tff(483,plain,
% 1.51/1.19 (![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))),
% 1.51/1.19 inference(modus_ponens,[status(thm)],[482, 478])).
% 1.51/1.19 tff(484,plain,(
% 1.51/1.19 ![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))),
% 1.51/1.19 inference(skolemize,[status(sab)],[483])).
% 1.51/1.19 tff(485,plain,
% 1.51/1.19 (![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))),
% 1.51/1.19 inference(modus_ponens,[status(thm)],[484, 477])).
% 1.51/1.19 tff(486,plain,
% 1.51/1.19 (((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))) | (hskp22 | hskp16 | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)))) <=> ((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))) | hskp22 | hskp16 | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)))),
% 1.51/1.19 inference(rewrite,[status(thm)],[])).
% 1.51/1.19 tff(487,plain,
% 1.51/1.19 ((hskp22 | hskp16 | (~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1762))) <=> (hskp22 | hskp16 | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)))),
% 1.51/1.19 inference(rewrite,[status(thm)],[])).
% 1.51/1.19 tff(488,plain,
% 1.51/1.19 (((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))) | (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1762)))) <=> ((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))) | (hskp22 | hskp16 | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762))))),
% 1.51/1.19 inference(monotonicity,[status(thm)],[487])).
% 1.51/1.19 tff(489,plain,
% 1.51/1.19 (((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))) | (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1762)))) <=> ((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))) | hskp22 | hskp16 | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)))),
% 1.51/1.19 inference(transitivity,[status(thm)],[488, 486])).
% 1.51/1.19 tff(490,plain,
% 1.51/1.19 ((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))) | (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1762)))),
% 1.51/1.19 inference(quant_inst,[status(thm)],[])).
% 1.51/1.19 tff(491,plain,
% 1.51/1.19 ((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))) | hskp22 | hskp16 | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762))),
% 1.51/1.19 inference(modus_ponens,[status(thm)],[490, 489])).
% 1.51/1.19 tff(492,plain,
% 1.51/1.19 (hskp16 | (~c1_1(a1762))),
% 1.51/1.19 inference(unit_resolution,[status(thm)],[491, 111, 355, 341, 340, 485])).
% 1.51/1.19 tff(493,plain,
% 1.51/1.19 (hskp16),
% 1.51/1.19 inference(unit_resolution,[status(thm)],[492, 465])).
% 1.51/1.19 tff(494,plain,
% 1.51/1.19 (((~hskp16) | (~c2_1(a1780))) <=> ((~hskp16) | (~c2_1(a1780)))),
% 1.51/1.19 inference(rewrite,[status(thm)],[])).
% 1.51/1.19 tff(495,plain,
% 1.51/1.19 (((~c2_1(a1780)) | (~hskp16)) <=> ((~hskp16) | (~c2_1(a1780)))),
% 1.51/1.19 inference(rewrite,[status(thm)],[])).
% 1.51/1.19 tff(496,axiom,((~c2_1(a1780)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause104')).
% 1.51/1.19 tff(497,plain,
% 1.51/1.19 ((~hskp16) | (~c2_1(a1780))),
% 1.51/1.19 inference(modus_ponens,[status(thm)],[496, 495])).
% 1.51/1.19 tff(498,plain,
% 1.51/1.19 ((~hskp16) | (~c2_1(a1780))),
% 1.51/1.19 inference(modus_ponens,[status(thm)],[497, 494])).
% 1.51/1.19 tff(499,plain,
% 1.51/1.19 (~c2_1(a1780)),
% 1.51/1.19 inference(unit_resolution,[status(thm)],[498, 493])).
% 1.51/1.19 tff(500,plain,
% 1.51/1.19 (((~hskp16) | c1_1(a1780)) <=> ((~hskp16) | c1_1(a1780))),
% 1.51/1.19 inference(rewrite,[status(thm)],[])).
% 1.51/1.19 tff(501,axiom,((~hskp16) | c1_1(a1780)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause61')).
% 1.51/1.19 tff(502,plain,
% 1.51/1.19 ((~hskp16) | c1_1(a1780)),
% 1.51/1.19 inference(modus_ponens,[status(thm)],[501, 500])).
% 1.51/1.19 tff(503,plain,
% 1.51/1.19 ((~hskp16) | c1_1(a1780)),
% 1.51/1.19 inference(modus_ponens,[status(thm)],[502, 500])).
% 1.51/1.19 tff(504,plain,
% 1.51/1.19 ((~hskp16) | c1_1(a1780)),
% 1.51/1.19 inference(modus_ponens,[status(thm)],[503, 500])).
% 1.51/1.19 tff(505,plain,
% 1.51/1.19 ((~hskp16) | c1_1(a1780)),
% 1.51/1.19 inference(modus_ponens,[status(thm)],[504, 500])).
% 1.51/1.19 tff(506,plain,
% 1.51/1.19 ((~hskp16) | c1_1(a1780)),
% 1.51/1.19 inference(modus_ponens,[status(thm)],[505, 500])).
% 1.51/1.19 tff(507,plain,
% 1.51/1.19 ((~hskp16) | c1_1(a1780)),
% 1.51/1.19 inference(modus_ponens,[status(thm)],[506, 500])).
% 1.51/1.19 tff(508,plain,
% 1.51/1.19 ((~hskp16) | c1_1(a1780)),
% 1.51/1.19 inference(modus_ponens,[status(thm)],[507, 500])).
% 1.51/1.19 tff(509,plain,
% 1.51/1.20 ((~hskp16) | c1_1(a1780)),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[508, 500])).
% 1.51/1.20 tff(510,plain,
% 1.51/1.20 (c1_1(a1780)),
% 1.51/1.20 inference(unit_resolution,[status(thm)],[509, 493])).
% 1.51/1.20 tff(511,plain,
% 1.51/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c2_1(a1780) | c1_1(a1765) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c1_1(a1762)) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c1_1(a1780)) | (~c0_1(a1780)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c2_1(a1780) | c1_1(a1765) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c1_1(a1762)) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c1_1(a1780)) | (~c0_1(a1780)))),
% 1.51/1.20 inference(rewrite,[status(thm)],[])).
% 1.51/1.20 tff(512,plain,
% 1.51/1.20 (((~ndr1_0) | c2_1(a1780) | (~c1_1(a1780)) | (~c0_1(a1780)) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1762) | (~c3_1(a1762)) | (~c1_1(a1762))) <=> (c2_1(a1780) | c1_1(a1765) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c1_1(a1762)) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c1_1(a1780)) | (~c0_1(a1780)))),
% 1.51/1.20 inference(rewrite,[status(thm)],[])).
% 1.51/1.20 tff(513,plain,
% 1.51/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1780) | (~c1_1(a1780)) | (~c0_1(a1780)) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1762) | (~c3_1(a1762)) | (~c1_1(a1762)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c2_1(a1780) | c1_1(a1765) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c1_1(a1762)) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c1_1(a1780)) | (~c0_1(a1780))))),
% 1.51/1.20 inference(monotonicity,[status(thm)],[512])).
% 1.51/1.20 tff(514,plain,
% 1.51/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1780) | (~c1_1(a1780)) | (~c0_1(a1780)) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1762) | (~c3_1(a1762)) | (~c1_1(a1762)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c2_1(a1780) | c1_1(a1765) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c1_1(a1762)) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c1_1(a1780)) | (~c0_1(a1780)))),
% 1.51/1.20 inference(transitivity,[status(thm)],[513, 511])).
% 1.51/1.20 tff(515,plain,
% 1.51/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1780) | (~c1_1(a1780)) | (~c0_1(a1780)) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1762) | (~c3_1(a1762)) | (~c1_1(a1762)))),
% 1.51/1.20 inference(quant_inst,[status(thm)],[])).
% 1.51/1.20 tff(516,plain,
% 1.51/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c2_1(a1780) | c1_1(a1765) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c1_1(a1762)) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c1_1(a1780)) | (~c0_1(a1780))),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[515, 514])).
% 1.51/1.20 tff(517,plain,
% 1.51/1.20 (~c0_1(a1780)),
% 1.51/1.20 inference(unit_resolution,[status(thm)],[516, 111, 510, 456, 445, 340, 499, 344, 339, 475, 465])).
% 1.51/1.20 tff(518,plain,
% 1.51/1.20 (((~hskp16) | c3_1(a1780)) <=> ((~hskp16) | c3_1(a1780))),
% 1.51/1.20 inference(rewrite,[status(thm)],[])).
% 1.51/1.20 tff(519,axiom,((~hskp16) | c3_1(a1780)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause62')).
% 1.51/1.20 tff(520,plain,
% 1.51/1.20 ((~hskp16) | c3_1(a1780)),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[519, 518])).
% 1.51/1.20 tff(521,plain,
% 1.51/1.20 ((~hskp16) | c3_1(a1780)),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[520, 518])).
% 1.51/1.20 tff(522,plain,
% 1.51/1.20 ((~hskp16) | c3_1(a1780)),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[521, 518])).
% 1.51/1.20 tff(523,plain,
% 1.51/1.20 ((~hskp16) | c3_1(a1780)),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[522, 518])).
% 1.51/1.20 tff(524,plain,
% 1.51/1.20 ((~hskp16) | c3_1(a1780)),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[523, 518])).
% 1.51/1.20 tff(525,plain,
% 1.51/1.20 ((~hskp16) | c3_1(a1780)),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[524, 518])).
% 1.51/1.20 tff(526,plain,
% 1.51/1.20 ((~hskp16) | c3_1(a1780)),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[525, 518])).
% 1.51/1.20 tff(527,plain,
% 1.51/1.20 ((~hskp16) | c3_1(a1780)),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[526, 518])).
% 1.51/1.20 tff(528,plain,
% 1.51/1.20 (c3_1(a1780)),
% 1.51/1.20 inference(unit_resolution,[status(thm)],[527, 493])).
% 1.51/1.20 tff(529,plain,
% 1.51/1.20 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | c2_1(a1780) | (~ndr1_0) | c0_1(a1780) | (~c3_1(a1780)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c2_1(a1780) | (~ndr1_0) | c0_1(a1780) | (~c3_1(a1780)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))),
% 1.51/1.20 inference(rewrite,[status(thm)],[])).
% 1.51/1.20 tff(530,plain,
% 1.51/1.20 ((hskp3 | (~ndr1_0) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)) | c2_1(a1780) | c0_1(a1780) | (~c3_1(a1780))) <=> (hskp3 | c2_1(a1780) | (~ndr1_0) | c0_1(a1780) | (~c3_1(a1780)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))),
% 1.51/1.20 inference(rewrite,[status(thm)],[])).
% 1.51/1.20 tff(531,plain,
% 1.51/1.20 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)) | c2_1(a1780) | c0_1(a1780) | (~c3_1(a1780)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | c2_1(a1780) | (~ndr1_0) | c0_1(a1780) | (~c3_1(a1780)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756))))),
% 1.51/1.20 inference(monotonicity,[status(thm)],[530])).
% 1.51/1.20 tff(532,plain,
% 1.51/1.20 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)) | c2_1(a1780) | c0_1(a1780) | (~c3_1(a1780)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c2_1(a1780) | (~ndr1_0) | c0_1(a1780) | (~c3_1(a1780)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))),
% 1.51/1.20 inference(transitivity,[status(thm)],[531, 529])).
% 1.51/1.20 tff(533,plain,
% 1.51/1.20 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)) | c2_1(a1780) | c0_1(a1780) | (~c3_1(a1780)))),
% 1.51/1.20 inference(quant_inst,[status(thm)],[])).
% 1.51/1.20 tff(534,plain,
% 1.51/1.20 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c2_1(a1780) | (~ndr1_0) | c0_1(a1780) | (~c3_1(a1780)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756))),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[533, 532])).
% 1.51/1.20 tff(535,plain,
% 1.51/1.20 ($false),
% 1.51/1.20 inference(unit_resolution,[status(thm)],[534, 111, 35, 395, 384, 373, 528, 499, 11, 517])).
% 1.51/1.20 tff(536,plain,((~hskp6) | hskp3 | hskp22 | hskp19 | hskp4), inference(lemma,lemma(discharge,[]))).
% 1.51/1.20 tff(537,plain,
% 1.51/1.20 (hskp22),
% 1.51/1.20 inference(unit_resolution,[status(thm)],[536, 286, 35, 12, 151])).
% 1.51/1.20 tff(538,plain,
% 1.51/1.20 (((~hskp22) | (~c2_1(a1799))) <=> ((~hskp22) | (~c2_1(a1799)))),
% 1.51/1.20 inference(rewrite,[status(thm)],[])).
% 1.51/1.20 tff(539,plain,
% 1.51/1.20 (((~c2_1(a1799)) | (~hskp22)) <=> ((~hskp22) | (~c2_1(a1799)))),
% 1.51/1.20 inference(rewrite,[status(thm)],[])).
% 1.51/1.20 tff(540,axiom,((~c2_1(a1799)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause96')).
% 1.51/1.20 tff(541,plain,
% 1.51/1.20 ((~hskp22) | (~c2_1(a1799))),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[540, 539])).
% 1.51/1.20 tff(542,plain,
% 1.51/1.20 ((~hskp22) | (~c2_1(a1799))),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[541, 538])).
% 1.51/1.20 tff(543,plain,
% 1.51/1.20 (~c2_1(a1799)),
% 1.51/1.20 inference(unit_resolution,[status(thm)],[542, 537])).
% 1.51/1.20 tff(544,plain,
% 1.51/1.20 (((~hskp22) | (~c0_1(a1799))) <=> ((~hskp22) | (~c0_1(a1799)))),
% 1.51/1.20 inference(rewrite,[status(thm)],[])).
% 1.51/1.20 tff(545,plain,
% 1.51/1.20 (((~c0_1(a1799)) | (~hskp22)) <=> ((~hskp22) | (~c0_1(a1799)))),
% 1.51/1.20 inference(rewrite,[status(thm)],[])).
% 1.51/1.20 tff(546,axiom,((~c0_1(a1799)) | (~hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause95')).
% 1.51/1.20 tff(547,plain,
% 1.51/1.20 ((~hskp22) | (~c0_1(a1799))),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[546, 545])).
% 1.51/1.20 tff(548,plain,
% 1.51/1.20 ((~hskp22) | (~c0_1(a1799))),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[547, 544])).
% 1.51/1.20 tff(549,plain,
% 1.51/1.20 (~c0_1(a1799)),
% 1.51/1.20 inference(unit_resolution,[status(thm)],[548, 537])).
% 1.51/1.20 tff(550,plain,
% 1.51/1.20 (((~hskp22) | c3_1(a1799)) <=> ((~hskp22) | c3_1(a1799))),
% 1.51/1.20 inference(rewrite,[status(thm)],[])).
% 1.51/1.20 tff(551,axiom,((~hskp22) | c3_1(a1799)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause52')).
% 1.51/1.20 tff(552,plain,
% 1.51/1.20 ((~hskp22) | c3_1(a1799)),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[551, 550])).
% 1.51/1.20 tff(553,plain,
% 1.51/1.20 ((~hskp22) | c3_1(a1799)),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[552, 550])).
% 1.51/1.20 tff(554,plain,
% 1.51/1.20 ((~hskp22) | c3_1(a1799)),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[553, 550])).
% 1.51/1.20 tff(555,plain,
% 1.51/1.20 ((~hskp22) | c3_1(a1799)),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[554, 550])).
% 1.51/1.20 tff(556,plain,
% 1.51/1.20 ((~hskp22) | c3_1(a1799)),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[555, 550])).
% 1.51/1.20 tff(557,plain,
% 1.51/1.20 ((~hskp22) | c3_1(a1799)),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[556, 550])).
% 1.51/1.20 tff(558,plain,
% 1.51/1.20 ((~hskp22) | c3_1(a1799)),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[557, 550])).
% 1.51/1.20 tff(559,plain,
% 1.51/1.20 ((~hskp22) | c3_1(a1799)),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[558, 550])).
% 1.51/1.20 tff(560,plain,
% 1.51/1.20 (c3_1(a1799)),
% 1.51/1.20 inference(unit_resolution,[status(thm)],[559, 537])).
% 1.51/1.20 tff(561,plain,
% 1.51/1.20 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c1_1(a1759) | c0_1(a1799) | c2_1(a1799) | c3_1(a1759) | (~ndr1_0) | (~c0_1(a1759)) | (~c3_1(a1799)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c1_1(a1759) | c0_1(a1799) | c2_1(a1799) | c3_1(a1759) | (~ndr1_0) | (~c0_1(a1759)) | (~c3_1(a1799)))),
% 1.51/1.20 inference(rewrite,[status(thm)],[])).
% 1.51/1.20 tff(562,plain,
% 1.51/1.20 ((hskp10 | (~ndr1_0) | c3_1(a1759) | c1_1(a1759) | (~c0_1(a1759)) | c2_1(a1799) | c0_1(a1799) | (~c3_1(a1799))) <=> (hskp10 | c1_1(a1759) | c0_1(a1799) | c2_1(a1799) | c3_1(a1759) | (~ndr1_0) | (~c0_1(a1759)) | (~c3_1(a1799)))),
% 1.51/1.20 inference(rewrite,[status(thm)],[])).
% 1.51/1.20 tff(563,plain,
% 1.51/1.20 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c3_1(a1759) | c1_1(a1759) | (~c0_1(a1759)) | c2_1(a1799) | c0_1(a1799) | (~c3_1(a1799)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c1_1(a1759) | c0_1(a1799) | c2_1(a1799) | c3_1(a1759) | (~ndr1_0) | (~c0_1(a1759)) | (~c3_1(a1799))))),
% 1.51/1.20 inference(monotonicity,[status(thm)],[562])).
% 1.51/1.20 tff(564,plain,
% 1.51/1.20 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c3_1(a1759) | c1_1(a1759) | (~c0_1(a1759)) | c2_1(a1799) | c0_1(a1799) | (~c3_1(a1799)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c1_1(a1759) | c0_1(a1799) | c2_1(a1799) | c3_1(a1759) | (~ndr1_0) | (~c0_1(a1759)) | (~c3_1(a1799)))),
% 1.51/1.20 inference(transitivity,[status(thm)],[563, 561])).
% 1.51/1.20 tff(565,plain,
% 1.51/1.20 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c3_1(a1759) | c1_1(a1759) | (~c0_1(a1759)) | c2_1(a1799) | c0_1(a1799) | (~c3_1(a1799)))),
% 1.51/1.20 inference(quant_inst,[status(thm)],[])).
% 1.51/1.20 tff(566,plain,
% 1.51/1.20 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c1_1(a1759) | c0_1(a1799) | c2_1(a1799) | c3_1(a1759) | (~ndr1_0) | (~c0_1(a1759)) | (~c3_1(a1799))),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[565, 564])).
% 1.51/1.20 tff(567,plain,
% 1.51/1.20 (hskp10),
% 1.51/1.20 inference(unit_resolution,[status(thm)],[566, 111, 560, 47, 549, 543, 34, 337, 200])).
% 1.51/1.20 tff(568,plain,
% 1.51/1.20 (((~hskp10) | (~c1_1(a1767))) <=> ((~hskp10) | (~c1_1(a1767)))),
% 1.51/1.20 inference(rewrite,[status(thm)],[])).
% 1.51/1.20 tff(569,plain,
% 1.51/1.20 (((~c1_1(a1767)) | (~hskp10)) <=> ((~hskp10) | (~c1_1(a1767)))),
% 1.51/1.20 inference(rewrite,[status(thm)],[])).
% 1.51/1.20 tff(570,axiom,((~c1_1(a1767)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause114')).
% 1.51/1.20 tff(571,plain,
% 1.51/1.20 ((~hskp10) | (~c1_1(a1767))),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[570, 569])).
% 1.51/1.20 tff(572,plain,
% 1.51/1.20 ((~hskp10) | (~c1_1(a1767))),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[571, 568])).
% 1.51/1.20 tff(573,plain,
% 1.51/1.20 (~c1_1(a1767)),
% 1.51/1.20 inference(unit_resolution,[status(thm)],[572, 567])).
% 1.51/1.20 tff(574,plain,
% 1.51/1.20 (((~hskp10) | (~c0_1(a1767))) <=> ((~hskp10) | (~c0_1(a1767)))),
% 1.51/1.20 inference(rewrite,[status(thm)],[])).
% 1.51/1.20 tff(575,plain,
% 1.51/1.20 (((~c0_1(a1767)) | (~hskp10)) <=> ((~hskp10) | (~c0_1(a1767)))),
% 1.51/1.20 inference(rewrite,[status(thm)],[])).
% 1.51/1.20 tff(576,axiom,((~c0_1(a1767)) | (~hskp10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause113')).
% 1.51/1.20 tff(577,plain,
% 1.51/1.20 ((~hskp10) | (~c0_1(a1767))),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[576, 575])).
% 1.51/1.20 tff(578,plain,
% 1.51/1.20 ((~hskp10) | (~c0_1(a1767))),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[577, 574])).
% 1.51/1.20 tff(579,plain,
% 1.51/1.20 (~c0_1(a1767)),
% 1.51/1.20 inference(unit_resolution,[status(thm)],[578, 567])).
% 1.51/1.20 tff(580,plain,
% 1.51/1.20 (c2_1(a1765)),
% 1.51/1.20 inference(unit_resolution,[status(thm)],[444, 321])).
% 1.51/1.20 tff(581,plain,
% 1.51/1.20 (c0_1(a1765)),
% 1.51/1.20 inference(unit_resolution,[status(thm)],[455, 321])).
% 1.51/1.20 tff(582,plain,
% 1.51/1.20 (((~hskp10) | c3_1(a1767)) <=> ((~hskp10) | c3_1(a1767))),
% 1.51/1.20 inference(rewrite,[status(thm)],[])).
% 1.51/1.20 tff(583,axiom,((~hskp10) | c3_1(a1767)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause70')).
% 1.51/1.20 tff(584,plain,
% 1.51/1.20 ((~hskp10) | c3_1(a1767)),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[583, 582])).
% 1.51/1.20 tff(585,plain,
% 1.51/1.20 ((~hskp10) | c3_1(a1767)),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[584, 582])).
% 1.51/1.20 tff(586,plain,
% 1.51/1.20 ((~hskp10) | c3_1(a1767)),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[585, 582])).
% 1.51/1.20 tff(587,plain,
% 1.51/1.20 ((~hskp10) | c3_1(a1767)),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[586, 582])).
% 1.51/1.20 tff(588,plain,
% 1.51/1.20 ((~hskp10) | c3_1(a1767)),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[587, 582])).
% 1.51/1.20 tff(589,plain,
% 1.51/1.20 ((~hskp10) | c3_1(a1767)),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[588, 582])).
% 1.51/1.20 tff(590,plain,
% 1.51/1.20 ((~hskp10) | c3_1(a1767)),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[589, 582])).
% 1.51/1.20 tff(591,plain,
% 1.51/1.20 ((~hskp10) | c3_1(a1767)),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[590, 582])).
% 1.51/1.20 tff(592,plain,
% 1.51/1.20 (c3_1(a1767)),
% 1.51/1.20 inference(unit_resolution,[status(thm)],[591, 567])).
% 1.51/1.20 tff(593,plain,
% 1.51/1.20 (c2_1(a1771)),
% 1.51/1.20 inference(unit_resolution,[status(thm)],[263, 233])).
% 1.51/1.20 tff(594,plain,
% 1.51/1.20 (c1_1(a1771)),
% 1.51/1.20 inference(unit_resolution,[status(thm)],[252, 233])).
% 1.51/1.20 tff(595,plain,
% 1.51/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c0_1(a1771) | c0_1(a1767) | c1_1(a1767) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c3_1(a1767)) | (~c1_1(a1771)) | (~c2_1(a1771)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1771) | c0_1(a1767) | c1_1(a1767) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c3_1(a1767)) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 1.51/1.20 inference(rewrite,[status(thm)],[])).
% 1.51/1.20 tff(596,plain,
% 1.51/1.20 (((~ndr1_0) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)) | c0_1(a1767) | c1_1(a1767) | (~c3_1(a1767))) <=> (c0_1(a1771) | c0_1(a1767) | c1_1(a1767) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c3_1(a1767)) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 1.51/1.20 inference(rewrite,[status(thm)],[])).
% 1.51/1.20 tff(597,plain,
% 1.51/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)) | c0_1(a1767) | c1_1(a1767) | (~c3_1(a1767)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c0_1(a1771) | c0_1(a1767) | c1_1(a1767) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c3_1(a1767)) | (~c1_1(a1771)) | (~c2_1(a1771))))),
% 1.51/1.20 inference(monotonicity,[status(thm)],[596])).
% 1.51/1.20 tff(598,plain,
% 1.51/1.20 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)) | c0_1(a1767) | c1_1(a1767) | (~c3_1(a1767)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1771) | c0_1(a1767) | c1_1(a1767) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c3_1(a1767)) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 1.51/1.20 inference(transitivity,[status(thm)],[597, 595])).
% 1.51/1.20 tff(599,plain,
% 1.51/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)) | c0_1(a1767) | c1_1(a1767) | (~c3_1(a1767)))),
% 1.51/1.20 inference(quant_inst,[status(thm)],[])).
% 1.51/1.20 tff(600,plain,
% 1.51/1.20 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1771) | c0_1(a1767) | c1_1(a1767) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c3_1(a1767)) | (~c1_1(a1771)) | (~c2_1(a1771))),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[599, 598])).
% 1.51/1.20 tff(601,plain,
% 1.51/1.20 ($false),
% 1.51/1.20 inference(unit_resolution,[status(thm)],[600, 111, 594, 593, 592, 581, 580, 239, 579, 573, 327, 46])).
% 1.51/1.20 tff(602,plain,(hskp3 | c1_1(a1759) | c3_1(a1759) | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.51/1.20 tff(603,plain,
% 1.51/1.20 (hskp3),
% 1.51/1.20 inference(unit_resolution,[status(thm)],[602, 47, 34, 12])).
% 1.51/1.20 tff(604,plain,
% 1.51/1.20 (((~hskp3) | c2_1(a1758)) <=> ((~hskp3) | c2_1(a1758))),
% 1.51/1.20 inference(rewrite,[status(thm)],[])).
% 1.51/1.20 tff(605,axiom,((~hskp3) | c2_1(a1758)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause80')).
% 1.51/1.20 tff(606,plain,
% 1.51/1.20 ((~hskp3) | c2_1(a1758)),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[605, 604])).
% 1.51/1.20 tff(607,plain,
% 1.51/1.20 ((~hskp3) | c2_1(a1758)),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[606, 604])).
% 1.51/1.20 tff(608,plain,
% 1.51/1.20 ((~hskp3) | c2_1(a1758)),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[607, 604])).
% 1.51/1.20 tff(609,plain,
% 1.51/1.20 ((~hskp3) | c2_1(a1758)),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[608, 604])).
% 1.51/1.20 tff(610,plain,
% 1.51/1.20 ((~hskp3) | c2_1(a1758)),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[609, 604])).
% 1.51/1.20 tff(611,plain,
% 1.51/1.20 ((~hskp3) | c2_1(a1758)),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[610, 604])).
% 1.51/1.20 tff(612,plain,
% 1.51/1.20 ((~hskp3) | c2_1(a1758)),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[611, 604])).
% 1.51/1.20 tff(613,plain,
% 1.51/1.20 ((~hskp3) | c2_1(a1758)),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[612, 604])).
% 1.51/1.20 tff(614,plain,
% 1.51/1.20 (c2_1(a1758)),
% 1.51/1.20 inference(unit_resolution,[status(thm)],[613, 603])).
% 1.51/1.20 tff(615,plain,
% 1.51/1.20 (((~hskp3) | c1_1(a1758)) <=> ((~hskp3) | c1_1(a1758))),
% 1.51/1.20 inference(rewrite,[status(thm)],[])).
% 1.51/1.20 tff(616,axiom,((~hskp3) | c1_1(a1758)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause79')).
% 1.51/1.20 tff(617,plain,
% 1.51/1.20 ((~hskp3) | c1_1(a1758)),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[616, 615])).
% 1.51/1.20 tff(618,plain,
% 1.51/1.20 ((~hskp3) | c1_1(a1758)),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[617, 615])).
% 1.51/1.20 tff(619,plain,
% 1.51/1.20 ((~hskp3) | c1_1(a1758)),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[618, 615])).
% 1.51/1.20 tff(620,plain,
% 1.51/1.20 ((~hskp3) | c1_1(a1758)),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[619, 615])).
% 1.51/1.20 tff(621,plain,
% 1.51/1.20 ((~hskp3) | c1_1(a1758)),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[620, 615])).
% 1.51/1.20 tff(622,plain,
% 1.51/1.20 ((~hskp3) | c1_1(a1758)),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[621, 615])).
% 1.51/1.20 tff(623,plain,
% 1.51/1.20 ((~hskp3) | c1_1(a1758)),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[622, 615])).
% 1.51/1.20 tff(624,plain,
% 1.51/1.20 ((~hskp3) | c1_1(a1758)),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[623, 615])).
% 1.51/1.20 tff(625,plain,
% 1.51/1.20 (c1_1(a1758)),
% 1.51/1.20 inference(unit_resolution,[status(thm)],[624, 603])).
% 1.51/1.20 tff(626,plain,
% 1.51/1.20 (((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c1_1(a1758)))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp13 | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c1_1(a1758)))),
% 1.51/1.20 inference(rewrite,[status(thm)],[])).
% 1.51/1.20 tff(627,plain,
% 1.51/1.20 ((hskp13 | (~ndr1_0) | c0_1(a1758) | (~c2_1(a1758)) | (~c1_1(a1758))) <=> (hskp13 | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c1_1(a1758)))),
% 1.51/1.20 inference(rewrite,[status(thm)],[])).
% 1.51/1.20 tff(628,plain,
% 1.51/1.20 (((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | (~ndr1_0) | c0_1(a1758) | (~c2_1(a1758)) | (~c1_1(a1758)))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c1_1(a1758))))),
% 1.51/1.20 inference(monotonicity,[status(thm)],[627])).
% 1.51/1.20 tff(629,plain,
% 1.51/1.20 (((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | (~ndr1_0) | c0_1(a1758) | (~c2_1(a1758)) | (~c1_1(a1758)))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp13 | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c1_1(a1758)))),
% 1.51/1.20 inference(transitivity,[status(thm)],[628, 626])).
% 1.51/1.20 tff(630,plain,
% 1.51/1.20 ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | (~ndr1_0) | c0_1(a1758) | (~c2_1(a1758)) | (~c1_1(a1758)))),
% 1.51/1.20 inference(quant_inst,[status(thm)],[])).
% 1.51/1.20 tff(631,plain,
% 1.51/1.20 ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp13 | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c1_1(a1758))),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[630, 629])).
% 1.51/1.20 tff(632,plain,
% 1.51/1.20 (hskp13 | c0_1(a1758)),
% 1.51/1.20 inference(unit_resolution,[status(thm)],[631, 111, 625, 614, 22])).
% 1.51/1.20 tff(633,plain,
% 1.51/1.20 (c0_1(a1758)),
% 1.51/1.20 inference(unit_resolution,[status(thm)],[632, 23])).
% 1.51/1.20 tff(634,plain,
% 1.51/1.20 (((~hskp3) | (~c3_1(a1758))) <=> ((~hskp3) | (~c3_1(a1758)))),
% 1.51/1.20 inference(rewrite,[status(thm)],[])).
% 1.51/1.20 tff(635,plain,
% 1.51/1.20 (((~c3_1(a1758)) | (~hskp3)) <=> ((~hskp3) | (~c3_1(a1758)))),
% 1.51/1.20 inference(rewrite,[status(thm)],[])).
% 1.51/1.20 tff(636,axiom,((~c3_1(a1758)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause125')).
% 1.51/1.20 tff(637,plain,
% 1.51/1.20 ((~hskp3) | (~c3_1(a1758))),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[636, 635])).
% 1.51/1.20 tff(638,plain,
% 1.51/1.20 ((~hskp3) | (~c3_1(a1758))),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[637, 634])).
% 1.51/1.20 tff(639,plain,
% 1.51/1.20 (~c3_1(a1758)),
% 1.51/1.20 inference(unit_resolution,[status(thm)],[638, 603])).
% 1.51/1.20 tff(640,plain,
% 1.51/1.20 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp2 | c1_1(a1759) | c3_1(a1759) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c0_1(a1758)) | (~c0_1(a1759)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp2 | c1_1(a1759) | c3_1(a1759) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c0_1(a1758)) | (~c0_1(a1759)))),
% 1.51/1.20 inference(rewrite,[status(thm)],[])).
% 1.51/1.20 tff(641,plain,
% 1.51/1.20 ((hskp2 | (~ndr1_0) | c3_1(a1758) | (~c2_1(a1758)) | (~c0_1(a1758)) | c1_1(a1759) | c3_1(a1759) | (~c0_1(a1759))) <=> (hskp2 | c1_1(a1759) | c3_1(a1759) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c0_1(a1758)) | (~c0_1(a1759)))),
% 1.51/1.20 inference(rewrite,[status(thm)],[])).
% 1.51/1.20 tff(642,plain,
% 1.51/1.20 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a1758) | (~c2_1(a1758)) | (~c0_1(a1758)) | c1_1(a1759) | c3_1(a1759) | (~c0_1(a1759)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp2 | c1_1(a1759) | c3_1(a1759) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c0_1(a1758)) | (~c0_1(a1759))))),
% 1.51/1.20 inference(monotonicity,[status(thm)],[641])).
% 1.51/1.20 tff(643,plain,
% 1.51/1.20 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a1758) | (~c2_1(a1758)) | (~c0_1(a1758)) | c1_1(a1759) | c3_1(a1759) | (~c0_1(a1759)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp2 | c1_1(a1759) | c3_1(a1759) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c0_1(a1758)) | (~c0_1(a1759)))),
% 1.51/1.20 inference(transitivity,[status(thm)],[642, 640])).
% 1.51/1.20 tff(644,plain,
% 1.51/1.20 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a1758) | (~c2_1(a1758)) | (~c0_1(a1758)) | c1_1(a1759) | c3_1(a1759) | (~c0_1(a1759)))),
% 1.51/1.20 inference(quant_inst,[status(thm)],[])).
% 1.51/1.20 tff(645,plain,
% 1.51/1.20 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp2 | c1_1(a1759) | c3_1(a1759) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c0_1(a1758)) | (~c0_1(a1759))),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[644, 643])).
% 1.51/1.20 tff(646,plain,
% 1.51/1.20 (hskp2 | (~c0_1(a1758)) | (~c0_1(a1759))),
% 1.51/1.20 inference(unit_resolution,[status(thm)],[645, 111, 47, 614, 34, 639, 210])).
% 1.51/1.20 tff(647,plain,
% 1.51/1.20 (~c0_1(a1759)),
% 1.51/1.20 inference(unit_resolution,[status(thm)],[646, 120, 633])).
% 1.51/1.20 tff(648,plain,
% 1.51/1.20 (^[U: $i] : refl((hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> (hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))),
% 1.51/1.20 inference(bind,[status(th)],[])).
% 1.51/1.20 tff(649,plain,
% 1.51/1.20 (![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.51/1.20 inference(quant_intro,[status(thm)],[648])).
% 1.51/1.20 tff(650,plain,
% 1.51/1.20 (![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) <=> ![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.51/1.20 inference(rewrite,[status(thm)],[])).
% 1.51/1.20 tff(651,plain,
% 1.51/1.20 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U)))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | 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))), (((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp27) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp27))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp27) | hskp2) <=> ((hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp2))), rewrite(((hskp27 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U)) | hskp2) <=> (hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))), (((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp27) | hskp2) <=> (hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))))),
% 1.51/1.20 inference(bind,[status(th)],[])).
% 1.51/1.20 tff(652,plain,
% 1.51/1.20 (![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp27) | hskp2) <=> ![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.51/1.20 inference(quant_intro,[status(thm)],[651])).
% 1.51/1.20 tff(653,axiom,(![U: $i] : ((((((~ndr1_0) | c0_1(U)) | c1_1(U)) | c3_1(U)) | hskp27) | hskp2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause132')).
% 1.51/1.20 tff(654,plain,
% 1.51/1.20 (![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[653, 652])).
% 1.51/1.20 tff(655,plain,
% 1.51/1.20 (![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[654, 650])).
% 1.51/1.20 tff(656,plain,(
% 1.51/1.20 ![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.51/1.20 inference(skolemize,[status(sab)],[655])).
% 1.51/1.20 tff(657,plain,
% 1.51/1.20 (![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[656, 649])).
% 1.51/1.20 tff(658,plain,
% 1.51/1.20 (((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp27 | hskp2 | c1_1(a1759) | c3_1(a1759) | (~ndr1_0) | c0_1(a1759))) <=> ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp27 | hskp2 | c1_1(a1759) | c3_1(a1759) | (~ndr1_0) | c0_1(a1759))),
% 1.51/1.20 inference(rewrite,[status(thm)],[])).
% 1.51/1.20 tff(659,plain,
% 1.51/1.20 ((hskp27 | hskp2 | (~ndr1_0) | c3_1(a1759) | c1_1(a1759) | c0_1(a1759)) <=> (hskp27 | hskp2 | c1_1(a1759) | c3_1(a1759) | (~ndr1_0) | c0_1(a1759))),
% 1.51/1.20 inference(rewrite,[status(thm)],[])).
% 1.51/1.20 tff(660,plain,
% 1.51/1.20 (((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp27 | hskp2 | (~ndr1_0) | c3_1(a1759) | c1_1(a1759) | c0_1(a1759))) <=> ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp27 | hskp2 | c1_1(a1759) | c3_1(a1759) | (~ndr1_0) | c0_1(a1759)))),
% 1.51/1.20 inference(monotonicity,[status(thm)],[659])).
% 1.51/1.20 tff(661,plain,
% 1.51/1.20 (((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp27 | hskp2 | (~ndr1_0) | c3_1(a1759) | c1_1(a1759) | c0_1(a1759))) <=> ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp27 | hskp2 | c1_1(a1759) | c3_1(a1759) | (~ndr1_0) | c0_1(a1759))),
% 1.51/1.20 inference(transitivity,[status(thm)],[660, 658])).
% 1.51/1.20 tff(662,plain,
% 1.51/1.20 ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp27 | hskp2 | (~ndr1_0) | c3_1(a1759) | c1_1(a1759) | c0_1(a1759))),
% 1.51/1.20 inference(quant_inst,[status(thm)],[])).
% 1.51/1.20 tff(663,plain,
% 1.51/1.20 ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp27 | hskp2 | c1_1(a1759) | c3_1(a1759) | (~ndr1_0) | c0_1(a1759)),
% 1.51/1.20 inference(modus_ponens,[status(thm)],[662, 661])).
% 1.51/1.20 tff(664,plain,
% 1.51/1.20 (hskp27 | hskp2 | c1_1(a1759) | c0_1(a1759)),
% 1.51/1.20 inference(unit_resolution,[status(thm)],[663, 111, 34, 657])).
% 1.51/1.20 tff(665,plain,
% 1.51/1.20 (hskp27),
% 1.51/1.20 inference(unit_resolution,[status(thm)],[664, 647, 47, 120])).
% 1.51/1.20 tff(666,plain,
% 1.51/1.20 (c1_1(a1756)),
% 1.51/1.20 inference(unit_resolution,[status(thm)],[383, 665])).
% 1.51/1.20 tff(667,plain,
% 1.51/1.20 (c0_1(a1756)),
% 1.51/1.20 inference(unit_resolution,[status(thm)],[394, 665])).
% 1.51/1.20 tff(668,plain,
% 1.51/1.20 (c2_1(a1756)),
% 1.51/1.20 inference(unit_resolution,[status(thm)],[400, 111, 12, 23, 667, 666, 33])).
% 1.51/1.20 tff(669,plain,
% 1.51/1.20 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W))))),
% 1.51/1.20 inference(bind,[status(th)],[])).
% 1.51/1.20 tff(670,plain,
% 1.51/1.20 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))),
% 1.51/1.20 inference(quant_intro,[status(thm)],[669])).
% 1.51/1.20 tff(671,plain,
% 1.51/1.20 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))),
% 1.51/1.20 inference(rewrite,[status(thm)],[])).
% 1.51/1.20 tff(672,plain,
% 1.51/1.20 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(W))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c0_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(W))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c0_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(W))) | (~c1_1(W))) | c3_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c0_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | (~c1_1(W)) | (~c0_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(W))) | (~c1_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))))),
% 1.51/1.21 inference(bind,[status(th)],[])).
% 1.51/1.21 tff(673,plain,
% 1.51/1.21 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(W))) | (~c1_1(W))) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))),
% 1.51/1.21 inference(quant_intro,[status(thm)],[672])).
% 1.51/1.21 tff(674,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(V))) | (~c0_1(W))) | (~c1_1(W))) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause200')).
% 1.51/1.21 tff(675,plain,
% 1.51/1.21 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))),
% 1.51/1.21 inference(modus_ponens,[status(thm)],[674, 673])).
% 1.51/1.21 tff(676,plain,
% 1.51/1.21 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))),
% 1.51/1.21 inference(modus_ponens,[status(thm)],[675, 671])).
% 1.51/1.21 tff(677,plain,(
% 1.51/1.21 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))),
% 1.51/1.21 inference(skolemize,[status(sab)],[676])).
% 1.51/1.21 tff(678,plain,
% 1.51/1.21 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))),
% 1.51/1.21 inference(modus_ponens,[status(thm)],[677, 670])).
% 1.51/1.21 tff(679,plain,
% 1.51/1.21 (c3_1(a1756)),
% 1.51/1.21 inference(unit_resolution,[status(thm)],[372, 665])).
% 1.51/1.21 tff(680,plain,
% 1.51/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c3_1(a1758) | (~ndr1_0) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c2_1(a1756)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a1758) | (~ndr1_0) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c2_1(a1756)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))),
% 1.51/1.21 inference(rewrite,[status(thm)],[])).
% 1.51/1.21 tff(681,plain,
% 1.51/1.21 (((~ndr1_0) | (~c2_1(a1756)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c2_1(a1756)) | (~c1_1(a1756)) | (~c0_1(a1756)) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758))) <=> (c3_1(a1758) | (~ndr1_0) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c2_1(a1756)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))),
% 1.51/1.21 inference(rewrite,[status(thm)],[])).
% 1.51/1.21 tff(682,plain,
% 1.51/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1756)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c2_1(a1756)) | (~c1_1(a1756)) | (~c0_1(a1756)) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c3_1(a1758) | (~ndr1_0) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c2_1(a1756)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756))))),
% 1.51/1.21 inference(monotonicity,[status(thm)],[681])).
% 1.51/1.21 tff(683,plain,
% 1.51/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1756)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c2_1(a1756)) | (~c1_1(a1756)) | (~c0_1(a1756)) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a1758) | (~ndr1_0) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c2_1(a1756)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))),
% 1.51/1.21 inference(transitivity,[status(thm)],[682, 680])).
% 1.51/1.21 tff(684,plain,
% 1.51/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1756)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c2_1(a1756)) | (~c1_1(a1756)) | (~c0_1(a1756)) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)))),
% 1.51/1.21 inference(quant_inst,[status(thm)],[])).
% 1.51/1.21 tff(685,plain,
% 1.51/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a1758) | (~ndr1_0) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c2_1(a1756)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756))),
% 1.51/1.21 inference(modus_ponens,[status(thm)],[684, 683])).
% 1.51/1.21 tff(686,plain,
% 1.51/1.21 ($false),
% 1.51/1.21 inference(unit_resolution,[status(thm)],[685, 111, 667, 666, 679, 625, 639, 678, 633, 668])).
% 1.51/1.21 tff(687,plain,(hskp13 | hskp19 | c1_1(a1759) | c3_1(a1759)), inference(lemma,lemma(discharge,[]))).
% 1.51/1.21 tff(688,plain,
% 1.51/1.21 (hskp13),
% 1.51/1.21 inference(unit_resolution,[status(thm)],[687, 47, 12, 34])).
% 1.51/1.21 tff(689,plain,
% 1.51/1.21 (~c0_1(a1771)),
% 1.51/1.21 inference(unit_resolution,[status(thm)],[238, 688])).
% 1.51/1.21 tff(690,plain,
% 1.51/1.21 (c2_1(a1771)),
% 1.51/1.21 inference(unit_resolution,[status(thm)],[263, 688])).
% 1.51/1.21 tff(691,plain,
% 1.51/1.21 (c1_1(a1771)),
% 1.51/1.21 inference(unit_resolution,[status(thm)],[252, 688])).
% 1.51/1.21 tff(692,plain,
% 1.51/1.21 (^[U: $i] : refl((hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) <=> (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))))),
% 1.51/1.21 inference(bind,[status(th)],[])).
% 1.51/1.21 tff(693,plain,
% 1.51/1.21 (![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.51/1.21 inference(quant_intro,[status(thm)],[692])).
% 1.51/1.21 tff(694,plain,
% 1.51/1.21 (![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.51/1.21 inference(rewrite,[status(thm)],[])).
% 1.51/1.21 tff(695,plain,
% 1.51/1.21 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp19) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | hskp19))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | hskp19) <=> (hskp19 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp19) <=> (hskp19 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp19) | hskp6) <=> ((hskp19 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | hskp6))), rewrite(((hskp19 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | hskp6) <=> (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp19) | hskp6) <=> (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))))),
% 1.51/1.21 inference(bind,[status(th)],[])).
% 1.51/1.21 tff(696,plain,
% 1.51/1.21 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp19) | hskp6) <=> ![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.51/1.21 inference(quant_intro,[status(thm)],[695])).
% 1.51/1.21 tff(697,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp19) | hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause138')).
% 1.51/1.21 tff(698,plain,
% 1.51/1.21 (![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.51/1.21 inference(modus_ponens,[status(thm)],[697, 696])).
% 1.51/1.21 tff(699,plain,
% 1.51/1.21 (![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.51/1.21 inference(modus_ponens,[status(thm)],[698, 694])).
% 1.51/1.21 tff(700,plain,(
% 1.51/1.21 ![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.51/1.21 inference(skolemize,[status(sab)],[699])).
% 1.51/1.21 tff(701,plain,
% 1.51/1.21 (![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.51/1.21 inference(modus_ponens,[status(thm)],[700, 693])).
% 1.51/1.21 tff(702,assumption,(~c3_1(a1758)), introduced(assumption)).
% 1.51/1.21 tff(703,assumption,(c1_1(a1758)), introduced(assumption)).
% 1.51/1.21 tff(704,plain,
% 1.51/1.21 (((~![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp19 | hskp6 | c3_1(a1758) | (~ndr1_0) | c0_1(a1758) | (~c1_1(a1758)))) <=> ((~![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | hskp19 | hskp6 | c3_1(a1758) | (~ndr1_0) | c0_1(a1758) | (~c1_1(a1758)))),
% 1.51/1.21 inference(rewrite,[status(thm)],[])).
% 1.51/1.21 tff(705,plain,
% 1.51/1.21 ((hskp19 | hskp6 | (~ndr1_0) | c3_1(a1758) | c0_1(a1758) | (~c1_1(a1758))) <=> (hskp19 | hskp6 | c3_1(a1758) | (~ndr1_0) | c0_1(a1758) | (~c1_1(a1758)))),
% 1.51/1.21 inference(rewrite,[status(thm)],[])).
% 1.51/1.21 tff(706,plain,
% 1.51/1.21 (((~![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp19 | hskp6 | (~ndr1_0) | c3_1(a1758) | c0_1(a1758) | (~c1_1(a1758)))) <=> ((~![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp19 | hskp6 | c3_1(a1758) | (~ndr1_0) | c0_1(a1758) | (~c1_1(a1758))))),
% 1.51/1.21 inference(monotonicity,[status(thm)],[705])).
% 1.51/1.21 tff(707,plain,
% 1.51/1.21 (((~![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp19 | hskp6 | (~ndr1_0) | c3_1(a1758) | c0_1(a1758) | (~c1_1(a1758)))) <=> ((~![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | hskp19 | hskp6 | c3_1(a1758) | (~ndr1_0) | c0_1(a1758) | (~c1_1(a1758)))),
% 1.51/1.21 inference(transitivity,[status(thm)],[706, 704])).
% 1.51/1.21 tff(708,plain,
% 1.51/1.21 ((~![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp19 | hskp6 | (~ndr1_0) | c3_1(a1758) | c0_1(a1758) | (~c1_1(a1758)))),
% 1.51/1.21 inference(quant_inst,[status(thm)],[])).
% 1.51/1.21 tff(709,plain,
% 1.51/1.21 ((~![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | hskp19 | hskp6 | c3_1(a1758) | (~ndr1_0) | c0_1(a1758) | (~c1_1(a1758))),
% 1.51/1.21 inference(modus_ponens,[status(thm)],[708, 707])).
% 1.51/1.21 tff(710,plain,
% 1.51/1.21 (hskp6 | c0_1(a1758)),
% 1.51/1.21 inference(unit_resolution,[status(thm)],[709, 111, 12, 703, 702, 701])).
% 1.51/1.21 tff(711,plain,
% 1.51/1.21 (c0_1(a1758)),
% 1.51/1.21 inference(unit_resolution,[status(thm)],[710, 240])).
% 1.51/1.21 tff(712,assumption,(c1_1(a1771)), introduced(assumption)).
% 1.51/1.21 tff(713,plain,
% 1.51/1.21 (((~![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp19 | hskp6 | c0_1(a1771) | (~ndr1_0) | c3_1(a1771) | (~c1_1(a1771)))) <=> ((~![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | hskp19 | hskp6 | c0_1(a1771) | (~ndr1_0) | c3_1(a1771) | (~c1_1(a1771)))),
% 1.51/1.21 inference(rewrite,[status(thm)],[])).
% 1.51/1.21 tff(714,plain,
% 1.51/1.21 ((hskp19 | hskp6 | (~ndr1_0) | c3_1(a1771) | c0_1(a1771) | (~c1_1(a1771))) <=> (hskp19 | hskp6 | c0_1(a1771) | (~ndr1_0) | c3_1(a1771) | (~c1_1(a1771)))),
% 1.51/1.21 inference(rewrite,[status(thm)],[])).
% 1.51/1.21 tff(715,plain,
% 1.51/1.21 (((~![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp19 | hskp6 | (~ndr1_0) | c3_1(a1771) | c0_1(a1771) | (~c1_1(a1771)))) <=> ((~![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp19 | hskp6 | c0_1(a1771) | (~ndr1_0) | c3_1(a1771) | (~c1_1(a1771))))),
% 1.51/1.21 inference(monotonicity,[status(thm)],[714])).
% 1.51/1.21 tff(716,plain,
% 1.51/1.21 (((~![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp19 | hskp6 | (~ndr1_0) | c3_1(a1771) | c0_1(a1771) | (~c1_1(a1771)))) <=> ((~![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | hskp19 | hskp6 | c0_1(a1771) | (~ndr1_0) | c3_1(a1771) | (~c1_1(a1771)))),
% 1.51/1.21 inference(transitivity,[status(thm)],[715, 713])).
% 1.51/1.21 tff(717,plain,
% 1.51/1.21 ((~![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp19 | hskp6 | (~ndr1_0) | c3_1(a1771) | c0_1(a1771) | (~c1_1(a1771)))),
% 1.51/1.21 inference(quant_inst,[status(thm)],[])).
% 1.51/1.21 tff(718,plain,
% 1.51/1.21 ((~![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | hskp19 | hskp6 | c0_1(a1771) | (~ndr1_0) | c3_1(a1771) | (~c1_1(a1771))),
% 1.51/1.21 inference(modus_ponens,[status(thm)],[717, 716])).
% 1.51/1.21 tff(719,plain,
% 1.51/1.21 (hskp6 | c3_1(a1771)),
% 1.51/1.21 inference(unit_resolution,[status(thm)],[718, 111, 12, 712, 275, 701])).
% 1.51/1.21 tff(720,plain,
% 1.51/1.21 (c3_1(a1771)),
% 1.51/1.21 inference(unit_resolution,[status(thm)],[719, 240])).
% 1.51/1.21 tff(721,assumption,(c2_1(a1758)), introduced(assumption)).
% 1.51/1.21 tff(722,assumption,(c2_1(a1771)), introduced(assumption)).
% 1.51/1.21 tff(723,plain,
% 1.51/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c2_1(a1771)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 1.51/1.21 inference(rewrite,[status(thm)],[])).
% 1.51/1.21 tff(724,plain,
% 1.51/1.21 (((~ndr1_0) | (~c2_1(a1771)) | (~c1_1(a1771)) | (~c3_1(a1771)) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758))) <=> (c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 1.51/1.21 inference(rewrite,[status(thm)],[])).
% 1.51/1.21 tff(725,plain,
% 1.51/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1771)) | (~c1_1(a1771)) | (~c3_1(a1771)) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c2_1(a1771))))),
% 1.51/1.21 inference(monotonicity,[status(thm)],[724])).
% 1.51/1.21 tff(726,plain,
% 1.51/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1771)) | (~c1_1(a1771)) | (~c3_1(a1771)) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 1.51/1.21 inference(transitivity,[status(thm)],[725, 723])).
% 1.51/1.21 tff(727,plain,
% 1.51/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1771)) | (~c1_1(a1771)) | (~c3_1(a1771)) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)))),
% 1.51/1.21 inference(quant_inst,[status(thm)],[])).
% 1.51/1.21 tff(728,plain,
% 1.51/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c2_1(a1771))),
% 1.51/1.21 inference(modus_ponens,[status(thm)],[727, 726])).
% 1.51/1.21 tff(729,plain,
% 1.51/1.21 ((~c0_1(a1758)) | (~c3_1(a1771))),
% 1.51/1.21 inference(unit_resolution,[status(thm)],[728, 111, 712, 722, 703, 721, 702, 678])).
% 1.51/1.21 tff(730,plain,
% 1.51/1.21 ($false),
% 1.51/1.21 inference(unit_resolution,[status(thm)],[729, 720, 711])).
% 1.51/1.21 tff(731,plain,(hskp6 | (~c1_1(a1771)) | (~c2_1(a1771)) | (~c1_1(a1758)) | (~c2_1(a1758)) | c3_1(a1758) | hskp19 | c0_1(a1771)), inference(lemma,lemma(discharge,[]))).
% 1.51/1.21 tff(732,plain,
% 1.51/1.21 (hskp6),
% 1.51/1.21 inference(unit_resolution,[status(thm)],[731, 691, 690, 625, 614, 639, 12, 689])).
% 1.51/1.21 tff(733,plain,
% 1.51/1.21 (~c0_1(a1762)),
% 1.51/1.21 inference(unit_resolution,[status(thm)],[291, 732])).
% 1.51/1.21 tff(734,plain,
% 1.51/1.21 (c3_1(a1762)),
% 1.51/1.21 inference(unit_resolution,[status(thm)],[302, 732])).
% 1.51/1.21 tff(735,plain,
% 1.51/1.21 (c2_1(a1762)),
% 1.51/1.21 inference(unit_resolution,[status(thm)],[313, 732])).
% 1.51/1.21 tff(736,plain,
% 1.51/1.21 (hskp8),
% 1.51/1.21 inference(unit_resolution,[status(thm)],[320, 111, 151, 735, 734, 733, 130])).
% 1.51/1.21 tff(737,plain,
% 1.51/1.21 (~c1_1(a1765)),
% 1.51/1.21 inference(unit_resolution,[status(thm)],[326, 736])).
% 1.51/1.21 tff(738,plain,
% 1.51/1.21 (c2_1(a1765)),
% 1.51/1.21 inference(unit_resolution,[status(thm)],[444, 736])).
% 1.51/1.21 tff(739,plain,
% 1.51/1.21 (c0_1(a1765)),
% 1.51/1.21 inference(unit_resolution,[status(thm)],[455, 736])).
% 1.51/1.21 tff(740,plain,
% 1.51/1.21 (c1_1(a1762)),
% 1.51/1.21 inference(unit_resolution,[status(thm)],[464, 111, 691, 690, 739, 738, 734, 689, 737, 733, 46])).
% 1.51/1.21 tff(741,plain,
% 1.51/1.21 (^[V: $i, U: $i] : refl((hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))),
% 1.51/1.21 inference(bind,[status(th)],[])).
% 1.51/1.21 tff(742,plain,
% 1.51/1.21 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.51/1.21 inference(quant_intro,[status(thm)],[741])).
% 1.51/1.21 tff(743,plain,
% 1.51/1.21 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.51/1.21 inference(rewrite,[status(thm)],[])).
% 1.51/1.21 tff(744,plain,
% 1.51/1.21 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | hskp21) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp21))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp21) <=> (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | hskp21) <=> (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))))),
% 1.51/1.21 inference(bind,[status(th)],[])).
% 1.51/1.21 tff(745,plain,
% 1.51/1.21 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | hskp21) <=> ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.51/1.21 inference(quant_intro,[status(thm)],[744])).
% 1.51/1.21 tff(746,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c1_1(U)) | c0_1(V)) | hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause179')).
% 1.51/1.21 tff(747,plain,
% 1.51/1.21 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.51/1.21 inference(modus_ponens,[status(thm)],[746, 745])).
% 1.51/1.21 tff(748,plain,
% 1.51/1.21 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.51/1.21 inference(modus_ponens,[status(thm)],[747, 743])).
% 1.51/1.21 tff(749,plain,(
% 1.51/1.21 ![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.51/1.21 inference(skolemize,[status(sab)],[748])).
% 1.51/1.21 tff(750,plain,
% 1.51/1.21 (![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 1.51/1.21 inference(modus_ponens,[status(thm)],[749, 742])).
% 1.51/1.21 tff(751,plain,
% 1.51/1.21 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp21 | c0_1(a1771) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c1_1(a1771)) | (~c2_1(a1771)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp21 | c0_1(a1771) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 1.51/1.21 inference(rewrite,[status(thm)],[])).
% 1.51/1.21 tff(752,plain,
% 1.51/1.21 ((hskp21 | (~ndr1_0) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771))) <=> (hskp21 | c0_1(a1771) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 1.51/1.21 inference(rewrite,[status(thm)],[])).
% 1.51/1.21 tff(753,plain,
% 1.51/1.21 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp21 | (~ndr1_0) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp21 | c0_1(a1771) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c1_1(a1771)) | (~c2_1(a1771))))),
% 1.51/1.21 inference(monotonicity,[status(thm)],[752])).
% 1.51/1.21 tff(754,plain,
% 1.51/1.21 (((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp21 | (~ndr1_0) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)))) <=> ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp21 | c0_1(a1771) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 1.51/1.21 inference(transitivity,[status(thm)],[753, 751])).
% 1.51/1.21 tff(755,plain,
% 1.51/1.21 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp21 | (~ndr1_0) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)))),
% 1.51/1.21 inference(quant_inst,[status(thm)],[])).
% 1.51/1.21 tff(756,plain,
% 1.51/1.21 ((~![V: $i, U: $i] : (hskp21 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp21 | c0_1(a1771) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c1_1(a1771)) | (~c2_1(a1771))),
% 1.51/1.21 inference(modus_ponens,[status(thm)],[755, 754])).
% 1.51/1.21 tff(757,plain,
% 1.51/1.21 (hskp21),
% 1.51/1.21 inference(unit_resolution,[status(thm)],[756, 111, 691, 690, 739, 738, 689, 737, 750])).
% 1.51/1.21 tff(758,plain,
% 1.51/1.21 (((~hskp21) | (~c3_1(a1788))) <=> ((~hskp21) | (~c3_1(a1788)))),
% 1.51/1.21 inference(rewrite,[status(thm)],[])).
% 1.51/1.21 tff(759,plain,
% 1.51/1.21 (((~c3_1(a1788)) | (~hskp21)) <=> ((~hskp21) | (~c3_1(a1788)))),
% 1.51/1.21 inference(rewrite,[status(thm)],[])).
% 1.51/1.21 tff(760,axiom,((~c3_1(a1788)) | (~hskp21)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause97')).
% 1.51/1.21 tff(761,plain,
% 1.51/1.21 ((~hskp21) | (~c3_1(a1788))),
% 1.51/1.21 inference(modus_ponens,[status(thm)],[760, 759])).
% 1.51/1.21 tff(762,plain,
% 1.51/1.21 ((~hskp21) | (~c3_1(a1788))),
% 1.51/1.21 inference(modus_ponens,[status(thm)],[761, 758])).
% 1.51/1.21 tff(763,plain,
% 1.51/1.21 (~c3_1(a1788)),
% 1.51/1.21 inference(unit_resolution,[status(thm)],[762, 757])).
% 1.51/1.21 tff(764,plain,
% 1.51/1.21 (((~hskp21) | c2_1(a1788)) <=> ((~hskp21) | c2_1(a1788))),
% 1.51/1.21 inference(rewrite,[status(thm)],[])).
% 1.51/1.21 tff(765,axiom,((~hskp21) | c2_1(a1788)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause54')).
% 1.51/1.21 tff(766,plain,
% 1.51/1.21 ((~hskp21) | c2_1(a1788)),
% 1.51/1.21 inference(modus_ponens,[status(thm)],[765, 764])).
% 1.51/1.21 tff(767,plain,
% 1.51/1.21 ((~hskp21) | c2_1(a1788)),
% 1.51/1.21 inference(modus_ponens,[status(thm)],[766, 764])).
% 1.51/1.21 tff(768,plain,
% 1.51/1.21 ((~hskp21) | c2_1(a1788)),
% 1.51/1.21 inference(modus_ponens,[status(thm)],[767, 764])).
% 1.51/1.21 tff(769,plain,
% 1.51/1.21 ((~hskp21) | c2_1(a1788)),
% 1.51/1.21 inference(modus_ponens,[status(thm)],[768, 764])).
% 1.51/1.21 tff(770,plain,
% 1.51/1.21 ((~hskp21) | c2_1(a1788)),
% 1.51/1.21 inference(modus_ponens,[status(thm)],[769, 764])).
% 1.51/1.21 tff(771,plain,
% 1.51/1.21 ((~hskp21) | c2_1(a1788)),
% 1.51/1.21 inference(modus_ponens,[status(thm)],[770, 764])).
% 1.51/1.21 tff(772,plain,
% 1.51/1.21 ((~hskp21) | c2_1(a1788)),
% 1.51/1.21 inference(modus_ponens,[status(thm)],[771, 764])).
% 1.51/1.21 tff(773,plain,
% 1.51/1.21 ((~hskp21) | c2_1(a1788)),
% 1.51/1.21 inference(modus_ponens,[status(thm)],[772, 764])).
% 1.51/1.21 tff(774,plain,
% 1.51/1.21 (c2_1(a1788)),
% 1.51/1.21 inference(unit_resolution,[status(thm)],[773, 757])).
% 1.51/1.21 tff(775,plain,
% 1.51/1.21 (((~hskp21) | c0_1(a1788)) <=> ((~hskp21) | c0_1(a1788))),
% 1.51/1.21 inference(rewrite,[status(thm)],[])).
% 1.51/1.21 tff(776,axiom,((~hskp21) | c0_1(a1788)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause53')).
% 1.51/1.21 tff(777,plain,
% 1.51/1.21 ((~hskp21) | c0_1(a1788)),
% 1.51/1.21 inference(modus_ponens,[status(thm)],[776, 775])).
% 1.51/1.21 tff(778,plain,
% 1.51/1.21 ((~hskp21) | c0_1(a1788)),
% 1.51/1.21 inference(modus_ponens,[status(thm)],[777, 775])).
% 1.51/1.21 tff(779,plain,
% 1.51/1.21 ((~hskp21) | c0_1(a1788)),
% 1.51/1.21 inference(modus_ponens,[status(thm)],[778, 775])).
% 1.51/1.21 tff(780,plain,
% 1.51/1.21 ((~hskp21) | c0_1(a1788)),
% 1.51/1.21 inference(modus_ponens,[status(thm)],[779, 775])).
% 1.51/1.21 tff(781,plain,
% 1.51/1.21 ((~hskp21) | c0_1(a1788)),
% 1.51/1.21 inference(modus_ponens,[status(thm)],[780, 775])).
% 1.51/1.21 tff(782,plain,
% 1.51/1.21 ((~hskp21) | c0_1(a1788)),
% 1.51/1.21 inference(modus_ponens,[status(thm)],[781, 775])).
% 1.51/1.21 tff(783,plain,
% 1.51/1.21 ((~hskp21) | c0_1(a1788)),
% 1.51/1.21 inference(modus_ponens,[status(thm)],[782, 775])).
% 1.51/1.21 tff(784,plain,
% 1.51/1.21 ((~hskp21) | c0_1(a1788)),
% 1.51/1.21 inference(modus_ponens,[status(thm)],[783, 775])).
% 1.51/1.21 tff(785,plain,
% 1.51/1.21 (c0_1(a1788)),
% 1.51/1.21 inference(unit_resolution,[status(thm)],[784, 757])).
% 1.51/1.21 tff(786,plain,
% 1.51/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c3_1(a1788) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c2_1(a1788)) | (~c1_1(a1788)) | (~c0_1(a1788)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a1788) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c2_1(a1788)) | (~c1_1(a1788)) | (~c0_1(a1788)))),
% 1.51/1.21 inference(rewrite,[status(thm)],[])).
% 1.51/1.21 tff(787,plain,
% 1.51/1.21 (((~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1762)) | (~c2_1(a1788)) | (~c1_1(a1788)) | (~c0_1(a1788)) | c3_1(a1788) | (~c1_1(a1788)) | (~c0_1(a1788))) <=> (c3_1(a1788) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c2_1(a1788)) | (~c1_1(a1788)) | (~c0_1(a1788)))),
% 1.51/1.21 inference(rewrite,[status(thm)],[])).
% 1.51/1.21 tff(788,plain,
% 1.51/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1762)) | (~c2_1(a1788)) | (~c1_1(a1788)) | (~c0_1(a1788)) | c3_1(a1788) | (~c1_1(a1788)) | (~c0_1(a1788)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c3_1(a1788) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c2_1(a1788)) | (~c1_1(a1788)) | (~c0_1(a1788))))),
% 1.54/1.21 inference(monotonicity,[status(thm)],[787])).
% 1.54/1.21 tff(789,plain,
% 1.54/1.21 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1762)) | (~c2_1(a1788)) | (~c1_1(a1788)) | (~c0_1(a1788)) | c3_1(a1788) | (~c1_1(a1788)) | (~c0_1(a1788)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a1788) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c2_1(a1788)) | (~c1_1(a1788)) | (~c0_1(a1788)))),
% 1.54/1.21 inference(transitivity,[status(thm)],[788, 786])).
% 1.54/1.21 tff(790,plain,
% 1.54/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1762)) | (~c2_1(a1788)) | (~c1_1(a1788)) | (~c0_1(a1788)) | c3_1(a1788) | (~c1_1(a1788)) | (~c0_1(a1788)))),
% 1.54/1.21 inference(quant_inst,[status(thm)],[])).
% 1.54/1.21 tff(791,plain,
% 1.54/1.21 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a1788) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c2_1(a1788)) | (~c1_1(a1788)) | (~c0_1(a1788))),
% 1.54/1.21 inference(modus_ponens,[status(thm)],[790, 789])).
% 1.54/1.21 tff(792,plain,
% 1.54/1.21 (~c1_1(a1788)),
% 1.54/1.21 inference(unit_resolution,[status(thm)],[791, 111, 785, 774, 735, 734, 763, 678, 740])).
% 1.54/1.21 tff(793,plain,
% 1.54/1.21 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W))))),
% 1.54/1.21 inference(bind,[status(th)],[])).
% 1.54/1.21 tff(794,plain,
% 1.54/1.21 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))),
% 1.54/1.21 inference(quant_intro,[status(thm)],[793])).
% 1.54/1.21 tff(795,plain,
% 1.54/1.21 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))),
% 1.54/1.21 inference(rewrite,[status(thm)],[])).
% 1.54/1.21 tff(796,plain,
% 1.54/1.21 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c0_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c3_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W)) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c3_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))))),
% 1.54/1.22 inference(bind,[status(th)],[])).
% 1.54/1.22 tff(797,plain,
% 1.54/1.22 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c3_1(V)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))),
% 1.54/1.22 inference(quant_intro,[status(thm)],[796])).
% 1.54/1.22 tff(798,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c0_1(W))) | (~c2_1(W))) | c3_1(V)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause199')).
% 1.54/1.22 tff(799,plain,
% 1.54/1.22 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))),
% 1.54/1.22 inference(modus_ponens,[status(thm)],[798, 797])).
% 1.54/1.22 tff(800,plain,
% 1.54/1.22 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))),
% 1.54/1.22 inference(modus_ponens,[status(thm)],[799, 795])).
% 1.54/1.22 tff(801,plain,(
% 1.54/1.22 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))),
% 1.54/1.22 inference(skolemize,[status(sab)],[800])).
% 1.54/1.22 tff(802,plain,
% 1.54/1.22 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))),
% 1.54/1.22 inference(modus_ponens,[status(thm)],[801, 794])).
% 1.54/1.22 tff(803,plain,
% 1.54/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c1_1(a1765) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c2_1(a1765)) | (~c0_1(a1765)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c1_1(a1765) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c2_1(a1765)) | (~c0_1(a1765)))),
% 1.54/1.22 inference(rewrite,[status(thm)],[])).
% 1.54/1.22 tff(804,plain,
% 1.54/1.22 (((~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765))) <=> (c1_1(a1765) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c2_1(a1765)) | (~c0_1(a1765)))),
% 1.54/1.22 inference(rewrite,[status(thm)],[])).
% 1.54/1.22 tff(805,plain,
% 1.54/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c1_1(a1765) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c2_1(a1765)) | (~c0_1(a1765))))),
% 1.54/1.22 inference(monotonicity,[status(thm)],[804])).
% 1.54/1.22 tff(806,plain,
% 1.54/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c1_1(a1765) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c2_1(a1765)) | (~c0_1(a1765)))),
% 1.54/1.22 inference(transitivity,[status(thm)],[805, 803])).
% 1.54/1.22 tff(807,plain,
% 1.54/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)))),
% 1.54/1.22 inference(quant_inst,[status(thm)],[])).
% 1.54/1.22 tff(808,plain,
% 1.54/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c1_1(a1765) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c2_1(a1765)) | (~c0_1(a1765))),
% 1.54/1.22 inference(modus_ponens,[status(thm)],[807, 806])).
% 1.54/1.22 tff(809,plain,
% 1.54/1.22 (~c0_1(a1758)),
% 1.54/1.22 inference(unit_resolution,[status(thm)],[808, 111, 739, 738, 625, 614, 737, 639, 802])).
% 1.54/1.22 tff(810,plain,
% 1.54/1.22 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))))),
% 1.54/1.22 inference(bind,[status(th)],[])).
% 1.54/1.22 tff(811,plain,
% 1.54/1.22 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.54/1.22 inference(quant_intro,[status(thm)],[810])).
% 1.54/1.22 tff(812,plain,
% 1.54/1.22 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.54/1.22 inference(rewrite,[status(thm)],[])).
% 1.54/1.22 tff(813,plain,
% 1.54/1.22 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W)))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | (~c2_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))))),
% 1.54/1.22 inference(bind,[status(th)],[])).
% 1.54/1.22 tff(814,plain,
% 1.54/1.22 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.54/1.22 inference(quant_intro,[status(thm)],[813])).
% 1.54/1.22 tff(815,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c2_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause193')).
% 1.54/1.22 tff(816,plain,
% 1.54/1.22 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.54/1.22 inference(modus_ponens,[status(thm)],[815, 814])).
% 1.54/1.22 tff(817,plain,
% 1.54/1.22 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.54/1.22 inference(modus_ponens,[status(thm)],[816, 812])).
% 1.54/1.22 tff(818,plain,(
% 1.54/1.22 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.54/1.22 inference(skolemize,[status(sab)],[817])).
% 1.54/1.22 tff(819,plain,
% 1.54/1.22 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))),
% 1.54/1.22 inference(modus_ponens,[status(thm)],[818, 811])).
% 1.54/1.22 tff(820,plain,
% 1.54/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1765) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c3_1(a1765)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1765) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c3_1(a1765)))),
% 1.54/1.22 inference(rewrite,[status(thm)],[])).
% 1.54/1.22 tff(821,plain,
% 1.54/1.22 (((~ndr1_0) | c1_1(a1765) | (~c2_1(a1765)) | (~c3_1(a1765)) | c1_1(a1765) | (~c3_1(a1765)) | (~c0_1(a1765)) | c3_1(a1758) | c0_1(a1758) | (~c2_1(a1758))) <=> (c1_1(a1765) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c3_1(a1765)))),
% 1.54/1.22 inference(rewrite,[status(thm)],[])).
% 1.54/1.22 tff(822,plain,
% 1.54/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1765) | (~c2_1(a1765)) | (~c3_1(a1765)) | c1_1(a1765) | (~c3_1(a1765)) | (~c0_1(a1765)) | c3_1(a1758) | c0_1(a1758) | (~c2_1(a1758)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1765) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c3_1(a1765))))),
% 1.54/1.22 inference(monotonicity,[status(thm)],[821])).
% 1.54/1.22 tff(823,plain,
% 1.54/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1765) | (~c2_1(a1765)) | (~c3_1(a1765)) | c1_1(a1765) | (~c3_1(a1765)) | (~c0_1(a1765)) | c3_1(a1758) | c0_1(a1758) | (~c2_1(a1758)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1765) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c3_1(a1765)))),
% 1.54/1.22 inference(transitivity,[status(thm)],[822, 820])).
% 1.54/1.22 tff(824,plain,
% 1.54/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1765) | (~c2_1(a1765)) | (~c3_1(a1765)) | c1_1(a1765) | (~c3_1(a1765)) | (~c0_1(a1765)) | c3_1(a1758) | c0_1(a1758) | (~c2_1(a1758)))),
% 1.54/1.22 inference(quant_inst,[status(thm)],[])).
% 1.54/1.22 tff(825,plain,
% 1.54/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1765) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c3_1(a1765))),
% 1.54/1.22 inference(modus_ponens,[status(thm)],[824, 823])).
% 1.54/1.22 tff(826,plain,
% 1.54/1.22 (~c3_1(a1765)),
% 1.54/1.22 inference(unit_resolution,[status(thm)],[825, 111, 739, 738, 614, 737, 639, 819, 809])).
% 1.54/1.22 tff(827,plain,
% 1.54/1.22 (^[V: $i, U: $i] : refl((hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))))),
% 1.54/1.22 inference(bind,[status(th)],[])).
% 1.54/1.22 tff(828,plain,
% 1.54/1.22 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.54/1.22 inference(quant_intro,[status(thm)],[827])).
% 1.54/1.22 tff(829,plain,
% 1.54/1.22 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.54/1.22 inference(rewrite,[status(thm)],[])).
% 1.54/1.22 tff(830,plain,
% 1.54/1.22 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp22) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) | hskp22))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) | hskp22) <=> (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp22) <=> (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))))),
% 1.54/1.22 inference(bind,[status(th)],[])).
% 1.54/1.22 tff(831,plain,
% 1.54/1.22 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp22) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.54/1.22 inference(quant_intro,[status(thm)],[830])).
% 1.54/1.22 tff(832,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp22)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause175')).
% 1.54/1.22 tff(833,plain,
% 1.54/1.22 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.54/1.22 inference(modus_ponens,[status(thm)],[832, 831])).
% 1.54/1.22 tff(834,plain,
% 1.54/1.22 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.54/1.22 inference(modus_ponens,[status(thm)],[833, 829])).
% 1.54/1.22 tff(835,plain,(
% 1.54/1.22 ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.54/1.22 inference(skolemize,[status(sab)],[834])).
% 1.54/1.22 tff(836,plain,
% 1.54/1.22 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.54/1.22 inference(modus_ponens,[status(thm)],[835, 828])).
% 1.54/1.22 tff(837,plain,
% 1.54/1.22 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp22 | c1_1(a1765) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c2_1(a1765)) | c3_1(a1765))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp22 | c1_1(a1765) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c2_1(a1765)) | c3_1(a1765))),
% 1.54/1.22 inference(rewrite,[status(thm)],[])).
% 1.54/1.22 tff(838,plain,
% 1.54/1.22 ((hskp22 | (~ndr1_0) | c3_1(a1758) | (~c2_1(a1758)) | (~c1_1(a1758)) | c1_1(a1765) | c3_1(a1765) | (~c2_1(a1765))) <=> (hskp22 | c1_1(a1765) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c2_1(a1765)) | c3_1(a1765))),
% 1.54/1.22 inference(rewrite,[status(thm)],[])).
% 1.54/1.22 tff(839,plain,
% 1.54/1.22 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a1758) | (~c2_1(a1758)) | (~c1_1(a1758)) | c1_1(a1765) | c3_1(a1765) | (~c2_1(a1765)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp22 | c1_1(a1765) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c2_1(a1765)) | c3_1(a1765)))),
% 1.54/1.22 inference(monotonicity,[status(thm)],[838])).
% 1.54/1.22 tff(840,plain,
% 1.54/1.22 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a1758) | (~c2_1(a1758)) | (~c1_1(a1758)) | c1_1(a1765) | c3_1(a1765) | (~c2_1(a1765)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp22 | c1_1(a1765) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c2_1(a1765)) | c3_1(a1765))),
% 1.54/1.22 inference(transitivity,[status(thm)],[839, 837])).
% 1.54/1.22 tff(841,plain,
% 1.54/1.22 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a1758) | (~c2_1(a1758)) | (~c1_1(a1758)) | c1_1(a1765) | c3_1(a1765) | (~c2_1(a1765)))),
% 1.54/1.22 inference(quant_inst,[status(thm)],[])).
% 1.54/1.22 tff(842,plain,
% 1.54/1.22 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp22 | c1_1(a1765) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c2_1(a1765)) | c3_1(a1765)),
% 1.54/1.22 inference(modus_ponens,[status(thm)],[841, 840])).
% 1.54/1.22 tff(843,plain,
% 1.54/1.22 (hskp22),
% 1.54/1.22 inference(unit_resolution,[status(thm)],[842, 111, 738, 625, 614, 737, 639, 836, 826])).
% 1.54/1.22 tff(844,plain,
% 1.54/1.22 (~c0_1(a1799)),
% 1.54/1.22 inference(unit_resolution,[status(thm)],[548, 843])).
% 1.54/1.22 tff(845,plain,
% 1.54/1.22 (c3_1(a1799)),
% 1.54/1.22 inference(unit_resolution,[status(thm)],[559, 843])).
% 1.54/1.22 tff(846,plain,
% 1.54/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c0_1(a1799) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c1_1(a1758)) | (~c2_1(a1765)) | (~c0_1(a1765)) | c1_1(a1799) | (~c3_1(a1799)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1799) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c1_1(a1758)) | (~c2_1(a1765)) | (~c0_1(a1765)) | c1_1(a1799) | (~c3_1(a1799)))),
% 1.54/1.22 inference(rewrite,[status(thm)],[])).
% 1.54/1.22 tff(847,plain,
% 1.54/1.22 (((~ndr1_0) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1758) | (~c2_1(a1758)) | (~c1_1(a1758)) | c0_1(a1799) | c1_1(a1799) | (~c3_1(a1799))) <=> (c0_1(a1799) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c1_1(a1758)) | (~c2_1(a1765)) | (~c0_1(a1765)) | c1_1(a1799) | (~c3_1(a1799)))),
% 1.54/1.22 inference(rewrite,[status(thm)],[])).
% 1.54/1.22 tff(848,plain,
% 1.54/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1758) | (~c2_1(a1758)) | (~c1_1(a1758)) | c0_1(a1799) | c1_1(a1799) | (~c3_1(a1799)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c0_1(a1799) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c1_1(a1758)) | (~c2_1(a1765)) | (~c0_1(a1765)) | c1_1(a1799) | (~c3_1(a1799))))),
% 1.54/1.22 inference(monotonicity,[status(thm)],[847])).
% 1.54/1.22 tff(849,plain,
% 1.54/1.22 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1758) | (~c2_1(a1758)) | (~c1_1(a1758)) | c0_1(a1799) | c1_1(a1799) | (~c3_1(a1799)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1799) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c1_1(a1758)) | (~c2_1(a1765)) | (~c0_1(a1765)) | c1_1(a1799) | (~c3_1(a1799)))),
% 1.54/1.22 inference(transitivity,[status(thm)],[848, 846])).
% 1.54/1.22 tff(850,plain,
% 1.54/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1758) | (~c2_1(a1758)) | (~c1_1(a1758)) | c0_1(a1799) | c1_1(a1799) | (~c3_1(a1799)))),
% 1.54/1.22 inference(quant_inst,[status(thm)],[])).
% 1.54/1.22 tff(851,plain,
% 1.54/1.22 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1799) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c1_1(a1758)) | (~c2_1(a1765)) | (~c0_1(a1765)) | c1_1(a1799) | (~c3_1(a1799))),
% 1.54/1.22 inference(modus_ponens,[status(thm)],[850, 849])).
% 1.54/1.22 tff(852,plain,
% 1.54/1.22 (c1_1(a1799)),
% 1.54/1.22 inference(unit_resolution,[status(thm)],[851, 111, 845, 739, 738, 625, 614, 844, 737, 46, 809])).
% 1.54/1.22 tff(853,plain,
% 1.54/1.22 (^[V: $i, U: $i] : refl((hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))))),
% 1.54/1.22 inference(bind,[status(th)],[])).
% 1.54/1.22 tff(854,plain,
% 1.54/1.22 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.54/1.22 inference(quant_intro,[status(thm)],[853])).
% 1.54/1.22 tff(855,plain,
% 1.54/1.22 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.54/1.22 inference(rewrite,[status(thm)],[])).
% 1.54/1.22 tff(856,plain,
% 1.54/1.22 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp24) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp24))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V))) | hskp24) <=> (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp24) <=> (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))))),
% 1.54/1.22 inference(bind,[status(th)],[])).
% 1.54/1.22 tff(857,plain,
% 1.54/1.22 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp24) <=> ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.54/1.22 inference(quant_intro,[status(thm)],[856])).
% 1.54/1.22 tff(858,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c3_1(V)) | hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause182')).
% 1.54/1.22 tff(859,plain,
% 1.54/1.22 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.54/1.22 inference(modus_ponens,[status(thm)],[858, 857])).
% 1.54/1.23 tff(860,plain,
% 1.54/1.23 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.54/1.23 inference(modus_ponens,[status(thm)],[859, 855])).
% 1.54/1.23 tff(861,plain,(
% 1.54/1.23 ![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.54/1.23 inference(skolemize,[status(sab)],[860])).
% 1.54/1.23 tff(862,plain,
% 1.54/1.23 (![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.54/1.23 inference(modus_ponens,[status(thm)],[861, 854])).
% 1.54/1.23 tff(863,plain,
% 1.54/1.23 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp24 | c1_1(a1765) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c0_1(a1765)) | c3_1(a1765))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp24 | c1_1(a1765) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c0_1(a1765)) | c3_1(a1765))),
% 1.54/1.23 inference(rewrite,[status(thm)],[])).
% 1.54/1.23 tff(864,plain,
% 1.54/1.23 ((hskp24 | (~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1762)) | c1_1(a1765) | c3_1(a1765) | (~c0_1(a1765))) <=> (hskp24 | c1_1(a1765) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c0_1(a1765)) | c3_1(a1765))),
% 1.54/1.23 inference(rewrite,[status(thm)],[])).
% 1.54/1.23 tff(865,plain,
% 1.54/1.23 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp24 | (~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1762)) | c1_1(a1765) | c3_1(a1765) | (~c0_1(a1765)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp24 | c1_1(a1765) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c0_1(a1765)) | c3_1(a1765)))),
% 1.54/1.23 inference(monotonicity,[status(thm)],[864])).
% 1.54/1.23 tff(866,plain,
% 1.54/1.23 (((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp24 | (~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1762)) | c1_1(a1765) | c3_1(a1765) | (~c0_1(a1765)))) <=> ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp24 | c1_1(a1765) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c0_1(a1765)) | c3_1(a1765))),
% 1.54/1.23 inference(transitivity,[status(thm)],[865, 863])).
% 1.54/1.23 tff(867,plain,
% 1.54/1.23 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp24 | (~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1762)) | c1_1(a1765) | c3_1(a1765) | (~c0_1(a1765)))),
% 1.54/1.23 inference(quant_inst,[status(thm)],[])).
% 1.54/1.23 tff(868,plain,
% 1.54/1.23 ((~![V: $i, U: $i] : (hskp24 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp24 | c1_1(a1765) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c0_1(a1765)) | c3_1(a1765)),
% 1.54/1.23 inference(modus_ponens,[status(thm)],[867, 866])).
% 1.54/1.23 tff(869,plain,
% 1.54/1.23 (hskp24),
% 1.54/1.23 inference(unit_resolution,[status(thm)],[868, 111, 739, 735, 734, 737, 862, 740, 826])).
% 1.54/1.23 tff(870,plain,
% 1.54/1.23 (((~hskp24) | (~c3_1(a1809))) <=> ((~hskp24) | (~c3_1(a1809)))),
% 1.54/1.23 inference(rewrite,[status(thm)],[])).
% 1.54/1.23 tff(871,plain,
% 1.54/1.23 (((~c3_1(a1809)) | (~hskp24)) <=> ((~hskp24) | (~c3_1(a1809)))),
% 1.54/1.23 inference(rewrite,[status(thm)],[])).
% 1.54/1.23 tff(872,axiom,((~c3_1(a1809)) | (~hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause91')).
% 1.54/1.23 tff(873,plain,
% 1.54/1.23 ((~hskp24) | (~c3_1(a1809))),
% 1.54/1.23 inference(modus_ponens,[status(thm)],[872, 871])).
% 1.54/1.23 tff(874,plain,
% 1.54/1.23 ((~hskp24) | (~c3_1(a1809))),
% 1.54/1.23 inference(modus_ponens,[status(thm)],[873, 870])).
% 1.54/1.23 tff(875,plain,
% 1.54/1.23 (~c3_1(a1809)),
% 1.54/1.23 inference(unit_resolution,[status(thm)],[874, 869])).
% 1.54/1.23 tff(876,plain,
% 1.54/1.23 (((~hskp24) | (~c1_1(a1809))) <=> ((~hskp24) | (~c1_1(a1809)))),
% 1.54/1.23 inference(rewrite,[status(thm)],[])).
% 1.54/1.23 tff(877,plain,
% 1.54/1.23 (((~c1_1(a1809)) | (~hskp24)) <=> ((~hskp24) | (~c1_1(a1809)))),
% 1.54/1.23 inference(rewrite,[status(thm)],[])).
% 1.54/1.23 tff(878,axiom,((~c1_1(a1809)) | (~hskp24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause90')).
% 1.54/1.23 tff(879,plain,
% 1.54/1.23 ((~hskp24) | (~c1_1(a1809))),
% 1.54/1.23 inference(modus_ponens,[status(thm)],[878, 877])).
% 1.54/1.23 tff(880,plain,
% 1.54/1.23 ((~hskp24) | (~c1_1(a1809))),
% 1.54/1.23 inference(modus_ponens,[status(thm)],[879, 876])).
% 1.54/1.23 tff(881,plain,
% 1.54/1.23 (~c1_1(a1809)),
% 1.54/1.23 inference(unit_resolution,[status(thm)],[880, 869])).
% 1.54/1.23 tff(882,plain,
% 1.54/1.23 (((~hskp24) | c0_1(a1809)) <=> ((~hskp24) | c0_1(a1809))),
% 1.54/1.23 inference(rewrite,[status(thm)],[])).
% 1.54/1.23 tff(883,axiom,((~hskp24) | c0_1(a1809)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause51')).
% 1.54/1.23 tff(884,plain,
% 1.54/1.23 ((~hskp24) | c0_1(a1809)),
% 1.54/1.23 inference(modus_ponens,[status(thm)],[883, 882])).
% 1.54/1.23 tff(885,plain,
% 1.54/1.23 ((~hskp24) | c0_1(a1809)),
% 1.54/1.23 inference(modus_ponens,[status(thm)],[884, 882])).
% 1.54/1.23 tff(886,plain,
% 1.54/1.23 ((~hskp24) | c0_1(a1809)),
% 1.54/1.23 inference(modus_ponens,[status(thm)],[885, 882])).
% 1.54/1.23 tff(887,plain,
% 1.54/1.23 ((~hskp24) | c0_1(a1809)),
% 1.54/1.23 inference(modus_ponens,[status(thm)],[886, 882])).
% 1.54/1.23 tff(888,plain,
% 1.54/1.23 ((~hskp24) | c0_1(a1809)),
% 1.54/1.23 inference(modus_ponens,[status(thm)],[887, 882])).
% 1.54/1.23 tff(889,plain,
% 1.54/1.23 ((~hskp24) | c0_1(a1809)),
% 1.54/1.23 inference(modus_ponens,[status(thm)],[888, 882])).
% 1.54/1.23 tff(890,plain,
% 1.54/1.23 ((~hskp24) | c0_1(a1809)),
% 1.54/1.23 inference(modus_ponens,[status(thm)],[889, 882])).
% 1.54/1.23 tff(891,plain,
% 1.54/1.23 ((~hskp24) | c0_1(a1809)),
% 1.54/1.23 inference(modus_ponens,[status(thm)],[890, 882])).
% 1.54/1.23 tff(892,plain,
% 1.54/1.23 (c0_1(a1809)),
% 1.54/1.23 inference(unit_resolution,[status(thm)],[891, 869])).
% 1.54/1.23 tff(893,plain,
% 1.54/1.23 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp2 | c1_1(a1809) | c3_1(a1809) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | c3_1(a1765) | (~c0_1(a1809)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp2 | c1_1(a1809) | c3_1(a1809) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | c3_1(a1765) | (~c0_1(a1809)))),
% 1.54/1.23 inference(rewrite,[status(thm)],[])).
% 1.54/1.23 tff(894,plain,
% 1.54/1.23 ((hskp2 | (~ndr1_0) | c3_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c1_1(a1809) | c3_1(a1809) | (~c0_1(a1809))) <=> (hskp2 | c1_1(a1809) | c3_1(a1809) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | c3_1(a1765) | (~c0_1(a1809)))),
% 1.54/1.23 inference(rewrite,[status(thm)],[])).
% 1.54/1.23 tff(895,plain,
% 1.54/1.23 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c1_1(a1809) | c3_1(a1809) | (~c0_1(a1809)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp2 | c1_1(a1809) | c3_1(a1809) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | c3_1(a1765) | (~c0_1(a1809))))),
% 1.54/1.23 inference(monotonicity,[status(thm)],[894])).
% 1.54/1.23 tff(896,plain,
% 1.54/1.23 (((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c1_1(a1809) | c3_1(a1809) | (~c0_1(a1809)))) <=> ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp2 | c1_1(a1809) | c3_1(a1809) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | c3_1(a1765) | (~c0_1(a1809)))),
% 1.54/1.23 inference(transitivity,[status(thm)],[895, 893])).
% 1.54/1.23 tff(897,plain,
% 1.54/1.23 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp2 | (~ndr1_0) | c3_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c1_1(a1809) | c3_1(a1809) | (~c0_1(a1809)))),
% 1.54/1.23 inference(quant_inst,[status(thm)],[])).
% 1.54/1.23 tff(898,plain,
% 1.54/1.23 ((~![V: $i, U: $i] : (hskp2 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c0_1(V)))) | hskp2 | c1_1(a1809) | c3_1(a1809) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | c3_1(a1765) | (~c0_1(a1809))),
% 1.54/1.23 inference(modus_ponens,[status(thm)],[897, 896])).
% 1.54/1.23 tff(899,plain,
% 1.54/1.23 (hskp2),
% 1.54/1.23 inference(unit_resolution,[status(thm)],[898, 111, 892, 739, 738, 881, 875, 210, 826])).
% 1.54/1.23 tff(900,plain,
% 1.54/1.23 (~c2_1(a1757)),
% 1.54/1.23 inference(unit_resolution,[status(thm)],[53, 899])).
% 1.54/1.23 tff(901,plain,
% 1.54/1.23 (c1_1(a1757)),
% 1.54/1.23 inference(unit_resolution,[status(thm)],[64, 899])).
% 1.54/1.23 tff(902,plain,
% 1.54/1.23 (c0_1(a1757)),
% 1.54/1.23 inference(unit_resolution,[status(thm)],[75, 899])).
% 1.54/1.23 tff(903,plain,
% 1.54/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c0_1(a1799) | c2_1(a1757) | (~ndr1_0) | (~c1_1(a1757)) | (~c0_1(a1757)) | (~c2_1(a1788)) | c1_1(a1788) | (~c0_1(a1788)) | (~c1_1(a1799)) | (~c3_1(a1799)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a1799) | c2_1(a1757) | (~ndr1_0) | (~c1_1(a1757)) | (~c0_1(a1757)) | (~c2_1(a1788)) | c1_1(a1788) | (~c0_1(a1788)) | (~c1_1(a1799)) | (~c3_1(a1799)))),
% 1.54/1.23 inference(rewrite,[status(thm)],[])).
% 1.54/1.23 tff(904,plain,
% 1.54/1.23 (((~ndr1_0) | c2_1(a1757) | (~c1_1(a1757)) | (~c0_1(a1757)) | c1_1(a1788) | (~c2_1(a1788)) | (~c0_1(a1788)) | c0_1(a1799) | (~c3_1(a1799)) | (~c1_1(a1799))) <=> (c0_1(a1799) | c2_1(a1757) | (~ndr1_0) | (~c1_1(a1757)) | (~c0_1(a1757)) | (~c2_1(a1788)) | c1_1(a1788) | (~c0_1(a1788)) | (~c1_1(a1799)) | (~c3_1(a1799)))),
% 1.54/1.23 inference(rewrite,[status(thm)],[])).
% 1.54/1.23 tff(905,plain,
% 1.54/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1757) | (~c1_1(a1757)) | (~c0_1(a1757)) | c1_1(a1788) | (~c2_1(a1788)) | (~c0_1(a1788)) | c0_1(a1799) | (~c3_1(a1799)) | (~c1_1(a1799)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c0_1(a1799) | c2_1(a1757) | (~ndr1_0) | (~c1_1(a1757)) | (~c0_1(a1757)) | (~c2_1(a1788)) | c1_1(a1788) | (~c0_1(a1788)) | (~c1_1(a1799)) | (~c3_1(a1799))))),
% 1.54/1.23 inference(monotonicity,[status(thm)],[904])).
% 1.54/1.23 tff(906,plain,
% 1.54/1.23 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1757) | (~c1_1(a1757)) | (~c0_1(a1757)) | c1_1(a1788) | (~c2_1(a1788)) | (~c0_1(a1788)) | c0_1(a1799) | (~c3_1(a1799)) | (~c1_1(a1799)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a1799) | c2_1(a1757) | (~ndr1_0) | (~c1_1(a1757)) | (~c0_1(a1757)) | (~c2_1(a1788)) | c1_1(a1788) | (~c0_1(a1788)) | (~c1_1(a1799)) | (~c3_1(a1799)))),
% 1.54/1.23 inference(transitivity,[status(thm)],[905, 903])).
% 1.54/1.23 tff(907,plain,
% 1.54/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1757) | (~c1_1(a1757)) | (~c0_1(a1757)) | c1_1(a1788) | (~c2_1(a1788)) | (~c0_1(a1788)) | c0_1(a1799) | (~c3_1(a1799)) | (~c1_1(a1799)))),
% 1.55/1.23 inference(quant_inst,[status(thm)],[])).
% 1.55/1.23 tff(908,plain,
% 1.55/1.23 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a1799) | c2_1(a1757) | (~ndr1_0) | (~c1_1(a1757)) | (~c0_1(a1757)) | (~c2_1(a1788)) | c1_1(a1788) | (~c0_1(a1788)) | (~c1_1(a1799)) | (~c3_1(a1799))),
% 1.55/1.23 inference(modus_ponens,[status(thm)],[907, 906])).
% 1.55/1.23 tff(909,plain,
% 1.55/1.23 ($false),
% 1.55/1.23 inference(unit_resolution,[status(thm)],[908, 111, 845, 785, 774, 902, 901, 844, 900, 475, 852, 792])).
% 1.55/1.23 tff(910,plain,(c1_1(a1759) | hskp19 | c3_1(a1759)), inference(lemma,lemma(discharge,[]))).
% 1.55/1.23 tff(911,plain,
% 1.55/1.23 (c1_1(a1759)),
% 1.55/1.23 inference(unit_resolution,[status(thm)],[910, 34, 12])).
% 1.55/1.23 tff(912,plain,
% 1.55/1.23 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp13 | c2_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp19 | hskp13 | c2_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)))),
% 1.55/1.23 inference(rewrite,[status(thm)],[])).
% 1.55/1.23 tff(913,plain,
% 1.55/1.23 ((hskp19 | hskp13 | (~ndr1_0) | c2_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759))) <=> (hskp19 | hskp13 | c2_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)))),
% 1.55/1.23 inference(rewrite,[status(thm)],[])).
% 1.55/1.23 tff(914,plain,
% 1.55/1.23 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | c2_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp13 | c2_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759))))),
% 1.55/1.23 inference(monotonicity,[status(thm)],[913])).
% 1.55/1.23 tff(915,plain,
% 1.55/1.23 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | c2_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp19 | hskp13 | c2_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)))),
% 1.55/1.23 inference(transitivity,[status(thm)],[914, 912])).
% 1.55/1.23 tff(916,plain,
% 1.55/1.23 ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | c2_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)))),
% 1.55/1.23 inference(quant_inst,[status(thm)],[])).
% 1.55/1.23 tff(917,plain,
% 1.55/1.23 ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp19 | hskp13 | c2_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759))),
% 1.55/1.23 inference(modus_ponens,[status(thm)],[916, 915])).
% 1.55/1.23 tff(918,plain,
% 1.55/1.23 (hskp13 | c2_1(a1759) | (~c0_1(a1759))),
% 1.55/1.23 inference(unit_resolution,[status(thm)],[917, 111, 12, 911, 33])).
% 1.55/1.23 tff(919,plain,
% 1.55/1.23 (~c0_1(a1759)),
% 1.55/1.23 inference(unit_resolution,[status(thm)],[918, 36, 23])).
% 1.55/1.23 tff(920,plain,
% 1.55/1.23 (^[V: $i, U: $i] : refl((hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))),
% 1.55/1.23 inference(bind,[status(th)],[])).
% 1.55/1.23 tff(921,plain,
% 1.55/1.23 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.55/1.23 inference(quant_intro,[status(thm)],[920])).
% 1.55/1.23 tff(922,plain,
% 1.55/1.23 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.55/1.23 inference(rewrite,[status(thm)],[])).
% 1.55/1.23 tff(923,plain,
% 1.55/1.23 (^[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)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | hskp11) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp11))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V))) | hskp11) <=> (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | hskp11) <=> (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))))),
% 1.55/1.23 inference(bind,[status(th)],[])).
% 1.55/1.23 tff(924,plain,
% 1.55/1.23 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | hskp11) <=> ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.55/1.23 inference(quant_intro,[status(thm)],[923])).
% 1.55/1.23 tff(925,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c2_1(V)) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause165')).
% 1.55/1.23 tff(926,plain,
% 1.55/1.23 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.55/1.23 inference(modus_ponens,[status(thm)],[925, 924])).
% 1.55/1.23 tff(927,plain,
% 1.55/1.23 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.55/1.23 inference(modus_ponens,[status(thm)],[926, 922])).
% 1.55/1.23 tff(928,plain,(
% 1.55/1.23 ![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.55/1.23 inference(skolemize,[status(sab)],[927])).
% 1.55/1.23 tff(929,plain,
% 1.55/1.23 (![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))),
% 1.55/1.23 inference(modus_ponens,[status(thm)],[928, 921])).
% 1.55/1.23 tff(930,plain,
% 1.55/1.23 (((~![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp19 | hskp6 | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759))) <=> ((~![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | hskp19 | hskp6 | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759))),
% 1.55/1.23 inference(rewrite,[status(thm)],[])).
% 1.55/1.23 tff(931,plain,
% 1.55/1.23 ((hskp19 | hskp6 | (~ndr1_0) | c3_1(a1759) | c0_1(a1759) | (~c1_1(a1759))) <=> (hskp19 | hskp6 | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759))),
% 1.55/1.23 inference(rewrite,[status(thm)],[])).
% 1.55/1.23 tff(932,plain,
% 1.55/1.23 (((~![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp19 | hskp6 | (~ndr1_0) | c3_1(a1759) | c0_1(a1759) | (~c1_1(a1759)))) <=> ((~![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp19 | hskp6 | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759)))),
% 1.55/1.23 inference(monotonicity,[status(thm)],[931])).
% 1.55/1.23 tff(933,plain,
% 1.55/1.23 (((~![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp19 | hskp6 | (~ndr1_0) | c3_1(a1759) | c0_1(a1759) | (~c1_1(a1759)))) <=> ((~![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | hskp19 | hskp6 | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759))),
% 1.55/1.23 inference(transitivity,[status(thm)],[932, 930])).
% 1.55/1.23 tff(934,plain,
% 1.55/1.23 ((~![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp19 | hskp6 | (~ndr1_0) | c3_1(a1759) | c0_1(a1759) | (~c1_1(a1759)))),
% 1.55/1.23 inference(quant_inst,[status(thm)],[])).
% 1.55/1.23 tff(935,plain,
% 1.55/1.23 ((~![U: $i] : (hskp19 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | hskp19 | hskp6 | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759)),
% 1.55/1.23 inference(modus_ponens,[status(thm)],[934, 933])).
% 1.55/1.23 tff(936,plain,
% 1.55/1.23 (hskp6 | (~c1_1(a1759)) | c0_1(a1759)),
% 1.55/1.23 inference(unit_resolution,[status(thm)],[935, 111, 12, 34, 701])).
% 1.55/1.23 tff(937,plain,
% 1.55/1.23 (c0_1(a1759)),
% 1.55/1.23 inference(unit_resolution,[status(thm)],[936, 240, 911])).
% 1.55/1.23 tff(938,assumption,(c1_1(a1759)), introduced(assumption)).
% 1.55/1.23 tff(939,plain,
% 1.55/1.23 (hskp19 | hskp6 | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759)),
% 1.55/1.23 inference(unit_resolution,[status(thm)],[935, 34, 701])).
% 1.55/1.23 tff(940,plain,
% 1.55/1.23 (c0_1(a1759)),
% 1.55/1.23 inference(unit_resolution,[status(thm)],[939, 12, 241, 938, 240])).
% 1.55/1.23 tff(941,plain,
% 1.55/1.23 (hskp19 | hskp13 | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759))),
% 1.55/1.23 inference(unit_resolution,[status(thm)],[917, 36, 33])).
% 1.55/1.23 tff(942,plain,
% 1.55/1.23 ($false),
% 1.55/1.23 inference(unit_resolution,[status(thm)],[941, 940, 12, 241, 938, 23])).
% 1.55/1.23 tff(943,plain,(hskp19 | (~ndr1_0) | (~c1_1(a1759)) | hskp13 | c2_1(a1759) | hskp6 | c3_1(a1759)), inference(lemma,lemma(discharge,[]))).
% 1.55/1.23 tff(944,plain,
% 1.55/1.23 (hskp19 | (~c1_1(a1759)) | hskp13 | c2_1(a1759) | hskp6 | c3_1(a1759)),
% 1.55/1.23 inference(unit_resolution,[status(thm)],[943, 111])).
% 1.55/1.23 tff(945,plain,
% 1.55/1.23 (c2_1(a1759)),
% 1.55/1.23 inference(unit_resolution,[status(thm)],[944, 240, 911, 23, 12, 34])).
% 1.55/1.23 tff(946,plain,
% 1.55/1.23 (((~hskp4) | (~c2_1(a1759))) <=> ((~hskp4) | (~c2_1(a1759)))),
% 1.55/1.23 inference(rewrite,[status(thm)],[])).
% 1.55/1.23 tff(947,plain,
% 1.55/1.23 (((~c2_1(a1759)) | (~hskp4)) <=> ((~hskp4) | (~c2_1(a1759)))),
% 1.55/1.23 inference(rewrite,[status(thm)],[])).
% 1.55/1.23 tff(948,axiom,((~c2_1(a1759)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause123')).
% 1.55/1.23 tff(949,plain,
% 1.55/1.23 ((~hskp4) | (~c2_1(a1759))),
% 1.55/1.23 inference(modus_ponens,[status(thm)],[948, 947])).
% 1.55/1.23 tff(950,plain,
% 1.55/1.23 ((~hskp4) | (~c2_1(a1759))),
% 1.55/1.23 inference(modus_ponens,[status(thm)],[949, 946])).
% 1.55/1.23 tff(951,plain,
% 1.55/1.23 (~hskp4),
% 1.55/1.23 inference(unit_resolution,[status(thm)],[950, 945])).
% 1.55/1.23 tff(952,plain,
% 1.55/1.23 (^[U: $i] : refl((hskp29 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp29 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))),
% 1.55/1.23 inference(bind,[status(th)],[])).
% 1.55/1.23 tff(953,plain,
% 1.55/1.23 (![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.55/1.23 inference(quant_intro,[status(thm)],[952])).
% 1.55/1.23 tff(954,plain,
% 1.55/1.23 (![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.55/1.23 inference(rewrite,[status(thm)],[])).
% 1.55/1.23 tff(955,plain,
% 1.55/1.23 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp29) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp29))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp29) <=> (hskp29 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp29) <=> (hskp29 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp29) | hskp4) <=> ((hskp29 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp4))), rewrite(((hskp29 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp4) <=> (hskp29 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp29) | hskp4) <=> (hskp29 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))))),
% 1.55/1.23 inference(bind,[status(th)],[])).
% 1.55/1.23 tff(956,plain,
% 1.55/1.23 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp29) | hskp4) <=> ![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.55/1.23 inference(quant_intro,[status(thm)],[955])).
% 1.55/1.23 tff(957,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp29) | hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause151')).
% 1.55/1.23 tff(958,plain,
% 1.55/1.23 (![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.55/1.23 inference(modus_ponens,[status(thm)],[957, 956])).
% 1.55/1.23 tff(959,plain,
% 1.55/1.23 (![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.55/1.23 inference(modus_ponens,[status(thm)],[958, 954])).
% 1.55/1.23 tff(960,plain,(
% 1.55/1.23 ![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.55/1.23 inference(skolemize,[status(sab)],[959])).
% 1.55/1.23 tff(961,plain,
% 1.55/1.23 (![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 1.55/1.23 inference(modus_ponens,[status(thm)],[960, 953])).
% 1.55/1.23 tff(962,plain,
% 1.55/1.23 (((~![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp4 | (~c2_1(a1759)) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)))) <=> ((~![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp4 | (~c2_1(a1759)) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)))),
% 1.55/1.23 inference(rewrite,[status(thm)],[])).
% 1.55/1.23 tff(963,plain,
% 1.55/1.23 ((hskp29 | hskp4 | (~ndr1_0) | (~c2_1(a1759)) | (~c1_1(a1759)) | (~c0_1(a1759))) <=> (hskp29 | hskp4 | (~c2_1(a1759)) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)))),
% 1.55/1.23 inference(rewrite,[status(thm)],[])).
% 1.55/1.23 tff(964,plain,
% 1.55/1.23 (((~![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp4 | (~ndr1_0) | (~c2_1(a1759)) | (~c1_1(a1759)) | (~c0_1(a1759)))) <=> ((~![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp4 | (~c2_1(a1759)) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759))))),
% 1.55/1.23 inference(monotonicity,[status(thm)],[963])).
% 1.55/1.23 tff(965,plain,
% 1.55/1.23 (((~![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp4 | (~ndr1_0) | (~c2_1(a1759)) | (~c1_1(a1759)) | (~c0_1(a1759)))) <=> ((~![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp4 | (~c2_1(a1759)) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)))),
% 1.55/1.23 inference(transitivity,[status(thm)],[964, 962])).
% 1.55/1.23 tff(966,plain,
% 1.55/1.23 ((~![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp29 | hskp4 | (~ndr1_0) | (~c2_1(a1759)) | (~c1_1(a1759)) | (~c0_1(a1759)))),
% 1.55/1.23 inference(quant_inst,[status(thm)],[])).
% 1.55/1.23 tff(967,plain,
% 1.55/1.23 ((~![U: $i] : (hskp29 | hskp4 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp29 | hskp4 | (~c2_1(a1759)) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759))),
% 1.55/1.23 inference(modus_ponens,[status(thm)],[966, 965])).
% 1.55/1.23 tff(968,plain,
% 1.55/1.23 (hskp29 | hskp4 | (~c2_1(a1759)) | (~c0_1(a1759))),
% 1.55/1.23 inference(unit_resolution,[status(thm)],[967, 111, 911, 961])).
% 1.55/1.23 tff(969,plain,
% 1.55/1.23 (hskp29),
% 1.55/1.23 inference(unit_resolution,[status(thm)],[968, 951, 945, 937])).
% 1.55/1.23 tff(970,plain,
% 1.55/1.23 (((~hskp29) | c3_1(a1805)) <=> ((~hskp29) | c3_1(a1805))),
% 1.55/1.23 inference(rewrite,[status(thm)],[])).
% 1.55/1.23 tff(971,axiom,((~hskp29) | c3_1(a1805)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause43')).
% 1.55/1.23 tff(972,plain,
% 1.55/1.23 ((~hskp29) | c3_1(a1805)),
% 1.55/1.23 inference(modus_ponens,[status(thm)],[971, 970])).
% 1.55/1.23 tff(973,plain,
% 1.55/1.23 ((~hskp29) | c3_1(a1805)),
% 1.55/1.23 inference(modus_ponens,[status(thm)],[972, 970])).
% 1.55/1.23 tff(974,plain,
% 1.55/1.23 ((~hskp29) | c3_1(a1805)),
% 1.55/1.23 inference(modus_ponens,[status(thm)],[973, 970])).
% 1.55/1.23 tff(975,plain,
% 1.55/1.23 ((~hskp29) | c3_1(a1805)),
% 1.55/1.23 inference(modus_ponens,[status(thm)],[974, 970])).
% 1.55/1.23 tff(976,plain,
% 1.55/1.23 ((~hskp29) | c3_1(a1805)),
% 1.55/1.23 inference(modus_ponens,[status(thm)],[975, 970])).
% 1.55/1.23 tff(977,plain,
% 1.55/1.23 ((~hskp29) | c3_1(a1805)),
% 1.55/1.23 inference(modus_ponens,[status(thm)],[976, 970])).
% 1.55/1.23 tff(978,plain,
% 1.55/1.23 ((~hskp29) | c3_1(a1805)),
% 1.55/1.23 inference(modus_ponens,[status(thm)],[977, 970])).
% 1.55/1.23 tff(979,plain,
% 1.55/1.23 ((~hskp29) | c3_1(a1805)),
% 1.55/1.23 inference(modus_ponens,[status(thm)],[978, 970])).
% 1.55/1.23 tff(980,plain,
% 1.55/1.23 (c3_1(a1805)),
% 1.55/1.23 inference(unit_resolution,[status(thm)],[979, 969])).
% 1.55/1.23 tff(981,plain,
% 1.55/1.23 (hskp25),
% 1.55/1.23 inference(unit_resolution,[status(thm)],[162, 951, 120])).
% 1.55/1.23 tff(982,plain,
% 1.55/1.23 (((~hskp29) | c0_1(a1805)) <=> ((~hskp29) | c0_1(a1805))),
% 1.55/1.23 inference(rewrite,[status(thm)],[])).
% 1.55/1.23 tff(983,axiom,((~hskp29) | c0_1(a1805)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause41')).
% 1.55/1.23 tff(984,plain,
% 1.55/1.23 ((~hskp29) | c0_1(a1805)),
% 1.55/1.23 inference(modus_ponens,[status(thm)],[983, 982])).
% 1.55/1.23 tff(985,plain,
% 1.55/1.23 ((~hskp29) | c0_1(a1805)),
% 1.55/1.23 inference(modus_ponens,[status(thm)],[984, 982])).
% 1.55/1.23 tff(986,plain,
% 1.55/1.23 ((~hskp29) | c0_1(a1805)),
% 1.55/1.23 inference(modus_ponens,[status(thm)],[985, 982])).
% 1.55/1.23 tff(987,plain,
% 1.55/1.23 ((~hskp29) | c0_1(a1805)),
% 1.55/1.23 inference(modus_ponens,[status(thm)],[986, 982])).
% 1.55/1.23 tff(988,plain,
% 1.55/1.23 ((~hskp29) | c0_1(a1805)),
% 1.55/1.23 inference(modus_ponens,[status(thm)],[987, 982])).
% 1.55/1.23 tff(989,plain,
% 1.55/1.23 ((~hskp29) | c0_1(a1805)),
% 1.55/1.23 inference(modus_ponens,[status(thm)],[988, 982])).
% 1.55/1.23 tff(990,plain,
% 1.55/1.23 ((~hskp29) | c0_1(a1805)),
% 1.55/1.23 inference(modus_ponens,[status(thm)],[989, 982])).
% 1.55/1.23 tff(991,plain,
% 1.55/1.23 ((~hskp29) | c0_1(a1805)),
% 1.55/1.23 inference(modus_ponens,[status(thm)],[990, 982])).
% 1.55/1.23 tff(992,plain,
% 1.55/1.23 (c0_1(a1805)),
% 1.55/1.23 inference(unit_resolution,[status(thm)],[991, 969])).
% 1.55/1.23 tff(993,plain,
% 1.55/1.23 (((~hskp29) | c2_1(a1805)) <=> ((~hskp29) | c2_1(a1805))),
% 1.55/1.23 inference(rewrite,[status(thm)],[])).
% 1.55/1.23 tff(994,axiom,((~hskp29) | c2_1(a1805)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause42')).
% 1.55/1.23 tff(995,plain,
% 1.55/1.23 ((~hskp29) | c2_1(a1805)),
% 1.55/1.23 inference(modus_ponens,[status(thm)],[994, 993])).
% 1.55/1.23 tff(996,plain,
% 1.55/1.23 ((~hskp29) | c2_1(a1805)),
% 1.55/1.23 inference(modus_ponens,[status(thm)],[995, 993])).
% 1.55/1.23 tff(997,plain,
% 1.55/1.23 ((~hskp29) | c2_1(a1805)),
% 1.55/1.23 inference(modus_ponens,[status(thm)],[996, 993])).
% 1.55/1.23 tff(998,plain,
% 1.55/1.23 ((~hskp29) | c2_1(a1805)),
% 1.55/1.23 inference(modus_ponens,[status(thm)],[997, 993])).
% 1.55/1.23 tff(999,plain,
% 1.55/1.23 ((~hskp29) | c2_1(a1805)),
% 1.55/1.23 inference(modus_ponens,[status(thm)],[998, 993])).
% 1.55/1.23 tff(1000,plain,
% 1.55/1.23 ((~hskp29) | c2_1(a1805)),
% 1.55/1.23 inference(modus_ponens,[status(thm)],[999, 993])).
% 1.55/1.23 tff(1001,plain,
% 1.55/1.23 ((~hskp29) | c2_1(a1805)),
% 1.55/1.23 inference(modus_ponens,[status(thm)],[1000, 993])).
% 1.55/1.23 tff(1002,plain,
% 1.55/1.23 ((~hskp29) | c2_1(a1805)),
% 1.55/1.23 inference(modus_ponens,[status(thm)],[1001, 993])).
% 1.55/1.23 tff(1003,plain,
% 1.55/1.23 (c2_1(a1805)),
% 1.55/1.23 inference(unit_resolution,[status(thm)],[1002, 969])).
% 1.55/1.23 tff(1004,plain,
% 1.55/1.23 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.55/1.23 inference(bind,[status(th)],[])).
% 1.55/1.23 tff(1005,plain,
% 1.55/1.23 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.55/1.23 inference(quant_intro,[status(thm)],[1004])).
% 1.55/1.23 tff(1006,plain,
% 1.55/1.23 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.55/1.23 inference(rewrite,[status(thm)],[])).
% 1.55/1.23 tff(1007,plain,
% 1.55/1.23 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp6) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp6))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp6) <=> (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.55/1.23 inference(bind,[status(th)],[])).
% 1.55/1.23 tff(1008,plain,
% 1.55/1.23 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.55/1.23 inference(quant_intro,[status(thm)],[1007])).
% 1.55/1.23 tff(1009,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause176')).
% 1.55/1.23 tff(1010,plain,
% 1.55/1.23 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.55/1.23 inference(modus_ponens,[status(thm)],[1009, 1008])).
% 1.55/1.23 tff(1011,plain,
% 1.55/1.23 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.55/1.23 inference(modus_ponens,[status(thm)],[1010, 1006])).
% 1.55/1.23 tff(1012,plain,(
% 1.55/1.24 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.55/1.24 inference(skolemize,[status(sab)],[1011])).
% 1.55/1.24 tff(1013,plain,
% 1.55/1.24 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.55/1.24 inference(modus_ponens,[status(thm)],[1012, 1005])).
% 1.55/1.24 tff(1014,assumption,(hskp25), introduced(assumption)).
% 1.55/1.24 tff(1015,plain,
% 1.55/1.24 (~c1_1(a1827)),
% 1.55/1.24 inference(unit_resolution,[status(thm)],[168, 1014])).
% 1.55/1.24 tff(1016,plain,
% 1.55/1.24 (~c0_1(a1827)),
% 1.55/1.24 inference(unit_resolution,[status(thm)],[174, 1014])).
% 1.55/1.24 tff(1017,assumption,(c3_1(a1805)), introduced(assumption)).
% 1.55/1.24 tff(1018,assumption,(c2_1(a1805)), introduced(assumption)).
% 1.55/1.24 tff(1019,assumption,(c0_1(a1805)), introduced(assumption)).
% 1.55/1.24 tff(1020,plain,
% 1.55/1.24 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | c0_1(a1827) | c1_1(a1827) | (~ndr1_0) | (~c3_1(a1827)) | (~c3_1(a1805)) | (~c2_1(a1805)) | (~c0_1(a1805)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c0_1(a1827) | c1_1(a1827) | (~ndr1_0) | (~c3_1(a1827)) | (~c3_1(a1805)) | (~c2_1(a1805)) | (~c0_1(a1805)))),
% 1.55/1.24 inference(rewrite,[status(thm)],[])).
% 1.55/1.24 tff(1021,plain,
% 1.55/1.24 ((hskp6 | (~ndr1_0) | (~c2_1(a1805)) | (~c3_1(a1805)) | (~c0_1(a1805)) | c1_1(a1827) | c0_1(a1827) | (~c3_1(a1827))) <=> (hskp6 | c0_1(a1827) | c1_1(a1827) | (~ndr1_0) | (~c3_1(a1827)) | (~c3_1(a1805)) | (~c2_1(a1805)) | (~c0_1(a1805)))),
% 1.55/1.24 inference(rewrite,[status(thm)],[])).
% 1.55/1.24 tff(1022,plain,
% 1.55/1.24 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a1805)) | (~c3_1(a1805)) | (~c0_1(a1805)) | c1_1(a1827) | c0_1(a1827) | (~c3_1(a1827)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | c0_1(a1827) | c1_1(a1827) | (~ndr1_0) | (~c3_1(a1827)) | (~c3_1(a1805)) | (~c2_1(a1805)) | (~c0_1(a1805))))),
% 1.55/1.24 inference(monotonicity,[status(thm)],[1021])).
% 1.55/1.24 tff(1023,plain,
% 1.55/1.24 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a1805)) | (~c3_1(a1805)) | (~c0_1(a1805)) | c1_1(a1827) | c0_1(a1827) | (~c3_1(a1827)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c0_1(a1827) | c1_1(a1827) | (~ndr1_0) | (~c3_1(a1827)) | (~c3_1(a1805)) | (~c2_1(a1805)) | (~c0_1(a1805)))),
% 1.55/1.24 inference(transitivity,[status(thm)],[1022, 1020])).
% 1.55/1.24 tff(1024,plain,
% 1.55/1.24 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp6 | (~ndr1_0) | (~c2_1(a1805)) | (~c3_1(a1805)) | (~c0_1(a1805)) | c1_1(a1827) | c0_1(a1827) | (~c3_1(a1827)))),
% 1.55/1.24 inference(quant_inst,[status(thm)],[])).
% 1.55/1.24 tff(1025,plain,
% 1.55/1.24 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp6 | c0_1(a1827) | c1_1(a1827) | (~ndr1_0) | (~c3_1(a1827)) | (~c3_1(a1805)) | (~c2_1(a1805)) | (~c0_1(a1805))),
% 1.55/1.24 inference(modus_ponens,[status(thm)],[1024, 1023])).
% 1.55/1.24 tff(1026,plain,
% 1.55/1.24 (~c3_1(a1827)),
% 1.55/1.24 inference(unit_resolution,[status(thm)],[1025, 111, 240, 1019, 1018, 1017, 1016, 1015, 1013])).
% 1.55/1.24 tff(1027,plain,
% 1.55/1.24 ($false),
% 1.55/1.24 inference(unit_resolution,[status(thm)],[181, 111, 342, 35, 1016, 1015, 140, 1026])).
% 1.55/1.24 tff(1028,plain,((~hskp25) | hskp4 | hskp3 | hskp6 | (~c0_1(a1805)) | (~c2_1(a1805)) | (~c3_1(a1805))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.24 tff(1029,plain,
% 1.55/1.24 (hskp3),
% 1.55/1.24 inference(unit_resolution,[status(thm)],[1028, 1003, 992, 240, 951, 981, 980])).
% 1.55/1.24 tff(1030,plain,
% 1.55/1.24 (c2_1(a1758)),
% 1.55/1.24 inference(unit_resolution,[status(thm)],[613, 1029])).
% 1.55/1.24 tff(1031,plain,
% 1.55/1.24 (c1_1(a1758)),
% 1.55/1.24 inference(unit_resolution,[status(thm)],[624, 1029])).
% 1.55/1.24 tff(1032,plain,
% 1.55/1.24 (c0_1(a1758)),
% 1.55/1.24 inference(unit_resolution,[status(thm)],[631, 111, 23, 1031, 1030, 22])).
% 1.55/1.24 tff(1033,plain,
% 1.55/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~c2_1(a1759)) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1805)) | (~c1_1(a1805)) | (~c2_1(a1805)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (~c2_1(a1759)) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1805)) | (~c1_1(a1805)) | (~c2_1(a1805)))),
% 1.55/1.24 inference(rewrite,[status(thm)],[])).
% 1.55/1.24 tff(1034,plain,
% 1.55/1.24 (((~ndr1_0) | (~c2_1(a1805)) | (~c1_1(a1805)) | (~c3_1(a1805)) | (~c2_1(a1759)) | (~c1_1(a1759)) | (~c0_1(a1759)) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759))) <=> ((~c2_1(a1759)) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1805)) | (~c1_1(a1805)) | (~c2_1(a1805)))),
% 1.55/1.24 inference(rewrite,[status(thm)],[])).
% 1.55/1.24 tff(1035,plain,
% 1.55/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1805)) | (~c1_1(a1805)) | (~c3_1(a1805)) | (~c2_1(a1759)) | (~c1_1(a1759)) | (~c0_1(a1759)) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~c2_1(a1759)) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1805)) | (~c1_1(a1805)) | (~c2_1(a1805))))),
% 1.55/1.24 inference(monotonicity,[status(thm)],[1034])).
% 1.55/1.24 tff(1036,plain,
% 1.55/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1805)) | (~c1_1(a1805)) | (~c3_1(a1805)) | (~c2_1(a1759)) | (~c1_1(a1759)) | (~c0_1(a1759)) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (~c2_1(a1759)) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1805)) | (~c1_1(a1805)) | (~c2_1(a1805)))),
% 1.55/1.24 inference(transitivity,[status(thm)],[1035, 1033])).
% 1.55/1.24 tff(1037,plain,
% 1.55/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1805)) | (~c1_1(a1805)) | (~c3_1(a1805)) | (~c2_1(a1759)) | (~c1_1(a1759)) | (~c0_1(a1759)) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)))),
% 1.55/1.24 inference(quant_inst,[status(thm)],[])).
% 1.55/1.24 tff(1038,plain,
% 1.55/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (~c2_1(a1759)) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1805)) | (~c1_1(a1805)) | (~c2_1(a1805))),
% 1.55/1.24 inference(modus_ponens,[status(thm)],[1037, 1036])).
% 1.55/1.24 tff(1039,plain,
% 1.55/1.24 (~c1_1(a1805)),
% 1.55/1.24 inference(unit_resolution,[status(thm)],[1038, 111, 1003, 980, 911, 945, 34, 678, 937])).
% 1.55/1.24 tff(1040,plain,
% 1.55/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c3_1(a1759) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c2_1(a1805)) | c1_1(a1805) | (~c0_1(a1805)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c3_1(a1759) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c2_1(a1805)) | c1_1(a1805) | (~c0_1(a1805)))),
% 1.55/1.24 inference(rewrite,[status(thm)],[])).
% 1.55/1.24 tff(1041,plain,
% 1.55/1.24 (((~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)) | c1_1(a1805) | (~c2_1(a1805)) | (~c0_1(a1805))) <=> (c3_1(a1759) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c2_1(a1805)) | c1_1(a1805) | (~c0_1(a1805)))),
% 1.55/1.24 inference(rewrite,[status(thm)],[])).
% 1.55/1.24 tff(1042,plain,
% 1.55/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)) | c1_1(a1805) | (~c2_1(a1805)) | (~c0_1(a1805)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c3_1(a1759) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c2_1(a1805)) | c1_1(a1805) | (~c0_1(a1805))))),
% 1.55/1.24 inference(monotonicity,[status(thm)],[1041])).
% 1.55/1.24 tff(1043,plain,
% 1.55/1.24 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)) | c1_1(a1805) | (~c2_1(a1805)) | (~c0_1(a1805)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c3_1(a1759) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c2_1(a1805)) | c1_1(a1805) | (~c0_1(a1805)))),
% 1.55/1.24 inference(transitivity,[status(thm)],[1042, 1040])).
% 1.55/1.24 tff(1044,plain,
% 1.55/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)) | c1_1(a1805) | (~c2_1(a1805)) | (~c0_1(a1805)))),
% 1.55/1.24 inference(quant_inst,[status(thm)],[])).
% 1.55/1.24 tff(1045,plain,
% 1.55/1.24 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c3_1(a1759) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c2_1(a1805)) | c1_1(a1805) | (~c0_1(a1805))),
% 1.55/1.24 inference(modus_ponens,[status(thm)],[1044, 1043])).
% 1.55/1.24 tff(1046,plain,
% 1.55/1.24 ($false),
% 1.55/1.24 inference(unit_resolution,[status(thm)],[1045, 111, 992, 1003, 911, 1031, 1030, 34, 802, 937, 1039, 1032])).
% 1.55/1.24 tff(1047,plain,(hskp6 | c3_1(a1759) | hskp13 | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.55/1.24 tff(1048,plain,
% 1.55/1.24 (hskp6),
% 1.55/1.24 inference(unit_resolution,[status(thm)],[1047, 23, 34, 12])).
% 1.55/1.24 tff(1049,plain,
% 1.55/1.24 (~c0_1(a1762)),
% 1.55/1.24 inference(unit_resolution,[status(thm)],[291, 1048])).
% 1.55/1.24 tff(1050,plain,
% 1.55/1.24 (c2_1(a1762)),
% 1.55/1.24 inference(unit_resolution,[status(thm)],[313, 1048])).
% 1.55/1.24 tff(1051,plain,
% 1.55/1.24 (~c1_1(a1762)),
% 1.55/1.24 inference(unit_resolution,[status(thm)],[410, 111, 23, 1050, 1049, 22])).
% 1.55/1.24 tff(1052,plain,
% 1.55/1.24 (^[V: $i, U: $i] : refl((hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.55/1.24 inference(bind,[status(th)],[])).
% 1.55/1.24 tff(1053,plain,
% 1.55/1.24 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.55/1.24 inference(quant_intro,[status(thm)],[1052])).
% 1.55/1.24 tff(1054,plain,
% 1.55/1.24 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.55/1.24 inference(rewrite,[status(thm)],[])).
% 1.55/1.24 tff(1055,plain,
% 1.55/1.24 (^[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)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp7) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp7))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp7) <=> (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.55/1.24 inference(bind,[status(th)],[])).
% 1.55/1.24 tff(1056,plain,
% 1.55/1.24 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp7) <=> ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.55/1.24 inference(quant_intro,[status(thm)],[1055])).
% 1.55/1.24 tff(1057,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause159')).
% 1.55/1.24 tff(1058,plain,
% 1.55/1.24 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.55/1.24 inference(modus_ponens,[status(thm)],[1057, 1056])).
% 1.55/1.24 tff(1059,plain,
% 1.55/1.24 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.55/1.24 inference(modus_ponens,[status(thm)],[1058, 1054])).
% 1.55/1.24 tff(1060,plain,(
% 1.55/1.24 ![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.55/1.24 inference(skolemize,[status(sab)],[1059])).
% 1.55/1.24 tff(1061,plain,
% 1.55/1.24 (![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.55/1.24 inference(modus_ponens,[status(thm)],[1060, 1053])).
% 1.55/1.24 tff(1062,plain,
% 1.55/1.24 (c3_1(a1762)),
% 1.55/1.24 inference(unit_resolution,[status(thm)],[302, 1048])).
% 1.55/1.24 tff(1063,plain,
% 1.55/1.24 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a1762) | c2_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | (~c3_1(a1762)) | c1_1(a1762))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a1762) | c2_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | (~c3_1(a1762)) | c1_1(a1762))),
% 1.55/1.24 inference(rewrite,[status(thm)],[])).
% 1.55/1.24 tff(1064,plain,
% 1.55/1.24 ((hskp7 | (~ndr1_0) | c2_1(a1759) | c0_1(a1759) | (~c1_1(a1759)) | c1_1(a1762) | c0_1(a1762) | (~c3_1(a1762))) <=> (hskp7 | c0_1(a1762) | c2_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | (~c3_1(a1762)) | c1_1(a1762))),
% 1.55/1.24 inference(rewrite,[status(thm)],[])).
% 1.55/1.24 tff(1065,plain,
% 1.55/1.24 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1759) | c0_1(a1759) | (~c1_1(a1759)) | c1_1(a1762) | c0_1(a1762) | (~c3_1(a1762)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a1762) | c2_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | (~c3_1(a1762)) | c1_1(a1762)))),
% 1.55/1.24 inference(monotonicity,[status(thm)],[1064])).
% 1.55/1.24 tff(1066,plain,
% 1.55/1.24 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1759) | c0_1(a1759) | (~c1_1(a1759)) | c1_1(a1762) | c0_1(a1762) | (~c3_1(a1762)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a1762) | c2_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | (~c3_1(a1762)) | c1_1(a1762))),
% 1.55/1.24 inference(transitivity,[status(thm)],[1065, 1063])).
% 1.55/1.24 tff(1067,plain,
% 1.55/1.24 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1759) | c0_1(a1759) | (~c1_1(a1759)) | c1_1(a1762) | c0_1(a1762) | (~c3_1(a1762)))),
% 1.55/1.24 inference(quant_inst,[status(thm)],[])).
% 1.55/1.24 tff(1068,plain,
% 1.55/1.24 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a1762) | c2_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | (~c3_1(a1762)) | c1_1(a1762)),
% 1.55/1.24 inference(modus_ponens,[status(thm)],[1067, 1066])).
% 1.55/1.24 tff(1069,plain,
% 1.55/1.24 (hskp7),
% 1.55/1.24 inference(unit_resolution,[status(thm)],[1068, 111, 1062, 911, 1049, 36, 1061, 919, 1051])).
% 1.55/1.24 tff(1070,plain,
% 1.55/1.24 (((~hskp7) | (~c1_1(a1763))) <=> ((~hskp7) | (~c1_1(a1763)))),
% 1.55/1.24 inference(rewrite,[status(thm)],[])).
% 1.55/1.24 tff(1071,plain,
% 1.55/1.24 (((~c1_1(a1763)) | (~hskp7)) <=> ((~hskp7) | (~c1_1(a1763)))),
% 1.55/1.24 inference(rewrite,[status(thm)],[])).
% 1.55/1.24 tff(1072,axiom,((~c1_1(a1763)) | (~hskp7)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause118')).
% 1.55/1.24 tff(1073,plain,
% 1.55/1.24 ((~hskp7) | (~c1_1(a1763))),
% 1.55/1.24 inference(modus_ponens,[status(thm)],[1072, 1071])).
% 1.55/1.24 tff(1074,plain,
% 1.55/1.24 ((~hskp7) | (~c1_1(a1763))),
% 1.55/1.24 inference(modus_ponens,[status(thm)],[1073, 1070])).
% 1.55/1.24 tff(1075,plain,
% 1.55/1.24 (~c1_1(a1763)),
% 1.55/1.24 inference(unit_resolution,[status(thm)],[1074, 1069])).
% 1.55/1.24 tff(1076,plain,
% 1.55/1.24 (((~hskp7) | c3_1(a1763)) <=> ((~hskp7) | c3_1(a1763))),
% 1.55/1.24 inference(rewrite,[status(thm)],[])).
% 1.55/1.24 tff(1077,axiom,((~hskp7) | c3_1(a1763)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause75')).
% 1.55/1.24 tff(1078,plain,
% 1.55/1.24 ((~hskp7) | c3_1(a1763)),
% 1.55/1.24 inference(modus_ponens,[status(thm)],[1077, 1076])).
% 1.55/1.24 tff(1079,plain,
% 1.55/1.24 ((~hskp7) | c3_1(a1763)),
% 1.55/1.24 inference(modus_ponens,[status(thm)],[1078, 1076])).
% 1.55/1.24 tff(1080,plain,
% 1.55/1.24 ((~hskp7) | c3_1(a1763)),
% 1.55/1.24 inference(modus_ponens,[status(thm)],[1079, 1076])).
% 1.55/1.24 tff(1081,plain,
% 1.55/1.24 ((~hskp7) | c3_1(a1763)),
% 1.55/1.24 inference(modus_ponens,[status(thm)],[1080, 1076])).
% 1.55/1.24 tff(1082,plain,
% 1.55/1.24 ((~hskp7) | c3_1(a1763)),
% 1.55/1.24 inference(modus_ponens,[status(thm)],[1081, 1076])).
% 1.55/1.24 tff(1083,plain,
% 1.55/1.24 ((~hskp7) | c3_1(a1763)),
% 1.55/1.24 inference(modus_ponens,[status(thm)],[1082, 1076])).
% 1.55/1.24 tff(1084,plain,
% 1.55/1.24 ((~hskp7) | c3_1(a1763)),
% 1.55/1.24 inference(modus_ponens,[status(thm)],[1083, 1076])).
% 1.55/1.24 tff(1085,plain,
% 1.55/1.24 ((~hskp7) | c3_1(a1763)),
% 1.55/1.24 inference(modus_ponens,[status(thm)],[1084, 1076])).
% 1.55/1.24 tff(1086,plain,
% 1.55/1.24 (c3_1(a1763)),
% 1.55/1.24 inference(unit_resolution,[status(thm)],[1085, 1069])).
% 1.55/1.24 tff(1087,plain,
% 1.55/1.24 (((~hskp7) | c0_1(a1763)) <=> ((~hskp7) | c0_1(a1763))),
% 1.55/1.24 inference(rewrite,[status(thm)],[])).
% 1.55/1.24 tff(1088,axiom,((~hskp7) | c0_1(a1763)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause74')).
% 1.55/1.24 tff(1089,plain,
% 1.55/1.24 ((~hskp7) | c0_1(a1763)),
% 1.55/1.24 inference(modus_ponens,[status(thm)],[1088, 1087])).
% 1.55/1.24 tff(1090,plain,
% 1.55/1.24 ((~hskp7) | c0_1(a1763)),
% 1.55/1.24 inference(modus_ponens,[status(thm)],[1089, 1087])).
% 1.55/1.24 tff(1091,plain,
% 1.55/1.24 ((~hskp7) | c0_1(a1763)),
% 1.55/1.24 inference(modus_ponens,[status(thm)],[1090, 1087])).
% 1.55/1.24 tff(1092,plain,
% 1.55/1.24 ((~hskp7) | c0_1(a1763)),
% 1.55/1.24 inference(modus_ponens,[status(thm)],[1091, 1087])).
% 1.55/1.24 tff(1093,plain,
% 1.55/1.24 ((~hskp7) | c0_1(a1763)),
% 1.55/1.24 inference(modus_ponens,[status(thm)],[1092, 1087])).
% 1.55/1.24 tff(1094,plain,
% 1.55/1.24 ((~hskp7) | c0_1(a1763)),
% 1.55/1.24 inference(modus_ponens,[status(thm)],[1093, 1087])).
% 1.55/1.24 tff(1095,plain,
% 1.55/1.24 ((~hskp7) | c0_1(a1763)),
% 1.55/1.24 inference(modus_ponens,[status(thm)],[1094, 1087])).
% 1.55/1.24 tff(1096,plain,
% 1.55/1.24 ((~hskp7) | c0_1(a1763)),
% 1.55/1.24 inference(modus_ponens,[status(thm)],[1095, 1087])).
% 1.55/1.24 tff(1097,plain,
% 1.55/1.24 (c0_1(a1763)),
% 1.55/1.24 inference(unit_resolution,[status(thm)],[1096, 1069])).
% 1.55/1.24 tff(1098,plain,
% 1.55/1.24 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c1_1(a1763) | c2_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | (~c0_1(a1763)) | (~c3_1(a1763)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c1_1(a1763) | c2_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | (~c0_1(a1763)) | (~c3_1(a1763)))),
% 1.55/1.24 inference(rewrite,[status(thm)],[])).
% 1.55/1.24 tff(1099,plain,
% 1.55/1.24 ((hskp11 | (~ndr1_0) | c1_1(a1763) | (~c3_1(a1763)) | (~c0_1(a1763)) | c2_1(a1759) | c0_1(a1759) | (~c1_1(a1759))) <=> (hskp11 | c1_1(a1763) | c2_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | (~c0_1(a1763)) | (~c3_1(a1763)))),
% 1.55/1.24 inference(rewrite,[status(thm)],[])).
% 1.55/1.24 tff(1100,plain,
% 1.55/1.24 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a1763) | (~c3_1(a1763)) | (~c0_1(a1763)) | c2_1(a1759) | c0_1(a1759) | (~c1_1(a1759)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c1_1(a1763) | c2_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | (~c0_1(a1763)) | (~c3_1(a1763))))),
% 1.55/1.24 inference(monotonicity,[status(thm)],[1099])).
% 1.55/1.24 tff(1101,plain,
% 1.55/1.24 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a1763) | (~c3_1(a1763)) | (~c0_1(a1763)) | c2_1(a1759) | c0_1(a1759) | (~c1_1(a1759)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c1_1(a1763) | c2_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | (~c0_1(a1763)) | (~c3_1(a1763)))),
% 1.55/1.24 inference(transitivity,[status(thm)],[1100, 1098])).
% 1.55/1.24 tff(1102,plain,
% 1.55/1.24 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a1763) | (~c3_1(a1763)) | (~c0_1(a1763)) | c2_1(a1759) | c0_1(a1759) | (~c1_1(a1759)))),
% 1.55/1.24 inference(quant_inst,[status(thm)],[])).
% 1.55/1.24 tff(1103,plain,
% 1.55/1.24 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c1_1(a1763) | c2_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | (~c0_1(a1763)) | (~c3_1(a1763))),
% 1.55/1.24 inference(modus_ponens,[status(thm)],[1102, 1101])).
% 1.55/1.24 tff(1104,plain,
% 1.55/1.24 (hskp11),
% 1.55/1.24 inference(unit_resolution,[status(thm)],[1103, 111, 1097, 1086, 911, 1075, 36, 929, 919])).
% 1.55/1.24 tff(1105,plain,
% 1.55/1.24 (((~hskp11) | (~c2_1(a1768))) <=> ((~hskp11) | (~c2_1(a1768)))),
% 1.55/1.24 inference(rewrite,[status(thm)],[])).
% 1.55/1.24 tff(1106,plain,
% 1.55/1.24 (((~c2_1(a1768)) | (~hskp11)) <=> ((~hskp11) | (~c2_1(a1768)))),
% 1.55/1.24 inference(rewrite,[status(thm)],[])).
% 1.55/1.24 tff(1107,axiom,((~c2_1(a1768)) | (~hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause112')).
% 1.55/1.24 tff(1108,plain,
% 1.55/1.24 ((~hskp11) | (~c2_1(a1768))),
% 1.55/1.24 inference(modus_ponens,[status(thm)],[1107, 1106])).
% 1.55/1.24 tff(1109,plain,
% 1.55/1.24 ((~hskp11) | (~c2_1(a1768))),
% 1.55/1.24 inference(modus_ponens,[status(thm)],[1108, 1105])).
% 1.55/1.24 tff(1110,plain,
% 1.55/1.24 (~c2_1(a1768)),
% 1.55/1.24 inference(unit_resolution,[status(thm)],[1109, 1104])).
% 1.55/1.24 tff(1111,plain,
% 1.55/1.24 (((~hskp11) | c0_1(a1768)) <=> ((~hskp11) | c0_1(a1768))),
% 1.55/1.24 inference(rewrite,[status(thm)],[])).
% 1.55/1.24 tff(1112,axiom,((~hskp11) | c0_1(a1768)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause68')).
% 1.55/1.24 tff(1113,plain,
% 1.55/1.24 ((~hskp11) | c0_1(a1768)),
% 1.55/1.24 inference(modus_ponens,[status(thm)],[1112, 1111])).
% 1.55/1.24 tff(1114,plain,
% 1.55/1.24 ((~hskp11) | c0_1(a1768)),
% 1.55/1.24 inference(modus_ponens,[status(thm)],[1113, 1111])).
% 1.55/1.24 tff(1115,plain,
% 1.55/1.24 ((~hskp11) | c0_1(a1768)),
% 1.55/1.24 inference(modus_ponens,[status(thm)],[1114, 1111])).
% 1.55/1.24 tff(1116,plain,
% 1.55/1.24 ((~hskp11) | c0_1(a1768)),
% 1.55/1.24 inference(modus_ponens,[status(thm)],[1115, 1111])).
% 1.55/1.24 tff(1117,plain,
% 1.55/1.24 ((~hskp11) | c0_1(a1768)),
% 1.55/1.24 inference(modus_ponens,[status(thm)],[1116, 1111])).
% 1.55/1.24 tff(1118,plain,
% 1.55/1.24 ((~hskp11) | c0_1(a1768)),
% 1.55/1.24 inference(modus_ponens,[status(thm)],[1117, 1111])).
% 1.55/1.24 tff(1119,plain,
% 1.55/1.24 ((~hskp11) | c0_1(a1768)),
% 1.55/1.24 inference(modus_ponens,[status(thm)],[1118, 1111])).
% 1.55/1.24 tff(1120,plain,
% 1.55/1.24 ((~hskp11) | c0_1(a1768)),
% 1.55/1.24 inference(modus_ponens,[status(thm)],[1119, 1111])).
% 1.55/1.24 tff(1121,plain,
% 1.55/1.24 (c0_1(a1768)),
% 1.55/1.24 inference(unit_resolution,[status(thm)],[1120, 1104])).
% 1.55/1.24 tff(1122,plain,
% 1.55/1.24 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp13 | c2_1(a1768) | (~ndr1_0) | (~c1_1(a1768)) | (~c0_1(a1768)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp19 | hskp13 | c2_1(a1768) | (~ndr1_0) | (~c1_1(a1768)) | (~c0_1(a1768)))),
% 1.55/1.24 inference(rewrite,[status(thm)],[])).
% 1.55/1.24 tff(1123,plain,
% 1.55/1.24 ((hskp19 | hskp13 | (~ndr1_0) | c2_1(a1768) | (~c1_1(a1768)) | (~c0_1(a1768))) <=> (hskp19 | hskp13 | c2_1(a1768) | (~ndr1_0) | (~c1_1(a1768)) | (~c0_1(a1768)))),
% 1.55/1.24 inference(rewrite,[status(thm)],[])).
% 1.55/1.24 tff(1124,plain,
% 1.55/1.24 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | c2_1(a1768) | (~c1_1(a1768)) | (~c0_1(a1768)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp13 | c2_1(a1768) | (~ndr1_0) | (~c1_1(a1768)) | (~c0_1(a1768))))),
% 1.55/1.24 inference(monotonicity,[status(thm)],[1123])).
% 1.55/1.24 tff(1125,plain,
% 1.55/1.24 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | c2_1(a1768) | (~c1_1(a1768)) | (~c0_1(a1768)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp19 | hskp13 | c2_1(a1768) | (~ndr1_0) | (~c1_1(a1768)) | (~c0_1(a1768)))),
% 1.55/1.24 inference(transitivity,[status(thm)],[1124, 1122])).
% 1.55/1.24 tff(1126,plain,
% 1.55/1.24 ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | c2_1(a1768) | (~c1_1(a1768)) | (~c0_1(a1768)))),
% 1.55/1.24 inference(quant_inst,[status(thm)],[])).
% 1.55/1.24 tff(1127,plain,
% 1.55/1.24 ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp19 | hskp13 | c2_1(a1768) | (~ndr1_0) | (~c1_1(a1768)) | (~c0_1(a1768))),
% 1.55/1.24 inference(modus_ponens,[status(thm)],[1126, 1125])).
% 1.55/1.24 tff(1128,plain,
% 1.55/1.24 (~c1_1(a1768)),
% 1.55/1.24 inference(unit_resolution,[status(thm)],[1127, 111, 12, 23, 1121, 1110, 33])).
% 1.55/1.24 tff(1129,plain,
% 1.55/1.24 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))))),
% 1.55/1.24 inference(bind,[status(th)],[])).
% 1.55/1.24 tff(1130,plain,
% 1.55/1.24 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.55/1.24 inference(quant_intro,[status(thm)],[1129])).
% 1.55/1.24 tff(1131,plain,
% 1.55/1.24 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.55/1.24 inference(rewrite,[status(thm)],[])).
% 1.55/1.24 tff(1132,plain,
% 1.55/1.24 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(W)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(W))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W)))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))))),
% 1.55/1.24 inference(bind,[status(th)],[])).
% 1.55/1.24 tff(1133,plain,
% 1.55/1.24 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.55/1.24 inference(quant_intro,[status(thm)],[1132])).
% 1.55/1.24 tff(1134,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause194')).
% 1.55/1.24 tff(1135,plain,
% 1.55/1.24 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.55/1.24 inference(modus_ponens,[status(thm)],[1134, 1133])).
% 1.55/1.24 tff(1136,plain,
% 1.55/1.24 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.55/1.24 inference(modus_ponens,[status(thm)],[1135, 1131])).
% 1.55/1.24 tff(1137,plain,(
% 1.55/1.24 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.55/1.24 inference(skolemize,[status(sab)],[1136])).
% 1.55/1.24 tff(1138,plain,
% 1.55/1.24 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.55/1.24 inference(modus_ponens,[status(thm)],[1137, 1130])).
% 1.55/1.24 tff(1139,plain,
% 1.55/1.24 (^[V: $i, U: $i] : refl((hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))))),
% 1.55/1.24 inference(bind,[status(th)],[])).
% 1.55/1.24 tff(1140,plain,
% 1.55/1.24 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.55/1.24 inference(quant_intro,[status(thm)],[1139])).
% 1.55/1.24 tff(1141,plain,
% 1.55/1.24 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.55/1.24 inference(rewrite,[status(thm)],[])).
% 1.55/1.24 tff(1142,plain,
% 1.55/1.24 (^[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) | (~c2_1(U)) | (~c3_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp17) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) | hskp17))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) | hskp17) <=> (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp17) <=> (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))))),
% 1.55/1.25 inference(bind,[status(th)],[])).
% 1.55/1.25 tff(1143,plain,
% 1.55/1.25 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp17) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.55/1.25 inference(quant_intro,[status(thm)],[1142])).
% 1.55/1.25 tff(1144,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c1_1(U)) | c0_1(V)) | c3_1(V)) | hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause168')).
% 1.55/1.25 tff(1145,plain,
% 1.55/1.25 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[1144, 1143])).
% 1.55/1.25 tff(1146,plain,
% 1.55/1.25 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[1145, 1141])).
% 1.55/1.25 tff(1147,plain,(
% 1.55/1.25 ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.55/1.25 inference(skolemize,[status(sab)],[1146])).
% 1.55/1.25 tff(1148,plain,
% 1.55/1.25 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[1147, 1140])).
% 1.55/1.25 tff(1149,plain,
% 1.55/1.25 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp17 | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp17 | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762))),
% 1.55/1.25 inference(rewrite,[status(thm)],[])).
% 1.55/1.25 tff(1150,plain,
% 1.55/1.25 ((hskp17 | (~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c0_1(a1759) | c3_1(a1759) | (~c1_1(a1759))) <=> (hskp17 | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762))),
% 1.55/1.25 inference(rewrite,[status(thm)],[])).
% 1.55/1.25 tff(1151,plain,
% 1.55/1.25 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c0_1(a1759) | c3_1(a1759) | (~c1_1(a1759)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp17 | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762)))),
% 1.55/1.25 inference(monotonicity,[status(thm)],[1150])).
% 1.55/1.25 tff(1152,plain,
% 1.55/1.25 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c0_1(a1759) | c3_1(a1759) | (~c1_1(a1759)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp17 | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762))),
% 1.55/1.25 inference(transitivity,[status(thm)],[1151, 1149])).
% 1.55/1.25 tff(1153,plain,
% 1.55/1.25 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c0_1(a1759) | c3_1(a1759) | (~c1_1(a1759)))),
% 1.55/1.25 inference(quant_inst,[status(thm)],[])).
% 1.55/1.25 tff(1154,plain,
% 1.55/1.25 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp17 | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[1153, 1152])).
% 1.55/1.25 tff(1155,plain,
% 1.55/1.25 (hskp17),
% 1.55/1.25 inference(unit_resolution,[status(thm)],[1154, 111, 1050, 1062, 911, 34, 1148, 919, 1051])).
% 1.55/1.25 tff(1156,plain,
% 1.55/1.25 (((~hskp17) | (~c1_1(a1781))) <=> ((~hskp17) | (~c1_1(a1781)))),
% 1.55/1.25 inference(rewrite,[status(thm)],[])).
% 1.55/1.25 tff(1157,plain,
% 1.55/1.25 (((~c1_1(a1781)) | (~hskp17)) <=> ((~hskp17) | (~c1_1(a1781)))),
% 1.55/1.25 inference(rewrite,[status(thm)],[])).
% 1.55/1.25 tff(1158,axiom,((~c1_1(a1781)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause103')).
% 1.55/1.25 tff(1159,plain,
% 1.55/1.25 ((~hskp17) | (~c1_1(a1781))),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[1158, 1157])).
% 1.55/1.25 tff(1160,plain,
% 1.55/1.25 ((~hskp17) | (~c1_1(a1781))),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[1159, 1156])).
% 1.55/1.25 tff(1161,plain,
% 1.55/1.25 (~c1_1(a1781)),
% 1.55/1.25 inference(unit_resolution,[status(thm)],[1160, 1155])).
% 1.55/1.25 tff(1162,plain,
% 1.55/1.25 (((~hskp11) | c3_1(a1768)) <=> ((~hskp11) | c3_1(a1768))),
% 1.55/1.25 inference(rewrite,[status(thm)],[])).
% 1.55/1.25 tff(1163,axiom,((~hskp11) | c3_1(a1768)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause69')).
% 1.55/1.25 tff(1164,plain,
% 1.55/1.25 ((~hskp11) | c3_1(a1768)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[1163, 1162])).
% 1.55/1.25 tff(1165,plain,
% 1.55/1.25 ((~hskp11) | c3_1(a1768)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[1164, 1162])).
% 1.55/1.25 tff(1166,plain,
% 1.55/1.25 ((~hskp11) | c3_1(a1768)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[1165, 1162])).
% 1.55/1.25 tff(1167,plain,
% 1.55/1.25 ((~hskp11) | c3_1(a1768)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[1166, 1162])).
% 1.55/1.25 tff(1168,plain,
% 1.55/1.25 ((~hskp11) | c3_1(a1768)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[1167, 1162])).
% 1.55/1.25 tff(1169,plain,
% 1.55/1.25 ((~hskp11) | c3_1(a1768)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[1168, 1162])).
% 1.55/1.25 tff(1170,plain,
% 1.55/1.25 ((~hskp11) | c3_1(a1768)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[1169, 1162])).
% 1.55/1.25 tff(1171,plain,
% 1.55/1.25 ((~hskp11) | c3_1(a1768)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[1170, 1162])).
% 1.55/1.25 tff(1172,plain,
% 1.55/1.25 (c3_1(a1768)),
% 1.55/1.25 inference(unit_resolution,[status(thm)],[1171, 1104])).
% 1.55/1.25 tff(1173,plain,
% 1.55/1.25 (((~hskp17) | c3_1(a1781)) <=> ((~hskp17) | c3_1(a1781))),
% 1.55/1.25 inference(rewrite,[status(thm)],[])).
% 1.55/1.25 tff(1174,axiom,((~hskp17) | c3_1(a1781)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause60')).
% 1.55/1.25 tff(1175,plain,
% 1.55/1.25 ((~hskp17) | c3_1(a1781)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[1174, 1173])).
% 1.55/1.25 tff(1176,plain,
% 1.55/1.25 ((~hskp17) | c3_1(a1781)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[1175, 1173])).
% 1.55/1.25 tff(1177,plain,
% 1.55/1.25 ((~hskp17) | c3_1(a1781)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[1176, 1173])).
% 1.55/1.25 tff(1178,plain,
% 1.55/1.25 ((~hskp17) | c3_1(a1781)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[1177, 1173])).
% 1.55/1.25 tff(1179,plain,
% 1.55/1.25 ((~hskp17) | c3_1(a1781)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[1178, 1173])).
% 1.55/1.25 tff(1180,plain,
% 1.55/1.25 ((~hskp17) | c3_1(a1781)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[1179, 1173])).
% 1.55/1.25 tff(1181,plain,
% 1.55/1.25 ((~hskp17) | c3_1(a1781)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[1180, 1173])).
% 1.55/1.25 tff(1182,plain,
% 1.55/1.25 ((~hskp17) | c3_1(a1781)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[1181, 1173])).
% 1.55/1.25 tff(1183,plain,
% 1.55/1.25 (c3_1(a1781)),
% 1.55/1.25 inference(unit_resolution,[status(thm)],[1182, 1155])).
% 1.55/1.25 tff(1184,plain,
% 1.55/1.25 (((~hskp17) | c2_1(a1781)) <=> ((~hskp17) | c2_1(a1781))),
% 1.55/1.25 inference(rewrite,[status(thm)],[])).
% 1.55/1.25 tff(1185,axiom,((~hskp17) | c2_1(a1781)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause59')).
% 1.55/1.25 tff(1186,plain,
% 1.55/1.25 ((~hskp17) | c2_1(a1781)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[1185, 1184])).
% 1.55/1.25 tff(1187,plain,
% 1.55/1.25 ((~hskp17) | c2_1(a1781)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[1186, 1184])).
% 1.55/1.25 tff(1188,plain,
% 1.55/1.25 ((~hskp17) | c2_1(a1781)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[1187, 1184])).
% 1.55/1.25 tff(1189,plain,
% 1.55/1.25 ((~hskp17) | c2_1(a1781)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[1188, 1184])).
% 1.55/1.25 tff(1190,plain,
% 1.55/1.25 ((~hskp17) | c2_1(a1781)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[1189, 1184])).
% 1.55/1.25 tff(1191,plain,
% 1.55/1.25 ((~hskp17) | c2_1(a1781)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[1190, 1184])).
% 1.55/1.25 tff(1192,plain,
% 1.55/1.25 ((~hskp17) | c2_1(a1781)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[1191, 1184])).
% 1.55/1.25 tff(1193,plain,
% 1.55/1.25 ((~hskp17) | c2_1(a1781)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[1192, 1184])).
% 1.55/1.25 tff(1194,plain,
% 1.55/1.25 (c2_1(a1781)),
% 1.55/1.25 inference(unit_resolution,[status(thm)],[1193, 1155])).
% 1.55/1.25 tff(1195,plain,
% 1.55/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a1781) | c2_1(a1768) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1768) | (~c3_1(a1768)) | (~c2_1(a1781)) | (~c3_1(a1781)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a1781) | c2_1(a1768) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1768) | (~c3_1(a1768)) | (~c2_1(a1781)) | (~c3_1(a1781)))),
% 1.55/1.25 inference(rewrite,[status(thm)],[])).
% 1.55/1.25 tff(1196,plain,
% 1.55/1.25 (((~ndr1_0) | c1_1(a1781) | (~c2_1(a1781)) | (~c3_1(a1781)) | c2_1(a1768) | c1_1(a1768) | (~c3_1(a1768)) | c0_1(a1762) | (~c3_1(a1762)) | (~c2_1(a1762))) <=> (c1_1(a1781) | c2_1(a1768) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1768) | (~c3_1(a1768)) | (~c2_1(a1781)) | (~c3_1(a1781)))),
% 1.55/1.25 inference(rewrite,[status(thm)],[])).
% 1.55/1.25 tff(1197,plain,
% 1.55/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1781) | (~c2_1(a1781)) | (~c3_1(a1781)) | c2_1(a1768) | c1_1(a1768) | (~c3_1(a1768)) | c0_1(a1762) | (~c3_1(a1762)) | (~c2_1(a1762)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a1781) | c2_1(a1768) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1768) | (~c3_1(a1768)) | (~c2_1(a1781)) | (~c3_1(a1781))))),
% 1.55/1.25 inference(monotonicity,[status(thm)],[1196])).
% 1.55/1.25 tff(1198,plain,
% 1.55/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1781) | (~c2_1(a1781)) | (~c3_1(a1781)) | c2_1(a1768) | c1_1(a1768) | (~c3_1(a1768)) | c0_1(a1762) | (~c3_1(a1762)) | (~c2_1(a1762)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a1781) | c2_1(a1768) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1768) | (~c3_1(a1768)) | (~c2_1(a1781)) | (~c3_1(a1781)))),
% 1.55/1.25 inference(transitivity,[status(thm)],[1197, 1195])).
% 1.55/1.25 tff(1199,plain,
% 1.55/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1781) | (~c2_1(a1781)) | (~c3_1(a1781)) | c2_1(a1768) | c1_1(a1768) | (~c3_1(a1768)) | c0_1(a1762) | (~c3_1(a1762)) | (~c2_1(a1762)))),
% 1.55/1.25 inference(quant_inst,[status(thm)],[])).
% 1.55/1.25 tff(1200,plain,
% 1.55/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a1781) | c2_1(a1768) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1768) | (~c3_1(a1768)) | (~c2_1(a1781)) | (~c3_1(a1781))),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[1199, 1198])).
% 1.55/1.25 tff(1201,plain,
% 1.55/1.25 ($false),
% 1.55/1.25 inference(unit_resolution,[status(thm)],[1200, 111, 1194, 1183, 1172, 1050, 1062, 1161, 1110, 1049, 1138, 1128])).
% 1.55/1.25 tff(1202,plain,(c2_1(a1759) | hskp19 | hskp13 | c3_1(a1759)), inference(lemma,lemma(discharge,[]))).
% 1.55/1.25 tff(1203,plain,
% 1.55/1.25 (c2_1(a1759)),
% 1.55/1.25 inference(unit_resolution,[status(thm)],[1202, 23, 12, 34])).
% 1.55/1.25 tff(1204,plain,
% 1.55/1.25 (((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | (~c2_1(a1759)) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp13 | (~c2_1(a1759)) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759))),
% 1.55/1.25 inference(rewrite,[status(thm)],[])).
% 1.55/1.25 tff(1205,plain,
% 1.55/1.25 ((hskp13 | (~ndr1_0) | c0_1(a1759) | (~c2_1(a1759)) | (~c1_1(a1759))) <=> (hskp13 | (~c2_1(a1759)) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759))),
% 1.55/1.25 inference(rewrite,[status(thm)],[])).
% 1.55/1.25 tff(1206,plain,
% 1.55/1.25 (((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | (~ndr1_0) | c0_1(a1759) | (~c2_1(a1759)) | (~c1_1(a1759)))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | (~c2_1(a1759)) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759)))),
% 1.55/1.25 inference(monotonicity,[status(thm)],[1205])).
% 1.55/1.25 tff(1207,plain,
% 1.55/1.25 (((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | (~ndr1_0) | c0_1(a1759) | (~c2_1(a1759)) | (~c1_1(a1759)))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp13 | (~c2_1(a1759)) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759))),
% 1.55/1.25 inference(transitivity,[status(thm)],[1206, 1204])).
% 1.55/1.25 tff(1208,plain,
% 1.55/1.25 ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | (~ndr1_0) | c0_1(a1759) | (~c2_1(a1759)) | (~c1_1(a1759)))),
% 1.55/1.25 inference(quant_inst,[status(thm)],[])).
% 1.55/1.25 tff(1209,plain,
% 1.55/1.25 ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp13 | (~c2_1(a1759)) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759)),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[1208, 1207])).
% 1.55/1.25 tff(1210,plain,
% 1.55/1.25 (hskp13 | (~c2_1(a1759)) | c0_1(a1759)),
% 1.55/1.25 inference(unit_resolution,[status(thm)],[1209, 111, 911, 22])).
% 1.55/1.25 tff(1211,plain,
% 1.55/1.25 (c0_1(a1759)),
% 1.55/1.25 inference(unit_resolution,[status(thm)],[1210, 1203, 23])).
% 1.55/1.25 tff(1212,plain,
% 1.55/1.25 (~hskp4),
% 1.55/1.25 inference(unit_resolution,[status(thm)],[950, 1203])).
% 1.55/1.25 tff(1213,plain,
% 1.55/1.25 (hskp8 | hskp4),
% 1.55/1.25 inference(unit_resolution,[status(thm)],[320, 111, 1050, 1062, 1049, 130])).
% 1.55/1.25 tff(1214,plain,
% 1.55/1.25 (hskp8),
% 1.55/1.25 inference(unit_resolution,[status(thm)],[1213, 1212])).
% 1.55/1.25 tff(1215,plain,
% 1.55/1.25 (~c1_1(a1765)),
% 1.55/1.25 inference(unit_resolution,[status(thm)],[326, 1214])).
% 1.55/1.25 tff(1216,plain,
% 1.55/1.25 (c2_1(a1765)),
% 1.55/1.25 inference(unit_resolution,[status(thm)],[444, 1214])).
% 1.55/1.25 tff(1217,plain,
% 1.55/1.25 (c0_1(a1765)),
% 1.55/1.25 inference(unit_resolution,[status(thm)],[455, 1214])).
% 1.55/1.25 tff(1218,plain,
% 1.55/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c1_1(a1765) | (~c2_1(a1759)) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c2_1(a1765)) | (~c0_1(a1765)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c1_1(a1765) | (~c2_1(a1759)) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c2_1(a1765)) | (~c0_1(a1765)))),
% 1.55/1.25 inference(rewrite,[status(thm)],[])).
% 1.55/1.25 tff(1219,plain,
% 1.55/1.25 (((~ndr1_0) | (~c2_1(a1759)) | (~c1_1(a1759)) | (~c0_1(a1759)) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765))) <=> (c1_1(a1765) | (~c2_1(a1759)) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c2_1(a1765)) | (~c0_1(a1765)))),
% 1.55/1.25 inference(rewrite,[status(thm)],[])).
% 1.55/1.25 tff(1220,plain,
% 1.55/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1759)) | (~c1_1(a1759)) | (~c0_1(a1759)) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c1_1(a1765) | (~c2_1(a1759)) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c2_1(a1765)) | (~c0_1(a1765))))),
% 1.55/1.25 inference(monotonicity,[status(thm)],[1219])).
% 1.55/1.25 tff(1221,plain,
% 1.55/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1759)) | (~c1_1(a1759)) | (~c0_1(a1759)) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c1_1(a1765) | (~c2_1(a1759)) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c2_1(a1765)) | (~c0_1(a1765)))),
% 1.55/1.25 inference(transitivity,[status(thm)],[1220, 1218])).
% 1.55/1.25 tff(1222,plain,
% 1.55/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1759)) | (~c1_1(a1759)) | (~c0_1(a1759)) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)))),
% 1.55/1.25 inference(quant_inst,[status(thm)],[])).
% 1.55/1.25 tff(1223,plain,
% 1.55/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c1_1(a1765) | (~c2_1(a1759)) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c2_1(a1765)) | (~c0_1(a1765))),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[1222, 1221])).
% 1.55/1.25 tff(1224,plain,
% 1.55/1.25 ($false),
% 1.55/1.25 inference(unit_resolution,[status(thm)],[1223, 111, 1217, 1216, 911, 1215, 1203, 34, 802, 1211])).
% 1.55/1.25 tff(1225,plain,(hskp13 | c3_1(a1759) | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.55/1.25 tff(1226,plain,
% 1.55/1.25 (hskp13),
% 1.55/1.25 inference(unit_resolution,[status(thm)],[1225, 34, 12])).
% 1.55/1.25 tff(1227,plain,
% 1.55/1.25 (c1_1(a1771)),
% 1.55/1.25 inference(unit_resolution,[status(thm)],[252, 1226])).
% 1.55/1.25 tff(1228,plain,
% 1.55/1.25 (~c0_1(a1771)),
% 1.55/1.25 inference(unit_resolution,[status(thm)],[238, 242])).
% 1.55/1.25 tff(1229,plain,
% 1.55/1.25 (hskp3),
% 1.55/1.25 inference(unit_resolution,[status(thm)],[285, 240, 1228, 242])).
% 1.55/1.25 tff(1230,plain,
% 1.55/1.25 (~c3_1(a1758)),
% 1.55/1.25 inference(unit_resolution,[status(thm)],[638, 1229])).
% 1.55/1.25 tff(1231,plain,
% 1.55/1.25 (c1_1(a1758)),
% 1.55/1.25 inference(unit_resolution,[status(thm)],[624, 1229])).
% 1.55/1.25 tff(1232,plain,
% 1.55/1.25 (c2_1(a1758)),
% 1.55/1.25 inference(unit_resolution,[status(thm)],[613, 1229])).
% 1.55/1.25 tff(1233,plain,
% 1.55/1.25 ($false),
% 1.55/1.25 inference(unit_resolution,[status(thm)],[731, 1232, 1231, 253, 264, 240, 1230, 12, 1228])).
% 1.55/1.25 tff(1234,plain,(hskp6 | hskp19 | (~hskp13)), inference(lemma,lemma(discharge,[]))).
% 1.55/1.25 tff(1235,plain,
% 1.55/1.25 (hskp6),
% 1.55/1.25 inference(unit_resolution,[status(thm)],[1234, 1226, 12])).
% 1.55/1.25 tff(1236,plain,
% 1.55/1.25 (~c0_1(a1762)),
% 1.55/1.25 inference(unit_resolution,[status(thm)],[291, 1235])).
% 1.55/1.25 tff(1237,plain,
% 1.55/1.25 (c3_1(a1762)),
% 1.55/1.25 inference(unit_resolution,[status(thm)],[302, 1235])).
% 1.55/1.25 tff(1238,plain,
% 1.55/1.25 (c2_1(a1762)),
% 1.55/1.25 inference(unit_resolution,[status(thm)],[313, 1235])).
% 1.55/1.25 tff(1239,plain,
% 1.55/1.25 (~c0_1(a1771)),
% 1.55/1.25 inference(unit_resolution,[status(thm)],[238, 1226])).
% 1.55/1.25 tff(1240,plain,
% 1.55/1.25 (c2_1(a1771)),
% 1.55/1.25 inference(unit_resolution,[status(thm)],[263, 1226])).
% 1.55/1.25 tff(1241,assumption,(hskp22), introduced(assumption)).
% 1.55/1.25 tff(1242,plain,
% 1.55/1.25 (~c2_1(a1799)),
% 1.55/1.25 inference(unit_resolution,[status(thm)],[542, 1241])).
% 1.55/1.25 tff(1243,plain,
% 1.55/1.25 (c3_1(a1799)),
% 1.55/1.25 inference(unit_resolution,[status(thm)],[559, 1241])).
% 1.55/1.25 tff(1244,plain,
% 1.55/1.25 (~c0_1(a1799)),
% 1.55/1.25 inference(unit_resolution,[status(thm)],[548, 1241])).
% 1.55/1.25 tff(1245,assumption,(~c1_1(a1762)), introduced(assumption)).
% 1.55/1.25 tff(1246,assumption,(~c2_1(a1799)), introduced(assumption)).
% 1.55/1.25 tff(1247,assumption,(c3_1(a1799)), introduced(assumption)).
% 1.55/1.25 tff(1248,plain,
% 1.55/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a1799) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | c1_1(a1799) | (~c3_1(a1799)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1799) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | c1_1(a1799) | (~c3_1(a1799)))),
% 1.55/1.25 inference(rewrite,[status(thm)],[])).
% 1.55/1.25 tff(1249,plain,
% 1.55/1.25 (((~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c2_1(a1799) | c1_1(a1799) | (~c3_1(a1799)) | c0_1(a1762) | (~c3_1(a1762)) | (~c2_1(a1762))) <=> (c2_1(a1799) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | c1_1(a1799) | (~c3_1(a1799)))),
% 1.55/1.25 inference(rewrite,[status(thm)],[])).
% 1.55/1.25 tff(1250,plain,
% 1.55/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c2_1(a1799) | c1_1(a1799) | (~c3_1(a1799)) | c0_1(a1762) | (~c3_1(a1762)) | (~c2_1(a1762)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a1799) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | c1_1(a1799) | (~c3_1(a1799))))),
% 1.55/1.25 inference(monotonicity,[status(thm)],[1249])).
% 1.55/1.25 tff(1251,plain,
% 1.55/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c2_1(a1799) | c1_1(a1799) | (~c3_1(a1799)) | c0_1(a1762) | (~c3_1(a1762)) | (~c2_1(a1762)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1799) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | c1_1(a1799) | (~c3_1(a1799)))),
% 1.55/1.25 inference(transitivity,[status(thm)],[1250, 1248])).
% 1.55/1.25 tff(1252,plain,
% 1.55/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c2_1(a1799) | c1_1(a1799) | (~c3_1(a1799)) | c0_1(a1762) | (~c3_1(a1762)) | (~c2_1(a1762)))),
% 1.55/1.25 inference(quant_inst,[status(thm)],[])).
% 1.55/1.25 tff(1253,plain,
% 1.55/1.25 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1799) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | c1_1(a1799) | (~c3_1(a1799))),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[1252, 1251])).
% 1.55/1.25 tff(1254,plain,
% 1.55/1.25 (c1_1(a1799)),
% 1.55/1.25 inference(unit_resolution,[status(thm)],[1253, 111, 1247, 404, 423, 1246, 403, 1138, 1245])).
% 1.55/1.25 tff(1255,assumption,(~c0_1(a1799)), introduced(assumption)).
% 1.55/1.25 tff(1256,plain,
% 1.55/1.25 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a1799) | c2_1(a1799) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c1_1(a1799)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a1799) | c2_1(a1799) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c1_1(a1799)))),
% 1.55/1.25 inference(rewrite,[status(thm)],[])).
% 1.55/1.25 tff(1257,plain,
% 1.55/1.25 ((hskp7 | (~ndr1_0) | c2_1(a1799) | c0_1(a1799) | (~c1_1(a1799)) | c1_1(a1762) | c0_1(a1762) | (~c3_1(a1762))) <=> (hskp7 | c0_1(a1799) | c2_1(a1799) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c1_1(a1799)))),
% 1.55/1.25 inference(rewrite,[status(thm)],[])).
% 1.55/1.25 tff(1258,plain,
% 1.55/1.25 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1799) | c0_1(a1799) | (~c1_1(a1799)) | c1_1(a1762) | c0_1(a1762) | (~c3_1(a1762)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a1799) | c2_1(a1799) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c1_1(a1799))))),
% 1.55/1.25 inference(monotonicity,[status(thm)],[1257])).
% 1.55/1.25 tff(1259,plain,
% 1.55/1.25 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1799) | c0_1(a1799) | (~c1_1(a1799)) | c1_1(a1762) | c0_1(a1762) | (~c3_1(a1762)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a1799) | c2_1(a1799) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c1_1(a1799)))),
% 1.55/1.25 inference(transitivity,[status(thm)],[1258, 1256])).
% 1.55/1.25 tff(1260,plain,
% 1.55/1.25 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1799) | c0_1(a1799) | (~c1_1(a1799)) | c1_1(a1762) | c0_1(a1762) | (~c3_1(a1762)))),
% 1.55/1.25 inference(quant_inst,[status(thm)],[])).
% 1.55/1.25 tff(1261,plain,
% 1.55/1.25 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a1799) | c2_1(a1799) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c1_1(a1799))),
% 1.55/1.25 inference(modus_ponens,[status(thm)],[1260, 1259])).
% 1.55/1.25 tff(1262,plain,
% 1.55/1.25 (hskp7),
% 1.55/1.25 inference(unit_resolution,[status(thm)],[1261, 111, 423, 1255, 1246, 403, 1061, 1245, 1254])).
% 1.55/1.25 tff(1263,plain,
% 1.55/1.25 (~c1_1(a1763)),
% 1.55/1.25 inference(unit_resolution,[status(thm)],[1074, 1262])).
% 1.55/1.25 tff(1264,assumption,(hskp7), introduced(assumption)).
% 1.55/1.25 tff(1265,plain,
% 1.55/1.25 (c0_1(a1763)),
% 1.55/1.25 inference(unit_resolution,[status(thm)],[1096, 1264])).
% 1.55/1.25 tff(1266,plain,
% 1.55/1.25 (c3_1(a1763)),
% 1.55/1.25 inference(unit_resolution,[status(thm)],[1085, 1264])).
% 1.55/1.25 tff(1267,assumption,(~c3_1(a1771)), introduced(assumption)).
% 1.55/1.25 tff(1268,assumption,(~c1_1(a1763)), introduced(assumption)).
% 1.55/1.25 tff(1269,plain,
% 1.55/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1771) | c1_1(a1763) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | (~c0_1(a1763)) | (~c3_1(a1763)) | c3_1(a1771) | (~c2_1(a1771)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1771) | c1_1(a1763) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | (~c0_1(a1763)) | (~c3_1(a1763)) | c3_1(a1771) | (~c2_1(a1771)))),
% 1.55/1.25 inference(rewrite,[status(thm)],[])).
% 1.55/1.25 tff(1270,plain,
% 1.55/1.25 (((~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c1_1(a1763) | (~c3_1(a1763)) | (~c0_1(a1763)) | c3_1(a1771) | c0_1(a1771) | (~c2_1(a1771))) <=> (c0_1(a1771) | c1_1(a1763) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | (~c0_1(a1763)) | (~c3_1(a1763)) | c3_1(a1771) | (~c2_1(a1771)))),
% 1.55/1.25 inference(rewrite,[status(thm)],[])).
% 1.55/1.25 tff(1271,plain,
% 1.55/1.25 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c1_1(a1763) | (~c3_1(a1763)) | (~c0_1(a1763)) | c3_1(a1771) | c0_1(a1771) | (~c2_1(a1771)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1771) | c1_1(a1763) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | (~c0_1(a1763)) | (~c3_1(a1763)) | c3_1(a1771) | (~c2_1(a1771))))),
% 1.55/1.26 inference(monotonicity,[status(thm)],[1270])).
% 1.55/1.26 tff(1272,plain,
% 1.55/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c1_1(a1763) | (~c3_1(a1763)) | (~c0_1(a1763)) | c3_1(a1771) | c0_1(a1771) | (~c2_1(a1771)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1771) | c1_1(a1763) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | (~c0_1(a1763)) | (~c3_1(a1763)) | c3_1(a1771) | (~c2_1(a1771)))),
% 1.55/1.26 inference(transitivity,[status(thm)],[1271, 1269])).
% 1.55/1.26 tff(1273,plain,
% 1.55/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c1_1(a1763) | (~c3_1(a1763)) | (~c0_1(a1763)) | c3_1(a1771) | c0_1(a1771) | (~c2_1(a1771)))),
% 1.55/1.26 inference(quant_inst,[status(thm)],[])).
% 1.55/1.26 tff(1274,plain,
% 1.55/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1771) | c1_1(a1763) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | (~c0_1(a1763)) | (~c3_1(a1763)) | c3_1(a1771) | (~c2_1(a1771))),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[1273, 1272])).
% 1.55/1.26 tff(1275,plain,
% 1.55/1.26 ((~c0_1(a1763)) | (~c3_1(a1763))),
% 1.55/1.26 inference(unit_resolution,[status(thm)],[1274, 241, 722, 404, 423, 275, 1268, 819, 1245, 1267])).
% 1.55/1.26 tff(1276,plain,
% 1.55/1.26 ($false),
% 1.55/1.26 inference(unit_resolution,[status(thm)],[1275, 1266, 1265])).
% 1.55/1.26 tff(1277,plain,((~hskp7) | (~ndr1_0) | (~c2_1(a1771)) | (~c2_1(a1762)) | (~c3_1(a1762)) | c0_1(a1771) | c1_1(a1763) | c1_1(a1762) | c3_1(a1771)), inference(lemma,lemma(discharge,[]))).
% 1.55/1.26 tff(1278,plain,
% 1.55/1.26 ((~hskp7) | (~c2_1(a1771)) | (~c2_1(a1762)) | (~c3_1(a1762)) | c0_1(a1771) | c1_1(a1763) | c1_1(a1762) | c3_1(a1771)),
% 1.55/1.26 inference(unit_resolution,[status(thm)],[1277, 111])).
% 1.55/1.26 tff(1279,plain,
% 1.55/1.26 (c3_1(a1771)),
% 1.55/1.26 inference(unit_resolution,[status(thm)],[1278, 1263, 722, 404, 423, 275, 1245, 1262])).
% 1.55/1.26 tff(1280,plain,
% 1.55/1.26 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.55/1.26 inference(bind,[status(th)],[])).
% 1.55/1.26 tff(1281,plain,
% 1.55/1.26 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.55/1.26 inference(quant_intro,[status(thm)],[1280])).
% 1.55/1.26 tff(1282,plain,
% 1.55/1.26 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.55/1.26 inference(rewrite,[status(thm)],[])).
% 1.55/1.26 tff(1283,plain,
% 1.55/1.26 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp8) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp8))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.55/1.26 inference(bind,[status(th)],[])).
% 1.55/1.26 tff(1284,plain,
% 1.55/1.26 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.55/1.26 inference(quant_intro,[status(thm)],[1283])).
% 1.55/1.26 tff(1285,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c0_1(V)) | c1_1(V)) | hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause177')).
% 1.55/1.26 tff(1286,plain,
% 1.55/1.26 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[1285, 1284])).
% 1.55/1.26 tff(1287,plain,
% 1.55/1.26 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[1286, 1282])).
% 1.55/1.26 tff(1288,plain,(
% 1.55/1.26 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.55/1.26 inference(skolemize,[status(sab)],[1287])).
% 1.55/1.26 tff(1289,plain,
% 1.55/1.26 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[1288, 1281])).
% 1.55/1.26 tff(1290,plain,
% 1.55/1.26 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c2_1(a1771)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 1.55/1.26 inference(rewrite,[status(thm)],[])).
% 1.55/1.26 tff(1291,plain,
% 1.55/1.26 ((hskp8 | (~ndr1_0) | (~c2_1(a1771)) | (~c1_1(a1771)) | (~c3_1(a1771)) | c1_1(a1762) | c0_1(a1762) | (~c3_1(a1762))) <=> (hskp8 | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 1.55/1.26 inference(rewrite,[status(thm)],[])).
% 1.55/1.26 tff(1292,plain,
% 1.55/1.26 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1771)) | (~c1_1(a1771)) | (~c3_1(a1771)) | c1_1(a1762) | c0_1(a1762) | (~c3_1(a1762)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c2_1(a1771))))),
% 1.55/1.26 inference(monotonicity,[status(thm)],[1291])).
% 1.55/1.26 tff(1293,plain,
% 1.55/1.26 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1771)) | (~c1_1(a1771)) | (~c3_1(a1771)) | c1_1(a1762) | c0_1(a1762) | (~c3_1(a1762)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 1.55/1.26 inference(transitivity,[status(thm)],[1292, 1290])).
% 1.55/1.26 tff(1294,plain,
% 1.55/1.26 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1771)) | (~c1_1(a1771)) | (~c3_1(a1771)) | c1_1(a1762) | c0_1(a1762) | (~c3_1(a1762)))),
% 1.55/1.26 inference(quant_inst,[status(thm)],[])).
% 1.55/1.26 tff(1295,plain,
% 1.55/1.26 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c2_1(a1771))),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[1294, 1293])).
% 1.55/1.26 tff(1296,plain,
% 1.55/1.26 (hskp8 | (~c3_1(a1771))),
% 1.55/1.26 inference(unit_resolution,[status(thm)],[1295, 111, 712, 722, 423, 403, 1289, 1245])).
% 1.55/1.26 tff(1297,plain,
% 1.55/1.26 (hskp8),
% 1.55/1.26 inference(unit_resolution,[status(thm)],[1296, 1279])).
% 1.55/1.26 tff(1298,plain,
% 1.55/1.26 (~c1_1(a1765)),
% 1.55/1.26 inference(unit_resolution,[status(thm)],[326, 1297])).
% 1.55/1.26 tff(1299,plain,
% 1.55/1.26 (c2_1(a1765)),
% 1.55/1.26 inference(unit_resolution,[status(thm)],[444, 1297])).
% 1.55/1.26 tff(1300,plain,
% 1.55/1.26 (c0_1(a1765)),
% 1.55/1.26 inference(unit_resolution,[status(thm)],[455, 1297])).
% 1.55/1.26 tff(1301,plain,
% 1.55/1.26 ($false),
% 1.55/1.26 inference(unit_resolution,[status(thm)],[464, 111, 712, 722, 1300, 1299, 423, 275, 1298, 403, 46, 1245])).
% 1.55/1.26 tff(1302,plain,(c1_1(a1762) | (~c1_1(a1771)) | (~c2_1(a1771)) | (~c3_1(a1762)) | c0_1(a1771) | c0_1(a1762) | (~c2_1(a1762)) | c0_1(a1799) | c2_1(a1799) | (~c3_1(a1799))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.26 tff(1303,plain,
% 1.55/1.26 (c1_1(a1762)),
% 1.55/1.26 inference(unit_resolution,[status(thm)],[1302, 1244, 722, 423, 275, 403, 404, 712, 1242, 1243])).
% 1.55/1.26 tff(1304,plain,
% 1.55/1.26 (^[V: $i, U: $i] : refl((hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 1.55/1.26 inference(bind,[status(th)],[])).
% 1.55/1.26 tff(1305,plain,
% 1.55/1.26 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.55/1.26 inference(quant_intro,[status(thm)],[1304])).
% 1.55/1.26 tff(1306,plain,
% 1.55/1.26 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.55/1.26 inference(rewrite,[status(thm)],[])).
% 1.55/1.26 tff(1307,plain,
% 1.55/1.26 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp17) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp17))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp17) <=> (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp17) <=> (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 1.55/1.26 inference(bind,[status(th)],[])).
% 1.55/1.26 tff(1308,plain,
% 1.55/1.26 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp17) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.55/1.26 inference(quant_intro,[status(thm)],[1307])).
% 1.55/1.26 tff(1309,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c0_1(V)) | hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause186')).
% 1.55/1.26 tff(1310,plain,
% 1.55/1.26 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[1309, 1308])).
% 1.55/1.26 tff(1311,plain,
% 1.55/1.26 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[1310, 1306])).
% 1.55/1.26 tff(1312,plain,(
% 1.55/1.26 ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.55/1.26 inference(skolemize,[status(sab)],[1311])).
% 1.55/1.26 tff(1313,plain,
% 1.55/1.26 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[1312, 1305])).
% 1.55/1.26 tff(1314,plain,
% 1.55/1.26 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)))),
% 1.55/1.26 inference(rewrite,[status(thm)],[])).
% 1.55/1.26 tff(1315,plain,
% 1.55/1.26 ((hskp17 | (~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1762)) | c0_1(a1762) | (~c3_1(a1762)) | (~c1_1(a1762))) <=> (hskp17 | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)))),
% 1.55/1.26 inference(rewrite,[status(thm)],[])).
% 1.55/1.26 tff(1316,plain,
% 1.55/1.26 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1762)) | c0_1(a1762) | (~c3_1(a1762)) | (~c1_1(a1762)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762))))),
% 1.55/1.26 inference(monotonicity,[status(thm)],[1315])).
% 1.55/1.26 tff(1317,plain,
% 1.55/1.26 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1762)) | c0_1(a1762) | (~c3_1(a1762)) | (~c1_1(a1762)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)))),
% 1.55/1.26 inference(transitivity,[status(thm)],[1316, 1314])).
% 1.55/1.26 tff(1318,plain,
% 1.55/1.26 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1762)) | c0_1(a1762) | (~c3_1(a1762)) | (~c1_1(a1762)))),
% 1.55/1.26 inference(quant_inst,[status(thm)],[])).
% 1.55/1.26 tff(1319,plain,
% 1.55/1.26 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762))),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[1318, 1317])).
% 1.55/1.26 tff(1320,plain,
% 1.55/1.26 (hskp17 | (~c1_1(a1762))),
% 1.55/1.26 inference(unit_resolution,[status(thm)],[1319, 111, 404, 423, 403, 1313])).
% 1.55/1.26 tff(1321,plain,
% 1.55/1.26 (hskp17),
% 1.55/1.26 inference(unit_resolution,[status(thm)],[1320, 1303])).
% 1.55/1.26 tff(1322,plain,
% 1.55/1.26 (c3_1(a1781)),
% 1.55/1.26 inference(unit_resolution,[status(thm)],[1182, 1321])).
% 1.55/1.26 tff(1323,plain,
% 1.55/1.26 (~c1_1(a1781)),
% 1.55/1.26 inference(unit_resolution,[status(thm)],[1160, 1321])).
% 1.55/1.26 tff(1324,plain,
% 1.55/1.26 (c2_1(a1781)),
% 1.55/1.26 inference(unit_resolution,[status(thm)],[1193, 1321])).
% 1.55/1.26 tff(1325,assumption,(c0_1(a1781)), introduced(assumption)).
% 1.55/1.26 tff(1326,plain,
% 1.55/1.26 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))))),
% 1.55/1.26 inference(bind,[status(th)],[])).
% 1.55/1.26 tff(1327,plain,
% 1.55/1.26 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.55/1.26 inference(quant_intro,[status(thm)],[1326])).
% 1.55/1.26 tff(1328,plain,
% 1.55/1.26 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.55/1.26 inference(rewrite,[status(thm)],[])).
% 1.55/1.26 tff(1329,plain,
% 1.55/1.26 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W)))), ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | (~c3_1(W)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))), (((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))))),
% 1.55/1.26 inference(bind,[status(th)],[])).
% 1.55/1.26 tff(1330,plain,
% 1.55/1.26 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.55/1.26 inference(quant_intro,[status(thm)],[1329])).
% 1.55/1.26 tff(1331,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c1_1(V)) | c2_1(V)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause197')).
% 1.55/1.26 tff(1332,plain,
% 1.55/1.26 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[1331, 1330])).
% 1.55/1.26 tff(1333,plain,
% 1.55/1.26 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[1332, 1328])).
% 1.55/1.26 tff(1334,plain,(
% 1.55/1.26 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.55/1.26 inference(skolemize,[status(sab)],[1333])).
% 1.55/1.26 tff(1335,plain,
% 1.55/1.26 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[1334, 1327])).
% 1.55/1.26 tff(1336,assumption,(~c1_1(a1781)), introduced(assumption)).
% 1.55/1.26 tff(1337,assumption,(c3_1(a1781)), introduced(assumption)).
% 1.55/1.26 tff(1338,assumption,(c2_1(a1781)), introduced(assumption)).
% 1.55/1.26 tff(1339,plain,
% 1.55/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a1799) | c1_1(a1781) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c2_1(a1781)) | (~c3_1(a1781)) | c1_1(a1799) | (~c3_1(a1799)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1799) | c1_1(a1781) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c2_1(a1781)) | (~c3_1(a1781)) | c1_1(a1799) | (~c3_1(a1799)))),
% 1.55/1.26 inference(rewrite,[status(thm)],[])).
% 1.55/1.26 tff(1340,plain,
% 1.55/1.26 (((~ndr1_0) | c1_1(a1781) | (~c2_1(a1781)) | (~c3_1(a1781)) | c2_1(a1799) | c1_1(a1799) | (~c3_1(a1799)) | c0_1(a1762) | (~c3_1(a1762)) | (~c2_1(a1762))) <=> (c2_1(a1799) | c1_1(a1781) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c2_1(a1781)) | (~c3_1(a1781)) | c1_1(a1799) | (~c3_1(a1799)))),
% 1.55/1.26 inference(rewrite,[status(thm)],[])).
% 1.55/1.26 tff(1341,plain,
% 1.55/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1781) | (~c2_1(a1781)) | (~c3_1(a1781)) | c2_1(a1799) | c1_1(a1799) | (~c3_1(a1799)) | c0_1(a1762) | (~c3_1(a1762)) | (~c2_1(a1762)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a1799) | c1_1(a1781) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c2_1(a1781)) | (~c3_1(a1781)) | c1_1(a1799) | (~c3_1(a1799))))),
% 1.55/1.26 inference(monotonicity,[status(thm)],[1340])).
% 1.55/1.26 tff(1342,plain,
% 1.55/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1781) | (~c2_1(a1781)) | (~c3_1(a1781)) | c2_1(a1799) | c1_1(a1799) | (~c3_1(a1799)) | c0_1(a1762) | (~c3_1(a1762)) | (~c2_1(a1762)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1799) | c1_1(a1781) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c2_1(a1781)) | (~c3_1(a1781)) | c1_1(a1799) | (~c3_1(a1799)))),
% 1.55/1.26 inference(transitivity,[status(thm)],[1341, 1339])).
% 1.55/1.26 tff(1343,plain,
% 1.55/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1781) | (~c2_1(a1781)) | (~c3_1(a1781)) | c2_1(a1799) | c1_1(a1799) | (~c3_1(a1799)) | c0_1(a1762) | (~c3_1(a1762)) | (~c2_1(a1762)))),
% 1.55/1.26 inference(quant_inst,[status(thm)],[])).
% 1.55/1.26 tff(1344,plain,
% 1.55/1.26 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1799) | c1_1(a1781) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c2_1(a1781)) | (~c3_1(a1781)) | c1_1(a1799) | (~c3_1(a1799))),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[1343, 1342])).
% 1.55/1.26 tff(1345,plain,
% 1.55/1.26 (c1_1(a1799)),
% 1.55/1.26 inference(unit_resolution,[status(thm)],[1344, 111, 1247, 1338, 1337, 404, 423, 1246, 1336, 403, 1138])).
% 1.55/1.26 tff(1346,plain,
% 1.55/1.26 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c0_1(a1799) | c2_1(a1799) | c1_1(a1781) | (~ndr1_0) | (~c0_1(a1781)) | (~c3_1(a1781)) | (~c1_1(a1799)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a1799) | c2_1(a1799) | c1_1(a1781) | (~ndr1_0) | (~c0_1(a1781)) | (~c3_1(a1781)) | (~c1_1(a1799)))),
% 1.55/1.26 inference(rewrite,[status(thm)],[])).
% 1.55/1.26 tff(1347,plain,
% 1.55/1.26 ((hskp11 | (~ndr1_0) | c1_1(a1781) | (~c3_1(a1781)) | (~c0_1(a1781)) | c2_1(a1799) | c0_1(a1799) | (~c1_1(a1799))) <=> (hskp11 | c0_1(a1799) | c2_1(a1799) | c1_1(a1781) | (~ndr1_0) | (~c0_1(a1781)) | (~c3_1(a1781)) | (~c1_1(a1799)))),
% 1.55/1.26 inference(rewrite,[status(thm)],[])).
% 1.55/1.26 tff(1348,plain,
% 1.55/1.26 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a1781) | (~c3_1(a1781)) | (~c0_1(a1781)) | c2_1(a1799) | c0_1(a1799) | (~c1_1(a1799)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c0_1(a1799) | c2_1(a1799) | c1_1(a1781) | (~ndr1_0) | (~c0_1(a1781)) | (~c3_1(a1781)) | (~c1_1(a1799))))),
% 1.55/1.26 inference(monotonicity,[status(thm)],[1347])).
% 1.55/1.26 tff(1349,plain,
% 1.55/1.26 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a1781) | (~c3_1(a1781)) | (~c0_1(a1781)) | c2_1(a1799) | c0_1(a1799) | (~c1_1(a1799)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a1799) | c2_1(a1799) | c1_1(a1781) | (~ndr1_0) | (~c0_1(a1781)) | (~c3_1(a1781)) | (~c1_1(a1799)))),
% 1.55/1.26 inference(transitivity,[status(thm)],[1348, 1346])).
% 1.55/1.26 tff(1350,plain,
% 1.55/1.26 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a1781) | (~c3_1(a1781)) | (~c0_1(a1781)) | c2_1(a1799) | c0_1(a1799) | (~c1_1(a1799)))),
% 1.55/1.26 inference(quant_inst,[status(thm)],[])).
% 1.55/1.26 tff(1351,plain,
% 1.55/1.26 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a1799) | c2_1(a1799) | c1_1(a1781) | (~ndr1_0) | (~c0_1(a1781)) | (~c3_1(a1781)) | (~c1_1(a1799))),
% 1.55/1.26 inference(modus_ponens,[status(thm)],[1350, 1349])).
% 1.55/1.26 tff(1352,plain,
% 1.55/1.26 (hskp11 | (~c0_1(a1781))),
% 1.55/1.26 inference(unit_resolution,[status(thm)],[1351, 111, 1337, 1255, 1246, 1336, 929, 1345])).
% 1.55/1.26 tff(1353,plain,
% 1.55/1.26 (hskp11),
% 1.55/1.26 inference(unit_resolution,[status(thm)],[1352, 1325])).
% 1.55/1.26 tff(1354,plain,
% 1.55/1.26 (~c2_1(a1768)),
% 1.55/1.26 inference(unit_resolution,[status(thm)],[1109, 1353])).
% 1.55/1.26 tff(1355,plain,
% 1.55/1.26 (c0_1(a1768)),
% 1.55/1.26 inference(unit_resolution,[status(thm)],[1120, 1353])).
% 1.55/1.26 tff(1356,plain,
% 1.55/1.26 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a1768) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1768) | (~c0_1(a1768)) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c3_1(a1781)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1768) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1768) | (~c0_1(a1768)) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c3_1(a1781)))),
% 1.55/1.26 inference(rewrite,[status(thm)],[])).
% 1.55/1.26 tff(1357,plain,
% 1.55/1.27 (((~ndr1_0) | (~c2_1(a1781)) | (~c3_1(a1781)) | (~c0_1(a1781)) | c2_1(a1768) | c1_1(a1768) | (~c0_1(a1768)) | c0_1(a1762) | (~c3_1(a1762)) | (~c2_1(a1762))) <=> (c2_1(a1768) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1768) | (~c0_1(a1768)) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c3_1(a1781)))),
% 1.55/1.27 inference(rewrite,[status(thm)],[])).
% 1.55/1.27 tff(1358,plain,
% 1.55/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1781)) | (~c3_1(a1781)) | (~c0_1(a1781)) | c2_1(a1768) | c1_1(a1768) | (~c0_1(a1768)) | c0_1(a1762) | (~c3_1(a1762)) | (~c2_1(a1762)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a1768) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1768) | (~c0_1(a1768)) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c3_1(a1781))))),
% 1.55/1.27 inference(monotonicity,[status(thm)],[1357])).
% 1.55/1.27 tff(1359,plain,
% 1.55/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1781)) | (~c3_1(a1781)) | (~c0_1(a1781)) | c2_1(a1768) | c1_1(a1768) | (~c0_1(a1768)) | c0_1(a1762) | (~c3_1(a1762)) | (~c2_1(a1762)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1768) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1768) | (~c0_1(a1768)) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c3_1(a1781)))),
% 1.55/1.27 inference(transitivity,[status(thm)],[1358, 1356])).
% 1.55/1.27 tff(1360,plain,
% 1.55/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a1781)) | (~c3_1(a1781)) | (~c0_1(a1781)) | c2_1(a1768) | c1_1(a1768) | (~c0_1(a1768)) | c0_1(a1762) | (~c3_1(a1762)) | (~c2_1(a1762)))),
% 1.55/1.27 inference(quant_inst,[status(thm)],[])).
% 1.55/1.27 tff(1361,plain,
% 1.55/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1768) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1768) | (~c0_1(a1768)) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c3_1(a1781))),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[1360, 1359])).
% 1.55/1.27 tff(1362,plain,
% 1.55/1.27 (c1_1(a1768)),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[1361, 111, 1338, 1337, 1355, 404, 423, 1354, 403, 1335, 1325])).
% 1.55/1.27 tff(1363,plain,
% 1.55/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c0_1(a1799) | c1_1(a1781) | c2_1(a1768) | (~ndr1_0) | (~c1_1(a1768)) | (~c0_1(a1768)) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c1_1(a1799)) | (~c3_1(a1799)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a1799) | c1_1(a1781) | c2_1(a1768) | (~ndr1_0) | (~c1_1(a1768)) | (~c0_1(a1768)) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c1_1(a1799)) | (~c3_1(a1799)))),
% 1.55/1.27 inference(rewrite,[status(thm)],[])).
% 1.55/1.27 tff(1364,plain,
% 1.55/1.27 (((~ndr1_0) | c2_1(a1768) | (~c1_1(a1768)) | (~c0_1(a1768)) | c1_1(a1781) | (~c2_1(a1781)) | (~c0_1(a1781)) | c0_1(a1799) | (~c3_1(a1799)) | (~c1_1(a1799))) <=> (c0_1(a1799) | c1_1(a1781) | c2_1(a1768) | (~ndr1_0) | (~c1_1(a1768)) | (~c0_1(a1768)) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c1_1(a1799)) | (~c3_1(a1799)))),
% 1.55/1.27 inference(rewrite,[status(thm)],[])).
% 1.55/1.27 tff(1365,plain,
% 1.55/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1768) | (~c1_1(a1768)) | (~c0_1(a1768)) | c1_1(a1781) | (~c2_1(a1781)) | (~c0_1(a1781)) | c0_1(a1799) | (~c3_1(a1799)) | (~c1_1(a1799)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c0_1(a1799) | c1_1(a1781) | c2_1(a1768) | (~ndr1_0) | (~c1_1(a1768)) | (~c0_1(a1768)) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c1_1(a1799)) | (~c3_1(a1799))))),
% 1.55/1.27 inference(monotonicity,[status(thm)],[1364])).
% 1.55/1.27 tff(1366,plain,
% 1.55/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1768) | (~c1_1(a1768)) | (~c0_1(a1768)) | c1_1(a1781) | (~c2_1(a1781)) | (~c0_1(a1781)) | c0_1(a1799) | (~c3_1(a1799)) | (~c1_1(a1799)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a1799) | c1_1(a1781) | c2_1(a1768) | (~ndr1_0) | (~c1_1(a1768)) | (~c0_1(a1768)) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c1_1(a1799)) | (~c3_1(a1799)))),
% 1.55/1.27 inference(transitivity,[status(thm)],[1365, 1363])).
% 1.55/1.27 tff(1367,plain,
% 1.55/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1768) | (~c1_1(a1768)) | (~c0_1(a1768)) | c1_1(a1781) | (~c2_1(a1781)) | (~c0_1(a1781)) | c0_1(a1799) | (~c3_1(a1799)) | (~c1_1(a1799)))),
% 1.55/1.27 inference(quant_inst,[status(thm)],[])).
% 1.55/1.27 tff(1368,plain,
% 1.55/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a1799) | c1_1(a1781) | c2_1(a1768) | (~ndr1_0) | (~c1_1(a1768)) | (~c0_1(a1768)) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c1_1(a1799)) | (~c3_1(a1799))),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[1367, 1366])).
% 1.55/1.27 tff(1369,plain,
% 1.55/1.27 ($false),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[1368, 111, 1247, 1338, 1355, 1255, 1336, 1354, 475, 1345, 1325, 1362])).
% 1.55/1.27 tff(1370,plain,((~c0_1(a1781)) | (~c3_1(a1799)) | (~c2_1(a1781)) | c0_1(a1799) | c1_1(a1781) | (~c3_1(a1781)) | (~c2_1(a1762)) | (~c3_1(a1762)) | c0_1(a1762) | c2_1(a1799)), inference(lemma,lemma(discharge,[]))).
% 1.55/1.27 tff(1371,plain,
% 1.55/1.27 (~c0_1(a1781)),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[1370, 1243, 1324, 1244, 1323, 1322, 404, 423, 403, 1242])).
% 1.55/1.27 tff(1372,plain,
% 1.55/1.27 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | c1_1(a1781) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)) | c0_1(a1781) | (~c3_1(a1781)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c1_1(a1781) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)) | c0_1(a1781) | (~c3_1(a1781)))),
% 1.55/1.27 inference(rewrite,[status(thm)],[])).
% 1.55/1.27 tff(1373,plain,
% 1.55/1.27 ((hskp8 | (~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1762)) | c1_1(a1781) | c0_1(a1781) | (~c3_1(a1781))) <=> (hskp8 | c1_1(a1781) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)) | c0_1(a1781) | (~c3_1(a1781)))),
% 1.55/1.27 inference(rewrite,[status(thm)],[])).
% 1.55/1.27 tff(1374,plain,
% 1.55/1.27 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1762)) | c1_1(a1781) | c0_1(a1781) | (~c3_1(a1781)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | c1_1(a1781) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)) | c0_1(a1781) | (~c3_1(a1781))))),
% 1.55/1.27 inference(monotonicity,[status(thm)],[1373])).
% 1.55/1.27 tff(1375,plain,
% 1.55/1.27 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1762)) | c1_1(a1781) | c0_1(a1781) | (~c3_1(a1781)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c1_1(a1781) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)) | c0_1(a1781) | (~c3_1(a1781)))),
% 1.55/1.27 inference(transitivity,[status(thm)],[1374, 1372])).
% 1.55/1.27 tff(1376,plain,
% 1.55/1.27 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1762)) | c1_1(a1781) | c0_1(a1781) | (~c3_1(a1781)))),
% 1.55/1.27 inference(quant_inst,[status(thm)],[])).
% 1.55/1.27 tff(1377,plain,
% 1.55/1.27 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c1_1(a1781) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)) | c0_1(a1781) | (~c3_1(a1781))),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[1376, 1375])).
% 1.55/1.27 tff(1378,plain,
% 1.55/1.27 (hskp8 | c0_1(a1781)),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[1377, 111, 1322, 404, 423, 1323, 1289, 1303])).
% 1.55/1.27 tff(1379,plain,
% 1.55/1.27 (hskp8),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[1378, 1371])).
% 1.55/1.27 tff(1380,plain,
% 1.55/1.27 (~c1_1(a1765)),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[326, 1379])).
% 1.55/1.27 tff(1381,plain,
% 1.55/1.27 (c2_1(a1765)),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[444, 1379])).
% 1.55/1.27 tff(1382,plain,
% 1.55/1.27 (c0_1(a1765)),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[455, 1379])).
% 1.55/1.27 tff(1383,plain,
% 1.55/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a1781) | c0_1(a1771) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c1_1(a1771)) | (~c2_1(a1771)) | c0_1(a1781) | (~c3_1(a1781)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1781) | c0_1(a1771) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c1_1(a1771)) | (~c2_1(a1771)) | c0_1(a1781) | (~c3_1(a1781)))),
% 1.55/1.27 inference(rewrite,[status(thm)],[])).
% 1.55/1.27 tff(1384,plain,
% 1.55/1.27 (((~ndr1_0) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)) | c0_1(a1781) | c1_1(a1781) | (~c3_1(a1781))) <=> (c1_1(a1781) | c0_1(a1771) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c1_1(a1771)) | (~c2_1(a1771)) | c0_1(a1781) | (~c3_1(a1781)))),
% 1.55/1.27 inference(rewrite,[status(thm)],[])).
% 1.55/1.27 tff(1385,plain,
% 1.55/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)) | c0_1(a1781) | c1_1(a1781) | (~c3_1(a1781)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a1781) | c0_1(a1771) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c1_1(a1771)) | (~c2_1(a1771)) | c0_1(a1781) | (~c3_1(a1781))))),
% 1.55/1.27 inference(monotonicity,[status(thm)],[1384])).
% 1.55/1.27 tff(1386,plain,
% 1.55/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)) | c0_1(a1781) | c1_1(a1781) | (~c3_1(a1781)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1781) | c0_1(a1771) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c1_1(a1771)) | (~c2_1(a1771)) | c0_1(a1781) | (~c3_1(a1781)))),
% 1.55/1.27 inference(transitivity,[status(thm)],[1385, 1383])).
% 1.55/1.27 tff(1387,plain,
% 1.55/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)) | c0_1(a1781) | c1_1(a1781) | (~c3_1(a1781)))),
% 1.55/1.27 inference(quant_inst,[status(thm)],[])).
% 1.55/1.27 tff(1388,plain,
% 1.55/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1781) | c0_1(a1771) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c1_1(a1771)) | (~c2_1(a1771)) | c0_1(a1781) | (~c3_1(a1781))),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[1387, 1386])).
% 1.55/1.27 tff(1389,plain,
% 1.55/1.27 ($false),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[1388, 111, 1322, 712, 722, 1382, 1381, 1323, 275, 1380, 46, 1371])).
% 1.55/1.27 tff(1390,plain,((~hskp22) | (~c1_1(a1771)) | (~c2_1(a1771)) | c0_1(a1771) | (~c2_1(a1762)) | (~c3_1(a1762)) | c0_1(a1762)), inference(lemma,lemma(discharge,[]))).
% 1.55/1.27 tff(1391,plain,
% 1.55/1.27 (~hskp22),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[1390, 1227, 1240, 1239, 1238, 1237, 1236])).
% 1.55/1.27 tff(1392,plain,
% 1.55/1.27 (hskp8 | hskp4),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[320, 111, 341, 340, 339, 130])).
% 1.55/1.27 tff(1393,plain,
% 1.55/1.27 (hskp8),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[1392, 342])).
% 1.55/1.27 tff(1394,plain,
% 1.55/1.27 (~c1_1(a1765)),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[326, 1393])).
% 1.55/1.27 tff(1395,plain,
% 1.55/1.27 (c2_1(a1765)),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[444, 1393])).
% 1.55/1.27 tff(1396,plain,
% 1.55/1.27 (c0_1(a1765)),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[455, 1393])).
% 1.55/1.27 tff(1397,plain,
% 1.55/1.27 (c1_1(a1762)),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[464, 111, 712, 722, 1396, 1395, 340, 275, 1394, 339, 46])).
% 1.55/1.27 tff(1398,plain,
% 1.55/1.27 (hskp21),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[756, 111, 712, 722, 1396, 1395, 275, 1394, 750])).
% 1.55/1.27 tff(1399,plain,
% 1.55/1.27 (~c3_1(a1788)),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[762, 1398])).
% 1.55/1.27 tff(1400,plain,
% 1.55/1.27 (c2_1(a1788)),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[773, 1398])).
% 1.55/1.27 tff(1401,plain,
% 1.55/1.27 (c0_1(a1788)),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[784, 1398])).
% 1.55/1.27 tff(1402,plain,
% 1.55/1.27 (~c1_1(a1788)),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[791, 111, 1401, 1400, 341, 340, 1399, 678, 1397])).
% 1.55/1.27 tff(1403,plain,
% 1.55/1.27 (hskp22),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[536, 342, 338, 12, 35])).
% 1.55/1.27 tff(1404,plain,
% 1.55/1.27 (~c2_1(a1799)),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[542, 1403])).
% 1.55/1.27 tff(1405,plain,
% 1.55/1.27 (~c0_1(a1799)),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[548, 1403])).
% 1.55/1.27 tff(1406,plain,
% 1.55/1.27 (c3_1(a1799)),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[559, 1403])).
% 1.55/1.27 tff(1407,plain,
% 1.55/1.27 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c0_1(a1799) | c2_1(a1799) | c3_1(a1788) | (~ndr1_0) | c1_1(a1788) | (~c0_1(a1788)) | (~c3_1(a1799)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a1799) | c2_1(a1799) | c3_1(a1788) | (~ndr1_0) | c1_1(a1788) | (~c0_1(a1788)) | (~c3_1(a1799)))),
% 1.55/1.27 inference(rewrite,[status(thm)],[])).
% 1.55/1.27 tff(1408,plain,
% 1.55/1.27 ((hskp10 | (~ndr1_0) | c3_1(a1788) | c1_1(a1788) | (~c0_1(a1788)) | c2_1(a1799) | c0_1(a1799) | (~c3_1(a1799))) <=> (hskp10 | c0_1(a1799) | c2_1(a1799) | c3_1(a1788) | (~ndr1_0) | c1_1(a1788) | (~c0_1(a1788)) | (~c3_1(a1799)))),
% 1.55/1.27 inference(rewrite,[status(thm)],[])).
% 1.55/1.27 tff(1409,plain,
% 1.55/1.27 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c3_1(a1788) | c1_1(a1788) | (~c0_1(a1788)) | c2_1(a1799) | c0_1(a1799) | (~c3_1(a1799)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | c0_1(a1799) | c2_1(a1799) | c3_1(a1788) | (~ndr1_0) | c1_1(a1788) | (~c0_1(a1788)) | (~c3_1(a1799))))),
% 1.55/1.27 inference(monotonicity,[status(thm)],[1408])).
% 1.55/1.27 tff(1410,plain,
% 1.55/1.27 (((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c3_1(a1788) | c1_1(a1788) | (~c0_1(a1788)) | c2_1(a1799) | c0_1(a1799) | (~c3_1(a1799)))) <=> ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a1799) | c2_1(a1799) | c3_1(a1788) | (~ndr1_0) | c1_1(a1788) | (~c0_1(a1788)) | (~c3_1(a1799)))),
% 1.55/1.27 inference(transitivity,[status(thm)],[1409, 1407])).
% 1.55/1.27 tff(1411,plain,
% 1.55/1.27 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp10 | (~ndr1_0) | c3_1(a1788) | c1_1(a1788) | (~c0_1(a1788)) | c2_1(a1799) | c0_1(a1799) | (~c3_1(a1799)))),
% 1.55/1.27 inference(quant_inst,[status(thm)],[])).
% 1.55/1.27 tff(1412,plain,
% 1.55/1.27 ((~![V: $i, U: $i] : (hskp10 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp10 | c0_1(a1799) | c2_1(a1799) | c3_1(a1788) | (~ndr1_0) | c1_1(a1788) | (~c0_1(a1788)) | (~c3_1(a1799))),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[1411, 1410])).
% 1.55/1.27 tff(1413,plain,
% 1.55/1.27 (hskp10),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[1412, 111, 1406, 1401, 1405, 1404, 1399, 337, 1402])).
% 1.55/1.27 tff(1414,plain,
% 1.55/1.27 (~c1_1(a1767)),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[572, 1413])).
% 1.55/1.27 tff(1415,plain,
% 1.55/1.27 (~c0_1(a1767)),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[578, 1413])).
% 1.55/1.27 tff(1416,plain,
% 1.55/1.27 (c3_1(a1767)),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[591, 1413])).
% 1.55/1.27 tff(1417,plain,
% 1.55/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c0_1(a1771) | c0_1(a1767) | c1_1(a1767) | (~ndr1_0) | (~c3_1(a1767)) | (~c1_1(a1771)) | (~c2_1(a1771)) | (~c2_1(a1788)) | c1_1(a1788) | (~c0_1(a1788)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1771) | c0_1(a1767) | c1_1(a1767) | (~ndr1_0) | (~c3_1(a1767)) | (~c1_1(a1771)) | (~c2_1(a1771)) | (~c2_1(a1788)) | c1_1(a1788) | (~c0_1(a1788)))),
% 1.55/1.27 inference(rewrite,[status(thm)],[])).
% 1.55/1.27 tff(1418,plain,
% 1.55/1.27 (((~ndr1_0) | c1_1(a1788) | (~c2_1(a1788)) | (~c0_1(a1788)) | c0_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)) | c0_1(a1767) | c1_1(a1767) | (~c3_1(a1767))) <=> (c0_1(a1771) | c0_1(a1767) | c1_1(a1767) | (~ndr1_0) | (~c3_1(a1767)) | (~c1_1(a1771)) | (~c2_1(a1771)) | (~c2_1(a1788)) | c1_1(a1788) | (~c0_1(a1788)))),
% 1.55/1.27 inference(rewrite,[status(thm)],[])).
% 1.55/1.27 tff(1419,plain,
% 1.55/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1788) | (~c2_1(a1788)) | (~c0_1(a1788)) | c0_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)) | c0_1(a1767) | c1_1(a1767) | (~c3_1(a1767)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c0_1(a1771) | c0_1(a1767) | c1_1(a1767) | (~ndr1_0) | (~c3_1(a1767)) | (~c1_1(a1771)) | (~c2_1(a1771)) | (~c2_1(a1788)) | c1_1(a1788) | (~c0_1(a1788))))),
% 1.55/1.27 inference(monotonicity,[status(thm)],[1418])).
% 1.55/1.27 tff(1420,plain,
% 1.55/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1788) | (~c2_1(a1788)) | (~c0_1(a1788)) | c0_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)) | c0_1(a1767) | c1_1(a1767) | (~c3_1(a1767)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1771) | c0_1(a1767) | c1_1(a1767) | (~ndr1_0) | (~c3_1(a1767)) | (~c1_1(a1771)) | (~c2_1(a1771)) | (~c2_1(a1788)) | c1_1(a1788) | (~c0_1(a1788)))),
% 1.55/1.27 inference(transitivity,[status(thm)],[1419, 1417])).
% 1.55/1.27 tff(1421,plain,
% 1.55/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1788) | (~c2_1(a1788)) | (~c0_1(a1788)) | c0_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)) | c0_1(a1767) | c1_1(a1767) | (~c3_1(a1767)))),
% 1.55/1.27 inference(quant_inst,[status(thm)],[])).
% 1.55/1.27 tff(1422,plain,
% 1.55/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1771) | c0_1(a1767) | c1_1(a1767) | (~ndr1_0) | (~c3_1(a1767)) | (~c1_1(a1771)) | (~c2_1(a1771)) | (~c2_1(a1788)) | c1_1(a1788) | (~c0_1(a1788))),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[1421, 1420])).
% 1.55/1.27 tff(1423,plain,
% 1.55/1.27 ($false),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[1422, 111, 1401, 1400, 712, 722, 1416, 275, 1415, 1414, 46, 1402])).
% 1.55/1.27 tff(1424,plain,(hskp4 | (~c1_1(a1771)) | (~c2_1(a1771)) | c0_1(a1771) | (~hskp6) | hskp19 | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.55/1.27 tff(1425,plain,
% 1.55/1.27 (hskp4),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[1424, 35, 1240, 1239, 1235, 12, 1227])).
% 1.55/1.27 tff(1426,plain,
% 1.55/1.27 (~c2_1(a1759)),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[950, 1425])).
% 1.55/1.27 tff(1427,assumption,(~c0_1(a1759)), introduced(assumption)).
% 1.55/1.27 tff(1428,plain,
% 1.55/1.27 (hskp7),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[1068, 111, 423, 938, 403, 36, 1061, 1427, 1245])).
% 1.55/1.27 tff(1429,plain,
% 1.55/1.27 (~c1_1(a1763)),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[1074, 1428])).
% 1.55/1.27 tff(1430,plain,
% 1.55/1.27 (c3_1(a1771)),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[1278, 1429, 722, 404, 423, 275, 1245, 1428])).
% 1.55/1.27 tff(1431,plain,
% 1.55/1.27 (hskp8),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[1296, 1430])).
% 1.55/1.27 tff(1432,plain,
% 1.55/1.27 (~c1_1(a1765)),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[326, 1431])).
% 1.55/1.27 tff(1433,plain,
% 1.55/1.27 (((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))) | (hskp22 | hskp16 | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c2_1(a1771)))) <=> ((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))) | hskp22 | hskp16 | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 1.55/1.27 inference(rewrite,[status(thm)],[])).
% 1.55/1.27 tff(1434,plain,
% 1.55/1.27 ((hskp22 | hskp16 | (~ndr1_0) | (~c2_1(a1771)) | (~c1_1(a1771)) | (~c3_1(a1771))) <=> (hskp22 | hskp16 | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 1.55/1.27 inference(rewrite,[status(thm)],[])).
% 1.55/1.27 tff(1435,plain,
% 1.55/1.27 (((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))) | (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(a1771)) | (~c1_1(a1771)) | (~c3_1(a1771)))) <=> ((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))) | (hskp22 | hskp16 | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c2_1(a1771))))),
% 1.55/1.27 inference(monotonicity,[status(thm)],[1434])).
% 1.55/1.27 tff(1436,plain,
% 1.55/1.27 (((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))) | (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(a1771)) | (~c1_1(a1771)) | (~c3_1(a1771)))) <=> ((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))) | hskp22 | hskp16 | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 1.55/1.27 inference(transitivity,[status(thm)],[1435, 1433])).
% 1.55/1.27 tff(1437,plain,
% 1.55/1.27 ((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))) | (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(a1771)) | (~c1_1(a1771)) | (~c3_1(a1771)))),
% 1.55/1.27 inference(quant_inst,[status(thm)],[])).
% 1.55/1.27 tff(1438,plain,
% 1.55/1.27 ((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))) | hskp22 | hskp16 | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c2_1(a1771))),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[1437, 1436])).
% 1.55/1.27 tff(1439,plain,
% 1.55/1.27 (hskp22 | hskp16 | (~c3_1(a1771))),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[1438, 111, 712, 722, 485])).
% 1.55/1.27 tff(1440,plain,
% 1.55/1.27 (hskp16),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[1439, 1430, 355])).
% 1.55/1.27 tff(1441,plain,
% 1.55/1.27 (~c2_1(a1780)),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[498, 1440])).
% 1.55/1.27 tff(1442,plain,
% 1.55/1.27 (c2_1(a1765)),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[444, 1431])).
% 1.55/1.27 tff(1443,plain,
% 1.55/1.27 (c0_1(a1765)),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[455, 1431])).
% 1.55/1.27 tff(1444,plain,
% 1.55/1.27 (c1_1(a1780)),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[509, 1440])).
% 1.55/1.27 tff(1445,plain,
% 1.55/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c2_1(a1780) | c0_1(a1771) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c1_1(a1780)) | (~c0_1(a1780)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c2_1(a1780) | c0_1(a1771) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c1_1(a1780)) | (~c0_1(a1780)))),
% 1.55/1.27 inference(rewrite,[status(thm)],[])).
% 1.55/1.27 tff(1446,plain,
% 1.55/1.27 (((~ndr1_0) | c2_1(a1780) | (~c1_1(a1780)) | (~c0_1(a1780)) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1771) | (~c3_1(a1771)) | (~c1_1(a1771))) <=> (c2_1(a1780) | c0_1(a1771) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c1_1(a1780)) | (~c0_1(a1780)))),
% 1.55/1.27 inference(rewrite,[status(thm)],[])).
% 1.55/1.27 tff(1447,plain,
% 1.55/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1780) | (~c1_1(a1780)) | (~c0_1(a1780)) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1771) | (~c3_1(a1771)) | (~c1_1(a1771)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c2_1(a1780) | c0_1(a1771) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c1_1(a1780)) | (~c0_1(a1780))))),
% 1.55/1.27 inference(monotonicity,[status(thm)],[1446])).
% 1.55/1.27 tff(1448,plain,
% 1.55/1.27 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1780) | (~c1_1(a1780)) | (~c0_1(a1780)) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1771) | (~c3_1(a1771)) | (~c1_1(a1771)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c2_1(a1780) | c0_1(a1771) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c1_1(a1780)) | (~c0_1(a1780)))),
% 1.55/1.27 inference(transitivity,[status(thm)],[1447, 1445])).
% 1.55/1.27 tff(1449,plain,
% 1.55/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1780) | (~c1_1(a1780)) | (~c0_1(a1780)) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1771) | (~c3_1(a1771)) | (~c1_1(a1771)))),
% 1.55/1.27 inference(quant_inst,[status(thm)],[])).
% 1.55/1.27 tff(1450,plain,
% 1.55/1.27 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c2_1(a1780) | c0_1(a1771) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c1_1(a1780)) | (~c0_1(a1780))),
% 1.55/1.27 inference(modus_ponens,[status(thm)],[1449, 1448])).
% 1.55/1.27 tff(1451,plain,
% 1.55/1.27 (~c0_1(a1780)),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[1450, 111, 1444, 712, 1443, 1442, 1441, 275, 1432, 475, 1430])).
% 1.55/1.27 tff(1452,plain,
% 1.55/1.27 (c3_1(a1780)),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[527, 1440])).
% 1.55/1.27 tff(1453,plain,
% 1.55/1.27 (hskp27 | hskp22),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[361, 111, 404, 423, 403, 354])).
% 1.55/1.27 tff(1454,plain,
% 1.55/1.27 (hskp27),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[1453, 355])).
% 1.55/1.27 tff(1455,plain,
% 1.55/1.27 (c3_1(a1756)),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[372, 1454])).
% 1.55/1.27 tff(1456,plain,
% 1.55/1.27 (c1_1(a1756)),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[383, 1454])).
% 1.55/1.27 tff(1457,plain,
% 1.55/1.27 (c0_1(a1756)),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[394, 1454])).
% 1.55/1.27 tff(1458,plain,
% 1.55/1.27 ($false),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[534, 111, 35, 1457, 1456, 1455, 1452, 1441, 11, 1451])).
% 1.55/1.27 tff(1459,plain,(c1_1(a1762) | hskp3 | (~c1_1(a1771)) | c0_1(a1771) | (~c2_1(a1771)) | (~c3_1(a1762)) | c0_1(a1762) | hskp22 | (~c2_1(a1762)) | (~c1_1(a1759)) | c2_1(a1759) | c0_1(a1759)), inference(lemma,lemma(discharge,[]))).
% 1.55/1.27 tff(1460,plain,
% 1.55/1.27 (c1_1(a1762)),
% 1.55/1.27 inference(unit_resolution,[status(thm)],[1459, 355, 712, 275, 722, 423, 403, 35, 404, 938, 36, 1427])).
% 1.55/1.27 tff(1461,plain,
% 1.55/1.28 (hskp22 | hskp16 | (~c1_1(a1762))),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[491, 111, 404, 423, 485])).
% 1.55/1.28 tff(1462,plain,
% 1.55/1.28 (hskp16),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[1461, 1460, 355])).
% 1.55/1.28 tff(1463,plain,
% 1.55/1.28 (~c2_1(a1780)),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[498, 1462])).
% 1.55/1.28 tff(1464,plain,
% 1.55/1.28 (c3_1(a1780)),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[527, 1462])).
% 1.55/1.28 tff(1465,plain,
% 1.55/1.28 (c0_1(a1780)),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[534, 111, 35, 1457, 1456, 1455, 1464, 1463, 11])).
% 1.55/1.28 tff(1466,plain,
% 1.55/1.28 (hskp17),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[1320, 1460])).
% 1.55/1.28 tff(1467,plain,
% 1.55/1.28 (~c1_1(a1781)),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[1160, 1466])).
% 1.55/1.28 tff(1468,plain,
% 1.55/1.28 (c1_1(a1780)),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[509, 1462])).
% 1.55/1.28 tff(1469,plain,
% 1.55/1.28 (c2_1(a1781)),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[1193, 1466])).
% 1.55/1.28 tff(1470,plain,
% 1.55/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a1781) | c2_1(a1780) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c1_1(a1762)) | (~c1_1(a1780)) | (~c0_1(a1780)) | (~c2_1(a1781)) | (~c0_1(a1781)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a1781) | c2_1(a1780) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c1_1(a1762)) | (~c1_1(a1780)) | (~c0_1(a1780)) | (~c2_1(a1781)) | (~c0_1(a1781)))),
% 1.55/1.28 inference(rewrite,[status(thm)],[])).
% 1.55/1.28 tff(1471,plain,
% 1.55/1.28 (((~ndr1_0) | c2_1(a1780) | (~c1_1(a1780)) | (~c0_1(a1780)) | c1_1(a1781) | (~c2_1(a1781)) | (~c0_1(a1781)) | c0_1(a1762) | (~c3_1(a1762)) | (~c1_1(a1762))) <=> (c1_1(a1781) | c2_1(a1780) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c1_1(a1762)) | (~c1_1(a1780)) | (~c0_1(a1780)) | (~c2_1(a1781)) | (~c0_1(a1781)))),
% 1.55/1.28 inference(rewrite,[status(thm)],[])).
% 1.55/1.28 tff(1472,plain,
% 1.55/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1780) | (~c1_1(a1780)) | (~c0_1(a1780)) | c1_1(a1781) | (~c2_1(a1781)) | (~c0_1(a1781)) | c0_1(a1762) | (~c3_1(a1762)) | (~c1_1(a1762)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a1781) | c2_1(a1780) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c1_1(a1762)) | (~c1_1(a1780)) | (~c0_1(a1780)) | (~c2_1(a1781)) | (~c0_1(a1781))))),
% 1.55/1.28 inference(monotonicity,[status(thm)],[1471])).
% 1.55/1.28 tff(1473,plain,
% 1.55/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1780) | (~c1_1(a1780)) | (~c0_1(a1780)) | c1_1(a1781) | (~c2_1(a1781)) | (~c0_1(a1781)) | c0_1(a1762) | (~c3_1(a1762)) | (~c1_1(a1762)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a1781) | c2_1(a1780) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c1_1(a1762)) | (~c1_1(a1780)) | (~c0_1(a1780)) | (~c2_1(a1781)) | (~c0_1(a1781)))),
% 1.55/1.28 inference(transitivity,[status(thm)],[1472, 1470])).
% 1.55/1.28 tff(1474,plain,
% 1.55/1.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1780) | (~c1_1(a1780)) | (~c0_1(a1780)) | c1_1(a1781) | (~c2_1(a1781)) | (~c0_1(a1781)) | c0_1(a1762) | (~c3_1(a1762)) | (~c1_1(a1762)))),
% 1.55/1.28 inference(quant_inst,[status(thm)],[])).
% 1.55/1.28 tff(1475,plain,
% 1.55/1.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a1781) | c2_1(a1780) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c1_1(a1762)) | (~c1_1(a1780)) | (~c0_1(a1780)) | (~c2_1(a1781)) | (~c0_1(a1781))),
% 1.55/1.28 inference(modus_ponens,[status(thm)],[1474, 1473])).
% 1.55/1.28 tff(1476,plain,
% 1.55/1.28 ((~c0_1(a1780)) | (~c0_1(a1781))),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[1475, 111, 1469, 1468, 423, 1467, 1463, 403, 475, 1460])).
% 1.55/1.28 tff(1477,plain,
% 1.55/1.28 (~c0_1(a1781)),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[1476, 1465])).
% 1.55/1.28 tff(1478,plain,
% 1.55/1.28 (c3_1(a1781)),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[1182, 1466])).
% 1.55/1.28 tff(1479,plain,
% 1.55/1.28 (hskp8 | c0_1(a1781)),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[1377, 111, 1478, 404, 423, 1467, 1289, 1460])).
% 1.55/1.28 tff(1480,plain,
% 1.55/1.28 (hskp8),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[1479, 1477])).
% 1.55/1.28 tff(1481,plain,
% 1.55/1.28 (~c1_1(a1765)),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[326, 1480])).
% 1.55/1.28 tff(1482,plain,
% 1.55/1.28 (c2_1(a1765)),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[444, 1480])).
% 1.55/1.28 tff(1483,plain,
% 1.55/1.28 (c0_1(a1765)),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[455, 1480])).
% 1.55/1.28 tff(1484,plain,
% 1.55/1.28 ($false),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[1388, 111, 1478, 712, 722, 1483, 1482, 1467, 275, 1481, 46, 1477])).
% 1.55/1.28 tff(1485,plain,(hskp22 | (~c1_1(a1771)) | (~c2_1(a1771)) | c0_1(a1771) | (~c2_1(a1762)) | (~c3_1(a1762)) | c0_1(a1762) | hskp3 | (~c1_1(a1759)) | c2_1(a1759) | c0_1(a1759)), inference(lemma,lemma(discharge,[]))).
% 1.55/1.28 tff(1486,plain,
% 1.55/1.28 (c0_1(a1759)),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[1485, 1426, 1240, 1239, 1238, 1237, 1236, 1391, 911, 35, 1227])).
% 1.55/1.28 tff(1487,plain,
% 1.55/1.28 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 1.55/1.28 inference(bind,[status(th)],[])).
% 1.55/1.28 tff(1488,plain,
% 1.55/1.28 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.55/1.28 inference(quant_intro,[status(thm)],[1487])).
% 1.55/1.28 tff(1489,plain,
% 1.55/1.28 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.55/1.28 inference(rewrite,[status(thm)],[])).
% 1.55/1.28 tff(1490,plain,
% 1.55/1.28 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~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)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp3) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp3))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 1.55/1.28 inference(bind,[status(th)],[])).
% 1.55/1.28 tff(1491,plain,
% 1.55/1.28 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.55/1.28 inference(quant_intro,[status(thm)],[1490])).
% 1.55/1.28 tff(1492,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause180')).
% 1.55/1.28 tff(1493,plain,
% 1.55/1.28 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.55/1.28 inference(modus_ponens,[status(thm)],[1492, 1491])).
% 1.55/1.28 tff(1494,plain,
% 1.55/1.28 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.55/1.28 inference(modus_ponens,[status(thm)],[1493, 1489])).
% 1.55/1.28 tff(1495,plain,(
% 1.55/1.28 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.55/1.28 inference(skolemize,[status(sab)],[1494])).
% 1.55/1.28 tff(1496,plain,
% 1.55/1.28 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.55/1.28 inference(modus_ponens,[status(thm)],[1495, 1488])).
% 1.55/1.28 tff(1497,plain,
% 1.55/1.28 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | c0_1(a1762) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1762)) | (~c1_1(a1762)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp3 | c0_1(a1762) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1762)) | (~c1_1(a1762)))),
% 1.55/1.28 inference(rewrite,[status(thm)],[])).
% 1.55/1.28 tff(1498,plain,
% 1.55/1.28 ((hskp3 | (~ndr1_0) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)) | c0_1(a1762) | (~c3_1(a1762)) | (~c1_1(a1762))) <=> (hskp3 | c0_1(a1762) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1762)) | (~c1_1(a1762)))),
% 1.55/1.28 inference(rewrite,[status(thm)],[])).
% 1.55/1.28 tff(1499,plain,
% 1.55/1.28 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)) | c0_1(a1762) | (~c3_1(a1762)) | (~c1_1(a1762)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | c0_1(a1762) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1762)) | (~c1_1(a1762))))),
% 1.55/1.28 inference(monotonicity,[status(thm)],[1498])).
% 1.55/1.28 tff(1500,plain,
% 1.55/1.28 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)) | c0_1(a1762) | (~c3_1(a1762)) | (~c1_1(a1762)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp3 | c0_1(a1762) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1762)) | (~c1_1(a1762)))),
% 1.55/1.28 inference(transitivity,[status(thm)],[1499, 1497])).
% 1.55/1.28 tff(1501,plain,
% 1.55/1.28 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)) | c0_1(a1762) | (~c3_1(a1762)) | (~c1_1(a1762)))),
% 1.55/1.28 inference(quant_inst,[status(thm)],[])).
% 1.55/1.28 tff(1502,plain,
% 1.55/1.28 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp3 | c0_1(a1762) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1762)) | (~c1_1(a1762))),
% 1.55/1.28 inference(modus_ponens,[status(thm)],[1501, 1500])).
% 1.55/1.28 tff(1503,plain,
% 1.55/1.28 (hskp3 | (~c0_1(a1759)) | (~c1_1(a1762))),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[1502, 111, 1237, 911, 1236, 34, 1496])).
% 1.55/1.28 tff(1504,plain,
% 1.55/1.28 (~c1_1(a1762)),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[1503, 1486, 35])).
% 1.55/1.28 tff(1505,plain,
% 1.55/1.28 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | c0_1(a1771) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1771)) | (~c1_1(a1771)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp3 | c0_1(a1771) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1771)) | (~c1_1(a1771)))),
% 1.55/1.28 inference(rewrite,[status(thm)],[])).
% 1.55/1.28 tff(1506,plain,
% 1.55/1.28 ((hskp3 | (~ndr1_0) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)) | c0_1(a1771) | (~c3_1(a1771)) | (~c1_1(a1771))) <=> (hskp3 | c0_1(a1771) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1771)) | (~c1_1(a1771)))),
% 1.55/1.28 inference(rewrite,[status(thm)],[])).
% 1.55/1.28 tff(1507,plain,
% 1.55/1.28 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)) | c0_1(a1771) | (~c3_1(a1771)) | (~c1_1(a1771)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | c0_1(a1771) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1771)) | (~c1_1(a1771))))),
% 1.55/1.28 inference(monotonicity,[status(thm)],[1506])).
% 1.55/1.28 tff(1508,plain,
% 1.55/1.28 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)) | c0_1(a1771) | (~c3_1(a1771)) | (~c1_1(a1771)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp3 | c0_1(a1771) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1771)) | (~c1_1(a1771)))),
% 1.55/1.28 inference(transitivity,[status(thm)],[1507, 1505])).
% 1.55/1.28 tff(1509,plain,
% 1.55/1.28 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)) | c0_1(a1771) | (~c3_1(a1771)) | (~c1_1(a1771)))),
% 1.55/1.28 inference(quant_inst,[status(thm)],[])).
% 1.55/1.28 tff(1510,plain,
% 1.55/1.28 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp3 | c0_1(a1771) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1771)) | (~c1_1(a1771))),
% 1.55/1.28 inference(modus_ponens,[status(thm)],[1509, 1508])).
% 1.55/1.28 tff(1511,plain,
% 1.55/1.28 (hskp3 | (~c0_1(a1759)) | (~c3_1(a1771))),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[1510, 111, 1227, 911, 1239, 34, 1496])).
% 1.55/1.28 tff(1512,plain,
% 1.55/1.28 (~c3_1(a1771)),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[1511, 1486, 35])).
% 1.55/1.28 tff(1513,plain,
% 1.55/1.28 (^[U: $i] : refl((hskp25 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> (hskp25 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))),
% 1.55/1.28 inference(bind,[status(th)],[])).
% 1.55/1.28 tff(1514,plain,
% 1.55/1.28 (![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.55/1.28 inference(quant_intro,[status(thm)],[1513])).
% 1.55/1.28 tff(1515,plain,
% 1.55/1.28 (![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.55/1.28 inference(rewrite,[status(thm)],[])).
% 1.55/1.28 tff(1516,plain,
% 1.55/1.28 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp3) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp3))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp3) | hskp25) <=> ((hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp25))), rewrite(((hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp25) <=> (hskp25 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp3) | hskp25) <=> (hskp25 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))))),
% 1.55/1.28 inference(bind,[status(th)],[])).
% 1.55/1.28 tff(1517,plain,
% 1.55/1.28 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp3) | hskp25) <=> ![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.55/1.28 inference(quant_intro,[status(thm)],[1516])).
% 1.55/1.28 tff(1518,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp3) | hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause150')).
% 1.55/1.28 tff(1519,plain,
% 1.55/1.28 (![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.55/1.28 inference(modus_ponens,[status(thm)],[1518, 1517])).
% 1.55/1.28 tff(1520,plain,
% 1.55/1.28 (![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.55/1.28 inference(modus_ponens,[status(thm)],[1519, 1515])).
% 1.55/1.28 tff(1521,plain,(
% 1.55/1.28 ![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.55/1.28 inference(skolemize,[status(sab)],[1520])).
% 1.55/1.28 tff(1522,plain,
% 1.55/1.28 (![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.55/1.28 inference(modus_ponens,[status(thm)],[1521, 1514])).
% 1.55/1.28 tff(1523,plain,
% 1.55/1.28 (((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp25 | hskp3 | (~ndr1_0) | c3_1(a1771) | (~c1_1(a1771)) | (~c2_1(a1771)))) <=> ((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp25 | hskp3 | (~ndr1_0) | c3_1(a1771) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 1.55/1.28 inference(rewrite,[status(thm)],[])).
% 1.55/1.28 tff(1524,plain,
% 1.55/1.28 ((hskp25 | hskp3 | (~ndr1_0) | c3_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771))) <=> (hskp25 | hskp3 | (~ndr1_0) | c3_1(a1771) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 1.55/1.28 inference(rewrite,[status(thm)],[])).
% 1.55/1.28 tff(1525,plain,
% 1.55/1.28 (((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp25 | hskp3 | (~ndr1_0) | c3_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)))) <=> ((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp25 | hskp3 | (~ndr1_0) | c3_1(a1771) | (~c1_1(a1771)) | (~c2_1(a1771))))),
% 1.55/1.28 inference(monotonicity,[status(thm)],[1524])).
% 1.55/1.28 tff(1526,plain,
% 1.55/1.28 (((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp25 | hskp3 | (~ndr1_0) | c3_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)))) <=> ((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp25 | hskp3 | (~ndr1_0) | c3_1(a1771) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 1.55/1.28 inference(transitivity,[status(thm)],[1525, 1523])).
% 1.55/1.28 tff(1527,plain,
% 1.55/1.28 ((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp25 | hskp3 | (~ndr1_0) | c3_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)))),
% 1.55/1.28 inference(quant_inst,[status(thm)],[])).
% 1.55/1.28 tff(1528,plain,
% 1.55/1.28 ((~![U: $i] : (hskp25 | hskp3 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp25 | hskp3 | (~ndr1_0) | c3_1(a1771) | (~c1_1(a1771)) | (~c2_1(a1771))),
% 1.55/1.28 inference(modus_ponens,[status(thm)],[1527, 1526])).
% 1.55/1.28 tff(1529,plain,
% 1.55/1.28 (hskp25 | hskp3 | c3_1(a1771)),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[1528, 111, 1227, 1240, 1522])).
% 1.55/1.28 tff(1530,plain,
% 1.55/1.28 (hskp25),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[1529, 1512, 35])).
% 1.55/1.28 tff(1531,plain,
% 1.55/1.28 (~c2_1(a1827)),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[223, 1530])).
% 1.55/1.28 tff(1532,plain,
% 1.55/1.28 (~c1_1(a1827)),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[168, 1530])).
% 1.55/1.28 tff(1533,plain,
% 1.55/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a1827) | c2_1(a1827) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | (~c3_1(a1827)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a1827) | c2_1(a1827) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | (~c3_1(a1827)))),
% 1.55/1.28 inference(rewrite,[status(thm)],[])).
% 1.55/1.28 tff(1534,plain,
% 1.55/1.28 (((~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c2_1(a1827) | c1_1(a1827) | (~c3_1(a1827)) | c0_1(a1762) | (~c3_1(a1762)) | (~c2_1(a1762))) <=> (c1_1(a1827) | c2_1(a1827) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | (~c3_1(a1827)))),
% 1.55/1.28 inference(rewrite,[status(thm)],[])).
% 1.55/1.28 tff(1535,plain,
% 1.55/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c2_1(a1827) | c1_1(a1827) | (~c3_1(a1827)) | c0_1(a1762) | (~c3_1(a1762)) | (~c2_1(a1762)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a1827) | c2_1(a1827) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | (~c3_1(a1827))))),
% 1.55/1.28 inference(monotonicity,[status(thm)],[1534])).
% 1.55/1.28 tff(1536,plain,
% 1.55/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c2_1(a1827) | c1_1(a1827) | (~c3_1(a1827)) | c0_1(a1762) | (~c3_1(a1762)) | (~c2_1(a1762)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a1827) | c2_1(a1827) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | (~c3_1(a1827)))),
% 1.55/1.28 inference(transitivity,[status(thm)],[1535, 1533])).
% 1.55/1.28 tff(1537,plain,
% 1.55/1.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c2_1(a1827) | c1_1(a1827) | (~c3_1(a1827)) | c0_1(a1762) | (~c3_1(a1762)) | (~c2_1(a1762)))),
% 1.55/1.28 inference(quant_inst,[status(thm)],[])).
% 1.55/1.28 tff(1538,plain,
% 1.55/1.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a1827) | c2_1(a1827) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | (~c3_1(a1827))),
% 1.55/1.28 inference(modus_ponens,[status(thm)],[1537, 1536])).
% 1.55/1.28 tff(1539,plain,
% 1.55/1.28 (~c3_1(a1827)),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[1538, 111, 1238, 1237, 1532, 1531, 1236, 1138, 1504])).
% 1.55/1.28 tff(1540,plain,
% 1.55/1.28 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W)))),
% 1.55/1.28 inference(bind,[status(th)],[])).
% 1.55/1.28 tff(1541,plain,
% 1.55/1.28 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.55/1.28 inference(quant_intro,[status(thm)],[1540])).
% 1.55/1.28 tff(1542,plain,
% 1.55/1.28 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.55/1.28 inference(rewrite,[status(thm)],[])).
% 1.55/1.28 tff(1543,plain,
% 1.55/1.28 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c0_1(W))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c0_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c0_1(W))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c0_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c0_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c2_1(W) | c0_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | c1_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))))),
% 1.55/1.28 inference(bind,[status(th)],[])).
% 1.55/1.28 tff(1544,plain,
% 1.55/1.28 (![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(V)) | c0_1(W)) | c2_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.55/1.28 inference(quant_intro,[status(thm)],[1543])).
% 1.55/1.28 tff(1545,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(V)) | c0_1(W)) | c2_1(W)) | c3_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause190')).
% 1.55/1.28 tff(1546,plain,
% 1.55/1.28 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.55/1.28 inference(modus_ponens,[status(thm)],[1545, 1544])).
% 1.55/1.28 tff(1547,plain,
% 1.55/1.28 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.55/1.28 inference(modus_ponens,[status(thm)],[1546, 1542])).
% 1.55/1.28 tff(1548,plain,(
% 1.55/1.28 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.55/1.28 inference(skolemize,[status(sab)],[1547])).
% 1.55/1.28 tff(1549,plain,
% 1.55/1.28 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))),
% 1.55/1.28 inference(modus_ponens,[status(thm)],[1548, 1541])).
% 1.55/1.28 tff(1550,plain,
% 1.55/1.28 (~c0_1(a1827)),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[174, 1530])).
% 1.55/1.28 tff(1551,plain,
% 1.55/1.28 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp17 | c0_1(a1771) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | c3_1(a1771) | (~c1_1(a1771)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a1771) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | c3_1(a1771) | (~c1_1(a1771)))),
% 1.55/1.28 inference(rewrite,[status(thm)],[])).
% 1.55/1.28 tff(1552,plain,
% 1.55/1.28 ((hskp17 | (~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c0_1(a1771) | c3_1(a1771) | (~c1_1(a1771))) <=> (hskp17 | c0_1(a1771) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | c3_1(a1771) | (~c1_1(a1771)))),
% 1.55/1.28 inference(rewrite,[status(thm)],[])).
% 1.55/1.28 tff(1553,plain,
% 1.55/1.28 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c0_1(a1771) | c3_1(a1771) | (~c1_1(a1771)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp17 | c0_1(a1771) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | c3_1(a1771) | (~c1_1(a1771))))),
% 1.55/1.28 inference(monotonicity,[status(thm)],[1552])).
% 1.55/1.28 tff(1554,plain,
% 1.55/1.28 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c0_1(a1771) | c3_1(a1771) | (~c1_1(a1771)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a1771) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | c3_1(a1771) | (~c1_1(a1771)))),
% 1.55/1.28 inference(transitivity,[status(thm)],[1553, 1551])).
% 1.55/1.28 tff(1555,plain,
% 1.55/1.28 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c0_1(a1771) | c3_1(a1771) | (~c1_1(a1771)))),
% 1.55/1.28 inference(quant_inst,[status(thm)],[])).
% 1.55/1.28 tff(1556,plain,
% 1.55/1.28 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp17 | c0_1(a1771) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | c3_1(a1771) | (~c1_1(a1771))),
% 1.55/1.28 inference(modus_ponens,[status(thm)],[1555, 1554])).
% 1.55/1.28 tff(1557,plain,
% 1.55/1.28 (hskp17),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[1556, 111, 1227, 1238, 1237, 1239, 1148, 1504, 1512])).
% 1.55/1.28 tff(1558,plain,
% 1.55/1.28 (c3_1(a1781)),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[1182, 1557])).
% 1.55/1.28 tff(1559,plain,
% 1.55/1.28 (~c1_1(a1781)),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[1160, 1557])).
% 1.55/1.28 tff(1560,plain,
% 1.55/1.28 (c2_1(a1781)),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[1193, 1557])).
% 1.55/1.28 tff(1561,assumption,(c0_1(a1759)), introduced(assumption)).
% 1.55/1.28 tff(1562,assumption,(hskp29), introduced(assumption)).
% 1.55/1.28 tff(1563,plain,
% 1.55/1.28 (c3_1(a1805)),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[979, 1562])).
% 1.55/1.28 tff(1564,plain,
% 1.55/1.28 (c2_1(a1805)),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[1002, 1562])).
% 1.55/1.28 tff(1565,plain,
% 1.55/1.28 (c0_1(a1805)),
% 1.55/1.28 inference(unit_resolution,[status(thm)],[991, 1562])).
% 1.55/1.28 tff(1566,plain,
% 1.55/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1805)) | (~c1_1(a1805)) | (~c2_1(a1805)) | (~c0_1(a1805)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1805)) | (~c1_1(a1805)) | (~c2_1(a1805)) | (~c0_1(a1805)))),
% 1.55/1.28 inference(rewrite,[status(thm)],[])).
% 1.55/1.28 tff(1567,plain,
% 1.55/1.28 (((~ndr1_0) | (~c2_1(a1805)) | (~c1_1(a1805)) | (~c3_1(a1805)) | (~c2_1(a1805)) | (~c1_1(a1805)) | (~c0_1(a1805)) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759))) <=> (c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1805)) | (~c1_1(a1805)) | (~c2_1(a1805)) | (~c0_1(a1805)))),
% 1.55/1.28 inference(rewrite,[status(thm)],[])).
% 1.55/1.28 tff(1568,plain,
% 1.55/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1805)) | (~c1_1(a1805)) | (~c3_1(a1805)) | (~c2_1(a1805)) | (~c1_1(a1805)) | (~c0_1(a1805)) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1805)) | (~c1_1(a1805)) | (~c2_1(a1805)) | (~c0_1(a1805))))),
% 1.55/1.28 inference(monotonicity,[status(thm)],[1567])).
% 1.55/1.28 tff(1569,plain,
% 1.55/1.28 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1805)) | (~c1_1(a1805)) | (~c3_1(a1805)) | (~c2_1(a1805)) | (~c1_1(a1805)) | (~c0_1(a1805)) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1805)) | (~c1_1(a1805)) | (~c2_1(a1805)) | (~c0_1(a1805)))),
% 1.55/1.28 inference(transitivity,[status(thm)],[1568, 1566])).
% 1.55/1.28 tff(1570,plain,
% 1.55/1.28 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1805)) | (~c1_1(a1805)) | (~c3_1(a1805)) | (~c2_1(a1805)) | (~c1_1(a1805)) | (~c0_1(a1805)) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)))),
% 1.55/1.29 inference(quant_inst,[status(thm)],[])).
% 1.55/1.29 tff(1571,plain,
% 1.55/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1805)) | (~c1_1(a1805)) | (~c2_1(a1805)) | (~c0_1(a1805))),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1570, 1569])).
% 1.55/1.29 tff(1572,plain,
% 1.55/1.29 (~c1_1(a1805)),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[1571, 241, 1565, 1564, 1563, 938, 34, 678, 1561])).
% 1.55/1.29 tff(1573,plain,
% 1.55/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1781) | c0_1(a1771) | (~ndr1_0) | c3_1(a1771) | (~c2_1(a1771)) | (~c2_1(a1781)) | (~c3_1(a1781)) | (~c3_1(a1805)) | c1_1(a1805) | (~c0_1(a1805)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1781) | c0_1(a1771) | (~ndr1_0) | c3_1(a1771) | (~c2_1(a1771)) | (~c2_1(a1781)) | (~c3_1(a1781)) | (~c3_1(a1805)) | c1_1(a1805) | (~c0_1(a1805)))),
% 1.55/1.29 inference(rewrite,[status(thm)],[])).
% 1.55/1.29 tff(1574,plain,
% 1.55/1.29 (((~ndr1_0) | c1_1(a1781) | (~c2_1(a1781)) | (~c3_1(a1781)) | c1_1(a1805) | (~c3_1(a1805)) | (~c0_1(a1805)) | c3_1(a1771) | c0_1(a1771) | (~c2_1(a1771))) <=> (c1_1(a1781) | c0_1(a1771) | (~ndr1_0) | c3_1(a1771) | (~c2_1(a1771)) | (~c2_1(a1781)) | (~c3_1(a1781)) | (~c3_1(a1805)) | c1_1(a1805) | (~c0_1(a1805)))),
% 1.55/1.29 inference(rewrite,[status(thm)],[])).
% 1.55/1.29 tff(1575,plain,
% 1.55/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1781) | (~c2_1(a1781)) | (~c3_1(a1781)) | c1_1(a1805) | (~c3_1(a1805)) | (~c0_1(a1805)) | c3_1(a1771) | c0_1(a1771) | (~c2_1(a1771)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1781) | c0_1(a1771) | (~ndr1_0) | c3_1(a1771) | (~c2_1(a1771)) | (~c2_1(a1781)) | (~c3_1(a1781)) | (~c3_1(a1805)) | c1_1(a1805) | (~c0_1(a1805))))),
% 1.55/1.29 inference(monotonicity,[status(thm)],[1574])).
% 1.55/1.29 tff(1576,plain,
% 1.55/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1781) | (~c2_1(a1781)) | (~c3_1(a1781)) | c1_1(a1805) | (~c3_1(a1805)) | (~c0_1(a1805)) | c3_1(a1771) | c0_1(a1771) | (~c2_1(a1771)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1781) | c0_1(a1771) | (~ndr1_0) | c3_1(a1771) | (~c2_1(a1771)) | (~c2_1(a1781)) | (~c3_1(a1781)) | (~c3_1(a1805)) | c1_1(a1805) | (~c0_1(a1805)))),
% 1.55/1.29 inference(transitivity,[status(thm)],[1575, 1573])).
% 1.55/1.29 tff(1577,plain,
% 1.55/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1781) | (~c2_1(a1781)) | (~c3_1(a1781)) | c1_1(a1805) | (~c3_1(a1805)) | (~c0_1(a1805)) | c3_1(a1771) | c0_1(a1771) | (~c2_1(a1771)))),
% 1.55/1.29 inference(quant_inst,[status(thm)],[])).
% 1.55/1.29 tff(1578,plain,
% 1.55/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1781) | c0_1(a1771) | (~ndr1_0) | c3_1(a1771) | (~c2_1(a1771)) | (~c2_1(a1781)) | (~c3_1(a1781)) | (~c3_1(a1805)) | c1_1(a1805) | (~c0_1(a1805))),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1577, 1576])).
% 1.55/1.29 tff(1579,plain,
% 1.55/1.29 ($false),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[1578, 241, 1565, 1563, 1338, 1337, 722, 1336, 275, 819, 1267, 1572])).
% 1.55/1.29 tff(1580,plain,((~hskp29) | (~ndr1_0) | (~c2_1(a1781)) | (~c3_1(a1781)) | (~c2_1(a1771)) | c1_1(a1781) | c0_1(a1771) | c3_1(a1771) | (~c1_1(a1759)) | c3_1(a1759) | (~c0_1(a1759))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.29 tff(1581,plain,
% 1.55/1.29 ((~hskp29) | (~c2_1(a1781)) | (~c3_1(a1781)) | (~c2_1(a1771)) | c1_1(a1781) | c0_1(a1771) | c3_1(a1771) | (~c1_1(a1759)) | c3_1(a1759) | (~c0_1(a1759))),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[1580, 111])).
% 1.55/1.29 tff(1582,plain,
% 1.55/1.29 (~hskp29),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[1581, 1560, 1486, 1512, 1240, 1559, 1239, 1558, 911, 34])).
% 1.55/1.29 tff(1583,plain,
% 1.55/1.29 (^[U: $i] : refl((hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> (hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))),
% 1.55/1.29 inference(bind,[status(th)],[])).
% 1.55/1.29 tff(1584,plain,
% 1.55/1.29 (![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.55/1.29 inference(quant_intro,[status(thm)],[1583])).
% 1.55/1.29 tff(1585,plain,
% 1.55/1.29 (![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.55/1.29 inference(rewrite,[status(thm)],[])).
% 1.55/1.29 tff(1586,plain,
% 1.55/1.29 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp29) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp29))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp29) <=> (hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp29) <=> (hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp29) | hskp30) <=> ((hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp30))), rewrite(((hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U))) | hskp30) <=> (hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp29) | hskp30) <=> (hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))))),
% 1.55/1.29 inference(bind,[status(th)],[])).
% 1.55/1.29 tff(1587,plain,
% 1.55/1.29 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp29) | hskp30) <=> ![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.55/1.29 inference(quant_intro,[status(thm)],[1586])).
% 1.55/1.29 tff(1588,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp29) | hskp30)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause148')).
% 1.55/1.29 tff(1589,plain,
% 1.55/1.29 (![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1588, 1587])).
% 1.55/1.29 tff(1590,plain,
% 1.55/1.29 (![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1589, 1585])).
% 1.55/1.29 tff(1591,plain,(
% 1.55/1.29 ![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.55/1.29 inference(skolemize,[status(sab)],[1590])).
% 1.55/1.29 tff(1592,plain,
% 1.55/1.29 (![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1591, 1584])).
% 1.55/1.29 tff(1593,plain,
% 1.55/1.29 (((~![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp30 | hskp29 | (~ndr1_0) | c3_1(a1771) | (~c1_1(a1771)) | (~c2_1(a1771)))) <=> ((~![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp30 | hskp29 | (~ndr1_0) | c3_1(a1771) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 1.55/1.29 inference(rewrite,[status(thm)],[])).
% 1.55/1.29 tff(1594,plain,
% 1.55/1.29 ((hskp30 | hskp29 | (~ndr1_0) | c3_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771))) <=> (hskp30 | hskp29 | (~ndr1_0) | c3_1(a1771) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 1.55/1.29 inference(rewrite,[status(thm)],[])).
% 1.55/1.29 tff(1595,plain,
% 1.55/1.29 (((~![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp30 | hskp29 | (~ndr1_0) | c3_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)))) <=> ((~![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp30 | hskp29 | (~ndr1_0) | c3_1(a1771) | (~c1_1(a1771)) | (~c2_1(a1771))))),
% 1.55/1.29 inference(monotonicity,[status(thm)],[1594])).
% 1.55/1.29 tff(1596,plain,
% 1.55/1.29 (((~![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp30 | hskp29 | (~ndr1_0) | c3_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)))) <=> ((~![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp30 | hskp29 | (~ndr1_0) | c3_1(a1771) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 1.55/1.29 inference(transitivity,[status(thm)],[1595, 1593])).
% 1.55/1.29 tff(1597,plain,
% 1.55/1.29 ((~![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp30 | hskp29 | (~ndr1_0) | c3_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)))),
% 1.55/1.29 inference(quant_inst,[status(thm)],[])).
% 1.55/1.29 tff(1598,plain,
% 1.55/1.29 ((~![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp30 | hskp29 | (~ndr1_0) | c3_1(a1771) | (~c1_1(a1771)) | (~c2_1(a1771))),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1597, 1596])).
% 1.55/1.29 tff(1599,plain,
% 1.55/1.29 (hskp30 | hskp29 | c3_1(a1771)),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[1598, 111, 1227, 1240, 1592])).
% 1.55/1.29 tff(1600,plain,
% 1.55/1.29 (hskp30),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[1599, 1582, 1512])).
% 1.55/1.29 tff(1601,plain,
% 1.55/1.29 (((~hskp30) | c3_1(a1823)) <=> ((~hskp30) | c3_1(a1823))),
% 1.55/1.29 inference(rewrite,[status(thm)],[])).
% 1.55/1.29 tff(1602,axiom,((~hskp30) | c3_1(a1823)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause40')).
% 1.55/1.29 tff(1603,plain,
% 1.55/1.29 ((~hskp30) | c3_1(a1823)),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1602, 1601])).
% 1.55/1.29 tff(1604,plain,
% 1.55/1.29 ((~hskp30) | c3_1(a1823)),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1603, 1601])).
% 1.55/1.29 tff(1605,plain,
% 1.55/1.29 ((~hskp30) | c3_1(a1823)),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1604, 1601])).
% 1.55/1.29 tff(1606,plain,
% 1.55/1.29 ((~hskp30) | c3_1(a1823)),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1605, 1601])).
% 1.55/1.29 tff(1607,plain,
% 1.55/1.29 ((~hskp30) | c3_1(a1823)),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1606, 1601])).
% 1.55/1.29 tff(1608,plain,
% 1.55/1.29 ((~hskp30) | c3_1(a1823)),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1607, 1601])).
% 1.55/1.29 tff(1609,plain,
% 1.55/1.29 ((~hskp30) | c3_1(a1823)),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1608, 1601])).
% 1.55/1.29 tff(1610,plain,
% 1.55/1.29 ((~hskp30) | c3_1(a1823)),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1609, 1601])).
% 1.55/1.29 tff(1611,plain,
% 1.55/1.29 (c3_1(a1823)),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[1610, 1600])).
% 1.55/1.29 tff(1612,plain,
% 1.55/1.29 (((~hskp30) | c2_1(a1823)) <=> ((~hskp30) | c2_1(a1823))),
% 1.55/1.29 inference(rewrite,[status(thm)],[])).
% 1.55/1.29 tff(1613,axiom,((~hskp30) | c2_1(a1823)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause39')).
% 1.55/1.29 tff(1614,plain,
% 1.55/1.29 ((~hskp30) | c2_1(a1823)),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1613, 1612])).
% 1.55/1.29 tff(1615,plain,
% 1.55/1.29 ((~hskp30) | c2_1(a1823)),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1614, 1612])).
% 1.55/1.29 tff(1616,plain,
% 1.55/1.29 ((~hskp30) | c2_1(a1823)),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1615, 1612])).
% 1.55/1.29 tff(1617,plain,
% 1.55/1.29 ((~hskp30) | c2_1(a1823)),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1616, 1612])).
% 1.55/1.29 tff(1618,plain,
% 1.55/1.29 ((~hskp30) | c2_1(a1823)),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1617, 1612])).
% 1.55/1.29 tff(1619,plain,
% 1.55/1.29 ((~hskp30) | c2_1(a1823)),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1618, 1612])).
% 1.55/1.29 tff(1620,plain,
% 1.55/1.29 ((~hskp30) | c2_1(a1823)),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1619, 1612])).
% 1.55/1.29 tff(1621,plain,
% 1.55/1.29 ((~hskp30) | c2_1(a1823)),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1620, 1612])).
% 1.55/1.29 tff(1622,plain,
% 1.55/1.29 (c2_1(a1823)),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[1621, 1600])).
% 1.55/1.29 tff(1623,plain,
% 1.55/1.29 (((~hskp30) | c1_1(a1823)) <=> ((~hskp30) | c1_1(a1823))),
% 1.55/1.29 inference(rewrite,[status(thm)],[])).
% 1.55/1.29 tff(1624,axiom,((~hskp30) | c1_1(a1823)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause38')).
% 1.55/1.29 tff(1625,plain,
% 1.55/1.29 ((~hskp30) | c1_1(a1823)),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1624, 1623])).
% 1.55/1.29 tff(1626,plain,
% 1.55/1.29 ((~hskp30) | c1_1(a1823)),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1625, 1623])).
% 1.55/1.29 tff(1627,plain,
% 1.55/1.29 ((~hskp30) | c1_1(a1823)),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1626, 1623])).
% 1.55/1.29 tff(1628,plain,
% 1.55/1.29 ((~hskp30) | c1_1(a1823)),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1627, 1623])).
% 1.55/1.29 tff(1629,plain,
% 1.55/1.29 ((~hskp30) | c1_1(a1823)),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1628, 1623])).
% 1.55/1.29 tff(1630,plain,
% 1.55/1.29 ((~hskp30) | c1_1(a1823)),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1629, 1623])).
% 1.55/1.29 tff(1631,plain,
% 1.55/1.29 ((~hskp30) | c1_1(a1823)),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1630, 1623])).
% 1.55/1.29 tff(1632,plain,
% 1.55/1.29 ((~hskp30) | c1_1(a1823)),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1631, 1623])).
% 1.55/1.29 tff(1633,plain,
% 1.55/1.29 (c1_1(a1823)),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[1632, 1600])).
% 1.55/1.29 tff(1634,plain,
% 1.55/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a1827) | c1_1(a1827) | c2_1(a1827) | (~ndr1_0) | c3_1(a1827) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a1827) | c1_1(a1827) | c2_1(a1827) | (~ndr1_0) | c3_1(a1827) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)))),
% 1.55/1.29 inference(rewrite,[status(thm)],[])).
% 1.55/1.29 tff(1635,plain,
% 1.55/1.29 (((~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | c2_1(a1827) | c1_1(a1827) | c3_1(a1827) | c3_1(a1827) | c2_1(a1827) | c0_1(a1827)) <=> (c0_1(a1827) | c1_1(a1827) | c2_1(a1827) | (~ndr1_0) | c3_1(a1827) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)))),
% 1.55/1.29 inference(rewrite,[status(thm)],[])).
% 1.55/1.29 tff(1636,plain,
% 1.55/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | c2_1(a1827) | c1_1(a1827) | c3_1(a1827) | c3_1(a1827) | c2_1(a1827) | c0_1(a1827))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a1827) | c1_1(a1827) | c2_1(a1827) | (~ndr1_0) | c3_1(a1827) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823))))),
% 1.55/1.29 inference(monotonicity,[status(thm)],[1635])).
% 1.55/1.29 tff(1637,plain,
% 1.55/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | c2_1(a1827) | c1_1(a1827) | c3_1(a1827) | c3_1(a1827) | c2_1(a1827) | c0_1(a1827))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a1827) | c1_1(a1827) | c2_1(a1827) | (~ndr1_0) | c3_1(a1827) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)))),
% 1.55/1.29 inference(transitivity,[status(thm)],[1636, 1634])).
% 1.55/1.29 tff(1638,plain,
% 1.55/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | c2_1(a1827) | c1_1(a1827) | c3_1(a1827) | c3_1(a1827) | c2_1(a1827) | c0_1(a1827))),
% 1.55/1.29 inference(quant_inst,[status(thm)],[])).
% 1.55/1.29 tff(1639,plain,
% 1.55/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a1827) | c1_1(a1827) | c2_1(a1827) | (~ndr1_0) | c3_1(a1827) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823))),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1638, 1637])).
% 1.55/1.29 tff(1640,plain,
% 1.55/1.29 ($false),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[1639, 111, 1633, 1622, 1611, 1550, 1532, 1531, 1549, 1539])).
% 1.55/1.29 tff(1641,plain,(hskp3 | c3_1(a1759) | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.55/1.29 tff(1642,plain,
% 1.55/1.29 (hskp3),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[1641, 34, 12])).
% 1.55/1.29 tff(1643,plain,
% 1.55/1.29 (c1_1(a1758)),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[624, 1642])).
% 1.55/1.29 tff(1644,plain,
% 1.55/1.29 (~c3_1(a1758)),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[638, 1642])).
% 1.55/1.29 tff(1645,plain,
% 1.55/1.29 (c2_1(a1758)),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[613, 1642])).
% 1.55/1.29 tff(1646,plain,
% 1.55/1.29 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W))))),
% 1.55/1.29 inference(bind,[status(th)],[])).
% 1.55/1.29 tff(1647,plain,
% 1.55/1.29 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.55/1.29 inference(quant_intro,[status(thm)],[1646])).
% 1.55/1.29 tff(1648,plain,
% 1.55/1.29 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.55/1.29 inference(rewrite,[status(thm)],[])).
% 1.55/1.29 tff(1649,plain,
% 1.55/1.29 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)))), ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))), (((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))))),
% 1.55/1.29 inference(bind,[status(th)],[])).
% 1.55/1.29 tff(1650,plain,
% 1.55/1.29 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.55/1.29 inference(quant_intro,[status(thm)],[1649])).
% 1.55/1.29 tff(1651,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c3_1(W))) | c3_1(V)) | c0_1(W)) | c1_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause195')).
% 1.55/1.29 tff(1652,plain,
% 1.55/1.29 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1651, 1650])).
% 1.55/1.29 tff(1653,plain,
% 1.55/1.29 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1652, 1648])).
% 1.55/1.29 tff(1654,plain,(
% 1.55/1.29 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.55/1.29 inference(skolemize,[status(sab)],[1653])).
% 1.55/1.29 tff(1655,plain,
% 1.55/1.29 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1654, 1647])).
% 1.55/1.29 tff(1656,plain,
% 1.55/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c0_1(a1762) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1762)) | c1_1(a1762))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1762) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1762)) | c1_1(a1762))),
% 1.55/1.29 inference(rewrite,[status(thm)],[])).
% 1.55/1.29 tff(1657,plain,
% 1.55/1.29 (((~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)) | c0_1(a1762) | c1_1(a1762) | (~c3_1(a1762))) <=> (c0_1(a1762) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1762)) | c1_1(a1762))),
% 1.55/1.29 inference(rewrite,[status(thm)],[])).
% 1.55/1.29 tff(1658,plain,
% 1.55/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)) | c0_1(a1762) | c1_1(a1762) | (~c3_1(a1762)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c0_1(a1762) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1762)) | c1_1(a1762)))),
% 1.55/1.29 inference(monotonicity,[status(thm)],[1657])).
% 1.55/1.29 tff(1659,plain,
% 1.55/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)) | c0_1(a1762) | c1_1(a1762) | (~c3_1(a1762)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1762) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1762)) | c1_1(a1762))),
% 1.55/1.29 inference(transitivity,[status(thm)],[1658, 1656])).
% 1.55/1.29 tff(1660,plain,
% 1.55/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)) | c0_1(a1762) | c1_1(a1762) | (~c3_1(a1762)))),
% 1.55/1.29 inference(quant_inst,[status(thm)],[])).
% 1.55/1.29 tff(1661,plain,
% 1.55/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1762) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1762)) | c1_1(a1762)),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1660, 1659])).
% 1.55/1.29 tff(1662,plain,
% 1.55/1.29 ((~c0_1(a1758)) | c1_1(a1762)),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[1661, 111, 423, 703, 721, 403, 702, 1655])).
% 1.55/1.29 tff(1663,plain,
% 1.55/1.29 (~c0_1(a1758)),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[1662, 1245])).
% 1.55/1.29 tff(1664,plain,
% 1.55/1.29 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp17 | c3_1(a1758) | (~ndr1_0) | c0_1(a1758) | (~c1_1(a1758)) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp17 | c3_1(a1758) | (~ndr1_0) | c0_1(a1758) | (~c1_1(a1758)) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762))),
% 1.55/1.29 inference(rewrite,[status(thm)],[])).
% 1.55/1.29 tff(1665,plain,
% 1.55/1.29 ((hskp17 | (~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c0_1(a1758) | c3_1(a1758) | (~c1_1(a1758))) <=> (hskp17 | c3_1(a1758) | (~ndr1_0) | c0_1(a1758) | (~c1_1(a1758)) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762))),
% 1.55/1.29 inference(rewrite,[status(thm)],[])).
% 1.55/1.29 tff(1666,plain,
% 1.55/1.29 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c0_1(a1758) | c3_1(a1758) | (~c1_1(a1758)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp17 | c3_1(a1758) | (~ndr1_0) | c0_1(a1758) | (~c1_1(a1758)) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762)))),
% 1.55/1.29 inference(monotonicity,[status(thm)],[1665])).
% 1.55/1.29 tff(1667,plain,
% 1.55/1.29 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c0_1(a1758) | c3_1(a1758) | (~c1_1(a1758)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp17 | c3_1(a1758) | (~ndr1_0) | c0_1(a1758) | (~c1_1(a1758)) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762))),
% 1.55/1.29 inference(transitivity,[status(thm)],[1666, 1664])).
% 1.55/1.29 tff(1668,plain,
% 1.55/1.29 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c0_1(a1758) | c3_1(a1758) | (~c1_1(a1758)))),
% 1.55/1.29 inference(quant_inst,[status(thm)],[])).
% 1.55/1.29 tff(1669,plain,
% 1.55/1.29 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp17 | c3_1(a1758) | (~ndr1_0) | c0_1(a1758) | (~c1_1(a1758)) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762)),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1668, 1667])).
% 1.55/1.29 tff(1670,plain,
% 1.55/1.29 (hskp17),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[1669, 111, 404, 423, 703, 702, 1148, 1245, 1663])).
% 1.55/1.29 tff(1671,plain,
% 1.55/1.29 (~c1_1(a1781)),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[1160, 1670])).
% 1.55/1.29 tff(1672,plain,
% 1.55/1.29 (c3_1(a1781)),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[1182, 1670])).
% 1.55/1.29 tff(1673,plain,
% 1.55/1.29 (c2_1(a1781)),
% 1.55/1.29 inference(unit_resolution,[status(thm)],[1193, 1670])).
% 1.55/1.29 tff(1674,plain,
% 1.55/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1781) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c3_1(a1781)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1781) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c3_1(a1781)))),
% 1.55/1.29 inference(rewrite,[status(thm)],[])).
% 1.55/1.29 tff(1675,plain,
% 1.55/1.29 (((~ndr1_0) | c1_1(a1781) | (~c2_1(a1781)) | (~c3_1(a1781)) | c1_1(a1781) | (~c3_1(a1781)) | (~c0_1(a1781)) | c3_1(a1758) | c0_1(a1758) | (~c2_1(a1758))) <=> (c1_1(a1781) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c3_1(a1781)))),
% 1.55/1.29 inference(rewrite,[status(thm)],[])).
% 1.55/1.29 tff(1676,plain,
% 1.55/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1781) | (~c2_1(a1781)) | (~c3_1(a1781)) | c1_1(a1781) | (~c3_1(a1781)) | (~c0_1(a1781)) | c3_1(a1758) | c0_1(a1758) | (~c2_1(a1758)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1781) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c3_1(a1781))))),
% 1.55/1.29 inference(monotonicity,[status(thm)],[1675])).
% 1.55/1.29 tff(1677,plain,
% 1.55/1.29 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1781) | (~c2_1(a1781)) | (~c3_1(a1781)) | c1_1(a1781) | (~c3_1(a1781)) | (~c0_1(a1781)) | c3_1(a1758) | c0_1(a1758) | (~c2_1(a1758)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1781) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c3_1(a1781)))),
% 1.55/1.29 inference(transitivity,[status(thm)],[1676, 1674])).
% 1.55/1.29 tff(1678,plain,
% 1.55/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1781) | (~c2_1(a1781)) | (~c3_1(a1781)) | c1_1(a1781) | (~c3_1(a1781)) | (~c0_1(a1781)) | c3_1(a1758) | c0_1(a1758) | (~c2_1(a1758)))),
% 1.55/1.29 inference(quant_inst,[status(thm)],[])).
% 1.55/1.29 tff(1679,plain,
% 1.55/1.29 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1781) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c3_1(a1781))),
% 1.55/1.29 inference(modus_ponens,[status(thm)],[1678, 1677])).
% 1.55/1.30 tff(1680,plain,
% 1.55/1.30 (~c0_1(a1781)),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[1679, 111, 1673, 1672, 721, 1671, 702, 819, 1663])).
% 1.55/1.30 tff(1681,assumption,(hskp8), introduced(assumption)).
% 1.55/1.30 tff(1682,plain,
% 1.55/1.30 (~c1_1(a1765)),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[326, 1681])).
% 1.55/1.30 tff(1683,plain,
% 1.55/1.30 (c2_1(a1765)),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[444, 1681])).
% 1.55/1.30 tff(1684,plain,
% 1.55/1.30 (c0_1(a1765)),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[455, 1681])).
% 1.55/1.30 tff(1685,plain,
% 1.55/1.30 ($false),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[464, 111, 712, 722, 1684, 1683, 423, 275, 1682, 403, 46, 1245])).
% 1.55/1.30 tff(1686,plain,((~hskp8) | (~c1_1(a1771)) | (~c2_1(a1771)) | (~c3_1(a1762)) | c0_1(a1771) | c0_1(a1762) | c1_1(a1762)), inference(lemma,lemma(discharge,[]))).
% 1.55/1.30 tff(1687,plain,
% 1.55/1.30 (~hskp8),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[1686, 1245, 722, 423, 275, 403, 712])).
% 1.55/1.30 tff(1688,plain,
% 1.55/1.30 (~c3_1(a1771)),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[1296, 1687])).
% 1.55/1.30 tff(1689,plain,
% 1.55/1.30 (~c1_1(a1763)),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[1074, 1264])).
% 1.55/1.30 tff(1690,plain,
% 1.55/1.30 ($false),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[1278, 1689, 1264, 722, 404, 423, 275, 1267, 1245])).
% 1.55/1.30 tff(1691,plain,((~hskp7) | (~c2_1(a1771)) | (~c2_1(a1762)) | (~c3_1(a1762)) | c0_1(a1771) | c3_1(a1771) | c1_1(a1762)), inference(lemma,lemma(discharge,[]))).
% 1.55/1.30 tff(1692,plain,
% 1.55/1.30 (~hskp7),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[1691, 1688, 404, 423, 275, 722, 1245])).
% 1.55/1.30 tff(1693,plain,
% 1.55/1.30 (hskp8 | hskp4),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[320, 111, 404, 423, 403, 130])).
% 1.55/1.30 tff(1694,plain,
% 1.55/1.30 (hskp4),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[1693, 1687])).
% 1.55/1.30 tff(1695,plain,
% 1.55/1.30 (~c2_1(a1759)),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[950, 1694])).
% 1.55/1.30 tff(1696,plain,
% 1.55/1.30 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c1_1(a1781) | c2_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | c0_1(a1781) | (~c3_1(a1781)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a1781) | c2_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | c0_1(a1781) | (~c3_1(a1781)))),
% 1.55/1.30 inference(rewrite,[status(thm)],[])).
% 1.55/1.30 tff(1697,plain,
% 1.55/1.30 ((hskp7 | (~ndr1_0) | c2_1(a1759) | c0_1(a1759) | (~c1_1(a1759)) | c1_1(a1781) | c0_1(a1781) | (~c3_1(a1781))) <=> (hskp7 | c1_1(a1781) | c2_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | c0_1(a1781) | (~c3_1(a1781)))),
% 1.55/1.30 inference(rewrite,[status(thm)],[])).
% 1.55/1.30 tff(1698,plain,
% 1.55/1.30 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1759) | c0_1(a1759) | (~c1_1(a1759)) | c1_1(a1781) | c0_1(a1781) | (~c3_1(a1781)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c1_1(a1781) | c2_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | c0_1(a1781) | (~c3_1(a1781))))),
% 1.55/1.30 inference(monotonicity,[status(thm)],[1697])).
% 1.55/1.30 tff(1699,plain,
% 1.55/1.30 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1759) | c0_1(a1759) | (~c1_1(a1759)) | c1_1(a1781) | c0_1(a1781) | (~c3_1(a1781)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a1781) | c2_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | c0_1(a1781) | (~c3_1(a1781)))),
% 1.55/1.30 inference(transitivity,[status(thm)],[1698, 1696])).
% 1.55/1.30 tff(1700,plain,
% 1.55/1.30 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1759) | c0_1(a1759) | (~c1_1(a1759)) | c1_1(a1781) | c0_1(a1781) | (~c3_1(a1781)))),
% 1.55/1.30 inference(quant_inst,[status(thm)],[])).
% 1.55/1.30 tff(1701,plain,
% 1.55/1.30 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a1781) | c2_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | c0_1(a1781) | (~c3_1(a1781))),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1700, 1699])).
% 1.55/1.30 tff(1702,plain,
% 1.55/1.30 (hskp7 | c0_1(a1759)),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[1701, 111, 1672, 938, 1671, 1695, 1061, 1680])).
% 1.55/1.30 tff(1703,plain,
% 1.55/1.30 (c0_1(a1759)),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[1702, 1692])).
% 1.55/1.30 tff(1704,plain,
% 1.55/1.30 (~hskp29),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[1581, 1703, 1673, 1688, 722, 1671, 275, 1672, 938, 34])).
% 1.55/1.30 tff(1705,plain,
% 1.55/1.30 (hskp30 | hskp29 | c3_1(a1771)),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[1598, 111, 712, 722, 1592])).
% 1.55/1.30 tff(1706,plain,
% 1.55/1.30 (hskp30),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[1705, 1704, 1688])).
% 1.55/1.30 tff(1707,plain,
% 1.55/1.30 (c3_1(a1823)),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[1610, 1706])).
% 1.55/1.30 tff(1708,plain,
% 1.55/1.30 (c2_1(a1823)),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[1621, 1706])).
% 1.55/1.30 tff(1709,plain,
% 1.55/1.30 (c1_1(a1823)),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[1632, 1706])).
% 1.55/1.30 tff(1710,plain,
% 1.55/1.30 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | c1_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c1_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)))),
% 1.55/1.30 inference(rewrite,[status(thm)],[])).
% 1.55/1.30 tff(1711,plain,
% 1.55/1.30 ((hskp8 | (~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | c1_1(a1781) | c0_1(a1781) | (~c3_1(a1781))) <=> (hskp8 | c1_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)))),
% 1.55/1.30 inference(rewrite,[status(thm)],[])).
% 1.55/1.30 tff(1712,plain,
% 1.55/1.30 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | c1_1(a1781) | c0_1(a1781) | (~c3_1(a1781)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | c1_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823))))),
% 1.55/1.30 inference(monotonicity,[status(thm)],[1711])).
% 1.55/1.30 tff(1713,plain,
% 1.55/1.30 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | c1_1(a1781) | c0_1(a1781) | (~c3_1(a1781)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c1_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)))),
% 1.55/1.30 inference(transitivity,[status(thm)],[1712, 1710])).
% 1.55/1.30 tff(1714,plain,
% 1.55/1.30 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | c1_1(a1781) | c0_1(a1781) | (~c3_1(a1781)))),
% 1.55/1.30 inference(quant_inst,[status(thm)],[])).
% 1.55/1.30 tff(1715,plain,
% 1.55/1.30 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c1_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823))),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1714, 1713])).
% 1.55/1.30 tff(1716,plain,
% 1.55/1.30 ($false),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[1715, 111, 1687, 1709, 1708, 1707, 1672, 1671, 1289, 1680])).
% 1.55/1.30 tff(1717,plain,(c1_1(a1762) | (~c1_1(a1771)) | (~c2_1(a1771)) | c0_1(a1771) | (~c1_1(a1759)) | c3_1(a1759) | (~c2_1(a1762)) | (~c3_1(a1762)) | c0_1(a1762) | (~c2_1(a1758)) | c3_1(a1758) | (~c1_1(a1758))), inference(lemma,lemma(discharge,[]))).
% 1.55/1.30 tff(1718,plain,
% 1.55/1.30 (c1_1(a1762)),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[1717, 1227, 1240, 1239, 911, 34, 1238, 1237, 1236, 1645, 1644, 1643])).
% 1.55/1.30 tff(1719,plain,
% 1.55/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)))),
% 1.55/1.30 inference(rewrite,[status(thm)],[])).
% 1.55/1.30 tff(1720,plain,
% 1.55/1.30 (((~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1762)) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758))) <=> (c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)))),
% 1.55/1.30 inference(rewrite,[status(thm)],[])).
% 1.55/1.30 tff(1721,plain,
% 1.55/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1762)) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762))))),
% 1.55/1.30 inference(monotonicity,[status(thm)],[1720])).
% 1.55/1.30 tff(1722,plain,
% 1.55/1.30 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1762)) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)))),
% 1.55/1.30 inference(transitivity,[status(thm)],[1721, 1719])).
% 1.55/1.30 tff(1723,plain,
% 1.55/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1762)) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)))),
% 1.55/1.30 inference(quant_inst,[status(thm)],[])).
% 1.55/1.30 tff(1724,plain,
% 1.55/1.30 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762))),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1723, 1722])).
% 1.55/1.30 tff(1725,plain,
% 1.55/1.30 ((~c0_1(a1758)) | (~c1_1(a1762))),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[1724, 111, 1238, 1237, 1643, 1645, 1644, 678])).
% 1.55/1.30 tff(1726,plain,
% 1.55/1.30 (~c0_1(a1758)),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[1725, 1718])).
% 1.55/1.30 tff(1727,plain,
% 1.55/1.30 (hskp17 | (~c1_1(a1762))),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[1319, 111, 1238, 1237, 1236, 1313])).
% 1.55/1.30 tff(1728,plain,
% 1.55/1.30 (hskp17),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[1727, 1718])).
% 1.55/1.30 tff(1729,plain,
% 1.55/1.30 (~c1_1(a1781)),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[1160, 1728])).
% 1.55/1.30 tff(1730,plain,
% 1.55/1.30 (c3_1(a1781)),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[1182, 1728])).
% 1.55/1.30 tff(1731,plain,
% 1.55/1.30 (c2_1(a1781)),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[1193, 1728])).
% 1.55/1.30 tff(1732,plain,
% 1.55/1.30 (~c0_1(a1781)),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[1679, 111, 1731, 1730, 1645, 1729, 1644, 819, 1726])).
% 1.55/1.30 tff(1733,plain,
% 1.55/1.30 (hskp8),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[1377, 111, 1730, 1238, 1237, 1729, 1289, 1718, 1732])).
% 1.55/1.30 tff(1734,plain,
% 1.55/1.30 (~c1_1(a1765)),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[326, 1733])).
% 1.55/1.30 tff(1735,plain,
% 1.55/1.30 (c2_1(a1765)),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[444, 1733])).
% 1.55/1.30 tff(1736,plain,
% 1.55/1.30 (c0_1(a1765)),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[455, 1733])).
% 1.55/1.30 tff(1737,plain,
% 1.55/1.30 ($false),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[1388, 111, 1730, 1227, 1240, 1736, 1735, 1729, 1239, 1734, 46, 1732])).
% 1.55/1.30 tff(1738,plain,(c3_1(a1759) | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.55/1.30 tff(1739,plain,
% 1.55/1.30 (c3_1(a1759)),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[1738, 12])).
% 1.55/1.30 tff(1740,plain,
% 1.55/1.30 (((~hskp4) | (~c3_1(a1759))) <=> ((~hskp4) | (~c3_1(a1759)))),
% 1.55/1.30 inference(rewrite,[status(thm)],[])).
% 1.55/1.30 tff(1741,plain,
% 1.55/1.30 (((~c3_1(a1759)) | (~hskp4)) <=> ((~hskp4) | (~c3_1(a1759)))),
% 1.55/1.30 inference(rewrite,[status(thm)],[])).
% 1.55/1.30 tff(1742,axiom,((~c3_1(a1759)) | (~hskp4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause124')).
% 1.55/1.30 tff(1743,plain,
% 1.55/1.30 ((~hskp4) | (~c3_1(a1759))),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1742, 1741])).
% 1.55/1.30 tff(1744,plain,
% 1.55/1.30 ((~hskp4) | (~c3_1(a1759))),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1743, 1740])).
% 1.55/1.30 tff(1745,plain,
% 1.55/1.30 (~hskp4),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[1744, 1739])).
% 1.55/1.30 tff(1746,plain,
% 1.55/1.30 (^[U: $i] : refl((hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))),
% 1.55/1.30 inference(bind,[status(th)],[])).
% 1.55/1.30 tff(1747,plain,
% 1.55/1.30 (![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.55/1.30 inference(quant_intro,[status(thm)],[1746])).
% 1.55/1.30 tff(1748,plain,
% 1.55/1.30 (![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.55/1.30 inference(rewrite,[status(thm)],[])).
% 1.55/1.30 tff(1749,plain,
% 1.55/1.30 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp4) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp4))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp4) <=> (hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp4) | hskp6) <=> ((hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp6))), rewrite(((hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp6) <=> (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp4) | hskp6) <=> (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))))),
% 1.55/1.30 inference(bind,[status(th)],[])).
% 1.55/1.30 tff(1750,plain,
% 1.55/1.30 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp4) | hskp6) <=> ![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.55/1.30 inference(quant_intro,[status(thm)],[1749])).
% 1.55/1.30 tff(1751,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp4) | hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause135')).
% 1.55/1.30 tff(1752,plain,
% 1.55/1.30 (![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1751, 1750])).
% 1.55/1.30 tff(1753,plain,
% 1.55/1.30 (![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1752, 1748])).
% 1.55/1.30 tff(1754,plain,(
% 1.55/1.30 ![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.55/1.30 inference(skolemize,[status(sab)],[1753])).
% 1.55/1.30 tff(1755,plain,
% 1.55/1.30 (![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1754, 1747])).
% 1.55/1.30 tff(1756,assumption,(hskp0), introduced(assumption)).
% 1.55/1.30 tff(1757,plain,
% 1.55/1.30 (((~hskp0) | (~c1_1(a1754))) <=> ((~hskp0) | (~c1_1(a1754)))),
% 1.55/1.30 inference(rewrite,[status(thm)],[])).
% 1.55/1.30 tff(1758,plain,
% 1.55/1.30 (((~c1_1(a1754)) | (~hskp0)) <=> ((~hskp0) | (~c1_1(a1754)))),
% 1.55/1.30 inference(rewrite,[status(thm)],[])).
% 1.55/1.30 tff(1759,axiom,((~c1_1(a1754)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause130')).
% 1.55/1.30 tff(1760,plain,
% 1.55/1.30 ((~hskp0) | (~c1_1(a1754))),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1759, 1758])).
% 1.55/1.30 tff(1761,plain,
% 1.55/1.30 ((~hskp0) | (~c1_1(a1754))),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1760, 1757])).
% 1.55/1.30 tff(1762,plain,
% 1.55/1.30 (~c1_1(a1754)),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[1761, 1756])).
% 1.55/1.30 tff(1763,plain,
% 1.55/1.30 (((~hskp0) | (~c0_1(a1754))) <=> ((~hskp0) | (~c0_1(a1754)))),
% 1.55/1.30 inference(rewrite,[status(thm)],[])).
% 1.55/1.30 tff(1764,plain,
% 1.55/1.30 (((~c0_1(a1754)) | (~hskp0)) <=> ((~hskp0) | (~c0_1(a1754)))),
% 1.55/1.30 inference(rewrite,[status(thm)],[])).
% 1.55/1.30 tff(1765,axiom,((~c0_1(a1754)) | (~hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause129')).
% 1.55/1.30 tff(1766,plain,
% 1.55/1.30 ((~hskp0) | (~c0_1(a1754))),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1765, 1764])).
% 1.55/1.30 tff(1767,plain,
% 1.55/1.30 ((~hskp0) | (~c0_1(a1754))),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1766, 1763])).
% 1.55/1.30 tff(1768,plain,
% 1.55/1.30 (~c0_1(a1754)),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[1767, 1756])).
% 1.55/1.30 tff(1769,plain,
% 1.55/1.30 (((~hskp0) | c2_1(a1754)) <=> ((~hskp0) | c2_1(a1754))),
% 1.55/1.30 inference(rewrite,[status(thm)],[])).
% 1.55/1.30 tff(1770,axiom,((~hskp0) | c2_1(a1754)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause84')).
% 1.55/1.30 tff(1771,plain,
% 1.55/1.30 ((~hskp0) | c2_1(a1754)),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1770, 1769])).
% 1.55/1.30 tff(1772,plain,
% 1.55/1.30 ((~hskp0) | c2_1(a1754)),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1771, 1769])).
% 1.55/1.30 tff(1773,plain,
% 1.55/1.30 ((~hskp0) | c2_1(a1754)),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1772, 1769])).
% 1.55/1.30 tff(1774,plain,
% 1.55/1.30 ((~hskp0) | c2_1(a1754)),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1773, 1769])).
% 1.55/1.30 tff(1775,plain,
% 1.55/1.30 ((~hskp0) | c2_1(a1754)),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1774, 1769])).
% 1.55/1.30 tff(1776,plain,
% 1.55/1.30 ((~hskp0) | c2_1(a1754)),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1775, 1769])).
% 1.55/1.30 tff(1777,plain,
% 1.55/1.30 ((~hskp0) | c2_1(a1754)),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1776, 1769])).
% 1.55/1.30 tff(1778,plain,
% 1.55/1.30 ((~hskp0) | c2_1(a1754)),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1777, 1769])).
% 1.55/1.30 tff(1779,plain,
% 1.55/1.30 (c2_1(a1754)),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[1778, 1756])).
% 1.55/1.30 tff(1780,plain,
% 1.55/1.30 (((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp4 | c0_1(a1754) | c1_1(a1754) | (~ndr1_0) | (~c2_1(a1754)))) <=> ((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp4 | c0_1(a1754) | c1_1(a1754) | (~ndr1_0) | (~c2_1(a1754)))),
% 1.55/1.30 inference(rewrite,[status(thm)],[])).
% 1.55/1.30 tff(1781,plain,
% 1.55/1.30 ((hskp6 | hskp4 | (~ndr1_0) | c1_1(a1754) | c0_1(a1754) | (~c2_1(a1754))) <=> (hskp6 | hskp4 | c0_1(a1754) | c1_1(a1754) | (~ndr1_0) | (~c2_1(a1754)))),
% 1.55/1.30 inference(rewrite,[status(thm)],[])).
% 1.55/1.30 tff(1782,plain,
% 1.55/1.30 (((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp4 | (~ndr1_0) | c1_1(a1754) | c0_1(a1754) | (~c2_1(a1754)))) <=> ((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp4 | c0_1(a1754) | c1_1(a1754) | (~ndr1_0) | (~c2_1(a1754))))),
% 1.55/1.30 inference(monotonicity,[status(thm)],[1781])).
% 1.55/1.30 tff(1783,plain,
% 1.55/1.30 (((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp4 | (~ndr1_0) | c1_1(a1754) | c0_1(a1754) | (~c2_1(a1754)))) <=> ((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp4 | c0_1(a1754) | c1_1(a1754) | (~ndr1_0) | (~c2_1(a1754)))),
% 1.55/1.30 inference(transitivity,[status(thm)],[1782, 1780])).
% 1.55/1.30 tff(1784,plain,
% 1.55/1.30 ((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp4 | (~ndr1_0) | c1_1(a1754) | c0_1(a1754) | (~c2_1(a1754)))),
% 1.55/1.30 inference(quant_inst,[status(thm)],[])).
% 1.55/1.30 tff(1785,plain,
% 1.55/1.30 ((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp4 | c0_1(a1754) | c1_1(a1754) | (~ndr1_0) | (~c2_1(a1754))),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1784, 1783])).
% 1.55/1.30 tff(1786,plain,
% 1.55/1.30 ($false),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[1785, 111, 240, 342, 1779, 1768, 1762, 1755])).
% 1.55/1.30 tff(1787,plain,((~hskp0) | hskp6 | hskp4), inference(lemma,lemma(discharge,[]))).
% 1.55/1.30 tff(1788,plain,
% 1.55/1.30 (~hskp0),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[1787, 240, 1745])).
% 1.55/1.30 tff(1789,plain,
% 1.55/1.30 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))),
% 1.55/1.30 inference(bind,[status(th)],[])).
% 1.55/1.30 tff(1790,plain,
% 1.55/1.30 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.55/1.30 inference(quant_intro,[status(thm)],[1789])).
% 1.55/1.30 tff(1791,plain,
% 1.55/1.30 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.55/1.30 inference(rewrite,[status(thm)],[])).
% 1.55/1.30 tff(1792,plain,
% 1.55/1.30 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))), (((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))))),
% 1.55/1.30 inference(bind,[status(th)],[])).
% 1.55/1.30 tff(1793,plain,
% 1.55/1.30 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.55/1.30 inference(quant_intro,[status(thm)],[1792])).
% 1.55/1.30 tff(1794,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause154')).
% 1.55/1.30 tff(1795,plain,
% 1.55/1.30 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1794, 1793])).
% 1.55/1.30 tff(1796,plain,
% 1.55/1.30 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1795, 1791])).
% 1.55/1.30 tff(1797,plain,(
% 1.55/1.30 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.55/1.30 inference(skolemize,[status(sab)],[1796])).
% 1.55/1.30 tff(1798,plain,
% 1.55/1.30 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1797, 1790])).
% 1.55/1.30 tff(1799,plain,
% 1.55/1.30 (~hskp13),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[1234, 240, 12])).
% 1.55/1.30 tff(1800,plain,
% 1.55/1.30 (~hskp2),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[119, 1799, 12])).
% 1.55/1.30 tff(1801,plain,
% 1.55/1.30 (hskp25),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[162, 1800, 1745])).
% 1.55/1.30 tff(1802,plain,
% 1.55/1.30 (~c2_1(a1827)),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[223, 1801])).
% 1.55/1.30 tff(1803,plain,
% 1.55/1.30 (~c1_1(a1827)),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[168, 1801])).
% 1.55/1.30 tff(1804,plain,
% 1.55/1.30 (~c0_1(a1827)),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[174, 1801])).
% 1.55/1.30 tff(1805,plain,
% 1.55/1.30 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a1827) | c1_1(a1827) | c2_1(a1827) | (~ndr1_0) | (~c3_1(a1827)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a1827) | c1_1(a1827) | c2_1(a1827) | (~ndr1_0) | (~c3_1(a1827)))),
% 1.55/1.30 inference(rewrite,[status(thm)],[])).
% 1.55/1.30 tff(1806,plain,
% 1.55/1.30 ((hskp0 | (~ndr1_0) | c2_1(a1827) | c0_1(a1827) | (~c3_1(a1827)) | c2_1(a1827) | c1_1(a1827) | c0_1(a1827)) <=> (hskp0 | c0_1(a1827) | c1_1(a1827) | c2_1(a1827) | (~ndr1_0) | (~c3_1(a1827)))),
% 1.55/1.30 inference(rewrite,[status(thm)],[])).
% 1.55/1.30 tff(1807,plain,
% 1.55/1.30 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1827) | c0_1(a1827) | (~c3_1(a1827)) | c2_1(a1827) | c1_1(a1827) | c0_1(a1827))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c0_1(a1827) | c1_1(a1827) | c2_1(a1827) | (~ndr1_0) | (~c3_1(a1827))))),
% 1.55/1.30 inference(monotonicity,[status(thm)],[1806])).
% 1.55/1.30 tff(1808,plain,
% 1.55/1.30 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1827) | c0_1(a1827) | (~c3_1(a1827)) | c2_1(a1827) | c1_1(a1827) | c0_1(a1827))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a1827) | c1_1(a1827) | c2_1(a1827) | (~ndr1_0) | (~c3_1(a1827)))),
% 1.55/1.30 inference(transitivity,[status(thm)],[1807, 1805])).
% 1.55/1.30 tff(1809,plain,
% 1.55/1.30 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1827) | c0_1(a1827) | (~c3_1(a1827)) | c2_1(a1827) | c1_1(a1827) | c0_1(a1827))),
% 1.55/1.30 inference(quant_inst,[status(thm)],[])).
% 1.55/1.30 tff(1810,plain,
% 1.55/1.30 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c0_1(a1827) | c1_1(a1827) | c2_1(a1827) | (~ndr1_0) | (~c3_1(a1827))),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1809, 1808])).
% 1.55/1.30 tff(1811,plain,
% 1.55/1.30 (hskp0 | (~c3_1(a1827))),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[1810, 111, 1804, 1803, 1802, 1798])).
% 1.55/1.30 tff(1812,plain,
% 1.55/1.30 (~c3_1(a1827)),
% 1.55/1.30 inference(unit_resolution,[status(thm)],[1811, 1788])).
% 1.55/1.30 tff(1813,plain,
% 1.55/1.30 (^[U: $i] : refl((hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) <=> (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)))),
% 1.55/1.30 inference(bind,[status(th)],[])).
% 1.55/1.30 tff(1814,plain,
% 1.55/1.30 (![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) <=> ![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 1.55/1.30 inference(quant_intro,[status(thm)],[1813])).
% 1.55/1.30 tff(1815,plain,
% 1.55/1.30 (![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) <=> ![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 1.55/1.30 inference(rewrite,[status(thm)],[])).
% 1.55/1.30 tff(1816,plain,
% 1.55/1.30 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U)))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))), (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp11) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) | hskp11))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U)) | hskp11) <=> (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))), ((((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp11) <=> (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))))),
% 1.55/1.30 inference(bind,[status(th)],[])).
% 1.55/1.30 tff(1817,plain,
% 1.55/1.30 (![U: $i] : (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp11) <=> ![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 1.55/1.30 inference(quant_intro,[status(thm)],[1816])).
% 1.55/1.30 tff(1818,axiom,(![U: $i] : (((((~ndr1_0) | c1_1(U)) | c2_1(U)) | c3_1(U)) | hskp11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause131')).
% 1.55/1.30 tff(1819,plain,
% 1.55/1.30 (![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1818, 1817])).
% 1.55/1.30 tff(1820,plain,
% 1.55/1.30 (![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1819, 1815])).
% 1.55/1.30 tff(1821,plain,(
% 1.55/1.30 ![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 1.55/1.30 inference(skolemize,[status(sab)],[1820])).
% 1.55/1.30 tff(1822,plain,
% 1.55/1.30 (![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))),
% 1.55/1.30 inference(modus_ponens,[status(thm)],[1821, 1814])).
% 1.55/1.30 tff(1823,plain,
% 1.55/1.30 (((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp11 | c1_1(a1827) | c2_1(a1827) | (~ndr1_0) | c3_1(a1827))) <=> ((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp11 | c1_1(a1827) | c2_1(a1827) | (~ndr1_0) | c3_1(a1827))),
% 1.55/1.30 inference(rewrite,[status(thm)],[])).
% 1.55/1.30 tff(1824,plain,
% 1.55/1.30 ((hskp11 | (~ndr1_0) | c3_1(a1827) | c2_1(a1827) | c1_1(a1827)) <=> (hskp11 | c1_1(a1827) | c2_1(a1827) | (~ndr1_0) | c3_1(a1827))),
% 1.55/1.30 inference(rewrite,[status(thm)],[])).
% 1.55/1.30 tff(1825,plain,
% 1.55/1.30 (((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp11 | (~ndr1_0) | c3_1(a1827) | c2_1(a1827) | c1_1(a1827))) <=> ((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp11 | c1_1(a1827) | c2_1(a1827) | (~ndr1_0) | c3_1(a1827)))),
% 1.55/1.30 inference(monotonicity,[status(thm)],[1824])).
% 1.55/1.30 tff(1826,plain,
% 1.55/1.30 (((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp11 | (~ndr1_0) | c3_1(a1827) | c2_1(a1827) | c1_1(a1827))) <=> ((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp11 | c1_1(a1827) | c2_1(a1827) | (~ndr1_0) | c3_1(a1827))),
% 1.55/1.31 inference(transitivity,[status(thm)],[1825, 1823])).
% 1.55/1.31 tff(1827,plain,
% 1.55/1.31 ((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | (hskp11 | (~ndr1_0) | c3_1(a1827) | c2_1(a1827) | c1_1(a1827))),
% 1.55/1.31 inference(quant_inst,[status(thm)],[])).
% 1.55/1.31 tff(1828,plain,
% 1.55/1.31 ((~![U: $i] : (hskp11 | (~ndr1_0) | c3_1(U) | c2_1(U) | c1_1(U))) | hskp11 | c1_1(a1827) | c2_1(a1827) | (~ndr1_0) | c3_1(a1827)),
% 1.55/1.31 inference(modus_ponens,[status(thm)],[1827, 1826])).
% 1.55/1.31 tff(1829,plain,
% 1.55/1.31 (hskp11 | c3_1(a1827)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[1828, 111, 1803, 1802, 1822])).
% 1.55/1.31 tff(1830,plain,
% 1.55/1.31 (hskp11),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[1829, 1812])).
% 1.55/1.31 tff(1831,plain,
% 1.55/1.31 (~c2_1(a1768)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[1109, 1830])).
% 1.55/1.31 tff(1832,plain,
% 1.55/1.31 (c0_1(a1768)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[1120, 1830])).
% 1.55/1.31 tff(1833,plain,
% 1.55/1.31 (~c1_1(a1768)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[1127, 111, 12, 1799, 1832, 1831, 33])).
% 1.55/1.31 tff(1834,plain,
% 1.55/1.31 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))),
% 1.55/1.31 inference(bind,[status(th)],[])).
% 1.55/1.31 tff(1835,plain,
% 1.55/1.31 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.55/1.31 inference(quant_intro,[status(thm)],[1834])).
% 1.55/1.31 tff(1836,plain,
% 1.55/1.31 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.55/1.31 inference(rewrite,[status(thm)],[])).
% 1.55/1.31 tff(1837,plain,
% 1.55/1.31 (^[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)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) | hskp0) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp0))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V))) | hskp0) <=> (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))))),
% 1.55/1.31 inference(bind,[status(th)],[])).
% 1.55/1.31 tff(1838,plain,
% 1.55/1.31 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.55/1.31 inference(quant_intro,[status(thm)],[1837])).
% 1.55/1.31 tff(1839,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(V)) | c2_1(V)) | hskp0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause181')).
% 1.55/1.31 tff(1840,plain,
% 1.55/1.31 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.55/1.31 inference(modus_ponens,[status(thm)],[1839, 1838])).
% 1.55/1.31 tff(1841,plain,
% 1.55/1.31 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.55/1.31 inference(modus_ponens,[status(thm)],[1840, 1836])).
% 1.55/1.31 tff(1842,plain,(
% 1.55/1.31 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.55/1.31 inference(skolemize,[status(sab)],[1841])).
% 1.55/1.31 tff(1843,plain,
% 1.55/1.31 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))),
% 1.55/1.31 inference(modus_ponens,[status(thm)],[1842, 1835])).
% 1.55/1.31 tff(1844,plain,
% 1.55/1.31 (c3_1(a1768)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[1171, 1830])).
% 1.55/1.31 tff(1845,plain,
% 1.55/1.31 (((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp27 | hskp2 | c0_1(a1827) | c1_1(a1827) | (~ndr1_0) | c3_1(a1827))) <=> ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp27 | hskp2 | c0_1(a1827) | c1_1(a1827) | (~ndr1_0) | c3_1(a1827))),
% 1.55/1.31 inference(rewrite,[status(thm)],[])).
% 1.55/1.31 tff(1846,plain,
% 1.55/1.31 ((hskp27 | hskp2 | (~ndr1_0) | c3_1(a1827) | c1_1(a1827) | c0_1(a1827)) <=> (hskp27 | hskp2 | c0_1(a1827) | c1_1(a1827) | (~ndr1_0) | c3_1(a1827))),
% 1.55/1.31 inference(rewrite,[status(thm)],[])).
% 1.55/1.31 tff(1847,plain,
% 1.55/1.31 (((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp27 | hskp2 | (~ndr1_0) | c3_1(a1827) | c1_1(a1827) | c0_1(a1827))) <=> ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp27 | hskp2 | c0_1(a1827) | c1_1(a1827) | (~ndr1_0) | c3_1(a1827)))),
% 1.55/1.31 inference(monotonicity,[status(thm)],[1846])).
% 1.55/1.31 tff(1848,plain,
% 1.55/1.31 (((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp27 | hskp2 | (~ndr1_0) | c3_1(a1827) | c1_1(a1827) | c0_1(a1827))) <=> ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp27 | hskp2 | c0_1(a1827) | c1_1(a1827) | (~ndr1_0) | c3_1(a1827))),
% 1.55/1.31 inference(transitivity,[status(thm)],[1847, 1845])).
% 1.55/1.31 tff(1849,plain,
% 1.55/1.31 ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp27 | hskp2 | (~ndr1_0) | c3_1(a1827) | c1_1(a1827) | c0_1(a1827))),
% 1.55/1.31 inference(quant_inst,[status(thm)],[])).
% 1.55/1.31 tff(1850,plain,
% 1.55/1.31 ((~![U: $i] : (hskp27 | hskp2 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp27 | hskp2 | c0_1(a1827) | c1_1(a1827) | (~ndr1_0) | c3_1(a1827)),
% 1.55/1.31 inference(modus_ponens,[status(thm)],[1849, 1848])).
% 1.55/1.31 tff(1851,plain,
% 1.55/1.31 (hskp27 | c3_1(a1827)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[1850, 111, 1800, 1804, 1803, 657])).
% 1.55/1.31 tff(1852,plain,
% 1.55/1.31 (hskp27),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[1851, 1812])).
% 1.55/1.31 tff(1853,plain,
% 1.55/1.31 (c3_1(a1756)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[372, 1852])).
% 1.55/1.31 tff(1854,plain,
% 1.55/1.31 (c1_1(a1756)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[383, 1852])).
% 1.55/1.31 tff(1855,plain,
% 1.55/1.31 (c0_1(a1756)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[394, 1852])).
% 1.55/1.31 tff(1856,plain,
% 1.55/1.31 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | c2_1(a1768) | (~ndr1_0) | c1_1(a1768) | (~c3_1(a1768)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c2_1(a1768) | (~ndr1_0) | c1_1(a1768) | (~c3_1(a1768)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))),
% 1.55/1.31 inference(rewrite,[status(thm)],[])).
% 1.55/1.31 tff(1857,plain,
% 1.55/1.31 ((hskp0 | (~ndr1_0) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)) | c2_1(a1768) | c1_1(a1768) | (~c3_1(a1768))) <=> (hskp0 | c2_1(a1768) | (~ndr1_0) | c1_1(a1768) | (~c3_1(a1768)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))),
% 1.55/1.31 inference(rewrite,[status(thm)],[])).
% 1.55/1.31 tff(1858,plain,
% 1.55/1.31 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)) | c2_1(a1768) | c1_1(a1768) | (~c3_1(a1768)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | c2_1(a1768) | (~ndr1_0) | c1_1(a1768) | (~c3_1(a1768)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756))))),
% 1.55/1.31 inference(monotonicity,[status(thm)],[1857])).
% 1.55/1.31 tff(1859,plain,
% 1.55/1.31 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)) | c2_1(a1768) | c1_1(a1768) | (~c3_1(a1768)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c2_1(a1768) | (~ndr1_0) | c1_1(a1768) | (~c3_1(a1768)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))),
% 1.55/1.31 inference(transitivity,[status(thm)],[1858, 1856])).
% 1.55/1.31 tff(1860,plain,
% 1.55/1.31 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)) | c2_1(a1768) | c1_1(a1768) | (~c3_1(a1768)))),
% 1.55/1.31 inference(quant_inst,[status(thm)],[])).
% 1.55/1.31 tff(1861,plain,
% 1.55/1.31 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c2_1(a1768) | (~ndr1_0) | c1_1(a1768) | (~c3_1(a1768)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756))),
% 1.55/1.31 inference(modus_ponens,[status(thm)],[1860, 1859])).
% 1.55/1.31 tff(1862,plain,
% 1.55/1.31 ($false),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[1861, 111, 1788, 1855, 1854, 1853, 1844, 1831, 1843, 1833])).
% 1.55/1.31 tff(1863,plain,(hskp6 | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.55/1.31 tff(1864,plain,
% 1.55/1.31 (hskp6),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[1863, 12])).
% 1.55/1.31 tff(1865,plain,
% 1.55/1.31 (~c0_1(a1762)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[291, 1864])).
% 1.55/1.31 tff(1866,plain,
% 1.55/1.31 (c2_1(a1762)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[313, 1864])).
% 1.55/1.31 tff(1867,plain,
% 1.55/1.31 (hskp13 | (~c1_1(a1762))),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[410, 111, 1866, 1865, 22])).
% 1.55/1.31 tff(1868,plain,
% 1.55/1.31 (~c1_1(a1762)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[1867, 23])).
% 1.55/1.31 tff(1869,plain,
% 1.55/1.31 (c3_1(a1762)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[302, 1864])).
% 1.55/1.31 tff(1870,assumption,(~hskp2), introduced(assumption)).
% 1.55/1.31 tff(1871,plain,
% 1.55/1.31 (hskp25),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[162, 342, 1870])).
% 1.55/1.31 tff(1872,plain,
% 1.55/1.31 (~c1_1(a1827)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[168, 1871])).
% 1.55/1.31 tff(1873,plain,
% 1.55/1.31 (~c0_1(a1827)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[174, 1871])).
% 1.55/1.31 tff(1874,plain,
% 1.55/1.31 (c3_1(a1827)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[181, 111, 342, 35, 1873, 1872, 140])).
% 1.55/1.31 tff(1875,plain,
% 1.55/1.31 (~c2_1(a1827)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[223, 1871])).
% 1.55/1.31 tff(1876,plain,
% 1.55/1.31 ($false),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[1538, 111, 404, 423, 1872, 1875, 403, 1138, 1245, 1874])).
% 1.55/1.31 tff(1877,plain,(hskp4 | (~c2_1(a1762)) | (~c3_1(a1762)) | c0_1(a1762) | c1_1(a1762) | hskp3 | hskp2), inference(lemma,lemma(discharge,[]))).
% 1.55/1.31 tff(1878,plain,
% 1.55/1.31 (hskp3),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[1877, 120, 1869, 1865, 1745, 1866, 1868])).
% 1.55/1.31 tff(1879,plain,
% 1.55/1.31 (c2_1(a1758)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[613, 1878])).
% 1.55/1.31 tff(1880,plain,
% 1.55/1.31 (c1_1(a1758)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[624, 1878])).
% 1.55/1.31 tff(1881,plain,
% 1.55/1.31 (c0_1(a1758)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[631, 111, 23, 1880, 1879, 22])).
% 1.55/1.31 tff(1882,plain,
% 1.55/1.31 (~c3_1(a1758)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[638, 1878])).
% 1.55/1.31 tff(1883,plain,
% 1.55/1.31 (hskp8),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[320, 111, 1745, 1866, 1869, 1865, 130])).
% 1.55/1.31 tff(1884,plain,
% 1.55/1.31 (~c1_1(a1765)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[326, 1883])).
% 1.55/1.31 tff(1885,plain,
% 1.55/1.31 (c2_1(a1765)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[444, 1883])).
% 1.55/1.31 tff(1886,plain,
% 1.55/1.31 (c0_1(a1765)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[455, 1883])).
% 1.55/1.31 tff(1887,plain,
% 1.55/1.31 ($false),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[808, 111, 1886, 1885, 1880, 1879, 1884, 1882, 802, 1881])).
% 1.55/1.31 tff(1888,plain,(hskp13 | hskp19), inference(lemma,lemma(discharge,[]))).
% 1.55/1.31 tff(1889,plain,
% 1.55/1.31 (hskp13),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[1888, 12])).
% 1.55/1.31 tff(1890,plain,
% 1.55/1.31 (c1_1(a1771)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[252, 1889])).
% 1.55/1.31 tff(1891,plain,
% 1.55/1.31 (~c0_1(a1771)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[238, 1889])).
% 1.55/1.31 tff(1892,plain,
% 1.55/1.31 (c2_1(a1771)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[263, 1889])).
% 1.55/1.31 tff(1893,plain,
% 1.55/1.31 (c1_1(a1762)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[1686, 1892, 1883, 1869, 1891, 1865, 1890])).
% 1.55/1.31 tff(1894,plain,
% 1.55/1.31 (hskp3),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[1424, 1892, 1745, 1891, 1864, 12, 1890])).
% 1.55/1.31 tff(1895,plain,
% 1.55/1.31 (~c3_1(a1758)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[638, 1894])).
% 1.55/1.31 tff(1896,plain,
% 1.55/1.31 (c2_1(a1758)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[613, 1894])).
% 1.55/1.31 tff(1897,plain,
% 1.55/1.31 (c1_1(a1758)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[624, 1894])).
% 1.55/1.31 tff(1898,plain,
% 1.55/1.31 (~c0_1(a1758)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[1724, 111, 1866, 1869, 1897, 1896, 1895, 678, 1893])).
% 1.55/1.31 tff(1899,plain,
% 1.55/1.31 (~c3_1(a1765)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[825, 111, 1886, 1885, 1896, 1884, 1895, 819, 1898])).
% 1.55/1.31 tff(1900,plain,
% 1.55/1.31 (~hskp22),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[1390, 1890, 1892, 1891, 1866, 1869, 1865])).
% 1.55/1.31 tff(1901,plain,
% 1.55/1.31 ($false),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[842, 111, 1900, 1885, 1897, 1896, 1884, 1895, 836, 1899])).
% 1.55/1.31 tff(1902,plain,(hskp19), inference(lemma,lemma(discharge,[]))).
% 1.55/1.31 tff(1903,plain,
% 1.55/1.31 (((~hskp19) | (~c0_1(a1783))) <=> ((~hskp19) | (~c0_1(a1783)))),
% 1.55/1.31 inference(rewrite,[status(thm)],[])).
% 1.55/1.31 tff(1904,plain,
% 1.55/1.31 (((~c0_1(a1783)) | (~hskp19)) <=> ((~hskp19) | (~c0_1(a1783)))),
% 1.55/1.31 inference(rewrite,[status(thm)],[])).
% 1.55/1.31 tff(1905,axiom,((~c0_1(a1783)) | (~hskp19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause99')).
% 1.55/1.31 tff(1906,plain,
% 1.55/1.31 ((~hskp19) | (~c0_1(a1783))),
% 1.55/1.31 inference(modus_ponens,[status(thm)],[1905, 1904])).
% 1.55/1.31 tff(1907,plain,
% 1.55/1.31 ((~hskp19) | (~c0_1(a1783))),
% 1.55/1.31 inference(modus_ponens,[status(thm)],[1906, 1903])).
% 1.55/1.31 tff(1908,plain,
% 1.55/1.31 (~c0_1(a1783)),
% 1.55/1.31 inference(unit_resolution,[status(thm)],[1907, 1902])).
% 1.55/1.31 tff(1909,plain,
% 1.55/1.31 (((~hskp19) | c3_1(a1783)) <=> ((~hskp19) | c3_1(a1783))),
% 1.55/1.31 inference(rewrite,[status(thm)],[])).
% 1.55/1.31 tff(1910,axiom,((~hskp19) | c3_1(a1783)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause58')).
% 1.55/1.31 tff(1911,plain,
% 1.55/1.31 ((~hskp19) | c3_1(a1783)),
% 1.55/1.31 inference(modus_ponens,[status(thm)],[1910, 1909])).
% 1.55/1.31 tff(1912,plain,
% 1.55/1.31 ((~hskp19) | c3_1(a1783)),
% 1.55/1.31 inference(modus_ponens,[status(thm)],[1911, 1909])).
% 1.55/1.31 tff(1913,plain,
% 1.55/1.31 ((~hskp19) | c3_1(a1783)),
% 1.55/1.31 inference(modus_ponens,[status(thm)],[1912, 1909])).
% 1.55/1.31 tff(1914,plain,
% 1.55/1.31 ((~hskp19) | c3_1(a1783)),
% 1.55/1.31 inference(modus_ponens,[status(thm)],[1913, 1909])).
% 1.55/1.31 tff(1915,plain,
% 1.63/1.31 ((~hskp19) | c3_1(a1783)),
% 1.63/1.31 inference(modus_ponens,[status(thm)],[1914, 1909])).
% 1.63/1.31 tff(1916,plain,
% 1.63/1.31 ((~hskp19) | c3_1(a1783)),
% 1.63/1.31 inference(modus_ponens,[status(thm)],[1915, 1909])).
% 1.63/1.31 tff(1917,plain,
% 1.63/1.31 ((~hskp19) | c3_1(a1783)),
% 1.63/1.31 inference(modus_ponens,[status(thm)],[1916, 1909])).
% 1.63/1.31 tff(1918,plain,
% 1.63/1.31 ((~hskp19) | c3_1(a1783)),
% 1.63/1.31 inference(modus_ponens,[status(thm)],[1917, 1909])).
% 1.63/1.31 tff(1919,plain,
% 1.63/1.31 (c3_1(a1783)),
% 1.63/1.31 inference(unit_resolution,[status(thm)],[1918, 1902])).
% 1.63/1.31 tff(1920,assumption,(~c2_1(a1771)), introduced(assumption)).
% 1.63/1.31 tff(1921,plain,
% 1.63/1.31 (~hskp13),
% 1.63/1.31 inference(unit_resolution,[status(thm)],[263, 1920])).
% 1.63/1.31 tff(1922,assumption,(hskp23), introduced(assumption)).
% 1.63/1.31 tff(1923,plain,
% 1.63/1.31 (((~hskp23) | (~c3_1(a1807))) <=> ((~hskp23) | (~c3_1(a1807)))),
% 1.63/1.31 inference(rewrite,[status(thm)],[])).
% 1.63/1.31 tff(1924,plain,
% 1.63/1.31 (((~c3_1(a1807)) | (~hskp23)) <=> ((~hskp23) | (~c3_1(a1807)))),
% 1.63/1.31 inference(rewrite,[status(thm)],[])).
% 1.63/1.31 tff(1925,axiom,((~c3_1(a1807)) | (~hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause94')).
% 1.63/1.31 tff(1926,plain,
% 1.63/1.31 ((~hskp23) | (~c3_1(a1807))),
% 1.63/1.31 inference(modus_ponens,[status(thm)],[1925, 1924])).
% 1.63/1.31 tff(1927,plain,
% 1.63/1.31 ((~hskp23) | (~c3_1(a1807))),
% 1.63/1.31 inference(modus_ponens,[status(thm)],[1926, 1923])).
% 1.63/1.31 tff(1928,plain,
% 1.63/1.31 (~c3_1(a1807)),
% 1.63/1.31 inference(unit_resolution,[status(thm)],[1927, 1922])).
% 1.63/1.31 tff(1929,plain,
% 1.63/1.31 (((~hskp23) | (~c1_1(a1807))) <=> ((~hskp23) | (~c1_1(a1807)))),
% 1.63/1.31 inference(rewrite,[status(thm)],[])).
% 1.63/1.31 tff(1930,plain,
% 1.63/1.31 (((~c1_1(a1807)) | (~hskp23)) <=> ((~hskp23) | (~c1_1(a1807)))),
% 1.63/1.31 inference(rewrite,[status(thm)],[])).
% 1.63/1.31 tff(1931,axiom,((~c1_1(a1807)) | (~hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause93')).
% 1.63/1.31 tff(1932,plain,
% 1.63/1.31 ((~hskp23) | (~c1_1(a1807))),
% 1.63/1.31 inference(modus_ponens,[status(thm)],[1931, 1930])).
% 1.63/1.31 tff(1933,plain,
% 1.63/1.31 ((~hskp23) | (~c1_1(a1807))),
% 1.63/1.31 inference(modus_ponens,[status(thm)],[1932, 1929])).
% 1.63/1.31 tff(1934,plain,
% 1.63/1.31 (~c1_1(a1807)),
% 1.63/1.31 inference(unit_resolution,[status(thm)],[1933, 1922])).
% 1.63/1.31 tff(1935,plain,
% 1.63/1.31 (((~hskp23) | (~c0_1(a1807))) <=> ((~hskp23) | (~c0_1(a1807)))),
% 1.63/1.31 inference(rewrite,[status(thm)],[])).
% 1.63/1.31 tff(1936,plain,
% 1.63/1.31 (((~c0_1(a1807)) | (~hskp23)) <=> ((~hskp23) | (~c0_1(a1807)))),
% 1.63/1.31 inference(rewrite,[status(thm)],[])).
% 1.63/1.31 tff(1937,axiom,((~c0_1(a1807)) | (~hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause92')).
% 1.63/1.31 tff(1938,plain,
% 1.63/1.31 ((~hskp23) | (~c0_1(a1807))),
% 1.63/1.31 inference(modus_ponens,[status(thm)],[1937, 1936])).
% 1.63/1.31 tff(1939,plain,
% 1.63/1.31 ((~hskp23) | (~c0_1(a1807))),
% 1.63/1.31 inference(modus_ponens,[status(thm)],[1938, 1935])).
% 1.63/1.31 tff(1940,plain,
% 1.63/1.31 (~c0_1(a1807)),
% 1.63/1.31 inference(unit_resolution,[status(thm)],[1939, 1922])).
% 1.63/1.31 tff(1941,plain,
% 1.63/1.31 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | c0_1(a1807) | c1_1(a1807) | c3_1(a1807) | (~ndr1_0))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp4 | hskp3 | c0_1(a1807) | c1_1(a1807) | c3_1(a1807) | (~ndr1_0))),
% 1.63/1.31 inference(rewrite,[status(thm)],[])).
% 1.63/1.31 tff(1942,plain,
% 1.63/1.31 ((hskp4 | hskp3 | (~ndr1_0) | c3_1(a1807) | c1_1(a1807) | c0_1(a1807)) <=> (hskp4 | hskp3 | c0_1(a1807) | c1_1(a1807) | c3_1(a1807) | (~ndr1_0))),
% 1.63/1.31 inference(rewrite,[status(thm)],[])).
% 1.63/1.31 tff(1943,plain,
% 1.63/1.31 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | (~ndr1_0) | c3_1(a1807) | c1_1(a1807) | c0_1(a1807))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | c0_1(a1807) | c1_1(a1807) | c3_1(a1807) | (~ndr1_0)))),
% 1.63/1.31 inference(monotonicity,[status(thm)],[1942])).
% 1.63/1.31 tff(1944,plain,
% 1.63/1.31 (((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | (~ndr1_0) | c3_1(a1807) | c1_1(a1807) | c0_1(a1807))) <=> ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp4 | hskp3 | c0_1(a1807) | c1_1(a1807) | c3_1(a1807) | (~ndr1_0))),
% 1.63/1.31 inference(transitivity,[status(thm)],[1943, 1941])).
% 1.63/1.31 tff(1945,plain,
% 1.63/1.31 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | (hskp4 | hskp3 | (~ndr1_0) | c3_1(a1807) | c1_1(a1807) | c0_1(a1807))),
% 1.63/1.31 inference(quant_inst,[status(thm)],[])).
% 1.63/1.31 tff(1946,plain,
% 1.63/1.31 ((~![U: $i] : (hskp4 | hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | c0_1(U))) | hskp4 | hskp3 | c0_1(a1807) | c1_1(a1807) | c3_1(a1807) | (~ndr1_0)),
% 1.63/1.31 inference(modus_ponens,[status(thm)],[1945, 1944])).
% 1.63/1.31 tff(1947,plain,
% 1.63/1.31 ($false),
% 1.63/1.31 inference(unit_resolution,[status(thm)],[1946, 111, 342, 35, 1940, 1934, 1928, 140])).
% 1.63/1.31 tff(1948,plain,((~hskp23) | hskp4 | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.63/1.31 tff(1949,plain,
% 1.63/1.31 (~hskp23),
% 1.63/1.31 inference(unit_resolution,[status(thm)],[1948, 35, 342])).
% 1.63/1.31 tff(1950,plain,
% 1.63/1.31 (~hskp0),
% 1.63/1.31 inference(unit_resolution,[status(thm)],[1787, 342, 240])).
% 1.63/1.31 tff(1951,plain,
% 1.63/1.31 (((~hskp19) | c1_1(a1783)) <=> ((~hskp19) | c1_1(a1783))),
% 1.63/1.31 inference(rewrite,[status(thm)],[])).
% 1.63/1.31 tff(1952,axiom,((~hskp19) | c1_1(a1783)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause57')).
% 1.63/1.31 tff(1953,plain,
% 1.63/1.31 ((~hskp19) | c1_1(a1783)),
% 1.63/1.31 inference(modus_ponens,[status(thm)],[1952, 1951])).
% 1.63/1.31 tff(1954,plain,
% 1.63/1.31 ((~hskp19) | c1_1(a1783)),
% 1.63/1.31 inference(modus_ponens,[status(thm)],[1953, 1951])).
% 1.63/1.31 tff(1955,plain,
% 1.63/1.31 ((~hskp19) | c1_1(a1783)),
% 1.63/1.31 inference(modus_ponens,[status(thm)],[1954, 1951])).
% 1.63/1.31 tff(1956,plain,
% 1.63/1.31 ((~hskp19) | c1_1(a1783)),
% 1.63/1.31 inference(modus_ponens,[status(thm)],[1955, 1951])).
% 1.63/1.31 tff(1957,plain,
% 1.63/1.31 ((~hskp19) | c1_1(a1783)),
% 1.63/1.31 inference(modus_ponens,[status(thm)],[1956, 1951])).
% 1.63/1.31 tff(1958,plain,
% 1.63/1.31 ((~hskp19) | c1_1(a1783)),
% 1.63/1.31 inference(modus_ponens,[status(thm)],[1957, 1951])).
% 1.63/1.31 tff(1959,plain,
% 1.63/1.31 ((~hskp19) | c1_1(a1783)),
% 1.63/1.31 inference(modus_ponens,[status(thm)],[1958, 1951])).
% 1.63/1.31 tff(1960,plain,
% 1.63/1.31 ((~hskp19) | c1_1(a1783)),
% 1.63/1.31 inference(modus_ponens,[status(thm)],[1959, 1951])).
% 1.63/1.31 tff(1961,plain,
% 1.63/1.31 (c1_1(a1783)),
% 1.63/1.31 inference(unit_resolution,[status(thm)],[1960, 1902])).
% 1.63/1.31 tff(1962,plain,
% 1.63/1.31 (((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | c0_1(a1783) | (~ndr1_0) | (~c1_1(a1783)) | (~c2_1(a1783)))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp13 | c0_1(a1783) | (~ndr1_0) | (~c1_1(a1783)) | (~c2_1(a1783)))),
% 1.63/1.31 inference(rewrite,[status(thm)],[])).
% 1.63/1.31 tff(1963,plain,
% 1.63/1.31 ((hskp13 | (~ndr1_0) | c0_1(a1783) | (~c2_1(a1783)) | (~c1_1(a1783))) <=> (hskp13 | c0_1(a1783) | (~ndr1_0) | (~c1_1(a1783)) | (~c2_1(a1783)))),
% 1.63/1.31 inference(rewrite,[status(thm)],[])).
% 1.63/1.31 tff(1964,plain,
% 1.63/1.31 (((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | (~ndr1_0) | c0_1(a1783) | (~c2_1(a1783)) | (~c1_1(a1783)))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | c0_1(a1783) | (~ndr1_0) | (~c1_1(a1783)) | (~c2_1(a1783))))),
% 1.63/1.31 inference(monotonicity,[status(thm)],[1963])).
% 1.63/1.31 tff(1965,plain,
% 1.63/1.31 (((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | (~ndr1_0) | c0_1(a1783) | (~c2_1(a1783)) | (~c1_1(a1783)))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp13 | c0_1(a1783) | (~ndr1_0) | (~c1_1(a1783)) | (~c2_1(a1783)))),
% 1.63/1.31 inference(transitivity,[status(thm)],[1964, 1962])).
% 1.63/1.31 tff(1966,plain,
% 1.63/1.31 ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | (~ndr1_0) | c0_1(a1783) | (~c2_1(a1783)) | (~c1_1(a1783)))),
% 1.63/1.31 inference(quant_inst,[status(thm)],[])).
% 1.63/1.31 tff(1967,plain,
% 1.63/1.31 ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp13 | c0_1(a1783) | (~ndr1_0) | (~c1_1(a1783)) | (~c2_1(a1783))),
% 1.63/1.31 inference(modus_ponens,[status(thm)],[1966, 1965])).
% 1.63/1.31 tff(1968,plain,
% 1.63/1.31 (hskp13 | (~c2_1(a1783))),
% 1.63/1.31 inference(unit_resolution,[status(thm)],[1967, 111, 1961, 1908, 22])).
% 1.63/1.31 tff(1969,plain,
% 1.63/1.31 (~c2_1(a1783)),
% 1.63/1.31 inference(unit_resolution,[status(thm)],[1968, 23])).
% 1.63/1.31 tff(1970,assumption,(~c2_1(a1781)), introduced(assumption)).
% 1.63/1.31 tff(1971,plain,
% 1.63/1.31 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp13 | c2_1(a1781) | c3_1(a1781) | c0_1(a1783) | c1_1(a1781) | (~ndr1_0) | (~c3_1(a1783)) | c2_1(a1783))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp13 | c2_1(a1781) | c3_1(a1781) | c0_1(a1783) | c1_1(a1781) | (~ndr1_0) | (~c3_1(a1783)) | c2_1(a1783))),
% 1.63/1.31 inference(rewrite,[status(thm)],[])).
% 1.63/1.31 tff(1972,plain,
% 1.63/1.31 ((hskp13 | (~ndr1_0) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)) | c2_1(a1781) | c1_1(a1781) | c3_1(a1781)) <=> (hskp13 | c2_1(a1781) | c3_1(a1781) | c0_1(a1783) | c1_1(a1781) | (~ndr1_0) | (~c3_1(a1783)) | c2_1(a1783))),
% 1.63/1.31 inference(rewrite,[status(thm)],[])).
% 1.63/1.31 tff(1973,plain,
% 1.63/1.31 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)) | c2_1(a1781) | c1_1(a1781) | c3_1(a1781))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp13 | c2_1(a1781) | c3_1(a1781) | c0_1(a1783) | c1_1(a1781) | (~ndr1_0) | (~c3_1(a1783)) | c2_1(a1783)))),
% 1.63/1.31 inference(monotonicity,[status(thm)],[1972])).
% 1.63/1.31 tff(1974,plain,
% 1.63/1.31 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)) | c2_1(a1781) | c1_1(a1781) | c3_1(a1781))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp13 | c2_1(a1781) | c3_1(a1781) | c0_1(a1783) | c1_1(a1781) | (~ndr1_0) | (~c3_1(a1783)) | c2_1(a1783))),
% 1.63/1.31 inference(transitivity,[status(thm)],[1973, 1971])).
% 1.63/1.31 tff(1975,plain,
% 1.63/1.31 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)) | c2_1(a1781) | c1_1(a1781) | c3_1(a1781))),
% 1.63/1.31 inference(quant_inst,[status(thm)],[])).
% 1.63/1.31 tff(1976,plain,
% 1.63/1.31 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp13 | c2_1(a1781) | c3_1(a1781) | c0_1(a1783) | c1_1(a1781) | (~ndr1_0) | (~c3_1(a1783)) | c2_1(a1783)),
% 1.63/1.31 inference(modus_ponens,[status(thm)],[1975, 1974])).
% 1.63/1.31 tff(1977,plain,
% 1.63/1.31 (c3_1(a1781)),
% 1.63/1.31 inference(unit_resolution,[status(thm)],[1976, 111, 23, 1919, 1970, 1908, 1336, 192, 1969])).
% 1.63/1.31 tff(1978,assumption,(~hskp0), introduced(assumption)).
% 1.63/1.31 tff(1979,plain,
% 1.63/1.31 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c2_1(a1781) | c1_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c2_1(a1781) | c1_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781)))),
% 1.63/1.31 inference(rewrite,[status(thm)],[])).
% 1.63/1.31 tff(1980,plain,
% 1.63/1.31 ((hskp0 | (~ndr1_0) | c2_1(a1781) | c0_1(a1781) | (~c3_1(a1781)) | c2_1(a1781) | c1_1(a1781) | c0_1(a1781)) <=> (hskp0 | c2_1(a1781) | c1_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781)))),
% 1.63/1.31 inference(rewrite,[status(thm)],[])).
% 1.63/1.31 tff(1981,plain,
% 1.63/1.31 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1781) | c0_1(a1781) | (~c3_1(a1781)) | c2_1(a1781) | c1_1(a1781) | c0_1(a1781))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c2_1(a1781) | c1_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781))))),
% 1.63/1.31 inference(monotonicity,[status(thm)],[1980])).
% 1.63/1.31 tff(1982,plain,
% 1.63/1.31 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1781) | c0_1(a1781) | (~c3_1(a1781)) | c2_1(a1781) | c1_1(a1781) | c0_1(a1781))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c2_1(a1781) | c1_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781)))),
% 1.63/1.31 inference(transitivity,[status(thm)],[1981, 1979])).
% 1.63/1.31 tff(1983,plain,
% 1.63/1.31 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1781) | c0_1(a1781) | (~c3_1(a1781)) | c2_1(a1781) | c1_1(a1781) | c0_1(a1781))),
% 1.63/1.31 inference(quant_inst,[status(thm)],[])).
% 1.63/1.31 tff(1984,plain,
% 1.63/1.31 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c2_1(a1781) | c1_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781))),
% 1.63/1.31 inference(modus_ponens,[status(thm)],[1983, 1982])).
% 1.63/1.31 tff(1985,plain,
% 1.63/1.31 (c0_1(a1781)),
% 1.63/1.31 inference(unit_resolution,[status(thm)],[1984, 111, 1978, 1970, 1977, 1336, 1798])).
% 1.63/1.31 tff(1986,plain,
% 1.63/1.31 (^[V: $i, U: $i] : refl((hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.63/1.31 inference(bind,[status(th)],[])).
% 1.63/1.31 tff(1987,plain,
% 1.63/1.31 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.63/1.31 inference(quant_intro,[status(thm)],[1986])).
% 1.63/1.31 tff(1988,plain,
% 1.63/1.31 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.63/1.31 inference(rewrite,[status(thm)],[])).
% 1.63/1.31 tff(1989,plain,
% 1.63/1.31 (^[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)) | 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)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | 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)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp27) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp27))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.63/1.32 inference(bind,[status(th)],[])).
% 1.63/1.32 tff(1990,plain,
% 1.63/1.32 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp27) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.63/1.32 inference(quant_intro,[status(thm)],[1989])).
% 1.63/1.32 tff(1991,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | hskp27)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause161')).
% 1.63/1.32 tff(1992,plain,
% 1.63/1.32 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.63/1.32 inference(modus_ponens,[status(thm)],[1991, 1990])).
% 1.63/1.32 tff(1993,plain,
% 1.63/1.32 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.63/1.32 inference(modus_ponens,[status(thm)],[1992, 1988])).
% 1.63/1.32 tff(1994,plain,(
% 1.63/1.32 ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.63/1.32 inference(skolemize,[status(sab)],[1993])).
% 1.63/1.32 tff(1995,plain,
% 1.63/1.32 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.63/1.32 inference(modus_ponens,[status(thm)],[1994, 1987])).
% 1.63/1.32 tff(1996,plain,
% 1.63/1.32 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp27 | c2_1(a1781) | c0_1(a1783) | c1_1(a1781) | (~ndr1_0) | (~c0_1(a1781)) | (~c3_1(a1783)) | c2_1(a1783))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp27 | c2_1(a1781) | c0_1(a1783) | c1_1(a1781) | (~ndr1_0) | (~c0_1(a1781)) | (~c3_1(a1783)) | c2_1(a1783))),
% 1.63/1.32 inference(rewrite,[status(thm)],[])).
% 1.63/1.32 tff(1997,plain,
% 1.63/1.32 ((hskp27 | (~ndr1_0) | c2_1(a1781) | c1_1(a1781) | (~c0_1(a1781)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783))) <=> (hskp27 | c2_1(a1781) | c0_1(a1783) | c1_1(a1781) | (~ndr1_0) | (~c0_1(a1781)) | (~c3_1(a1783)) | c2_1(a1783))),
% 1.63/1.32 inference(rewrite,[status(thm)],[])).
% 1.63/1.32 tff(1998,plain,
% 1.63/1.32 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1781) | c1_1(a1781) | (~c0_1(a1781)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp27 | c2_1(a1781) | c0_1(a1783) | c1_1(a1781) | (~ndr1_0) | (~c0_1(a1781)) | (~c3_1(a1783)) | c2_1(a1783)))),
% 1.63/1.32 inference(monotonicity,[status(thm)],[1997])).
% 1.63/1.32 tff(1999,plain,
% 1.63/1.32 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1781) | c1_1(a1781) | (~c0_1(a1781)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp27 | c2_1(a1781) | c0_1(a1783) | c1_1(a1781) | (~ndr1_0) | (~c0_1(a1781)) | (~c3_1(a1783)) | c2_1(a1783))),
% 1.63/1.32 inference(transitivity,[status(thm)],[1998, 1996])).
% 1.63/1.32 tff(2000,plain,
% 1.63/1.32 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1781) | c1_1(a1781) | (~c0_1(a1781)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)))),
% 1.63/1.32 inference(quant_inst,[status(thm)],[])).
% 1.63/1.32 tff(2001,plain,
% 1.63/1.32 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp27 | c2_1(a1781) | c0_1(a1783) | c1_1(a1781) | (~ndr1_0) | (~c0_1(a1781)) | (~c3_1(a1783)) | c2_1(a1783)),
% 1.63/1.32 inference(modus_ponens,[status(thm)],[2000, 1999])).
% 1.63/1.32 tff(2002,plain,
% 1.63/1.32 (hskp27 | (~c0_1(a1781))),
% 1.63/1.32 inference(unit_resolution,[status(thm)],[2001, 111, 1919, 1970, 1908, 1336, 1995, 1969])).
% 1.63/1.32 tff(2003,plain,
% 1.63/1.32 (hskp27),
% 1.63/1.32 inference(unit_resolution,[status(thm)],[2002, 1985])).
% 1.63/1.32 tff(2004,plain,
% 1.63/1.32 (c3_1(a1756)),
% 1.63/1.32 inference(unit_resolution,[status(thm)],[372, 2003])).
% 1.63/1.32 tff(2005,plain,
% 1.63/1.32 (c1_1(a1756)),
% 1.63/1.32 inference(unit_resolution,[status(thm)],[383, 2003])).
% 1.63/1.32 tff(2006,plain,
% 1.63/1.32 (c0_1(a1756)),
% 1.63/1.32 inference(unit_resolution,[status(thm)],[394, 2003])).
% 1.63/1.32 tff(2007,plain,
% 1.63/1.32 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | c2_1(a1781) | c1_1(a1781) | (~ndr1_0) | (~c3_1(a1781)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c2_1(a1781) | c1_1(a1781) | (~ndr1_0) | (~c3_1(a1781)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))),
% 1.63/1.32 inference(rewrite,[status(thm)],[])).
% 1.63/1.32 tff(2008,plain,
% 1.63/1.32 ((hskp0 | (~ndr1_0) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)) | c2_1(a1781) | c1_1(a1781) | (~c3_1(a1781))) <=> (hskp0 | c2_1(a1781) | c1_1(a1781) | (~ndr1_0) | (~c3_1(a1781)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))),
% 1.63/1.32 inference(rewrite,[status(thm)],[])).
% 1.63/1.32 tff(2009,plain,
% 1.63/1.32 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)) | c2_1(a1781) | c1_1(a1781) | (~c3_1(a1781)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | c2_1(a1781) | c1_1(a1781) | (~ndr1_0) | (~c3_1(a1781)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756))))),
% 1.63/1.32 inference(monotonicity,[status(thm)],[2008])).
% 1.63/1.32 tff(2010,plain,
% 1.63/1.32 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)) | c2_1(a1781) | c1_1(a1781) | (~c3_1(a1781)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c2_1(a1781) | c1_1(a1781) | (~ndr1_0) | (~c3_1(a1781)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))),
% 1.63/1.32 inference(transitivity,[status(thm)],[2009, 2007])).
% 1.63/1.32 tff(2011,plain,
% 1.63/1.32 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)) | c2_1(a1781) | c1_1(a1781) | (~c3_1(a1781)))),
% 1.63/1.32 inference(quant_inst,[status(thm)],[])).
% 1.63/1.32 tff(2012,plain,
% 1.63/1.32 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c2_1(a1781) | c1_1(a1781) | (~ndr1_0) | (~c3_1(a1781)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756))),
% 1.63/1.32 inference(modus_ponens,[status(thm)],[2011, 2010])).
% 1.63/1.32 tff(2013,plain,
% 1.63/1.32 ($false),
% 1.63/1.32 inference(unit_resolution,[status(thm)],[2012, 111, 1978, 2006, 2005, 2004, 1970, 1977, 1336, 1843])).
% 1.63/1.32 tff(2014,plain,(c2_1(a1781) | hskp0 | c1_1(a1781) | hskp13), inference(lemma,lemma(discharge,[]))).
% 1.63/1.32 tff(2015,plain,
% 1.63/1.32 (c2_1(a1781)),
% 1.63/1.32 inference(unit_resolution,[status(thm)],[2014, 1336, 1950, 1921])).
% 1.63/1.32 tff(2016,plain,
% 1.63/1.32 (((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp4 | c1_1(a1781) | (~ndr1_0) | (~c2_1(a1781)) | c0_1(a1781))) <=> ((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp4 | c1_1(a1781) | (~ndr1_0) | (~c2_1(a1781)) | c0_1(a1781))),
% 1.63/1.32 inference(rewrite,[status(thm)],[])).
% 1.63/1.32 tff(2017,plain,
% 1.63/1.32 ((hskp6 | hskp4 | (~ndr1_0) | c1_1(a1781) | c0_1(a1781) | (~c2_1(a1781))) <=> (hskp6 | hskp4 | c1_1(a1781) | (~ndr1_0) | (~c2_1(a1781)) | c0_1(a1781))),
% 1.63/1.32 inference(rewrite,[status(thm)],[])).
% 1.63/1.32 tff(2018,plain,
% 1.63/1.32 (((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp4 | (~ndr1_0) | c1_1(a1781) | c0_1(a1781) | (~c2_1(a1781)))) <=> ((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp4 | c1_1(a1781) | (~ndr1_0) | (~c2_1(a1781)) | c0_1(a1781)))),
% 1.63/1.32 inference(monotonicity,[status(thm)],[2017])).
% 1.63/1.32 tff(2019,plain,
% 1.63/1.32 (((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp4 | (~ndr1_0) | c1_1(a1781) | c0_1(a1781) | (~c2_1(a1781)))) <=> ((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp4 | c1_1(a1781) | (~ndr1_0) | (~c2_1(a1781)) | c0_1(a1781))),
% 1.63/1.32 inference(transitivity,[status(thm)],[2018, 2016])).
% 1.63/1.32 tff(2020,plain,
% 1.63/1.32 ((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp4 | (~ndr1_0) | c1_1(a1781) | c0_1(a1781) | (~c2_1(a1781)))),
% 1.63/1.32 inference(quant_inst,[status(thm)],[])).
% 1.63/1.32 tff(2021,plain,
% 1.63/1.32 ((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp4 | c1_1(a1781) | (~ndr1_0) | (~c2_1(a1781)) | c0_1(a1781)),
% 1.63/1.32 inference(modus_ponens,[status(thm)],[2020, 2019])).
% 1.63/1.32 tff(2022,plain,
% 1.63/1.32 (c0_1(a1781)),
% 1.63/1.32 inference(unit_resolution,[status(thm)],[2021, 111, 240, 342, 2015, 1336, 1755])).
% 1.63/1.32 tff(2023,plain,
% 1.63/1.32 (~c2_1(a1783)),
% 1.63/1.32 inference(unit_resolution,[status(thm)],[1968, 1921])).
% 1.63/1.32 tff(2024,plain,
% 1.63/1.32 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a1771) | c2_1(a1771) | c0_1(a1783) | c0_1(a1771) | (~ndr1_0) | (~c3_1(a1783)) | c2_1(a1783))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a1771) | c2_1(a1771) | c0_1(a1783) | c0_1(a1771) | (~ndr1_0) | (~c3_1(a1783)) | c2_1(a1783))),
% 1.63/1.32 inference(rewrite,[status(thm)],[])).
% 1.63/1.32 tff(2025,plain,
% 1.63/1.32 ((hskp0 | (~ndr1_0) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)) | c2_1(a1771) | c1_1(a1771) | c0_1(a1771)) <=> (hskp0 | c1_1(a1771) | c2_1(a1771) | c0_1(a1783) | c0_1(a1771) | (~ndr1_0) | (~c3_1(a1783)) | c2_1(a1783))),
% 1.63/1.32 inference(rewrite,[status(thm)],[])).
% 1.63/1.32 tff(2026,plain,
% 1.63/1.32 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)) | c2_1(a1771) | c1_1(a1771) | c0_1(a1771))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a1771) | c2_1(a1771) | c0_1(a1783) | c0_1(a1771) | (~ndr1_0) | (~c3_1(a1783)) | c2_1(a1783)))),
% 1.63/1.32 inference(monotonicity,[status(thm)],[2025])).
% 1.63/1.32 tff(2027,plain,
% 1.63/1.32 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)) | c2_1(a1771) | c1_1(a1771) | c0_1(a1771))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a1771) | c2_1(a1771) | c0_1(a1783) | c0_1(a1771) | (~ndr1_0) | (~c3_1(a1783)) | c2_1(a1783))),
% 1.63/1.32 inference(transitivity,[status(thm)],[2026, 2024])).
% 1.63/1.32 tff(2028,plain,
% 1.63/1.32 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)) | c2_1(a1771) | c1_1(a1771) | c0_1(a1771))),
% 1.63/1.32 inference(quant_inst,[status(thm)],[])).
% 1.63/1.32 tff(2029,plain,
% 1.63/1.32 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a1771) | c2_1(a1771) | c0_1(a1783) | c0_1(a1771) | (~ndr1_0) | (~c3_1(a1783)) | c2_1(a1783)),
% 1.63/1.32 inference(modus_ponens,[status(thm)],[2028, 2027])).
% 1.63/1.32 tff(2030,plain,
% 1.63/1.32 (hskp0 | c1_1(a1771)),
% 1.63/1.32 inference(unit_resolution,[status(thm)],[2029, 111, 1919, 1920, 1908, 275, 1798, 2023])).
% 1.63/1.32 tff(2031,plain,
% 1.63/1.32 (c1_1(a1771)),
% 1.63/1.32 inference(unit_resolution,[status(thm)],[2030, 1950])).
% 1.63/1.32 tff(2032,plain,
% 1.63/1.32 (^[V: $i, U: $i] : refl((hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))))),
% 1.63/1.32 inference(bind,[status(th)],[])).
% 1.63/1.32 tff(2033,plain,
% 1.63/1.32 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.63/1.32 inference(quant_intro,[status(thm)],[2032])).
% 1.63/1.32 tff(2034,plain,
% 1.63/1.32 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.63/1.32 inference(rewrite,[status(thm)],[])).
% 1.63/1.32 tff(2035,plain,
% 1.63/1.32 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~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))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp23) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) | hskp23))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) | hskp23) <=> (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp23) <=> (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))))),
% 1.63/1.32 inference(bind,[status(th)],[])).
% 1.63/1.32 tff(2036,plain,
% 1.63/1.32 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp23) <=> ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.63/1.32 inference(quant_intro,[status(thm)],[2035])).
% 1.63/1.32 tff(2037,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause173')).
% 1.63/1.32 tff(2038,plain,
% 1.63/1.32 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.63/1.32 inference(modus_ponens,[status(thm)],[2037, 2036])).
% 1.63/1.32 tff(2039,plain,
% 1.63/1.32 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.63/1.32 inference(modus_ponens,[status(thm)],[2038, 2034])).
% 1.63/1.32 tff(2040,plain,(
% 1.63/1.32 ![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.63/1.32 inference(skolemize,[status(sab)],[2039])).
% 1.63/1.32 tff(2041,plain,
% 1.63/1.32 (![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.63/1.32 inference(modus_ponens,[status(thm)],[2040, 2033])).
% 1.63/1.32 tff(2042,assumption,(~hskp23), introduced(assumption)).
% 1.63/1.32 tff(2043,plain,
% 1.63/1.32 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | c3_1(a1781) | c1_1(a1781) | (~ndr1_0) | (~c2_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783)) | c2_1(a1783))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp23 | c3_1(a1781) | c1_1(a1781) | (~ndr1_0) | (~c2_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783)) | c2_1(a1783))),
% 1.63/1.32 inference(rewrite,[status(thm)],[])).
% 1.63/1.32 tff(2044,plain,
% 1.63/1.32 ((hskp23 | (~ndr1_0) | c2_1(a1783) | (~c1_1(a1783)) | (~c3_1(a1783)) | c1_1(a1781) | c3_1(a1781) | (~c2_1(a1781))) <=> (hskp23 | c3_1(a1781) | c1_1(a1781) | (~ndr1_0) | (~c2_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783)) | c2_1(a1783))),
% 1.63/1.32 inference(rewrite,[status(thm)],[])).
% 1.63/1.32 tff(2045,plain,
% 1.63/1.32 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a1783) | (~c1_1(a1783)) | (~c3_1(a1783)) | c1_1(a1781) | c3_1(a1781) | (~c2_1(a1781)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | c3_1(a1781) | c1_1(a1781) | (~ndr1_0) | (~c2_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783)) | c2_1(a1783)))),
% 1.63/1.32 inference(monotonicity,[status(thm)],[2044])).
% 1.63/1.32 tff(2046,plain,
% 1.63/1.32 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a1783) | (~c1_1(a1783)) | (~c3_1(a1783)) | c1_1(a1781) | c3_1(a1781) | (~c2_1(a1781)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp23 | c3_1(a1781) | c1_1(a1781) | (~ndr1_0) | (~c2_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783)) | c2_1(a1783))),
% 1.63/1.32 inference(transitivity,[status(thm)],[2045, 2043])).
% 1.63/1.32 tff(2047,plain,
% 1.63/1.32 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a1783) | (~c1_1(a1783)) | (~c3_1(a1783)) | c1_1(a1781) | c3_1(a1781) | (~c2_1(a1781)))),
% 1.63/1.32 inference(quant_inst,[status(thm)],[])).
% 1.63/1.32 tff(2048,plain,
% 1.63/1.32 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp23 | c3_1(a1781) | c1_1(a1781) | (~ndr1_0) | (~c2_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783)) | c2_1(a1783)),
% 1.63/1.32 inference(modus_ponens,[status(thm)],[2047, 2046])).
% 1.63/1.32 tff(2049,plain,
% 1.63/1.32 (c3_1(a1781)),
% 1.63/1.32 inference(unit_resolution,[status(thm)],[2048, 111, 2042, 1961, 1919, 2015, 1336, 2041, 2023])).
% 1.63/1.32 tff(2050,plain,
% 1.63/1.32 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c2_1(a1771) | c1_1(a1781) | c0_1(a1771) | (~ndr1_0) | (~c1_1(a1771)) | (~c0_1(a1781)) | (~c3_1(a1781)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c2_1(a1771) | c1_1(a1781) | c0_1(a1771) | (~ndr1_0) | (~c1_1(a1771)) | (~c0_1(a1781)) | (~c3_1(a1781)))),
% 1.63/1.32 inference(rewrite,[status(thm)],[])).
% 1.63/1.32 tff(2051,plain,
% 1.63/1.32 ((hskp11 | (~ndr1_0) | c1_1(a1781) | (~c3_1(a1781)) | (~c0_1(a1781)) | c2_1(a1771) | c0_1(a1771) | (~c1_1(a1771))) <=> (hskp11 | c2_1(a1771) | c1_1(a1781) | c0_1(a1771) | (~ndr1_0) | (~c1_1(a1771)) | (~c0_1(a1781)) | (~c3_1(a1781)))),
% 1.63/1.32 inference(rewrite,[status(thm)],[])).
% 1.63/1.32 tff(2052,plain,
% 1.63/1.32 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a1781) | (~c3_1(a1781)) | (~c0_1(a1781)) | c2_1(a1771) | c0_1(a1771) | (~c1_1(a1771)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c2_1(a1771) | c1_1(a1781) | c0_1(a1771) | (~ndr1_0) | (~c1_1(a1771)) | (~c0_1(a1781)) | (~c3_1(a1781))))),
% 1.63/1.32 inference(monotonicity,[status(thm)],[2051])).
% 1.63/1.32 tff(2053,plain,
% 1.63/1.32 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a1781) | (~c3_1(a1781)) | (~c0_1(a1781)) | c2_1(a1771) | c0_1(a1771) | (~c1_1(a1771)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c2_1(a1771) | c1_1(a1781) | c0_1(a1771) | (~ndr1_0) | (~c1_1(a1771)) | (~c0_1(a1781)) | (~c3_1(a1781)))),
% 1.63/1.32 inference(transitivity,[status(thm)],[2052, 2050])).
% 1.63/1.32 tff(2054,plain,
% 1.63/1.32 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a1781) | (~c3_1(a1781)) | (~c0_1(a1781)) | c2_1(a1771) | c0_1(a1771) | (~c1_1(a1771)))),
% 1.63/1.32 inference(quant_inst,[status(thm)],[])).
% 1.63/1.32 tff(2055,plain,
% 1.63/1.32 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c2_1(a1771) | c1_1(a1781) | c0_1(a1771) | (~ndr1_0) | (~c1_1(a1771)) | (~c0_1(a1781)) | (~c3_1(a1781))),
% 1.63/1.32 inference(modus_ponens,[status(thm)],[2054, 2053])).
% 1.63/1.32 tff(2056,plain,
% 1.63/1.32 (hskp11),
% 1.63/1.32 inference(unit_resolution,[status(thm)],[2055, 111, 2049, 2031, 1920, 1336, 275, 929, 2022])).
% 1.63/1.32 tff(2057,plain,
% 1.63/1.32 (~c2_1(a1768)),
% 1.63/1.32 inference(unit_resolution,[status(thm)],[1109, 2056])).
% 1.63/1.32 tff(2058,plain,
% 1.63/1.32 (c0_1(a1768)),
% 1.63/1.32 inference(unit_resolution,[status(thm)],[1120, 2056])).
% 1.63/1.32 tff(2059,plain,
% 1.63/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c0_1(a1783) | c1_1(a1781) | c2_1(a1768) | (~ndr1_0) | (~c1_1(a1768)) | (~c0_1(a1768)) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a1783) | c1_1(a1781) | c2_1(a1768) | (~ndr1_0) | (~c1_1(a1768)) | (~c0_1(a1768)) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.63/1.32 inference(rewrite,[status(thm)],[])).
% 1.63/1.32 tff(2060,plain,
% 1.63/1.32 (((~ndr1_0) | c2_1(a1768) | (~c1_1(a1768)) | (~c0_1(a1768)) | c1_1(a1781) | (~c2_1(a1781)) | (~c0_1(a1781)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783))) <=> (c0_1(a1783) | c1_1(a1781) | c2_1(a1768) | (~ndr1_0) | (~c1_1(a1768)) | (~c0_1(a1768)) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.63/1.32 inference(rewrite,[status(thm)],[])).
% 1.63/1.32 tff(2061,plain,
% 1.63/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1768) | (~c1_1(a1768)) | (~c0_1(a1768)) | c1_1(a1781) | (~c2_1(a1781)) | (~c0_1(a1781)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c0_1(a1783) | c1_1(a1781) | c2_1(a1768) | (~ndr1_0) | (~c1_1(a1768)) | (~c0_1(a1768)) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783))))),
% 1.63/1.32 inference(monotonicity,[status(thm)],[2060])).
% 1.63/1.32 tff(2062,plain,
% 1.63/1.32 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1768) | (~c1_1(a1768)) | (~c0_1(a1768)) | c1_1(a1781) | (~c2_1(a1781)) | (~c0_1(a1781)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a1783) | c1_1(a1781) | c2_1(a1768) | (~ndr1_0) | (~c1_1(a1768)) | (~c0_1(a1768)) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.63/1.32 inference(transitivity,[status(thm)],[2061, 2059])).
% 1.63/1.32 tff(2063,plain,
% 1.63/1.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1768) | (~c1_1(a1768)) | (~c0_1(a1768)) | c1_1(a1781) | (~c2_1(a1781)) | (~c0_1(a1781)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.63/1.32 inference(quant_inst,[status(thm)],[])).
% 1.63/1.32 tff(2064,plain,
% 1.63/1.32 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a1783) | c1_1(a1781) | c2_1(a1768) | (~ndr1_0) | (~c1_1(a1768)) | (~c0_1(a1768)) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783))),
% 1.63/1.32 inference(modus_ponens,[status(thm)],[2063, 2062])).
% 1.63/1.32 tff(2065,plain,
% 1.63/1.32 (~c1_1(a1768)),
% 1.63/1.32 inference(unit_resolution,[status(thm)],[2064, 111, 1961, 1919, 2015, 2058, 1908, 1336, 2057, 475, 2022])).
% 1.63/1.32 tff(2066,plain,
% 1.63/1.32 (c3_1(a1768)),
% 1.63/1.32 inference(unit_resolution,[status(thm)],[1171, 2056])).
% 1.63/1.32 tff(2067,plain,
% 1.63/1.32 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp27 | c0_1(a1783) | c2_1(a1768) | (~ndr1_0) | c1_1(a1768) | (~c0_1(a1768)) | (~c3_1(a1783)) | c2_1(a1783))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp27 | c0_1(a1783) | c2_1(a1768) | (~ndr1_0) | c1_1(a1768) | (~c0_1(a1768)) | (~c3_1(a1783)) | c2_1(a1783))),
% 1.63/1.32 inference(rewrite,[status(thm)],[])).
% 1.63/1.32 tff(2068,plain,
% 1.63/1.32 ((hskp27 | (~ndr1_0) | c2_1(a1768) | c1_1(a1768) | (~c0_1(a1768)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783))) <=> (hskp27 | c0_1(a1783) | c2_1(a1768) | (~ndr1_0) | c1_1(a1768) | (~c0_1(a1768)) | (~c3_1(a1783)) | c2_1(a1783))),
% 1.63/1.32 inference(rewrite,[status(thm)],[])).
% 1.63/1.32 tff(2069,plain,
% 1.63/1.32 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1768) | c1_1(a1768) | (~c0_1(a1768)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp27 | c0_1(a1783) | c2_1(a1768) | (~ndr1_0) | c1_1(a1768) | (~c0_1(a1768)) | (~c3_1(a1783)) | c2_1(a1783)))),
% 1.63/1.32 inference(monotonicity,[status(thm)],[2068])).
% 1.63/1.32 tff(2070,plain,
% 1.63/1.32 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1768) | c1_1(a1768) | (~c0_1(a1768)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp27 | c0_1(a1783) | c2_1(a1768) | (~ndr1_0) | c1_1(a1768) | (~c0_1(a1768)) | (~c3_1(a1783)) | c2_1(a1783))),
% 1.63/1.32 inference(transitivity,[status(thm)],[2069, 2067])).
% 1.63/1.32 tff(2071,plain,
% 1.63/1.32 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1768) | c1_1(a1768) | (~c0_1(a1768)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)))),
% 1.63/1.32 inference(quant_inst,[status(thm)],[])).
% 1.63/1.32 tff(2072,plain,
% 1.63/1.32 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp27 | c0_1(a1783) | c2_1(a1768) | (~ndr1_0) | c1_1(a1768) | (~c0_1(a1768)) | (~c3_1(a1783)) | c2_1(a1783)),
% 1.63/1.32 inference(modus_ponens,[status(thm)],[2071, 2070])).
% 1.63/1.32 tff(2073,plain,
% 1.63/1.32 (hskp27),
% 1.63/1.32 inference(unit_resolution,[status(thm)],[2072, 111, 1919, 2058, 1908, 2057, 1995, 2023, 2065])).
% 1.63/1.32 tff(2074,plain,
% 1.63/1.32 (c3_1(a1756)),
% 1.63/1.32 inference(unit_resolution,[status(thm)],[372, 2073])).
% 1.63/1.32 tff(2075,plain,
% 1.63/1.32 (c1_1(a1756)),
% 1.63/1.32 inference(unit_resolution,[status(thm)],[383, 2073])).
% 1.63/1.32 tff(2076,plain,
% 1.63/1.32 (c0_1(a1756)),
% 1.63/1.32 inference(unit_resolution,[status(thm)],[394, 2073])).
% 1.63/1.32 tff(2077,plain,
% 1.63/1.32 ($false),
% 1.63/1.32 inference(unit_resolution,[status(thm)],[1861, 111, 1950, 2076, 2075, 2074, 2066, 2057, 1843, 2065])).
% 1.63/1.32 tff(2078,plain,(c1_1(a1781) | c2_1(a1771) | c0_1(a1771) | hskp23 | hskp6 | hskp4), inference(lemma,lemma(discharge,[]))).
% 1.63/1.33 tff(2079,plain,
% 1.63/1.33 (c1_1(a1781)),
% 1.63/1.33 inference(unit_resolution,[status(thm)],[2078, 1949, 275, 1920, 240, 342])).
% 1.63/1.33 tff(2080,assumption,(c1_1(a1781)), introduced(assumption)).
% 1.63/1.33 tff(2081,assumption,(~c3_1(a1781)), introduced(assumption)).
% 1.63/1.33 tff(2082,plain,
% 1.63/1.33 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | c3_1(a1781) | c0_1(a1783) | (~c1_1(a1781)) | (~ndr1_0) | (~c0_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp3 | c3_1(a1781) | c0_1(a1783) | (~c1_1(a1781)) | (~ndr1_0) | (~c0_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.63/1.33 inference(rewrite,[status(thm)],[])).
% 1.63/1.33 tff(2083,plain,
% 1.63/1.33 ((hskp3 | (~ndr1_0) | c3_1(a1781) | (~c1_1(a1781)) | (~c0_1(a1781)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783))) <=> (hskp3 | c3_1(a1781) | c0_1(a1783) | (~c1_1(a1781)) | (~ndr1_0) | (~c0_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.63/1.33 inference(rewrite,[status(thm)],[])).
% 1.63/1.33 tff(2084,plain,
% 1.63/1.33 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a1781) | (~c1_1(a1781)) | (~c0_1(a1781)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | c3_1(a1781) | c0_1(a1783) | (~c1_1(a1781)) | (~ndr1_0) | (~c0_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783))))),
% 1.63/1.33 inference(monotonicity,[status(thm)],[2083])).
% 1.63/1.33 tff(2085,plain,
% 1.63/1.33 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a1781) | (~c1_1(a1781)) | (~c0_1(a1781)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp3 | c3_1(a1781) | c0_1(a1783) | (~c1_1(a1781)) | (~ndr1_0) | (~c0_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.63/1.33 inference(transitivity,[status(thm)],[2084, 2082])).
% 1.63/1.33 tff(2086,plain,
% 1.63/1.33 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a1781) | (~c1_1(a1781)) | (~c0_1(a1781)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.63/1.33 inference(quant_inst,[status(thm)],[])).
% 1.63/1.33 tff(2087,plain,
% 1.63/1.33 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp3 | c3_1(a1781) | c0_1(a1783) | (~c1_1(a1781)) | (~ndr1_0) | (~c0_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783))),
% 1.63/1.33 inference(modus_ponens,[status(thm)],[2086, 2085])).
% 1.63/1.33 tff(2088,plain,
% 1.63/1.33 (~c0_1(a1781)),
% 1.63/1.33 inference(unit_resolution,[status(thm)],[2087, 111, 35, 1961, 1919, 2081, 1908, 2080, 1496])).
% 1.63/1.33 tff(2089,plain,
% 1.63/1.33 (^[V: $i, U: $i] : refl((hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.63/1.33 inference(bind,[status(th)],[])).
% 1.63/1.33 tff(2090,plain,
% 1.63/1.33 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.63/1.33 inference(quant_intro,[status(thm)],[2089])).
% 1.63/1.33 tff(2091,plain,
% 1.63/1.33 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.63/1.33 inference(rewrite,[status(thm)],[])).
% 1.63/1.33 tff(2092,plain,
% 1.63/1.33 (^[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)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp13) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp13))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp13) <=> (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp13) <=> (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.63/1.33 inference(bind,[status(th)],[])).
% 1.63/1.33 tff(2093,plain,
% 1.63/1.33 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp13) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.63/1.33 inference(quant_intro,[status(thm)],[2092])).
% 1.63/1.33 tff(2094,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause160')).
% 1.63/1.33 tff(2095,plain,
% 1.63/1.33 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.63/1.33 inference(modus_ponens,[status(thm)],[2094, 2093])).
% 1.63/1.33 tff(2096,plain,
% 1.63/1.33 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.63/1.33 inference(modus_ponens,[status(thm)],[2095, 2091])).
% 1.63/1.33 tff(2097,plain,(
% 1.63/1.33 ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.63/1.33 inference(skolemize,[status(sab)],[2096])).
% 1.63/1.33 tff(2098,plain,
% 1.63/1.33 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.63/1.33 inference(modus_ponens,[status(thm)],[2097, 2090])).
% 1.63/1.33 tff(2099,plain,
% 1.63/1.33 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp13 | c3_1(a1781) | c0_1(a1783) | (~c1_1(a1781)) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1783)) | c2_1(a1783))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp13 | c3_1(a1781) | c0_1(a1783) | (~c1_1(a1781)) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1783)) | c2_1(a1783))),
% 1.63/1.33 inference(rewrite,[status(thm)],[])).
% 1.63/1.33 tff(2100,plain,
% 1.63/1.33 ((hskp13 | (~ndr1_0) | c3_1(a1781) | c0_1(a1781) | (~c1_1(a1781)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783))) <=> (hskp13 | c3_1(a1781) | c0_1(a1783) | (~c1_1(a1781)) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1783)) | c2_1(a1783))),
% 1.63/1.33 inference(rewrite,[status(thm)],[])).
% 1.63/1.33 tff(2101,plain,
% 1.63/1.33 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp13 | (~ndr1_0) | c3_1(a1781) | c0_1(a1781) | (~c1_1(a1781)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp13 | c3_1(a1781) | c0_1(a1783) | (~c1_1(a1781)) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1783)) | c2_1(a1783)))),
% 1.63/1.33 inference(monotonicity,[status(thm)],[2100])).
% 1.63/1.33 tff(2102,plain,
% 1.63/1.33 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp13 | (~ndr1_0) | c3_1(a1781) | c0_1(a1781) | (~c1_1(a1781)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp13 | c3_1(a1781) | c0_1(a1783) | (~c1_1(a1781)) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1783)) | c2_1(a1783))),
% 1.63/1.33 inference(transitivity,[status(thm)],[2101, 2099])).
% 1.63/1.33 tff(2103,plain,
% 1.63/1.33 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp13 | (~ndr1_0) | c3_1(a1781) | c0_1(a1781) | (~c1_1(a1781)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)))),
% 1.63/1.33 inference(quant_inst,[status(thm)],[])).
% 1.63/1.33 tff(2104,plain,
% 1.63/1.33 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp13 | c3_1(a1781) | c0_1(a1783) | (~c1_1(a1781)) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1783)) | c2_1(a1783)),
% 1.63/1.33 inference(modus_ponens,[status(thm)],[2103, 2102])).
% 1.63/1.33 tff(2105,plain,
% 1.63/1.33 ($false),
% 1.63/1.33 inference(unit_resolution,[status(thm)],[2104, 111, 23, 1919, 2081, 1908, 2080, 2098, 2088, 1969])).
% 1.63/1.33 tff(2106,plain,(c3_1(a1781) | hskp13 | (~c1_1(a1781)) | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.63/1.33 tff(2107,plain,
% 1.63/1.33 (c3_1(a1781)),
% 1.63/1.33 inference(unit_resolution,[status(thm)],[2106, 2079, 1921, 35])).
% 1.63/1.33 tff(2108,plain,
% 1.63/1.33 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | c0_1(a1783) | (~c1_1(a1781)) | (~ndr1_0) | (~c0_1(a1781)) | (~c3_1(a1781)) | (~c3_1(a1783)) | c2_1(a1783))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a1783) | (~c1_1(a1781)) | (~ndr1_0) | (~c0_1(a1781)) | (~c3_1(a1781)) | (~c3_1(a1783)) | c2_1(a1783))),
% 1.63/1.33 inference(rewrite,[status(thm)],[])).
% 1.63/1.33 tff(2109,plain,
% 1.63/1.33 ((hskp3 | (~ndr1_0) | (~c1_1(a1781)) | (~c3_1(a1781)) | (~c0_1(a1781)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783))) <=> (hskp3 | c0_1(a1783) | (~c1_1(a1781)) | (~ndr1_0) | (~c0_1(a1781)) | (~c3_1(a1781)) | (~c3_1(a1783)) | c2_1(a1783))),
% 1.63/1.33 inference(rewrite,[status(thm)],[])).
% 1.63/1.33 tff(2110,plain,
% 1.63/1.33 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | (~c1_1(a1781)) | (~c3_1(a1781)) | (~c0_1(a1781)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | c0_1(a1783) | (~c1_1(a1781)) | (~ndr1_0) | (~c0_1(a1781)) | (~c3_1(a1781)) | (~c3_1(a1783)) | c2_1(a1783)))),
% 1.63/1.33 inference(monotonicity,[status(thm)],[2109])).
% 1.63/1.33 tff(2111,plain,
% 1.63/1.33 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | (~c1_1(a1781)) | (~c3_1(a1781)) | (~c0_1(a1781)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a1783) | (~c1_1(a1781)) | (~ndr1_0) | (~c0_1(a1781)) | (~c3_1(a1781)) | (~c3_1(a1783)) | c2_1(a1783))),
% 1.63/1.33 inference(transitivity,[status(thm)],[2110, 2108])).
% 1.63/1.33 tff(2112,plain,
% 1.63/1.33 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | (~c1_1(a1781)) | (~c3_1(a1781)) | (~c0_1(a1781)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)))),
% 1.63/1.33 inference(quant_inst,[status(thm)],[])).
% 1.63/1.33 tff(2113,plain,
% 1.63/1.33 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a1783) | (~c1_1(a1781)) | (~ndr1_0) | (~c0_1(a1781)) | (~c3_1(a1781)) | (~c3_1(a1783)) | c2_1(a1783)),
% 1.63/1.33 inference(modus_ponens,[status(thm)],[2112, 2111])).
% 1.63/1.33 tff(2114,plain,
% 1.63/1.33 ((~c0_1(a1781)) | (~c3_1(a1781))),
% 1.63/1.33 inference(unit_resolution,[status(thm)],[2113, 111, 35, 1919, 1908, 2079, 11, 2023])).
% 1.63/1.33 tff(2115,plain,
% 1.63/1.33 (~c0_1(a1781)),
% 1.63/1.33 inference(unit_resolution,[status(thm)],[2114, 2107])).
% 1.63/1.33 tff(2116,plain,
% 1.63/1.33 (((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp6 | hskp3 | (~c1_1(a1781)) | (~ndr1_0) | (~c2_1(a1781)) | c0_1(a1781))) <=> ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp6 | hskp3 | (~c1_1(a1781)) | (~ndr1_0) | (~c2_1(a1781)) | c0_1(a1781))),
% 1.63/1.33 inference(rewrite,[status(thm)],[])).
% 1.63/1.33 tff(2117,plain,
% 1.63/1.33 ((hskp6 | hskp3 | (~ndr1_0) | c0_1(a1781) | (~c2_1(a1781)) | (~c1_1(a1781))) <=> (hskp6 | hskp3 | (~c1_1(a1781)) | (~ndr1_0) | (~c2_1(a1781)) | c0_1(a1781))),
% 1.63/1.33 inference(rewrite,[status(thm)],[])).
% 1.63/1.33 tff(2118,plain,
% 1.63/1.33 (((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp6 | hskp3 | (~ndr1_0) | c0_1(a1781) | (~c2_1(a1781)) | (~c1_1(a1781)))) <=> ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp6 | hskp3 | (~c1_1(a1781)) | (~ndr1_0) | (~c2_1(a1781)) | c0_1(a1781)))),
% 1.63/1.33 inference(monotonicity,[status(thm)],[2117])).
% 1.63/1.33 tff(2119,plain,
% 1.63/1.33 (((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp6 | hskp3 | (~ndr1_0) | c0_1(a1781) | (~c2_1(a1781)) | (~c1_1(a1781)))) <=> ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp6 | hskp3 | (~c1_1(a1781)) | (~ndr1_0) | (~c2_1(a1781)) | c0_1(a1781))),
% 1.63/1.33 inference(transitivity,[status(thm)],[2118, 2116])).
% 1.63/1.33 tff(2120,plain,
% 1.63/1.33 ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp6 | hskp3 | (~ndr1_0) | c0_1(a1781) | (~c2_1(a1781)) | (~c1_1(a1781)))),
% 1.63/1.33 inference(quant_inst,[status(thm)],[])).
% 1.63/1.33 tff(2121,plain,
% 1.63/1.33 ((~![U: $i] : (hskp6 | hskp3 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp6 | hskp3 | (~c1_1(a1781)) | (~ndr1_0) | (~c2_1(a1781)) | c0_1(a1781)),
% 1.63/1.33 inference(modus_ponens,[status(thm)],[2120, 2119])).
% 1.63/1.33 tff(2122,plain,
% 1.63/1.33 ((~c2_1(a1781)) | c0_1(a1781)),
% 1.63/1.33 inference(unit_resolution,[status(thm)],[2121, 111, 240, 35, 2079, 274])).
% 1.63/1.33 tff(2123,plain,
% 1.63/1.33 (~c2_1(a1781)),
% 1.63/1.33 inference(unit_resolution,[status(thm)],[2122, 2115])).
% 1.63/1.33 tff(2124,assumption,(~c0_1(a1781)), introduced(assumption)).
% 1.63/1.33 tff(2125,assumption,(hskp12), introduced(assumption)).
% 1.63/1.33 tff(2126,plain,
% 1.63/1.33 (((~hskp12) | (~c3_1(a1770))) <=> ((~hskp12) | (~c3_1(a1770)))),
% 1.63/1.33 inference(rewrite,[status(thm)],[])).
% 1.63/1.33 tff(2127,plain,
% 1.63/1.33 (((~c3_1(a1770)) | (~hskp12)) <=> ((~hskp12) | (~c3_1(a1770)))),
% 1.63/1.33 inference(rewrite,[status(thm)],[])).
% 1.63/1.33 tff(2128,axiom,((~c3_1(a1770)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause111')).
% 1.63/1.33 tff(2129,plain,
% 1.63/1.33 ((~hskp12) | (~c3_1(a1770))),
% 1.63/1.33 inference(modus_ponens,[status(thm)],[2128, 2127])).
% 1.63/1.33 tff(2130,plain,
% 1.63/1.33 ((~hskp12) | (~c3_1(a1770))),
% 1.63/1.33 inference(modus_ponens,[status(thm)],[2129, 2126])).
% 1.63/1.33 tff(2131,plain,
% 1.63/1.33 (~c3_1(a1770)),
% 1.63/1.33 inference(unit_resolution,[status(thm)],[2130, 2125])).
% 1.63/1.33 tff(2132,plain,
% 1.63/1.33 (((~hskp12) | (~c0_1(a1770))) <=> ((~hskp12) | (~c0_1(a1770)))),
% 1.63/1.33 inference(rewrite,[status(thm)],[])).
% 1.63/1.33 tff(2133,plain,
% 1.63/1.33 (((~c0_1(a1770)) | (~hskp12)) <=> ((~hskp12) | (~c0_1(a1770)))),
% 1.63/1.33 inference(rewrite,[status(thm)],[])).
% 1.63/1.33 tff(2134,axiom,((~c0_1(a1770)) | (~hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause110')).
% 1.63/1.33 tff(2135,plain,
% 1.63/1.33 ((~hskp12) | (~c0_1(a1770))),
% 1.63/1.33 inference(modus_ponens,[status(thm)],[2134, 2133])).
% 1.63/1.33 tff(2136,plain,
% 1.63/1.33 ((~hskp12) | (~c0_1(a1770))),
% 1.63/1.33 inference(modus_ponens,[status(thm)],[2135, 2132])).
% 1.63/1.33 tff(2137,plain,
% 1.63/1.33 (~c0_1(a1770)),
% 1.63/1.33 inference(unit_resolution,[status(thm)],[2136, 2125])).
% 1.63/1.33 tff(2138,plain,
% 1.63/1.33 (((~hskp12) | c1_1(a1770)) <=> ((~hskp12) | c1_1(a1770))),
% 1.63/1.33 inference(rewrite,[status(thm)],[])).
% 1.63/1.33 tff(2139,axiom,((~hskp12) | c1_1(a1770)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause67')).
% 1.63/1.33 tff(2140,plain,
% 1.63/1.33 ((~hskp12) | c1_1(a1770)),
% 1.63/1.33 inference(modus_ponens,[status(thm)],[2139, 2138])).
% 1.63/1.33 tff(2141,plain,
% 1.63/1.33 ((~hskp12) | c1_1(a1770)),
% 1.63/1.33 inference(modus_ponens,[status(thm)],[2140, 2138])).
% 1.63/1.33 tff(2142,plain,
% 1.63/1.33 ((~hskp12) | c1_1(a1770)),
% 1.63/1.33 inference(modus_ponens,[status(thm)],[2141, 2138])).
% 1.63/1.33 tff(2143,plain,
% 1.63/1.33 ((~hskp12) | c1_1(a1770)),
% 1.63/1.33 inference(modus_ponens,[status(thm)],[2142, 2138])).
% 1.63/1.33 tff(2144,plain,
% 1.63/1.33 ((~hskp12) | c1_1(a1770)),
% 1.63/1.33 inference(modus_ponens,[status(thm)],[2143, 2138])).
% 1.63/1.33 tff(2145,plain,
% 1.63/1.33 ((~hskp12) | c1_1(a1770)),
% 1.63/1.33 inference(modus_ponens,[status(thm)],[2144, 2138])).
% 1.63/1.33 tff(2146,plain,
% 1.63/1.33 ((~hskp12) | c1_1(a1770)),
% 1.63/1.33 inference(modus_ponens,[status(thm)],[2145, 2138])).
% 1.63/1.33 tff(2147,plain,
% 1.63/1.33 ((~hskp12) | c1_1(a1770)),
% 1.63/1.33 inference(modus_ponens,[status(thm)],[2146, 2138])).
% 1.63/1.33 tff(2148,plain,
% 1.63/1.33 (c1_1(a1770)),
% 1.63/1.33 inference(unit_resolution,[status(thm)],[2147, 2125])).
% 1.63/1.33 tff(2149,plain,
% 1.63/1.33 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp13 | c2_1(a1781) | c0_1(a1770) | c3_1(a1770) | (~ndr1_0) | (~c1_1(a1770)) | c0_1(a1781) | (~c3_1(a1781)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp13 | c2_1(a1781) | c0_1(a1770) | c3_1(a1770) | (~ndr1_0) | (~c1_1(a1770)) | c0_1(a1781) | (~c3_1(a1781)))),
% 1.63/1.33 inference(rewrite,[status(thm)],[])).
% 1.63/1.33 tff(2150,plain,
% 1.63/1.33 ((hskp13 | (~ndr1_0) | c3_1(a1770) | c0_1(a1770) | (~c1_1(a1770)) | c2_1(a1781) | c0_1(a1781) | (~c3_1(a1781))) <=> (hskp13 | c2_1(a1781) | c0_1(a1770) | c3_1(a1770) | (~ndr1_0) | (~c1_1(a1770)) | c0_1(a1781) | (~c3_1(a1781)))),
% 1.63/1.33 inference(rewrite,[status(thm)],[])).
% 1.63/1.33 tff(2151,plain,
% 1.63/1.33 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp13 | (~ndr1_0) | c3_1(a1770) | c0_1(a1770) | (~c1_1(a1770)) | c2_1(a1781) | c0_1(a1781) | (~c3_1(a1781)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp13 | c2_1(a1781) | c0_1(a1770) | c3_1(a1770) | (~ndr1_0) | (~c1_1(a1770)) | c0_1(a1781) | (~c3_1(a1781))))),
% 1.63/1.33 inference(monotonicity,[status(thm)],[2150])).
% 1.63/1.33 tff(2152,plain,
% 1.63/1.33 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp13 | (~ndr1_0) | c3_1(a1770) | c0_1(a1770) | (~c1_1(a1770)) | c2_1(a1781) | c0_1(a1781) | (~c3_1(a1781)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp13 | c2_1(a1781) | c0_1(a1770) | c3_1(a1770) | (~ndr1_0) | (~c1_1(a1770)) | c0_1(a1781) | (~c3_1(a1781)))),
% 1.63/1.33 inference(transitivity,[status(thm)],[2151, 2149])).
% 1.63/1.33 tff(2153,plain,
% 1.63/1.33 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp13 | (~ndr1_0) | c3_1(a1770) | c0_1(a1770) | (~c1_1(a1770)) | c2_1(a1781) | c0_1(a1781) | (~c3_1(a1781)))),
% 1.63/1.33 inference(quant_inst,[status(thm)],[])).
% 1.63/1.33 tff(2154,plain,
% 1.63/1.33 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp13 | c2_1(a1781) | c0_1(a1770) | c3_1(a1770) | (~ndr1_0) | (~c1_1(a1770)) | c0_1(a1781) | (~c3_1(a1781))),
% 1.63/1.33 inference(modus_ponens,[status(thm)],[2153, 2152])).
% 1.63/1.33 tff(2155,plain,
% 1.63/1.33 ($false),
% 1.63/1.33 inference(unit_resolution,[status(thm)],[2154, 111, 23, 1970, 1337, 2148, 2137, 2131, 2098, 2124])).
% 1.63/1.33 tff(2156,plain,((~hskp12) | hskp13 | c2_1(a1781) | (~c3_1(a1781)) | c0_1(a1781)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.33 tff(2157,plain,
% 1.63/1.33 (~hskp12),
% 1.63/1.33 inference(unit_resolution,[status(thm)],[2156, 2123, 1921, 2107, 2115])).
% 1.63/1.33 tff(2158,plain,
% 1.63/1.33 (^[U: $i] : refl((hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))),
% 1.63/1.33 inference(bind,[status(th)],[])).
% 1.63/1.33 tff(2159,plain,
% 1.63/1.33 (![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.63/1.33 inference(quant_intro,[status(thm)],[2158])).
% 1.63/1.33 tff(2160,plain,
% 1.63/1.33 (![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.63/1.33 inference(rewrite,[status(thm)],[])).
% 1.63/1.33 tff(2161,plain,
% 1.63/1.33 (^[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)) | hskp27) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp27))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp27) | hskp12) <=> ((hskp27 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp12))), rewrite(((hskp27 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U))) | hskp12) <=> (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp27) | hskp12) <=> (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))))),
% 1.63/1.33 inference(bind,[status(th)],[])).
% 1.63/1.33 tff(2162,plain,
% 1.63/1.33 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp27) | hskp12) <=> ![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.63/1.33 inference(quant_intro,[status(thm)],[2161])).
% 1.63/1.33 tff(2163,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp27) | hskp12)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause136')).
% 1.63/1.33 tff(2164,plain,
% 1.63/1.33 (![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.63/1.33 inference(modus_ponens,[status(thm)],[2163, 2162])).
% 1.63/1.33 tff(2165,plain,
% 1.63/1.33 (![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.63/1.33 inference(modus_ponens,[status(thm)],[2164, 2160])).
% 1.63/1.33 tff(2166,plain,(
% 1.63/1.33 ![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.63/1.33 inference(skolemize,[status(sab)],[2165])).
% 1.63/1.33 tff(2167,plain,
% 1.63/1.33 (![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))),
% 1.63/1.33 inference(modus_ponens,[status(thm)],[2166, 2159])).
% 1.63/1.33 tff(2168,plain,
% 1.63/1.33 (((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp12 | c0_1(a1783) | (~ndr1_0) | (~c1_1(a1783)) | c2_1(a1783))) <=> ((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp27 | hskp12 | c0_1(a1783) | (~ndr1_0) | (~c1_1(a1783)) | c2_1(a1783))),
% 1.63/1.33 inference(rewrite,[status(thm)],[])).
% 1.63/1.33 tff(2169,plain,
% 1.63/1.33 ((hskp27 | hskp12 | (~ndr1_0) | c2_1(a1783) | c0_1(a1783) | (~c1_1(a1783))) <=> (hskp27 | hskp12 | c0_1(a1783) | (~ndr1_0) | (~c1_1(a1783)) | c2_1(a1783))),
% 1.63/1.33 inference(rewrite,[status(thm)],[])).
% 1.63/1.33 tff(2170,plain,
% 1.63/1.33 (((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp12 | (~ndr1_0) | c2_1(a1783) | c0_1(a1783) | (~c1_1(a1783)))) <=> ((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp12 | c0_1(a1783) | (~ndr1_0) | (~c1_1(a1783)) | c2_1(a1783)))),
% 1.63/1.33 inference(monotonicity,[status(thm)],[2169])).
% 1.63/1.33 tff(2171,plain,
% 1.63/1.33 (((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp12 | (~ndr1_0) | c2_1(a1783) | c0_1(a1783) | (~c1_1(a1783)))) <=> ((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp27 | hskp12 | c0_1(a1783) | (~ndr1_0) | (~c1_1(a1783)) | c2_1(a1783))),
% 1.63/1.33 inference(transitivity,[status(thm)],[2170, 2168])).
% 1.63/1.33 tff(2172,plain,
% 1.63/1.33 ((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp12 | (~ndr1_0) | c2_1(a1783) | c0_1(a1783) | (~c1_1(a1783)))),
% 1.63/1.33 inference(quant_inst,[status(thm)],[])).
% 1.63/1.33 tff(2173,plain,
% 1.63/1.33 ((~![U: $i] : (hskp27 | hskp12 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)))) | hskp27 | hskp12 | c0_1(a1783) | (~ndr1_0) | (~c1_1(a1783)) | c2_1(a1783)),
% 1.63/1.33 inference(modus_ponens,[status(thm)],[2172, 2171])).
% 1.63/1.33 tff(2174,plain,
% 1.63/1.33 (hskp27 | hskp12 | c2_1(a1783)),
% 1.63/1.33 inference(unit_resolution,[status(thm)],[2173, 111, 1961, 1908, 2167])).
% 1.63/1.33 tff(2175,plain,
% 1.63/1.33 (hskp27),
% 1.63/1.33 inference(unit_resolution,[status(thm)],[2174, 2157, 2023])).
% 1.63/1.33 tff(2176,plain,
% 1.63/1.33 (c3_1(a1756)),
% 1.63/1.33 inference(unit_resolution,[status(thm)],[372, 2175])).
% 1.63/1.33 tff(2177,plain,
% 1.63/1.33 (c1_1(a1756)),
% 1.63/1.33 inference(unit_resolution,[status(thm)],[383, 2175])).
% 1.63/1.33 tff(2178,plain,
% 1.63/1.33 (c0_1(a1756)),
% 1.63/1.33 inference(unit_resolution,[status(thm)],[394, 2175])).
% 1.63/1.33 tff(2179,plain,
% 1.63/1.33 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | c2_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c2_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))),
% 1.63/1.33 inference(rewrite,[status(thm)],[])).
% 1.63/1.33 tff(2180,plain,
% 1.63/1.33 ((hskp3 | (~ndr1_0) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)) | c2_1(a1781) | c0_1(a1781) | (~c3_1(a1781))) <=> (hskp3 | c2_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))),
% 1.63/1.33 inference(rewrite,[status(thm)],[])).
% 1.63/1.33 tff(2181,plain,
% 1.63/1.33 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)) | c2_1(a1781) | c0_1(a1781) | (~c3_1(a1781)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | c2_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756))))),
% 1.63/1.33 inference(monotonicity,[status(thm)],[2180])).
% 1.63/1.33 tff(2182,plain,
% 1.63/1.33 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)) | c2_1(a1781) | c0_1(a1781) | (~c3_1(a1781)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c2_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))),
% 1.63/1.33 inference(transitivity,[status(thm)],[2181, 2179])).
% 1.63/1.33 tff(2183,plain,
% 1.63/1.33 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)) | c2_1(a1781) | c0_1(a1781) | (~c3_1(a1781)))),
% 1.63/1.33 inference(quant_inst,[status(thm)],[])).
% 1.63/1.33 tff(2184,plain,
% 1.63/1.33 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c2_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756))),
% 1.63/1.33 inference(modus_ponens,[status(thm)],[2183, 2182])).
% 1.63/1.33 tff(2185,plain,
% 1.63/1.33 ($false),
% 1.63/1.33 inference(unit_resolution,[status(thm)],[2184, 111, 35, 2178, 2177, 2176, 2123, 2107, 11, 2115])).
% 1.63/1.33 tff(2186,plain,(hskp3 | hskp6 | c0_1(a1771) | c2_1(a1771) | hskp4), inference(lemma,lemma(discharge,[]))).
% 1.63/1.33 tff(2187,plain,
% 1.63/1.33 (hskp3),
% 1.63/1.33 inference(unit_resolution,[status(thm)],[2186, 342, 275, 1920, 240])).
% 1.63/1.33 tff(2188,plain,
% 1.63/1.33 (c2_1(a1758)),
% 1.63/1.33 inference(unit_resolution,[status(thm)],[613, 2187])).
% 1.63/1.33 tff(2189,plain,
% 1.63/1.33 (c1_1(a1758)),
% 1.63/1.33 inference(unit_resolution,[status(thm)],[624, 2187])).
% 1.63/1.33 tff(2190,plain,
% 1.63/1.33 (c0_1(a1758)),
% 1.63/1.33 inference(unit_resolution,[status(thm)],[631, 111, 1921, 2189, 2188, 22])).
% 1.63/1.33 tff(2191,plain,
% 1.63/1.33 (^[V: $i, U: $i] : refl((hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))),
% 1.63/1.33 inference(bind,[status(th)],[])).
% 1.63/1.33 tff(2192,plain,
% 1.63/1.33 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.63/1.33 inference(quant_intro,[status(thm)],[2191])).
% 1.63/1.33 tff(2193,plain,
% 1.63/1.33 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.63/1.33 inference(rewrite,[status(thm)],[])).
% 1.63/1.33 tff(2194,plain,
% 1.63/1.33 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp14) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp14))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V))) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp14) <=> (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))))),
% 1.63/1.34 inference(bind,[status(th)],[])).
% 1.63/1.34 tff(2195,plain,
% 1.63/1.34 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp14) <=> ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.63/1.34 inference(quant_intro,[status(thm)],[2194])).
% 1.63/1.34 tff(2196,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause167')).
% 1.63/1.34 tff(2197,plain,
% 1.63/1.34 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2196, 2195])).
% 1.63/1.34 tff(2198,plain,
% 1.63/1.34 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2197, 2193])).
% 1.63/1.34 tff(2199,plain,(
% 1.63/1.34 ![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.63/1.34 inference(skolemize,[status(sab)],[2198])).
% 1.63/1.34 tff(2200,plain,
% 1.63/1.34 (![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2199, 2192])).
% 1.63/1.34 tff(2201,plain,
% 1.63/1.34 (~c3_1(a1758)),
% 1.63/1.34 inference(unit_resolution,[status(thm)],[638, 2187])).
% 1.63/1.34 tff(2202,plain,
% 1.63/1.34 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp14 | c0_1(a1783) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1783)) | c2_1(a1783))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp14 | c0_1(a1783) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1783)) | c2_1(a1783))),
% 1.63/1.34 inference(rewrite,[status(thm)],[])).
% 1.63/1.34 tff(2203,plain,
% 1.63/1.34 ((hskp14 | (~ndr1_0) | c3_1(a1758) | (~c2_1(a1758)) | (~c0_1(a1758)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783))) <=> (hskp14 | c0_1(a1783) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1783)) | c2_1(a1783))),
% 1.63/1.34 inference(rewrite,[status(thm)],[])).
% 1.63/1.34 tff(2204,plain,
% 1.63/1.34 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a1758) | (~c2_1(a1758)) | (~c0_1(a1758)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp14 | c0_1(a1783) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1783)) | c2_1(a1783)))),
% 1.63/1.34 inference(monotonicity,[status(thm)],[2203])).
% 1.63/1.34 tff(2205,plain,
% 1.63/1.34 (((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a1758) | (~c2_1(a1758)) | (~c0_1(a1758)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp14 | c0_1(a1783) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1783)) | c2_1(a1783))),
% 1.63/1.34 inference(transitivity,[status(thm)],[2204, 2202])).
% 1.63/1.34 tff(2206,plain,
% 1.63/1.34 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp14 | (~ndr1_0) | c3_1(a1758) | (~c2_1(a1758)) | (~c0_1(a1758)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)))),
% 1.63/1.34 inference(quant_inst,[status(thm)],[])).
% 1.63/1.34 tff(2207,plain,
% 1.63/1.34 ((~![V: $i, U: $i] : (hskp14 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp14 | c0_1(a1783) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1783)) | c2_1(a1783)),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2206, 2205])).
% 1.63/1.34 tff(2208,plain,
% 1.63/1.34 (hskp14),
% 1.63/1.34 inference(unit_resolution,[status(thm)],[2207, 111, 1919, 2188, 1908, 2201, 2200, 2023, 2190])).
% 1.63/1.34 tff(2209,plain,
% 1.63/1.34 (((~hskp14) | (~c0_1(a1777))) <=> ((~hskp14) | (~c0_1(a1777)))),
% 1.63/1.34 inference(rewrite,[status(thm)],[])).
% 1.63/1.34 tff(2210,plain,
% 1.63/1.34 (((~c0_1(a1777)) | (~hskp14)) <=> ((~hskp14) | (~c0_1(a1777)))),
% 1.63/1.34 inference(rewrite,[status(thm)],[])).
% 1.63/1.34 tff(2211,axiom,((~c0_1(a1777)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause107')).
% 1.63/1.34 tff(2212,plain,
% 1.63/1.34 ((~hskp14) | (~c0_1(a1777))),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2211, 2210])).
% 1.63/1.34 tff(2213,plain,
% 1.63/1.34 ((~hskp14) | (~c0_1(a1777))),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2212, 2209])).
% 1.63/1.34 tff(2214,plain,
% 1.63/1.34 (~c0_1(a1777)),
% 1.63/1.34 inference(unit_resolution,[status(thm)],[2213, 2208])).
% 1.63/1.34 tff(2215,plain,
% 1.63/1.34 (((~hskp14) | c2_1(a1777)) <=> ((~hskp14) | c2_1(a1777))),
% 1.63/1.34 inference(rewrite,[status(thm)],[])).
% 1.63/1.34 tff(2216,axiom,((~hskp14) | c2_1(a1777)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause64')).
% 1.63/1.34 tff(2217,plain,
% 1.63/1.34 ((~hskp14) | c2_1(a1777)),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2216, 2215])).
% 1.63/1.34 tff(2218,plain,
% 1.63/1.34 ((~hskp14) | c2_1(a1777)),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2217, 2215])).
% 1.63/1.34 tff(2219,plain,
% 1.63/1.34 ((~hskp14) | c2_1(a1777)),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2218, 2215])).
% 1.63/1.34 tff(2220,plain,
% 1.63/1.34 ((~hskp14) | c2_1(a1777)),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2219, 2215])).
% 1.63/1.34 tff(2221,plain,
% 1.63/1.34 ((~hskp14) | c2_1(a1777)),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2220, 2215])).
% 1.63/1.34 tff(2222,plain,
% 1.63/1.34 ((~hskp14) | c2_1(a1777)),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2221, 2215])).
% 1.63/1.34 tff(2223,plain,
% 1.63/1.34 ((~hskp14) | c2_1(a1777)),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2222, 2215])).
% 1.63/1.34 tff(2224,plain,
% 1.63/1.34 ((~hskp14) | c2_1(a1777)),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2223, 2215])).
% 1.63/1.34 tff(2225,plain,
% 1.63/1.34 (c2_1(a1777)),
% 1.63/1.34 inference(unit_resolution,[status(thm)],[2224, 2208])).
% 1.63/1.34 tff(2226,plain,
% 1.63/1.34 (((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | c0_1(a1777) | (~ndr1_0) | (~c2_1(a1777)) | (~c1_1(a1777)))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp13 | c0_1(a1777) | (~ndr1_0) | (~c2_1(a1777)) | (~c1_1(a1777)))),
% 1.63/1.34 inference(rewrite,[status(thm)],[])).
% 1.63/1.34 tff(2227,plain,
% 1.63/1.34 ((hskp13 | (~ndr1_0) | c0_1(a1777) | (~c2_1(a1777)) | (~c1_1(a1777))) <=> (hskp13 | c0_1(a1777) | (~ndr1_0) | (~c2_1(a1777)) | (~c1_1(a1777)))),
% 1.63/1.34 inference(rewrite,[status(thm)],[])).
% 1.63/1.34 tff(2228,plain,
% 1.63/1.34 (((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | (~ndr1_0) | c0_1(a1777) | (~c2_1(a1777)) | (~c1_1(a1777)))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | c0_1(a1777) | (~ndr1_0) | (~c2_1(a1777)) | (~c1_1(a1777))))),
% 1.63/1.34 inference(monotonicity,[status(thm)],[2227])).
% 1.63/1.34 tff(2229,plain,
% 1.63/1.34 (((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | (~ndr1_0) | c0_1(a1777) | (~c2_1(a1777)) | (~c1_1(a1777)))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp13 | c0_1(a1777) | (~ndr1_0) | (~c2_1(a1777)) | (~c1_1(a1777)))),
% 1.63/1.34 inference(transitivity,[status(thm)],[2228, 2226])).
% 1.63/1.34 tff(2230,plain,
% 1.63/1.34 ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | (~ndr1_0) | c0_1(a1777) | (~c2_1(a1777)) | (~c1_1(a1777)))),
% 1.63/1.34 inference(quant_inst,[status(thm)],[])).
% 1.63/1.34 tff(2231,plain,
% 1.63/1.34 ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp13 | c0_1(a1777) | (~ndr1_0) | (~c2_1(a1777)) | (~c1_1(a1777))),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2230, 2229])).
% 1.63/1.34 tff(2232,plain,
% 1.63/1.34 (~c1_1(a1777)),
% 1.63/1.34 inference(unit_resolution,[status(thm)],[2231, 111, 1921, 2225, 2214, 22])).
% 1.63/1.34 tff(2233,plain,
% 1.63/1.34 (((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp4 | c0_1(a1777) | (~ndr1_0) | (~c2_1(a1777)) | c1_1(a1777))) <=> ((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp4 | c0_1(a1777) | (~ndr1_0) | (~c2_1(a1777)) | c1_1(a1777))),
% 1.63/1.34 inference(rewrite,[status(thm)],[])).
% 1.63/1.34 tff(2234,plain,
% 1.63/1.34 ((hskp6 | hskp4 | (~ndr1_0) | c1_1(a1777) | c0_1(a1777) | (~c2_1(a1777))) <=> (hskp6 | hskp4 | c0_1(a1777) | (~ndr1_0) | (~c2_1(a1777)) | c1_1(a1777))),
% 1.63/1.34 inference(rewrite,[status(thm)],[])).
% 1.63/1.34 tff(2235,plain,
% 1.63/1.34 (((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp4 | (~ndr1_0) | c1_1(a1777) | c0_1(a1777) | (~c2_1(a1777)))) <=> ((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp4 | c0_1(a1777) | (~ndr1_0) | (~c2_1(a1777)) | c1_1(a1777)))),
% 1.63/1.34 inference(monotonicity,[status(thm)],[2234])).
% 1.63/1.34 tff(2236,plain,
% 1.63/1.34 (((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp4 | (~ndr1_0) | c1_1(a1777) | c0_1(a1777) | (~c2_1(a1777)))) <=> ((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp4 | c0_1(a1777) | (~ndr1_0) | (~c2_1(a1777)) | c1_1(a1777))),
% 1.63/1.34 inference(transitivity,[status(thm)],[2235, 2233])).
% 1.63/1.34 tff(2237,plain,
% 1.63/1.34 ((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp4 | (~ndr1_0) | c1_1(a1777) | c0_1(a1777) | (~c2_1(a1777)))),
% 1.63/1.34 inference(quant_inst,[status(thm)],[])).
% 1.63/1.34 tff(2238,plain,
% 1.63/1.34 ((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp4 | c0_1(a1777) | (~ndr1_0) | (~c2_1(a1777)) | c1_1(a1777)),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2237, 2236])).
% 1.63/1.34 tff(2239,plain,
% 1.63/1.34 ($false),
% 1.63/1.34 inference(unit_resolution,[status(thm)],[2238, 111, 240, 342, 2225, 2214, 1755, 2232])).
% 1.63/1.34 tff(2240,plain,(hskp4 | hskp6 | c0_1(a1771) | c2_1(a1771)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.34 tff(2241,plain,
% 1.63/1.34 (hskp4),
% 1.63/1.34 inference(unit_resolution,[status(thm)],[2240, 1920, 275, 240])).
% 1.63/1.34 tff(2242,plain,
% 1.63/1.34 (~c3_1(a1759)),
% 1.63/1.34 inference(unit_resolution,[status(thm)],[1744, 2241])).
% 1.63/1.34 tff(2243,plain,
% 1.63/1.34 (c1_1(a1759)),
% 1.63/1.34 inference(unit_resolution,[status(thm)],[150, 2241])).
% 1.63/1.34 tff(2244,plain,
% 1.63/1.34 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp13 | c0_1(a1783) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | (~c3_1(a1783)) | c2_1(a1783))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp13 | c0_1(a1783) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | (~c3_1(a1783)) | c2_1(a1783))),
% 1.63/1.34 inference(rewrite,[status(thm)],[])).
% 1.63/1.34 tff(2245,plain,
% 1.63/1.34 ((hskp13 | (~ndr1_0) | c3_1(a1759) | c0_1(a1759) | (~c1_1(a1759)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783))) <=> (hskp13 | c0_1(a1783) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | (~c3_1(a1783)) | c2_1(a1783))),
% 1.63/1.34 inference(rewrite,[status(thm)],[])).
% 1.63/1.34 tff(2246,plain,
% 1.63/1.34 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp13 | (~ndr1_0) | c3_1(a1759) | c0_1(a1759) | (~c1_1(a1759)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp13 | c0_1(a1783) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | (~c3_1(a1783)) | c2_1(a1783)))),
% 1.63/1.34 inference(monotonicity,[status(thm)],[2245])).
% 1.63/1.34 tff(2247,plain,
% 1.63/1.34 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp13 | (~ndr1_0) | c3_1(a1759) | c0_1(a1759) | (~c1_1(a1759)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp13 | c0_1(a1783) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | (~c3_1(a1783)) | c2_1(a1783))),
% 1.63/1.34 inference(transitivity,[status(thm)],[2246, 2244])).
% 1.63/1.34 tff(2248,plain,
% 1.63/1.34 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp13 | (~ndr1_0) | c3_1(a1759) | c0_1(a1759) | (~c1_1(a1759)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)))),
% 1.63/1.34 inference(quant_inst,[status(thm)],[])).
% 1.63/1.34 tff(2249,plain,
% 1.63/1.34 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp13 | c0_1(a1783) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | c0_1(a1759) | (~c3_1(a1783)) | c2_1(a1783)),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2248, 2247])).
% 1.63/1.34 tff(2250,plain,
% 1.63/1.34 (c0_1(a1759)),
% 1.63/1.34 inference(unit_resolution,[status(thm)],[2249, 111, 1921, 1919, 2243, 1908, 2242, 2098, 2023])).
% 1.63/1.34 tff(2251,assumption,(hskp19), introduced(assumption)).
% 1.63/1.34 tff(2252,plain,
% 1.63/1.34 (c1_1(a1783)),
% 1.63/1.34 inference(unit_resolution,[status(thm)],[1960, 2251])).
% 1.63/1.34 tff(2253,plain,
% 1.63/1.34 (c3_1(a1783)),
% 1.63/1.34 inference(unit_resolution,[status(thm)],[1918, 2251])).
% 1.63/1.34 tff(2254,assumption,(~c0_1(a1783)), introduced(assumption)).
% 1.63/1.34 tff(2255,plain,
% 1.63/1.34 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | c0_1(a1783) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp3 | c0_1(a1783) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.63/1.34 inference(rewrite,[status(thm)],[])).
% 1.63/1.34 tff(2256,plain,
% 1.63/1.34 ((hskp3 | (~ndr1_0) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783))) <=> (hskp3 | c0_1(a1783) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.63/1.34 inference(rewrite,[status(thm)],[])).
% 1.63/1.34 tff(2257,plain,
% 1.63/1.34 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | c0_1(a1783) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1783)) | (~c1_1(a1783))))),
% 1.63/1.34 inference(monotonicity,[status(thm)],[2256])).
% 1.63/1.34 tff(2258,plain,
% 1.63/1.34 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp3 | c0_1(a1783) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.63/1.34 inference(transitivity,[status(thm)],[2257, 2255])).
% 1.63/1.34 tff(2259,plain,
% 1.63/1.34 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.63/1.34 inference(quant_inst,[status(thm)],[])).
% 1.63/1.34 tff(2260,plain,
% 1.63/1.34 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp3 | c0_1(a1783) | c3_1(a1759) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1783)) | (~c1_1(a1783))),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2259, 2258])).
% 1.63/1.34 tff(2261,plain,
% 1.63/1.34 ((~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1783)) | (~c1_1(a1783))),
% 1.63/1.34 inference(unit_resolution,[status(thm)],[2260, 35, 2254, 34, 1496])).
% 1.63/1.34 tff(2262,plain,
% 1.63/1.34 ($false),
% 1.63/1.34 inference(unit_resolution,[status(thm)],[2261, 2253, 2252, 241, 938, 1561])).
% 1.63/1.34 tff(2263,plain,((~hskp19) | (~ndr1_0) | (~c1_1(a1759)) | (~c0_1(a1759)) | hskp3 | c0_1(a1783) | c3_1(a1759)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.34 tff(2264,plain,
% 1.63/1.34 ((~hskp19) | (~c1_1(a1759)) | (~c0_1(a1759)) | hskp3 | c0_1(a1783) | c3_1(a1759)),
% 1.63/1.34 inference(unit_resolution,[status(thm)],[2263, 111])).
% 1.63/1.34 tff(2265,plain,
% 1.63/1.34 ((~c1_1(a1759)) | (~c0_1(a1759)) | hskp3 | c3_1(a1759)),
% 1.63/1.34 inference(unit_resolution,[status(thm)],[2264, 1902, 1908])).
% 1.63/1.34 tff(2266,plain,
% 1.63/1.34 (hskp3),
% 1.63/1.34 inference(unit_resolution,[status(thm)],[2265, 2250, 2243, 2242])).
% 1.63/1.34 tff(2267,plain,
% 1.63/1.34 (c2_1(a1758)),
% 1.63/1.34 inference(unit_resolution,[status(thm)],[613, 2266])).
% 1.63/1.34 tff(2268,plain,
% 1.63/1.34 (c1_1(a1758)),
% 1.63/1.34 inference(unit_resolution,[status(thm)],[624, 2266])).
% 1.63/1.34 tff(2269,plain,
% 1.63/1.34 (c0_1(a1758)),
% 1.63/1.34 inference(unit_resolution,[status(thm)],[631, 111, 1921, 2268, 2267, 22])).
% 1.63/1.34 tff(2270,plain,
% 1.63/1.34 (~c3_1(a1758)),
% 1.63/1.34 inference(unit_resolution,[status(thm)],[638, 2266])).
% 1.63/1.34 tff(2271,plain,
% 1.63/1.34 (hskp14),
% 1.63/1.34 inference(unit_resolution,[status(thm)],[2207, 111, 1919, 2267, 1908, 2270, 2200, 2023, 2269])).
% 1.63/1.34 tff(2272,plain,
% 1.63/1.34 (~c0_1(a1777)),
% 1.63/1.34 inference(unit_resolution,[status(thm)],[2213, 2271])).
% 1.63/1.34 tff(2273,plain,
% 1.63/1.34 (c2_1(a1777)),
% 1.63/1.34 inference(unit_resolution,[status(thm)],[2224, 2271])).
% 1.63/1.34 tff(2274,plain,
% 1.63/1.34 (~c1_1(a1777)),
% 1.63/1.34 inference(unit_resolution,[status(thm)],[2231, 111, 1921, 2273, 2272, 22])).
% 1.63/1.34 tff(2275,plain,
% 1.63/1.34 (^[V: $i, U: $i] : refl((hskp15 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> (hskp15 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))))),
% 1.63/1.34 inference(bind,[status(th)],[])).
% 1.63/1.34 tff(2276,plain,
% 1.63/1.34 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.63/1.34 inference(quant_intro,[status(thm)],[2275])).
% 1.63/1.34 tff(2277,plain,
% 1.63/1.34 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.63/1.34 inference(rewrite,[status(thm)],[])).
% 1.63/1.34 tff(2278,plain,
% 1.63/1.34 (^[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(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_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)) | (~c2_1(V))) | c3_1(U)) | c1_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)) | (~c2_1(V))) | c3_1(U)) | c1_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)) | c1_1(V) | c3_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_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(U)) | c1_1(V)) | c3_1(V)) | hskp15) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) | hskp15))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V))) | hskp15) <=> (hskp15 | (~ndr1_0) | c3_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(U)) | c1_1(V)) | c3_1(V)) | hskp15) <=> (hskp15 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))))),
% 1.63/1.34 inference(bind,[status(th)],[])).
% 1.63/1.34 tff(2279,plain,
% 1.63/1.34 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp15) <=> ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.63/1.34 inference(quant_intro,[status(thm)],[2278])).
% 1.63/1.34 tff(2280,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c3_1(U)) | c1_1(V)) | c3_1(V)) | hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause174')).
% 1.63/1.34 tff(2281,plain,
% 1.63/1.34 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2280, 2279])).
% 1.63/1.34 tff(2282,plain,
% 1.63/1.34 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2281, 2277])).
% 1.63/1.34 tff(2283,plain,(
% 1.63/1.34 ![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.63/1.34 inference(skolemize,[status(sab)],[2282])).
% 1.63/1.34 tff(2284,plain,
% 1.63/1.34 (![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2283, 2276])).
% 1.63/1.34 tff(2285,plain,
% 1.63/1.34 (((~hskp14) | (~c3_1(a1777))) <=> ((~hskp14) | (~c3_1(a1777)))),
% 1.63/1.34 inference(rewrite,[status(thm)],[])).
% 1.63/1.34 tff(2286,plain,
% 1.63/1.34 (((~c3_1(a1777)) | (~hskp14)) <=> ((~hskp14) | (~c3_1(a1777)))),
% 1.63/1.34 inference(rewrite,[status(thm)],[])).
% 1.63/1.34 tff(2287,axiom,((~c3_1(a1777)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause108')).
% 1.63/1.34 tff(2288,plain,
% 1.63/1.34 ((~hskp14) | (~c3_1(a1777))),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2287, 2286])).
% 1.63/1.34 tff(2289,plain,
% 1.63/1.34 ((~hskp14) | (~c3_1(a1777))),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2288, 2285])).
% 1.63/1.34 tff(2290,plain,
% 1.63/1.34 (~c3_1(a1777)),
% 1.63/1.34 inference(unit_resolution,[status(thm)],[2289, 2271])).
% 1.63/1.34 tff(2291,plain,
% 1.63/1.34 (^[U: $i] : refl((hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))))),
% 1.63/1.34 inference(bind,[status(th)],[])).
% 1.63/1.34 tff(2292,plain,
% 1.63/1.34 (![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.63/1.34 inference(quant_intro,[status(thm)],[2291])).
% 1.63/1.34 tff(2293,plain,
% 1.63/1.34 (![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.63/1.34 inference(rewrite,[status(thm)],[])).
% 1.63/1.34 tff(2294,plain,
% 1.63/1.34 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp20) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp20))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp20) <=> (hskp20 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp20) <=> (hskp20 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp20) | hskp6) <=> ((hskp20 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp6))), rewrite(((hskp20 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp6) <=> (hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp20) | hskp6) <=> (hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))))),
% 1.63/1.34 inference(bind,[status(th)],[])).
% 1.63/1.34 tff(2295,plain,
% 1.63/1.34 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp20) | hskp6) <=> ![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.63/1.34 inference(quant_intro,[status(thm)],[2294])).
% 1.63/1.34 tff(2296,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp20) | hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause139')).
% 1.63/1.34 tff(2297,plain,
% 1.63/1.34 (![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2296, 2295])).
% 1.63/1.34 tff(2298,plain,
% 1.63/1.34 (![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2297, 2293])).
% 1.63/1.34 tff(2299,plain,(
% 1.63/1.34 ![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.63/1.34 inference(skolemize,[status(sab)],[2298])).
% 1.63/1.34 tff(2300,plain,
% 1.63/1.34 (![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2299, 2292])).
% 1.63/1.34 tff(2301,plain,
% 1.63/1.34 (((~![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp20 | hskp6 | c0_1(a1777) | c3_1(a1777) | (~ndr1_0) | (~c2_1(a1777)))) <=> ((~![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp20 | hskp6 | c0_1(a1777) | c3_1(a1777) | (~ndr1_0) | (~c2_1(a1777)))),
% 1.63/1.34 inference(rewrite,[status(thm)],[])).
% 1.63/1.34 tff(2302,plain,
% 1.63/1.34 ((hskp20 | hskp6 | (~ndr1_0) | c3_1(a1777) | c0_1(a1777) | (~c2_1(a1777))) <=> (hskp20 | hskp6 | c0_1(a1777) | c3_1(a1777) | (~ndr1_0) | (~c2_1(a1777)))),
% 1.63/1.34 inference(rewrite,[status(thm)],[])).
% 1.63/1.34 tff(2303,plain,
% 1.63/1.34 (((~![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp20 | hskp6 | (~ndr1_0) | c3_1(a1777) | c0_1(a1777) | (~c2_1(a1777)))) <=> ((~![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp20 | hskp6 | c0_1(a1777) | c3_1(a1777) | (~ndr1_0) | (~c2_1(a1777))))),
% 1.63/1.34 inference(monotonicity,[status(thm)],[2302])).
% 1.63/1.34 tff(2304,plain,
% 1.63/1.34 (((~![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp20 | hskp6 | (~ndr1_0) | c3_1(a1777) | c0_1(a1777) | (~c2_1(a1777)))) <=> ((~![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp20 | hskp6 | c0_1(a1777) | c3_1(a1777) | (~ndr1_0) | (~c2_1(a1777)))),
% 1.63/1.34 inference(transitivity,[status(thm)],[2303, 2301])).
% 1.63/1.34 tff(2305,plain,
% 1.63/1.34 ((~![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp20 | hskp6 | (~ndr1_0) | c3_1(a1777) | c0_1(a1777) | (~c2_1(a1777)))),
% 1.63/1.34 inference(quant_inst,[status(thm)],[])).
% 1.63/1.34 tff(2306,plain,
% 1.63/1.34 ((~![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp20 | hskp6 | c0_1(a1777) | c3_1(a1777) | (~ndr1_0) | (~c2_1(a1777))),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2305, 2304])).
% 1.63/1.34 tff(2307,plain,
% 1.63/1.34 (hskp20),
% 1.63/1.34 inference(unit_resolution,[status(thm)],[2306, 111, 240, 2273, 2272, 2290, 2300])).
% 1.63/1.34 tff(2308,plain,
% 1.63/1.34 (((~hskp20) | (~c3_1(a1786))) <=> ((~hskp20) | (~c3_1(a1786)))),
% 1.63/1.34 inference(rewrite,[status(thm)],[])).
% 1.63/1.34 tff(2309,plain,
% 1.63/1.34 (((~c3_1(a1786)) | (~hskp20)) <=> ((~hskp20) | (~c3_1(a1786)))),
% 1.63/1.34 inference(rewrite,[status(thm)],[])).
% 1.63/1.34 tff(2310,axiom,((~c3_1(a1786)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause98')).
% 1.63/1.34 tff(2311,plain,
% 1.63/1.34 ((~hskp20) | (~c3_1(a1786))),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2310, 2309])).
% 1.63/1.34 tff(2312,plain,
% 1.63/1.34 ((~hskp20) | (~c3_1(a1786))),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2311, 2308])).
% 1.63/1.34 tff(2313,plain,
% 1.63/1.34 (~c3_1(a1786)),
% 1.63/1.34 inference(unit_resolution,[status(thm)],[2312, 2307])).
% 1.63/1.34 tff(2314,plain,
% 1.63/1.34 (((~hskp20) | c1_1(a1786)) <=> ((~hskp20) | c1_1(a1786))),
% 1.63/1.34 inference(rewrite,[status(thm)],[])).
% 1.63/1.34 tff(2315,axiom,((~hskp20) | c1_1(a1786)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause56')).
% 1.63/1.34 tff(2316,plain,
% 1.63/1.34 ((~hskp20) | c1_1(a1786)),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2315, 2314])).
% 1.63/1.34 tff(2317,plain,
% 1.63/1.34 ((~hskp20) | c1_1(a1786)),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2316, 2314])).
% 1.63/1.34 tff(2318,plain,
% 1.63/1.34 ((~hskp20) | c1_1(a1786)),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2317, 2314])).
% 1.63/1.34 tff(2319,plain,
% 1.63/1.34 ((~hskp20) | c1_1(a1786)),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2318, 2314])).
% 1.63/1.34 tff(2320,plain,
% 1.63/1.34 ((~hskp20) | c1_1(a1786)),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2319, 2314])).
% 1.63/1.34 tff(2321,plain,
% 1.63/1.34 ((~hskp20) | c1_1(a1786)),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2320, 2314])).
% 1.63/1.34 tff(2322,plain,
% 1.63/1.34 ((~hskp20) | c1_1(a1786)),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2321, 2314])).
% 1.63/1.34 tff(2323,plain,
% 1.63/1.34 ((~hskp20) | c1_1(a1786)),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2322, 2314])).
% 1.63/1.34 tff(2324,plain,
% 1.63/1.34 (c1_1(a1786)),
% 1.63/1.34 inference(unit_resolution,[status(thm)],[2323, 2307])).
% 1.63/1.34 tff(2325,plain,
% 1.63/1.34 (((~hskp20) | c0_1(a1786)) <=> ((~hskp20) | c0_1(a1786))),
% 1.63/1.34 inference(rewrite,[status(thm)],[])).
% 1.63/1.34 tff(2326,axiom,((~hskp20) | c0_1(a1786)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause55')).
% 1.63/1.34 tff(2327,plain,
% 1.63/1.34 ((~hskp20) | c0_1(a1786)),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2326, 2325])).
% 1.63/1.34 tff(2328,plain,
% 1.63/1.34 ((~hskp20) | c0_1(a1786)),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2327, 2325])).
% 1.63/1.34 tff(2329,plain,
% 1.63/1.34 ((~hskp20) | c0_1(a1786)),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2328, 2325])).
% 1.63/1.34 tff(2330,plain,
% 1.63/1.34 ((~hskp20) | c0_1(a1786)),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2329, 2325])).
% 1.63/1.34 tff(2331,plain,
% 1.63/1.34 ((~hskp20) | c0_1(a1786)),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2330, 2325])).
% 1.63/1.34 tff(2332,plain,
% 1.63/1.34 ((~hskp20) | c0_1(a1786)),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2331, 2325])).
% 1.63/1.34 tff(2333,plain,
% 1.63/1.34 ((~hskp20) | c0_1(a1786)),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2332, 2325])).
% 1.63/1.34 tff(2334,plain,
% 1.63/1.34 ((~hskp20) | c0_1(a1786)),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2333, 2325])).
% 1.63/1.34 tff(2335,plain,
% 1.63/1.34 (c0_1(a1786)),
% 1.63/1.34 inference(unit_resolution,[status(thm)],[2334, 2307])).
% 1.63/1.34 tff(2336,plain,
% 1.63/1.34 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp15 | c3_1(a1786) | c3_1(a1777) | (~ndr1_0) | (~c2_1(a1777)) | c1_1(a1777) | (~c1_1(a1786)) | (~c0_1(a1786)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp15 | c3_1(a1786) | c3_1(a1777) | (~ndr1_0) | (~c2_1(a1777)) | c1_1(a1777) | (~c1_1(a1786)) | (~c0_1(a1786)))),
% 1.63/1.34 inference(rewrite,[status(thm)],[])).
% 1.63/1.34 tff(2337,plain,
% 1.63/1.34 ((hskp15 | (~ndr1_0) | c3_1(a1786) | (~c1_1(a1786)) | (~c0_1(a1786)) | c1_1(a1777) | c3_1(a1777) | (~c2_1(a1777))) <=> (hskp15 | c3_1(a1786) | c3_1(a1777) | (~ndr1_0) | (~c2_1(a1777)) | c1_1(a1777) | (~c1_1(a1786)) | (~c0_1(a1786)))),
% 1.63/1.34 inference(rewrite,[status(thm)],[])).
% 1.63/1.34 tff(2338,plain,
% 1.63/1.34 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a1786) | (~c1_1(a1786)) | (~c0_1(a1786)) | c1_1(a1777) | c3_1(a1777) | (~c2_1(a1777)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp15 | c3_1(a1786) | c3_1(a1777) | (~ndr1_0) | (~c2_1(a1777)) | c1_1(a1777) | (~c1_1(a1786)) | (~c0_1(a1786))))),
% 1.63/1.34 inference(monotonicity,[status(thm)],[2337])).
% 1.63/1.34 tff(2339,plain,
% 1.63/1.34 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a1786) | (~c1_1(a1786)) | (~c0_1(a1786)) | c1_1(a1777) | c3_1(a1777) | (~c2_1(a1777)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp15 | c3_1(a1786) | c3_1(a1777) | (~ndr1_0) | (~c2_1(a1777)) | c1_1(a1777) | (~c1_1(a1786)) | (~c0_1(a1786)))),
% 1.63/1.34 inference(transitivity,[status(thm)],[2338, 2336])).
% 1.63/1.34 tff(2340,plain,
% 1.63/1.34 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a1786) | (~c1_1(a1786)) | (~c0_1(a1786)) | c1_1(a1777) | c3_1(a1777) | (~c2_1(a1777)))),
% 1.63/1.34 inference(quant_inst,[status(thm)],[])).
% 1.63/1.34 tff(2341,plain,
% 1.63/1.34 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp15 | c3_1(a1786) | c3_1(a1777) | (~ndr1_0) | (~c2_1(a1777)) | c1_1(a1777) | (~c1_1(a1786)) | (~c0_1(a1786))),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2340, 2339])).
% 1.63/1.34 tff(2342,plain,
% 1.63/1.34 (hskp15),
% 1.63/1.34 inference(unit_resolution,[status(thm)],[2341, 111, 2335, 2324, 2273, 2313, 2290, 2284, 2274])).
% 1.63/1.34 tff(2343,plain,
% 1.63/1.34 (((~hskp15) | (~c3_1(a1779))) <=> ((~hskp15) | (~c3_1(a1779)))),
% 1.63/1.34 inference(rewrite,[status(thm)],[])).
% 1.63/1.34 tff(2344,plain,
% 1.63/1.34 (((~c3_1(a1779)) | (~hskp15)) <=> ((~hskp15) | (~c3_1(a1779)))),
% 1.63/1.34 inference(rewrite,[status(thm)],[])).
% 1.63/1.34 tff(2345,axiom,((~c3_1(a1779)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause106')).
% 1.63/1.34 tff(2346,plain,
% 1.63/1.34 ((~hskp15) | (~c3_1(a1779))),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2345, 2344])).
% 1.63/1.34 tff(2347,plain,
% 1.63/1.34 ((~hskp15) | (~c3_1(a1779))),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2346, 2343])).
% 1.63/1.34 tff(2348,plain,
% 1.63/1.34 (~c3_1(a1779)),
% 1.63/1.34 inference(unit_resolution,[status(thm)],[2347, 2342])).
% 1.63/1.34 tff(2349,plain,
% 1.63/1.34 (((~hskp15) | (~c2_1(a1779))) <=> ((~hskp15) | (~c2_1(a1779)))),
% 1.63/1.34 inference(rewrite,[status(thm)],[])).
% 1.63/1.34 tff(2350,plain,
% 1.63/1.34 (((~c2_1(a1779)) | (~hskp15)) <=> ((~hskp15) | (~c2_1(a1779)))),
% 1.63/1.34 inference(rewrite,[status(thm)],[])).
% 1.63/1.34 tff(2351,axiom,((~c2_1(a1779)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause105')).
% 1.63/1.34 tff(2352,plain,
% 1.63/1.34 ((~hskp15) | (~c2_1(a1779))),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2351, 2350])).
% 1.63/1.34 tff(2353,plain,
% 1.63/1.34 ((~hskp15) | (~c2_1(a1779))),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2352, 2349])).
% 1.63/1.34 tff(2354,plain,
% 1.63/1.34 (~c2_1(a1779)),
% 1.63/1.34 inference(unit_resolution,[status(thm)],[2353, 2342])).
% 1.63/1.34 tff(2355,plain,
% 1.63/1.34 (((~hskp15) | c0_1(a1779)) <=> ((~hskp15) | c0_1(a1779))),
% 1.63/1.34 inference(rewrite,[status(thm)],[])).
% 1.63/1.34 tff(2356,axiom,((~hskp15) | c0_1(a1779)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause63')).
% 1.63/1.34 tff(2357,plain,
% 1.63/1.34 ((~hskp15) | c0_1(a1779)),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2356, 2355])).
% 1.63/1.34 tff(2358,plain,
% 1.63/1.34 ((~hskp15) | c0_1(a1779)),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2357, 2355])).
% 1.63/1.34 tff(2359,plain,
% 1.63/1.34 ((~hskp15) | c0_1(a1779)),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2358, 2355])).
% 1.63/1.34 tff(2360,plain,
% 1.63/1.34 ((~hskp15) | c0_1(a1779)),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2359, 2355])).
% 1.63/1.34 tff(2361,plain,
% 1.63/1.34 ((~hskp15) | c0_1(a1779)),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2360, 2355])).
% 1.63/1.34 tff(2362,plain,
% 1.63/1.34 ((~hskp15) | c0_1(a1779)),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2361, 2355])).
% 1.63/1.34 tff(2363,plain,
% 1.63/1.34 ((~hskp15) | c0_1(a1779)),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2362, 2355])).
% 1.63/1.34 tff(2364,plain,
% 1.63/1.34 ((~hskp15) | c0_1(a1779)),
% 1.63/1.34 inference(modus_ponens,[status(thm)],[2363, 2355])).
% 1.63/1.34 tff(2365,plain,
% 1.63/1.34 (c0_1(a1779)),
% 1.63/1.34 inference(unit_resolution,[status(thm)],[2364, 2342])).
% 1.63/1.34 tff(2366,plain,
% 1.63/1.34 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp22 | c3_1(a1777) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c2_1(a1777)) | c1_1(a1777))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp22 | c3_1(a1777) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c2_1(a1777)) | c1_1(a1777))),
% 1.63/1.34 inference(rewrite,[status(thm)],[])).
% 1.63/1.34 tff(2367,plain,
% 1.63/1.34 ((hskp22 | (~ndr1_0) | c3_1(a1758) | (~c2_1(a1758)) | (~c1_1(a1758)) | c1_1(a1777) | c3_1(a1777) | (~c2_1(a1777))) <=> (hskp22 | c3_1(a1777) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c2_1(a1777)) | c1_1(a1777))),
% 1.63/1.35 inference(rewrite,[status(thm)],[])).
% 1.63/1.35 tff(2368,plain,
% 1.63/1.35 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a1758) | (~c2_1(a1758)) | (~c1_1(a1758)) | c1_1(a1777) | c3_1(a1777) | (~c2_1(a1777)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp22 | c3_1(a1777) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c2_1(a1777)) | c1_1(a1777)))),
% 1.63/1.35 inference(monotonicity,[status(thm)],[2367])).
% 1.63/1.35 tff(2369,plain,
% 1.63/1.35 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a1758) | (~c2_1(a1758)) | (~c1_1(a1758)) | c1_1(a1777) | c3_1(a1777) | (~c2_1(a1777)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp22 | c3_1(a1777) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c2_1(a1777)) | c1_1(a1777))),
% 1.63/1.35 inference(transitivity,[status(thm)],[2368, 2366])).
% 1.63/1.35 tff(2370,plain,
% 1.63/1.35 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a1758) | (~c2_1(a1758)) | (~c1_1(a1758)) | c1_1(a1777) | c3_1(a1777) | (~c2_1(a1777)))),
% 1.63/1.35 inference(quant_inst,[status(thm)],[])).
% 1.63/1.35 tff(2371,plain,
% 1.63/1.35 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp22 | c3_1(a1777) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c2_1(a1777)) | c1_1(a1777)),
% 1.63/1.35 inference(modus_ponens,[status(thm)],[2370, 2369])).
% 1.63/1.35 tff(2372,plain,
% 1.63/1.35 (hskp22),
% 1.63/1.35 inference(unit_resolution,[status(thm)],[2371, 111, 2273, 2268, 2267, 2290, 2270, 836, 2274])).
% 1.63/1.35 tff(2373,plain,
% 1.63/1.35 (~c2_1(a1799)),
% 1.63/1.35 inference(unit_resolution,[status(thm)],[542, 2372])).
% 1.63/1.35 tff(2374,plain,
% 1.63/1.35 (~c0_1(a1799)),
% 1.63/1.35 inference(unit_resolution,[status(thm)],[548, 2372])).
% 1.63/1.35 tff(2375,plain,
% 1.63/1.35 (c3_1(a1799)),
% 1.63/1.35 inference(unit_resolution,[status(thm)],[559, 2372])).
% 1.63/1.35 tff(2376,assumption,(hskp18), introduced(assumption)).
% 1.63/1.35 tff(2377,plain,
% 1.63/1.35 (((~hskp18) | (~c3_1(a1782))) <=> ((~hskp18) | (~c3_1(a1782)))),
% 1.63/1.35 inference(rewrite,[status(thm)],[])).
% 1.63/1.35 tff(2378,plain,
% 1.63/1.35 (((~c3_1(a1782)) | (~hskp18)) <=> ((~hskp18) | (~c3_1(a1782)))),
% 1.63/1.35 inference(rewrite,[status(thm)],[])).
% 1.63/1.35 tff(2379,axiom,((~c3_1(a1782)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause102')).
% 1.63/1.35 tff(2380,plain,
% 1.63/1.35 ((~hskp18) | (~c3_1(a1782))),
% 1.63/1.35 inference(modus_ponens,[status(thm)],[2379, 2378])).
% 1.63/1.35 tff(2381,plain,
% 1.63/1.35 ((~hskp18) | (~c3_1(a1782))),
% 1.63/1.35 inference(modus_ponens,[status(thm)],[2380, 2377])).
% 1.63/1.35 tff(2382,plain,
% 1.63/1.35 (~c3_1(a1782)),
% 1.63/1.35 inference(unit_resolution,[status(thm)],[2381, 2376])).
% 1.63/1.35 tff(2383,plain,
% 1.63/1.35 (((~hskp18) | (~c2_1(a1782))) <=> ((~hskp18) | (~c2_1(a1782)))),
% 1.63/1.35 inference(rewrite,[status(thm)],[])).
% 1.63/1.35 tff(2384,plain,
% 1.63/1.35 (((~c2_1(a1782)) | (~hskp18)) <=> ((~hskp18) | (~c2_1(a1782)))),
% 1.63/1.35 inference(rewrite,[status(thm)],[])).
% 1.63/1.35 tff(2385,axiom,((~c2_1(a1782)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause101')).
% 1.63/1.35 tff(2386,plain,
% 1.63/1.35 ((~hskp18) | (~c2_1(a1782))),
% 1.63/1.35 inference(modus_ponens,[status(thm)],[2385, 2384])).
% 1.63/1.35 tff(2387,plain,
% 1.63/1.35 ((~hskp18) | (~c2_1(a1782))),
% 1.63/1.35 inference(modus_ponens,[status(thm)],[2386, 2383])).
% 1.63/1.35 tff(2388,plain,
% 1.63/1.35 (~c2_1(a1782)),
% 1.63/1.35 inference(unit_resolution,[status(thm)],[2387, 2376])).
% 1.63/1.35 tff(2389,plain,
% 1.63/1.35 (((~hskp18) | (~c1_1(a1782))) <=> ((~hskp18) | (~c1_1(a1782)))),
% 1.63/1.35 inference(rewrite,[status(thm)],[])).
% 1.63/1.35 tff(2390,plain,
% 1.63/1.35 (((~c1_1(a1782)) | (~hskp18)) <=> ((~hskp18) | (~c1_1(a1782)))),
% 1.63/1.35 inference(rewrite,[status(thm)],[])).
% 1.63/1.35 tff(2391,axiom,((~c1_1(a1782)) | (~hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause100')).
% 1.63/1.35 tff(2392,plain,
% 1.63/1.35 ((~hskp18) | (~c1_1(a1782))),
% 1.63/1.35 inference(modus_ponens,[status(thm)],[2391, 2390])).
% 1.63/1.35 tff(2393,plain,
% 1.63/1.35 ((~hskp18) | (~c1_1(a1782))),
% 1.63/1.35 inference(modus_ponens,[status(thm)],[2392, 2389])).
% 1.63/1.35 tff(2394,plain,
% 1.63/1.35 (~c1_1(a1782)),
% 1.63/1.35 inference(unit_resolution,[status(thm)],[2393, 2376])).
% 1.63/1.35 tff(2395,plain,
% 1.63/1.35 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp13 | c0_1(a1799) | c2_1(a1799) | c1_1(a1782) | c2_1(a1782) | c3_1(a1782) | (~ndr1_0) | (~c3_1(a1799)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp13 | c0_1(a1799) | c2_1(a1799) | c1_1(a1782) | c2_1(a1782) | c3_1(a1782) | (~ndr1_0) | (~c3_1(a1799)))),
% 1.63/1.35 inference(rewrite,[status(thm)],[])).
% 1.63/1.35 tff(2396,plain,
% 1.63/1.35 ((hskp13 | (~ndr1_0) | c2_1(a1799) | c0_1(a1799) | (~c3_1(a1799)) | c2_1(a1782) | c1_1(a1782) | c3_1(a1782)) <=> (hskp13 | c0_1(a1799) | c2_1(a1799) | c1_1(a1782) | c2_1(a1782) | c3_1(a1782) | (~ndr1_0) | (~c3_1(a1799)))),
% 1.63/1.35 inference(rewrite,[status(thm)],[])).
% 1.63/1.35 tff(2397,plain,
% 1.63/1.35 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | c2_1(a1799) | c0_1(a1799) | (~c3_1(a1799)) | c2_1(a1782) | c1_1(a1782) | c3_1(a1782))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp13 | c0_1(a1799) | c2_1(a1799) | c1_1(a1782) | c2_1(a1782) | c3_1(a1782) | (~ndr1_0) | (~c3_1(a1799))))),
% 1.63/1.35 inference(monotonicity,[status(thm)],[2396])).
% 1.63/1.35 tff(2398,plain,
% 1.63/1.35 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | c2_1(a1799) | c0_1(a1799) | (~c3_1(a1799)) | c2_1(a1782) | c1_1(a1782) | c3_1(a1782))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp13 | c0_1(a1799) | c2_1(a1799) | c1_1(a1782) | c2_1(a1782) | c3_1(a1782) | (~ndr1_0) | (~c3_1(a1799)))),
% 1.63/1.35 inference(transitivity,[status(thm)],[2397, 2395])).
% 1.63/1.35 tff(2399,plain,
% 1.63/1.35 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | c2_1(a1799) | c0_1(a1799) | (~c3_1(a1799)) | c2_1(a1782) | c1_1(a1782) | c3_1(a1782))),
% 1.63/1.35 inference(quant_inst,[status(thm)],[])).
% 1.63/1.35 tff(2400,plain,
% 1.63/1.35 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp13 | c0_1(a1799) | c2_1(a1799) | c1_1(a1782) | c2_1(a1782) | c3_1(a1782) | (~ndr1_0) | (~c3_1(a1799))),
% 1.63/1.35 inference(modus_ponens,[status(thm)],[2399, 2398])).
% 1.63/1.35 tff(2401,plain,
% 1.63/1.35 ($false),
% 1.63/1.35 inference(unit_resolution,[status(thm)],[2400, 111, 23, 1247, 1255, 1246, 2394, 2388, 2382, 192])).
% 1.63/1.35 tff(2402,plain,((~hskp18) | hskp13 | (~c3_1(a1799)) | c0_1(a1799) | c2_1(a1799)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.35 tff(2403,plain,
% 1.63/1.35 (~hskp18),
% 1.63/1.35 inference(unit_resolution,[status(thm)],[2402, 1921, 2375, 2374, 2373])).
% 1.63/1.35 tff(2404,plain,
% 1.63/1.35 (^[V: $i, U: $i] : refl((hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) <=> (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))))),
% 1.63/1.35 inference(bind,[status(th)],[])).
% 1.63/1.35 tff(2405,plain,
% 1.63/1.35 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.63/1.35 inference(quant_intro,[status(thm)],[2404])).
% 1.63/1.35 tff(2406,plain,
% 1.63/1.35 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.63/1.35 inference(rewrite,[status(thm)],[])).
% 1.63/1.35 tff(2407,plain,
% 1.63/1.35 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | hskp18) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) | hskp18))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V))) | hskp18) <=> (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | hskp18) <=> (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))))),
% 1.63/1.35 inference(bind,[status(th)],[])).
% 1.63/1.35 tff(2408,plain,
% 1.63/1.35 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | hskp18) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.63/1.35 inference(quant_intro,[status(thm)],[2407])).
% 1.63/1.35 tff(2409,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(V)) | c3_1(V)) | hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause184')).
% 1.63/1.35 tff(2410,plain,
% 1.63/1.35 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.63/1.35 inference(modus_ponens,[status(thm)],[2409, 2408])).
% 1.63/1.35 tff(2411,plain,
% 1.63/1.35 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.63/1.35 inference(modus_ponens,[status(thm)],[2410, 2406])).
% 1.63/1.35 tff(2412,plain,(
% 1.63/1.35 ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.63/1.35 inference(skolemize,[status(sab)],[2411])).
% 1.63/1.35 tff(2413,plain,
% 1.63/1.35 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))),
% 1.63/1.35 inference(modus_ponens,[status(thm)],[2412, 2405])).
% 1.63/1.35 tff(2414,assumption,(~c3_1(a1779)), introduced(assumption)).
% 1.63/1.35 tff(2415,assumption,(~c2_1(a1779)), introduced(assumption)).
% 1.63/1.35 tff(2416,assumption,(c0_1(a1779)), introduced(assumption)).
% 1.63/1.35 tff(2417,assumption,(~hskp18), introduced(assumption)).
% 1.63/1.35 tff(2418,plain,
% 1.63/1.35 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp18 | c2_1(a1779) | c3_1(a1779) | (~ndr1_0) | (~c0_1(a1779)) | (~c3_1(a1805)) | (~c2_1(a1805)) | (~c0_1(a1805)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp18 | c2_1(a1779) | c3_1(a1779) | (~ndr1_0) | (~c0_1(a1779)) | (~c3_1(a1805)) | (~c2_1(a1805)) | (~c0_1(a1805)))),
% 1.63/1.35 inference(rewrite,[status(thm)],[])).
% 1.63/1.35 tff(2419,plain,
% 1.63/1.35 ((hskp18 | (~ndr1_0) | (~c2_1(a1805)) | (~c3_1(a1805)) | (~c0_1(a1805)) | c2_1(a1779) | c3_1(a1779) | (~c0_1(a1779))) <=> (hskp18 | c2_1(a1779) | c3_1(a1779) | (~ndr1_0) | (~c0_1(a1779)) | (~c3_1(a1805)) | (~c2_1(a1805)) | (~c0_1(a1805)))),
% 1.63/1.35 inference(rewrite,[status(thm)],[])).
% 1.63/1.35 tff(2420,plain,
% 1.63/1.35 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | (~c2_1(a1805)) | (~c3_1(a1805)) | (~c0_1(a1805)) | c2_1(a1779) | c3_1(a1779) | (~c0_1(a1779)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp18 | c2_1(a1779) | c3_1(a1779) | (~ndr1_0) | (~c0_1(a1779)) | (~c3_1(a1805)) | (~c2_1(a1805)) | (~c0_1(a1805))))),
% 1.63/1.35 inference(monotonicity,[status(thm)],[2419])).
% 1.63/1.35 tff(2421,plain,
% 1.63/1.35 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | (~c2_1(a1805)) | (~c3_1(a1805)) | (~c0_1(a1805)) | c2_1(a1779) | c3_1(a1779) | (~c0_1(a1779)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp18 | c2_1(a1779) | c3_1(a1779) | (~ndr1_0) | (~c0_1(a1779)) | (~c3_1(a1805)) | (~c2_1(a1805)) | (~c0_1(a1805)))),
% 1.63/1.35 inference(transitivity,[status(thm)],[2420, 2418])).
% 1.63/1.35 tff(2422,plain,
% 1.63/1.35 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | (hskp18 | (~ndr1_0) | (~c2_1(a1805)) | (~c3_1(a1805)) | (~c0_1(a1805)) | c2_1(a1779) | c3_1(a1779) | (~c0_1(a1779)))),
% 1.63/1.35 inference(quant_inst,[status(thm)],[])).
% 1.63/1.35 tff(2423,plain,
% 1.63/1.35 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c3_1(V) | (~c0_1(V)))) | hskp18 | c2_1(a1779) | c3_1(a1779) | (~ndr1_0) | (~c0_1(a1779)) | (~c3_1(a1805)) | (~c2_1(a1805)) | (~c0_1(a1805))),
% 1.63/1.35 inference(modus_ponens,[status(thm)],[2422, 2421])).
% 1.63/1.35 tff(2424,plain,
% 1.63/1.35 ($false),
% 1.63/1.35 inference(unit_resolution,[status(thm)],[2423, 111, 2417, 1565, 1564, 1563, 2416, 2415, 2414, 2413])).
% 1.63/1.35 tff(2425,plain,((~hskp29) | hskp18 | (~c0_1(a1779)) | c2_1(a1779) | c3_1(a1779)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.35 tff(2426,plain,
% 1.63/1.35 (~hskp29),
% 1.63/1.35 inference(unit_resolution,[status(thm)],[2425, 2403, 2365, 2354, 2348])).
% 1.63/1.35 tff(2427,plain,
% 1.63/1.35 (((~![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp30 | hskp29 | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)))) <=> ((~![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp30 | hskp29 | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)))),
% 1.63/1.35 inference(rewrite,[status(thm)],[])).
% 1.63/1.35 tff(2428,plain,
% 1.63/1.35 ((hskp30 | hskp29 | (~ndr1_0) | c3_1(a1758) | (~c2_1(a1758)) | (~c1_1(a1758))) <=> (hskp30 | hskp29 | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)))),
% 1.63/1.35 inference(rewrite,[status(thm)],[])).
% 1.63/1.35 tff(2429,plain,
% 1.63/1.35 (((~![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp30 | hskp29 | (~ndr1_0) | c3_1(a1758) | (~c2_1(a1758)) | (~c1_1(a1758)))) <=> ((~![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp30 | hskp29 | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758))))),
% 1.63/1.35 inference(monotonicity,[status(thm)],[2428])).
% 1.63/1.35 tff(2430,plain,
% 1.63/1.35 (((~![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp30 | hskp29 | (~ndr1_0) | c3_1(a1758) | (~c2_1(a1758)) | (~c1_1(a1758)))) <=> ((~![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp30 | hskp29 | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)))),
% 1.63/1.35 inference(transitivity,[status(thm)],[2429, 2427])).
% 1.63/1.35 tff(2431,plain,
% 1.63/1.35 ((~![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp30 | hskp29 | (~ndr1_0) | c3_1(a1758) | (~c2_1(a1758)) | (~c1_1(a1758)))),
% 1.63/1.35 inference(quant_inst,[status(thm)],[])).
% 1.63/1.35 tff(2432,plain,
% 1.63/1.35 ((~![U: $i] : (hskp30 | hskp29 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp30 | hskp29 | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758))),
% 1.63/1.35 inference(modus_ponens,[status(thm)],[2431, 2430])).
% 1.63/1.35 tff(2433,plain,
% 1.63/1.35 (hskp30 | hskp29),
% 1.63/1.35 inference(unit_resolution,[status(thm)],[2432, 111, 2268, 2267, 2270, 1592])).
% 1.63/1.35 tff(2434,plain,
% 1.63/1.35 (hskp30),
% 1.63/1.35 inference(unit_resolution,[status(thm)],[2433, 2426])).
% 1.63/1.35 tff(2435,plain,
% 1.63/1.35 (c2_1(a1823)),
% 1.63/1.35 inference(unit_resolution,[status(thm)],[1621, 2434])).
% 1.63/1.35 tff(2436,plain,
% 1.63/1.35 (c1_1(a1823)),
% 1.63/1.35 inference(unit_resolution,[status(thm)],[1632, 2434])).
% 1.63/1.35 tff(2437,plain,
% 1.63/1.35 (((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | (~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | c0_1(a1823))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp13 | (~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | c0_1(a1823))),
% 1.63/1.35 inference(rewrite,[status(thm)],[])).
% 1.63/1.35 tff(2438,plain,
% 1.63/1.35 ((hskp13 | (~ndr1_0) | c0_1(a1823) | (~c2_1(a1823)) | (~c1_1(a1823))) <=> (hskp13 | (~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | c0_1(a1823))),
% 1.63/1.35 inference(rewrite,[status(thm)],[])).
% 1.63/1.35 tff(2439,plain,
% 1.63/1.35 (((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | (~ndr1_0) | c0_1(a1823) | (~c2_1(a1823)) | (~c1_1(a1823)))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | (~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | c0_1(a1823)))),
% 1.63/1.35 inference(monotonicity,[status(thm)],[2438])).
% 1.63/1.35 tff(2440,plain,
% 1.63/1.35 (((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | (~ndr1_0) | c0_1(a1823) | (~c2_1(a1823)) | (~c1_1(a1823)))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp13 | (~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | c0_1(a1823))),
% 1.63/1.35 inference(transitivity,[status(thm)],[2439, 2437])).
% 1.63/1.35 tff(2441,plain,
% 1.63/1.35 ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | (~ndr1_0) | c0_1(a1823) | (~c2_1(a1823)) | (~c1_1(a1823)))),
% 1.63/1.35 inference(quant_inst,[status(thm)],[])).
% 1.63/1.35 tff(2442,plain,
% 1.63/1.35 ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp13 | (~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | c0_1(a1823)),
% 1.63/1.35 inference(modus_ponens,[status(thm)],[2441, 2440])).
% 1.63/1.35 tff(2443,plain,
% 1.63/1.35 (c0_1(a1823)),
% 1.63/1.35 inference(unit_resolution,[status(thm)],[2442, 111, 1921, 2436, 2435, 22])).
% 1.63/1.35 tff(2444,plain,
% 1.63/1.35 (c3_1(a1823)),
% 1.63/1.35 inference(unit_resolution,[status(thm)],[1610, 2434])).
% 1.63/1.35 tff(2445,plain,
% 1.63/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c3_1(a1786) | (~ndr1_0) | (~c1_1(a1786)) | (~c0_1(a1786)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | (~c0_1(a1823)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a1786) | (~ndr1_0) | (~c1_1(a1786)) | (~c0_1(a1786)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | (~c0_1(a1823)))),
% 1.63/1.35 inference(rewrite,[status(thm)],[])).
% 1.63/1.35 tff(2446,plain,
% 1.63/1.35 (((~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c0_1(a1823)) | c3_1(a1786) | (~c1_1(a1786)) | (~c0_1(a1786))) <=> (c3_1(a1786) | (~ndr1_0) | (~c1_1(a1786)) | (~c0_1(a1786)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | (~c0_1(a1823)))),
% 1.63/1.35 inference(rewrite,[status(thm)],[])).
% 1.63/1.35 tff(2447,plain,
% 1.63/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c0_1(a1823)) | c3_1(a1786) | (~c1_1(a1786)) | (~c0_1(a1786)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c3_1(a1786) | (~ndr1_0) | (~c1_1(a1786)) | (~c0_1(a1786)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | (~c0_1(a1823))))),
% 1.63/1.35 inference(monotonicity,[status(thm)],[2446])).
% 1.63/1.35 tff(2448,plain,
% 1.63/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c0_1(a1823)) | c3_1(a1786) | (~c1_1(a1786)) | (~c0_1(a1786)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a1786) | (~ndr1_0) | (~c1_1(a1786)) | (~c0_1(a1786)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | (~c0_1(a1823)))),
% 1.63/1.35 inference(transitivity,[status(thm)],[2447, 2445])).
% 1.63/1.35 tff(2449,plain,
% 1.63/1.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c0_1(a1823)) | c3_1(a1786) | (~c1_1(a1786)) | (~c0_1(a1786)))),
% 1.63/1.35 inference(quant_inst,[status(thm)],[])).
% 1.63/1.35 tff(2450,plain,
% 1.63/1.35 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a1786) | (~ndr1_0) | (~c1_1(a1786)) | (~c0_1(a1786)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | (~c0_1(a1823))),
% 1.63/1.35 inference(modus_ponens,[status(thm)],[2449, 2448])).
% 1.63/1.35 tff(2451,plain,
% 1.63/1.35 ($false),
% 1.63/1.35 inference(unit_resolution,[status(thm)],[2450, 111, 2436, 2435, 2444, 2335, 2324, 2313, 678, 2443])).
% 1.63/1.35 tff(2452,plain,(c2_1(a1771) | hskp6 | c0_1(a1771)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.35 tff(2453,plain,
% 1.63/1.35 (c2_1(a1771)),
% 1.63/1.35 inference(unit_resolution,[status(thm)],[2452, 275, 240])).
% 1.63/1.35 tff(2454,plain,
% 1.63/1.35 (((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | c0_1(a1771) | (~ndr1_0) | (~c1_1(a1771)) | (~c2_1(a1771)))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp13 | c0_1(a1771) | (~ndr1_0) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 1.63/1.35 inference(rewrite,[status(thm)],[])).
% 1.63/1.35 tff(2455,plain,
% 1.63/1.35 ((hskp13 | (~ndr1_0) | c0_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771))) <=> (hskp13 | c0_1(a1771) | (~ndr1_0) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 1.63/1.35 inference(rewrite,[status(thm)],[])).
% 1.63/1.35 tff(2456,plain,
% 1.63/1.35 (((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | (~ndr1_0) | c0_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | c0_1(a1771) | (~ndr1_0) | (~c1_1(a1771)) | (~c2_1(a1771))))),
% 1.63/1.35 inference(monotonicity,[status(thm)],[2455])).
% 1.63/1.35 tff(2457,plain,
% 1.63/1.35 (((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | (~ndr1_0) | c0_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)))) <=> ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp13 | c0_1(a1771) | (~ndr1_0) | (~c1_1(a1771)) | (~c2_1(a1771)))),
% 1.63/1.35 inference(transitivity,[status(thm)],[2456, 2454])).
% 1.63/1.35 tff(2458,plain,
% 1.63/1.35 ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | (hskp13 | (~ndr1_0) | c0_1(a1771) | (~c2_1(a1771)) | (~c1_1(a1771)))),
% 1.63/1.35 inference(quant_inst,[status(thm)],[])).
% 1.63/1.35 tff(2459,plain,
% 1.63/1.35 ((~![U: $i] : (hskp13 | (~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c1_1(U)))) | hskp13 | c0_1(a1771) | (~ndr1_0) | (~c1_1(a1771)) | (~c2_1(a1771))),
% 1.63/1.35 inference(modus_ponens,[status(thm)],[2458, 2457])).
% 1.63/1.35 tff(2460,plain,
% 1.63/1.35 (hskp13 | (~c1_1(a1771)) | (~c2_1(a1771))),
% 1.63/1.35 inference(unit_resolution,[status(thm)],[2459, 111, 275, 22])).
% 1.63/1.35 tff(2461,plain,
% 1.63/1.35 (~c1_1(a1771)),
% 1.63/1.35 inference(unit_resolution,[status(thm)],[2460, 23, 2453])).
% 1.63/1.35 tff(2462,plain,
% 1.63/1.35 (((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp4 | c1_1(a1771) | c0_1(a1771) | (~ndr1_0) | (~c2_1(a1771)))) <=> ((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp4 | c1_1(a1771) | c0_1(a1771) | (~ndr1_0) | (~c2_1(a1771)))),
% 1.63/1.35 inference(rewrite,[status(thm)],[])).
% 1.63/1.35 tff(2463,plain,
% 1.63/1.35 ((hskp6 | hskp4 | (~ndr1_0) | c1_1(a1771) | c0_1(a1771) | (~c2_1(a1771))) <=> (hskp6 | hskp4 | c1_1(a1771) | c0_1(a1771) | (~ndr1_0) | (~c2_1(a1771)))),
% 1.63/1.35 inference(rewrite,[status(thm)],[])).
% 1.63/1.35 tff(2464,plain,
% 1.63/1.35 (((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp4 | (~ndr1_0) | c1_1(a1771) | c0_1(a1771) | (~c2_1(a1771)))) <=> ((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp4 | c1_1(a1771) | c0_1(a1771) | (~ndr1_0) | (~c2_1(a1771))))),
% 1.63/1.35 inference(monotonicity,[status(thm)],[2463])).
% 1.63/1.35 tff(2465,plain,
% 1.63/1.35 (((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp4 | (~ndr1_0) | c1_1(a1771) | c0_1(a1771) | (~c2_1(a1771)))) <=> ((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp4 | c1_1(a1771) | c0_1(a1771) | (~ndr1_0) | (~c2_1(a1771)))),
% 1.63/1.35 inference(transitivity,[status(thm)],[2464, 2462])).
% 1.63/1.35 tff(2466,plain,
% 1.63/1.35 ((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp6 | hskp4 | (~ndr1_0) | c1_1(a1771) | c0_1(a1771) | (~c2_1(a1771)))),
% 1.63/1.35 inference(quant_inst,[status(thm)],[])).
% 1.63/1.35 tff(2467,plain,
% 1.63/1.35 ((~![U: $i] : (hskp6 | hskp4 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp6 | hskp4 | c1_1(a1771) | c0_1(a1771) | (~ndr1_0) | (~c2_1(a1771))),
% 1.63/1.35 inference(modus_ponens,[status(thm)],[2466, 2465])).
% 1.63/1.35 tff(2468,plain,
% 1.63/1.35 (hskp4 | c1_1(a1771) | (~c2_1(a1771))),
% 1.63/1.35 inference(unit_resolution,[status(thm)],[2467, 111, 240, 275, 1755])).
% 1.63/1.35 tff(2469,plain,
% 1.63/1.35 (hskp4),
% 1.63/1.35 inference(unit_resolution,[status(thm)],[2468, 2461, 2453])).
% 1.63/1.35 tff(2470,plain,
% 1.63/1.35 (~c3_1(a1759)),
% 1.63/1.35 inference(unit_resolution,[status(thm)],[1744, 2469])).
% 1.63/1.35 tff(2471,plain,
% 1.63/1.35 (c1_1(a1759)),
% 1.63/1.35 inference(unit_resolution,[status(thm)],[150, 2469])).
% 1.63/1.35 tff(2472,plain,
% 1.63/1.35 (c0_1(a1759)),
% 1.63/1.35 inference(unit_resolution,[status(thm)],[2249, 111, 23, 1919, 2471, 1908, 2470, 2098, 1969])).
% 1.63/1.35 tff(2473,plain,
% 1.63/1.35 (hskp3),
% 1.63/1.35 inference(unit_resolution,[status(thm)],[2260, 111, 1961, 1919, 2471, 1908, 2470, 1496, 2472])).
% 1.63/1.35 tff(2474,plain,
% 1.63/1.35 (c2_1(a1758)),
% 1.63/1.35 inference(unit_resolution,[status(thm)],[613, 2473])).
% 1.63/1.35 tff(2475,plain,
% 1.63/1.35 (c1_1(a1758)),
% 1.63/1.35 inference(unit_resolution,[status(thm)],[624, 2473])).
% 1.63/1.35 tff(2476,plain,
% 1.63/1.35 (c0_1(a1758)),
% 1.63/1.35 inference(unit_resolution,[status(thm)],[631, 111, 23, 2475, 2474, 22])).
% 1.63/1.35 tff(2477,plain,
% 1.63/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a1771) | c0_1(a1771) | c3_1(a1759) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1771)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1771) | c0_1(a1771) | c3_1(a1759) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1771)))),
% 1.63/1.35 inference(rewrite,[status(thm)],[])).
% 1.63/1.35 tff(2478,plain,
% 1.63/1.35 (((~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)) | c0_1(a1771) | c1_1(a1771) | (~c3_1(a1771))) <=> (c1_1(a1771) | c0_1(a1771) | c3_1(a1759) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1771)))),
% 1.63/1.35 inference(rewrite,[status(thm)],[])).
% 1.63/1.35 tff(2479,plain,
% 1.63/1.35 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)) | c0_1(a1771) | c1_1(a1771) | (~c3_1(a1771)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a1771) | c0_1(a1771) | c3_1(a1759) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1771))))),
% 1.63/1.36 inference(monotonicity,[status(thm)],[2478])).
% 1.63/1.36 tff(2480,plain,
% 1.63/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)) | c0_1(a1771) | c1_1(a1771) | (~c3_1(a1771)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1771) | c0_1(a1771) | c3_1(a1759) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1771)))),
% 1.63/1.36 inference(transitivity,[status(thm)],[2479, 2477])).
% 1.63/1.36 tff(2481,plain,
% 1.63/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)) | c0_1(a1771) | c1_1(a1771) | (~c3_1(a1771)))),
% 1.63/1.36 inference(quant_inst,[status(thm)],[])).
% 1.63/1.36 tff(2482,plain,
% 1.63/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1771) | c0_1(a1771) | c3_1(a1759) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c1_1(a1759)) | (~c0_1(a1759)) | (~c3_1(a1771))),
% 1.63/1.36 inference(modus_ponens,[status(thm)],[2481, 2480])).
% 1.63/1.36 tff(2483,plain,
% 1.63/1.36 (~c3_1(a1771)),
% 1.63/1.36 inference(unit_resolution,[status(thm)],[2482, 111, 2461, 2471, 2475, 2474, 275, 2470, 1655, 2472, 2476])).
% 1.63/1.36 tff(2484,plain,
% 1.63/1.36 (((~![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp20 | hskp6 | c0_1(a1771) | (~ndr1_0) | c3_1(a1771) | (~c2_1(a1771)))) <=> ((~![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp20 | hskp6 | c0_1(a1771) | (~ndr1_0) | c3_1(a1771) | (~c2_1(a1771)))),
% 1.63/1.36 inference(rewrite,[status(thm)],[])).
% 1.63/1.36 tff(2485,plain,
% 1.63/1.36 ((hskp20 | hskp6 | (~ndr1_0) | c3_1(a1771) | c0_1(a1771) | (~c2_1(a1771))) <=> (hskp20 | hskp6 | c0_1(a1771) | (~ndr1_0) | c3_1(a1771) | (~c2_1(a1771)))),
% 1.63/1.36 inference(rewrite,[status(thm)],[])).
% 1.63/1.36 tff(2486,plain,
% 1.63/1.36 (((~![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp20 | hskp6 | (~ndr1_0) | c3_1(a1771) | c0_1(a1771) | (~c2_1(a1771)))) <=> ((~![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp20 | hskp6 | c0_1(a1771) | (~ndr1_0) | c3_1(a1771) | (~c2_1(a1771))))),
% 1.63/1.36 inference(monotonicity,[status(thm)],[2485])).
% 1.63/1.36 tff(2487,plain,
% 1.63/1.36 (((~![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp20 | hskp6 | (~ndr1_0) | c3_1(a1771) | c0_1(a1771) | (~c2_1(a1771)))) <=> ((~![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp20 | hskp6 | c0_1(a1771) | (~ndr1_0) | c3_1(a1771) | (~c2_1(a1771)))),
% 1.63/1.36 inference(transitivity,[status(thm)],[2486, 2484])).
% 1.63/1.36 tff(2488,plain,
% 1.63/1.36 ((~![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp20 | hskp6 | (~ndr1_0) | c3_1(a1771) | c0_1(a1771) | (~c2_1(a1771)))),
% 1.63/1.36 inference(quant_inst,[status(thm)],[])).
% 1.63/1.36 tff(2489,plain,
% 1.63/1.36 ((~![U: $i] : (hskp20 | hskp6 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp20 | hskp6 | c0_1(a1771) | (~ndr1_0) | c3_1(a1771) | (~c2_1(a1771))),
% 1.63/1.36 inference(modus_ponens,[status(thm)],[2488, 2487])).
% 1.63/1.36 tff(2490,plain,
% 1.63/1.36 (hskp20 | c3_1(a1771) | (~c2_1(a1771))),
% 1.63/1.36 inference(unit_resolution,[status(thm)],[2489, 111, 240, 275, 2300])).
% 1.63/1.36 tff(2491,plain,
% 1.63/1.36 (hskp20),
% 1.63/1.36 inference(unit_resolution,[status(thm)],[2490, 2483, 2453])).
% 1.63/1.36 tff(2492,plain,
% 1.63/1.36 (~c3_1(a1786)),
% 1.63/1.36 inference(unit_resolution,[status(thm)],[2312, 2491])).
% 1.63/1.36 tff(2493,plain,
% 1.63/1.36 (c1_1(a1786)),
% 1.63/1.36 inference(unit_resolution,[status(thm)],[2323, 2491])).
% 1.63/1.36 tff(2494,plain,
% 1.63/1.36 (c0_1(a1786)),
% 1.63/1.36 inference(unit_resolution,[status(thm)],[2334, 2491])).
% 1.63/1.36 tff(2495,plain,
% 1.63/1.36 (^[V: $i, U: $i] : refl((hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))),
% 1.63/1.36 inference(bind,[status(th)],[])).
% 1.63/1.36 tff(2496,plain,
% 1.63/1.36 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.63/1.36 inference(quant_intro,[status(thm)],[2495])).
% 1.63/1.36 tff(2497,plain,
% 1.63/1.36 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.63/1.36 inference(rewrite,[status(thm)],[])).
% 1.63/1.36 tff(2498,plain,
% 1.63/1.36 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c1_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp28) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp28))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V))) | hskp28) <=> (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp28) <=> (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))))),
% 1.63/1.36 inference(bind,[status(th)],[])).
% 1.63/1.36 tff(2499,plain,
% 1.63/1.36 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp28) <=> ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.63/1.36 inference(quant_intro,[status(thm)],[2498])).
% 1.63/1.36 tff(2500,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp28)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause189')).
% 1.63/1.36 tff(2501,plain,
% 1.63/1.36 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.63/1.36 inference(modus_ponens,[status(thm)],[2500, 2499])).
% 1.63/1.36 tff(2502,plain,
% 1.63/1.36 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.63/1.36 inference(modus_ponens,[status(thm)],[2501, 2497])).
% 1.63/1.36 tff(2503,plain,(
% 1.63/1.36 ![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.63/1.36 inference(skolemize,[status(sab)],[2502])).
% 1.63/1.36 tff(2504,plain,
% 1.63/1.36 (![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))),
% 1.63/1.36 inference(modus_ponens,[status(thm)],[2503, 2496])).
% 1.63/1.36 tff(2505,plain,
% 1.63/1.36 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1783)) | (~c1_1(a1783)) | c2_1(a1783))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp28 | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1783)) | (~c1_1(a1783)) | c2_1(a1783))),
% 1.63/1.36 inference(rewrite,[status(thm)],[])).
% 1.63/1.36 tff(2506,plain,
% 1.63/1.36 ((hskp28 | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c2_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783))) <=> (hskp28 | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1783)) | (~c1_1(a1783)) | c2_1(a1783))),
% 1.63/1.36 inference(rewrite,[status(thm)],[])).
% 1.63/1.36 tff(2507,plain,
% 1.63/1.36 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c2_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1783)) | (~c1_1(a1783)) | c2_1(a1783)))),
% 1.63/1.36 inference(monotonicity,[status(thm)],[2506])).
% 1.63/1.36 tff(2508,plain,
% 1.63/1.36 (((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c2_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp28 | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1783)) | (~c1_1(a1783)) | c2_1(a1783))),
% 1.63/1.36 inference(transitivity,[status(thm)],[2507, 2505])).
% 1.63/1.36 tff(2509,plain,
% 1.63/1.36 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp28 | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c2_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.63/1.36 inference(quant_inst,[status(thm)],[])).
% 1.63/1.36 tff(2510,plain,
% 1.63/1.36 ((~![V: $i, U: $i] : (hskp28 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp28 | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c3_1(a1783)) | (~c1_1(a1783)) | c2_1(a1783)),
% 1.63/1.36 inference(modus_ponens,[status(thm)],[2509, 2508])).
% 1.63/1.36 tff(2511,plain,
% 1.63/1.36 (hskp28),
% 1.63/1.36 inference(unit_resolution,[status(thm)],[2510, 111, 1961, 1919, 2475, 2474, 2504, 1969, 2476])).
% 1.63/1.36 tff(2512,plain,
% 1.63/1.36 (((~hskp28) | c2_1(a1795)) <=> ((~hskp28) | c2_1(a1795))),
% 1.63/1.36 inference(rewrite,[status(thm)],[])).
% 1.63/1.36 tff(2513,axiom,((~hskp28) | c2_1(a1795)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause46')).
% 1.63/1.36 tff(2514,plain,
% 1.63/1.36 ((~hskp28) | c2_1(a1795)),
% 1.63/1.36 inference(modus_ponens,[status(thm)],[2513, 2512])).
% 1.63/1.36 tff(2515,plain,
% 1.63/1.36 ((~hskp28) | c2_1(a1795)),
% 1.63/1.36 inference(modus_ponens,[status(thm)],[2514, 2512])).
% 1.63/1.36 tff(2516,plain,
% 1.63/1.36 ((~hskp28) | c2_1(a1795)),
% 1.63/1.36 inference(modus_ponens,[status(thm)],[2515, 2512])).
% 1.63/1.36 tff(2517,plain,
% 1.63/1.36 ((~hskp28) | c2_1(a1795)),
% 1.63/1.36 inference(modus_ponens,[status(thm)],[2516, 2512])).
% 1.63/1.36 tff(2518,plain,
% 1.63/1.36 ((~hskp28) | c2_1(a1795)),
% 1.63/1.36 inference(modus_ponens,[status(thm)],[2517, 2512])).
% 1.63/1.36 tff(2519,plain,
% 1.63/1.36 ((~hskp28) | c2_1(a1795)),
% 1.63/1.36 inference(modus_ponens,[status(thm)],[2518, 2512])).
% 1.63/1.36 tff(2520,plain,
% 1.63/1.36 ((~hskp28) | c2_1(a1795)),
% 1.63/1.36 inference(modus_ponens,[status(thm)],[2519, 2512])).
% 1.63/1.36 tff(2521,plain,
% 1.63/1.36 ((~hskp28) | c2_1(a1795)),
% 1.63/1.36 inference(modus_ponens,[status(thm)],[2520, 2512])).
% 1.63/1.36 tff(2522,plain,
% 1.63/1.36 (c2_1(a1795)),
% 1.63/1.36 inference(unit_resolution,[status(thm)],[2521, 2511])).
% 1.63/1.36 tff(2523,plain,
% 1.63/1.36 (((~hskp28) | c1_1(a1795)) <=> ((~hskp28) | c1_1(a1795))),
% 1.63/1.36 inference(rewrite,[status(thm)],[])).
% 1.63/1.36 tff(2524,axiom,((~hskp28) | c1_1(a1795)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause45')).
% 1.63/1.36 tff(2525,plain,
% 1.63/1.36 ((~hskp28) | c1_1(a1795)),
% 1.63/1.36 inference(modus_ponens,[status(thm)],[2524, 2523])).
% 1.63/1.36 tff(2526,plain,
% 1.63/1.36 ((~hskp28) | c1_1(a1795)),
% 1.63/1.36 inference(modus_ponens,[status(thm)],[2525, 2523])).
% 1.63/1.36 tff(2527,plain,
% 1.63/1.36 ((~hskp28) | c1_1(a1795)),
% 1.63/1.36 inference(modus_ponens,[status(thm)],[2526, 2523])).
% 1.63/1.36 tff(2528,plain,
% 1.63/1.36 ((~hskp28) | c1_1(a1795)),
% 1.63/1.36 inference(modus_ponens,[status(thm)],[2527, 2523])).
% 1.63/1.36 tff(2529,plain,
% 1.63/1.36 ((~hskp28) | c1_1(a1795)),
% 1.63/1.36 inference(modus_ponens,[status(thm)],[2528, 2523])).
% 1.63/1.36 tff(2530,plain,
% 1.63/1.36 ((~hskp28) | c1_1(a1795)),
% 1.63/1.36 inference(modus_ponens,[status(thm)],[2529, 2523])).
% 1.63/1.36 tff(2531,plain,
% 1.63/1.36 ((~hskp28) | c1_1(a1795)),
% 1.63/1.36 inference(modus_ponens,[status(thm)],[2530, 2523])).
% 1.63/1.36 tff(2532,plain,
% 1.63/1.36 ((~hskp28) | c1_1(a1795)),
% 1.63/1.36 inference(modus_ponens,[status(thm)],[2531, 2523])).
% 1.63/1.36 tff(2533,plain,
% 1.63/1.36 (c1_1(a1795)),
% 1.63/1.36 inference(unit_resolution,[status(thm)],[2532, 2511])).
% 1.63/1.36 tff(2534,plain,
% 1.63/1.36 (((~hskp28) | c0_1(a1795)) <=> ((~hskp28) | c0_1(a1795))),
% 1.63/1.36 inference(rewrite,[status(thm)],[])).
% 1.63/1.36 tff(2535,axiom,((~hskp28) | c0_1(a1795)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause44')).
% 1.63/1.36 tff(2536,plain,
% 1.63/1.36 ((~hskp28) | c0_1(a1795)),
% 1.63/1.36 inference(modus_ponens,[status(thm)],[2535, 2534])).
% 1.63/1.36 tff(2537,plain,
% 1.63/1.36 ((~hskp28) | c0_1(a1795)),
% 1.63/1.36 inference(modus_ponens,[status(thm)],[2536, 2534])).
% 1.63/1.36 tff(2538,plain,
% 1.63/1.36 ((~hskp28) | c0_1(a1795)),
% 1.63/1.36 inference(modus_ponens,[status(thm)],[2537, 2534])).
% 1.63/1.36 tff(2539,plain,
% 1.63/1.36 ((~hskp28) | c0_1(a1795)),
% 1.63/1.36 inference(modus_ponens,[status(thm)],[2538, 2534])).
% 1.63/1.36 tff(2540,plain,
% 1.63/1.36 ((~hskp28) | c0_1(a1795)),
% 1.63/1.36 inference(modus_ponens,[status(thm)],[2539, 2534])).
% 1.63/1.36 tff(2541,plain,
% 1.63/1.36 ((~hskp28) | c0_1(a1795)),
% 1.63/1.36 inference(modus_ponens,[status(thm)],[2540, 2534])).
% 1.63/1.36 tff(2542,plain,
% 1.63/1.36 ((~hskp28) | c0_1(a1795)),
% 1.63/1.36 inference(modus_ponens,[status(thm)],[2541, 2534])).
% 1.63/1.36 tff(2543,plain,
% 1.63/1.36 ((~hskp28) | c0_1(a1795)),
% 1.63/1.36 inference(modus_ponens,[status(thm)],[2542, 2534])).
% 1.63/1.36 tff(2544,plain,
% 1.63/1.36 (c0_1(a1795)),
% 1.63/1.36 inference(unit_resolution,[status(thm)],[2543, 2511])).
% 1.63/1.36 tff(2545,plain,
% 1.63/1.36 (~c3_1(a1758)),
% 1.63/1.36 inference(unit_resolution,[status(thm)],[638, 2473])).
% 1.63/1.36 tff(2546,plain,
% 1.63/1.36 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp15 | c1_1(a1771) | c3_1(a1758) | (~ndr1_0) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1771) | (~c2_1(a1771)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp15 | c1_1(a1771) | c3_1(a1758) | (~ndr1_0) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1771) | (~c2_1(a1771)))),
% 1.63/1.36 inference(rewrite,[status(thm)],[])).
% 1.63/1.36 tff(2547,plain,
% 1.63/1.36 ((hskp15 | (~ndr1_0) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)) | c1_1(a1771) | c3_1(a1771) | (~c2_1(a1771))) <=> (hskp15 | c1_1(a1771) | c3_1(a1758) | (~ndr1_0) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1771) | (~c2_1(a1771)))),
% 1.63/1.36 inference(rewrite,[status(thm)],[])).
% 1.63/1.36 tff(2548,plain,
% 1.63/1.36 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)) | c1_1(a1771) | c3_1(a1771) | (~c2_1(a1771)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp15 | c1_1(a1771) | c3_1(a1758) | (~ndr1_0) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1771) | (~c2_1(a1771))))),
% 1.63/1.36 inference(monotonicity,[status(thm)],[2547])).
% 1.63/1.36 tff(2549,plain,
% 1.63/1.36 (((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)) | c1_1(a1771) | c3_1(a1771) | (~c2_1(a1771)))) <=> ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp15 | c1_1(a1771) | c3_1(a1758) | (~ndr1_0) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1771) | (~c2_1(a1771)))),
% 1.63/1.36 inference(transitivity,[status(thm)],[2548, 2546])).
% 1.63/1.36 tff(2550,plain,
% 1.63/1.36 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp15 | (~ndr1_0) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)) | c1_1(a1771) | c3_1(a1771) | (~c2_1(a1771)))),
% 1.63/1.36 inference(quant_inst,[status(thm)],[])).
% 1.63/1.36 tff(2551,plain,
% 1.63/1.36 ((~![V: $i, U: $i] : (hskp15 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp15 | c1_1(a1771) | c3_1(a1758) | (~ndr1_0) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1771) | (~c2_1(a1771))),
% 1.63/1.36 inference(modus_ponens,[status(thm)],[2550, 2549])).
% 1.63/1.36 tff(2552,plain,
% 1.63/1.36 (hskp15),
% 1.63/1.36 inference(unit_resolution,[status(thm)],[2551, 111, 2461, 2453, 2475, 2545, 2284, 2483, 2476])).
% 1.63/1.36 tff(2553,plain,
% 1.63/1.36 (~c3_1(a1779)),
% 1.63/1.36 inference(unit_resolution,[status(thm)],[2347, 2552])).
% 1.63/1.36 tff(2554,plain,
% 1.63/1.36 (~c2_1(a1779)),
% 1.63/1.36 inference(unit_resolution,[status(thm)],[2353, 2552])).
% 1.63/1.36 tff(2555,plain,
% 1.63/1.36 (c0_1(a1779)),
% 1.63/1.36 inference(unit_resolution,[status(thm)],[2364, 2552])).
% 1.63/1.36 tff(2556,plain,
% 1.63/1.36 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp22 | c1_1(a1771) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | c3_1(a1771) | (~c2_1(a1771)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp22 | c1_1(a1771) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | c3_1(a1771) | (~c2_1(a1771)))),
% 1.63/1.36 inference(rewrite,[status(thm)],[])).
% 1.63/1.36 tff(2557,plain,
% 1.63/1.36 ((hskp22 | (~ndr1_0) | c3_1(a1758) | (~c2_1(a1758)) | (~c1_1(a1758)) | c1_1(a1771) | c3_1(a1771) | (~c2_1(a1771))) <=> (hskp22 | c1_1(a1771) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | c3_1(a1771) | (~c2_1(a1771)))),
% 1.63/1.36 inference(rewrite,[status(thm)],[])).
% 1.63/1.36 tff(2558,plain,
% 1.63/1.36 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a1758) | (~c2_1(a1758)) | (~c1_1(a1758)) | c1_1(a1771) | c3_1(a1771) | (~c2_1(a1771)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp22 | c1_1(a1771) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | c3_1(a1771) | (~c2_1(a1771))))),
% 1.63/1.36 inference(monotonicity,[status(thm)],[2557])).
% 1.63/1.36 tff(2559,plain,
% 1.63/1.36 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a1758) | (~c2_1(a1758)) | (~c1_1(a1758)) | c1_1(a1771) | c3_1(a1771) | (~c2_1(a1771)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp22 | c1_1(a1771) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | c3_1(a1771) | (~c2_1(a1771)))),
% 1.63/1.36 inference(transitivity,[status(thm)],[2558, 2556])).
% 1.63/1.36 tff(2560,plain,
% 1.63/1.36 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp22 | (~ndr1_0) | c3_1(a1758) | (~c2_1(a1758)) | (~c1_1(a1758)) | c1_1(a1771) | c3_1(a1771) | (~c2_1(a1771)))),
% 1.63/1.36 inference(quant_inst,[status(thm)],[])).
% 1.63/1.36 tff(2561,plain,
% 1.63/1.36 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | c3_1(U) | (~c2_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp22 | c1_1(a1771) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | c3_1(a1771) | (~c2_1(a1771))),
% 1.63/1.36 inference(modus_ponens,[status(thm)],[2560, 2559])).
% 1.63/1.36 tff(2562,plain,
% 1.63/1.36 (hskp22),
% 1.63/1.36 inference(unit_resolution,[status(thm)],[2561, 111, 2461, 2453, 2475, 2474, 2545, 836, 2483])).
% 1.63/1.36 tff(2563,plain,
% 1.63/1.36 (~c2_1(a1799)),
% 1.63/1.36 inference(unit_resolution,[status(thm)],[542, 2562])).
% 1.63/1.36 tff(2564,plain,
% 1.63/1.36 (~c0_1(a1799)),
% 1.63/1.36 inference(unit_resolution,[status(thm)],[548, 2562])).
% 1.63/1.36 tff(2565,plain,
% 1.63/1.36 (c3_1(a1799)),
% 1.63/1.36 inference(unit_resolution,[status(thm)],[559, 2562])).
% 1.63/1.36 tff(2566,plain,
% 1.63/1.36 (~hskp18),
% 1.63/1.36 inference(unit_resolution,[status(thm)],[2402, 2565, 23, 2564, 2563])).
% 1.63/1.36 tff(2567,plain,
% 1.63/1.36 (~hskp29),
% 1.63/1.36 inference(unit_resolution,[status(thm)],[2425, 2566, 2555, 2554, 2553])).
% 1.63/1.36 tff(2568,plain,
% 1.63/1.36 (hskp30 | hskp29),
% 1.63/1.36 inference(unit_resolution,[status(thm)],[2432, 111, 2475, 2474, 2545, 1592])).
% 1.63/1.36 tff(2569,plain,
% 1.63/1.36 (hskp30),
% 1.63/1.36 inference(unit_resolution,[status(thm)],[2568, 2567])).
% 1.63/1.36 tff(2570,plain,
% 1.63/1.36 (c3_1(a1823)),
% 1.63/1.36 inference(unit_resolution,[status(thm)],[1610, 2569])).
% 1.63/1.36 tff(2571,plain,
% 1.63/1.36 (c2_1(a1823)),
% 1.63/1.36 inference(unit_resolution,[status(thm)],[1621, 2569])).
% 1.63/1.36 tff(2572,plain,
% 1.63/1.36 (c1_1(a1823)),
% 1.63/1.36 inference(unit_resolution,[status(thm)],[1632, 2569])).
% 1.63/1.36 tff(2573,plain,
% 1.63/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c3_1(a1786) | (~ndr1_0) | (~c1_1(a1786)) | (~c0_1(a1786)) | (~c0_1(a1795)) | (~c1_1(a1795)) | (~c2_1(a1795)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a1786) | (~ndr1_0) | (~c1_1(a1786)) | (~c0_1(a1786)) | (~c0_1(a1795)) | (~c1_1(a1795)) | (~c2_1(a1795)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)))),
% 1.63/1.36 inference(rewrite,[status(thm)],[])).
% 1.63/1.36 tff(2574,plain,
% 1.63/1.36 (((~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | (~c2_1(a1795)) | (~c1_1(a1795)) | (~c0_1(a1795)) | c3_1(a1786) | (~c1_1(a1786)) | (~c0_1(a1786))) <=> (c3_1(a1786) | (~ndr1_0) | (~c1_1(a1786)) | (~c0_1(a1786)) | (~c0_1(a1795)) | (~c1_1(a1795)) | (~c2_1(a1795)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)))),
% 1.63/1.36 inference(rewrite,[status(thm)],[])).
% 1.63/1.36 tff(2575,plain,
% 1.63/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | (~c2_1(a1795)) | (~c1_1(a1795)) | (~c0_1(a1795)) | c3_1(a1786) | (~c1_1(a1786)) | (~c0_1(a1786)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c3_1(a1786) | (~ndr1_0) | (~c1_1(a1786)) | (~c0_1(a1786)) | (~c0_1(a1795)) | (~c1_1(a1795)) | (~c2_1(a1795)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823))))),
% 1.63/1.36 inference(monotonicity,[status(thm)],[2574])).
% 1.63/1.36 tff(2576,plain,
% 1.63/1.36 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | (~c2_1(a1795)) | (~c1_1(a1795)) | (~c0_1(a1795)) | c3_1(a1786) | (~c1_1(a1786)) | (~c0_1(a1786)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a1786) | (~ndr1_0) | (~c1_1(a1786)) | (~c0_1(a1786)) | (~c0_1(a1795)) | (~c1_1(a1795)) | (~c2_1(a1795)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)))),
% 1.63/1.36 inference(transitivity,[status(thm)],[2575, 2573])).
% 1.63/1.36 tff(2577,plain,
% 1.63/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | (~c2_1(a1795)) | (~c1_1(a1795)) | (~c0_1(a1795)) | c3_1(a1786) | (~c1_1(a1786)) | (~c0_1(a1786)))),
% 1.63/1.36 inference(quant_inst,[status(thm)],[])).
% 1.63/1.36 tff(2578,plain,
% 1.63/1.36 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a1786) | (~ndr1_0) | (~c1_1(a1786)) | (~c0_1(a1786)) | (~c0_1(a1795)) | (~c1_1(a1795)) | (~c2_1(a1795)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823))),
% 1.63/1.36 inference(modus_ponens,[status(thm)],[2577, 2576])).
% 1.63/1.36 tff(2579,plain,
% 1.63/1.36 ($false),
% 1.63/1.36 inference(unit_resolution,[status(thm)],[2578, 111, 2572, 2571, 2570, 2544, 2533, 2522, 2494, 2493, 2492, 678])).
% 1.63/1.36 tff(2580,plain,(hskp13 | hskp6 | c0_1(a1771)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.36 tff(2581,plain,
% 1.63/1.36 (hskp13),
% 1.63/1.36 inference(unit_resolution,[status(thm)],[2580, 275, 240])).
% 1.63/1.36 tff(2582,plain,
% 1.63/1.36 (hskp3),
% 1.63/1.36 inference(unit_resolution,[status(thm)],[285, 2581, 240, 275])).
% 1.63/1.36 tff(2583,plain,
% 1.63/1.36 (c1_1(a1758)),
% 1.63/1.36 inference(unit_resolution,[status(thm)],[624, 2582])).
% 1.63/1.36 tff(2584,plain,
% 1.63/1.36 (~c3_1(a1758)),
% 1.63/1.36 inference(unit_resolution,[status(thm)],[638, 2582])).
% 1.63/1.36 tff(2585,plain,
% 1.63/1.36 (c1_1(a1771)),
% 1.63/1.36 inference(unit_resolution,[status(thm)],[252, 2581])).
% 1.63/1.36 tff(2586,assumption,(~hskp17), introduced(assumption)).
% 1.63/1.36 tff(2587,plain,
% 1.63/1.36 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c2_1(a1771)) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c2_1(a1771)) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.63/1.36 inference(rewrite,[status(thm)],[])).
% 1.63/1.36 tff(2588,plain,
% 1.63/1.36 ((hskp17 | (~ndr1_0) | (~c2_1(a1771)) | (~c1_1(a1771)) | (~c3_1(a1771)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783))) <=> (hskp17 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c2_1(a1771)) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.63/1.36 inference(rewrite,[status(thm)],[])).
% 1.63/1.36 tff(2589,plain,
% 1.63/1.36 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | (~c2_1(a1771)) | (~c1_1(a1771)) | (~c3_1(a1771)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c2_1(a1771)) | (~c3_1(a1783)) | (~c1_1(a1783))))),
% 1.63/1.36 inference(monotonicity,[status(thm)],[2588])).
% 1.63/1.36 tff(2590,plain,
% 1.63/1.36 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | (~c2_1(a1771)) | (~c1_1(a1771)) | (~c3_1(a1771)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c2_1(a1771)) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.63/1.36 inference(transitivity,[status(thm)],[2589, 2587])).
% 1.63/1.36 tff(2591,plain,
% 1.63/1.36 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | (~c2_1(a1771)) | (~c1_1(a1771)) | (~c3_1(a1771)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.63/1.36 inference(quant_inst,[status(thm)],[])).
% 1.63/1.36 tff(2592,plain,
% 1.63/1.36 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c2_1(a1771)) | (~c3_1(a1783)) | (~c1_1(a1783))),
% 1.63/1.36 inference(modus_ponens,[status(thm)],[2591, 2590])).
% 1.63/1.36 tff(2593,plain,
% 1.63/1.36 (hskp17 | (~c3_1(a1771)) | (~c1_1(a1771))),
% 1.63/1.36 inference(unit_resolution,[status(thm)],[2592, 111, 1961, 1919, 2453, 1908, 1313])).
% 1.63/1.36 tff(2594,plain,
% 1.63/1.36 (~c3_1(a1771)),
% 1.63/1.36 inference(unit_resolution,[status(thm)],[2593, 2586, 2585])).
% 1.63/1.36 tff(2595,plain,
% 1.63/1.36 (hskp20),
% 1.63/1.36 inference(unit_resolution,[status(thm)],[2490, 2594, 2453])).
% 1.63/1.36 tff(2596,plain,
% 1.63/1.36 (~c3_1(a1786)),
% 1.63/1.36 inference(unit_resolution,[status(thm)],[2312, 2595])).
% 1.63/1.36 tff(2597,plain,
% 1.63/1.36 (c1_1(a1786)),
% 1.63/1.36 inference(unit_resolution,[status(thm)],[2323, 2595])).
% 1.63/1.36 tff(2598,plain,
% 1.63/1.36 (c0_1(a1786)),
% 1.63/1.36 inference(unit_resolution,[status(thm)],[2334, 2595])).
% 1.63/1.36 tff(2599,assumption,(hskp30), introduced(assumption)).
% 1.63/1.36 tff(2600,plain,
% 1.63/1.36 (c3_1(a1823)),
% 1.63/1.36 inference(unit_resolution,[status(thm)],[1610, 2599])).
% 1.63/1.36 tff(2601,plain,
% 1.63/1.36 (c2_1(a1823)),
% 1.63/1.36 inference(unit_resolution,[status(thm)],[1621, 2599])).
% 1.63/1.36 tff(2602,plain,
% 1.63/1.36 (c1_1(a1823)),
% 1.63/1.36 inference(unit_resolution,[status(thm)],[1632, 2599])).
% 1.63/1.36 tff(2603,plain,
% 1.63/1.36 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)))),
% 1.63/1.36 inference(rewrite,[status(thm)],[])).
% 1.63/1.36 tff(2604,plain,
% 1.63/1.36 ((hskp17 | (~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783))) <=> (hskp17 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)))),
% 1.63/1.36 inference(rewrite,[status(thm)],[])).
% 1.63/1.36 tff(2605,plain,
% 1.63/1.36 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823))))),
% 1.63/1.36 inference(monotonicity,[status(thm)],[2604])).
% 1.63/1.36 tff(2606,plain,
% 1.63/1.36 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)))),
% 1.63/1.36 inference(transitivity,[status(thm)],[2605, 2603])).
% 1.63/1.36 tff(2607,plain,
% 1.63/1.36 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.63/1.36 inference(quant_inst,[status(thm)],[])).
% 1.63/1.36 tff(2608,plain,
% 1.63/1.36 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823))),
% 1.63/1.36 inference(modus_ponens,[status(thm)],[2607, 2606])).
% 1.63/1.36 tff(2609,plain,
% 1.63/1.36 ($false),
% 1.63/1.36 inference(unit_resolution,[status(thm)],[2608, 111, 2586, 2602, 2601, 2600, 1961, 1919, 1908, 1313])).
% 1.63/1.37 tff(2610,plain,((~hskp30) | hskp17), inference(lemma,lemma(discharge,[]))).
% 1.63/1.37 tff(2611,plain,
% 1.63/1.37 (~hskp30),
% 1.63/1.37 inference(unit_resolution,[status(thm)],[2610, 2586])).
% 1.63/1.37 tff(2612,plain,
% 1.63/1.37 (hskp30 | hskp29 | c3_1(a1771) | (~c1_1(a1771))),
% 1.63/1.37 inference(unit_resolution,[status(thm)],[1598, 111, 2453, 1592])).
% 1.63/1.37 tff(2613,plain,
% 1.63/1.37 (hskp29),
% 1.63/1.37 inference(unit_resolution,[status(thm)],[2612, 2611, 2585, 2594])).
% 1.63/1.37 tff(2614,plain,
% 1.63/1.37 (c3_1(a1805)),
% 1.63/1.37 inference(unit_resolution,[status(thm)],[979, 2613])).
% 1.63/1.37 tff(2615,plain,
% 1.63/1.37 (c2_1(a1805)),
% 1.63/1.37 inference(unit_resolution,[status(thm)],[1002, 2613])).
% 1.63/1.37 tff(2616,plain,
% 1.63/1.37 (c0_1(a1805)),
% 1.63/1.37 inference(unit_resolution,[status(thm)],[991, 2613])).
% 1.63/1.37 tff(2617,plain,
% 1.63/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c3_1(a1786) | (~ndr1_0) | (~c1_1(a1786)) | (~c0_1(a1786)) | (~c3_1(a1805)) | (~c1_1(a1805)) | (~c2_1(a1805)) | (~c0_1(a1805)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a1786) | (~ndr1_0) | (~c1_1(a1786)) | (~c0_1(a1786)) | (~c3_1(a1805)) | (~c1_1(a1805)) | (~c2_1(a1805)) | (~c0_1(a1805)))),
% 1.63/1.37 inference(rewrite,[status(thm)],[])).
% 1.63/1.37 tff(2618,plain,
% 1.63/1.37 (((~ndr1_0) | (~c2_1(a1805)) | (~c1_1(a1805)) | (~c3_1(a1805)) | (~c2_1(a1805)) | (~c1_1(a1805)) | (~c0_1(a1805)) | c3_1(a1786) | (~c1_1(a1786)) | (~c0_1(a1786))) <=> (c3_1(a1786) | (~ndr1_0) | (~c1_1(a1786)) | (~c0_1(a1786)) | (~c3_1(a1805)) | (~c1_1(a1805)) | (~c2_1(a1805)) | (~c0_1(a1805)))),
% 1.63/1.37 inference(rewrite,[status(thm)],[])).
% 1.63/1.37 tff(2619,plain,
% 1.63/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1805)) | (~c1_1(a1805)) | (~c3_1(a1805)) | (~c2_1(a1805)) | (~c1_1(a1805)) | (~c0_1(a1805)) | c3_1(a1786) | (~c1_1(a1786)) | (~c0_1(a1786)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c3_1(a1786) | (~ndr1_0) | (~c1_1(a1786)) | (~c0_1(a1786)) | (~c3_1(a1805)) | (~c1_1(a1805)) | (~c2_1(a1805)) | (~c0_1(a1805))))),
% 1.63/1.37 inference(monotonicity,[status(thm)],[2618])).
% 1.63/1.37 tff(2620,plain,
% 1.63/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1805)) | (~c1_1(a1805)) | (~c3_1(a1805)) | (~c2_1(a1805)) | (~c1_1(a1805)) | (~c0_1(a1805)) | c3_1(a1786) | (~c1_1(a1786)) | (~c0_1(a1786)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a1786) | (~ndr1_0) | (~c1_1(a1786)) | (~c0_1(a1786)) | (~c3_1(a1805)) | (~c1_1(a1805)) | (~c2_1(a1805)) | (~c0_1(a1805)))),
% 1.63/1.37 inference(transitivity,[status(thm)],[2619, 2617])).
% 1.63/1.37 tff(2621,plain,
% 1.63/1.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1805)) | (~c1_1(a1805)) | (~c3_1(a1805)) | (~c2_1(a1805)) | (~c1_1(a1805)) | (~c0_1(a1805)) | c3_1(a1786) | (~c1_1(a1786)) | (~c0_1(a1786)))),
% 1.63/1.37 inference(quant_inst,[status(thm)],[])).
% 1.63/1.37 tff(2622,plain,
% 1.63/1.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a1786) | (~ndr1_0) | (~c1_1(a1786)) | (~c0_1(a1786)) | (~c3_1(a1805)) | (~c1_1(a1805)) | (~c2_1(a1805)) | (~c0_1(a1805))),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[2621, 2620])).
% 1.63/1.37 tff(2623,plain,
% 1.63/1.37 (~c1_1(a1805)),
% 1.63/1.37 inference(unit_resolution,[status(thm)],[2622, 111, 2616, 2615, 2614, 2598, 2597, 2596, 678])).
% 1.63/1.37 tff(2624,plain,
% 1.63/1.37 (c2_1(a1758)),
% 1.63/1.37 inference(unit_resolution,[status(thm)],[613, 2582])).
% 1.63/1.37 tff(2625,plain,
% 1.63/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c3_1(a1786) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c1_1(a1786)) | (~c0_1(a1786)) | (~c2_1(a1805)) | c1_1(a1805) | (~c0_1(a1805)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c3_1(a1786) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c1_1(a1786)) | (~c0_1(a1786)) | (~c2_1(a1805)) | c1_1(a1805) | (~c0_1(a1805)))),
% 1.63/1.37 inference(rewrite,[status(thm)],[])).
% 1.63/1.37 tff(2626,plain,
% 1.63/1.37 (((~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1786) | (~c1_1(a1786)) | (~c0_1(a1786)) | c1_1(a1805) | (~c2_1(a1805)) | (~c0_1(a1805))) <=> (c3_1(a1786) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c1_1(a1786)) | (~c0_1(a1786)) | (~c2_1(a1805)) | c1_1(a1805) | (~c0_1(a1805)))),
% 1.63/1.37 inference(rewrite,[status(thm)],[])).
% 1.63/1.37 tff(2627,plain,
% 1.63/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1786) | (~c1_1(a1786)) | (~c0_1(a1786)) | c1_1(a1805) | (~c2_1(a1805)) | (~c0_1(a1805)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c3_1(a1786) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c1_1(a1786)) | (~c0_1(a1786)) | (~c2_1(a1805)) | c1_1(a1805) | (~c0_1(a1805))))),
% 1.63/1.37 inference(monotonicity,[status(thm)],[2626])).
% 1.63/1.37 tff(2628,plain,
% 1.63/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1786) | (~c1_1(a1786)) | (~c0_1(a1786)) | c1_1(a1805) | (~c2_1(a1805)) | (~c0_1(a1805)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c3_1(a1786) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c1_1(a1786)) | (~c0_1(a1786)) | (~c2_1(a1805)) | c1_1(a1805) | (~c0_1(a1805)))),
% 1.63/1.37 inference(transitivity,[status(thm)],[2627, 2625])).
% 1.63/1.37 tff(2629,plain,
% 1.63/1.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1786) | (~c1_1(a1786)) | (~c0_1(a1786)) | c1_1(a1805) | (~c2_1(a1805)) | (~c0_1(a1805)))),
% 1.63/1.37 inference(quant_inst,[status(thm)],[])).
% 1.63/1.37 tff(2630,plain,
% 1.63/1.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c3_1(a1786) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c1_1(a1786)) | (~c0_1(a1786)) | (~c2_1(a1805)) | c1_1(a1805) | (~c0_1(a1805))),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[2629, 2628])).
% 1.63/1.37 tff(2631,plain,
% 1.63/1.37 (~c0_1(a1758)),
% 1.63/1.37 inference(unit_resolution,[status(thm)],[2630, 111, 2616, 2615, 2598, 2597, 2583, 2624, 2596, 802, 2623])).
% 1.63/1.37 tff(2632,plain,
% 1.63/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c3_1(a1805)) | (~c2_1(a1805)) | c1_1(a1805) | (~c0_1(a1805)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c3_1(a1805)) | (~c2_1(a1805)) | c1_1(a1805) | (~c0_1(a1805)))),
% 1.63/1.37 inference(rewrite,[status(thm)],[])).
% 1.63/1.37 tff(2633,plain,
% 1.63/1.37 (((~ndr1_0) | c1_1(a1805) | (~c2_1(a1805)) | (~c3_1(a1805)) | c1_1(a1805) | (~c3_1(a1805)) | (~c0_1(a1805)) | c3_1(a1758) | c0_1(a1758) | (~c2_1(a1758))) <=> (c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c3_1(a1805)) | (~c2_1(a1805)) | c1_1(a1805) | (~c0_1(a1805)))),
% 1.63/1.37 inference(rewrite,[status(thm)],[])).
% 1.63/1.37 tff(2634,plain,
% 1.63/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1805) | (~c2_1(a1805)) | (~c3_1(a1805)) | c1_1(a1805) | (~c3_1(a1805)) | (~c0_1(a1805)) | c3_1(a1758) | c0_1(a1758) | (~c2_1(a1758)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c3_1(a1805)) | (~c2_1(a1805)) | c1_1(a1805) | (~c0_1(a1805))))),
% 1.63/1.37 inference(monotonicity,[status(thm)],[2633])).
% 1.63/1.37 tff(2635,plain,
% 1.63/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1805) | (~c2_1(a1805)) | (~c3_1(a1805)) | c1_1(a1805) | (~c3_1(a1805)) | (~c0_1(a1805)) | c3_1(a1758) | c0_1(a1758) | (~c2_1(a1758)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c3_1(a1805)) | (~c2_1(a1805)) | c1_1(a1805) | (~c0_1(a1805)))),
% 1.63/1.37 inference(transitivity,[status(thm)],[2634, 2632])).
% 1.63/1.37 tff(2636,plain,
% 1.63/1.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1805) | (~c2_1(a1805)) | (~c3_1(a1805)) | c1_1(a1805) | (~c3_1(a1805)) | (~c0_1(a1805)) | c3_1(a1758) | c0_1(a1758) | (~c2_1(a1758)))),
% 1.63/1.37 inference(quant_inst,[status(thm)],[])).
% 1.63/1.37 tff(2637,plain,
% 1.63/1.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c3_1(a1805)) | (~c2_1(a1805)) | c1_1(a1805) | (~c0_1(a1805))),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[2636, 2635])).
% 1.63/1.37 tff(2638,plain,
% 1.63/1.37 ($false),
% 1.63/1.37 inference(unit_resolution,[status(thm)],[2637, 111, 2616, 2615, 2614, 2624, 2584, 819, 2631, 2623])).
% 1.63/1.37 tff(2639,plain,(hskp17 | hskp6 | c0_1(a1771)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.37 tff(2640,plain,
% 1.63/1.37 (hskp17),
% 1.63/1.37 inference(unit_resolution,[status(thm)],[2639, 275, 240])).
% 1.63/1.37 tff(2641,plain,
% 1.63/1.37 (~c1_1(a1781)),
% 1.63/1.37 inference(unit_resolution,[status(thm)],[1160, 2640])).
% 1.63/1.37 tff(2642,plain,
% 1.63/1.37 (c3_1(a1781)),
% 1.63/1.37 inference(unit_resolution,[status(thm)],[1182, 2640])).
% 1.63/1.37 tff(2643,plain,
% 1.63/1.37 (c2_1(a1781)),
% 1.63/1.37 inference(unit_resolution,[status(thm)],[1193, 2640])).
% 1.63/1.37 tff(2644,plain,
% 1.63/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c1_1(a1781) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c2_1(a1781)) | (~c0_1(a1781)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c1_1(a1781) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c2_1(a1781)) | (~c0_1(a1781)))),
% 1.63/1.37 inference(rewrite,[status(thm)],[])).
% 1.63/1.37 tff(2645,plain,
% 1.63/1.37 (((~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)) | c1_1(a1781) | (~c2_1(a1781)) | (~c0_1(a1781))) <=> (c1_1(a1781) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c2_1(a1781)) | (~c0_1(a1781)))),
% 1.63/1.37 inference(rewrite,[status(thm)],[])).
% 1.63/1.37 tff(2646,plain,
% 1.63/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)) | c1_1(a1781) | (~c2_1(a1781)) | (~c0_1(a1781)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | (c1_1(a1781) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c2_1(a1781)) | (~c0_1(a1781))))),
% 1.63/1.37 inference(monotonicity,[status(thm)],[2645])).
% 1.63/1.37 tff(2647,plain,
% 1.63/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)) | c1_1(a1781) | (~c2_1(a1781)) | (~c0_1(a1781)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c1_1(a1781) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c2_1(a1781)) | (~c0_1(a1781)))),
% 1.63/1.37 inference(transitivity,[status(thm)],[2646, 2644])).
% 1.63/1.37 tff(2648,plain,
% 1.63/1.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)) | c1_1(a1781) | (~c2_1(a1781)) | (~c0_1(a1781)))),
% 1.63/1.37 inference(quant_inst,[status(thm)],[])).
% 1.63/1.37 tff(2649,plain,
% 1.63/1.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)) | (~c0_1(W)))) | c1_1(a1781) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | (~c2_1(a1781)) | (~c0_1(a1781))),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[2648, 2647])).
% 1.63/1.37 tff(2650,plain,
% 1.63/1.37 ((~c0_1(a1758)) | (~c0_1(a1781))),
% 1.63/1.37 inference(unit_resolution,[status(thm)],[2649, 111, 1338, 703, 721, 1336, 702, 802])).
% 1.63/1.37 tff(2651,plain,
% 1.63/1.37 (~c0_1(a1758)),
% 1.63/1.37 inference(unit_resolution,[status(thm)],[2650, 1325])).
% 1.63/1.37 tff(2652,plain,
% 1.63/1.37 (c0_1(a1758) | (~c0_1(a1781))),
% 1.63/1.37 inference(unit_resolution,[status(thm)],[1679, 111, 1338, 1337, 721, 1336, 702, 819])).
% 1.63/1.37 tff(2653,plain,
% 1.63/1.37 ($false),
% 1.63/1.37 inference(unit_resolution,[status(thm)],[2652, 2651, 1325])).
% 1.63/1.37 tff(2654,plain,((~c0_1(a1781)) | (~c2_1(a1781)) | (~c3_1(a1781)) | (~c2_1(a1758)) | c1_1(a1781) | c3_1(a1758) | (~c1_1(a1758))), inference(lemma,lemma(discharge,[]))).
% 1.63/1.37 tff(2655,plain,
% 1.63/1.37 (~c0_1(a1781)),
% 1.63/1.37 inference(unit_resolution,[status(thm)],[2654, 2643, 2642, 2624, 2641, 2584, 2583])).
% 1.63/1.37 tff(2656,plain,
% 1.63/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a1781) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c0_1(a1781) | (~c3_1(a1781)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1781) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c0_1(a1781) | (~c3_1(a1781)))),
% 1.63/1.37 inference(rewrite,[status(thm)],[])).
% 1.63/1.37 tff(2657,plain,
% 1.63/1.37 (((~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)) | c0_1(a1781) | c1_1(a1781) | (~c3_1(a1781))) <=> (c1_1(a1781) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c0_1(a1781) | (~c3_1(a1781)))),
% 1.63/1.37 inference(rewrite,[status(thm)],[])).
% 1.63/1.37 tff(2658,plain,
% 1.63/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)) | c0_1(a1781) | c1_1(a1781) | (~c3_1(a1781)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a1781) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c0_1(a1781) | (~c3_1(a1781))))),
% 1.63/1.37 inference(monotonicity,[status(thm)],[2657])).
% 1.63/1.37 tff(2659,plain,
% 1.63/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)) | c0_1(a1781) | c1_1(a1781) | (~c3_1(a1781)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1781) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c0_1(a1781) | (~c3_1(a1781)))),
% 1.63/1.37 inference(transitivity,[status(thm)],[2658, 2656])).
% 1.63/1.37 tff(2660,plain,
% 1.63/1.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c3_1(a1758) | (~c1_1(a1758)) | (~c0_1(a1758)) | c0_1(a1781) | c1_1(a1781) | (~c3_1(a1781)))),
% 1.63/1.37 inference(quant_inst,[status(thm)],[])).
% 1.63/1.37 tff(2661,plain,
% 1.63/1.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a1781) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | (~c1_1(a1758)) | (~c0_1(a1758)) | c0_1(a1781) | (~c3_1(a1781))),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[2660, 2659])).
% 1.63/1.37 tff(2662,plain,
% 1.63/1.37 (~c0_1(a1758)),
% 1.63/1.37 inference(unit_resolution,[status(thm)],[2661, 111, 2642, 2583, 2624, 2641, 2584, 1655, 2655])).
% 1.63/1.37 tff(2663,assumption,(~c0_1(a1758)), introduced(assumption)).
% 1.63/1.37 tff(2664,plain,
% 1.63/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1781) | c1_1(a1763) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c0_1(a1763)) | (~c3_1(a1763)) | (~c2_1(a1781)) | (~c3_1(a1781)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1781) | c1_1(a1763) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c0_1(a1763)) | (~c3_1(a1763)) | (~c2_1(a1781)) | (~c3_1(a1781)))),
% 1.63/1.37 inference(rewrite,[status(thm)],[])).
% 1.63/1.37 tff(2665,plain,
% 1.63/1.37 (((~ndr1_0) | c1_1(a1781) | (~c2_1(a1781)) | (~c3_1(a1781)) | c1_1(a1763) | (~c3_1(a1763)) | (~c0_1(a1763)) | c3_1(a1758) | c0_1(a1758) | (~c2_1(a1758))) <=> (c1_1(a1781) | c1_1(a1763) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c0_1(a1763)) | (~c3_1(a1763)) | (~c2_1(a1781)) | (~c3_1(a1781)))),
% 1.63/1.37 inference(rewrite,[status(thm)],[])).
% 1.63/1.37 tff(2666,plain,
% 1.63/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1781) | (~c2_1(a1781)) | (~c3_1(a1781)) | c1_1(a1763) | (~c3_1(a1763)) | (~c0_1(a1763)) | c3_1(a1758) | c0_1(a1758) | (~c2_1(a1758)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c1_1(a1781) | c1_1(a1763) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c0_1(a1763)) | (~c3_1(a1763)) | (~c2_1(a1781)) | (~c3_1(a1781))))),
% 1.63/1.37 inference(monotonicity,[status(thm)],[2665])).
% 1.63/1.37 tff(2667,plain,
% 1.63/1.37 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1781) | (~c2_1(a1781)) | (~c3_1(a1781)) | c1_1(a1763) | (~c3_1(a1763)) | (~c0_1(a1763)) | c3_1(a1758) | c0_1(a1758) | (~c2_1(a1758)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1781) | c1_1(a1763) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c0_1(a1763)) | (~c3_1(a1763)) | (~c2_1(a1781)) | (~c3_1(a1781)))),
% 1.63/1.37 inference(transitivity,[status(thm)],[2666, 2664])).
% 1.63/1.37 tff(2668,plain,
% 1.63/1.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1781) | (~c2_1(a1781)) | (~c3_1(a1781)) | c1_1(a1763) | (~c3_1(a1763)) | (~c0_1(a1763)) | c3_1(a1758) | c0_1(a1758) | (~c2_1(a1758)))),
% 1.63/1.37 inference(quant_inst,[status(thm)],[])).
% 1.63/1.37 tff(2669,plain,
% 1.63/1.37 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c1_1(a1781) | c1_1(a1763) | c3_1(a1758) | (~ndr1_0) | (~c2_1(a1758)) | c0_1(a1758) | (~c0_1(a1763)) | (~c3_1(a1763)) | (~c2_1(a1781)) | (~c3_1(a1781))),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[2668, 2667])).
% 1.63/1.37 tff(2670,plain,
% 1.63/1.37 ($false),
% 1.63/1.37 inference(unit_resolution,[status(thm)],[2669, 111, 1338, 1337, 1265, 1266, 721, 1336, 1689, 702, 819, 2663])).
% 1.63/1.37 tff(2671,plain,((~hskp7) | (~c2_1(a1781)) | (~c3_1(a1781)) | (~c2_1(a1758)) | c1_1(a1781) | c3_1(a1758) | c0_1(a1758)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.37 tff(2672,plain,
% 1.63/1.37 (~hskp7),
% 1.63/1.37 inference(unit_resolution,[status(thm)],[2671, 2643, 2642, 2624, 2641, 2584, 2662])).
% 1.63/1.37 tff(2673,assumption,(~hskp7), introduced(assumption)).
% 1.63/1.37 tff(2674,plain,
% 1.63/1.37 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a1783) | c1_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781)) | (~c1_1(a1783)) | c2_1(a1783))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a1783) | c1_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781)) | (~c1_1(a1783)) | c2_1(a1783))),
% 1.63/1.37 inference(rewrite,[status(thm)],[])).
% 1.63/1.37 tff(2675,plain,
% 1.63/1.37 ((hskp7 | (~ndr1_0) | c2_1(a1783) | c0_1(a1783) | (~c1_1(a1783)) | c1_1(a1781) | c0_1(a1781) | (~c3_1(a1781))) <=> (hskp7 | c0_1(a1783) | c1_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781)) | (~c1_1(a1783)) | c2_1(a1783))),
% 1.63/1.37 inference(rewrite,[status(thm)],[])).
% 1.63/1.37 tff(2676,plain,
% 1.63/1.37 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1783) | c0_1(a1783) | (~c1_1(a1783)) | c1_1(a1781) | c0_1(a1781) | (~c3_1(a1781)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a1783) | c1_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781)) | (~c1_1(a1783)) | c2_1(a1783)))),
% 1.63/1.37 inference(monotonicity,[status(thm)],[2675])).
% 1.63/1.37 tff(2677,plain,
% 1.63/1.37 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1783) | c0_1(a1783) | (~c1_1(a1783)) | c1_1(a1781) | c0_1(a1781) | (~c3_1(a1781)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a1783) | c1_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781)) | (~c1_1(a1783)) | c2_1(a1783))),
% 1.63/1.37 inference(transitivity,[status(thm)],[2676, 2674])).
% 1.63/1.37 tff(2678,plain,
% 1.63/1.37 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1783) | c0_1(a1783) | (~c1_1(a1783)) | c1_1(a1781) | c0_1(a1781) | (~c3_1(a1781)))),
% 1.63/1.37 inference(quant_inst,[status(thm)],[])).
% 1.63/1.37 tff(2679,plain,
% 1.63/1.37 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a1783) | c1_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781)) | (~c1_1(a1783)) | c2_1(a1783)),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[2678, 2677])).
% 1.63/1.37 tff(2680,plain,
% 1.63/1.37 ($false),
% 1.63/1.37 inference(unit_resolution,[status(thm)],[2679, 111, 2673, 1961, 1337, 1908, 1336, 1061, 2124, 1])).
% 1.63/1.37 tff(2681,plain,(c2_1(a1783) | hskp7 | (~c3_1(a1781)) | c1_1(a1781) | c0_1(a1781)), inference(lemma,lemma(discharge,[]))).
% 1.63/1.37 tff(2682,plain,
% 1.63/1.37 (c2_1(a1783)),
% 1.63/1.37 inference(unit_resolution,[status(thm)],[2681, 2672, 2642, 2641, 2655])).
% 1.63/1.37 tff(2683,plain,
% 1.63/1.37 (hskp4 | c0_1(a1781)),
% 1.63/1.37 inference(unit_resolution,[status(thm)],[2021, 111, 240, 2643, 2641, 1755])).
% 1.63/1.37 tff(2684,plain,
% 1.63/1.37 (hskp4),
% 1.63/1.37 inference(unit_resolution,[status(thm)],[2683, 2655])).
% 1.63/1.37 tff(2685,plain,
% 1.63/1.37 (~c2_1(a1759)),
% 1.63/1.37 inference(unit_resolution,[status(thm)],[950, 2684])).
% 1.63/1.37 tff(2686,plain,
% 1.63/1.37 (c1_1(a1759)),
% 1.63/1.37 inference(unit_resolution,[status(thm)],[150, 2684])).
% 1.63/1.37 tff(2687,plain,
% 1.63/1.37 (hskp7 | c0_1(a1759)),
% 1.63/1.37 inference(unit_resolution,[status(thm)],[1701, 111, 2642, 2686, 2641, 2685, 1061, 2655])).
% 1.63/1.37 tff(2688,plain,
% 1.63/1.37 (c0_1(a1759)),
% 1.63/1.37 inference(unit_resolution,[status(thm)],[2687, 2672])).
% 1.63/1.37 tff(2689,plain,
% 1.63/1.37 (^[V: $i, U: $i] : refl((hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))))),
% 1.63/1.37 inference(bind,[status(th)],[])).
% 1.63/1.37 tff(2690,plain,
% 1.63/1.37 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.63/1.37 inference(quant_intro,[status(thm)],[2689])).
% 1.63/1.37 tff(2691,plain,
% 1.63/1.37 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.63/1.37 inference(rewrite,[status(thm)],[])).
% 1.63/1.37 tff(2692,plain,
% 1.63/1.37 (^[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(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp18) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) | hskp18))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V))) | hskp18) <=> (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp18) <=> (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))))),
% 1.63/1.37 inference(bind,[status(th)],[])).
% 1.63/1.37 tff(2693,plain,
% 1.63/1.37 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp18) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.63/1.37 inference(quant_intro,[status(thm)],[2692])).
% 1.63/1.37 tff(2694,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c2_1(U)) | c0_1(V)) | c3_1(V)) | hskp18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause169')).
% 1.63/1.37 tff(2695,plain,
% 1.63/1.37 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[2694, 2693])).
% 1.63/1.37 tff(2696,plain,
% 1.63/1.37 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[2695, 2691])).
% 1.63/1.37 tff(2697,plain,(
% 1.63/1.37 ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.63/1.37 inference(skolemize,[status(sab)],[2696])).
% 1.63/1.37 tff(2698,plain,
% 1.63/1.37 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[2697, 2690])).
% 1.63/1.37 tff(2699,plain,
% 1.63/1.37 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp18 | c2_1(a1759) | c3_1(a1758) | (~ndr1_0) | c0_1(a1758) | (~c1_1(a1758)) | (~c1_1(a1759)) | (~c0_1(a1759)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp18 | c2_1(a1759) | c3_1(a1758) | (~ndr1_0) | c0_1(a1758) | (~c1_1(a1758)) | (~c1_1(a1759)) | (~c0_1(a1759)))),
% 1.63/1.37 inference(rewrite,[status(thm)],[])).
% 1.63/1.37 tff(2700,plain,
% 1.63/1.37 ((hskp18 | (~ndr1_0) | c2_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)) | c0_1(a1758) | c3_1(a1758) | (~c1_1(a1758))) <=> (hskp18 | c2_1(a1759) | c3_1(a1758) | (~ndr1_0) | c0_1(a1758) | (~c1_1(a1758)) | (~c1_1(a1759)) | (~c0_1(a1759)))),
% 1.63/1.37 inference(rewrite,[status(thm)],[])).
% 1.63/1.37 tff(2701,plain,
% 1.63/1.37 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)) | c0_1(a1758) | c3_1(a1758) | (~c1_1(a1758)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp18 | c2_1(a1759) | c3_1(a1758) | (~ndr1_0) | c0_1(a1758) | (~c1_1(a1758)) | (~c1_1(a1759)) | (~c0_1(a1759))))),
% 1.63/1.37 inference(monotonicity,[status(thm)],[2700])).
% 1.63/1.37 tff(2702,plain,
% 1.63/1.37 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)) | c0_1(a1758) | c3_1(a1758) | (~c1_1(a1758)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp18 | c2_1(a1759) | c3_1(a1758) | (~ndr1_0) | c0_1(a1758) | (~c1_1(a1758)) | (~c1_1(a1759)) | (~c0_1(a1759)))),
% 1.63/1.37 inference(transitivity,[status(thm)],[2701, 2699])).
% 1.63/1.37 tff(2703,plain,
% 1.63/1.37 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | c2_1(a1759) | (~c1_1(a1759)) | (~c0_1(a1759)) | c0_1(a1758) | c3_1(a1758) | (~c1_1(a1758)))),
% 1.63/1.37 inference(quant_inst,[status(thm)],[])).
% 1.63/1.37 tff(2704,plain,
% 1.63/1.37 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | c3_1(V) | (~c1_1(V)))) | hskp18 | c2_1(a1759) | c3_1(a1758) | (~ndr1_0) | c0_1(a1758) | (~c1_1(a1758)) | (~c1_1(a1759)) | (~c0_1(a1759))),
% 1.63/1.37 inference(modus_ponens,[status(thm)],[2703, 2702])).
% 1.63/1.37 tff(2705,plain,
% 1.63/1.37 (hskp18 | (~c0_1(a1759))),
% 1.63/1.37 inference(unit_resolution,[status(thm)],[2704, 111, 2686, 2583, 2685, 2584, 2698, 2662])).
% 1.63/1.37 tff(2706,plain,
% 1.63/1.37 (hskp18),
% 1.63/1.37 inference(unit_resolution,[status(thm)],[2705, 2688])).
% 1.63/1.37 tff(2707,plain,
% 1.63/1.37 (~c3_1(a1782)),
% 1.63/1.37 inference(unit_resolution,[status(thm)],[2381, 2706])).
% 1.63/1.37 tff(2708,plain,
% 1.63/1.37 (~c2_1(a1782)),
% 1.63/1.38 inference(unit_resolution,[status(thm)],[2387, 2706])).
% 1.63/1.38 tff(2709,plain,
% 1.63/1.38 (~c1_1(a1782)),
% 1.63/1.38 inference(unit_resolution,[status(thm)],[2393, 2706])).
% 1.63/1.38 tff(2710,plain,
% 1.63/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c1_1(a1782) | c2_1(a1782) | c3_1(a1782) | (~ndr1_0) | c0_1(a1782) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c1_1(a1782) | c2_1(a1782) | c3_1(a1782) | (~ndr1_0) | c0_1(a1782) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783)))),
% 1.63/1.38 inference(rewrite,[status(thm)],[])).
% 1.63/1.38 tff(2711,plain,
% 1.63/1.38 (((~ndr1_0) | (~c2_1(a1783)) | (~c1_1(a1783)) | (~c3_1(a1783)) | c2_1(a1782) | c1_1(a1782) | c3_1(a1782) | c3_1(a1782) | c2_1(a1782) | c0_1(a1782)) <=> (c1_1(a1782) | c2_1(a1782) | c3_1(a1782) | (~ndr1_0) | c0_1(a1782) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783)))),
% 1.63/1.38 inference(rewrite,[status(thm)],[])).
% 1.63/1.38 tff(2712,plain,
% 1.63/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1783)) | (~c1_1(a1783)) | (~c3_1(a1783)) | c2_1(a1782) | c1_1(a1782) | c3_1(a1782) | c3_1(a1782) | c2_1(a1782) | c0_1(a1782))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c1_1(a1782) | c2_1(a1782) | c3_1(a1782) | (~ndr1_0) | c0_1(a1782) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783))))),
% 1.63/1.38 inference(monotonicity,[status(thm)],[2711])).
% 1.63/1.38 tff(2713,plain,
% 1.63/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1783)) | (~c1_1(a1783)) | (~c3_1(a1783)) | c2_1(a1782) | c1_1(a1782) | c3_1(a1782) | c3_1(a1782) | c2_1(a1782) | c0_1(a1782))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c1_1(a1782) | c2_1(a1782) | c3_1(a1782) | (~ndr1_0) | c0_1(a1782) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783)))),
% 1.63/1.38 inference(transitivity,[status(thm)],[2712, 2710])).
% 1.63/1.38 tff(2714,plain,
% 1.63/1.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1783)) | (~c1_1(a1783)) | (~c3_1(a1783)) | c2_1(a1782) | c1_1(a1782) | c3_1(a1782) | c3_1(a1782) | c2_1(a1782) | c0_1(a1782))),
% 1.63/1.38 inference(quant_inst,[status(thm)],[])).
% 1.63/1.38 tff(2715,plain,
% 1.63/1.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c1_1(a1782) | c2_1(a1782) | c3_1(a1782) | (~ndr1_0) | c0_1(a1782) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783))),
% 1.63/1.38 inference(modus_ponens,[status(thm)],[2714, 2713])).
% 1.63/1.38 tff(2716,plain,
% 1.63/1.38 (c0_1(a1782)),
% 1.63/1.38 inference(unit_resolution,[status(thm)],[2715, 111, 1961, 1919, 2709, 2708, 2707, 1549, 2682])).
% 1.63/1.38 tff(2717,plain,
% 1.63/1.38 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))))),
% 1.63/1.38 inference(bind,[status(th)],[])).
% 1.63/1.38 tff(2718,plain,
% 1.63/1.38 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.63/1.38 inference(quant_intro,[status(thm)],[2717])).
% 1.63/1.38 tff(2719,plain,
% 1.63/1.38 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.63/1.38 inference(rewrite,[status(thm)],[])).
% 1.63/1.38 tff(2720,plain,
% 1.63/1.38 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)))), ((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c0_1(V) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | 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) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp5) <=> (((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp5))), rewrite((((~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))))),
% 1.63/1.38 inference(bind,[status(th)],[])).
% 1.63/1.38 tff(2721,plain,
% 1.63/1.38 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.63/1.38 inference(quant_intro,[status(thm)],[2720])).
% 1.63/1.38 tff(2722,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause158')).
% 1.63/1.38 tff(2723,plain,
% 1.63/1.38 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.63/1.38 inference(modus_ponens,[status(thm)],[2722, 2721])).
% 1.63/1.38 tff(2724,plain,
% 1.63/1.38 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.63/1.38 inference(modus_ponens,[status(thm)],[2723, 2719])).
% 1.63/1.38 tff(2725,plain,(
% 1.63/1.38 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.63/1.38 inference(skolemize,[status(sab)],[2724])).
% 1.63/1.38 tff(2726,plain,
% 1.63/1.38 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))),
% 1.63/1.38 inference(modus_ponens,[status(thm)],[2725, 2718])).
% 1.63/1.38 tff(2727,plain,
% 1.63/1.38 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c1_1(a1782) | c2_1(a1782) | c1_1(a1781) | (~ndr1_0) | (~c2_1(a1781)) | c0_1(a1781) | (~c0_1(a1782)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a1782) | c2_1(a1782) | c1_1(a1781) | (~ndr1_0) | (~c2_1(a1781)) | c0_1(a1781) | (~c0_1(a1782)))),
% 1.70/1.38 inference(rewrite,[status(thm)],[])).
% 1.70/1.38 tff(2728,plain,
% 1.70/1.38 ((hskp5 | (~ndr1_0) | c2_1(a1782) | c1_1(a1782) | (~c0_1(a1782)) | c1_1(a1781) | c0_1(a1781) | (~c2_1(a1781))) <=> (hskp5 | c1_1(a1782) | c2_1(a1782) | c1_1(a1781) | (~ndr1_0) | (~c2_1(a1781)) | c0_1(a1781) | (~c0_1(a1782)))),
% 1.70/1.38 inference(rewrite,[status(thm)],[])).
% 1.70/1.38 tff(2729,plain,
% 1.70/1.38 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a1782) | c1_1(a1782) | (~c0_1(a1782)) | c1_1(a1781) | c0_1(a1781) | (~c2_1(a1781)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | c1_1(a1782) | c2_1(a1782) | c1_1(a1781) | (~ndr1_0) | (~c2_1(a1781)) | c0_1(a1781) | (~c0_1(a1782))))),
% 1.70/1.38 inference(monotonicity,[status(thm)],[2728])).
% 1.70/1.38 tff(2730,plain,
% 1.70/1.38 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a1782) | c1_1(a1782) | (~c0_1(a1782)) | c1_1(a1781) | c0_1(a1781) | (~c2_1(a1781)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a1782) | c2_1(a1782) | c1_1(a1781) | (~ndr1_0) | (~c2_1(a1781)) | c0_1(a1781) | (~c0_1(a1782)))),
% 1.70/1.38 inference(transitivity,[status(thm)],[2729, 2727])).
% 1.70/1.38 tff(2731,plain,
% 1.70/1.38 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp5 | (~ndr1_0) | c2_1(a1782) | c1_1(a1782) | (~c0_1(a1782)) | c1_1(a1781) | c0_1(a1781) | (~c2_1(a1781)))),
% 1.70/1.38 inference(quant_inst,[status(thm)],[])).
% 1.70/1.38 tff(2732,plain,
% 1.70/1.38 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)))) | hskp5 | c1_1(a1782) | c2_1(a1782) | c1_1(a1781) | (~ndr1_0) | (~c2_1(a1781)) | c0_1(a1781) | (~c0_1(a1782))),
% 1.70/1.38 inference(modus_ponens,[status(thm)],[2731, 2730])).
% 1.70/1.38 tff(2733,plain,
% 1.70/1.38 (hskp5 | (~c0_1(a1782))),
% 1.70/1.38 inference(unit_resolution,[status(thm)],[2732, 111, 2643, 2709, 2708, 2641, 2726, 2655])).
% 1.70/1.38 tff(2734,plain,
% 1.70/1.38 (hskp5),
% 1.70/1.38 inference(unit_resolution,[status(thm)],[2733, 2716])).
% 1.70/1.38 tff(2735,plain,
% 1.70/1.38 (((~hskp5) | (~c3_1(a1760))) <=> ((~hskp5) | (~c3_1(a1760)))),
% 1.70/1.38 inference(rewrite,[status(thm)],[])).
% 1.70/1.38 tff(2736,plain,
% 1.70/1.38 (((~c3_1(a1760)) | (~hskp5)) <=> ((~hskp5) | (~c3_1(a1760)))),
% 1.70/1.38 inference(rewrite,[status(thm)],[])).
% 1.70/1.38 tff(2737,axiom,((~c3_1(a1760)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause122')).
% 1.70/1.38 tff(2738,plain,
% 1.70/1.38 ((~hskp5) | (~c3_1(a1760))),
% 1.70/1.38 inference(modus_ponens,[status(thm)],[2737, 2736])).
% 1.70/1.38 tff(2739,plain,
% 1.70/1.38 ((~hskp5) | (~c3_1(a1760))),
% 1.70/1.38 inference(modus_ponens,[status(thm)],[2738, 2735])).
% 1.70/1.38 tff(2740,plain,
% 1.70/1.38 (~c3_1(a1760)),
% 1.70/1.38 inference(unit_resolution,[status(thm)],[2739, 2734])).
% 1.70/1.38 tff(2741,plain,
% 1.70/1.38 (((~hskp5) | (~c2_1(a1760))) <=> ((~hskp5) | (~c2_1(a1760)))),
% 1.70/1.38 inference(rewrite,[status(thm)],[])).
% 1.70/1.38 tff(2742,plain,
% 1.70/1.38 (((~c2_1(a1760)) | (~hskp5)) <=> ((~hskp5) | (~c2_1(a1760)))),
% 1.70/1.38 inference(rewrite,[status(thm)],[])).
% 1.70/1.38 tff(2743,axiom,((~c2_1(a1760)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause121')).
% 1.70/1.38 tff(2744,plain,
% 1.70/1.38 ((~hskp5) | (~c2_1(a1760))),
% 1.70/1.38 inference(modus_ponens,[status(thm)],[2743, 2742])).
% 1.70/1.38 tff(2745,plain,
% 1.70/1.38 ((~hskp5) | (~c2_1(a1760))),
% 1.70/1.38 inference(modus_ponens,[status(thm)],[2744, 2741])).
% 1.70/1.38 tff(2746,plain,
% 1.70/1.38 (~c2_1(a1760)),
% 1.70/1.38 inference(unit_resolution,[status(thm)],[2745, 2734])).
% 1.70/1.38 tff(2747,plain,
% 1.70/1.38 (((~hskp5) | (~c0_1(a1760))) <=> ((~hskp5) | (~c0_1(a1760)))),
% 1.70/1.38 inference(rewrite,[status(thm)],[])).
% 1.70/1.38 tff(2748,plain,
% 1.70/1.38 (((~c0_1(a1760)) | (~hskp5)) <=> ((~hskp5) | (~c0_1(a1760)))),
% 1.70/1.38 inference(rewrite,[status(thm)],[])).
% 1.70/1.38 tff(2749,axiom,((~c0_1(a1760)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause120')).
% 1.70/1.38 tff(2750,plain,
% 1.70/1.38 ((~hskp5) | (~c0_1(a1760))),
% 1.70/1.38 inference(modus_ponens,[status(thm)],[2749, 2748])).
% 1.70/1.38 tff(2751,plain,
% 1.70/1.38 ((~hskp5) | (~c0_1(a1760))),
% 1.70/1.38 inference(modus_ponens,[status(thm)],[2750, 2747])).
% 1.70/1.38 tff(2752,plain,
% 1.70/1.38 (~c0_1(a1760)),
% 1.70/1.38 inference(unit_resolution,[status(thm)],[2751, 2734])).
% 1.70/1.38 tff(2753,plain,
% 1.70/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a1760) | c2_1(a1760) | c3_1(a1760) | (~ndr1_0) | c1_1(a1760) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a1760) | c2_1(a1760) | c3_1(a1760) | (~ndr1_0) | c1_1(a1760) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783)))),
% 1.70/1.38 inference(rewrite,[status(thm)],[])).
% 1.70/1.38 tff(2754,plain,
% 1.70/1.38 (((~ndr1_0) | (~c2_1(a1783)) | (~c1_1(a1783)) | (~c3_1(a1783)) | c2_1(a1760) | c1_1(a1760) | c3_1(a1760) | c3_1(a1760) | c2_1(a1760) | c0_1(a1760)) <=> (c0_1(a1760) | c2_1(a1760) | c3_1(a1760) | (~ndr1_0) | c1_1(a1760) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783)))),
% 1.70/1.38 inference(rewrite,[status(thm)],[])).
% 1.70/1.38 tff(2755,plain,
% 1.70/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1783)) | (~c1_1(a1783)) | (~c3_1(a1783)) | c2_1(a1760) | c1_1(a1760) | c3_1(a1760) | c3_1(a1760) | c2_1(a1760) | c0_1(a1760))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a1760) | c2_1(a1760) | c3_1(a1760) | (~ndr1_0) | c1_1(a1760) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783))))),
% 1.70/1.38 inference(monotonicity,[status(thm)],[2754])).
% 1.70/1.38 tff(2756,plain,
% 1.70/1.38 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1783)) | (~c1_1(a1783)) | (~c3_1(a1783)) | c2_1(a1760) | c1_1(a1760) | c3_1(a1760) | c3_1(a1760) | c2_1(a1760) | c0_1(a1760))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a1760) | c2_1(a1760) | c3_1(a1760) | (~ndr1_0) | c1_1(a1760) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783)))),
% 1.70/1.38 inference(transitivity,[status(thm)],[2755, 2753])).
% 1.70/1.38 tff(2757,plain,
% 1.70/1.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1783)) | (~c1_1(a1783)) | (~c3_1(a1783)) | c2_1(a1760) | c1_1(a1760) | c3_1(a1760) | c3_1(a1760) | c2_1(a1760) | c0_1(a1760))),
% 1.70/1.38 inference(quant_inst,[status(thm)],[])).
% 1.70/1.38 tff(2758,plain,
% 1.70/1.38 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a1760) | c2_1(a1760) | c3_1(a1760) | (~ndr1_0) | c1_1(a1760) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783))),
% 1.70/1.38 inference(modus_ponens,[status(thm)],[2757, 2756])).
% 1.70/1.38 tff(2759,plain,
% 1.70/1.38 (c1_1(a1760)),
% 1.70/1.38 inference(unit_resolution,[status(thm)],[2758, 111, 1961, 1919, 2752, 2746, 2740, 1549, 2682])).
% 1.70/1.38 tff(2760,plain,
% 1.70/1.38 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c1_1(a1781) | c0_1(a1760) | c2_1(a1760) | (~ndr1_0) | (~c1_1(a1760)) | c0_1(a1781) | (~c3_1(a1781)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a1781) | c0_1(a1760) | c2_1(a1760) | (~ndr1_0) | (~c1_1(a1760)) | c0_1(a1781) | (~c3_1(a1781)))),
% 1.70/1.38 inference(rewrite,[status(thm)],[])).
% 1.70/1.38 tff(2761,plain,
% 1.70/1.38 ((hskp7 | (~ndr1_0) | c2_1(a1760) | c0_1(a1760) | (~c1_1(a1760)) | c1_1(a1781) | c0_1(a1781) | (~c3_1(a1781))) <=> (hskp7 | c1_1(a1781) | c0_1(a1760) | c2_1(a1760) | (~ndr1_0) | (~c1_1(a1760)) | c0_1(a1781) | (~c3_1(a1781)))),
% 1.70/1.38 inference(rewrite,[status(thm)],[])).
% 1.70/1.38 tff(2762,plain,
% 1.70/1.38 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1760) | c0_1(a1760) | (~c1_1(a1760)) | c1_1(a1781) | c0_1(a1781) | (~c3_1(a1781)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c1_1(a1781) | c0_1(a1760) | c2_1(a1760) | (~ndr1_0) | (~c1_1(a1760)) | c0_1(a1781) | (~c3_1(a1781))))),
% 1.70/1.38 inference(monotonicity,[status(thm)],[2761])).
% 1.70/1.38 tff(2763,plain,
% 1.70/1.38 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1760) | c0_1(a1760) | (~c1_1(a1760)) | c1_1(a1781) | c0_1(a1781) | (~c3_1(a1781)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a1781) | c0_1(a1760) | c2_1(a1760) | (~ndr1_0) | (~c1_1(a1760)) | c0_1(a1781) | (~c3_1(a1781)))),
% 1.70/1.38 inference(transitivity,[status(thm)],[2762, 2760])).
% 1.70/1.38 tff(2764,plain,
% 1.70/1.38 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1760) | c0_1(a1760) | (~c1_1(a1760)) | c1_1(a1781) | c0_1(a1781) | (~c3_1(a1781)))),
% 1.70/1.38 inference(quant_inst,[status(thm)],[])).
% 1.70/1.38 tff(2765,plain,
% 1.70/1.38 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c1_1(a1781) | c0_1(a1760) | c2_1(a1760) | (~ndr1_0) | (~c1_1(a1760)) | c0_1(a1781) | (~c3_1(a1781))),
% 1.70/1.38 inference(modus_ponens,[status(thm)],[2764, 2763])).
% 1.70/1.38 tff(2766,plain,
% 1.70/1.38 ($false),
% 1.70/1.38 inference(unit_resolution,[status(thm)],[2765, 111, 2672, 2642, 2641, 2752, 2746, 1061, 2655, 2759])).
% 1.70/1.38 tff(2767,plain,(c0_1(a1771) | hskp6), inference(lemma,lemma(discharge,[]))).
% 1.70/1.38 tff(2768,plain,
% 1.70/1.38 (c0_1(a1771)),
% 1.70/1.38 inference(unit_resolution,[status(thm)],[2767, 240])).
% 1.70/1.38 tff(2769,plain,
% 1.70/1.38 (~hskp13),
% 1.70/1.38 inference(unit_resolution,[status(thm)],[238, 2768])).
% 1.70/1.38 tff(2770,assumption,(hskp4), introduced(assumption)).
% 1.70/1.38 tff(2771,plain,
% 1.70/1.38 (~c3_1(a1759)),
% 1.70/1.38 inference(unit_resolution,[status(thm)],[1744, 2770])).
% 1.70/1.38 tff(2772,plain,
% 1.70/1.38 (c1_1(a1759)),
% 1.70/1.38 inference(unit_resolution,[status(thm)],[150, 2770])).
% 1.70/1.38 tff(2773,plain,
% 1.70/1.38 (~c0_1(a1759)),
% 1.70/1.38 inference(unit_resolution,[status(thm)],[2265, 2772, 35, 2771])).
% 1.70/1.38 tff(2774,plain,
% 1.70/1.38 ($false),
% 1.70/1.38 inference(unit_resolution,[status(thm)],[2249, 111, 23, 1919, 2772, 1908, 2771, 2098, 2773, 1969])).
% 1.70/1.38 tff(2775,plain,((~hskp4) | hskp13 | hskp3), inference(lemma,lemma(discharge,[]))).
% 1.70/1.38 tff(2776,plain,
% 1.70/1.38 (~hskp4),
% 1.70/1.38 inference(unit_resolution,[status(thm)],[2775, 35, 2769])).
% 1.70/1.38 tff(2777,plain,
% 1.70/1.38 (~hskp23),
% 1.70/1.38 inference(unit_resolution,[status(thm)],[1948, 2776, 35])).
% 1.70/1.38 tff(2778,assumption,(c0_1(a1771)), introduced(assumption)).
% 1.70/1.38 tff(2779,plain,
% 1.70/1.38 (~hskp13),
% 1.70/1.38 inference(unit_resolution,[status(thm)],[238, 2778])).
% 1.70/1.38 tff(2780,plain,
% 1.70/1.38 (~c2_1(a1783)),
% 1.70/1.38 inference(unit_resolution,[status(thm)],[1968, 2779])).
% 1.70/1.38 tff(2781,plain,
% 1.70/1.38 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | c0_1(a1783) | (~c0_1(a1771)) | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c3_1(a1783)) | c2_1(a1783))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a1783) | (~c0_1(a1771)) | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c3_1(a1783)) | c2_1(a1783))),
% 1.70/1.38 inference(rewrite,[status(thm)],[])).
% 1.70/1.38 tff(2782,plain,
% 1.70/1.38 ((hskp3 | (~ndr1_0) | (~c1_1(a1771)) | (~c3_1(a1771)) | (~c0_1(a1771)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783))) <=> (hskp3 | c0_1(a1783) | (~c0_1(a1771)) | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c3_1(a1783)) | c2_1(a1783))),
% 1.70/1.38 inference(rewrite,[status(thm)],[])).
% 1.70/1.38 tff(2783,plain,
% 1.70/1.38 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | (~c1_1(a1771)) | (~c3_1(a1771)) | (~c0_1(a1771)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | c0_1(a1783) | (~c0_1(a1771)) | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c3_1(a1783)) | c2_1(a1783)))),
% 1.70/1.38 inference(monotonicity,[status(thm)],[2782])).
% 1.70/1.38 tff(2784,plain,
% 1.70/1.38 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | (~c1_1(a1771)) | (~c3_1(a1771)) | (~c0_1(a1771)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a1783) | (~c0_1(a1771)) | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c3_1(a1783)) | c2_1(a1783))),
% 1.70/1.38 inference(transitivity,[status(thm)],[2783, 2781])).
% 1.70/1.38 tff(2785,plain,
% 1.70/1.38 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | (~c1_1(a1771)) | (~c3_1(a1771)) | (~c0_1(a1771)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)))),
% 1.70/1.38 inference(quant_inst,[status(thm)],[])).
% 1.70/1.38 tff(2786,plain,
% 1.70/1.38 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a1783) | (~c0_1(a1771)) | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1771)) | (~c3_1(a1783)) | c2_1(a1783)),
% 1.70/1.38 inference(modus_ponens,[status(thm)],[2785, 2784])).
% 1.70/1.38 tff(2787,plain,
% 1.70/1.38 (~c3_1(a1771)),
% 1.70/1.38 inference(unit_resolution,[status(thm)],[2786, 111, 35, 1919, 712, 1908, 2778, 11, 2780])).
% 1.70/1.38 tff(2788,plain,
% 1.70/1.38 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | c0_1(a1783) | (~c0_1(a1771)) | (~ndr1_0) | c3_1(a1771) | (~c1_1(a1771)) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp3 | c0_1(a1783) | (~c0_1(a1771)) | (~ndr1_0) | c3_1(a1771) | (~c1_1(a1771)) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.70/1.38 inference(rewrite,[status(thm)],[])).
% 1.70/1.38 tff(2789,plain,
% 1.70/1.38 ((hskp3 | (~ndr1_0) | c3_1(a1771) | (~c1_1(a1771)) | (~c0_1(a1771)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783))) <=> (hskp3 | c0_1(a1783) | (~c0_1(a1771)) | (~ndr1_0) | c3_1(a1771) | (~c1_1(a1771)) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.70/1.38 inference(rewrite,[status(thm)],[])).
% 1.70/1.38 tff(2790,plain,
% 1.70/1.38 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a1771) | (~c1_1(a1771)) | (~c0_1(a1771)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | c0_1(a1783) | (~c0_1(a1771)) | (~ndr1_0) | c3_1(a1771) | (~c1_1(a1771)) | (~c3_1(a1783)) | (~c1_1(a1783))))),
% 1.70/1.38 inference(monotonicity,[status(thm)],[2789])).
% 1.70/1.38 tff(2791,plain,
% 1.70/1.38 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a1771) | (~c1_1(a1771)) | (~c0_1(a1771)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp3 | c0_1(a1783) | (~c0_1(a1771)) | (~ndr1_0) | c3_1(a1771) | (~c1_1(a1771)) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.70/1.38 inference(transitivity,[status(thm)],[2790, 2788])).
% 1.70/1.38 tff(2792,plain,
% 1.70/1.38 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a1771) | (~c1_1(a1771)) | (~c0_1(a1771)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.70/1.38 inference(quant_inst,[status(thm)],[])).
% 1.70/1.38 tff(2793,plain,
% 1.70/1.38 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp3 | c0_1(a1783) | (~c0_1(a1771)) | (~ndr1_0) | c3_1(a1771) | (~c1_1(a1771)) | (~c3_1(a1783)) | (~c1_1(a1783))),
% 1.70/1.38 inference(modus_ponens,[status(thm)],[2792, 2791])).
% 1.70/1.38 tff(2794,plain,
% 1.70/1.38 ($false),
% 1.70/1.38 inference(unit_resolution,[status(thm)],[2793, 111, 35, 1961, 1919, 712, 1908, 2778, 1496, 2787])).
% 1.70/1.38 tff(2795,plain,((~c1_1(a1771)) | hskp3 | (~c0_1(a1771))), inference(lemma,lemma(discharge,[]))).
% 1.70/1.38 tff(2796,plain,
% 1.70/1.38 (~c1_1(a1771)),
% 1.70/1.38 inference(unit_resolution,[status(thm)],[2795, 35, 2768])).
% 1.70/1.38 tff(2797,plain,
% 1.70/1.38 (~hskp0),
% 1.70/1.38 inference(unit_resolution,[status(thm)],[1787, 2776, 240])).
% 1.70/1.38 tff(2798,assumption,(~c1_1(a1771)), introduced(assumption)).
% 1.70/1.38 tff(2799,plain,
% 1.70/1.38 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp13 | c1_1(a1771) | c2_1(a1771) | c0_1(a1783) | (~ndr1_0) | c3_1(a1771) | (~c3_1(a1783)) | c2_1(a1783))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp13 | c1_1(a1771) | c2_1(a1771) | c0_1(a1783) | (~ndr1_0) | c3_1(a1771) | (~c3_1(a1783)) | c2_1(a1783))),
% 1.70/1.38 inference(rewrite,[status(thm)],[])).
% 1.70/1.38 tff(2800,plain,
% 1.70/1.38 ((hskp13 | (~ndr1_0) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)) | c2_1(a1771) | c1_1(a1771) | c3_1(a1771)) <=> (hskp13 | c1_1(a1771) | c2_1(a1771) | c0_1(a1783) | (~ndr1_0) | c3_1(a1771) | (~c3_1(a1783)) | c2_1(a1783))),
% 1.70/1.38 inference(rewrite,[status(thm)],[])).
% 1.70/1.38 tff(2801,plain,
% 1.70/1.38 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)) | c2_1(a1771) | c1_1(a1771) | c3_1(a1771))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp13 | c1_1(a1771) | c2_1(a1771) | c0_1(a1783) | (~ndr1_0) | c3_1(a1771) | (~c3_1(a1783)) | c2_1(a1783)))),
% 1.70/1.38 inference(monotonicity,[status(thm)],[2800])).
% 1.70/1.38 tff(2802,plain,
% 1.70/1.38 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)) | c2_1(a1771) | c1_1(a1771) | c3_1(a1771))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp13 | c1_1(a1771) | c2_1(a1771) | c0_1(a1783) | (~ndr1_0) | c3_1(a1771) | (~c3_1(a1783)) | c2_1(a1783))),
% 1.70/1.38 inference(transitivity,[status(thm)],[2801, 2799])).
% 1.70/1.38 tff(2803,plain,
% 1.70/1.38 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | (hskp13 | (~ndr1_0) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)) | c2_1(a1771) | c1_1(a1771) | c3_1(a1771))),
% 1.70/1.38 inference(quant_inst,[status(thm)],[])).
% 1.70/1.38 tff(2804,plain,
% 1.70/1.38 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V))) | hskp13 | c1_1(a1771) | c2_1(a1771) | c0_1(a1783) | (~ndr1_0) | c3_1(a1771) | (~c3_1(a1783)) | c2_1(a1783)),
% 1.70/1.38 inference(modus_ponens,[status(thm)],[2803, 2802])).
% 1.70/1.38 tff(2805,plain,
% 1.70/1.38 (c1_1(a1771) | c3_1(a1771)),
% 1.70/1.38 inference(unit_resolution,[status(thm)],[2804, 111, 2779, 1919, 1920, 1908, 192, 2780])).
% 1.70/1.38 tff(2806,plain,
% 1.70/1.38 (c3_1(a1771)),
% 1.70/1.38 inference(unit_resolution,[status(thm)],[2805, 2798])).
% 1.70/1.38 tff(2807,plain,
% 1.70/1.38 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp27 | c1_1(a1771) | c2_1(a1771) | c0_1(a1783) | (~c0_1(a1771)) | (~ndr1_0) | (~c3_1(a1783)) | c2_1(a1783))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp27 | c1_1(a1771) | c2_1(a1771) | c0_1(a1783) | (~c0_1(a1771)) | (~ndr1_0) | (~c3_1(a1783)) | c2_1(a1783))),
% 1.70/1.38 inference(rewrite,[status(thm)],[])).
% 1.70/1.38 tff(2808,plain,
% 1.70/1.38 ((hskp27 | (~ndr1_0) | c2_1(a1771) | c1_1(a1771) | (~c0_1(a1771)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783))) <=> (hskp27 | c1_1(a1771) | c2_1(a1771) | c0_1(a1783) | (~c0_1(a1771)) | (~ndr1_0) | (~c3_1(a1783)) | c2_1(a1783))),
% 1.70/1.38 inference(rewrite,[status(thm)],[])).
% 1.70/1.39 tff(2809,plain,
% 1.70/1.39 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1771) | c1_1(a1771) | (~c0_1(a1771)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp27 | c1_1(a1771) | c2_1(a1771) | c0_1(a1783) | (~c0_1(a1771)) | (~ndr1_0) | (~c3_1(a1783)) | c2_1(a1783)))),
% 1.70/1.39 inference(monotonicity,[status(thm)],[2808])).
% 1.70/1.39 tff(2810,plain,
% 1.70/1.39 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1771) | c1_1(a1771) | (~c0_1(a1771)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp27 | c1_1(a1771) | c2_1(a1771) | c0_1(a1783) | (~c0_1(a1771)) | (~ndr1_0) | (~c3_1(a1783)) | c2_1(a1783))),
% 1.70/1.39 inference(transitivity,[status(thm)],[2809, 2807])).
% 1.70/1.39 tff(2811,plain,
% 1.70/1.39 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp27 | (~ndr1_0) | c2_1(a1771) | c1_1(a1771) | (~c0_1(a1771)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)))),
% 1.70/1.39 inference(quant_inst,[status(thm)],[])).
% 1.70/1.39 tff(2812,plain,
% 1.70/1.39 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c2_1(U) | c1_1(U) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp27 | c1_1(a1771) | c2_1(a1771) | c0_1(a1783) | (~c0_1(a1771)) | (~ndr1_0) | (~c3_1(a1783)) | c2_1(a1783)),
% 1.70/1.39 inference(modus_ponens,[status(thm)],[2811, 2810])).
% 1.70/1.39 tff(2813,plain,
% 1.70/1.39 (hskp27 | c1_1(a1771)),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[2812, 111, 1919, 1920, 1908, 2778, 1995, 2780])).
% 1.70/1.39 tff(2814,plain,
% 1.70/1.39 (hskp27),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[2813, 2798])).
% 1.70/1.39 tff(2815,plain,
% 1.70/1.39 (c3_1(a1756)),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[372, 2814])).
% 1.70/1.39 tff(2816,plain,
% 1.70/1.39 (c1_1(a1756)),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[383, 2814])).
% 1.70/1.39 tff(2817,plain,
% 1.70/1.39 (c0_1(a1756)),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[394, 2814])).
% 1.70/1.39 tff(2818,plain,
% 1.70/1.39 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | c1_1(a1771) | c2_1(a1771) | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c1_1(a1771) | c2_1(a1771) | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))),
% 1.70/1.39 inference(rewrite,[status(thm)],[])).
% 1.70/1.39 tff(2819,plain,
% 1.70/1.39 ((hskp0 | (~ndr1_0) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)) | c2_1(a1771) | c1_1(a1771) | (~c3_1(a1771))) <=> (hskp0 | c1_1(a1771) | c2_1(a1771) | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))),
% 1.70/1.39 inference(rewrite,[status(thm)],[])).
% 1.70/1.39 tff(2820,plain,
% 1.70/1.39 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)) | c2_1(a1771) | c1_1(a1771) | (~c3_1(a1771)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | c1_1(a1771) | c2_1(a1771) | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756))))),
% 1.70/1.39 inference(monotonicity,[status(thm)],[2819])).
% 1.70/1.39 tff(2821,plain,
% 1.70/1.39 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)) | c2_1(a1771) | c1_1(a1771) | (~c3_1(a1771)))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c1_1(a1771) | c2_1(a1771) | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))),
% 1.70/1.39 inference(transitivity,[status(thm)],[2820, 2818])).
% 1.70/1.39 tff(2822,plain,
% 1.70/1.39 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | (hskp0 | (~ndr1_0) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)) | c2_1(a1771) | c1_1(a1771) | (~c3_1(a1771)))),
% 1.70/1.39 inference(quant_inst,[status(thm)],[])).
% 1.70/1.39 tff(2823,plain,
% 1.70/1.39 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)))) | hskp0 | c1_1(a1771) | c2_1(a1771) | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756))),
% 1.70/1.39 inference(modus_ponens,[status(thm)],[2822, 2821])).
% 1.70/1.39 tff(2824,plain,
% 1.70/1.39 ($false),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[2823, 111, 1978, 2817, 2816, 2815, 2798, 1920, 1843, 2806])).
% 1.70/1.39 tff(2825,plain,(c1_1(a1771) | hskp0 | c2_1(a1771) | (~c0_1(a1771))), inference(lemma,lemma(discharge,[]))).
% 1.70/1.39 tff(2826,plain,
% 1.70/1.39 (c2_1(a1771)),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[2825, 2797, 2796, 2768])).
% 1.70/1.39 tff(2827,plain,
% 1.70/1.39 (~c2_1(a1783)),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[1968, 2769])).
% 1.70/1.39 tff(2828,plain,
% 1.70/1.39 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | c1_1(a1771) | (~ndr1_0) | c3_1(a1771) | (~c2_1(a1771)) | (~c3_1(a1783)) | (~c1_1(a1783)) | c2_1(a1783))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp23 | c1_1(a1771) | (~ndr1_0) | c3_1(a1771) | (~c2_1(a1771)) | (~c3_1(a1783)) | (~c1_1(a1783)) | c2_1(a1783))),
% 1.70/1.39 inference(rewrite,[status(thm)],[])).
% 1.70/1.39 tff(2829,plain,
% 1.70/1.39 ((hskp23 | (~ndr1_0) | c2_1(a1783) | (~c1_1(a1783)) | (~c3_1(a1783)) | c1_1(a1771) | c3_1(a1771) | (~c2_1(a1771))) <=> (hskp23 | c1_1(a1771) | (~ndr1_0) | c3_1(a1771) | (~c2_1(a1771)) | (~c3_1(a1783)) | (~c1_1(a1783)) | c2_1(a1783))),
% 1.70/1.39 inference(rewrite,[status(thm)],[])).
% 1.70/1.39 tff(2830,plain,
% 1.70/1.39 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a1783) | (~c1_1(a1783)) | (~c3_1(a1783)) | c1_1(a1771) | c3_1(a1771) | (~c2_1(a1771)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | c1_1(a1771) | (~ndr1_0) | c3_1(a1771) | (~c2_1(a1771)) | (~c3_1(a1783)) | (~c1_1(a1783)) | c2_1(a1783)))),
% 1.70/1.39 inference(monotonicity,[status(thm)],[2829])).
% 1.70/1.39 tff(2831,plain,
% 1.70/1.39 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a1783) | (~c1_1(a1783)) | (~c3_1(a1783)) | c1_1(a1771) | c3_1(a1771) | (~c2_1(a1771)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp23 | c1_1(a1771) | (~ndr1_0) | c3_1(a1771) | (~c2_1(a1771)) | (~c3_1(a1783)) | (~c1_1(a1783)) | c2_1(a1783))),
% 1.70/1.39 inference(transitivity,[status(thm)],[2830, 2828])).
% 1.70/1.39 tff(2832,plain,
% 1.70/1.39 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a1783) | (~c1_1(a1783)) | (~c3_1(a1783)) | c1_1(a1771) | c3_1(a1771) | (~c2_1(a1771)))),
% 1.70/1.39 inference(quant_inst,[status(thm)],[])).
% 1.70/1.39 tff(2833,plain,
% 1.70/1.39 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp23 | c1_1(a1771) | (~ndr1_0) | c3_1(a1771) | (~c2_1(a1771)) | (~c3_1(a1783)) | (~c1_1(a1783)) | c2_1(a1783)),
% 1.70/1.39 inference(modus_ponens,[status(thm)],[2832, 2831])).
% 1.70/1.39 tff(2834,plain,
% 1.70/1.39 (hskp23 | c3_1(a1771) | (~c2_1(a1771))),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[2833, 111, 1961, 1919, 2796, 2041, 2827])).
% 1.70/1.39 tff(2835,plain,
% 1.70/1.39 (c3_1(a1771)),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[2834, 2826, 2777])).
% 1.70/1.39 tff(2836,plain,
% 1.70/1.39 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c1_1(a1771) | c0_1(a1783) | (~c0_1(a1771)) | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1783)) | c2_1(a1783))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c1_1(a1771) | c0_1(a1783) | (~c0_1(a1771)) | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1783)) | c2_1(a1783))),
% 1.70/1.39 inference(rewrite,[status(thm)],[])).
% 1.70/1.39 tff(2837,plain,
% 1.70/1.39 ((hskp11 | (~ndr1_0) | c1_1(a1771) | (~c3_1(a1771)) | (~c0_1(a1771)) | c2_1(a1783) | c0_1(a1783) | (~c1_1(a1783))) <=> (hskp11 | c1_1(a1771) | c0_1(a1783) | (~c0_1(a1771)) | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1783)) | c2_1(a1783))),
% 1.70/1.39 inference(rewrite,[status(thm)],[])).
% 1.70/1.39 tff(2838,plain,
% 1.70/1.39 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a1771) | (~c3_1(a1771)) | (~c0_1(a1771)) | c2_1(a1783) | c0_1(a1783) | (~c1_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c1_1(a1771) | c0_1(a1783) | (~c0_1(a1771)) | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1783)) | c2_1(a1783)))),
% 1.70/1.39 inference(monotonicity,[status(thm)],[2837])).
% 1.70/1.39 tff(2839,plain,
% 1.70/1.39 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a1771) | (~c3_1(a1771)) | (~c0_1(a1771)) | c2_1(a1783) | c0_1(a1783) | (~c1_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c1_1(a1771) | c0_1(a1783) | (~c0_1(a1771)) | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1783)) | c2_1(a1783))),
% 1.70/1.39 inference(transitivity,[status(thm)],[2838, 2836])).
% 1.70/1.39 tff(2840,plain,
% 1.70/1.39 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a1771) | (~c3_1(a1771)) | (~c0_1(a1771)) | c2_1(a1783) | c0_1(a1783) | (~c1_1(a1783)))),
% 1.70/1.39 inference(quant_inst,[status(thm)],[])).
% 1.70/1.39 tff(2841,plain,
% 1.70/1.39 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c1_1(a1771) | c0_1(a1783) | (~c0_1(a1771)) | (~ndr1_0) | (~c3_1(a1771)) | (~c1_1(a1783)) | c2_1(a1783)),
% 1.70/1.39 inference(modus_ponens,[status(thm)],[2840, 2839])).
% 1.70/1.39 tff(2842,plain,
% 1.70/1.39 (hskp11 | (~c3_1(a1771))),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[2841, 111, 1961, 2796, 1908, 2768, 929, 2827])).
% 1.70/1.39 tff(2843,plain,
% 1.70/1.39 (hskp11),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[2842, 2835])).
% 1.70/1.39 tff(2844,plain,
% 1.70/1.39 (~c2_1(a1768)),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[1109, 2843])).
% 1.70/1.39 tff(2845,plain,
% 1.70/1.39 (c0_1(a1768)),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[1120, 2843])).
% 1.70/1.39 tff(2846,plain,
% 1.70/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a1771) | c0_1(a1783) | (~c0_1(a1771)) | c2_1(a1768) | (~ndr1_0) | (~c1_1(a1768)) | (~c0_1(a1768)) | (~c2_1(a1771)) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a1771) | c0_1(a1783) | (~c0_1(a1771)) | c2_1(a1768) | (~ndr1_0) | (~c1_1(a1768)) | (~c0_1(a1768)) | (~c2_1(a1771)) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.70/1.39 inference(rewrite,[status(thm)],[])).
% 1.70/1.39 tff(2847,plain,
% 1.70/1.39 (((~ndr1_0) | c2_1(a1768) | (~c1_1(a1768)) | (~c0_1(a1768)) | c1_1(a1771) | (~c2_1(a1771)) | (~c0_1(a1771)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783))) <=> (c1_1(a1771) | c0_1(a1783) | (~c0_1(a1771)) | c2_1(a1768) | (~ndr1_0) | (~c1_1(a1768)) | (~c0_1(a1768)) | (~c2_1(a1771)) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.70/1.39 inference(rewrite,[status(thm)],[])).
% 1.70/1.39 tff(2848,plain,
% 1.70/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1768) | (~c1_1(a1768)) | (~c0_1(a1768)) | c1_1(a1771) | (~c2_1(a1771)) | (~c0_1(a1771)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c1_1(a1771) | c0_1(a1783) | (~c0_1(a1771)) | c2_1(a1768) | (~ndr1_0) | (~c1_1(a1768)) | (~c0_1(a1768)) | (~c2_1(a1771)) | (~c3_1(a1783)) | (~c1_1(a1783))))),
% 1.70/1.39 inference(monotonicity,[status(thm)],[2847])).
% 1.70/1.39 tff(2849,plain,
% 1.70/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1768) | (~c1_1(a1768)) | (~c0_1(a1768)) | c1_1(a1771) | (~c2_1(a1771)) | (~c0_1(a1771)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a1771) | c0_1(a1783) | (~c0_1(a1771)) | c2_1(a1768) | (~ndr1_0) | (~c1_1(a1768)) | (~c0_1(a1768)) | (~c2_1(a1771)) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.70/1.39 inference(transitivity,[status(thm)],[2848, 2846])).
% 1.70/1.39 tff(2850,plain,
% 1.70/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1768) | (~c1_1(a1768)) | (~c0_1(a1768)) | c1_1(a1771) | (~c2_1(a1771)) | (~c0_1(a1771)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.70/1.39 inference(quant_inst,[status(thm)],[])).
% 1.70/1.39 tff(2851,plain,
% 1.70/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c1_1(a1771) | c0_1(a1783) | (~c0_1(a1771)) | c2_1(a1768) | (~ndr1_0) | (~c1_1(a1768)) | (~c0_1(a1768)) | (~c2_1(a1771)) | (~c3_1(a1783)) | (~c1_1(a1783))),
% 1.70/1.39 inference(modus_ponens,[status(thm)],[2850, 2849])).
% 1.70/1.39 tff(2852,plain,
% 1.70/1.39 (~c1_1(a1768)),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[2851, 111, 1961, 1919, 2796, 2826, 2845, 1908, 2768, 2844, 475])).
% 1.70/1.39 tff(2853,plain,
% 1.70/1.39 (c3_1(a1768)),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[1171, 2843])).
% 1.70/1.39 tff(2854,plain,
% 1.70/1.39 (hskp27),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[2072, 111, 1919, 2845, 1908, 2844, 1995, 2827, 2852])).
% 1.70/1.39 tff(2855,plain,
% 1.70/1.39 (c3_1(a1756)),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[372, 2854])).
% 1.70/1.39 tff(2856,plain,
% 1.70/1.39 (c1_1(a1756)),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[383, 2854])).
% 1.70/1.39 tff(2857,plain,
% 1.70/1.39 (c0_1(a1756)),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[394, 2854])).
% 1.70/1.39 tff(2858,plain,
% 1.70/1.39 ($false),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[1861, 111, 2797, 2857, 2856, 2855, 2853, 2844, 1843, 2852])).
% 1.70/1.39 tff(2859,plain,(hskp3 | hskp6), inference(lemma,lemma(discharge,[]))).
% 1.70/1.39 tff(2860,plain,
% 1.70/1.39 (hskp3),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[2859, 240])).
% 1.70/1.39 tff(2861,plain,
% 1.70/1.39 (c2_1(a1758)),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[613, 2860])).
% 1.70/1.39 tff(2862,plain,
% 1.70/1.39 (c1_1(a1758)),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[624, 2860])).
% 1.70/1.39 tff(2863,plain,
% 1.70/1.39 (c0_1(a1758)),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[631, 111, 2769, 2862, 2861, 22])).
% 1.70/1.39 tff(2864,plain,
% 1.70/1.39 (~c3_1(a1758)),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[638, 2860])).
% 1.70/1.39 tff(2865,plain,
% 1.70/1.39 (hskp14),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[2207, 111, 1919, 2861, 1908, 2864, 2200, 2827, 2863])).
% 1.70/1.39 tff(2866,plain,
% 1.70/1.39 (~c0_1(a1777)),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[2213, 2865])).
% 1.70/1.39 tff(2867,plain,
% 1.70/1.39 (c2_1(a1777)),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[2224, 2865])).
% 1.70/1.39 tff(2868,plain,
% 1.70/1.39 (~c1_1(a1777)),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[2231, 111, 2769, 2867, 2866, 22])).
% 1.70/1.39 tff(2869,plain,
% 1.70/1.39 (~c3_1(a1777)),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[2289, 2865])).
% 1.70/1.39 tff(2870,plain,
% 1.70/1.39 (hskp20),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[2306, 111, 240, 2867, 2866, 2869, 2300])).
% 1.70/1.39 tff(2871,plain,
% 1.70/1.39 (~c3_1(a1786)),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[2312, 2870])).
% 1.70/1.39 tff(2872,plain,
% 1.70/1.39 (c1_1(a1786)),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[2323, 2870])).
% 1.70/1.39 tff(2873,plain,
% 1.70/1.39 (c0_1(a1786)),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[2334, 2870])).
% 1.70/1.39 tff(2874,plain,
% 1.70/1.39 (hskp15),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[2341, 111, 2873, 2872, 2867, 2871, 2869, 2284, 2868])).
% 1.70/1.39 tff(2875,plain,
% 1.70/1.39 (~c3_1(a1779)),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[2347, 2874])).
% 1.70/1.39 tff(2876,plain,
% 1.70/1.39 (~c2_1(a1779)),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[2353, 2874])).
% 1.70/1.39 tff(2877,plain,
% 1.70/1.39 (c0_1(a1779)),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[2364, 2874])).
% 1.70/1.39 tff(2878,plain,
% 1.70/1.39 (hskp22),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[2371, 111, 2867, 2862, 2861, 2869, 2864, 836, 2868])).
% 1.70/1.39 tff(2879,plain,
% 1.70/1.39 (~c2_1(a1799)),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[542, 2878])).
% 1.70/1.39 tff(2880,plain,
% 1.70/1.39 (~c0_1(a1799)),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[548, 2878])).
% 1.70/1.39 tff(2881,plain,
% 1.70/1.39 (c3_1(a1799)),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[559, 2878])).
% 1.70/1.39 tff(2882,plain,
% 1.70/1.39 (~hskp18),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[2402, 2881, 2769, 2880, 2879])).
% 1.70/1.39 tff(2883,plain,
% 1.70/1.39 (~hskp29),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[2425, 2882, 2877, 2876, 2875])).
% 1.70/1.39 tff(2884,plain,
% 1.70/1.39 (hskp30 | hskp29),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[2432, 111, 2862, 2861, 2864, 1592])).
% 1.70/1.39 tff(2885,plain,
% 1.70/1.39 (hskp30),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[2884, 2883])).
% 1.70/1.39 tff(2886,plain,
% 1.70/1.39 (hskp17),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[2610, 2885])).
% 1.70/1.39 tff(2887,plain,
% 1.70/1.39 (c3_1(a1781)),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[1182, 2886])).
% 1.70/1.39 tff(2888,plain,
% 1.70/1.39 (~c1_1(a1781)),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[1160, 2886])).
% 1.70/1.39 tff(2889,plain,
% 1.70/1.39 (c2_1(a1781)),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[1193, 2886])).
% 1.70/1.39 tff(2890,plain,
% 1.70/1.39 (~c0_1(a1781)),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[2654, 2887, 2889, 2861, 2888, 2864, 2862])).
% 1.70/1.39 tff(2891,plain,
% 1.70/1.39 (hskp7),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[2681, 2890, 2827, 2888, 2887])).
% 1.70/1.39 tff(2892,plain,
% 1.70/1.39 (~c1_1(a1763)),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[1074, 2891])).
% 1.70/1.39 tff(2893,plain,
% 1.70/1.39 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | c3_1(a1777) | (~ndr1_0) | (~c2_1(a1777)) | c1_1(a1777) | (~c3_1(a1783)) | (~c1_1(a1783)) | c2_1(a1783))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp23 | c3_1(a1777) | (~ndr1_0) | (~c2_1(a1777)) | c1_1(a1777) | (~c3_1(a1783)) | (~c1_1(a1783)) | c2_1(a1783))),
% 1.70/1.39 inference(rewrite,[status(thm)],[])).
% 1.70/1.39 tff(2894,plain,
% 1.70/1.39 ((hskp23 | (~ndr1_0) | c2_1(a1783) | (~c1_1(a1783)) | (~c3_1(a1783)) | c1_1(a1777) | c3_1(a1777) | (~c2_1(a1777))) <=> (hskp23 | c3_1(a1777) | (~ndr1_0) | (~c2_1(a1777)) | c1_1(a1777) | (~c3_1(a1783)) | (~c1_1(a1783)) | c2_1(a1783))),
% 1.70/1.39 inference(rewrite,[status(thm)],[])).
% 1.70/1.39 tff(2895,plain,
% 1.70/1.39 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a1783) | (~c1_1(a1783)) | (~c3_1(a1783)) | c1_1(a1777) | c3_1(a1777) | (~c2_1(a1777)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | c3_1(a1777) | (~ndr1_0) | (~c2_1(a1777)) | c1_1(a1777) | (~c3_1(a1783)) | (~c1_1(a1783)) | c2_1(a1783)))),
% 1.70/1.39 inference(monotonicity,[status(thm)],[2894])).
% 1.70/1.39 tff(2896,plain,
% 1.70/1.39 (((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a1783) | (~c1_1(a1783)) | (~c3_1(a1783)) | c1_1(a1777) | c3_1(a1777) | (~c2_1(a1777)))) <=> ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp23 | c3_1(a1777) | (~ndr1_0) | (~c2_1(a1777)) | c1_1(a1777) | (~c3_1(a1783)) | (~c1_1(a1783)) | c2_1(a1783))),
% 1.70/1.39 inference(transitivity,[status(thm)],[2895, 2893])).
% 1.70/1.39 tff(2897,plain,
% 1.70/1.39 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | (hskp23 | (~ndr1_0) | c2_1(a1783) | (~c1_1(a1783)) | (~c3_1(a1783)) | c1_1(a1777) | c3_1(a1777) | (~c2_1(a1777)))),
% 1.70/1.39 inference(quant_inst,[status(thm)],[])).
% 1.70/1.39 tff(2898,plain,
% 1.70/1.39 ((~![V: $i, U: $i] : (hskp23 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c3_1(V) | (~c2_1(V)))) | hskp23 | c3_1(a1777) | (~ndr1_0) | (~c2_1(a1777)) | c1_1(a1777) | (~c3_1(a1783)) | (~c1_1(a1783)) | c2_1(a1783)),
% 1.70/1.39 inference(modus_ponens,[status(thm)],[2897, 2896])).
% 1.70/1.39 tff(2899,plain,
% 1.70/1.39 (hskp23),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[2898, 111, 1961, 1919, 2867, 2869, 2041, 2827, 2868])).
% 1.70/1.39 tff(2900,plain,
% 1.70/1.39 (~c3_1(a1807)),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[1927, 2899])).
% 1.70/1.39 tff(2901,plain,
% 1.70/1.39 (~c0_1(a1807)),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[1939, 2899])).
% 1.70/1.39 tff(2902,plain,
% 1.70/1.39 (c3_1(a1763)),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[1085, 2891])).
% 1.70/1.39 tff(2903,plain,
% 1.70/1.39 (c0_1(a1763)),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[1096, 2891])).
% 1.70/1.39 tff(2904,plain,
% 1.70/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1807) | c3_1(a1807) | c1_1(a1781) | c1_1(a1763) | (~ndr1_0) | (~c0_1(a1763)) | (~c3_1(a1763)) | (~c2_1(a1781)) | (~c3_1(a1781)) | (~c2_1(a1807)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1807) | c3_1(a1807) | c1_1(a1781) | c1_1(a1763) | (~ndr1_0) | (~c0_1(a1763)) | (~c3_1(a1763)) | (~c2_1(a1781)) | (~c3_1(a1781)) | (~c2_1(a1807)))),
% 1.70/1.39 inference(rewrite,[status(thm)],[])).
% 1.70/1.39 tff(2905,plain,
% 1.70/1.39 (((~ndr1_0) | c1_1(a1781) | (~c2_1(a1781)) | (~c3_1(a1781)) | c1_1(a1763) | (~c3_1(a1763)) | (~c0_1(a1763)) | c3_1(a1807) | c0_1(a1807) | (~c2_1(a1807))) <=> (c0_1(a1807) | c3_1(a1807) | c1_1(a1781) | c1_1(a1763) | (~ndr1_0) | (~c0_1(a1763)) | (~c3_1(a1763)) | (~c2_1(a1781)) | (~c3_1(a1781)) | (~c2_1(a1807)))),
% 1.70/1.39 inference(rewrite,[status(thm)],[])).
% 1.70/1.39 tff(2906,plain,
% 1.70/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1781) | (~c2_1(a1781)) | (~c3_1(a1781)) | c1_1(a1763) | (~c3_1(a1763)) | (~c0_1(a1763)) | c3_1(a1807) | c0_1(a1807) | (~c2_1(a1807)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | (c0_1(a1807) | c3_1(a1807) | c1_1(a1781) | c1_1(a1763) | (~ndr1_0) | (~c0_1(a1763)) | (~c3_1(a1763)) | (~c2_1(a1781)) | (~c3_1(a1781)) | (~c2_1(a1807))))),
% 1.70/1.39 inference(monotonicity,[status(thm)],[2905])).
% 1.70/1.39 tff(2907,plain,
% 1.70/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1781) | (~c2_1(a1781)) | (~c3_1(a1781)) | c1_1(a1763) | (~c3_1(a1763)) | (~c0_1(a1763)) | c3_1(a1807) | c0_1(a1807) | (~c2_1(a1807)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1807) | c3_1(a1807) | c1_1(a1781) | c1_1(a1763) | (~ndr1_0) | (~c0_1(a1763)) | (~c3_1(a1763)) | (~c2_1(a1781)) | (~c3_1(a1781)) | (~c2_1(a1807)))),
% 1.70/1.39 inference(transitivity,[status(thm)],[2906, 2904])).
% 1.70/1.39 tff(2908,plain,
% 1.70/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1781) | (~c2_1(a1781)) | (~c3_1(a1781)) | c1_1(a1763) | (~c3_1(a1763)) | (~c0_1(a1763)) | c3_1(a1807) | c0_1(a1807) | (~c2_1(a1807)))),
% 1.70/1.39 inference(quant_inst,[status(thm)],[])).
% 1.70/1.39 tff(2909,plain,
% 1.70/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W) | c0_1(W) | (~c2_1(W)))) | c0_1(a1807) | c3_1(a1807) | c1_1(a1781) | c1_1(a1763) | (~ndr1_0) | (~c0_1(a1763)) | (~c3_1(a1763)) | (~c2_1(a1781)) | (~c3_1(a1781)) | (~c2_1(a1807))),
% 1.70/1.39 inference(modus_ponens,[status(thm)],[2908, 2907])).
% 1.70/1.39 tff(2910,plain,
% 1.70/1.39 (~c2_1(a1807)),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[2909, 111, 2889, 2887, 2903, 2902, 2901, 2900, 2888, 2892, 819])).
% 1.70/1.39 tff(2911,plain,
% 1.70/1.39 (hskp28),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[2510, 111, 1961, 1919, 2862, 2861, 2504, 2827, 2863])).
% 1.70/1.39 tff(2912,plain,
% 1.70/1.39 (c2_1(a1795)),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[2521, 2911])).
% 1.70/1.39 tff(2913,plain,
% 1.70/1.39 (c1_1(a1795)),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[2532, 2911])).
% 1.70/1.39 tff(2914,plain,
% 1.70/1.39 (c0_1(a1795)),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[2543, 2911])).
% 1.70/1.39 tff(2915,plain,
% 1.70/1.39 (c3_1(a1823)),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[1610, 2885])).
% 1.70/1.39 tff(2916,plain,
% 1.70/1.39 (c2_1(a1823)),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[1621, 2885])).
% 1.70/1.39 tff(2917,plain,
% 1.70/1.39 (c1_1(a1823)),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[1632, 2885])).
% 1.70/1.39 tff(2918,plain,
% 1.70/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c3_1(a1779) | (~ndr1_0) | (~c1_1(a1779)) | (~c0_1(a1779)) | (~c0_1(a1795)) | (~c1_1(a1795)) | (~c2_1(a1795)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a1779) | (~ndr1_0) | (~c1_1(a1779)) | (~c0_1(a1779)) | (~c0_1(a1795)) | (~c1_1(a1795)) | (~c2_1(a1795)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)))),
% 1.70/1.39 inference(rewrite,[status(thm)],[])).
% 1.70/1.39 tff(2919,plain,
% 1.70/1.39 (((~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | (~c2_1(a1795)) | (~c1_1(a1795)) | (~c0_1(a1795)) | c3_1(a1779) | (~c1_1(a1779)) | (~c0_1(a1779))) <=> (c3_1(a1779) | (~ndr1_0) | (~c1_1(a1779)) | (~c0_1(a1779)) | (~c0_1(a1795)) | (~c1_1(a1795)) | (~c2_1(a1795)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)))),
% 1.70/1.39 inference(rewrite,[status(thm)],[])).
% 1.70/1.39 tff(2920,plain,
% 1.70/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | (~c2_1(a1795)) | (~c1_1(a1795)) | (~c0_1(a1795)) | c3_1(a1779) | (~c1_1(a1779)) | (~c0_1(a1779)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | (c3_1(a1779) | (~ndr1_0) | (~c1_1(a1779)) | (~c0_1(a1779)) | (~c0_1(a1795)) | (~c1_1(a1795)) | (~c2_1(a1795)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823))))),
% 1.70/1.39 inference(monotonicity,[status(thm)],[2919])).
% 1.70/1.39 tff(2921,plain,
% 1.70/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | (~c2_1(a1795)) | (~c1_1(a1795)) | (~c0_1(a1795)) | c3_1(a1779) | (~c1_1(a1779)) | (~c0_1(a1779)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a1779) | (~ndr1_0) | (~c1_1(a1779)) | (~c0_1(a1779)) | (~c0_1(a1795)) | (~c1_1(a1795)) | (~c2_1(a1795)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)))),
% 1.70/1.39 inference(transitivity,[status(thm)],[2920, 2918])).
% 1.70/1.39 tff(2922,plain,
% 1.70/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | (~c2_1(a1795)) | (~c1_1(a1795)) | (~c0_1(a1795)) | c3_1(a1779) | (~c1_1(a1779)) | (~c0_1(a1779)))),
% 1.70/1.39 inference(quant_inst,[status(thm)],[])).
% 1.70/1.39 tff(2923,plain,
% 1.70/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | (~c2_1(V)) | (~c1_1(V)) | (~c0_1(V)) | c3_1(W) | (~c1_1(W)) | (~c0_1(W)))) | c3_1(a1779) | (~ndr1_0) | (~c1_1(a1779)) | (~c0_1(a1779)) | (~c0_1(a1795)) | (~c1_1(a1795)) | (~c2_1(a1795)) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823))),
% 1.70/1.39 inference(modus_ponens,[status(thm)],[2922, 2921])).
% 1.70/1.39 tff(2924,plain,
% 1.70/1.39 (~c1_1(a1779)),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[2923, 111, 2917, 2916, 2915, 2914, 2913, 2912, 2877, 2875, 678])).
% 1.70/1.39 tff(2925,plain,
% 1.70/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a1807) | c3_1(a1807) | c2_1(a1779) | c3_1(a1779) | (~ndr1_0) | c1_1(a1779) | c2_1(a1807) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a1807) | c3_1(a1807) | c2_1(a1779) | c3_1(a1779) | (~ndr1_0) | c1_1(a1779) | c2_1(a1807) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)))),
% 1.70/1.39 inference(rewrite,[status(thm)],[])).
% 1.70/1.39 tff(2926,plain,
% 1.70/1.39 (((~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | c2_1(a1779) | c1_1(a1779) | c3_1(a1779) | c3_1(a1807) | c2_1(a1807) | c0_1(a1807)) <=> (c0_1(a1807) | c3_1(a1807) | c2_1(a1779) | c3_1(a1779) | (~ndr1_0) | c1_1(a1779) | c2_1(a1807) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)))),
% 1.70/1.39 inference(rewrite,[status(thm)],[])).
% 1.70/1.39 tff(2927,plain,
% 1.70/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | c2_1(a1779) | c1_1(a1779) | c3_1(a1779) | c3_1(a1807) | c2_1(a1807) | c0_1(a1807))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | (c0_1(a1807) | c3_1(a1807) | c2_1(a1779) | c3_1(a1779) | (~ndr1_0) | c1_1(a1779) | c2_1(a1807) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823))))),
% 1.70/1.39 inference(monotonicity,[status(thm)],[2926])).
% 1.70/1.39 tff(2928,plain,
% 1.70/1.39 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | c2_1(a1779) | c1_1(a1779) | c3_1(a1779) | c3_1(a1807) | c2_1(a1807) | c0_1(a1807))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a1807) | c3_1(a1807) | c2_1(a1779) | c3_1(a1779) | (~ndr1_0) | c1_1(a1779) | c2_1(a1807) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)))),
% 1.70/1.39 inference(transitivity,[status(thm)],[2927, 2925])).
% 1.70/1.39 tff(2929,plain,
% 1.70/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | ((~ndr1_0) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823)) | c2_1(a1779) | c1_1(a1779) | c3_1(a1779) | c3_1(a1807) | c2_1(a1807) | c0_1(a1807))),
% 1.70/1.39 inference(quant_inst,[status(thm)],[])).
% 1.70/1.39 tff(2930,plain,
% 1.70/1.39 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | c3_1(V) | c3_1(W) | c2_1(W) | c0_1(W))) | c0_1(a1807) | c3_1(a1807) | c2_1(a1779) | c3_1(a1779) | (~ndr1_0) | c1_1(a1779) | c2_1(a1807) | (~c2_1(a1823)) | (~c1_1(a1823)) | (~c3_1(a1823))),
% 1.70/1.39 inference(modus_ponens,[status(thm)],[2929, 2928])).
% 1.70/1.39 tff(2931,plain,
% 1.70/1.39 ($false),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[2930, 111, 2917, 2916, 2915, 2901, 2900, 2876, 2875, 1549, 2924, 2910])).
% 1.70/1.39 tff(2932,plain,(hskp6), inference(lemma,lemma(discharge,[]))).
% 1.70/1.39 tff(2933,plain,
% 1.70/1.39 (~c0_1(a1762)),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[291, 2932])).
% 1.70/1.39 tff(2934,plain,
% 1.70/1.39 (c2_1(a1762)),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[313, 2932])).
% 1.70/1.39 tff(2935,plain,
% 1.70/1.39 (hskp13 | (~c1_1(a1762))),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[410, 111, 2934, 2933, 22])).
% 1.70/1.39 tff(2936,plain,
% 1.70/1.39 (~c1_1(a1762)),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[2935, 23])).
% 1.70/1.39 tff(2937,plain,
% 1.70/1.39 (c3_1(a1762)),
% 1.70/1.39 inference(unit_resolution,[status(thm)],[302, 2932])).
% 1.70/1.39 tff(2938,plain,
% 1.70/1.39 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a1783) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c1_1(a1783)) | c2_1(a1783))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a1783) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c1_1(a1783)) | c2_1(a1783))),
% 1.70/1.40 inference(rewrite,[status(thm)],[])).
% 1.70/1.40 tff(2939,plain,
% 1.70/1.40 ((hskp7 | (~ndr1_0) | c2_1(a1783) | c0_1(a1783) | (~c1_1(a1783)) | c1_1(a1762) | c0_1(a1762) | (~c3_1(a1762))) <=> (hskp7 | c0_1(a1783) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c1_1(a1783)) | c2_1(a1783))),
% 1.70/1.40 inference(rewrite,[status(thm)],[])).
% 1.70/1.40 tff(2940,plain,
% 1.70/1.40 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1783) | c0_1(a1783) | (~c1_1(a1783)) | c1_1(a1762) | c0_1(a1762) | (~c3_1(a1762)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | c0_1(a1783) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c1_1(a1783)) | c2_1(a1783)))),
% 1.70/1.40 inference(monotonicity,[status(thm)],[2939])).
% 1.70/1.40 tff(2941,plain,
% 1.70/1.40 (((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1783) | c0_1(a1783) | (~c1_1(a1783)) | c1_1(a1762) | c0_1(a1762) | (~c3_1(a1762)))) <=> ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a1783) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c1_1(a1783)) | c2_1(a1783))),
% 1.70/1.40 inference(transitivity,[status(thm)],[2940, 2938])).
% 1.70/1.40 tff(2942,plain,
% 1.70/1.40 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp7 | (~ndr1_0) | c2_1(a1783) | c0_1(a1783) | (~c1_1(a1783)) | c1_1(a1762) | c0_1(a1762) | (~c3_1(a1762)))),
% 1.70/1.40 inference(quant_inst,[status(thm)],[])).
% 1.70/1.40 tff(2943,plain,
% 1.70/1.40 ((~![V: $i, U: $i] : (hskp7 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c1_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp7 | c0_1(a1783) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | c1_1(a1762) | (~c1_1(a1783)) | c2_1(a1783)),
% 1.70/1.40 inference(modus_ponens,[status(thm)],[2942, 2941])).
% 1.70/1.40 tff(2944,plain,
% 1.70/1.40 (hskp7),
% 1.70/1.40 inference(unit_resolution,[status(thm)],[2943, 111, 1961, 2937, 1908, 2933, 1061, 2936, 1969])).
% 1.70/1.40 tff(2945,plain,
% 1.70/1.40 (~c1_1(a1763)),
% 1.70/1.40 inference(unit_resolution,[status(thm)],[1074, 2944])).
% 1.70/1.40 tff(2946,plain,
% 1.70/1.40 (c3_1(a1763)),
% 1.70/1.40 inference(unit_resolution,[status(thm)],[1085, 2944])).
% 1.70/1.40 tff(2947,plain,
% 1.70/1.40 (c0_1(a1763)),
% 1.70/1.40 inference(unit_resolution,[status(thm)],[1096, 2944])).
% 1.70/1.40 tff(2948,plain,
% 1.70/1.40 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c0_1(a1783) | c1_1(a1763) | (~ndr1_0) | (~c0_1(a1763)) | (~c3_1(a1763)) | (~c1_1(a1783)) | c2_1(a1783))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a1783) | c1_1(a1763) | (~ndr1_0) | (~c0_1(a1763)) | (~c3_1(a1763)) | (~c1_1(a1783)) | c2_1(a1783))),
% 1.70/1.40 inference(rewrite,[status(thm)],[])).
% 1.70/1.40 tff(2949,plain,
% 1.70/1.40 ((hskp11 | (~ndr1_0) | c1_1(a1763) | (~c3_1(a1763)) | (~c0_1(a1763)) | c2_1(a1783) | c0_1(a1783) | (~c1_1(a1783))) <=> (hskp11 | c0_1(a1783) | c1_1(a1763) | (~ndr1_0) | (~c0_1(a1763)) | (~c3_1(a1763)) | (~c1_1(a1783)) | c2_1(a1783))),
% 1.70/1.40 inference(rewrite,[status(thm)],[])).
% 1.70/1.40 tff(2950,plain,
% 1.70/1.40 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a1763) | (~c3_1(a1763)) | (~c0_1(a1763)) | c2_1(a1783) | c0_1(a1783) | (~c1_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | c0_1(a1783) | c1_1(a1763) | (~ndr1_0) | (~c0_1(a1763)) | (~c3_1(a1763)) | (~c1_1(a1783)) | c2_1(a1783)))),
% 1.70/1.40 inference(monotonicity,[status(thm)],[2949])).
% 1.70/1.40 tff(2951,plain,
% 1.70/1.40 (((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a1763) | (~c3_1(a1763)) | (~c0_1(a1763)) | c2_1(a1783) | c0_1(a1783) | (~c1_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a1783) | c1_1(a1763) | (~ndr1_0) | (~c0_1(a1763)) | (~c3_1(a1763)) | (~c1_1(a1783)) | c2_1(a1783))),
% 1.70/1.40 inference(transitivity,[status(thm)],[2950, 2948])).
% 1.70/1.40 tff(2952,plain,
% 1.70/1.40 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp11 | (~ndr1_0) | c1_1(a1763) | (~c3_1(a1763)) | (~c0_1(a1763)) | c2_1(a1783) | c0_1(a1783) | (~c1_1(a1783)))),
% 1.70/1.40 inference(quant_inst,[status(thm)],[])).
% 1.70/1.40 tff(2953,plain,
% 1.70/1.40 ((~![V: $i, U: $i] : (hskp11 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c1_1(V)))) | hskp11 | c0_1(a1783) | c1_1(a1763) | (~ndr1_0) | (~c0_1(a1763)) | (~c3_1(a1763)) | (~c1_1(a1783)) | c2_1(a1783)),
% 1.70/1.40 inference(modus_ponens,[status(thm)],[2952, 2951])).
% 1.70/1.40 tff(2954,plain,
% 1.70/1.40 (hskp11),
% 1.70/1.40 inference(unit_resolution,[status(thm)],[2953, 111, 1961, 2947, 2946, 1908, 2945, 929, 1969])).
% 1.70/1.40 tff(2955,plain,
% 1.70/1.40 (~c2_1(a1768)),
% 1.70/1.40 inference(unit_resolution,[status(thm)],[1109, 2954])).
% 1.70/1.40 tff(2956,plain,
% 1.70/1.40 (c3_1(a1768)),
% 1.70/1.40 inference(unit_resolution,[status(thm)],[1171, 2954])).
% 1.70/1.40 tff(2957,plain,
% 1.70/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a1768) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | c1_1(a1768) | (~c3_1(a1768)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1768) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | c1_1(a1768) | (~c3_1(a1768)))),
% 1.70/1.40 inference(rewrite,[status(thm)],[])).
% 1.70/1.40 tff(2958,plain,
% 1.70/1.40 (((~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c2_1(a1768) | c1_1(a1768) | (~c3_1(a1768)) | c0_1(a1762) | (~c3_1(a1762)) | (~c2_1(a1762))) <=> (c2_1(a1768) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | c1_1(a1768) | (~c3_1(a1768)))),
% 1.70/1.40 inference(rewrite,[status(thm)],[])).
% 1.70/1.40 tff(2959,plain,
% 1.70/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c2_1(a1768) | c1_1(a1768) | (~c3_1(a1768)) | c0_1(a1762) | (~c3_1(a1762)) | (~c2_1(a1762)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c2_1(a1768) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | c1_1(a1768) | (~c3_1(a1768))))),
% 1.70/1.40 inference(monotonicity,[status(thm)],[2958])).
% 1.70/1.40 tff(2960,plain,
% 1.70/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c2_1(a1768) | c1_1(a1768) | (~c3_1(a1768)) | c0_1(a1762) | (~c3_1(a1762)) | (~c2_1(a1762)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1768) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | c1_1(a1768) | (~c3_1(a1768)))),
% 1.70/1.40 inference(transitivity,[status(thm)],[2959, 2957])).
% 1.70/1.40 tff(2961,plain,
% 1.70/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c2_1(a1768) | c1_1(a1768) | (~c3_1(a1768)) | c0_1(a1762) | (~c3_1(a1762)) | (~c2_1(a1762)))),
% 1.70/1.40 inference(quant_inst,[status(thm)],[])).
% 1.70/1.40 tff(2962,plain,
% 1.70/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c2_1(a1768) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | c1_1(a1768) | (~c3_1(a1768))),
% 1.70/1.40 inference(modus_ponens,[status(thm)],[2961, 2960])).
% 1.70/1.40 tff(2963,plain,
% 1.70/1.40 (c1_1(a1768)),
% 1.70/1.40 inference(unit_resolution,[status(thm)],[2962, 111, 2956, 2934, 2937, 2955, 2933, 1138, 2936])).
% 1.70/1.40 tff(2964,plain,
% 1.70/1.40 (c0_1(a1768)),
% 1.70/1.40 inference(unit_resolution,[status(thm)],[1120, 2954])).
% 1.70/1.40 tff(2965,plain,
% 1.70/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c0_1(a1783) | c2_1(a1768) | c1_1(a1763) | (~ndr1_0) | (~c2_1(a1763)) | (~c0_1(a1763)) | (~c1_1(a1768)) | (~c0_1(a1768)) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a1783) | c2_1(a1768) | c1_1(a1763) | (~ndr1_0) | (~c2_1(a1763)) | (~c0_1(a1763)) | (~c1_1(a1768)) | (~c0_1(a1768)) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.70/1.40 inference(rewrite,[status(thm)],[])).
% 1.70/1.40 tff(2966,plain,
% 1.70/1.40 (((~ndr1_0) | c2_1(a1768) | (~c1_1(a1768)) | (~c0_1(a1768)) | c1_1(a1763) | (~c2_1(a1763)) | (~c0_1(a1763)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783))) <=> (c0_1(a1783) | c2_1(a1768) | c1_1(a1763) | (~ndr1_0) | (~c2_1(a1763)) | (~c0_1(a1763)) | (~c1_1(a1768)) | (~c0_1(a1768)) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.70/1.40 inference(rewrite,[status(thm)],[])).
% 1.70/1.40 tff(2967,plain,
% 1.70/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1768) | (~c1_1(a1768)) | (~c0_1(a1768)) | c1_1(a1763) | (~c2_1(a1763)) | (~c0_1(a1763)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c0_1(a1783) | c2_1(a1768) | c1_1(a1763) | (~ndr1_0) | (~c2_1(a1763)) | (~c0_1(a1763)) | (~c1_1(a1768)) | (~c0_1(a1768)) | (~c3_1(a1783)) | (~c1_1(a1783))))),
% 1.70/1.40 inference(monotonicity,[status(thm)],[2966])).
% 1.70/1.40 tff(2968,plain,
% 1.70/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1768) | (~c1_1(a1768)) | (~c0_1(a1768)) | c1_1(a1763) | (~c2_1(a1763)) | (~c0_1(a1763)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a1783) | c2_1(a1768) | c1_1(a1763) | (~ndr1_0) | (~c2_1(a1763)) | (~c0_1(a1763)) | (~c1_1(a1768)) | (~c0_1(a1768)) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.70/1.40 inference(transitivity,[status(thm)],[2967, 2965])).
% 1.70/1.40 tff(2969,plain,
% 1.70/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1768) | (~c1_1(a1768)) | (~c0_1(a1768)) | c1_1(a1763) | (~c2_1(a1763)) | (~c0_1(a1763)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.70/1.40 inference(quant_inst,[status(thm)],[])).
% 1.70/1.40 tff(2970,plain,
% 1.70/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a1783) | c2_1(a1768) | c1_1(a1763) | (~ndr1_0) | (~c2_1(a1763)) | (~c0_1(a1763)) | (~c1_1(a1768)) | (~c0_1(a1768)) | (~c3_1(a1783)) | (~c1_1(a1783))),
% 1.70/1.40 inference(modus_ponens,[status(thm)],[2969, 2968])).
% 1.70/1.40 tff(2971,plain,
% 1.70/1.40 ((~c2_1(a1763)) | (~c1_1(a1768))),
% 1.70/1.40 inference(unit_resolution,[status(thm)],[2970, 111, 1961, 1919, 2964, 2947, 1908, 2955, 2945, 475])).
% 1.70/1.40 tff(2972,plain,
% 1.70/1.40 (~c2_1(a1763)),
% 1.70/1.40 inference(unit_resolution,[status(thm)],[2971, 2963])).
% 1.70/1.40 tff(2973,plain,
% 1.70/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a1763) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | c2_1(a1763) | (~c3_1(a1763)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a1763) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | c2_1(a1763) | (~c3_1(a1763)))),
% 1.70/1.40 inference(rewrite,[status(thm)],[])).
% 1.70/1.40 tff(2974,plain,
% 1.70/1.40 (((~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c2_1(a1763) | c1_1(a1763) | (~c3_1(a1763)) | c0_1(a1762) | (~c3_1(a1762)) | (~c2_1(a1762))) <=> (c1_1(a1763) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | c2_1(a1763) | (~c3_1(a1763)))),
% 1.70/1.40 inference(rewrite,[status(thm)],[])).
% 1.70/1.40 tff(2975,plain,
% 1.70/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c2_1(a1763) | c1_1(a1763) | (~c3_1(a1763)) | c0_1(a1762) | (~c3_1(a1762)) | (~c2_1(a1762)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | (c1_1(a1763) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | c2_1(a1763) | (~c3_1(a1763))))),
% 1.70/1.40 inference(monotonicity,[status(thm)],[2974])).
% 1.70/1.40 tff(2976,plain,
% 1.70/1.40 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c2_1(a1763) | c1_1(a1763) | (~c3_1(a1763)) | c0_1(a1762) | (~c3_1(a1762)) | (~c2_1(a1762)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a1763) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | c2_1(a1763) | (~c3_1(a1763)))),
% 1.70/1.40 inference(transitivity,[status(thm)],[2975, 2973])).
% 1.70/1.40 tff(2977,plain,
% 1.70/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a1762) | (~c2_1(a1762)) | (~c3_1(a1762)) | c2_1(a1763) | c1_1(a1763) | (~c3_1(a1763)) | c0_1(a1762) | (~c3_1(a1762)) | (~c2_1(a1762)))),
% 1.70/1.40 inference(quant_inst,[status(thm)],[])).
% 1.70/1.40 tff(2978,plain,
% 1.70/1.40 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(U)) | c2_1(V) | c1_1(V) | (~c3_1(V)) | c0_1(W) | (~c3_1(W)) | (~c2_1(W)))) | c1_1(a1763) | c0_1(a1762) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | c1_1(a1762) | c2_1(a1763) | (~c3_1(a1763))),
% 1.70/1.40 inference(modus_ponens,[status(thm)],[2977, 2976])).
% 1.70/1.40 tff(2979,plain,
% 1.70/1.40 ($false),
% 1.70/1.40 inference(unit_resolution,[status(thm)],[2978, 111, 2946, 2934, 2937, 2945, 2933, 1138, 2936, 2972])).
% 1.70/1.40 tff(2980,plain,(hskp13), inference(lemma,lemma(discharge,[]))).
% 1.70/1.40 tff(2981,plain,
% 1.70/1.40 (c1_1(a1771)),
% 1.70/1.40 inference(unit_resolution,[status(thm)],[252, 2980])).
% 1.70/1.40 tff(2982,plain,
% 1.70/1.40 (~c0_1(a1771)),
% 1.70/1.40 inference(unit_resolution,[status(thm)],[238, 2980])).
% 1.70/1.40 tff(2983,plain,
% 1.70/1.40 (c2_1(a1771)),
% 1.70/1.40 inference(unit_resolution,[status(thm)],[263, 2980])).
% 1.70/1.40 tff(2984,plain,
% 1.70/1.40 ((~hskp22) | (~c1_1(a1771)) | (~c2_1(a1771)) | c0_1(a1771)),
% 1.70/1.40 inference(unit_resolution,[status(thm)],[1390, 2934, 2937, 2933])).
% 1.70/1.40 tff(2985,plain,
% 1.70/1.40 (~hskp22),
% 1.70/1.40 inference(unit_resolution,[status(thm)],[2984, 2983, 2982, 2981])).
% 1.70/1.40 tff(2986,plain,
% 1.70/1.40 (hskp27 | hskp22),
% 1.70/1.40 inference(unit_resolution,[status(thm)],[361, 111, 2934, 2937, 2933, 354])).
% 1.70/1.40 tff(2987,plain,
% 1.70/1.40 (hskp27),
% 1.70/1.40 inference(unit_resolution,[status(thm)],[2986, 2985])).
% 1.70/1.40 tff(2988,plain,
% 1.70/1.40 (c3_1(a1756)),
% 1.70/1.40 inference(unit_resolution,[status(thm)],[372, 2987])).
% 1.70/1.40 tff(2989,plain,
% 1.70/1.40 (c1_1(a1756)),
% 1.70/1.40 inference(unit_resolution,[status(thm)],[383, 2987])).
% 1.70/1.40 tff(2990,plain,
% 1.70/1.40 (c0_1(a1756)),
% 1.70/1.40 inference(unit_resolution,[status(thm)],[394, 2987])).
% 1.70/1.40 tff(2991,plain,
% 1.70/1.40 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1783)) | c2_1(a1783) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1783)) | c2_1(a1783) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))),
% 1.70/1.40 inference(rewrite,[status(thm)],[])).
% 1.70/1.40 tff(2992,plain,
% 1.70/1.40 ((hskp3 | (~ndr1_0) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783))) <=> (hskp3 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1783)) | c2_1(a1783) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))),
% 1.70/1.40 inference(rewrite,[status(thm)],[])).
% 1.70/1.40 tff(2993,plain,
% 1.70/1.40 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1783)) | c2_1(a1783) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756))))),
% 1.70/1.40 inference(monotonicity,[status(thm)],[2992])).
% 1.70/1.40 tff(2994,plain,
% 1.70/1.40 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1783)) | c2_1(a1783) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)))),
% 1.70/1.40 inference(transitivity,[status(thm)],[2993, 2991])).
% 1.70/1.40 tff(2995,plain,
% 1.70/1.40 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756)) | c2_1(a1783) | c0_1(a1783) | (~c3_1(a1783)))),
% 1.70/1.40 inference(quant_inst,[status(thm)],[])).
% 1.70/1.40 tff(2996,plain,
% 1.70/1.40 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | (~c1_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | c0_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1783)) | c2_1(a1783) | (~c1_1(a1756)) | (~c3_1(a1756)) | (~c0_1(a1756))),
% 1.70/1.40 inference(modus_ponens,[status(thm)],[2995, 2994])).
% 1.70/1.40 tff(2997,plain,
% 1.70/1.40 (hskp3),
% 1.70/1.40 inference(unit_resolution,[status(thm)],[2996, 111, 2990, 2989, 2988, 1919, 1908, 11, 1])).
% 1.70/1.40 tff(2998,plain,
% 1.70/1.40 (c1_1(a1758)),
% 1.70/1.40 inference(unit_resolution,[status(thm)],[624, 2997])).
% 1.70/1.40 tff(2999,plain,
% 1.70/1.40 (~c3_1(a1758)),
% 1.70/1.40 inference(unit_resolution,[status(thm)],[638, 2997])).
% 1.70/1.40 tff(3000,plain,
% 1.70/1.40 (c2_1(a1758)),
% 1.70/1.40 inference(unit_resolution,[status(thm)],[613, 2997])).
% 1.70/1.40 tff(3001,assumption,(c1_1(a1762)), introduced(assumption)).
% 1.70/1.40 tff(3002,plain,
% 1.70/1.40 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.70/1.40 inference(rewrite,[status(thm)],[])).
% 1.70/1.40 tff(3003,plain,
% 1.70/1.40 ((hskp17 | (~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1762)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783))) <=> (hskp17 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.70/1.40 inference(rewrite,[status(thm)],[])).
% 1.70/1.40 tff(3004,plain,
% 1.70/1.40 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1762)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1783)) | (~c1_1(a1783))))),
% 1.70/1.40 inference(monotonicity,[status(thm)],[3003])).
% 1.70/1.40 tff(3005,plain,
% 1.70/1.40 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1762)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.70/1.40 inference(transitivity,[status(thm)],[3004, 3002])).
% 1.70/1.40 tff(3006,plain,
% 1.70/1.40 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1762)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.70/1.40 inference(quant_inst,[status(thm)],[])).
% 1.70/1.40 tff(3007,plain,
% 1.70/1.40 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1762)) | (~c2_1(a1762)) | (~c1_1(a1762)) | (~c3_1(a1783)) | (~c1_1(a1783))),
% 1.70/1.40 inference(modus_ponens,[status(thm)],[3006, 3005])).
% 1.70/1.40 tff(3008,plain,
% 1.70/1.40 (hskp17 | (~c1_1(a1762))),
% 1.70/1.40 inference(unit_resolution,[status(thm)],[3007, 111, 1961, 1919, 2934, 2937, 1908, 1313])).
% 1.70/1.40 tff(3009,plain,
% 1.70/1.40 (hskp17),
% 1.70/1.40 inference(unit_resolution,[status(thm)],[3008, 3001])).
% 1.70/1.40 tff(3010,plain,
% 1.70/1.40 (c3_1(a1781)),
% 1.70/1.40 inference(unit_resolution,[status(thm)],[1182, 3009])).
% 1.70/1.40 tff(3011,plain,
% 1.70/1.40 (~c1_1(a1781)),
% 1.70/1.40 inference(unit_resolution,[status(thm)],[1160, 3009])).
% 1.70/1.40 tff(3012,plain,
% 1.70/1.40 (c2_1(a1781)),
% 1.70/1.40 inference(unit_resolution,[status(thm)],[1193, 3009])).
% 1.70/1.40 tff(3013,plain,
% 1.70/1.40 (~c0_1(a1781)),
% 1.70/1.40 inference(unit_resolution,[status(thm)],[2654, 3010, 3012, 3000, 3011, 2999, 2998])).
% 1.70/1.40 tff(3014,plain,
% 1.70/1.40 ((~c0_1(a1758)) | (~c1_1(a1762))),
% 1.70/1.40 inference(unit_resolution,[status(thm)],[1724, 111, 2934, 2937, 2998, 3000, 2999, 678])).
% 1.70/1.40 tff(3015,plain,
% 1.70/1.40 (~c0_1(a1758)),
% 1.70/1.40 inference(unit_resolution,[status(thm)],[3014, 3001])).
% 1.70/1.40 tff(3016,plain,
% 1.70/1.40 (~hskp7),
% 1.70/1.40 inference(unit_resolution,[status(thm)],[2671, 3010, 3015, 3000, 3011, 2999, 3012])).
% 1.70/1.40 tff(3017,plain,
% 1.70/1.40 ($false),
% 1.70/1.40 inference(unit_resolution,[status(thm)],[2681, 3016, 3013, 1, 3011, 3010])).
% 1.70/1.40 tff(3018,plain,((~c1_1(a1762)) | c2_1(a1783)), inference(lemma,lemma(discharge,[]))).
% 1.70/1.40 tff(3019,plain,
% 1.70/1.40 (~c1_1(a1762)),
% 1.70/1.40 inference(unit_resolution,[status(thm)],[3018, 1])).
% 1.70/1.40 tff(3020,plain,
% 1.70/1.40 ((~hskp8) | (~c1_1(a1771)) | (~c2_1(a1771)) | c0_1(a1771) | c1_1(a1762)),
% 1.70/1.40 inference(unit_resolution,[status(thm)],[1686, 2937, 2933])).
% 1.70/1.40 tff(3021,plain,
% 1.70/1.40 (~hskp8),
% 1.70/1.40 inference(unit_resolution,[status(thm)],[3020, 3019, 2983, 2982, 2981])).
% 1.70/1.40 tff(3022,plain,
% 1.70/1.40 (hskp8 | hskp4),
% 1.70/1.40 inference(unit_resolution,[status(thm)],[320, 111, 2934, 2937, 2933, 130])).
% 1.70/1.40 tff(3023,plain,
% 1.70/1.40 (hskp4),
% 1.70/1.40 inference(unit_resolution,[status(thm)],[3022, 3021])).
% 1.70/1.40 tff(3024,plain,
% 1.70/1.40 (c1_1(a1759)),
% 1.70/1.40 inference(unit_resolution,[status(thm)],[150, 3023])).
% 1.70/1.40 tff(3025,plain,
% 1.70/1.40 (~c3_1(a1759)),
% 1.70/1.40 inference(unit_resolution,[status(thm)],[1744, 3023])).
% 1.70/1.40 tff(3026,plain,
% 1.70/1.40 (c1_1(a1762) | (~c1_1(a1771)) | (~c2_1(a1771)) | c0_1(a1771) | (~c1_1(a1759)) | c3_1(a1759) | (~c2_1(a1758)) | c3_1(a1758) | (~c1_1(a1758))),
% 1.70/1.40 inference(unit_resolution,[status(thm)],[1717, 2934, 2937, 2933])).
% 1.70/1.40 tff(3027,plain,
% 1.70/1.40 ($false),
% 1.70/1.40 inference(unit_resolution,[status(thm)],[3026, 3025, 3024, 2983, 2981, 2982, 3019, 3000, 2999, 2998])).
% 1.70/1.40 tff(3028,plain,(c2_1(a1783)), inference(lemma,lemma(discharge,[]))).
% 1.70/1.40 tff(3029,plain,
% 1.70/1.40 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783)))),
% 1.70/1.40 inference(rewrite,[status(thm)],[])).
% 1.70/1.40 tff(3030,plain,
% 1.70/1.40 ((hskp17 | (~ndr1_0) | (~c2_1(a1783)) | (~c1_1(a1783)) | (~c3_1(a1783)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783))) <=> (hskp17 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783)))),
% 1.70/1.40 inference(rewrite,[status(thm)],[])).
% 1.70/1.40 tff(3031,plain,
% 1.70/1.40 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | (~c2_1(a1783)) | (~c1_1(a1783)) | (~c3_1(a1783)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783))))),
% 1.70/1.40 inference(monotonicity,[status(thm)],[3030])).
% 1.70/1.40 tff(3032,plain,
% 1.70/1.40 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | (~c2_1(a1783)) | (~c1_1(a1783)) | (~c3_1(a1783)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783)))),
% 1.70/1.40 inference(transitivity,[status(thm)],[3031, 3029])).
% 1.70/1.40 tff(3033,plain,
% 1.70/1.40 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | (hskp17 | (~ndr1_0) | (~c2_1(a1783)) | (~c1_1(a1783)) | (~c3_1(a1783)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.70/1.40 inference(quant_inst,[status(thm)],[])).
% 1.70/1.40 tff(3034,plain,
% 1.70/1.40 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c0_1(V) | (~c3_1(V)) | (~c1_1(V)))) | hskp17 | c0_1(a1783) | (~ndr1_0) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783))),
% 1.70/1.40 inference(modus_ponens,[status(thm)],[3033, 3032])).
% 1.70/1.40 tff(3035,plain,
% 1.70/1.40 (hskp17),
% 1.70/1.40 inference(unit_resolution,[status(thm)],[3034, 111, 1961, 1919, 1908, 1313, 3028])).
% 1.70/1.40 tff(3036,plain,
% 1.70/1.40 (~c1_1(a1781)),
% 1.70/1.40 inference(unit_resolution,[status(thm)],[1160, 3035])).
% 1.70/1.40 tff(3037,plain,
% 1.70/1.40 (c3_1(a1781)),
% 1.70/1.40 inference(unit_resolution,[status(thm)],[1182, 3035])).
% 1.70/1.40 tff(3038,plain,
% 1.70/1.40 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | c1_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c1_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783)))),
% 1.70/1.40 inference(rewrite,[status(thm)],[])).
% 1.70/1.40 tff(3039,plain,
% 1.70/1.40 ((hskp8 | (~ndr1_0) | (~c2_1(a1783)) | (~c1_1(a1783)) | (~c3_1(a1783)) | c1_1(a1781) | c0_1(a1781) | (~c3_1(a1781))) <=> (hskp8 | c1_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783)))),
% 1.70/1.40 inference(rewrite,[status(thm)],[])).
% 1.70/1.40 tff(3040,plain,
% 1.70/1.40 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1783)) | (~c1_1(a1783)) | (~c3_1(a1783)) | c1_1(a1781) | c0_1(a1781) | (~c3_1(a1781)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | c1_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783))))),
% 1.70/1.40 inference(monotonicity,[status(thm)],[3039])).
% 1.70/1.40 tff(3041,plain,
% 1.70/1.40 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1783)) | (~c1_1(a1783)) | (~c3_1(a1783)) | c1_1(a1781) | c0_1(a1781) | (~c3_1(a1781)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c1_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783)))),
% 1.70/1.41 inference(transitivity,[status(thm)],[3040, 3038])).
% 1.70/1.41 tff(3042,plain,
% 1.70/1.41 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp8 | (~ndr1_0) | (~c2_1(a1783)) | (~c1_1(a1783)) | (~c3_1(a1783)) | c1_1(a1781) | c0_1(a1781) | (~c3_1(a1781)))),
% 1.70/1.41 inference(quant_inst,[status(thm)],[])).
% 1.70/1.41 tff(3043,plain,
% 1.70/1.41 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp8 | c1_1(a1781) | (~ndr1_0) | c0_1(a1781) | (~c3_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783))),
% 1.70/1.41 inference(modus_ponens,[status(thm)],[3042, 3041])).
% 1.70/1.41 tff(3044,plain,
% 1.70/1.41 (hskp8 | c0_1(a1781)),
% 1.70/1.41 inference(unit_resolution,[status(thm)],[3043, 111, 1961, 1919, 3037, 3036, 1289, 3028])).
% 1.70/1.41 tff(3045,plain,
% 1.70/1.41 (hskp8),
% 1.70/1.41 inference(unit_resolution,[status(thm)],[3044, 2124])).
% 1.70/1.41 tff(3046,plain,
% 1.70/1.41 (~c1_1(a1765)),
% 1.70/1.41 inference(unit_resolution,[status(thm)],[326, 3045])).
% 1.70/1.41 tff(3047,plain,
% 1.70/1.41 (c2_1(a1765)),
% 1.70/1.41 inference(unit_resolution,[status(thm)],[444, 3045])).
% 1.70/1.41 tff(3048,plain,
% 1.70/1.41 (c0_1(a1765)),
% 1.70/1.41 inference(unit_resolution,[status(thm)],[455, 3045])).
% 1.70/1.41 tff(3049,plain,
% 1.70/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c0_1(a1783) | c1_1(a1781) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1781) | (~c3_1(a1781)) | (~c1_1(a1783)) | (~c2_1(a1783)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1783) | c1_1(a1781) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1781) | (~c3_1(a1781)) | (~c1_1(a1783)) | (~c2_1(a1783)))),
% 1.70/1.41 inference(rewrite,[status(thm)],[])).
% 1.70/1.41 tff(3050,plain,
% 1.70/1.41 (((~ndr1_0) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1783) | (~c2_1(a1783)) | (~c1_1(a1783)) | c0_1(a1781) | c1_1(a1781) | (~c3_1(a1781))) <=> (c0_1(a1783) | c1_1(a1781) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1781) | (~c3_1(a1781)) | (~c1_1(a1783)) | (~c2_1(a1783)))),
% 1.70/1.41 inference(rewrite,[status(thm)],[])).
% 1.70/1.41 tff(3051,plain,
% 1.70/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1783) | (~c2_1(a1783)) | (~c1_1(a1783)) | c0_1(a1781) | c1_1(a1781) | (~c3_1(a1781)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | (c0_1(a1783) | c1_1(a1781) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1781) | (~c3_1(a1781)) | (~c1_1(a1783)) | (~c2_1(a1783))))),
% 1.70/1.41 inference(monotonicity,[status(thm)],[3050])).
% 1.70/1.41 tff(3052,plain,
% 1.70/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1783) | (~c2_1(a1783)) | (~c1_1(a1783)) | c0_1(a1781) | c1_1(a1781) | (~c3_1(a1781)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1783) | c1_1(a1781) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1781) | (~c3_1(a1781)) | (~c1_1(a1783)) | (~c2_1(a1783)))),
% 1.70/1.41 inference(transitivity,[status(thm)],[3051, 3049])).
% 1.70/1.41 tff(3053,plain,
% 1.70/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c1_1(a1765) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1783) | (~c2_1(a1783)) | (~c1_1(a1783)) | c0_1(a1781) | c1_1(a1781) | (~c3_1(a1781)))),
% 1.70/1.41 inference(quant_inst,[status(thm)],[])).
% 1.70/1.41 tff(3054,plain,
% 1.70/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)) | c0_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a1783) | c1_1(a1781) | c1_1(a1765) | (~ndr1_0) | (~c2_1(a1765)) | (~c0_1(a1765)) | c0_1(a1781) | (~c3_1(a1781)) | (~c1_1(a1783)) | (~c2_1(a1783))),
% 1.70/1.41 inference(modus_ponens,[status(thm)],[3053, 3052])).
% 1.70/1.41 tff(3055,plain,
% 1.70/1.41 ($false),
% 1.70/1.41 inference(unit_resolution,[status(thm)],[3054, 111, 1961, 3037, 3048, 3047, 1908, 3036, 3046, 46, 2124, 3028])).
% 1.70/1.41 tff(3056,plain,(c0_1(a1781)), inference(lemma,lemma(discharge,[]))).
% 1.70/1.41 tff(3057,plain,
% 1.70/1.41 (((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))) | (hskp22 | hskp16 | (~ndr1_0) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783)))) <=> ((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))) | hskp22 | hskp16 | (~ndr1_0) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783)))),
% 1.70/1.41 inference(rewrite,[status(thm)],[])).
% 1.70/1.41 tff(3058,plain,
% 1.70/1.41 ((hskp22 | hskp16 | (~ndr1_0) | (~c2_1(a1783)) | (~c1_1(a1783)) | (~c3_1(a1783))) <=> (hskp22 | hskp16 | (~ndr1_0) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783)))),
% 1.70/1.41 inference(rewrite,[status(thm)],[])).
% 1.70/1.41 tff(3059,plain,
% 1.70/1.41 (((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))) | (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(a1783)) | (~c1_1(a1783)) | (~c3_1(a1783)))) <=> ((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))) | (hskp22 | hskp16 | (~ndr1_0) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783))))),
% 1.70/1.41 inference(monotonicity,[status(thm)],[3058])).
% 1.70/1.41 tff(3060,plain,
% 1.70/1.41 (((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))) | (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(a1783)) | (~c1_1(a1783)) | (~c3_1(a1783)))) <=> ((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))) | hskp22 | hskp16 | (~ndr1_0) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783)))),
% 1.70/1.41 inference(transitivity,[status(thm)],[3059, 3057])).
% 1.70/1.41 tff(3061,plain,
% 1.70/1.41 ((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))) | (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(a1783)) | (~c1_1(a1783)) | (~c3_1(a1783)))),
% 1.70/1.41 inference(quant_inst,[status(thm)],[])).
% 1.70/1.41 tff(3062,plain,
% 1.70/1.41 ((~![U: $i] : (hskp22 | hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c3_1(U)))) | hskp22 | hskp16 | (~ndr1_0) | (~c3_1(a1783)) | (~c1_1(a1783)) | (~c2_1(a1783))),
% 1.70/1.41 inference(modus_ponens,[status(thm)],[3061, 3060])).
% 1.70/1.41 tff(3063,plain,
% 1.70/1.41 (hskp22 | hskp16 | (~c2_1(a1783))),
% 1.70/1.41 inference(unit_resolution,[status(thm)],[3062, 111, 1961, 1919, 485])).
% 1.70/1.41 tff(3064,plain,
% 1.70/1.41 (hskp16),
% 1.70/1.41 inference(unit_resolution,[status(thm)],[3063, 3028, 2985])).
% 1.70/1.41 tff(3065,plain,
% 1.70/1.41 (~c2_1(a1780)),
% 1.70/1.41 inference(unit_resolution,[status(thm)],[498, 3064])).
% 1.70/1.41 tff(3066,plain,
% 1.70/1.41 (c1_1(a1780)),
% 1.70/1.41 inference(unit_resolution,[status(thm)],[509, 3064])).
% 1.70/1.41 tff(3067,plain,
% 1.70/1.41 (c2_1(a1781)),
% 1.70/1.41 inference(unit_resolution,[status(thm)],[1193, 3035])).
% 1.70/1.41 tff(3068,plain,
% 1.70/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c0_1(a1783) | c1_1(a1781) | c2_1(a1780) | (~ndr1_0) | (~c1_1(a1780)) | (~c0_1(a1780)) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a1783) | c1_1(a1781) | c2_1(a1780) | (~ndr1_0) | (~c1_1(a1780)) | (~c0_1(a1780)) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.70/1.41 inference(rewrite,[status(thm)],[])).
% 1.70/1.41 tff(3069,plain,
% 1.70/1.41 (((~ndr1_0) | c2_1(a1780) | (~c1_1(a1780)) | (~c0_1(a1780)) | c1_1(a1781) | (~c2_1(a1781)) | (~c0_1(a1781)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783))) <=> (c0_1(a1783) | c1_1(a1781) | c2_1(a1780) | (~ndr1_0) | (~c1_1(a1780)) | (~c0_1(a1780)) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.70/1.41 inference(rewrite,[status(thm)],[])).
% 1.70/1.41 tff(3070,plain,
% 1.70/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1780) | (~c1_1(a1780)) | (~c0_1(a1780)) | c1_1(a1781) | (~c2_1(a1781)) | (~c0_1(a1781)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | (c0_1(a1783) | c1_1(a1781) | c2_1(a1780) | (~ndr1_0) | (~c1_1(a1780)) | (~c0_1(a1780)) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783))))),
% 1.70/1.41 inference(monotonicity,[status(thm)],[3069])).
% 1.70/1.41 tff(3071,plain,
% 1.70/1.41 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1780) | (~c1_1(a1780)) | (~c0_1(a1780)) | c1_1(a1781) | (~c2_1(a1781)) | (~c0_1(a1781)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a1783) | c1_1(a1781) | c2_1(a1780) | (~ndr1_0) | (~c1_1(a1780)) | (~c0_1(a1780)) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.70/1.41 inference(transitivity,[status(thm)],[3070, 3068])).
% 1.70/1.41 tff(3072,plain,
% 1.70/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | ((~ndr1_0) | c2_1(a1780) | (~c1_1(a1780)) | (~c0_1(a1780)) | c1_1(a1781) | (~c2_1(a1781)) | (~c0_1(a1781)) | c0_1(a1783) | (~c3_1(a1783)) | (~c1_1(a1783)))),
% 1.70/1.41 inference(quant_inst,[status(thm)],[])).
% 1.70/1.41 tff(3073,plain,
% 1.70/1.41 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c0_1(W) | (~c3_1(W)) | (~c1_1(W)))) | c0_1(a1783) | c1_1(a1781) | c2_1(a1780) | (~ndr1_0) | (~c1_1(a1780)) | (~c0_1(a1780)) | (~c2_1(a1781)) | (~c0_1(a1781)) | (~c3_1(a1783)) | (~c1_1(a1783))),
% 1.70/1.41 inference(modus_ponens,[status(thm)],[3072, 3071])).
% 1.70/1.41 tff(3074,plain,
% 1.70/1.41 ((~c0_1(a1780)) | (~c0_1(a1781))),
% 1.70/1.41 inference(unit_resolution,[status(thm)],[3073, 111, 1961, 1919, 3067, 3066, 1908, 3036, 3065, 475])).
% 1.70/1.41 tff(3075,plain,
% 1.70/1.41 (~c0_1(a1780)),
% 1.70/1.41 inference(unit_resolution,[status(thm)],[3074, 3056])).
% 1.70/1.41 tff(3076,plain,
% 1.70/1.41 (c3_1(a1780)),
% 1.70/1.41 inference(unit_resolution,[status(thm)],[527, 3064])).
% 1.70/1.41 tff(3077,plain,
% 1.70/1.41 (hskp3 | c0_1(a1780)),
% 1.70/1.41 inference(unit_resolution,[status(thm)],[534, 111, 2990, 2989, 2988, 3076, 3065, 11])).
% 1.70/1.41 tff(3078,plain,
% 1.70/1.41 (hskp3),
% 1.70/1.41 inference(unit_resolution,[status(thm)],[3077, 3075])).
% 1.70/1.41 tff(3079,plain,
% 1.70/1.41 (c1_1(a1758)),
% 1.70/1.41 inference(unit_resolution,[status(thm)],[624, 3078])).
% 1.70/1.41 tff(3080,plain,
% 1.70/1.41 (c2_1(a1758)),
% 1.70/1.41 inference(unit_resolution,[status(thm)],[613, 3078])).
% 1.70/1.41 tff(3081,plain,
% 1.70/1.41 (~c3_1(a1758)),
% 1.70/1.41 inference(unit_resolution,[status(thm)],[638, 3078])).
% 1.70/1.41 tff(3082,plain,
% 1.70/1.41 ($false),
% 1.70/1.41 inference(unit_resolution,[status(thm)],[2654, 3081, 3080, 3067, 3037, 3036, 3056, 3079])).
% 1.70/1.41 % SZS output end Proof
%------------------------------------------------------------------------------