%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN440-1 : TPTP v9.0.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 : Sat Jun 21 05:39:07 AM UTC 2025
% Result : Unsatisfiable 2.31s 2.53s
% Output : Proof 2.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN440-1 : TPTP v9.0.0. Released v2.1.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 12:34:55 EDT 2025
% 0.12/0.34 % CPUTime :
% 2.31/2.53 % SZS status Unsatisfiable
% 2.31/2.53 % SZS output start Proof
% 2.31/2.53 tff(c3_1_type, type, (
% 2.31/2.53 c3_1: $i > $o)).
% 2.31/2.53 tff(a606_type, type, (
% 2.31/2.53 a606: $i)).
% 2.31/2.53 tff(hskp5_type, type, (
% 2.31/2.53 hskp5: $o)).
% 2.31/2.53 tff(c0_1_type, type, (
% 2.31/2.53 c0_1: $i > $o)).
% 2.31/2.53 tff(a618_type, type, (
% 2.31/2.53 a618: $i)).
% 2.31/2.53 tff(a628_type, type, (
% 2.31/2.53 a628: $i)).
% 2.31/2.53 tff(c2_1_type, type, (
% 2.31/2.53 c2_1: $i > $o)).
% 2.31/2.53 tff(c1_1_type, type, (
% 2.31/2.53 c1_1: $i > $o)).
% 2.31/2.53 tff(ndr1_0_type, type, (
% 2.31/2.53 ndr1_0: $o)).
% 2.31/2.53 tff(hskp38_type, type, (
% 2.31/2.53 hskp38: $o)).
% 2.31/2.53 tff(hskp17_type, type, (
% 2.31/2.53 hskp17: $o)).
% 2.31/2.53 tff(a673_type, type, (
% 2.31/2.53 a673: $i)).
% 2.31/2.53 tff(a648_type, type, (
% 2.31/2.53 a648: $i)).
% 2.31/2.53 tff(hskp53_type, type, (
% 2.31/2.53 hskp53: $o)).
% 2.31/2.53 tff(hskp14_type, type, (
% 2.31/2.53 hskp14: $o)).
% 2.31/2.53 tff(a603_type, type, (
% 2.31/2.53 a603: $i)).
% 2.31/2.53 tff(hskp3_type, type, (
% 2.31/2.53 hskp3: $o)).
% 2.31/2.53 tff(hskp29_type, type, (
% 2.31/2.53 hskp29: $o)).
% 2.31/2.53 tff(hskp64_type, type, (
% 2.31/2.53 hskp64: $o)).
% 2.31/2.53 tff(a617_type, type, (
% 2.31/2.53 a617: $i)).
% 2.31/2.53 tff(a651_type, type, (
% 2.31/2.53 a651: $i)).
% 2.31/2.53 tff(hskp41_type, type, (
% 2.31/2.53 hskp41: $o)).
% 2.31/2.53 tff(a670_type, type, (
% 2.31/2.53 a670: $i)).
% 2.31/2.53 tff(hskp61_type, type, (
% 2.31/2.53 hskp61: $o)).
% 2.31/2.53 tff(hskp33_type, type, (
% 2.31/2.53 hskp33: $o)).
% 2.31/2.53 tff(hskp58_type, type, (
% 2.31/2.53 hskp58: $o)).
% 2.31/2.53 tff(a663_type, type, (
% 2.31/2.53 a663: $i)).
% 2.31/2.53 tff(hskp66_type, type, (
% 2.31/2.53 hskp66: $o)).
% 2.31/2.53 tff(hskp65_type, type, (
% 2.31/2.53 hskp65: $o)).
% 2.31/2.53 tff(a599_type, type, (
% 2.31/2.53 a599: $i)).
% 2.31/2.53 tff(hskp60_type, type, (
% 2.31/2.53 hskp60: $o)).
% 2.31/2.53 tff(a675_type, type, (
% 2.31/2.53 a675: $i)).
% 2.31/2.53 tff(hskp15_type, type, (
% 2.31/2.53 hskp15: $o)).
% 2.31/2.53 tff(a625_type, type, (
% 2.31/2.53 a625: $i)).
% 2.31/2.53 tff(a624_type, type, (
% 2.31/2.53 a624: $i)).
% 2.31/2.53 tff(a674_type, type, (
% 2.31/2.53 a674: $i)).
% 2.31/2.53 tff(a669_type, type, (
% 2.31/2.53 a669: $i)).
% 2.31/2.53 tff(hskp54_type, type, (
% 2.31/2.53 hskp54: $o)).
% 2.31/2.53 tff(hskp37_type, type, (
% 2.31/2.53 hskp37: $o)).
% 2.31/2.53 tff(a607_type, type, (
% 2.31/2.53 a607: $i)).
% 2.31/2.53 tff(hskp20_type, type, (
% 2.31/2.53 hskp20: $o)).
% 2.31/2.53 tff(a635_type, type, (
% 2.31/2.53 a635: $i)).
% 2.31/2.53 tff(a609_type, type, (
% 2.31/2.53 a609: $i)).
% 2.31/2.53 tff(hskp6_type, type, (
% 2.31/2.53 hskp6: $o)).
% 2.31/2.53 tff(a662_type, type, (
% 2.31/2.53 a662: $i)).
% 2.31/2.53 tff(hskp57_type, type, (
% 2.31/2.53 hskp57: $o)).
% 2.31/2.53 tff(hskp42_type, type, (
% 2.31/2.53 hskp42: $o)).
% 2.31/2.53 tff(a653_type, type, (
% 2.31/2.53 a653: $i)).
% 2.31/2.53 tff(hskp55_type, type, (
% 2.31/2.53 hskp55: $o)).
% 2.31/2.53 tff(a627_type, type, (
% 2.31/2.53 a627: $i)).
% 2.31/2.53 tff(hskp16_type, type, (
% 2.31/2.53 hskp16: $o)).
% 2.31/2.53 tff(hskp9_type, type, (
% 2.31/2.53 hskp9: $o)).
% 2.31/2.53 tff(a623_type, type, (
% 2.31/2.53 a623: $i)).
% 2.31/2.53 tff(hskp45_type, type, (
% 2.31/2.53 hskp45: $o)).
% 2.31/2.53 tff(a613_type, type, (
% 2.31/2.53 a613: $i)).
% 2.31/2.53 tff(a658_type, type, (
% 2.31/2.53 a658: $i)).
% 2.31/2.53 tff(hskp56_type, type, (
% 2.31/2.53 hskp56: $o)).
% 2.31/2.53 tff(a660_type, type, (
% 2.31/2.53 a660: $i)).
% 2.31/2.53 tff(a644_type, type, (
% 2.31/2.53 a644: $i)).
% 2.31/2.53 tff(hskp51_type, type, (
% 2.31/2.53 hskp51: $o)).
% 2.31/2.53 tff(hskp62_type, type, (
% 2.31/2.53 hskp62: $o)).
% 2.31/2.53 tff(a671_type, type, (
% 2.31/2.53 a671: $i)).
% 2.31/2.53 tff(a612_type, type, (
% 2.31/2.53 a612: $i)).
% 2.31/2.53 tff(hskp8_type, type, (
% 2.31/2.53 hskp8: $o)).
% 2.31/2.53 tff(a672_type, type, (
% 2.31/2.53 a672: $i)).
% 2.31/2.53 tff(hskp63_type, type, (
% 2.31/2.53 hskp63: $o)).
% 2.31/2.53 tff(a647_type, type, (
% 2.31/2.53 a647: $i)).
% 2.31/2.53 tff(hskp52_type, type, (
% 2.31/2.53 hskp52: $o)).
% 2.31/2.53 tff(hskp25_type, type, (
% 2.31/2.53 hskp25: $o)).
% 2.31/2.53 tff(a646_type, type, (
% 2.31/2.53 a646: $i)).
% 2.31/2.53 tff(a608_type, type, (
% 2.31/2.53 a608: $i)).
% 2.31/2.53 tff(a605_type, type, (
% 2.31/2.53 a605: $i)).
% 2.31/2.53 tff(hskp36_type, type, (
% 2.31/2.53 hskp36: $o)).
% 2.31/2.53 tff(1,assumption,(~c0_1(a628)), introduced(assumption)).
% 2.31/2.53 tff(2,plain,
% 2.31/2.53 (^[V: $i, U: $i] : refl((hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) <=> (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)))),
% 2.31/2.53 inference(bind,[status(th)],[])).
% 2.31/2.53 tff(3,plain,
% 2.31/2.53 (![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 2.31/2.53 inference(quant_intro,[status(thm)],[2])).
% 2.31/2.53 tff(4,plain,
% 2.31/2.53 (![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 2.31/2.53 inference(rewrite,[status(thm)],[])).
% 2.31/2.53 tff(5,plain,
% 2.31/2.53 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~c1_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)))), ((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), ((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))))), (((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c0_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V))), ((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c0_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V)))), (((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c0_1(U)) | c2_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V))), (((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c0_1(U)) | c2_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V)))), ((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c0_1(U)) | c2_1(V)) | c1_1(V)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V)) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))), ((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c0_1(U)) | c2_1(V)) | c1_1(V)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)))), (((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c0_1(U)) | c2_1(V)) | c1_1(V)) | c0_1(V)) | hskp38) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) | hskp38))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V)) | hskp38) <=> (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))), (((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c0_1(U)) | c2_1(V)) | c1_1(V)) | c0_1(V)) | hskp38) <=> (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))))),
% 2.31/2.53 inference(bind,[status(th)],[])).
% 2.31/2.53 tff(6,plain,
% 2.31/2.53 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c0_1(U)) | c2_1(V)) | c1_1(V)) | c0_1(V)) | hskp38) <=> ![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 2.31/2.53 inference(quant_intro,[status(thm)],[5])).
% 2.31/2.53 tff(7,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c0_1(U)) | c2_1(V)) | c1_1(V)) | c0_1(V)) | hskp38)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause302')).
% 2.31/2.53 tff(8,plain,
% 2.31/2.53 (![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 2.31/2.53 inference(modus_ponens,[status(thm)],[7, 6])).
% 2.31/2.53 tff(9,plain,
% 2.31/2.53 (![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 2.31/2.53 inference(modus_ponens,[status(thm)],[8, 4])).
% 2.31/2.53 tff(10,plain,(
% 2.31/2.53 ![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 2.31/2.53 inference(skolemize,[status(sab)],[9])).
% 2.31/2.53 tff(11,plain,
% 2.31/2.53 (![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))),
% 2.31/2.53 inference(modus_ponens,[status(thm)],[10, 3])).
% 2.31/2.53 tff(12,assumption,(~hskp17), introduced(assumption)).
% 2.31/2.53 tff(13,assumption,(~c2_1(a673)), introduced(assumption)).
% 2.31/2.53 tff(14,plain,
% 2.31/2.53 (^[V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))),
% 2.31/2.53 inference(bind,[status(th)],[])).
% 2.31/2.53 tff(15,plain,
% 2.31/2.53 (![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 2.31/2.53 inference(quant_intro,[status(thm)],[14])).
% 2.31/2.53 tff(16,plain,
% 2.31/2.53 (![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 2.31/2.53 inference(rewrite,[status(thm)],[])).
% 2.31/2.53 tff(17,plain,
% 2.31/2.53 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~c1_1(V))) <=> ((~c2_1(U)) | (~c1_1(V)))), ((((~c2_1(U)) | (~c1_1(V))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(V))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(V))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V)))), ((((~c2_1(U)) | (~c1_1(V))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))))), (((((~c2_1(U)) | (~c1_1(V))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((~c2_1(U)) | (~c1_1(V))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((~c2_1(U)) | (~c1_1(V))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V)))), ((((((~c2_1(U)) | (~c1_1(V))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V))))), (((((((~c2_1(U)) | (~c1_1(V))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((((~c2_1(U)) | (~c1_1(V))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((((~c2_1(U)) | (~c1_1(V))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), ((((((((~c2_1(U)) | (~c1_1(V))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))))),
% 2.31/2.53 inference(bind,[status(th)],[])).
% 2.31/2.53 tff(18,plain,
% 2.31/2.53 (![V: $i, U: $i] : (((((((~c2_1(U)) | (~c1_1(V))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V)) <=> ![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 2.31/2.53 inference(quant_intro,[status(thm)],[17])).
% 2.31/2.53 tff(19,axiom,(![V: $i, U: $i] : (((((((~c2_1(U)) | (~c1_1(V))) | (~ndr1_0)) | (~c2_1(V))) | c0_1(U)) | c3_1(U)) | c0_1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause301')).
% 2.31/2.53 tff(20,plain,
% 2.31/2.53 (![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 2.31/2.53 inference(modus_ponens,[status(thm)],[19, 18])).
% 2.31/2.53 tff(21,plain,
% 2.31/2.53 (![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 2.31/2.53 inference(modus_ponens,[status(thm)],[20, 16])).
% 2.31/2.53 tff(22,plain,(
% 2.31/2.53 ![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 2.31/2.53 inference(skolemize,[status(sab)],[21])).
% 2.31/2.53 tff(23,plain,
% 2.31/2.53 (![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 2.31/2.53 inference(modus_ponens,[status(thm)],[22, 15])).
% 2.31/2.53 tff(24,assumption,(~hskp64), introduced(assumption)).
% 2.31/2.53 tff(25,plain,
% 2.31/2.53 (^[U: $i] : refl((hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))),
% 2.31/2.53 inference(bind,[status(th)],[])).
% 2.31/2.53 tff(26,plain,
% 2.31/2.53 (![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 2.31/2.53 inference(quant_intro,[status(thm)],[25])).
% 2.31/2.53 tff(27,plain,
% 2.31/2.53 (![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 2.31/2.53 inference(rewrite,[status(thm)],[])).
% 2.31/2.53 tff(28,plain,
% 2.31/2.53 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp53) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp53))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp53) <=> (hskp53 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp53) <=> (hskp53 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp53) | hskp17) <=> ((hskp53 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp17))), rewrite(((hskp53 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | hskp17) <=> (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp53) | hskp17) <=> (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))))),
% 2.31/2.53 inference(bind,[status(th)],[])).
% 2.31/2.53 tff(29,plain,
% 2.31/2.53 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp53) | hskp17) <=> ![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 2.31/2.53 inference(quant_intro,[status(thm)],[28])).
% 2.31/2.53 tff(30,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp53) | hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause285')).
% 2.31/2.53 tff(31,plain,
% 2.31/2.53 (![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 2.31/2.53 inference(modus_ponens,[status(thm)],[30, 29])).
% 2.31/2.53 tff(32,plain,
% 2.31/2.53 (![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 2.31/2.53 inference(modus_ponens,[status(thm)],[31, 27])).
% 2.31/2.53 tff(33,plain,(
% 2.31/2.53 ![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 2.31/2.53 inference(skolemize,[status(sab)],[32])).
% 2.31/2.53 tff(34,plain,
% 2.31/2.53 (![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))),
% 2.31/2.53 inference(modus_ponens,[status(thm)],[33, 26])).
% 2.31/2.53 tff(35,assumption,(~hskp53), introduced(assumption)).
% 2.31/2.53 tff(36,assumption,(hskp58), introduced(assumption)).
% 2.31/2.53 tff(37,plain,
% 2.31/2.53 (((~hskp58) | (~c1_1(a663))) <=> ((~hskp58) | (~c1_1(a663)))),
% 2.31/2.53 inference(rewrite,[status(thm)],[])).
% 2.31/2.53 tff(38,plain,
% 2.31/2.53 (((~c1_1(a663)) | (~hskp58)) <=> ((~hskp58) | (~c1_1(a663)))),
% 2.31/2.53 inference(rewrite,[status(thm)],[])).
% 2.31/2.53 tff(39,axiom,((~c1_1(a663)) | (~hskp58)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause182')).
% 2.31/2.53 tff(40,plain,
% 2.31/2.53 ((~hskp58) | (~c1_1(a663))),
% 2.31/2.53 inference(modus_ponens,[status(thm)],[39, 38])).
% 2.31/2.53 tff(41,plain,
% 2.31/2.53 ((~hskp58) | (~c1_1(a663))),
% 2.31/2.53 inference(modus_ponens,[status(thm)],[40, 37])).
% 2.31/2.53 tff(42,plain,
% 2.31/2.53 (~c1_1(a663)),
% 2.31/2.53 inference(unit_resolution,[status(thm)],[41, 36])).
% 2.31/2.53 tff(43,plain,
% 2.31/2.53 (((~hskp58) | (~c0_1(a663))) <=> ((~hskp58) | (~c0_1(a663)))),
% 2.31/2.53 inference(rewrite,[status(thm)],[])).
% 2.31/2.53 tff(44,plain,
% 2.31/2.53 (((~c0_1(a663)) | (~hskp58)) <=> ((~hskp58) | (~c0_1(a663)))),
% 2.31/2.53 inference(rewrite,[status(thm)],[])).
% 2.31/2.53 tff(45,axiom,((~c0_1(a663)) | (~hskp58)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause181')).
% 2.31/2.53 tff(46,plain,
% 2.31/2.53 ((~hskp58) | (~c0_1(a663))),
% 2.31/2.53 inference(modus_ponens,[status(thm)],[45, 44])).
% 2.31/2.53 tff(47,plain,
% 2.31/2.53 ((~hskp58) | (~c0_1(a663))),
% 2.31/2.53 inference(modus_ponens,[status(thm)],[46, 43])).
% 2.31/2.53 tff(48,plain,
% 2.31/2.53 (~c0_1(a663)),
% 2.31/2.53 inference(unit_resolution,[status(thm)],[47, 36])).
% 2.31/2.53 tff(49,plain,
% 2.31/2.53 (((~hskp58) | c3_1(a663)) <=> ((~hskp58) | c3_1(a663))),
% 2.31/2.53 inference(rewrite,[status(thm)],[])).
% 2.31/2.53 tff(50,axiom,((~hskp58) | c3_1(a663)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause90')).
% 2.31/2.53 tff(51,plain,
% 2.31/2.53 ((~hskp58) | c3_1(a663)),
% 2.31/2.53 inference(modus_ponens,[status(thm)],[50, 49])).
% 2.31/2.53 tff(52,plain,
% 2.31/2.53 ((~hskp58) | c3_1(a663)),
% 2.31/2.53 inference(modus_ponens,[status(thm)],[51, 49])).
% 2.31/2.53 tff(53,plain,
% 2.31/2.53 ((~hskp58) | c3_1(a663)),
% 2.31/2.53 inference(modus_ponens,[status(thm)],[52, 49])).
% 2.31/2.53 tff(54,plain,
% 2.31/2.53 ((~hskp58) | c3_1(a663)),
% 2.31/2.53 inference(modus_ponens,[status(thm)],[53, 49])).
% 2.31/2.53 tff(55,plain,
% 2.31/2.53 ((~hskp58) | c3_1(a663)),
% 2.31/2.53 inference(modus_ponens,[status(thm)],[54, 49])).
% 2.31/2.53 tff(56,plain,
% 2.31/2.53 (c3_1(a663)),
% 2.31/2.53 inference(unit_resolution,[status(thm)],[55, 36])).
% 2.31/2.53 tff(57,assumption,(~ndr1_0), introduced(assumption)).
% 2.31/2.53 tff(58,plain,
% 2.31/2.53 ((ndr1_0 | (~hskp64)) <=> (ndr1_0 | (~hskp64))),
% 2.31/2.53 inference(rewrite,[status(thm)],[])).
% 2.31/2.53 tff(59,plain,
% 2.31/2.53 (((~hskp64) | ndr1_0) <=> (ndr1_0 | (~hskp64))),
% 2.31/2.53 inference(rewrite,[status(thm)],[])).
% 2.31/2.53 tff(60,axiom,((~hskp64) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause4')).
% 2.31/2.53 tff(61,plain,
% 2.31/2.53 (ndr1_0 | (~hskp64)),
% 2.31/2.53 inference(modus_ponens,[status(thm)],[60, 59])).
% 2.31/2.53 tff(62,plain,
% 2.31/2.53 (ndr1_0 | (~hskp64)),
% 2.31/2.53 inference(modus_ponens,[status(thm)],[61, 58])).
% 2.31/2.53 tff(63,plain,
% 2.31/2.53 (~hskp64),
% 2.31/2.53 inference(unit_resolution,[status(thm)],[62, 57])).
% 2.31/2.53 tff(64,plain,
% 2.31/2.53 (((~hskp66) | ndr1_0) <=> ((~hskp66) | ndr1_0)),
% 2.31/2.53 inference(rewrite,[status(thm)],[])).
% 2.31/2.53 tff(65,axiom,((~hskp66) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause2')).
% 2.31/2.53 tff(66,plain,
% 2.31/2.53 ((~hskp66) | ndr1_0),
% 2.31/2.53 inference(modus_ponens,[status(thm)],[65, 64])).
% 2.31/2.53 tff(67,plain,
% 2.31/2.53 ((~hskp66) | ndr1_0),
% 2.31/2.53 inference(modus_ponens,[status(thm)],[66, 64])).
% 2.31/2.53 tff(68,plain,
% 2.31/2.53 ((~hskp66) | ndr1_0),
% 2.31/2.53 inference(modus_ponens,[status(thm)],[67, 64])).
% 2.31/2.53 tff(69,plain,
% 2.31/2.53 ((~hskp66) | ndr1_0),
% 2.31/2.53 inference(modus_ponens,[status(thm)],[68, 64])).
% 2.31/2.53 tff(70,plain,
% 2.31/2.53 ((~hskp66) | ndr1_0),
% 2.31/2.53 inference(modus_ponens,[status(thm)],[69, 64])).
% 2.31/2.53 tff(71,plain,
% 2.31/2.53 (~hskp66),
% 2.31/2.53 inference(unit_resolution,[status(thm)],[70, 57])).
% 2.31/2.53 tff(72,plain,
% 2.31/2.53 ((ndr1_0 | (~hskp65)) <=> (ndr1_0 | (~hskp65))),
% 2.31/2.53 inference(rewrite,[status(thm)],[])).
% 2.31/2.53 tff(73,plain,
% 2.31/2.53 (((~hskp65) | ndr1_0) <=> (ndr1_0 | (~hskp65))),
% 2.31/2.53 inference(rewrite,[status(thm)],[])).
% 2.31/2.53 tff(74,axiom,((~hskp65) | ndr1_0), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause3')).
% 2.31/2.53 tff(75,plain,
% 2.31/2.53 (ndr1_0 | (~hskp65)),
% 2.31/2.53 inference(modus_ponens,[status(thm)],[74, 73])).
% 2.31/2.53 tff(76,plain,
% 2.31/2.53 (ndr1_0 | (~hskp65)),
% 2.31/2.53 inference(modus_ponens,[status(thm)],[75, 72])).
% 2.31/2.53 tff(77,plain,
% 2.31/2.53 (~hskp65),
% 2.31/2.53 inference(unit_resolution,[status(thm)],[76, 57])).
% 2.31/2.53 tff(78,plain,
% 2.31/2.53 ((hskp66 | hskp65 | hskp64) <=> (hskp66 | hskp65 | hskp64)),
% 2.31/2.53 inference(rewrite,[status(thm)],[])).
% 2.31/2.53 tff(79,plain,
% 2.31/2.53 (((hskp64 | hskp65) | hskp66) <=> (hskp66 | hskp65 | hskp64)),
% 2.31/2.53 inference(rewrite,[status(thm)],[])).
% 2.31/2.53 tff(80,axiom,((hskp64 | hskp65) | hskp66), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause75')).
% 2.31/2.53 tff(81,plain,
% 2.31/2.53 (hskp66 | hskp65 | hskp64),
% 2.31/2.53 inference(modus_ponens,[status(thm)],[80, 79])).
% 2.31/2.53 tff(82,plain,
% 2.31/2.53 (hskp66 | hskp65 | hskp64),
% 2.31/2.53 inference(modus_ponens,[status(thm)],[81, 78])).
% 2.31/2.53 tff(83,plain,
% 2.31/2.53 (hskp66 | hskp65 | hskp64),
% 2.31/2.53 inference(modus_ponens,[status(thm)],[82, 78])).
% 2.31/2.53 tff(84,plain,
% 2.31/2.53 (hskp66 | hskp65 | hskp64),
% 2.31/2.53 inference(modus_ponens,[status(thm)],[83, 78])).
% 2.31/2.53 tff(85,plain,
% 2.31/2.53 (hskp66 | hskp65 | hskp64),
% 2.31/2.53 inference(modus_ponens,[status(thm)],[84, 78])).
% 2.31/2.53 tff(86,plain,
% 2.31/2.53 ($false),
% 2.31/2.53 inference(unit_resolution,[status(thm)],[85, 77, 71, 63])).
% 2.31/2.53 tff(87,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 2.31/2.53 tff(88,plain,
% 2.31/2.53 (((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | c0_1(a663) | c1_1(a663) | (~ndr1_0) | (~c3_1(a663)))) <=> ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp53 | hskp17 | c0_1(a663) | c1_1(a663) | (~ndr1_0) | (~c3_1(a663)))),
% 2.31/2.53 inference(rewrite,[status(thm)],[])).
% 2.31/2.53 tff(89,plain,
% 2.31/2.53 ((hskp53 | hskp17 | (~ndr1_0) | c1_1(a663) | c0_1(a663) | (~c3_1(a663))) <=> (hskp53 | hskp17 | c0_1(a663) | c1_1(a663) | (~ndr1_0) | (~c3_1(a663)))),
% 2.31/2.53 inference(rewrite,[status(thm)],[])).
% 2.31/2.53 tff(90,plain,
% 2.31/2.53 (((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | (~ndr1_0) | c1_1(a663) | c0_1(a663) | (~c3_1(a663)))) <=> ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | c0_1(a663) | c1_1(a663) | (~ndr1_0) | (~c3_1(a663))))),
% 2.31/2.53 inference(monotonicity,[status(thm)],[89])).
% 2.31/2.53 tff(91,plain,
% 2.31/2.53 (((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | (~ndr1_0) | c1_1(a663) | c0_1(a663) | (~c3_1(a663)))) <=> ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp53 | hskp17 | c0_1(a663) | c1_1(a663) | (~ndr1_0) | (~c3_1(a663)))),
% 2.31/2.53 inference(transitivity,[status(thm)],[90, 88])).
% 2.31/2.53 tff(92,plain,
% 2.31/2.53 ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | (~ndr1_0) | c1_1(a663) | c0_1(a663) | (~c3_1(a663)))),
% 2.31/2.53 inference(quant_inst,[status(thm)],[])).
% 2.31/2.53 tff(93,plain,
% 2.31/2.53 ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp53 | hskp17 | c0_1(a663) | c1_1(a663) | (~ndr1_0) | (~c3_1(a663))),
% 2.31/2.53 inference(modus_ponens,[status(thm)],[92, 91])).
% 2.31/2.53 tff(94,plain,
% 2.31/2.53 ($false),
% 2.31/2.53 inference(unit_resolution,[status(thm)],[93, 87, 35, 12, 56, 48, 42, 34])).
% 2.31/2.53 tff(95,plain,((~hskp58) | hskp53 | hskp17), inference(lemma,lemma(discharge,[]))).
% 2.31/2.53 tff(96,plain,
% 2.31/2.53 (~hskp58),
% 2.31/2.53 inference(unit_resolution,[status(thm)],[95, 35, 12])).
% 2.31/2.53 tff(97,assumption,(~hskp41), introduced(assumption)).
% 2.31/2.53 tff(98,plain,
% 2.31/2.53 (^[U: $i] : refl((hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 2.31/2.53 inference(bind,[status(th)],[])).
% 2.31/2.53 tff(99,plain,
% 2.31/2.53 (![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.31/2.53 inference(quant_intro,[status(thm)],[98])).
% 2.31/2.53 tff(100,plain,
% 2.31/2.53 (![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.31/2.53 inference(rewrite,[status(thm)],[])).
% 2.31/2.53 tff(101,plain,
% 2.31/2.53 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~c0_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)))), ((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), ((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))))), (((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp58) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp58))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp58) <=> (hskp58 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp58) <=> (hskp58 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp58) | hskp41) <=> ((hskp58 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp41))), rewrite(((hskp58 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp41) <=> (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp58) | hskp41) <=> (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 2.31/2.53 inference(bind,[status(th)],[])).
% 2.31/2.53 tff(102,plain,
% 2.31/2.53 (![U: $i] : ((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp58) | hskp41) <=> ![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.31/2.53 inference(quant_intro,[status(thm)],[101])).
% 2.31/2.53 tff(103,axiom,(![U: $i] : ((((((~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp58) | hskp41)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause295')).
% 2.31/2.53 tff(104,plain,
% 2.31/2.53 (![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.31/2.53 inference(modus_ponens,[status(thm)],[103, 102])).
% 2.31/2.53 tff(105,plain,
% 2.31/2.53 (![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.31/2.53 inference(modus_ponens,[status(thm)],[104, 100])).
% 2.31/2.53 tff(106,plain,(
% 2.31/2.53 ![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.31/2.53 inference(skolemize,[status(sab)],[105])).
% 2.31/2.53 tff(107,plain,
% 2.31/2.53 (![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 2.31/2.53 inference(modus_ponens,[status(thm)],[106, 99])).
% 2.31/2.53 tff(108,assumption,(hskp33), introduced(assumption)).
% 2.31/2.53 tff(109,plain,
% 2.31/2.53 (((~hskp33) | (~c2_1(a599))) <=> ((~hskp33) | (~c2_1(a599)))),
% 2.31/2.53 inference(rewrite,[status(thm)],[])).
% 2.31/2.53 tff(110,plain,
% 2.31/2.53 (((~c2_1(a599)) | (~hskp33)) <=> ((~hskp33) | (~c2_1(a599)))),
% 2.31/2.53 inference(rewrite,[status(thm)],[])).
% 2.31/2.53 tff(111,axiom,((~c2_1(a599)) | (~hskp33)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause210')).
% 2.31/2.53 tff(112,plain,
% 2.31/2.53 ((~hskp33) | (~c2_1(a599))),
% 2.31/2.53 inference(modus_ponens,[status(thm)],[111, 110])).
% 2.31/2.53 tff(113,plain,
% 2.31/2.53 ((~hskp33) | (~c2_1(a599))),
% 2.31/2.53 inference(modus_ponens,[status(thm)],[112, 109])).
% 2.31/2.53 tff(114,plain,
% 2.31/2.53 (~c2_1(a599)),
% 2.31/2.53 inference(unit_resolution,[status(thm)],[113, 108])).
% 2.31/2.53 tff(115,plain,
% 2.31/2.53 (((~hskp33) | c3_1(a599)) <=> ((~hskp33) | c3_1(a599))),
% 2.31/2.53 inference(rewrite,[status(thm)],[])).
% 2.31/2.53 tff(116,axiom,((~hskp33) | c3_1(a599)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause137')).
% 2.31/2.53 tff(117,plain,
% 2.31/2.53 ((~hskp33) | c3_1(a599)),
% 2.31/2.53 inference(modus_ponens,[status(thm)],[116, 115])).
% 2.31/2.53 tff(118,plain,
% 2.31/2.53 ((~hskp33) | c3_1(a599)),
% 2.31/2.53 inference(modus_ponens,[status(thm)],[117, 115])).
% 2.31/2.53 tff(119,plain,
% 2.31/2.53 ((~hskp33) | c3_1(a599)),
% 2.31/2.53 inference(modus_ponens,[status(thm)],[118, 115])).
% 2.31/2.53 tff(120,plain,
% 2.31/2.53 ((~hskp33) | c3_1(a599)),
% 2.31/2.53 inference(modus_ponens,[status(thm)],[119, 115])).
% 2.31/2.53 tff(121,plain,
% 2.31/2.53 ((~hskp33) | c3_1(a599)),
% 2.31/2.53 inference(modus_ponens,[status(thm)],[120, 115])).
% 2.31/2.53 tff(122,plain,
% 2.31/2.53 (c3_1(a599)),
% 2.31/2.53 inference(unit_resolution,[status(thm)],[121, 108])).
% 2.31/2.53 tff(123,plain,
% 2.31/2.53 (((~hskp33) | c0_1(a599)) <=> ((~hskp33) | c0_1(a599))),
% 2.31/2.53 inference(rewrite,[status(thm)],[])).
% 2.31/2.53 tff(124,axiom,((~hskp33) | c0_1(a599)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause136')).
% 2.31/2.53 tff(125,plain,
% 2.31/2.53 ((~hskp33) | c0_1(a599)),
% 2.31/2.53 inference(modus_ponens,[status(thm)],[124, 123])).
% 2.31/2.53 tff(126,plain,
% 2.31/2.53 ((~hskp33) | c0_1(a599)),
% 2.31/2.53 inference(modus_ponens,[status(thm)],[125, 123])).
% 2.31/2.53 tff(127,plain,
% 2.31/2.53 ((~hskp33) | c0_1(a599)),
% 2.31/2.53 inference(modus_ponens,[status(thm)],[126, 123])).
% 2.31/2.53 tff(128,plain,
% 2.31/2.53 ((~hskp33) | c0_1(a599)),
% 2.31/2.53 inference(modus_ponens,[status(thm)],[127, 123])).
% 2.31/2.53 tff(129,plain,
% 2.31/2.53 ((~hskp33) | c0_1(a599)),
% 2.31/2.53 inference(modus_ponens,[status(thm)],[128, 123])).
% 2.31/2.53 tff(130,plain,
% 2.31/2.53 (c0_1(a599)),
% 2.31/2.53 inference(unit_resolution,[status(thm)],[129, 108])).
% 2.31/2.53 tff(131,assumption,(~hskp58), introduced(assumption)).
% 2.31/2.53 tff(132,plain,
% 2.31/2.53 (((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | c2_1(a599) | (~ndr1_0) | (~c0_1(a599)) | (~c3_1(a599)))) <=> ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp58 | hskp41 | c2_1(a599) | (~ndr1_0) | (~c0_1(a599)) | (~c3_1(a599)))),
% 2.31/2.53 inference(rewrite,[status(thm)],[])).
% 2.31/2.53 tff(133,plain,
% 2.31/2.53 ((hskp58 | hskp41 | (~ndr1_0) | c2_1(a599) | (~c3_1(a599)) | (~c0_1(a599))) <=> (hskp58 | hskp41 | c2_1(a599) | (~ndr1_0) | (~c0_1(a599)) | (~c3_1(a599)))),
% 2.31/2.53 inference(rewrite,[status(thm)],[])).
% 2.31/2.53 tff(134,plain,
% 2.31/2.53 (((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | (~ndr1_0) | c2_1(a599) | (~c3_1(a599)) | (~c0_1(a599)))) <=> ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | c2_1(a599) | (~ndr1_0) | (~c0_1(a599)) | (~c3_1(a599))))),
% 2.31/2.53 inference(monotonicity,[status(thm)],[133])).
% 2.31/2.53 tff(135,plain,
% 2.31/2.53 (((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | (~ndr1_0) | c2_1(a599) | (~c3_1(a599)) | (~c0_1(a599)))) <=> ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp58 | hskp41 | c2_1(a599) | (~ndr1_0) | (~c0_1(a599)) | (~c3_1(a599)))),
% 2.31/2.53 inference(transitivity,[status(thm)],[134, 132])).
% 2.31/2.53 tff(136,plain,
% 2.31/2.53 ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | (~ndr1_0) | c2_1(a599) | (~c3_1(a599)) | (~c0_1(a599)))),
% 2.31/2.53 inference(quant_inst,[status(thm)],[])).
% 2.31/2.53 tff(137,plain,
% 2.31/2.53 ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp58 | hskp41 | c2_1(a599) | (~ndr1_0) | (~c0_1(a599)) | (~c3_1(a599))),
% 2.31/2.53 inference(modus_ponens,[status(thm)],[136, 135])).
% 2.31/2.53 tff(138,plain,
% 2.31/2.53 ($false),
% 2.31/2.53 inference(unit_resolution,[status(thm)],[137, 87, 131, 97, 130, 122, 114, 107])).
% 2.31/2.53 tff(139,plain,((~hskp33) | hskp58 | hskp41), inference(lemma,lemma(discharge,[]))).
% 2.31/2.53 tff(140,plain,
% 2.31/2.53 (~hskp33),
% 2.31/2.53 inference(unit_resolution,[status(thm)],[139, 97, 96])).
% 2.31/2.53 tff(141,assumption,(hskp15), introduced(assumption)).
% 2.31/2.53 tff(142,plain,
% 2.31/2.53 (((~hskp15) | (~c0_1(a625))) <=> ((~hskp15) | (~c0_1(a625)))),
% 2.31/2.53 inference(rewrite,[status(thm)],[])).
% 2.31/2.53 tff(143,plain,
% 2.31/2.53 (((~c0_1(a625)) | (~hskp15)) <=> ((~hskp15) | (~c0_1(a625)))),
% 2.31/2.53 inference(rewrite,[status(thm)],[])).
% 2.31/2.53 tff(144,axiom,((~c0_1(a625)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause247')).
% 2.31/2.53 tff(145,plain,
% 2.31/2.53 ((~hskp15) | (~c0_1(a625))),
% 2.31/2.53 inference(modus_ponens,[status(thm)],[144, 143])).
% 2.31/2.53 tff(146,plain,
% 2.31/2.53 ((~hskp15) | (~c0_1(a625))),
% 2.31/2.53 inference(modus_ponens,[status(thm)],[145, 142])).
% 2.31/2.53 tff(147,plain,
% 2.31/2.53 (~c0_1(a625)),
% 2.31/2.53 inference(unit_resolution,[status(thm)],[146, 141])).
% 2.31/2.53 tff(148,plain,
% 2.31/2.53 (((~hskp15) | (~c1_1(a625))) <=> ((~hskp15) | (~c1_1(a625)))),
% 2.31/2.53 inference(rewrite,[status(thm)],[])).
% 2.31/2.53 tff(149,plain,
% 2.31/2.53 (((~c1_1(a625)) | (~hskp15)) <=> ((~hskp15) | (~c1_1(a625)))),
% 2.31/2.53 inference(rewrite,[status(thm)],[])).
% 2.31/2.53 tff(150,axiom,((~c1_1(a625)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause246')).
% 2.31/2.53 tff(151,plain,
% 2.31/2.53 ((~hskp15) | (~c1_1(a625))),
% 2.31/2.53 inference(modus_ponens,[status(thm)],[150, 149])).
% 2.31/2.53 tff(152,plain,
% 2.31/2.53 ((~hskp15) | (~c1_1(a625))),
% 2.31/2.53 inference(modus_ponens,[status(thm)],[151, 148])).
% 2.31/2.53 tff(153,plain,
% 2.31/2.53 (~c1_1(a625)),
% 2.31/2.53 inference(unit_resolution,[status(thm)],[152, 141])).
% 2.31/2.53 tff(154,plain,
% 2.31/2.53 (((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | c1_1(a625) | c0_1(a625) | (~ndr1_0) | (~c3_1(a625)))) <=> ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp53 | hskp17 | c1_1(a625) | c0_1(a625) | (~ndr1_0) | (~c3_1(a625)))),
% 2.31/2.53 inference(rewrite,[status(thm)],[])).
% 2.31/2.53 tff(155,plain,
% 2.31/2.53 ((hskp53 | hskp17 | (~ndr1_0) | c1_1(a625) | c0_1(a625) | (~c3_1(a625))) <=> (hskp53 | hskp17 | c1_1(a625) | c0_1(a625) | (~ndr1_0) | (~c3_1(a625)))),
% 2.31/2.53 inference(rewrite,[status(thm)],[])).
% 2.31/2.53 tff(156,plain,
% 2.31/2.53 (((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | (~ndr1_0) | c1_1(a625) | c0_1(a625) | (~c3_1(a625)))) <=> ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | c1_1(a625) | c0_1(a625) | (~ndr1_0) | (~c3_1(a625))))),
% 2.31/2.53 inference(monotonicity,[status(thm)],[155])).
% 2.31/2.53 tff(157,plain,
% 2.31/2.53 (((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | (~ndr1_0) | c1_1(a625) | c0_1(a625) | (~c3_1(a625)))) <=> ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp53 | hskp17 | c1_1(a625) | c0_1(a625) | (~ndr1_0) | (~c3_1(a625)))),
% 2.31/2.53 inference(transitivity,[status(thm)],[156, 154])).
% 2.31/2.53 tff(158,plain,
% 2.31/2.53 ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | (~ndr1_0) | c1_1(a625) | c0_1(a625) | (~c3_1(a625)))),
% 2.31/2.53 inference(quant_inst,[status(thm)],[])).
% 2.31/2.53 tff(159,plain,
% 2.31/2.53 ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp53 | hskp17 | c1_1(a625) | c0_1(a625) | (~ndr1_0) | (~c3_1(a625))),
% 2.31/2.53 inference(modus_ponens,[status(thm)],[158, 157])).
% 2.31/2.53 tff(160,plain,
% 2.31/2.53 (~c3_1(a625)),
% 2.31/2.53 inference(unit_resolution,[status(thm)],[159, 87, 35, 12, 153, 147, 34])).
% 2.31/2.53 tff(161,plain,
% 2.31/2.53 (^[V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V)))),
% 2.31/2.53 inference(bind,[status(th)],[])).
% 2.31/2.53 tff(162,plain,
% 2.31/2.53 (![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))),
% 2.31/2.53 inference(quant_intro,[status(thm)],[161])).
% 2.31/2.53 tff(163,plain,
% 2.31/2.53 (![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))),
% 2.31/2.53 inference(rewrite,[status(thm)],[])).
% 2.31/2.53 tff(164,plain,
% 2.31/2.53 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U))), ((((~ndr1_0) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U)) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c0_1(V))), ((((~ndr1_0) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c0_1(V)))), (((((~ndr1_0) | c0_1(U)) | c0_1(V)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | c0_1(V)) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | c0_1(V)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c0_1(V))), (((((~ndr1_0) | c0_1(U)) | c0_1(V)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c0_1(V)))), ((((((~ndr1_0) | c0_1(U)) | c0_1(V)) | c2_1(U)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V))), ((((((~ndr1_0) | c0_1(U)) | c0_1(V)) | c2_1(U)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V)))), (((((((~ndr1_0) | c0_1(U)) | c0_1(V)) | c2_1(U)) | c3_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | c3_1(V) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))), (((((((~ndr1_0) | c0_1(U)) | c0_1(V)) | c2_1(U)) | c3_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V)))), ((((((((~ndr1_0) | c0_1(U)) | c0_1(V)) | c2_1(U)) | c3_1(V)) | c1_1(V)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V)) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))), ((((((((~ndr1_0) | c0_1(U)) | c0_1(V)) | c2_1(U)) | c3_1(V)) | c1_1(V)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))))),
% 2.31/2.53 inference(bind,[status(th)],[])).
% 2.31/2.53 tff(165,plain,
% 2.31/2.53 (![V: $i, U: $i] : (((((((~ndr1_0) | c0_1(U)) | c0_1(V)) | c2_1(U)) | c3_1(V)) | c1_1(V)) | c3_1(U)) <=> ![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))),
% 2.31/2.54 inference(quant_intro,[status(thm)],[164])).
% 2.31/2.54 tff(166,axiom,(![V: $i, U: $i] : (((((((~ndr1_0) | c0_1(U)) | c0_1(V)) | c2_1(U)) | c3_1(V)) | c1_1(V)) | c3_1(U))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause297')).
% 2.31/2.54 tff(167,plain,
% 2.31/2.54 (![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[166, 165])).
% 2.31/2.54 tff(168,plain,
% 2.31/2.54 (![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[167, 163])).
% 2.31/2.54 tff(169,plain,(
% 2.31/2.54 ![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))),
% 2.31/2.54 inference(skolemize,[status(sab)],[168])).
% 2.31/2.54 tff(170,plain,
% 2.31/2.54 (![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[169, 162])).
% 2.31/2.54 tff(171,plain,
% 2.31/2.54 (((~hskp15) | (~c2_1(a625))) <=> ((~hskp15) | (~c2_1(a625)))),
% 2.31/2.54 inference(rewrite,[status(thm)],[])).
% 2.31/2.54 tff(172,plain,
% 2.31/2.54 (((~c2_1(a625)) | (~hskp15)) <=> ((~hskp15) | (~c2_1(a625)))),
% 2.31/2.54 inference(rewrite,[status(thm)],[])).
% 2.31/2.54 tff(173,axiom,((~c2_1(a625)) | (~hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause245')).
% 2.31/2.54 tff(174,plain,
% 2.31/2.54 ((~hskp15) | (~c2_1(a625))),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[173, 172])).
% 2.31/2.54 tff(175,plain,
% 2.31/2.54 ((~hskp15) | (~c2_1(a625))),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[174, 171])).
% 2.31/2.54 tff(176,plain,
% 2.31/2.54 (~c2_1(a625)),
% 2.31/2.54 inference(unit_resolution,[status(thm)],[175, 141])).
% 2.31/2.54 tff(177,plain,
% 2.31/2.54 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | (c2_1(a625) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | c3_1(a625))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | c2_1(a625) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | c3_1(a625))),
% 2.31/2.54 inference(rewrite,[status(thm)],[])).
% 2.31/2.54 tff(178,plain,
% 2.31/2.54 (((~ndr1_0) | c3_1(a625) | c2_1(a625) | c0_1(a625) | c1_1(a625) | c3_1(a625) | c0_1(a625)) <=> (c2_1(a625) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | c3_1(a625))),
% 2.31/2.54 inference(rewrite,[status(thm)],[])).
% 2.31/2.54 tff(179,plain,
% 2.31/2.54 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | ((~ndr1_0) | c3_1(a625) | c2_1(a625) | c0_1(a625) | c1_1(a625) | c3_1(a625) | c0_1(a625))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | (c2_1(a625) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | c3_1(a625)))),
% 2.31/2.54 inference(monotonicity,[status(thm)],[178])).
% 2.31/2.54 tff(180,plain,
% 2.31/2.54 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | ((~ndr1_0) | c3_1(a625) | c2_1(a625) | c0_1(a625) | c1_1(a625) | c3_1(a625) | c0_1(a625))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | c2_1(a625) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | c3_1(a625))),
% 2.31/2.54 inference(transitivity,[status(thm)],[179, 177])).
% 2.31/2.54 tff(181,plain,
% 2.31/2.54 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | ((~ndr1_0) | c3_1(a625) | c2_1(a625) | c0_1(a625) | c1_1(a625) | c3_1(a625) | c0_1(a625))),
% 2.31/2.54 inference(quant_inst,[status(thm)],[])).
% 2.31/2.54 tff(182,plain,
% 2.31/2.54 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | c2_1(a625) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | c3_1(a625)),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[181, 180])).
% 2.31/2.54 tff(183,plain,
% 2.31/2.54 ($false),
% 2.31/2.54 inference(unit_resolution,[status(thm)],[182, 87, 176, 153, 147, 170, 160])).
% 2.31/2.54 tff(184,plain,((~hskp15) | hskp53 | hskp17), inference(lemma,lemma(discharge,[]))).
% 2.31/2.54 tff(185,plain,
% 2.31/2.54 (~hskp15),
% 2.31/2.54 inference(unit_resolution,[status(thm)],[184, 35, 12])).
% 2.31/2.54 tff(186,assumption,(hskp14), introduced(assumption)).
% 2.31/2.54 tff(187,plain,
% 2.31/2.54 (((~hskp14) | (~c2_1(a624))) <=> ((~hskp14) | (~c2_1(a624)))),
% 2.31/2.54 inference(rewrite,[status(thm)],[])).
% 2.31/2.54 tff(188,plain,
% 2.31/2.54 (((~c2_1(a624)) | (~hskp14)) <=> ((~hskp14) | (~c2_1(a624)))),
% 2.31/2.54 inference(rewrite,[status(thm)],[])).
% 2.31/2.54 tff(189,axiom,((~c2_1(a624)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause249')).
% 2.31/2.54 tff(190,plain,
% 2.31/2.54 ((~hskp14) | (~c2_1(a624))),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[189, 188])).
% 2.31/2.54 tff(191,plain,
% 2.31/2.54 ((~hskp14) | (~c2_1(a624))),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[190, 187])).
% 2.31/2.54 tff(192,plain,
% 2.31/2.54 (~c2_1(a624)),
% 2.31/2.54 inference(unit_resolution,[status(thm)],[191, 186])).
% 2.31/2.54 tff(193,plain,
% 2.31/2.54 (((~hskp14) | c3_1(a624)) <=> ((~hskp14) | c3_1(a624))),
% 2.31/2.54 inference(rewrite,[status(thm)],[])).
% 2.31/2.54 tff(194,axiom,((~hskp14) | c3_1(a624)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause155')).
% 2.31/2.54 tff(195,plain,
% 2.31/2.54 ((~hskp14) | c3_1(a624)),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[194, 193])).
% 2.31/2.54 tff(196,plain,
% 2.31/2.54 ((~hskp14) | c3_1(a624)),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[195, 193])).
% 2.31/2.54 tff(197,plain,
% 2.31/2.54 ((~hskp14) | c3_1(a624)),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[196, 193])).
% 2.31/2.54 tff(198,plain,
% 2.31/2.54 ((~hskp14) | c3_1(a624)),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[197, 193])).
% 2.31/2.54 tff(199,plain,
% 2.31/2.54 ((~hskp14) | c3_1(a624)),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[198, 193])).
% 2.31/2.54 tff(200,plain,
% 2.31/2.54 (c3_1(a624)),
% 2.31/2.54 inference(unit_resolution,[status(thm)],[199, 186])).
% 2.31/2.54 tff(201,plain,
% 2.31/2.54 (((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | c2_1(a624) | (~ndr1_0) | (~c0_1(a624)) | (~c3_1(a624)))) <=> ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp58 | hskp41 | c2_1(a624) | (~ndr1_0) | (~c0_1(a624)) | (~c3_1(a624)))),
% 2.31/2.54 inference(rewrite,[status(thm)],[])).
% 2.31/2.54 tff(202,plain,
% 2.31/2.54 ((hskp58 | hskp41 | (~ndr1_0) | c2_1(a624) | (~c3_1(a624)) | (~c0_1(a624))) <=> (hskp58 | hskp41 | c2_1(a624) | (~ndr1_0) | (~c0_1(a624)) | (~c3_1(a624)))),
% 2.31/2.54 inference(rewrite,[status(thm)],[])).
% 2.31/2.54 tff(203,plain,
% 2.31/2.54 (((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | (~ndr1_0) | c2_1(a624) | (~c3_1(a624)) | (~c0_1(a624)))) <=> ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | c2_1(a624) | (~ndr1_0) | (~c0_1(a624)) | (~c3_1(a624))))),
% 2.31/2.54 inference(monotonicity,[status(thm)],[202])).
% 2.31/2.54 tff(204,plain,
% 2.31/2.54 (((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | (~ndr1_0) | c2_1(a624) | (~c3_1(a624)) | (~c0_1(a624)))) <=> ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp58 | hskp41 | c2_1(a624) | (~ndr1_0) | (~c0_1(a624)) | (~c3_1(a624)))),
% 2.31/2.54 inference(transitivity,[status(thm)],[203, 201])).
% 2.31/2.54 tff(205,plain,
% 2.31/2.54 ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | (~ndr1_0) | c2_1(a624) | (~c3_1(a624)) | (~c0_1(a624)))),
% 2.31/2.54 inference(quant_inst,[status(thm)],[])).
% 2.31/2.54 tff(206,plain,
% 2.31/2.54 ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp58 | hskp41 | c2_1(a624) | (~ndr1_0) | (~c0_1(a624)) | (~c3_1(a624))),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[205, 204])).
% 2.31/2.54 tff(207,plain,
% 2.31/2.54 (~c0_1(a624)),
% 2.31/2.54 inference(unit_resolution,[status(thm)],[206, 87, 96, 97, 200, 192, 107])).
% 2.31/2.54 tff(208,plain,
% 2.31/2.54 (((~hskp14) | (~c1_1(a624))) <=> ((~hskp14) | (~c1_1(a624)))),
% 2.31/2.54 inference(rewrite,[status(thm)],[])).
% 2.31/2.54 tff(209,plain,
% 2.31/2.54 (((~c1_1(a624)) | (~hskp14)) <=> ((~hskp14) | (~c1_1(a624)))),
% 2.31/2.54 inference(rewrite,[status(thm)],[])).
% 2.31/2.54 tff(210,axiom,((~c1_1(a624)) | (~hskp14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause248')).
% 2.31/2.54 tff(211,plain,
% 2.31/2.54 ((~hskp14) | (~c1_1(a624))),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[210, 209])).
% 2.31/2.54 tff(212,plain,
% 2.31/2.54 ((~hskp14) | (~c1_1(a624))),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[211, 208])).
% 2.31/2.54 tff(213,plain,
% 2.31/2.54 (~c1_1(a624)),
% 2.31/2.54 inference(unit_resolution,[status(thm)],[212, 186])).
% 2.31/2.54 tff(214,plain,
% 2.31/2.54 (((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | c1_1(a624) | (~ndr1_0) | c0_1(a624) | (~c3_1(a624)))) <=> ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp53 | hskp17 | c1_1(a624) | (~ndr1_0) | c0_1(a624) | (~c3_1(a624)))),
% 2.31/2.54 inference(rewrite,[status(thm)],[])).
% 2.31/2.54 tff(215,plain,
% 2.31/2.54 ((hskp53 | hskp17 | (~ndr1_0) | c1_1(a624) | c0_1(a624) | (~c3_1(a624))) <=> (hskp53 | hskp17 | c1_1(a624) | (~ndr1_0) | c0_1(a624) | (~c3_1(a624)))),
% 2.31/2.54 inference(rewrite,[status(thm)],[])).
% 2.31/2.54 tff(216,plain,
% 2.31/2.54 (((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | (~ndr1_0) | c1_1(a624) | c0_1(a624) | (~c3_1(a624)))) <=> ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | c1_1(a624) | (~ndr1_0) | c0_1(a624) | (~c3_1(a624))))),
% 2.31/2.54 inference(monotonicity,[status(thm)],[215])).
% 2.31/2.54 tff(217,plain,
% 2.31/2.54 (((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | (~ndr1_0) | c1_1(a624) | c0_1(a624) | (~c3_1(a624)))) <=> ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp53 | hskp17 | c1_1(a624) | (~ndr1_0) | c0_1(a624) | (~c3_1(a624)))),
% 2.31/2.54 inference(transitivity,[status(thm)],[216, 214])).
% 2.31/2.54 tff(218,plain,
% 2.31/2.54 ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | (~ndr1_0) | c1_1(a624) | c0_1(a624) | (~c3_1(a624)))),
% 2.31/2.54 inference(quant_inst,[status(thm)],[])).
% 2.31/2.54 tff(219,plain,
% 2.31/2.54 ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp53 | hskp17 | c1_1(a624) | (~ndr1_0) | c0_1(a624) | (~c3_1(a624))),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[218, 217])).
% 2.31/2.54 tff(220,plain,
% 2.31/2.54 ($false),
% 2.31/2.54 inference(unit_resolution,[status(thm)],[219, 87, 35, 12, 200, 213, 34, 207])).
% 2.31/2.54 tff(221,plain,((~hskp14) | hskp53 | hskp17 | hskp41), inference(lemma,lemma(discharge,[]))).
% 2.31/2.54 tff(222,plain,
% 2.31/2.54 (~hskp14),
% 2.31/2.54 inference(unit_resolution,[status(thm)],[221, 97, 12, 35])).
% 2.31/2.54 tff(223,plain,
% 2.31/2.54 (^[U: $i] : refl((hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) <=> (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))))),
% 2.31/2.54 inference(bind,[status(th)],[])).
% 2.31/2.54 tff(224,plain,
% 2.31/2.54 (![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 2.31/2.54 inference(quant_intro,[status(thm)],[223])).
% 2.31/2.54 tff(225,plain,
% 2.31/2.54 (![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 2.31/2.54 inference(rewrite,[status(thm)],[])).
% 2.31/2.54 tff(226,plain,
% 2.31/2.54 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~c0_1(U))) <=> ((~c0_1(U)) | (~c2_1(U)))), ((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)))), ((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))))), (((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | 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)) | (~c0_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))))), ((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp14))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))), ((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))))), (((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) | hskp15) <=> ((hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp15))), rewrite(((hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U))) | hskp15) <=> (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))), (((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) | hskp15) <=> (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))))),
% 2.31/2.54 inference(bind,[status(th)],[])).
% 2.31/2.54 tff(227,plain,
% 2.31/2.54 (![U: $i] : ((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) | hskp15) <=> ![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 2.31/2.54 inference(quant_intro,[status(thm)],[226])).
% 2.31/2.54 tff(228,axiom,(![U: $i] : ((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp14) | hskp15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause293')).
% 2.31/2.54 tff(229,plain,
% 2.31/2.54 (![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[228, 227])).
% 2.31/2.54 tff(230,plain,
% 2.31/2.54 (![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[229, 225])).
% 2.31/2.54 tff(231,plain,(
% 2.31/2.54 ![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 2.31/2.54 inference(skolemize,[status(sab)],[230])).
% 2.31/2.54 tff(232,plain,
% 2.31/2.54 (![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[231, 224])).
% 2.31/2.54 tff(233,assumption,(hskp65), introduced(assumption)).
% 2.31/2.54 tff(234,plain,
% 2.31/2.54 (((~hskp65) | (~c1_1(a674))) <=> ((~hskp65) | (~c1_1(a674)))),
% 2.31/2.54 inference(rewrite,[status(thm)],[])).
% 2.31/2.54 tff(235,plain,
% 2.31/2.54 (((~c1_1(a674)) | (~hskp65)) <=> ((~hskp65) | (~c1_1(a674)))),
% 2.31/2.54 inference(rewrite,[status(thm)],[])).
% 2.31/2.54 tff(236,axiom,((~c1_1(a674)) | (~hskp65)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause172')).
% 2.31/2.54 tff(237,plain,
% 2.31/2.54 ((~hskp65) | (~c1_1(a674))),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[236, 235])).
% 2.31/2.54 tff(238,plain,
% 2.31/2.54 ((~hskp65) | (~c1_1(a674))),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[237, 234])).
% 2.31/2.54 tff(239,plain,
% 2.31/2.54 (~c1_1(a674)),
% 2.31/2.54 inference(unit_resolution,[status(thm)],[238, 233])).
% 2.31/2.54 tff(240,plain,
% 2.31/2.54 (((~hskp65) | c0_1(a674)) <=> ((~hskp65) | c0_1(a674))),
% 2.31/2.54 inference(rewrite,[status(thm)],[])).
% 2.31/2.54 tff(241,axiom,((~hskp65) | c0_1(a674)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause79')).
% 2.31/2.54 tff(242,plain,
% 2.31/2.54 ((~hskp65) | c0_1(a674)),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[241, 240])).
% 2.31/2.54 tff(243,plain,
% 2.31/2.54 ((~hskp65) | c0_1(a674)),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[242, 240])).
% 2.31/2.54 tff(244,plain,
% 2.31/2.54 ((~hskp65) | c0_1(a674)),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[243, 240])).
% 2.31/2.54 tff(245,plain,
% 2.31/2.54 ((~hskp65) | c0_1(a674)),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[244, 240])).
% 2.31/2.54 tff(246,plain,
% 2.31/2.54 ((~hskp65) | c0_1(a674)),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[245, 240])).
% 2.31/2.54 tff(247,plain,
% 2.31/2.54 (c0_1(a674)),
% 2.31/2.54 inference(unit_resolution,[status(thm)],[246, 233])).
% 2.31/2.54 tff(248,plain,
% 2.31/2.54 (((~hskp65) | c2_1(a674)) <=> ((~hskp65) | c2_1(a674))),
% 2.31/2.54 inference(rewrite,[status(thm)],[])).
% 2.31/2.54 tff(249,axiom,((~hskp65) | c2_1(a674)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause78')).
% 2.31/2.54 tff(250,plain,
% 2.31/2.54 ((~hskp65) | c2_1(a674)),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[249, 248])).
% 2.31/2.54 tff(251,plain,
% 2.31/2.54 ((~hskp65) | c2_1(a674)),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[250, 248])).
% 2.31/2.54 tff(252,plain,
% 2.31/2.54 ((~hskp65) | c2_1(a674)),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[251, 248])).
% 2.31/2.54 tff(253,plain,
% 2.31/2.54 ((~hskp65) | c2_1(a674)),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[252, 248])).
% 2.31/2.54 tff(254,plain,
% 2.31/2.54 ((~hskp65) | c2_1(a674)),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[253, 248])).
% 2.31/2.54 tff(255,plain,
% 2.31/2.54 (c2_1(a674)),
% 2.31/2.54 inference(unit_resolution,[status(thm)],[254, 233])).
% 2.31/2.54 tff(256,assumption,(~hskp14), introduced(assumption)).
% 2.31/2.54 tff(257,assumption,(~hskp15), introduced(assumption)).
% 2.31/2.54 tff(258,plain,
% 2.31/2.54 (((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp15 | hskp14 | c1_1(a674) | (~ndr1_0) | (~c0_1(a674)) | (~c2_1(a674)))) <=> ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp15 | hskp14 | c1_1(a674) | (~ndr1_0) | (~c0_1(a674)) | (~c2_1(a674)))),
% 2.31/2.54 inference(rewrite,[status(thm)],[])).
% 2.31/2.54 tff(259,plain,
% 2.31/2.54 ((hskp15 | hskp14 | (~ndr1_0) | c1_1(a674) | (~c0_1(a674)) | (~c2_1(a674))) <=> (hskp15 | hskp14 | c1_1(a674) | (~ndr1_0) | (~c0_1(a674)) | (~c2_1(a674)))),
% 2.31/2.54 inference(rewrite,[status(thm)],[])).
% 2.31/2.54 tff(260,plain,
% 2.31/2.54 (((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp15 | hskp14 | (~ndr1_0) | c1_1(a674) | (~c0_1(a674)) | (~c2_1(a674)))) <=> ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp15 | hskp14 | c1_1(a674) | (~ndr1_0) | (~c0_1(a674)) | (~c2_1(a674))))),
% 2.31/2.54 inference(monotonicity,[status(thm)],[259])).
% 2.31/2.54 tff(261,plain,
% 2.31/2.54 (((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp15 | hskp14 | (~ndr1_0) | c1_1(a674) | (~c0_1(a674)) | (~c2_1(a674)))) <=> ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp15 | hskp14 | c1_1(a674) | (~ndr1_0) | (~c0_1(a674)) | (~c2_1(a674)))),
% 2.31/2.54 inference(transitivity,[status(thm)],[260, 258])).
% 2.31/2.54 tff(262,plain,
% 2.31/2.54 ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp15 | hskp14 | (~ndr1_0) | c1_1(a674) | (~c0_1(a674)) | (~c2_1(a674)))),
% 2.31/2.54 inference(quant_inst,[status(thm)],[])).
% 2.31/2.54 tff(263,plain,
% 2.31/2.54 ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp15 | hskp14 | c1_1(a674) | (~ndr1_0) | (~c0_1(a674)) | (~c2_1(a674))),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[262, 261])).
% 2.31/2.54 tff(264,plain,
% 2.31/2.54 ($false),
% 2.31/2.54 inference(unit_resolution,[status(thm)],[263, 87, 257, 256, 255, 247, 239, 232])).
% 2.31/2.54 tff(265,plain,((~hskp65) | hskp15 | hskp14), inference(lemma,lemma(discharge,[]))).
% 2.31/2.54 tff(266,plain,
% 2.31/2.54 (~hskp65),
% 2.31/2.54 inference(unit_resolution,[status(thm)],[265, 222, 185])).
% 2.31/2.54 tff(267,plain,
% 2.31/2.54 (hskp66),
% 2.31/2.54 inference(unit_resolution,[status(thm)],[85, 266, 24])).
% 2.31/2.54 tff(268,plain,
% 2.31/2.54 (((~hskp66) | (~c2_1(a675))) <=> ((~hskp66) | (~c2_1(a675)))),
% 2.31/2.54 inference(rewrite,[status(thm)],[])).
% 2.31/2.54 tff(269,plain,
% 2.31/2.54 (((~c2_1(a675)) | (~hskp66)) <=> ((~hskp66) | (~c2_1(a675)))),
% 2.31/2.54 inference(rewrite,[status(thm)],[])).
% 2.31/2.54 tff(270,axiom,((~c2_1(a675)) | (~hskp66)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause171')).
% 2.31/2.54 tff(271,plain,
% 2.31/2.54 ((~hskp66) | (~c2_1(a675))),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[270, 269])).
% 2.31/2.54 tff(272,plain,
% 2.31/2.54 ((~hskp66) | (~c2_1(a675))),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[271, 268])).
% 2.31/2.54 tff(273,plain,
% 2.31/2.54 (~c2_1(a675)),
% 2.31/2.54 inference(unit_resolution,[status(thm)],[272, 267])).
% 2.31/2.54 tff(274,plain,
% 2.31/2.54 (((~hskp66) | c3_1(a675)) <=> ((~hskp66) | c3_1(a675))),
% 2.31/2.54 inference(rewrite,[status(thm)],[])).
% 2.31/2.54 tff(275,axiom,((~hskp66) | c3_1(a675)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause77')).
% 2.31/2.54 tff(276,plain,
% 2.31/2.54 ((~hskp66) | c3_1(a675)),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[275, 274])).
% 2.31/2.54 tff(277,plain,
% 2.31/2.54 ((~hskp66) | c3_1(a675)),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[276, 274])).
% 2.31/2.54 tff(278,plain,
% 2.31/2.54 ((~hskp66) | c3_1(a675)),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[277, 274])).
% 2.31/2.54 tff(279,plain,
% 2.31/2.54 ((~hskp66) | c3_1(a675)),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[278, 274])).
% 2.31/2.54 tff(280,plain,
% 2.31/2.54 ((~hskp66) | c3_1(a675)),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[279, 274])).
% 2.31/2.54 tff(281,plain,
% 2.31/2.54 (c3_1(a675)),
% 2.31/2.54 inference(unit_resolution,[status(thm)],[280, 267])).
% 2.31/2.54 tff(282,plain,
% 2.31/2.54 (((~hskp66) | c1_1(a675)) <=> ((~hskp66) | c1_1(a675))),
% 2.31/2.54 inference(rewrite,[status(thm)],[])).
% 2.31/2.54 tff(283,axiom,((~hskp66) | c1_1(a675)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause76')).
% 2.31/2.54 tff(284,plain,
% 2.31/2.54 ((~hskp66) | c1_1(a675)),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[283, 282])).
% 2.31/2.54 tff(285,plain,
% 2.31/2.54 ((~hskp66) | c1_1(a675)),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[284, 282])).
% 2.31/2.54 tff(286,plain,
% 2.31/2.54 ((~hskp66) | c1_1(a675)),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[285, 282])).
% 2.31/2.54 tff(287,plain,
% 2.31/2.54 ((~hskp66) | c1_1(a675)),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[286, 282])).
% 2.31/2.54 tff(288,plain,
% 2.31/2.54 ((~hskp66) | c1_1(a675)),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[287, 282])).
% 2.31/2.54 tff(289,plain,
% 2.31/2.54 (c1_1(a675)),
% 2.31/2.54 inference(unit_resolution,[status(thm)],[288, 267])).
% 2.31/2.54 tff(290,plain,
% 2.31/2.54 (^[V: $i, U: $i] : refl((hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))),
% 2.31/2.54 inference(bind,[status(th)],[])).
% 2.31/2.54 tff(291,plain,
% 2.31/2.54 (![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 2.31/2.54 inference(quant_intro,[status(thm)],[290])).
% 2.31/2.54 tff(292,plain,
% 2.31/2.54 (![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 2.31/2.54 inference(rewrite,[status(thm)],[])).
% 2.31/2.54 tff(293,plain,
% 2.31/2.54 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | hskp41) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp41))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp41) <=> (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | hskp41) <=> (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))))),
% 2.31/2.54 inference(bind,[status(th)],[])).
% 2.31/2.54 tff(294,plain,
% 2.31/2.54 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | hskp41) <=> ![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 2.31/2.54 inference(quant_intro,[status(thm)],[293])).
% 2.31/2.54 tff(295,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | hskp41)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause314')).
% 2.31/2.54 tff(296,plain,
% 2.31/2.54 (![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[295, 294])).
% 2.31/2.54 tff(297,plain,
% 2.31/2.54 (![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[296, 292])).
% 2.31/2.54 tff(298,plain,(
% 2.31/2.54 ![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 2.31/2.54 inference(skolemize,[status(sab)],[297])).
% 2.31/2.54 tff(299,plain,
% 2.31/2.54 (![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[298, 291])).
% 2.31/2.54 tff(300,assumption,(hskp60), introduced(assumption)).
% 2.31/2.54 tff(301,plain,
% 2.31/2.54 (((~hskp60) | (~c2_1(a669))) <=> ((~hskp60) | (~c2_1(a669)))),
% 2.31/2.54 inference(rewrite,[status(thm)],[])).
% 2.31/2.54 tff(302,plain,
% 2.31/2.54 (((~c2_1(a669)) | (~hskp60)) <=> ((~hskp60) | (~c2_1(a669)))),
% 2.31/2.54 inference(rewrite,[status(thm)],[])).
% 2.31/2.54 tff(303,axiom,((~c2_1(a669)) | (~hskp60)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause179')).
% 2.31/2.54 tff(304,plain,
% 2.31/2.54 ((~hskp60) | (~c2_1(a669))),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[303, 302])).
% 2.31/2.54 tff(305,plain,
% 2.31/2.54 ((~hskp60) | (~c2_1(a669))),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[304, 301])).
% 2.31/2.54 tff(306,plain,
% 2.31/2.54 (~c2_1(a669)),
% 2.31/2.54 inference(unit_resolution,[status(thm)],[305, 300])).
% 2.31/2.54 tff(307,assumption,(~c2_1(a675)), introduced(assumption)).
% 2.31/2.54 tff(308,plain,
% 2.31/2.54 (((~hskp60) | c1_1(a669)) <=> ((~hskp60) | c1_1(a669))),
% 2.31/2.54 inference(rewrite,[status(thm)],[])).
% 2.31/2.54 tff(309,axiom,((~hskp60) | c1_1(a669)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause87')).
% 2.31/2.54 tff(310,plain,
% 2.31/2.54 ((~hskp60) | c1_1(a669)),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[309, 308])).
% 2.31/2.54 tff(311,plain,
% 2.31/2.54 ((~hskp60) | c1_1(a669)),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[310, 308])).
% 2.31/2.54 tff(312,plain,
% 2.31/2.54 ((~hskp60) | c1_1(a669)),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[311, 308])).
% 2.31/2.54 tff(313,plain,
% 2.31/2.54 ((~hskp60) | c1_1(a669)),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[312, 308])).
% 2.31/2.54 tff(314,plain,
% 2.31/2.54 ((~hskp60) | c1_1(a669)),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[313, 308])).
% 2.31/2.54 tff(315,plain,
% 2.31/2.54 (c1_1(a669)),
% 2.31/2.54 inference(unit_resolution,[status(thm)],[314, 300])).
% 2.31/2.54 tff(316,plain,
% 2.31/2.54 (((~hskp60) | c0_1(a669)) <=> ((~hskp60) | c0_1(a669))),
% 2.31/2.54 inference(rewrite,[status(thm)],[])).
% 2.31/2.54 tff(317,axiom,((~hskp60) | c0_1(a669)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause86')).
% 2.31/2.54 tff(318,plain,
% 2.31/2.54 ((~hskp60) | c0_1(a669)),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[317, 316])).
% 2.31/2.54 tff(319,plain,
% 2.31/2.54 ((~hskp60) | c0_1(a669)),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[318, 316])).
% 2.31/2.54 tff(320,plain,
% 2.31/2.54 ((~hskp60) | c0_1(a669)),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[319, 316])).
% 2.31/2.54 tff(321,plain,
% 2.31/2.54 ((~hskp60) | c0_1(a669)),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[320, 316])).
% 2.31/2.54 tff(322,plain,
% 2.31/2.54 ((~hskp60) | c0_1(a669)),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[321, 316])).
% 2.31/2.54 tff(323,plain,
% 2.31/2.54 (c0_1(a669)),
% 2.31/2.54 inference(unit_resolution,[status(thm)],[322, 300])).
% 2.31/2.54 tff(324,assumption,(c3_1(a675)), introduced(assumption)).
% 2.31/2.54 tff(325,assumption,(c1_1(a675)), introduced(assumption)).
% 2.31/2.54 tff(326,plain,
% 2.31/2.54 (((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | c2_1(a675) | c2_1(a669) | (~ndr1_0) | (~c1_1(a675)) | (~c3_1(a675)) | (~c0_1(a669)) | (~c1_1(a669)))) <=> ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp41 | c2_1(a675) | c2_1(a669) | (~ndr1_0) | (~c1_1(a675)) | (~c3_1(a675)) | (~c0_1(a669)) | (~c1_1(a669)))),
% 2.31/2.54 inference(rewrite,[status(thm)],[])).
% 2.31/2.54 tff(327,plain,
% 2.31/2.54 ((hskp41 | (~ndr1_0) | c2_1(a675) | (~c3_1(a675)) | (~c1_1(a675)) | c2_1(a669) | (~c1_1(a669)) | (~c0_1(a669))) <=> (hskp41 | c2_1(a675) | c2_1(a669) | (~ndr1_0) | (~c1_1(a675)) | (~c3_1(a675)) | (~c0_1(a669)) | (~c1_1(a669)))),
% 2.31/2.54 inference(rewrite,[status(thm)],[])).
% 2.31/2.54 tff(328,plain,
% 2.31/2.54 (((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | (~ndr1_0) | c2_1(a675) | (~c3_1(a675)) | (~c1_1(a675)) | c2_1(a669) | (~c1_1(a669)) | (~c0_1(a669)))) <=> ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | c2_1(a675) | c2_1(a669) | (~ndr1_0) | (~c1_1(a675)) | (~c3_1(a675)) | (~c0_1(a669)) | (~c1_1(a669))))),
% 2.31/2.54 inference(monotonicity,[status(thm)],[327])).
% 2.31/2.54 tff(329,plain,
% 2.31/2.54 (((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | (~ndr1_0) | c2_1(a675) | (~c3_1(a675)) | (~c1_1(a675)) | c2_1(a669) | (~c1_1(a669)) | (~c0_1(a669)))) <=> ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp41 | c2_1(a675) | c2_1(a669) | (~ndr1_0) | (~c1_1(a675)) | (~c3_1(a675)) | (~c0_1(a669)) | (~c1_1(a669)))),
% 2.31/2.54 inference(transitivity,[status(thm)],[328, 326])).
% 2.31/2.54 tff(330,plain,
% 2.31/2.54 ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | (~ndr1_0) | c2_1(a675) | (~c3_1(a675)) | (~c1_1(a675)) | c2_1(a669) | (~c1_1(a669)) | (~c0_1(a669)))),
% 2.31/2.54 inference(quant_inst,[status(thm)],[])).
% 2.31/2.54 tff(331,plain,
% 2.31/2.54 ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp41 | c2_1(a675) | c2_1(a669) | (~ndr1_0) | (~c1_1(a675)) | (~c3_1(a675)) | (~c0_1(a669)) | (~c1_1(a669))),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[330, 329])).
% 2.31/2.54 tff(332,plain,
% 2.31/2.54 ($false),
% 2.31/2.54 inference(unit_resolution,[status(thm)],[331, 87, 97, 325, 324, 323, 315, 307, 306, 299])).
% 2.31/2.54 tff(333,plain,((~hskp60) | hskp41 | (~c1_1(a675)) | (~c3_1(a675)) | c2_1(a675)), inference(lemma,lemma(discharge,[]))).
% 2.31/2.54 tff(334,plain,
% 2.31/2.54 (~hskp60),
% 2.31/2.54 inference(unit_resolution,[status(thm)],[333, 97, 289, 281, 273])).
% 2.31/2.54 tff(335,plain,
% 2.31/2.54 ((hskp61 | hskp60 | hskp33) <=> (hskp61 | hskp60 | hskp33)),
% 2.31/2.54 inference(rewrite,[status(thm)],[])).
% 2.31/2.54 tff(336,plain,
% 2.31/2.54 (((hskp33 | hskp60) | hskp61) <=> (hskp61 | hskp60 | hskp33)),
% 2.31/2.54 inference(rewrite,[status(thm)],[])).
% 2.31/2.54 tff(337,axiom,((hskp33 | hskp60) | hskp61), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause74')).
% 2.31/2.54 tff(338,plain,
% 2.31/2.54 (hskp61 | hskp60 | hskp33),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[337, 336])).
% 2.31/2.54 tff(339,plain,
% 2.31/2.54 (hskp61 | hskp60 | hskp33),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[338, 335])).
% 2.31/2.54 tff(340,plain,
% 2.31/2.54 (hskp61 | hskp60 | hskp33),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[339, 335])).
% 2.31/2.54 tff(341,plain,
% 2.31/2.54 (hskp61 | hskp60 | hskp33),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[340, 335])).
% 2.31/2.54 tff(342,plain,
% 2.31/2.54 (hskp61 | hskp60 | hskp33),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[341, 335])).
% 2.31/2.54 tff(343,plain,
% 2.31/2.54 (hskp61),
% 2.31/2.54 inference(unit_resolution,[status(thm)],[342, 334, 140])).
% 2.31/2.54 tff(344,plain,
% 2.31/2.54 (((~hskp61) | (~c0_1(a670))) <=> ((~hskp61) | (~c0_1(a670)))),
% 2.31/2.54 inference(rewrite,[status(thm)],[])).
% 2.31/2.54 tff(345,plain,
% 2.31/2.54 (((~c0_1(a670)) | (~hskp61)) <=> ((~hskp61) | (~c0_1(a670)))),
% 2.31/2.54 inference(rewrite,[status(thm)],[])).
% 2.31/2.54 tff(346,axiom,((~c0_1(a670)) | (~hskp61)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause178')).
% 2.31/2.54 tff(347,plain,
% 2.31/2.54 ((~hskp61) | (~c0_1(a670))),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[346, 345])).
% 2.31/2.54 tff(348,plain,
% 2.31/2.54 ((~hskp61) | (~c0_1(a670))),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[347, 344])).
% 2.31/2.54 tff(349,plain,
% 2.31/2.54 (~c0_1(a670)),
% 2.31/2.54 inference(unit_resolution,[status(thm)],[348, 343])).
% 2.31/2.54 tff(350,plain,
% 2.31/2.54 (((~hskp61) | (~c1_1(a670))) <=> ((~hskp61) | (~c1_1(a670)))),
% 2.31/2.54 inference(rewrite,[status(thm)],[])).
% 2.31/2.54 tff(351,plain,
% 2.31/2.54 (((~c1_1(a670)) | (~hskp61)) <=> ((~hskp61) | (~c1_1(a670)))),
% 2.31/2.54 inference(rewrite,[status(thm)],[])).
% 2.31/2.54 tff(352,axiom,((~c1_1(a670)) | (~hskp61)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause177')).
% 2.31/2.54 tff(353,plain,
% 2.31/2.54 ((~hskp61) | (~c1_1(a670))),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[352, 351])).
% 2.31/2.54 tff(354,plain,
% 2.31/2.54 ((~hskp61) | (~c1_1(a670))),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[353, 350])).
% 2.31/2.54 tff(355,plain,
% 2.31/2.54 (~c1_1(a670)),
% 2.31/2.54 inference(unit_resolution,[status(thm)],[354, 343])).
% 2.31/2.54 tff(356,plain,
% 2.31/2.54 (((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | c1_1(a670) | c0_1(a670) | (~ndr1_0) | (~c3_1(a670)))) <=> ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp53 | hskp17 | c1_1(a670) | c0_1(a670) | (~ndr1_0) | (~c3_1(a670)))),
% 2.31/2.54 inference(rewrite,[status(thm)],[])).
% 2.31/2.54 tff(357,plain,
% 2.31/2.54 ((hskp53 | hskp17 | (~ndr1_0) | c1_1(a670) | c0_1(a670) | (~c3_1(a670))) <=> (hskp53 | hskp17 | c1_1(a670) | c0_1(a670) | (~ndr1_0) | (~c3_1(a670)))),
% 2.31/2.54 inference(rewrite,[status(thm)],[])).
% 2.31/2.54 tff(358,plain,
% 2.31/2.54 (((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | (~ndr1_0) | c1_1(a670) | c0_1(a670) | (~c3_1(a670)))) <=> ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | c1_1(a670) | c0_1(a670) | (~ndr1_0) | (~c3_1(a670))))),
% 2.31/2.54 inference(monotonicity,[status(thm)],[357])).
% 2.31/2.54 tff(359,plain,
% 2.31/2.54 (((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | (~ndr1_0) | c1_1(a670) | c0_1(a670) | (~c3_1(a670)))) <=> ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp53 | hskp17 | c1_1(a670) | c0_1(a670) | (~ndr1_0) | (~c3_1(a670)))),
% 2.31/2.54 inference(transitivity,[status(thm)],[358, 356])).
% 2.31/2.54 tff(360,plain,
% 2.31/2.54 ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | (~ndr1_0) | c1_1(a670) | c0_1(a670) | (~c3_1(a670)))),
% 2.31/2.54 inference(quant_inst,[status(thm)],[])).
% 2.31/2.54 tff(361,plain,
% 2.31/2.54 ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp53 | hskp17 | c1_1(a670) | c0_1(a670) | (~ndr1_0) | (~c3_1(a670))),
% 2.31/2.54 inference(modus_ponens,[status(thm)],[360, 359])).
% 2.31/2.54 tff(362,plain,
% 2.31/2.54 (~c3_1(a670)),
% 2.31/2.54 inference(unit_resolution,[status(thm)],[361, 87, 35, 12, 355, 349, 34])).
% 2.31/2.54 tff(363,plain,
% 2.31/2.54 (^[U: $i] : refl((hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))))),
% 2.31/2.54 inference(bind,[status(th)],[])).
% 2.31/2.54 tff(364,plain,
% 2.31/2.54 (![U: $i] : (hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 2.31/2.54 inference(quant_intro,[status(thm)],[363])).
% 2.31/2.54 tff(365,plain,
% 2.31/2.54 (![U: $i] : (hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 2.31/2.54 inference(rewrite,[status(thm)],[])).
% 2.31/2.54 tff(366,plain,
% 2.31/2.54 (^[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)) | c3_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c3_1(U)) | c0_1(U)) <=> (((~ndr1_0) | c3_1(U) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | c3_1(U) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c3_1(U)) | c0_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c3_1(U)) | c0_1(U)) | hskp37) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp37))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp37) <=> (hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c3_1(U)) | c0_1(U)) | hskp37) <=> (hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c3_1(U)) | c0_1(U)) | hskp37) | hskp54) <=> ((hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp54))), rewrite(((hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp54) <=> (hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c3_1(U)) | c0_1(U)) | hskp37) | hskp54) <=> (hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))))),
% 2.31/2.55 inference(bind,[status(th)],[])).
% 2.31/2.55 tff(367,plain,
% 2.31/2.55 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c3_1(U)) | c0_1(U)) | hskp37) | hskp54) <=> ![U: $i] : (hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 2.31/2.55 inference(quant_intro,[status(thm)],[366])).
% 2.31/2.55 tff(368,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c3_1(U)) | c0_1(U)) | hskp37) | hskp54)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause286')).
% 2.31/2.55 tff(369,plain,
% 2.31/2.55 (![U: $i] : (hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[368, 367])).
% 2.31/2.55 tff(370,plain,
% 2.31/2.55 (![U: $i] : (hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[369, 365])).
% 2.31/2.55 tff(371,plain,(
% 2.31/2.55 ![U: $i] : (hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 2.31/2.55 inference(skolemize,[status(sab)],[370])).
% 2.31/2.55 tff(372,plain,
% 2.31/2.55 (![U: $i] : (hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[371, 364])).
% 2.31/2.55 tff(373,plain,
% 2.31/2.55 (((~hskp61) | c2_1(a670)) <=> ((~hskp61) | c2_1(a670))),
% 2.31/2.55 inference(rewrite,[status(thm)],[])).
% 2.31/2.55 tff(374,axiom,((~hskp61) | c2_1(a670)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause85')).
% 2.31/2.55 tff(375,plain,
% 2.31/2.55 ((~hskp61) | c2_1(a670)),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[374, 373])).
% 2.31/2.55 tff(376,plain,
% 2.31/2.55 ((~hskp61) | c2_1(a670)),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[375, 373])).
% 2.31/2.55 tff(377,plain,
% 2.31/2.55 ((~hskp61) | c2_1(a670)),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[376, 373])).
% 2.31/2.55 tff(378,plain,
% 2.31/2.55 ((~hskp61) | c2_1(a670)),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[377, 373])).
% 2.31/2.55 tff(379,plain,
% 2.31/2.55 ((~hskp61) | c2_1(a670)),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[378, 373])).
% 2.31/2.55 tff(380,plain,
% 2.31/2.55 (c2_1(a670)),
% 2.31/2.55 inference(unit_resolution,[status(thm)],[379, 343])).
% 2.31/2.55 tff(381,assumption,(hskp37), introduced(assumption)).
% 2.31/2.55 tff(382,plain,
% 2.31/2.55 (((~hskp37) | (~c2_1(a607))) <=> ((~hskp37) | (~c2_1(a607)))),
% 2.31/2.55 inference(rewrite,[status(thm)],[])).
% 2.31/2.55 tff(383,plain,
% 2.31/2.55 (((~c2_1(a607)) | (~hskp37)) <=> ((~hskp37) | (~c2_1(a607)))),
% 2.31/2.55 inference(rewrite,[status(thm)],[])).
% 2.31/2.55 tff(384,axiom,((~c2_1(a607)) | (~hskp37)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause205')).
% 2.31/2.55 tff(385,plain,
% 2.31/2.55 ((~hskp37) | (~c2_1(a607))),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[384, 383])).
% 2.31/2.55 tff(386,plain,
% 2.31/2.55 ((~hskp37) | (~c2_1(a607))),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[385, 382])).
% 2.31/2.55 tff(387,plain,
% 2.31/2.55 (~c2_1(a607)),
% 2.31/2.55 inference(unit_resolution,[status(thm)],[386, 381])).
% 2.31/2.55 tff(388,plain,
% 2.31/2.55 (((~hskp37) | c0_1(a607)) <=> ((~hskp37) | c0_1(a607))),
% 2.31/2.55 inference(rewrite,[status(thm)],[])).
% 2.31/2.55 tff(389,axiom,((~hskp37) | c0_1(a607)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause130')).
% 2.31/2.55 tff(390,plain,
% 2.31/2.55 ((~hskp37) | c0_1(a607)),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[389, 388])).
% 2.31/2.55 tff(391,plain,
% 2.31/2.55 ((~hskp37) | c0_1(a607)),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[390, 388])).
% 2.31/2.55 tff(392,plain,
% 2.31/2.55 ((~hskp37) | c0_1(a607)),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[391, 388])).
% 2.31/2.55 tff(393,plain,
% 2.31/2.55 ((~hskp37) | c0_1(a607)),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[392, 388])).
% 2.31/2.55 tff(394,plain,
% 2.31/2.55 ((~hskp37) | c0_1(a607)),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[393, 388])).
% 2.31/2.55 tff(395,plain,
% 2.31/2.55 (c0_1(a607)),
% 2.31/2.55 inference(unit_resolution,[status(thm)],[394, 381])).
% 2.31/2.55 tff(396,plain,
% 2.31/2.55 (((~hskp37) | c1_1(a607)) <=> ((~hskp37) | c1_1(a607))),
% 2.31/2.55 inference(rewrite,[status(thm)],[])).
% 2.31/2.55 tff(397,axiom,((~hskp37) | c1_1(a607)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause129')).
% 2.31/2.55 tff(398,plain,
% 2.31/2.55 ((~hskp37) | c1_1(a607)),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[397, 396])).
% 2.31/2.55 tff(399,plain,
% 2.31/2.55 ((~hskp37) | c1_1(a607)),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[398, 396])).
% 2.31/2.55 tff(400,plain,
% 2.31/2.55 ((~hskp37) | c1_1(a607)),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[399, 396])).
% 2.31/2.55 tff(401,plain,
% 2.31/2.55 ((~hskp37) | c1_1(a607)),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[400, 396])).
% 2.31/2.55 tff(402,plain,
% 2.31/2.55 ((~hskp37) | c1_1(a607)),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[401, 396])).
% 2.31/2.55 tff(403,plain,
% 2.31/2.55 (c1_1(a607)),
% 2.31/2.55 inference(unit_resolution,[status(thm)],[402, 381])).
% 2.31/2.55 tff(404,plain,
% 2.31/2.55 (((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | c2_1(a675) | c2_1(a607) | (~ndr1_0) | (~c1_1(a675)) | (~c3_1(a675)) | (~c0_1(a607)) | (~c1_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp41 | c2_1(a675) | c2_1(a607) | (~ndr1_0) | (~c1_1(a675)) | (~c3_1(a675)) | (~c0_1(a607)) | (~c1_1(a607)))),
% 2.31/2.55 inference(rewrite,[status(thm)],[])).
% 2.31/2.55 tff(405,plain,
% 2.31/2.55 ((hskp41 | (~ndr1_0) | c2_1(a675) | (~c3_1(a675)) | (~c1_1(a675)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607))) <=> (hskp41 | c2_1(a675) | c2_1(a607) | (~ndr1_0) | (~c1_1(a675)) | (~c3_1(a675)) | (~c0_1(a607)) | (~c1_1(a607)))),
% 2.31/2.55 inference(rewrite,[status(thm)],[])).
% 2.31/2.55 tff(406,plain,
% 2.31/2.55 (((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | (~ndr1_0) | c2_1(a675) | (~c3_1(a675)) | (~c1_1(a675)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | c2_1(a675) | c2_1(a607) | (~ndr1_0) | (~c1_1(a675)) | (~c3_1(a675)) | (~c0_1(a607)) | (~c1_1(a607))))),
% 2.31/2.55 inference(monotonicity,[status(thm)],[405])).
% 2.31/2.55 tff(407,plain,
% 2.31/2.55 (((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | (~ndr1_0) | c2_1(a675) | (~c3_1(a675)) | (~c1_1(a675)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp41 | c2_1(a675) | c2_1(a607) | (~ndr1_0) | (~c1_1(a675)) | (~c3_1(a675)) | (~c0_1(a607)) | (~c1_1(a607)))),
% 2.31/2.55 inference(transitivity,[status(thm)],[406, 404])).
% 2.31/2.55 tff(408,plain,
% 2.31/2.55 ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | (~ndr1_0) | c2_1(a675) | (~c3_1(a675)) | (~c1_1(a675)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))),
% 2.31/2.55 inference(quant_inst,[status(thm)],[])).
% 2.31/2.55 tff(409,plain,
% 2.31/2.55 ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp41 | c2_1(a675) | c2_1(a607) | (~ndr1_0) | (~c1_1(a675)) | (~c3_1(a675)) | (~c0_1(a607)) | (~c1_1(a607))),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[408, 407])).
% 2.31/2.55 tff(410,plain,
% 2.31/2.55 ($false),
% 2.31/2.55 inference(unit_resolution,[status(thm)],[409, 87, 97, 325, 324, 403, 395, 307, 387, 299])).
% 2.31/2.55 tff(411,plain,((~hskp37) | hskp41 | (~c1_1(a675)) | (~c3_1(a675)) | c2_1(a675)), inference(lemma,lemma(discharge,[]))).
% 2.31/2.55 tff(412,plain,
% 2.31/2.55 (~hskp37),
% 2.31/2.55 inference(unit_resolution,[status(thm)],[411, 97, 289, 281, 273])).
% 2.31/2.55 tff(413,plain,
% 2.31/2.55 (((~![U: $i] : (hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp54 | hskp37 | c0_1(a670) | (~ndr1_0) | (~c2_1(a670)) | c3_1(a670))) <=> ((~![U: $i] : (hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp54 | hskp37 | c0_1(a670) | (~ndr1_0) | (~c2_1(a670)) | c3_1(a670))),
% 2.31/2.55 inference(rewrite,[status(thm)],[])).
% 2.31/2.55 tff(414,plain,
% 2.31/2.55 ((hskp54 | hskp37 | (~ndr1_0) | c3_1(a670) | c0_1(a670) | (~c2_1(a670))) <=> (hskp54 | hskp37 | c0_1(a670) | (~ndr1_0) | (~c2_1(a670)) | c3_1(a670))),
% 2.31/2.55 inference(rewrite,[status(thm)],[])).
% 2.31/2.55 tff(415,plain,
% 2.31/2.55 (((~![U: $i] : (hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp54 | hskp37 | (~ndr1_0) | c3_1(a670) | c0_1(a670) | (~c2_1(a670)))) <=> ((~![U: $i] : (hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp54 | hskp37 | c0_1(a670) | (~ndr1_0) | (~c2_1(a670)) | c3_1(a670)))),
% 2.31/2.55 inference(monotonicity,[status(thm)],[414])).
% 2.31/2.55 tff(416,plain,
% 2.31/2.55 (((~![U: $i] : (hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp54 | hskp37 | (~ndr1_0) | c3_1(a670) | c0_1(a670) | (~c2_1(a670)))) <=> ((~![U: $i] : (hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp54 | hskp37 | c0_1(a670) | (~ndr1_0) | (~c2_1(a670)) | c3_1(a670))),
% 2.31/2.55 inference(transitivity,[status(thm)],[415, 413])).
% 2.31/2.55 tff(417,plain,
% 2.31/2.55 ((~![U: $i] : (hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp54 | hskp37 | (~ndr1_0) | c3_1(a670) | c0_1(a670) | (~c2_1(a670)))),
% 2.31/2.55 inference(quant_inst,[status(thm)],[])).
% 2.31/2.55 tff(418,plain,
% 2.31/2.55 ((~![U: $i] : (hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp54 | hskp37 | c0_1(a670) | (~ndr1_0) | (~c2_1(a670)) | c3_1(a670)),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[417, 416])).
% 2.31/2.55 tff(419,plain,
% 2.31/2.55 (hskp54 | c3_1(a670)),
% 2.31/2.55 inference(unit_resolution,[status(thm)],[418, 87, 412, 380, 349, 372])).
% 2.31/2.55 tff(420,plain,
% 2.31/2.55 (hskp54),
% 2.31/2.55 inference(unit_resolution,[status(thm)],[419, 362])).
% 2.31/2.55 tff(421,plain,
% 2.31/2.55 (((~hskp54) | (~c0_1(a651))) <=> ((~hskp54) | (~c0_1(a651)))),
% 2.31/2.55 inference(rewrite,[status(thm)],[])).
% 2.31/2.55 tff(422,plain,
% 2.31/2.55 (((~c0_1(a651)) | (~hskp54)) <=> ((~hskp54) | (~c0_1(a651)))),
% 2.31/2.55 inference(rewrite,[status(thm)],[])).
% 2.31/2.55 tff(423,axiom,((~c0_1(a651)) | (~hskp54)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause186')).
% 2.31/2.55 tff(424,plain,
% 2.31/2.55 ((~hskp54) | (~c0_1(a651))),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[423, 422])).
% 2.31/2.55 tff(425,plain,
% 2.31/2.55 ((~hskp54) | (~c0_1(a651))),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[424, 421])).
% 2.31/2.55 tff(426,plain,
% 2.31/2.55 (~c0_1(a651)),
% 2.31/2.55 inference(unit_resolution,[status(thm)],[425, 420])).
% 2.31/2.55 tff(427,plain,
% 2.31/2.55 (((~hskp54) | c2_1(a651)) <=> ((~hskp54) | c2_1(a651))),
% 2.31/2.55 inference(rewrite,[status(thm)],[])).
% 2.31/2.55 tff(428,axiom,((~hskp54) | c2_1(a651)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause98')).
% 2.31/2.55 tff(429,plain,
% 2.31/2.55 ((~hskp54) | c2_1(a651)),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[428, 427])).
% 2.31/2.55 tff(430,plain,
% 2.31/2.55 ((~hskp54) | c2_1(a651)),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[429, 427])).
% 2.31/2.55 tff(431,plain,
% 2.31/2.55 ((~hskp54) | c2_1(a651)),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[430, 427])).
% 2.31/2.55 tff(432,plain,
% 2.31/2.55 ((~hskp54) | c2_1(a651)),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[431, 427])).
% 2.31/2.55 tff(433,plain,
% 2.31/2.55 ((~hskp54) | c2_1(a651)),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[432, 427])).
% 2.31/2.55 tff(434,plain,
% 2.31/2.55 (c2_1(a651)),
% 2.31/2.55 inference(unit_resolution,[status(thm)],[433, 420])).
% 2.31/2.55 tff(435,plain,
% 2.31/2.55 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (c0_1(a670) | c0_1(a651) | (~ndr1_0) | (~c2_1(a651)) | (~c1_1(a651)) | (~c2_1(a670)) | c3_1(a670))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | c0_1(a670) | c0_1(a651) | (~ndr1_0) | (~c2_1(a651)) | (~c1_1(a651)) | (~c2_1(a670)) | c3_1(a670))),
% 2.31/2.55 inference(rewrite,[status(thm)],[])).
% 2.31/2.55 tff(436,plain,
% 2.31/2.55 (((~ndr1_0) | c3_1(a670) | c0_1(a670) | (~c2_1(a670)) | c0_1(a651) | (~c2_1(a651)) | (~c1_1(a651))) <=> (c0_1(a670) | c0_1(a651) | (~ndr1_0) | (~c2_1(a651)) | (~c1_1(a651)) | (~c2_1(a670)) | c3_1(a670))),
% 2.31/2.55 inference(rewrite,[status(thm)],[])).
% 2.31/2.55 tff(437,plain,
% 2.31/2.55 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c3_1(a670) | c0_1(a670) | (~c2_1(a670)) | c0_1(a651) | (~c2_1(a651)) | (~c1_1(a651)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (c0_1(a670) | c0_1(a651) | (~ndr1_0) | (~c2_1(a651)) | (~c1_1(a651)) | (~c2_1(a670)) | c3_1(a670)))),
% 2.31/2.55 inference(monotonicity,[status(thm)],[436])).
% 2.31/2.55 tff(438,plain,
% 2.31/2.55 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c3_1(a670) | c0_1(a670) | (~c2_1(a670)) | c0_1(a651) | (~c2_1(a651)) | (~c1_1(a651)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | c0_1(a670) | c0_1(a651) | (~ndr1_0) | (~c2_1(a651)) | (~c1_1(a651)) | (~c2_1(a670)) | c3_1(a670))),
% 2.31/2.55 inference(transitivity,[status(thm)],[437, 435])).
% 2.31/2.55 tff(439,plain,
% 2.31/2.55 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c3_1(a670) | c0_1(a670) | (~c2_1(a670)) | c0_1(a651) | (~c2_1(a651)) | (~c1_1(a651)))),
% 2.31/2.55 inference(quant_inst,[status(thm)],[])).
% 2.31/2.55 tff(440,plain,
% 2.31/2.55 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | c0_1(a670) | c0_1(a651) | (~ndr1_0) | (~c2_1(a651)) | (~c1_1(a651)) | (~c2_1(a670)) | c3_1(a670)),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[439, 438])).
% 2.31/2.55 tff(441,plain,
% 2.31/2.55 (~c1_1(a651)),
% 2.31/2.55 inference(unit_resolution,[status(thm)],[440, 87, 380, 434, 349, 426, 23, 362])).
% 2.31/2.55 tff(442,plain,
% 2.31/2.55 (((~hskp54) | c3_1(a651)) <=> ((~hskp54) | c3_1(a651))),
% 2.31/2.55 inference(rewrite,[status(thm)],[])).
% 2.31/2.55 tff(443,axiom,((~hskp54) | c3_1(a651)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause97')).
% 2.31/2.55 tff(444,plain,
% 2.31/2.55 ((~hskp54) | c3_1(a651)),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[443, 442])).
% 2.31/2.55 tff(445,plain,
% 2.31/2.55 ((~hskp54) | c3_1(a651)),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[444, 442])).
% 2.31/2.55 tff(446,plain,
% 2.31/2.55 ((~hskp54) | c3_1(a651)),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[445, 442])).
% 2.31/2.55 tff(447,plain,
% 2.31/2.55 ((~hskp54) | c3_1(a651)),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[446, 442])).
% 2.31/2.55 tff(448,plain,
% 2.31/2.55 ((~hskp54) | c3_1(a651)),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[447, 442])).
% 2.31/2.55 tff(449,plain,
% 2.31/2.55 (c3_1(a651)),
% 2.31/2.55 inference(unit_resolution,[status(thm)],[448, 420])).
% 2.31/2.55 tff(450,plain,
% 2.31/2.55 (((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | c0_1(a651) | (~ndr1_0) | (~c3_1(a651)) | c1_1(a651))) <=> ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp53 | hskp17 | c0_1(a651) | (~ndr1_0) | (~c3_1(a651)) | c1_1(a651))),
% 2.31/2.55 inference(rewrite,[status(thm)],[])).
% 2.31/2.55 tff(451,plain,
% 2.31/2.55 ((hskp53 | hskp17 | (~ndr1_0) | c1_1(a651) | c0_1(a651) | (~c3_1(a651))) <=> (hskp53 | hskp17 | c0_1(a651) | (~ndr1_0) | (~c3_1(a651)) | c1_1(a651))),
% 2.31/2.55 inference(rewrite,[status(thm)],[])).
% 2.31/2.55 tff(452,plain,
% 2.31/2.55 (((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | (~ndr1_0) | c1_1(a651) | c0_1(a651) | (~c3_1(a651)))) <=> ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | c0_1(a651) | (~ndr1_0) | (~c3_1(a651)) | c1_1(a651)))),
% 2.31/2.55 inference(monotonicity,[status(thm)],[451])).
% 2.31/2.55 tff(453,plain,
% 2.31/2.55 (((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | (~ndr1_0) | c1_1(a651) | c0_1(a651) | (~c3_1(a651)))) <=> ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp53 | hskp17 | c0_1(a651) | (~ndr1_0) | (~c3_1(a651)) | c1_1(a651))),
% 2.31/2.55 inference(transitivity,[status(thm)],[452, 450])).
% 2.31/2.55 tff(454,plain,
% 2.31/2.55 ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | (~ndr1_0) | c1_1(a651) | c0_1(a651) | (~c3_1(a651)))),
% 2.31/2.55 inference(quant_inst,[status(thm)],[])).
% 2.31/2.55 tff(455,plain,
% 2.31/2.55 ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp53 | hskp17 | c0_1(a651) | (~ndr1_0) | (~c3_1(a651)) | c1_1(a651)),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[454, 453])).
% 2.31/2.55 tff(456,plain,
% 2.31/2.55 ($false),
% 2.31/2.55 inference(unit_resolution,[status(thm)],[455, 87, 35, 12, 449, 426, 34, 441])).
% 2.31/2.55 tff(457,plain,(hskp41 | hskp53 | hskp17 | hskp64), inference(lemma,lemma(discharge,[]))).
% 2.31/2.55 tff(458,plain,
% 2.31/2.55 (hskp41),
% 2.31/2.55 inference(unit_resolution,[status(thm)],[457, 35, 12, 24])).
% 2.31/2.55 tff(459,plain,
% 2.31/2.55 (((~hskp41) | (~c1_1(a617))) <=> ((~hskp41) | (~c1_1(a617)))),
% 2.31/2.55 inference(rewrite,[status(thm)],[])).
% 2.31/2.55 tff(460,plain,
% 2.31/2.55 (((~c1_1(a617)) | (~hskp41)) <=> ((~hskp41) | (~c1_1(a617)))),
% 2.31/2.55 inference(rewrite,[status(thm)],[])).
% 2.31/2.55 tff(461,axiom,((~c1_1(a617)) | (~hskp41)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause203')).
% 2.31/2.55 tff(462,plain,
% 2.31/2.55 ((~hskp41) | (~c1_1(a617))),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[461, 460])).
% 2.31/2.55 tff(463,plain,
% 2.31/2.55 ((~hskp41) | (~c1_1(a617))),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[462, 459])).
% 2.31/2.55 tff(464,plain,
% 2.31/2.55 (~c1_1(a617)),
% 2.31/2.55 inference(unit_resolution,[status(thm)],[463, 458])).
% 2.31/2.55 tff(465,plain,
% 2.31/2.55 (((~hskp41) | c3_1(a617)) <=> ((~hskp41) | c3_1(a617))),
% 2.31/2.55 inference(rewrite,[status(thm)],[])).
% 2.31/2.55 tff(466,axiom,((~hskp41) | c3_1(a617)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause120')).
% 2.31/2.55 tff(467,plain,
% 2.31/2.55 ((~hskp41) | c3_1(a617)),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[466, 465])).
% 2.31/2.55 tff(468,plain,
% 2.31/2.55 ((~hskp41) | c3_1(a617)),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[467, 465])).
% 2.31/2.55 tff(469,plain,
% 2.31/2.55 ((~hskp41) | c3_1(a617)),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[468, 465])).
% 2.31/2.55 tff(470,plain,
% 2.31/2.55 ((~hskp41) | c3_1(a617)),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[469, 465])).
% 2.31/2.55 tff(471,plain,
% 2.31/2.55 ((~hskp41) | c3_1(a617)),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[470, 465])).
% 2.31/2.55 tff(472,plain,
% 2.31/2.55 (c3_1(a617)),
% 2.31/2.55 inference(unit_resolution,[status(thm)],[471, 458])).
% 2.31/2.55 tff(473,plain,
% 2.31/2.55 (((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | c1_1(a617) | (~ndr1_0) | c0_1(a617) | (~c3_1(a617)))) <=> ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp53 | hskp17 | c1_1(a617) | (~ndr1_0) | c0_1(a617) | (~c3_1(a617)))),
% 2.31/2.55 inference(rewrite,[status(thm)],[])).
% 2.31/2.55 tff(474,plain,
% 2.31/2.55 ((hskp53 | hskp17 | (~ndr1_0) | c1_1(a617) | c0_1(a617) | (~c3_1(a617))) <=> (hskp53 | hskp17 | c1_1(a617) | (~ndr1_0) | c0_1(a617) | (~c3_1(a617)))),
% 2.31/2.55 inference(rewrite,[status(thm)],[])).
% 2.31/2.55 tff(475,plain,
% 2.31/2.55 (((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | (~ndr1_0) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)))) <=> ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | c1_1(a617) | (~ndr1_0) | c0_1(a617) | (~c3_1(a617))))),
% 2.31/2.55 inference(monotonicity,[status(thm)],[474])).
% 2.31/2.55 tff(476,plain,
% 2.31/2.55 (((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | (~ndr1_0) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)))) <=> ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp53 | hskp17 | c1_1(a617) | (~ndr1_0) | c0_1(a617) | (~c3_1(a617)))),
% 2.31/2.55 inference(transitivity,[status(thm)],[475, 473])).
% 2.31/2.55 tff(477,plain,
% 2.31/2.55 ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | (~ndr1_0) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)))),
% 2.31/2.55 inference(quant_inst,[status(thm)],[])).
% 2.31/2.55 tff(478,plain,
% 2.31/2.55 ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp53 | hskp17 | c1_1(a617) | (~ndr1_0) | c0_1(a617) | (~c3_1(a617))),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[477, 476])).
% 2.31/2.55 tff(479,plain,
% 2.31/2.55 (c0_1(a617)),
% 2.31/2.55 inference(unit_resolution,[status(thm)],[478, 87, 35, 12, 472, 464, 34])).
% 2.31/2.55 tff(480,plain,
% 2.31/2.55 (^[V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 2.31/2.55 inference(bind,[status(th)],[])).
% 2.31/2.55 tff(481,plain,
% 2.31/2.55 (![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 2.31/2.55 inference(quant_intro,[status(thm)],[480])).
% 2.31/2.55 tff(482,plain,
% 2.31/2.55 (![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 2.31/2.55 inference(rewrite,[status(thm)],[])).
% 2.31/2.55 tff(483,plain,
% 2.31/2.55 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(U))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c1_1(U))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c1_1(U))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(U))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(U))) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(U))) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(U))) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(U))) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(U))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c2_1(U))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c2_1(U))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(U))) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(U))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(U))) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(U))) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(U))) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(U))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 2.31/2.55 inference(bind,[status(th)],[])).
% 2.31/2.55 tff(484,plain,
% 2.31/2.55 (![V: $i, U: $i] : (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(U))) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(U))) | c1_1(V)) <=> ![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 2.31/2.55 inference(quant_intro,[status(thm)],[483])).
% 2.31/2.55 tff(485,axiom,(![V: $i, U: $i] : (((((((~c3_1(U)) | (~ndr1_0)) | (~c1_1(U))) | (~c0_1(V))) | (~c2_1(V))) | (~c2_1(U))) | c1_1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause316')).
% 2.31/2.55 tff(486,plain,
% 2.31/2.55 (![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[485, 484])).
% 2.31/2.55 tff(487,plain,
% 2.31/2.55 (![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[486, 482])).
% 2.31/2.55 tff(488,plain,(
% 2.31/2.55 ![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 2.31/2.55 inference(skolemize,[status(sab)],[487])).
% 2.31/2.55 tff(489,plain,
% 2.31/2.55 (![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[488, 481])).
% 2.31/2.55 tff(490,plain,
% 2.31/2.55 (((~hskp41) | c2_1(a617)) <=> ((~hskp41) | c2_1(a617))),
% 2.31/2.55 inference(rewrite,[status(thm)],[])).
% 2.31/2.55 tff(491,axiom,((~hskp41) | c2_1(a617)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause119')).
% 2.31/2.55 tff(492,plain,
% 2.31/2.55 ((~hskp41) | c2_1(a617)),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[491, 490])).
% 2.31/2.55 tff(493,plain,
% 2.31/2.55 ((~hskp41) | c2_1(a617)),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[492, 490])).
% 2.31/2.55 tff(494,plain,
% 2.31/2.55 ((~hskp41) | c2_1(a617)),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[493, 490])).
% 2.31/2.55 tff(495,plain,
% 2.31/2.55 ((~hskp41) | c2_1(a617)),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[494, 490])).
% 2.31/2.55 tff(496,plain,
% 2.31/2.55 ((~hskp41) | c2_1(a617)),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[495, 490])).
% 2.31/2.55 tff(497,plain,
% 2.31/2.55 (c2_1(a617)),
% 2.31/2.55 inference(unit_resolution,[status(thm)],[496, 458])).
% 2.31/2.55 tff(498,plain,
% 2.31/2.55 (^[V: $i, U: $i] : refl((hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))),
% 2.31/2.55 inference(bind,[status(th)],[])).
% 2.31/2.55 tff(499,plain,
% 2.31/2.55 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 2.31/2.55 inference(quant_intro,[status(thm)],[498])).
% 2.31/2.55 tff(500,plain,
% 2.31/2.55 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 2.31/2.55 inference(rewrite,[status(thm)],[])).
% 2.31/2.55 tff(501,plain,
% 2.31/2.55 (^[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(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c1_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c1_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c1_1(U)) | c2_1(V)) | hskp5) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp5))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c1_1(U)) | c2_1(V)) | hskp5) <=> (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))))),
% 2.31/2.55 inference(bind,[status(th)],[])).
% 2.31/2.55 tff(502,plain,
% 2.31/2.55 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c1_1(U)) | c2_1(V)) | hskp5) <=> ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 2.31/2.55 inference(quant_intro,[status(thm)],[501])).
% 2.31/2.55 tff(503,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c2_1(U)) | c1_1(U)) | c2_1(V)) | hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause312')).
% 2.31/2.55 tff(504,plain,
% 2.31/2.55 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[503, 502])).
% 2.31/2.55 tff(505,plain,
% 2.31/2.55 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[504, 500])).
% 2.31/2.55 tff(506,plain,(
% 2.31/2.55 ![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 2.31/2.55 inference(skolemize,[status(sab)],[505])).
% 2.31/2.55 tff(507,plain,
% 2.31/2.55 (![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[506, 499])).
% 2.31/2.55 tff(508,assumption,(hskp41), introduced(assumption)).
% 2.31/2.55 tff(509,plain,
% 2.31/2.55 (~c1_1(a617)),
% 2.31/2.55 inference(unit_resolution,[status(thm)],[463, 508])).
% 2.31/2.55 tff(510,plain,
% 2.31/2.55 (c3_1(a617)),
% 2.31/2.55 inference(unit_resolution,[status(thm)],[471, 508])).
% 2.31/2.55 tff(511,plain,
% 2.31/2.55 (c0_1(a617)),
% 2.31/2.55 inference(unit_resolution,[status(thm)],[478, 87, 35, 12, 510, 509, 34])).
% 2.31/2.55 tff(512,plain,
% 2.31/2.55 (^[U: $i] : refl((hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) <=> (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))))),
% 2.31/2.55 inference(bind,[status(th)],[])).
% 2.31/2.55 tff(513,plain,
% 2.31/2.55 (![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 2.31/2.55 inference(quant_intro,[status(thm)],[512])).
% 2.31/2.55 tff(514,plain,
% 2.31/2.55 (![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) <=> ![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 2.31/2.55 inference(rewrite,[status(thm)],[])).
% 2.31/2.55 tff(515,plain,
% 2.31/2.55 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp5) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | hskp5))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | hskp5) <=> (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp5) <=> (hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp5) | hskp37) <=> ((hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | hskp37))), rewrite(((hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | hskp37) <=> (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp5) | hskp37) <=> (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))))),
% 2.31/2.55 inference(bind,[status(th)],[])).
% 2.31/2.55 tff(516,plain,
% 2.31/2.55 (![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp5) | hskp37) <=> ![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 2.31/2.55 inference(quant_intro,[status(thm)],[515])).
% 2.31/2.55 tff(517,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp5) | hskp37)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause298')).
% 2.31/2.55 tff(518,plain,
% 2.31/2.55 (![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[517, 516])).
% 2.31/2.55 tff(519,plain,
% 2.31/2.55 (![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[518, 514])).
% 2.31/2.55 tff(520,plain,(
% 2.31/2.55 ![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 2.31/2.55 inference(skolemize,[status(sab)],[519])).
% 2.31/2.55 tff(521,plain,
% 2.31/2.55 (![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[520, 513])).
% 2.31/2.55 tff(522,plain,
% 2.31/2.55 (c2_1(a617)),
% 2.31/2.55 inference(unit_resolution,[status(thm)],[496, 508])).
% 2.31/2.55 tff(523,assumption,(~hskp5), introduced(assumption)).
% 2.31/2.55 tff(524,plain,
% 2.31/2.55 (((~![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp37 | hskp5 | (~ndr1_0) | (~c2_1(a617)) | (~c3_1(a617)) | (~c0_1(a617)))) <=> ((~![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp37 | hskp5 | (~ndr1_0) | (~c2_1(a617)) | (~c3_1(a617)) | (~c0_1(a617)))),
% 2.31/2.55 inference(rewrite,[status(thm)],[])).
% 2.31/2.55 tff(525,plain,
% 2.31/2.55 ((hskp37 | hskp5 | (~ndr1_0) | (~c3_1(a617)) | (~c0_1(a617)) | (~c2_1(a617))) <=> (hskp37 | hskp5 | (~ndr1_0) | (~c2_1(a617)) | (~c3_1(a617)) | (~c0_1(a617)))),
% 2.31/2.55 inference(rewrite,[status(thm)],[])).
% 2.31/2.55 tff(526,plain,
% 2.31/2.55 (((~![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(a617)) | (~c0_1(a617)) | (~c2_1(a617)))) <=> ((~![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp37 | hskp5 | (~ndr1_0) | (~c2_1(a617)) | (~c3_1(a617)) | (~c0_1(a617))))),
% 2.31/2.55 inference(monotonicity,[status(thm)],[525])).
% 2.31/2.55 tff(527,plain,
% 2.31/2.55 (((~![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(a617)) | (~c0_1(a617)) | (~c2_1(a617)))) <=> ((~![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp37 | hskp5 | (~ndr1_0) | (~c2_1(a617)) | (~c3_1(a617)) | (~c0_1(a617)))),
% 2.31/2.55 inference(transitivity,[status(thm)],[526, 524])).
% 2.31/2.55 tff(528,plain,
% 2.31/2.55 ((~![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(a617)) | (~c0_1(a617)) | (~c2_1(a617)))),
% 2.31/2.55 inference(quant_inst,[status(thm)],[])).
% 2.31/2.55 tff(529,plain,
% 2.31/2.55 ((~![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp37 | hskp5 | (~ndr1_0) | (~c2_1(a617)) | (~c3_1(a617)) | (~c0_1(a617))),
% 2.31/2.55 inference(modus_ponens,[status(thm)],[528, 527])).
% 2.31/2.55 tff(530,plain,
% 2.31/2.55 (hskp37 | (~c0_1(a617))),
% 2.31/2.55 inference(unit_resolution,[status(thm)],[529, 87, 523, 522, 510, 521])).
% 2.31/2.55 tff(531,plain,
% 2.31/2.55 (hskp37),
% 2.31/2.55 inference(unit_resolution,[status(thm)],[530, 511])).
% 2.31/2.55 tff(532,plain,
% 2.31/2.55 (~c2_1(a607)),
% 2.31/2.55 inference(unit_resolution,[status(thm)],[386, 531])).
% 2.31/2.55 tff(533,plain,
% 2.31/2.55 (c0_1(a607)),
% 2.31/2.55 inference(unit_resolution,[status(thm)],[394, 531])).
% 2.31/2.55 tff(534,plain,
% 2.31/2.55 (c1_1(a607)),
% 2.31/2.55 inference(unit_resolution,[status(thm)],[402, 531])).
% 2.31/2.55 tff(535,assumption,(~c2_1(a607)), introduced(assumption)).
% 2.31/2.55 tff(536,assumption,(c0_1(a607)), introduced(assumption)).
% 2.31/2.55 tff(537,assumption,(c1_1(a607)), introduced(assumption)).
% 2.31/2.55 tff(538,plain,
% 2.31/2.55 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a607) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | (~c3_1(a624)) | (~c0_1(a607)) | (~c1_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a607) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | (~c3_1(a624)) | (~c0_1(a607)) | (~c1_1(a607)))),
% 2.31/2.55 inference(rewrite,[status(thm)],[])).
% 2.31/2.55 tff(539,plain,
% 2.31/2.55 ((hskp5 | (~ndr1_0) | c1_1(a624) | c2_1(a624) | (~c3_1(a624)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607))) <=> (hskp5 | c2_1(a607) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | (~c3_1(a624)) | (~c0_1(a607)) | (~c1_1(a607)))),
% 2.31/2.55 inference(rewrite,[status(thm)],[])).
% 2.31/2.55 tff(540,plain,
% 2.31/2.55 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a624) | c2_1(a624) | (~c3_1(a624)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a607) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | (~c3_1(a624)) | (~c0_1(a607)) | (~c1_1(a607))))),
% 2.31/2.56 inference(monotonicity,[status(thm)],[539])).
% 2.31/2.56 tff(541,plain,
% 2.31/2.56 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a624) | c2_1(a624) | (~c3_1(a624)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a607) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | (~c3_1(a624)) | (~c0_1(a607)) | (~c1_1(a607)))),
% 2.31/2.56 inference(transitivity,[status(thm)],[540, 538])).
% 2.31/2.56 tff(542,plain,
% 2.31/2.56 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a624) | c2_1(a624) | (~c3_1(a624)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))),
% 2.31/2.56 inference(quant_inst,[status(thm)],[])).
% 2.31/2.56 tff(543,plain,
% 2.31/2.56 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a607) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | (~c3_1(a624)) | (~c0_1(a607)) | (~c1_1(a607))),
% 2.31/2.56 inference(modus_ponens,[status(thm)],[542, 541])).
% 2.31/2.56 tff(544,plain,
% 2.31/2.56 ($false),
% 2.31/2.56 inference(unit_resolution,[status(thm)],[543, 87, 523, 537, 536, 200, 535, 213, 192, 507])).
% 2.31/2.56 tff(545,plain,((~hskp14) | hskp5 | (~c1_1(a607)) | (~c0_1(a607)) | c2_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.31/2.56 tff(546,plain,
% 2.31/2.56 (~hskp14),
% 2.31/2.56 inference(unit_resolution,[status(thm)],[545, 534, 523, 533, 532])).
% 2.31/2.56 tff(547,plain,
% 2.31/2.56 (((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp15 | hskp14 | c1_1(a617) | (~ndr1_0) | (~c2_1(a617)) | (~c0_1(a617)))) <=> ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp15 | hskp14 | c1_1(a617) | (~ndr1_0) | (~c2_1(a617)) | (~c0_1(a617)))),
% 2.31/2.56 inference(rewrite,[status(thm)],[])).
% 2.31/2.56 tff(548,plain,
% 2.31/2.56 ((hskp15 | hskp14 | (~ndr1_0) | c1_1(a617) | (~c0_1(a617)) | (~c2_1(a617))) <=> (hskp15 | hskp14 | c1_1(a617) | (~ndr1_0) | (~c2_1(a617)) | (~c0_1(a617)))),
% 2.31/2.56 inference(rewrite,[status(thm)],[])).
% 2.31/2.56 tff(549,plain,
% 2.31/2.56 (((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp15 | hskp14 | (~ndr1_0) | c1_1(a617) | (~c0_1(a617)) | (~c2_1(a617)))) <=> ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp15 | hskp14 | c1_1(a617) | (~ndr1_0) | (~c2_1(a617)) | (~c0_1(a617))))),
% 2.31/2.56 inference(monotonicity,[status(thm)],[548])).
% 2.31/2.56 tff(550,plain,
% 2.31/2.56 (((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp15 | hskp14 | (~ndr1_0) | c1_1(a617) | (~c0_1(a617)) | (~c2_1(a617)))) <=> ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp15 | hskp14 | c1_1(a617) | (~ndr1_0) | (~c2_1(a617)) | (~c0_1(a617)))),
% 2.31/2.56 inference(transitivity,[status(thm)],[549, 547])).
% 2.31/2.56 tff(551,plain,
% 2.31/2.56 ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp15 | hskp14 | (~ndr1_0) | c1_1(a617) | (~c0_1(a617)) | (~c2_1(a617)))),
% 2.31/2.56 inference(quant_inst,[status(thm)],[])).
% 2.31/2.56 tff(552,plain,
% 2.31/2.56 ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp15 | hskp14 | c1_1(a617) | (~ndr1_0) | (~c2_1(a617)) | (~c0_1(a617))),
% 2.31/2.56 inference(modus_ponens,[status(thm)],[551, 550])).
% 2.31/2.56 tff(553,plain,
% 2.31/2.56 (~c0_1(a617)),
% 2.31/2.56 inference(unit_resolution,[status(thm)],[552, 87, 257, 256, 522, 509, 232])).
% 2.31/2.56 tff(554,plain,
% 2.31/2.56 ($false),
% 2.31/2.56 inference(unit_resolution,[status(thm)],[478, 87, 35, 12, 510, 509, 34, 553])).
% 2.31/2.56 tff(555,plain,((~hskp41) | hskp53 | hskp17 | hskp15 | hskp14), inference(lemma,lemma(discharge,[]))).
% 2.31/2.56 tff(556,plain,
% 2.31/2.56 (hskp15),
% 2.31/2.56 inference(unit_resolution,[status(thm)],[555, 546, 12, 35, 508])).
% 2.31/2.56 tff(557,plain,
% 2.31/2.56 (~c1_1(a625)),
% 2.31/2.56 inference(unit_resolution,[status(thm)],[152, 556])).
% 2.31/2.56 tff(558,plain,
% 2.31/2.56 (~c2_1(a625)),
% 2.31/2.56 inference(unit_resolution,[status(thm)],[175, 556])).
% 2.31/2.56 tff(559,plain,
% 2.31/2.56 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a607) | c2_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c0_1(a607)) | (~c1_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a607) | c2_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c0_1(a607)) | (~c1_1(a607)))),
% 2.31/2.56 inference(rewrite,[status(thm)],[])).
% 2.31/2.56 tff(560,plain,
% 2.31/2.56 ((hskp5 | (~ndr1_0) | c1_1(a625) | c2_1(a625) | (~c3_1(a625)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607))) <=> (hskp5 | c2_1(a607) | c2_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c0_1(a607)) | (~c1_1(a607)))),
% 2.31/2.56 inference(rewrite,[status(thm)],[])).
% 2.31/2.56 tff(561,plain,
% 2.31/2.56 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a625) | c2_1(a625) | (~c3_1(a625)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a607) | c2_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c0_1(a607)) | (~c1_1(a607))))),
% 2.31/2.56 inference(monotonicity,[status(thm)],[560])).
% 2.31/2.56 tff(562,plain,
% 2.31/2.56 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a625) | c2_1(a625) | (~c3_1(a625)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a607) | c2_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c0_1(a607)) | (~c1_1(a607)))),
% 2.31/2.56 inference(transitivity,[status(thm)],[561, 559])).
% 2.31/2.56 tff(563,plain,
% 2.31/2.56 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a625) | c2_1(a625) | (~c3_1(a625)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))),
% 2.31/2.56 inference(quant_inst,[status(thm)],[])).
% 2.31/2.56 tff(564,plain,
% 2.31/2.56 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a607) | c2_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c0_1(a607)) | (~c1_1(a607))),
% 2.31/2.56 inference(modus_ponens,[status(thm)],[563, 562])).
% 2.31/2.56 tff(565,plain,
% 2.31/2.56 (~c3_1(a625)),
% 2.31/2.56 inference(unit_resolution,[status(thm)],[564, 87, 523, 534, 533, 532, 558, 557, 507])).
% 2.31/2.56 tff(566,plain,
% 2.31/2.56 (~c0_1(a625)),
% 2.31/2.56 inference(unit_resolution,[status(thm)],[146, 556])).
% 2.31/2.56 tff(567,plain,
% 2.31/2.56 ($false),
% 2.31/2.56 inference(unit_resolution,[status(thm)],[182, 87, 558, 557, 566, 170, 565])).
% 2.31/2.56 tff(568,plain,((~hskp41) | hskp5 | hskp17 | hskp53), inference(lemma,lemma(discharge,[]))).
% 2.31/2.56 tff(569,plain,
% 2.31/2.56 (hskp5),
% 2.31/2.56 inference(unit_resolution,[status(thm)],[568, 458, 12, 35])).
% 2.31/2.56 tff(570,plain,
% 2.31/2.56 (((~hskp5) | (~c3_1(a606))) <=> ((~hskp5) | (~c3_1(a606)))),
% 2.31/2.56 inference(rewrite,[status(thm)],[])).
% 2.31/2.56 tff(571,plain,
% 2.31/2.56 (((~c3_1(a606)) | (~hskp5)) <=> ((~hskp5) | (~c3_1(a606)))),
% 2.31/2.56 inference(rewrite,[status(thm)],[])).
% 2.31/2.56 tff(572,axiom,((~c3_1(a606)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause266')).
% 2.31/2.56 tff(573,plain,
% 2.31/2.56 ((~hskp5) | (~c3_1(a606))),
% 2.31/2.56 inference(modus_ponens,[status(thm)],[572, 571])).
% 2.31/2.56 tff(574,plain,
% 2.31/2.56 ((~hskp5) | (~c3_1(a606))),
% 2.31/2.56 inference(modus_ponens,[status(thm)],[573, 570])).
% 2.31/2.56 tff(575,plain,
% 2.31/2.56 (~c3_1(a606)),
% 2.31/2.56 inference(unit_resolution,[status(thm)],[574, 569])).
% 2.31/2.56 tff(576,plain,
% 2.31/2.56 (((~hskp5) | (~c0_1(a606))) <=> ((~hskp5) | (~c0_1(a606)))),
% 2.31/2.56 inference(rewrite,[status(thm)],[])).
% 2.31/2.56 tff(577,plain,
% 2.31/2.56 (((~c0_1(a606)) | (~hskp5)) <=> ((~hskp5) | (~c0_1(a606)))),
% 2.31/2.56 inference(rewrite,[status(thm)],[])).
% 2.31/2.56 tff(578,axiom,((~c0_1(a606)) | (~hskp5)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause265')).
% 2.31/2.56 tff(579,plain,
% 2.31/2.56 ((~hskp5) | (~c0_1(a606))),
% 2.31/2.56 inference(modus_ponens,[status(thm)],[578, 577])).
% 2.31/2.56 tff(580,plain,
% 2.31/2.56 ((~hskp5) | (~c0_1(a606))),
% 2.31/2.56 inference(modus_ponens,[status(thm)],[579, 576])).
% 2.31/2.56 tff(581,plain,
% 2.31/2.56 (~c0_1(a606)),
% 2.31/2.56 inference(unit_resolution,[status(thm)],[580, 569])).
% 2.31/2.56 tff(582,plain,
% 2.31/2.56 (((~hskp5) | c2_1(a606)) <=> ((~hskp5) | c2_1(a606))),
% 2.31/2.56 inference(rewrite,[status(thm)],[])).
% 2.31/2.56 tff(583,axiom,((~hskp5) | c2_1(a606)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause165')).
% 2.31/2.56 tff(584,plain,
% 2.31/2.56 ((~hskp5) | c2_1(a606)),
% 2.31/2.56 inference(modus_ponens,[status(thm)],[583, 582])).
% 2.31/2.56 tff(585,plain,
% 2.31/2.56 ((~hskp5) | c2_1(a606)),
% 2.31/2.56 inference(modus_ponens,[status(thm)],[584, 582])).
% 2.31/2.56 tff(586,plain,
% 2.31/2.56 ((~hskp5) | c2_1(a606)),
% 2.31/2.56 inference(modus_ponens,[status(thm)],[585, 582])).
% 2.31/2.56 tff(587,plain,
% 2.31/2.56 ((~hskp5) | c2_1(a606)),
% 2.31/2.56 inference(modus_ponens,[status(thm)],[586, 582])).
% 2.31/2.56 tff(588,plain,
% 2.31/2.56 ((~hskp5) | c2_1(a606)),
% 2.31/2.56 inference(modus_ponens,[status(thm)],[587, 582])).
% 2.31/2.56 tff(589,plain,
% 2.31/2.56 (c2_1(a606)),
% 2.31/2.56 inference(unit_resolution,[status(thm)],[588, 569])).
% 2.31/2.56 tff(590,plain,
% 2.31/2.56 (^[V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)))),
% 2.31/2.56 inference(bind,[status(th)],[])).
% 2.31/2.56 tff(591,plain,
% 2.31/2.56 (![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))),
% 2.31/2.56 inference(quant_intro,[status(thm)],[590])).
% 2.31/2.56 tff(592,plain,
% 2.31/2.56 (![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))),
% 2.31/2.56 inference(rewrite,[status(thm)],[])).
% 2.31/2.56 tff(593,plain,
% 2.31/2.56 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), (((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | c1_1(V))), (((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | c1_1(V)))), ((((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | c1_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V))), ((((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V)))), (((((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V)) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V))), (((((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V)))), ((((((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(U)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))), ((((((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(U)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))))),
% 2.31/2.56 inference(bind,[status(th)],[])).
% 2.31/2.56 tff(594,plain,
% 2.31/2.56 (![V: $i, U: $i] : (((((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(U)) | c3_1(V)) <=> ![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))),
% 2.31/2.56 inference(quant_intro,[status(thm)],[593])).
% 2.31/2.56 tff(595,axiom,(![V: $i, U: $i] : (((((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) | c1_1(V)) | c2_1(V)) | c3_1(U)) | c3_1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause299')).
% 2.31/2.56 tff(596,plain,
% 2.31/2.56 (![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))),
% 2.31/2.56 inference(modus_ponens,[status(thm)],[595, 594])).
% 2.31/2.56 tff(597,plain,
% 2.31/2.56 (![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))),
% 2.31/2.56 inference(modus_ponens,[status(thm)],[596, 592])).
% 2.31/2.56 tff(598,plain,(
% 2.31/2.56 ![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))),
% 2.31/2.56 inference(skolemize,[status(sab)],[597])).
% 2.31/2.56 tff(599,plain,
% 2.31/2.56 (![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))),
% 2.31/2.56 inference(modus_ponens,[status(thm)],[598, 591])).
% 2.31/2.56 tff(600,assumption,(~c3_1(a606)), introduced(assumption)).
% 2.31/2.56 tff(601,assumption,(~c0_1(a606)), introduced(assumption)).
% 2.31/2.56 tff(602,assumption,(hskp20), introduced(assumption)).
% 2.31/2.56 tff(603,plain,
% 2.31/2.56 (((~hskp20) | (~c3_1(a635))) <=> ((~hskp20) | (~c3_1(a635)))),
% 2.31/2.56 inference(rewrite,[status(thm)],[])).
% 2.31/2.56 tff(604,plain,
% 2.31/2.56 (((~c3_1(a635)) | (~hskp20)) <=> ((~hskp20) | (~c3_1(a635)))),
% 2.31/2.56 inference(rewrite,[status(thm)],[])).
% 2.31/2.56 tff(605,axiom,((~c3_1(a635)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause237')).
% 2.31/2.56 tff(606,plain,
% 2.31/2.56 ((~hskp20) | (~c3_1(a635))),
% 2.31/2.56 inference(modus_ponens,[status(thm)],[605, 604])).
% 2.31/2.56 tff(607,plain,
% 2.31/2.56 ((~hskp20) | (~c3_1(a635))),
% 2.31/2.56 inference(modus_ponens,[status(thm)],[606, 603])).
% 2.31/2.56 tff(608,plain,
% 2.31/2.56 (~c3_1(a635)),
% 2.31/2.56 inference(unit_resolution,[status(thm)],[607, 602])).
% 2.31/2.56 tff(609,plain,
% 2.31/2.56 (((~hskp20) | (~c2_1(a635))) <=> ((~hskp20) | (~c2_1(a635)))),
% 2.31/2.56 inference(rewrite,[status(thm)],[])).
% 2.31/2.56 tff(610,plain,
% 2.31/2.56 (((~c2_1(a635)) | (~hskp20)) <=> ((~hskp20) | (~c2_1(a635)))),
% 2.31/2.56 inference(rewrite,[status(thm)],[])).
% 2.31/2.56 tff(611,axiom,((~c2_1(a635)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause236')).
% 2.31/2.56 tff(612,plain,
% 2.31/2.56 ((~hskp20) | (~c2_1(a635))),
% 2.31/2.56 inference(modus_ponens,[status(thm)],[611, 610])).
% 2.31/2.56 tff(613,plain,
% 2.31/2.56 ((~hskp20) | (~c2_1(a635))),
% 2.31/2.56 inference(modus_ponens,[status(thm)],[612, 609])).
% 2.31/2.56 tff(614,plain,
% 2.31/2.56 (~c2_1(a635)),
% 2.31/2.56 inference(unit_resolution,[status(thm)],[613, 602])).
% 2.31/2.56 tff(615,plain,
% 2.31/2.56 (((~hskp20) | (~c1_1(a635))) <=> ((~hskp20) | (~c1_1(a635)))),
% 2.31/2.56 inference(rewrite,[status(thm)],[])).
% 2.31/2.56 tff(616,plain,
% 2.31/2.56 (((~c1_1(a635)) | (~hskp20)) <=> ((~hskp20) | (~c1_1(a635)))),
% 2.31/2.56 inference(rewrite,[status(thm)],[])).
% 2.31/2.56 tff(617,axiom,((~c1_1(a635)) | (~hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause235')).
% 2.31/2.56 tff(618,plain,
% 2.31/2.56 ((~hskp20) | (~c1_1(a635))),
% 2.31/2.56 inference(modus_ponens,[status(thm)],[617, 616])).
% 2.31/2.56 tff(619,plain,
% 2.31/2.56 ((~hskp20) | (~c1_1(a635))),
% 2.31/2.56 inference(modus_ponens,[status(thm)],[618, 615])).
% 2.31/2.56 tff(620,plain,
% 2.31/2.56 (~c1_1(a635)),
% 2.31/2.56 inference(unit_resolution,[status(thm)],[619, 602])).
% 2.31/2.56 tff(621,assumption,(c2_1(a606)), introduced(assumption)).
% 2.31/2.56 tff(622,plain,
% 2.31/2.56 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (c1_1(a635) | c2_1(a635) | c3_1(a635) | c0_1(a606) | c3_1(a606) | (~ndr1_0) | (~c2_1(a606)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | c1_1(a635) | c2_1(a635) | c3_1(a635) | c0_1(a606) | c3_1(a606) | (~ndr1_0) | (~c2_1(a606)))),
% 2.31/2.56 inference(rewrite,[status(thm)],[])).
% 2.31/2.56 tff(623,plain,
% 2.31/2.56 (((~ndr1_0) | c3_1(a606) | c0_1(a606) | (~c2_1(a606)) | c1_1(a635) | c3_1(a635) | c2_1(a635)) <=> (c1_1(a635) | c2_1(a635) | c3_1(a635) | c0_1(a606) | c3_1(a606) | (~ndr1_0) | (~c2_1(a606)))),
% 2.31/2.56 inference(rewrite,[status(thm)],[])).
% 2.31/2.56 tff(624,plain,
% 2.31/2.56 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | ((~ndr1_0) | c3_1(a606) | c0_1(a606) | (~c2_1(a606)) | c1_1(a635) | c3_1(a635) | c2_1(a635))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (c1_1(a635) | c2_1(a635) | c3_1(a635) | c0_1(a606) | c3_1(a606) | (~ndr1_0) | (~c2_1(a606))))),
% 2.31/2.56 inference(monotonicity,[status(thm)],[623])).
% 2.31/2.56 tff(625,plain,
% 2.31/2.56 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | ((~ndr1_0) | c3_1(a606) | c0_1(a606) | (~c2_1(a606)) | c1_1(a635) | c3_1(a635) | c2_1(a635))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | c1_1(a635) | c2_1(a635) | c3_1(a635) | c0_1(a606) | c3_1(a606) | (~ndr1_0) | (~c2_1(a606)))),
% 2.31/2.56 inference(transitivity,[status(thm)],[624, 622])).
% 2.31/2.56 tff(626,plain,
% 2.31/2.56 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | ((~ndr1_0) | c3_1(a606) | c0_1(a606) | (~c2_1(a606)) | c1_1(a635) | c3_1(a635) | c2_1(a635))),
% 2.31/2.56 inference(quant_inst,[status(thm)],[])).
% 2.31/2.56 tff(627,plain,
% 2.31/2.56 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | c1_1(a635) | c2_1(a635) | c3_1(a635) | c0_1(a606) | c3_1(a606) | (~ndr1_0) | (~c2_1(a606))),
% 2.31/2.56 inference(modus_ponens,[status(thm)],[626, 625])).
% 2.31/2.56 tff(628,plain,
% 2.31/2.56 ($false),
% 2.31/2.56 inference(unit_resolution,[status(thm)],[627, 87, 621, 620, 614, 608, 601, 600, 599])).
% 2.31/2.56 tff(629,plain,((~hskp20) | (~c2_1(a606)) | c0_1(a606) | c3_1(a606)), inference(lemma,lemma(discharge,[]))).
% 2.31/2.56 tff(630,plain,
% 2.31/2.56 (~hskp20),
% 2.31/2.56 inference(unit_resolution,[status(thm)],[629, 589, 581, 575])).
% 2.31/2.56 tff(631,plain,
% 2.31/2.56 (hskp14),
% 2.31/2.56 inference(unit_resolution,[status(thm)],[555, 458, 12, 35, 185])).
% 2.31/2.56 tff(632,plain,
% 2.31/2.56 (~c2_1(a624)),
% 2.31/2.56 inference(unit_resolution,[status(thm)],[191, 631])).
% 2.31/2.56 tff(633,plain,
% 2.31/2.56 (~c1_1(a624)),
% 2.31/2.56 inference(unit_resolution,[status(thm)],[212, 631])).
% 2.31/2.56 tff(634,plain,
% 2.31/2.56 (c3_1(a624)),
% 2.31/2.56 inference(unit_resolution,[status(thm)],[199, 631])).
% 2.31/2.56 tff(635,assumption,(c0_1(a617)), introduced(assumption)).
% 2.31/2.56 tff(636,plain,
% 2.31/2.56 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))))),
% 2.31/2.56 inference(bind,[status(th)],[])).
% 2.31/2.56 tff(637,plain,
% 2.31/2.56 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 2.31/2.56 inference(quant_intro,[status(thm)],[636])).
% 2.31/2.56 tff(638,plain,
% 2.31/2.56 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 2.31/2.56 inference(rewrite,[status(thm)],[])).
% 2.31/2.56 tff(639,plain,
% 2.31/2.56 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~c2_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)))), ((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), ((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))))), (((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)))), (((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))))), ((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)))), (((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W))))), ((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | (~c3_1(W))) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)))), ((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | (~c3_1(W))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W))))), (((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | (~c3_1(W))) | c0_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W)))), (((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | (~c3_1(W))) | c0_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W))))), ((((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | (~c3_1(W))) | c0_1(U)) | c1_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c3_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W)))), ((((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | (~c3_1(W))) | c0_1(U)) | c1_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W))))), (((((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | (~c3_1(W))) | c0_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c1_1(W) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))), (((((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | (~c3_1(W))) | c0_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))))),
% 2.31/2.56 inference(bind,[status(th)],[])).
% 2.31/2.56 tff(640,plain,
% 2.31/2.56 (![W: $i, V: $i, U: $i] : ((((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | (~c3_1(W))) | c0_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 2.31/2.56 inference(quant_intro,[status(thm)],[639])).
% 2.31/2.56 tff(641,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | (~c3_1(W))) | c0_1(U)) | c1_1(V)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause325')).
% 2.31/2.56 tff(642,plain,
% 2.31/2.56 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 2.31/2.56 inference(modus_ponens,[status(thm)],[641, 640])).
% 2.31/2.56 tff(643,plain,
% 2.31/2.56 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 2.31/2.56 inference(modus_ponens,[status(thm)],[642, 638])).
% 2.31/2.56 tff(644,plain,(
% 2.31/2.56 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 2.31/2.56 inference(skolemize,[status(sab)],[643])).
% 2.31/2.56 tff(645,plain,
% 2.31/2.56 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))),
% 2.31/2.56 inference(modus_ponens,[status(thm)],[644, 637])).
% 2.31/2.56 tff(646,assumption,(~hskp20), introduced(assumption)).
% 2.31/2.56 tff(647,assumption,(~c1_1(a617)), introduced(assumption)).
% 2.31/2.56 tff(648,assumption,(c3_1(a617)), introduced(assumption)).
% 2.31/2.56 tff(649,assumption,(c2_1(a617)), introduced(assumption)).
% 2.31/2.56 tff(650,assumption,(~c3_1(a607)), introduced(assumption)).
% 2.31/2.56 tff(651,plain,
% 2.31/2.56 (^[V: $i, U: $i] : refl((hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V))))),
% 2.31/2.56 inference(bind,[status(th)],[])).
% 2.31/2.56 tff(652,plain,
% 2.31/2.56 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 2.31/2.56 inference(quant_intro,[status(thm)],[651])).
% 2.31/2.56 tff(653,plain,
% 2.31/2.56 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 2.31/2.56 inference(rewrite,[status(thm)],[])).
% 2.31/2.56 tff(654,plain,
% 2.31/2.56 (^[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))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(U)) | c1_1(V)) | hskp20) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp20))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp20) <=> (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(U)) | c1_1(V)) | hskp20) <=> (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))))),
% 2.31/2.56 inference(bind,[status(th)],[])).
% 2.31/2.56 tff(655,plain,
% 2.31/2.56 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(U)) | c1_1(V)) | hskp20) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 2.31/2.56 inference(quant_intro,[status(thm)],[654])).
% 2.31/2.56 tff(656,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | c3_1(U)) | c2_1(U)) | c1_1(V)) | hskp20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause311')).
% 2.31/2.56 tff(657,plain,
% 2.31/2.56 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 2.31/2.56 inference(modus_ponens,[status(thm)],[656, 655])).
% 2.31/2.56 tff(658,plain,
% 2.31/2.56 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 2.31/2.56 inference(modus_ponens,[status(thm)],[657, 653])).
% 2.31/2.56 tff(659,plain,(
% 2.31/2.56 ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 2.31/2.56 inference(skolemize,[status(sab)],[658])).
% 2.31/2.56 tff(660,plain,
% 2.31/2.56 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 2.31/2.56 inference(modus_ponens,[status(thm)],[659, 652])).
% 2.31/2.56 tff(661,plain,
% 2.31/2.56 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | c1_1(a617) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | c3_1(a607) | (~c2_1(a617)) | (~c3_1(a617)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp20 | c1_1(a617) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | c3_1(a607) | (~c2_1(a617)) | (~c3_1(a617)))),
% 2.31/2.56 inference(rewrite,[status(thm)],[])).
% 2.31/2.56 tff(662,plain,
% 2.31/2.56 ((hskp20 | (~ndr1_0) | c3_1(a607) | c2_1(a607) | (~c0_1(a607)) | c1_1(a617) | (~c2_1(a617)) | (~c3_1(a617))) <=> (hskp20 | c1_1(a617) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | c3_1(a607) | (~c2_1(a617)) | (~c3_1(a617)))),
% 2.31/2.56 inference(rewrite,[status(thm)],[])).
% 2.31/2.56 tff(663,plain,
% 2.31/2.56 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a607) | c2_1(a607) | (~c0_1(a607)) | c1_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | c1_1(a617) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | c3_1(a607) | (~c2_1(a617)) | (~c3_1(a617))))),
% 2.31/2.56 inference(monotonicity,[status(thm)],[662])).
% 2.31/2.56 tff(664,plain,
% 2.31/2.56 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a607) | c2_1(a607) | (~c0_1(a607)) | c1_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp20 | c1_1(a617) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | c3_1(a607) | (~c2_1(a617)) | (~c3_1(a617)))),
% 2.31/2.56 inference(transitivity,[status(thm)],[663, 661])).
% 2.31/2.56 tff(665,plain,
% 2.31/2.56 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a607) | c2_1(a607) | (~c0_1(a607)) | c1_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 2.31/2.56 inference(quant_inst,[status(thm)],[])).
% 2.31/2.56 tff(666,plain,
% 2.31/2.56 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp20 | c1_1(a617) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | c3_1(a607) | (~c2_1(a617)) | (~c3_1(a617))),
% 2.31/2.56 inference(modus_ponens,[status(thm)],[665, 664])).
% 2.31/2.56 tff(667,plain,
% 2.31/2.56 ($false),
% 2.31/2.56 inference(unit_resolution,[status(thm)],[666, 87, 646, 649, 648, 536, 647, 535, 660, 650])).
% 2.31/2.56 tff(668,plain,(c3_1(a607) | hskp20 | (~c2_1(a617)) | (~c3_1(a617)) | (~c0_1(a607)) | c1_1(a617) | c2_1(a607)), inference(lemma,lemma(discharge,[]))).
% 2.31/2.56 tff(669,plain,
% 2.31/2.56 (c3_1(a607)),
% 2.31/2.56 inference(unit_resolution,[status(thm)],[668, 387, 649, 648, 395, 647, 646])).
% 2.31/2.56 tff(670,plain,
% 2.31/2.56 (^[U: $i] : refl((hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))),
% 2.31/2.56 inference(bind,[status(th)],[])).
% 2.31/2.56 tff(671,plain,
% 2.31/2.56 (![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 2.31/2.56 inference(quant_intro,[status(thm)],[670])).
% 2.31/2.56 tff(672,plain,
% 2.31/2.56 (![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 2.31/2.56 inference(rewrite,[status(thm)],[])).
% 2.31/2.56 tff(673,plain,
% 2.31/2.56 (^[U: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~c1_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~c1_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~c1_1(U))) | (~ndr1_0)) | hskp6) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp6))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp6) <=> (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~c1_1(U))) | (~ndr1_0)) | hskp6) <=> (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))))),
% 2.31/2.56 inference(bind,[status(th)],[])).
% 2.31/2.56 tff(674,plain,
% 2.31/2.56 (![U: $i] : (((((~c0_1(U)) | (~c3_1(U))) | (~c1_1(U))) | (~ndr1_0)) | hskp6) <=> ![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 2.31/2.56 inference(quant_intro,[status(thm)],[673])).
% 2.31/2.56 tff(675,axiom,(![U: $i] : (((((~c0_1(U)) | (~c3_1(U))) | (~c1_1(U))) | (~ndr1_0)) | hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause289')).
% 2.31/2.56 tff(676,plain,
% 2.31/2.56 (![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 2.31/2.56 inference(modus_ponens,[status(thm)],[675, 674])).
% 2.31/2.56 tff(677,plain,
% 2.31/2.56 (![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 2.31/2.56 inference(modus_ponens,[status(thm)],[676, 672])).
% 2.31/2.56 tff(678,plain,(
% 2.31/2.56 ![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 2.31/2.56 inference(skolemize,[status(sab)],[677])).
% 2.31/2.56 tff(679,plain,
% 2.31/2.56 (![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 2.31/2.56 inference(modus_ponens,[status(thm)],[678, 671])).
% 2.31/2.56 tff(680,plain,
% 2.31/2.56 (((~![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp6 | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)) | (~c1_1(a607)))) <=> ((~![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp6 | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)) | (~c1_1(a607)))),
% 2.31/2.56 inference(rewrite,[status(thm)],[])).
% 2.31/2.56 tff(681,plain,
% 2.31/2.56 ((hskp6 | (~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607))) <=> (hskp6 | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)) | (~c1_1(a607)))),
% 2.31/2.56 inference(rewrite,[status(thm)],[])).
% 2.31/2.56 tff(682,plain,
% 2.31/2.56 (((~![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp6 | (~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp6 | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)) | (~c1_1(a607))))),
% 2.31/2.56 inference(monotonicity,[status(thm)],[681])).
% 2.31/2.56 tff(683,plain,
% 2.31/2.56 (((~![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp6 | (~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)))) <=> ((~![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp6 | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)) | (~c1_1(a607)))),
% 2.31/2.57 inference(transitivity,[status(thm)],[682, 680])).
% 2.31/2.57 tff(684,plain,
% 2.31/2.57 ((~![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp6 | (~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)))),
% 2.31/2.57 inference(quant_inst,[status(thm)],[])).
% 2.31/2.57 tff(685,plain,
% 2.31/2.57 ((~![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp6 | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)) | (~c1_1(a607))),
% 2.31/2.57 inference(modus_ponens,[status(thm)],[684, 683])).
% 2.31/2.57 tff(686,plain,
% 2.31/2.57 (hskp6),
% 2.31/2.57 inference(unit_resolution,[status(thm)],[685, 87, 403, 395, 679, 669])).
% 2.31/2.57 tff(687,plain,
% 2.31/2.57 (((~hskp6) | (~c0_1(a609))) <=> ((~hskp6) | (~c0_1(a609)))),
% 2.31/2.57 inference(rewrite,[status(thm)],[])).
% 2.31/2.57 tff(688,plain,
% 2.31/2.57 (((~c0_1(a609)) | (~hskp6)) <=> ((~hskp6) | (~c0_1(a609)))),
% 2.31/2.57 inference(rewrite,[status(thm)],[])).
% 2.31/2.57 tff(689,axiom,((~c0_1(a609)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause263')).
% 2.31/2.57 tff(690,plain,
% 2.31/2.57 ((~hskp6) | (~c0_1(a609))),
% 2.31/2.57 inference(modus_ponens,[status(thm)],[689, 688])).
% 2.31/2.57 tff(691,plain,
% 2.31/2.57 ((~hskp6) | (~c0_1(a609))),
% 2.31/2.57 inference(modus_ponens,[status(thm)],[690, 687])).
% 2.31/2.57 tff(692,plain,
% 2.31/2.57 (~c0_1(a609)),
% 2.31/2.57 inference(unit_resolution,[status(thm)],[691, 686])).
% 2.31/2.57 tff(693,assumption,(~c2_1(a624)), introduced(assumption)).
% 2.31/2.57 tff(694,assumption,(~c1_1(a624)), introduced(assumption)).
% 2.31/2.57 tff(695,plain,
% 2.31/2.57 (((~hskp6) | c2_1(a609)) <=> ((~hskp6) | c2_1(a609))),
% 2.31/2.57 inference(rewrite,[status(thm)],[])).
% 2.31/2.57 tff(696,axiom,((~hskp6) | c2_1(a609)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause164')).
% 2.31/2.57 tff(697,plain,
% 2.31/2.57 ((~hskp6) | c2_1(a609)),
% 2.31/2.57 inference(modus_ponens,[status(thm)],[696, 695])).
% 2.31/2.57 tff(698,plain,
% 2.31/2.57 ((~hskp6) | c2_1(a609)),
% 2.31/2.57 inference(modus_ponens,[status(thm)],[697, 695])).
% 2.31/2.57 tff(699,plain,
% 2.31/2.57 ((~hskp6) | c2_1(a609)),
% 2.31/2.57 inference(modus_ponens,[status(thm)],[698, 695])).
% 2.31/2.57 tff(700,plain,
% 2.31/2.57 ((~hskp6) | c2_1(a609)),
% 2.31/2.57 inference(modus_ponens,[status(thm)],[699, 695])).
% 2.31/2.57 tff(701,plain,
% 2.31/2.57 ((~hskp6) | c2_1(a609)),
% 2.31/2.57 inference(modus_ponens,[status(thm)],[700, 695])).
% 2.31/2.57 tff(702,plain,
% 2.31/2.57 (c2_1(a609)),
% 2.31/2.57 inference(unit_resolution,[status(thm)],[701, 686])).
% 2.31/2.57 tff(703,assumption,(c3_1(a624)), introduced(assumption)).
% 2.31/2.57 tff(704,plain,
% 2.31/2.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a617) | c1_1(a624) | c2_1(a624) | c0_1(a609) | (~ndr1_0) | (~c3_1(a609)) | (~c2_1(a609)) | (~c3_1(a624)) | (~c2_1(a617)) | (~c0_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a617) | c1_1(a624) | c2_1(a624) | c0_1(a609) | (~ndr1_0) | (~c3_1(a609)) | (~c2_1(a609)) | (~c3_1(a624)) | (~c2_1(a617)) | (~c0_1(a617)))),
% 2.31/2.57 inference(rewrite,[status(thm)],[])).
% 2.31/2.57 tff(705,plain,
% 2.31/2.57 (((~ndr1_0) | c0_1(a609) | (~c3_1(a609)) | (~c2_1(a609)) | c1_1(a617) | (~c2_1(a617)) | (~c0_1(a617)) | c2_1(a624) | c1_1(a624) | (~c3_1(a624))) <=> (c1_1(a617) | c1_1(a624) | c2_1(a624) | c0_1(a609) | (~ndr1_0) | (~c3_1(a609)) | (~c2_1(a609)) | (~c3_1(a624)) | (~c2_1(a617)) | (~c0_1(a617)))),
% 2.31/2.57 inference(rewrite,[status(thm)],[])).
% 2.31/2.57 tff(706,plain,
% 2.31/2.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a609) | (~c3_1(a609)) | (~c2_1(a609)) | c1_1(a617) | (~c2_1(a617)) | (~c0_1(a617)) | c2_1(a624) | c1_1(a624) | (~c3_1(a624)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a617) | c1_1(a624) | c2_1(a624) | c0_1(a609) | (~ndr1_0) | (~c3_1(a609)) | (~c2_1(a609)) | (~c3_1(a624)) | (~c2_1(a617)) | (~c0_1(a617))))),
% 2.31/2.57 inference(monotonicity,[status(thm)],[705])).
% 2.31/2.57 tff(707,plain,
% 2.31/2.57 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a609) | (~c3_1(a609)) | (~c2_1(a609)) | c1_1(a617) | (~c2_1(a617)) | (~c0_1(a617)) | c2_1(a624) | c1_1(a624) | (~c3_1(a624)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a617) | c1_1(a624) | c2_1(a624) | c0_1(a609) | (~ndr1_0) | (~c3_1(a609)) | (~c2_1(a609)) | (~c3_1(a624)) | (~c2_1(a617)) | (~c0_1(a617)))),
% 2.31/2.57 inference(transitivity,[status(thm)],[706, 704])).
% 2.31/2.57 tff(708,plain,
% 2.31/2.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a609) | (~c3_1(a609)) | (~c2_1(a609)) | c1_1(a617) | (~c2_1(a617)) | (~c0_1(a617)) | c2_1(a624) | c1_1(a624) | (~c3_1(a624)))),
% 2.31/2.57 inference(quant_inst,[status(thm)],[])).
% 2.31/2.57 tff(709,plain,
% 2.31/2.57 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a617) | c1_1(a624) | c2_1(a624) | c0_1(a609) | (~ndr1_0) | (~c3_1(a609)) | (~c2_1(a609)) | (~c3_1(a624)) | (~c2_1(a617)) | (~c0_1(a617))),
% 2.31/2.57 inference(modus_ponens,[status(thm)],[708, 707])).
% 2.31/2.57 tff(710,plain,
% 2.31/2.57 (~c3_1(a609)),
% 2.31/2.57 inference(unit_resolution,[status(thm)],[709, 87, 649, 703, 702, 647, 694, 693, 692, 645, 635])).
% 2.31/2.57 tff(711,plain,
% 2.31/2.57 (^[V: $i, U: $i] : refl((hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))),
% 2.31/2.57 inference(bind,[status(th)],[])).
% 2.31/2.57 tff(712,plain,
% 2.31/2.57 (![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 2.31/2.57 inference(quant_intro,[status(thm)],[711])).
% 2.31/2.57 tff(713,plain,
% 2.31/2.57 (![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 2.31/2.57 inference(rewrite,[status(thm)],[])).
% 2.31/2.57 tff(714,plain,
% 2.31/2.57 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(V)) | hskp57) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp57))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp57) <=> (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(V)) | hskp57) <=> (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))))),
% 2.31/2.57 inference(bind,[status(th)],[])).
% 2.31/2.57 tff(715,plain,
% 2.31/2.57 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(V)) | hskp57) <=> ![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 2.31/2.57 inference(quant_intro,[status(thm)],[714])).
% 2.31/2.57 tff(716,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(V)) | hskp57)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause319')).
% 2.31/2.57 tff(717,plain,
% 2.31/2.57 (![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 2.31/2.57 inference(modus_ponens,[status(thm)],[716, 715])).
% 2.31/2.57 tff(718,plain,
% 2.31/2.57 (![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 2.31/2.57 inference(modus_ponens,[status(thm)],[717, 713])).
% 2.31/2.57 tff(719,plain,(
% 2.31/2.57 ![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 2.31/2.57 inference(skolemize,[status(sab)],[718])).
% 2.31/2.57 tff(720,plain,
% 2.31/2.57 (![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 2.31/2.57 inference(modus_ponens,[status(thm)],[719, 712])).
% 2.31/2.57 tff(721,plain,
% 2.31/2.57 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | c1_1(a617) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)) | (~c1_1(a607)) | (~c3_1(a617)) | (~c0_1(a617)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | c1_1(a617) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)) | (~c1_1(a607)) | (~c3_1(a617)) | (~c0_1(a617)))),
% 2.31/2.57 inference(rewrite,[status(thm)],[])).
% 2.31/2.57 tff(722,plain,
% 2.31/2.57 ((hskp57 | (~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c1_1(a617) | (~c3_1(a617)) | (~c0_1(a617))) <=> (hskp57 | c1_1(a617) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)) | (~c1_1(a607)) | (~c3_1(a617)) | (~c0_1(a617)))),
% 2.31/2.57 inference(rewrite,[status(thm)],[])).
% 2.31/2.57 tff(723,plain,
% 2.31/2.57 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c1_1(a617) | (~c3_1(a617)) | (~c0_1(a617)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | c1_1(a617) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)) | (~c1_1(a607)) | (~c3_1(a617)) | (~c0_1(a617))))),
% 2.31/2.57 inference(monotonicity,[status(thm)],[722])).
% 2.31/2.57 tff(724,plain,
% 2.31/2.57 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c1_1(a617) | (~c3_1(a617)) | (~c0_1(a617)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | c1_1(a617) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)) | (~c1_1(a607)) | (~c3_1(a617)) | (~c0_1(a617)))),
% 2.31/2.57 inference(transitivity,[status(thm)],[723, 721])).
% 2.31/2.57 tff(725,plain,
% 2.31/2.57 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | (~c3_1(a607)) | (~c1_1(a607)) | (~c0_1(a607)) | c1_1(a617) | (~c3_1(a617)) | (~c0_1(a617)))),
% 2.31/2.57 inference(quant_inst,[status(thm)],[])).
% 2.31/2.57 tff(726,plain,
% 2.31/2.57 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | c1_1(a617) | (~ndr1_0) | (~c0_1(a607)) | (~c3_1(a607)) | (~c1_1(a607)) | (~c3_1(a617)) | (~c0_1(a617))),
% 2.31/2.57 inference(modus_ponens,[status(thm)],[725, 724])).
% 2.31/2.57 tff(727,plain,
% 2.31/2.57 (hskp57),
% 2.31/2.57 inference(unit_resolution,[status(thm)],[726, 87, 648, 403, 395, 647, 720, 635, 669])).
% 2.31/2.57 tff(728,plain,
% 2.31/2.57 (((~hskp57) | (~c0_1(a662))) <=> ((~hskp57) | (~c0_1(a662)))),
% 2.31/2.57 inference(rewrite,[status(thm)],[])).
% 2.31/2.57 tff(729,plain,
% 2.31/2.57 (((~c0_1(a662)) | (~hskp57)) <=> ((~hskp57) | (~c0_1(a662)))),
% 2.31/2.57 inference(rewrite,[status(thm)],[])).
% 2.31/2.57 tff(730,axiom,((~c0_1(a662)) | (~hskp57)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause183')).
% 2.31/2.57 tff(731,plain,
% 2.31/2.57 ((~hskp57) | (~c0_1(a662))),
% 2.31/2.57 inference(modus_ponens,[status(thm)],[730, 729])).
% 2.31/2.57 tff(732,plain,
% 2.31/2.57 ((~hskp57) | (~c0_1(a662))),
% 2.31/2.57 inference(modus_ponens,[status(thm)],[731, 728])).
% 2.31/2.57 tff(733,plain,
% 2.31/2.57 (~c0_1(a662)),
% 2.31/2.57 inference(unit_resolution,[status(thm)],[732, 727])).
% 2.31/2.57 tff(734,plain,
% 2.31/2.57 (((~hskp57) | c2_1(a662)) <=> ((~hskp57) | c2_1(a662))),
% 2.31/2.57 inference(rewrite,[status(thm)],[])).
% 2.31/2.57 tff(735,axiom,((~hskp57) | c2_1(a662)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause92')).
% 2.31/2.57 tff(736,plain,
% 2.31/2.57 ((~hskp57) | c2_1(a662)),
% 2.31/2.57 inference(modus_ponens,[status(thm)],[735, 734])).
% 2.31/2.57 tff(737,plain,
% 2.31/2.57 ((~hskp57) | c2_1(a662)),
% 2.31/2.57 inference(modus_ponens,[status(thm)],[736, 734])).
% 2.31/2.57 tff(738,plain,
% 2.31/2.57 ((~hskp57) | c2_1(a662)),
% 2.31/2.57 inference(modus_ponens,[status(thm)],[737, 734])).
% 2.31/2.57 tff(739,plain,
% 2.31/2.57 ((~hskp57) | c2_1(a662)),
% 2.31/2.57 inference(modus_ponens,[status(thm)],[738, 734])).
% 2.31/2.57 tff(740,plain,
% 2.31/2.57 ((~hskp57) | c2_1(a662)),
% 2.31/2.57 inference(modus_ponens,[status(thm)],[739, 734])).
% 2.31/2.57 tff(741,plain,
% 2.31/2.57 (c2_1(a662)),
% 2.31/2.57 inference(unit_resolution,[status(thm)],[740, 727])).
% 2.31/2.57 tff(742,plain,
% 2.31/2.57 (((~hskp57) | c1_1(a662)) <=> ((~hskp57) | c1_1(a662))),
% 2.31/2.57 inference(rewrite,[status(thm)],[])).
% 2.31/2.57 tff(743,axiom,((~hskp57) | c1_1(a662)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause91')).
% 2.31/2.57 tff(744,plain,
% 2.31/2.57 ((~hskp57) | c1_1(a662)),
% 2.31/2.57 inference(modus_ponens,[status(thm)],[743, 742])).
% 2.31/2.57 tff(745,plain,
% 2.31/2.57 ((~hskp57) | c1_1(a662)),
% 2.31/2.57 inference(modus_ponens,[status(thm)],[744, 742])).
% 2.31/2.57 tff(746,plain,
% 2.31/2.57 ((~hskp57) | c1_1(a662)),
% 2.31/2.57 inference(modus_ponens,[status(thm)],[745, 742])).
% 2.31/2.57 tff(747,plain,
% 2.31/2.57 ((~hskp57) | c1_1(a662)),
% 2.31/2.57 inference(modus_ponens,[status(thm)],[746, 742])).
% 2.31/2.57 tff(748,plain,
% 2.31/2.57 ((~hskp57) | c1_1(a662)),
% 2.31/2.57 inference(modus_ponens,[status(thm)],[747, 742])).
% 2.31/2.57 tff(749,plain,
% 2.31/2.57 (c1_1(a662)),
% 2.31/2.57 inference(unit_resolution,[status(thm)],[748, 727])).
% 2.31/2.57 tff(750,plain,
% 2.31/2.57 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (c0_1(a662) | c0_1(a609) | (~ndr1_0) | c3_1(a609) | (~c2_1(a609)) | (~c2_1(a662)) | (~c1_1(a662)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | c0_1(a662) | c0_1(a609) | (~ndr1_0) | c3_1(a609) | (~c2_1(a609)) | (~c2_1(a662)) | (~c1_1(a662)))),
% 2.31/2.57 inference(rewrite,[status(thm)],[])).
% 2.31/2.57 tff(751,plain,
% 2.31/2.57 (((~ndr1_0) | c3_1(a609) | c0_1(a609) | (~c2_1(a609)) | c0_1(a662) | (~c2_1(a662)) | (~c1_1(a662))) <=> (c0_1(a662) | c0_1(a609) | (~ndr1_0) | c3_1(a609) | (~c2_1(a609)) | (~c2_1(a662)) | (~c1_1(a662)))),
% 2.31/2.57 inference(rewrite,[status(thm)],[])).
% 2.31/2.57 tff(752,plain,
% 2.31/2.57 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c3_1(a609) | c0_1(a609) | (~c2_1(a609)) | c0_1(a662) | (~c2_1(a662)) | (~c1_1(a662)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (c0_1(a662) | c0_1(a609) | (~ndr1_0) | c3_1(a609) | (~c2_1(a609)) | (~c2_1(a662)) | (~c1_1(a662))))),
% 2.31/2.57 inference(monotonicity,[status(thm)],[751])).
% 2.31/2.57 tff(753,plain,
% 2.31/2.57 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c3_1(a609) | c0_1(a609) | (~c2_1(a609)) | c0_1(a662) | (~c2_1(a662)) | (~c1_1(a662)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | c0_1(a662) | c0_1(a609) | (~ndr1_0) | c3_1(a609) | (~c2_1(a609)) | (~c2_1(a662)) | (~c1_1(a662)))),
% 2.31/2.57 inference(transitivity,[status(thm)],[752, 750])).
% 2.31/2.57 tff(754,plain,
% 2.31/2.57 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c3_1(a609) | c0_1(a609) | (~c2_1(a609)) | c0_1(a662) | (~c2_1(a662)) | (~c1_1(a662)))),
% 2.31/2.57 inference(quant_inst,[status(thm)],[])).
% 2.31/2.57 tff(755,plain,
% 2.31/2.57 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | c0_1(a662) | c0_1(a609) | (~ndr1_0) | c3_1(a609) | (~c2_1(a609)) | (~c2_1(a662)) | (~c1_1(a662))),
% 2.31/2.57 inference(modus_ponens,[status(thm)],[754, 753])).
% 2.31/2.57 tff(756,plain,
% 2.31/2.57 ($false),
% 2.31/2.57 inference(unit_resolution,[status(thm)],[755, 87, 749, 741, 702, 733, 692, 23, 710])).
% 2.31/2.57 tff(757,plain,((~hskp37) | (~c2_1(a617)) | (~c3_1(a624)) | c1_1(a617) | c1_1(a624) | c2_1(a624) | (~c0_1(a617)) | (~c3_1(a617)) | hskp20), inference(lemma,lemma(discharge,[]))).
% 2.31/2.57 tff(758,plain,
% 2.31/2.57 (~hskp37),
% 2.31/2.57 inference(unit_resolution,[status(thm)],[757, 497, 634, 464, 633, 632, 479, 472, 630])).
% 2.31/2.57 tff(759,plain,
% 2.31/2.57 (((~![U: $i] : (hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp54 | hskp37 | c0_1(a606) | c3_1(a606) | (~ndr1_0) | (~c2_1(a606)))) <=> ((~![U: $i] : (hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp54 | hskp37 | c0_1(a606) | c3_1(a606) | (~ndr1_0) | (~c2_1(a606)))),
% 2.31/2.57 inference(rewrite,[status(thm)],[])).
% 2.31/2.57 tff(760,plain,
% 2.31/2.57 ((hskp54 | hskp37 | (~ndr1_0) | c3_1(a606) | c0_1(a606) | (~c2_1(a606))) <=> (hskp54 | hskp37 | c0_1(a606) | c3_1(a606) | (~ndr1_0) | (~c2_1(a606)))),
% 2.31/2.57 inference(rewrite,[status(thm)],[])).
% 2.31/2.57 tff(761,plain,
% 2.31/2.57 (((~![U: $i] : (hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp54 | hskp37 | (~ndr1_0) | c3_1(a606) | c0_1(a606) | (~c2_1(a606)))) <=> ((~![U: $i] : (hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp54 | hskp37 | c0_1(a606) | c3_1(a606) | (~ndr1_0) | (~c2_1(a606))))),
% 2.31/2.57 inference(monotonicity,[status(thm)],[760])).
% 2.31/2.57 tff(762,plain,
% 2.31/2.57 (((~![U: $i] : (hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp54 | hskp37 | (~ndr1_0) | c3_1(a606) | c0_1(a606) | (~c2_1(a606)))) <=> ((~![U: $i] : (hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp54 | hskp37 | c0_1(a606) | c3_1(a606) | (~ndr1_0) | (~c2_1(a606)))),
% 2.31/2.57 inference(transitivity,[status(thm)],[761, 759])).
% 2.31/2.57 tff(763,plain,
% 2.31/2.57 ((~![U: $i] : (hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp54 | hskp37 | (~ndr1_0) | c3_1(a606) | c0_1(a606) | (~c2_1(a606)))),
% 2.31/2.57 inference(quant_inst,[status(thm)],[])).
% 2.31/2.57 tff(764,plain,
% 2.31/2.57 ((~![U: $i] : (hskp54 | hskp37 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp54 | hskp37 | c0_1(a606) | c3_1(a606) | (~ndr1_0) | (~c2_1(a606))),
% 2.31/2.57 inference(modus_ponens,[status(thm)],[763, 762])).
% 2.31/2.57 tff(765,plain,
% 2.31/2.57 (hskp54 | hskp37),
% 2.31/2.57 inference(unit_resolution,[status(thm)],[764, 87, 589, 581, 575, 372])).
% 2.31/2.57 tff(766,plain,
% 2.31/2.57 (hskp54),
% 2.31/2.57 inference(unit_resolution,[status(thm)],[765, 758])).
% 2.31/2.57 tff(767,plain,
% 2.31/2.57 (c2_1(a651)),
% 2.31/2.57 inference(unit_resolution,[status(thm)],[433, 766])).
% 2.31/2.57 tff(768,plain,
% 2.31/2.57 (c3_1(a651)),
% 2.31/2.57 inference(unit_resolution,[status(thm)],[448, 766])).
% 2.31/2.57 tff(769,plain,
% 2.31/2.57 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (c1_1(a617) | (~ndr1_0) | (~c2_1(a617)) | (~c0_1(a617)) | (~c2_1(a651)) | (~c3_1(a651)) | (~c1_1(a651)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | c1_1(a617) | (~ndr1_0) | (~c2_1(a617)) | (~c0_1(a617)) | (~c2_1(a651)) | (~c3_1(a651)) | (~c1_1(a651)))),
% 2.31/2.57 inference(rewrite,[status(thm)],[])).
% 2.31/2.57 tff(770,plain,
% 2.31/2.57 (((~ndr1_0) | (~c3_1(a651)) | (~c1_1(a651)) | (~c2_1(a651)) | c1_1(a617) | (~c2_1(a617)) | (~c0_1(a617))) <=> (c1_1(a617) | (~ndr1_0) | (~c2_1(a617)) | (~c0_1(a617)) | (~c2_1(a651)) | (~c3_1(a651)) | (~c1_1(a651)))),
% 2.31/2.57 inference(rewrite,[status(thm)],[])).
% 2.31/2.57 tff(771,plain,
% 2.31/2.57 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | ((~ndr1_0) | (~c3_1(a651)) | (~c1_1(a651)) | (~c2_1(a651)) | c1_1(a617) | (~c2_1(a617)) | (~c0_1(a617)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (c1_1(a617) | (~ndr1_0) | (~c2_1(a617)) | (~c0_1(a617)) | (~c2_1(a651)) | (~c3_1(a651)) | (~c1_1(a651))))),
% 2.31/2.57 inference(monotonicity,[status(thm)],[770])).
% 2.31/2.57 tff(772,plain,
% 2.31/2.57 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | ((~ndr1_0) | (~c3_1(a651)) | (~c1_1(a651)) | (~c2_1(a651)) | c1_1(a617) | (~c2_1(a617)) | (~c0_1(a617)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | c1_1(a617) | (~ndr1_0) | (~c2_1(a617)) | (~c0_1(a617)) | (~c2_1(a651)) | (~c3_1(a651)) | (~c1_1(a651)))),
% 2.31/2.57 inference(transitivity,[status(thm)],[771, 769])).
% 2.31/2.57 tff(773,plain,
% 2.31/2.57 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | ((~ndr1_0) | (~c3_1(a651)) | (~c1_1(a651)) | (~c2_1(a651)) | c1_1(a617) | (~c2_1(a617)) | (~c0_1(a617)))),
% 2.31/2.57 inference(quant_inst,[status(thm)],[])).
% 2.31/2.57 tff(774,plain,
% 2.31/2.57 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | c1_1(a617) | (~ndr1_0) | (~c2_1(a617)) | (~c0_1(a617)) | (~c2_1(a651)) | (~c3_1(a651)) | (~c1_1(a651))),
% 2.31/2.57 inference(modus_ponens,[status(thm)],[773, 772])).
% 2.31/2.57 tff(775,plain,
% 2.31/2.57 (~c1_1(a651)),
% 2.31/2.57 inference(unit_resolution,[status(thm)],[774, 87, 768, 767, 497, 464, 489, 479])).
% 2.31/2.57 tff(776,plain,
% 2.31/2.57 (~c0_1(a651)),
% 2.31/2.57 inference(unit_resolution,[status(thm)],[425, 766])).
% 2.31/2.57 tff(777,plain,
% 2.31/2.57 ($false),
% 2.31/2.57 inference(unit_resolution,[status(thm)],[455, 87, 35, 12, 768, 776, 34, 775])).
% 2.31/2.57 tff(778,plain,(hskp53 | hskp17 | hskp64), inference(lemma,lemma(discharge,[]))).
% 2.31/2.57 tff(779,plain,
% 2.31/2.57 (hskp53),
% 2.31/2.57 inference(unit_resolution,[status(thm)],[778, 24, 12])).
% 2.31/2.57 tff(780,plain,
% 2.31/2.57 (((~hskp53) | (~c2_1(a648))) <=> ((~hskp53) | (~c2_1(a648)))),
% 2.31/2.57 inference(rewrite,[status(thm)],[])).
% 2.31/2.57 tff(781,plain,
% 2.31/2.57 (((~c2_1(a648)) | (~hskp53)) <=> ((~hskp53) | (~c2_1(a648)))),
% 2.31/2.57 inference(rewrite,[status(thm)],[])).
% 2.31/2.57 tff(782,axiom,((~c2_1(a648)) | (~hskp53)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause187')).
% 2.31/2.57 tff(783,plain,
% 2.31/2.57 ((~hskp53) | (~c2_1(a648))),
% 2.31/2.57 inference(modus_ponens,[status(thm)],[782, 781])).
% 2.31/2.57 tff(784,plain,
% 2.31/2.57 ((~hskp53) | (~c2_1(a648))),
% 2.31/2.57 inference(modus_ponens,[status(thm)],[783, 780])).
% 2.31/2.57 tff(785,plain,
% 2.31/2.57 (~c2_1(a648)),
% 2.31/2.57 inference(unit_resolution,[status(thm)],[784, 779])).
% 2.31/2.57 tff(786,plain,
% 2.31/2.57 (((~hskp53) | c0_1(a648)) <=> ((~hskp53) | c0_1(a648))),
% 2.31/2.57 inference(rewrite,[status(thm)],[])).
% 2.31/2.57 tff(787,axiom,((~hskp53) | c0_1(a648)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause100')).
% 2.31/2.57 tff(788,plain,
% 2.31/2.57 ((~hskp53) | c0_1(a648)),
% 2.31/2.57 inference(modus_ponens,[status(thm)],[787, 786])).
% 2.31/2.57 tff(789,plain,
% 2.31/2.57 ((~hskp53) | c0_1(a648)),
% 2.31/2.57 inference(modus_ponens,[status(thm)],[788, 786])).
% 2.31/2.57 tff(790,plain,
% 2.31/2.57 ((~hskp53) | c0_1(a648)),
% 2.31/2.57 inference(modus_ponens,[status(thm)],[789, 786])).
% 2.31/2.57 tff(791,plain,
% 2.31/2.57 ((~hskp53) | c0_1(a648)),
% 2.31/2.57 inference(modus_ponens,[status(thm)],[790, 786])).
% 2.31/2.57 tff(792,plain,
% 2.31/2.57 ((~hskp53) | c0_1(a648)),
% 2.31/2.57 inference(modus_ponens,[status(thm)],[791, 786])).
% 2.31/2.57 tff(793,plain,
% 2.31/2.57 (c0_1(a648)),
% 2.31/2.57 inference(unit_resolution,[status(thm)],[792, 779])).
% 2.31/2.57 tff(794,plain,
% 2.31/2.57 (((~hskp53) | c3_1(a648)) <=> ((~hskp53) | c3_1(a648))),
% 2.31/2.57 inference(rewrite,[status(thm)],[])).
% 2.31/2.57 tff(795,axiom,((~hskp53) | c3_1(a648)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause99')).
% 2.31/2.57 tff(796,plain,
% 2.31/2.57 ((~hskp53) | c3_1(a648)),
% 2.31/2.57 inference(modus_ponens,[status(thm)],[795, 794])).
% 2.31/2.57 tff(797,plain,
% 2.31/2.57 ((~hskp53) | c3_1(a648)),
% 2.31/2.57 inference(modus_ponens,[status(thm)],[796, 794])).
% 2.31/2.57 tff(798,plain,
% 2.31/2.57 ((~hskp53) | c3_1(a648)),
% 2.31/2.57 inference(modus_ponens,[status(thm)],[797, 794])).
% 2.31/2.57 tff(799,plain,
% 2.31/2.57 ((~hskp53) | c3_1(a648)),
% 2.31/2.57 inference(modus_ponens,[status(thm)],[798, 794])).
% 2.31/2.57 tff(800,plain,
% 2.31/2.57 ((~hskp53) | c3_1(a648)),
% 2.31/2.57 inference(modus_ponens,[status(thm)],[799, 794])).
% 2.31/2.57 tff(801,plain,
% 2.31/2.57 (c3_1(a648)),
% 2.31/2.57 inference(unit_resolution,[status(thm)],[800, 779])).
% 2.31/2.57 tff(802,assumption,(~c2_1(a648)), introduced(assumption)).
% 2.31/2.57 tff(803,assumption,(c0_1(a648)), introduced(assumption)).
% 2.31/2.57 tff(804,assumption,(c3_1(a648)), introduced(assumption)).
% 2.31/2.57 tff(805,plain,
% 2.31/2.57 (((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c3_1(a648)) | (~c1_1(a648)))) <=> ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp41 | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c3_1(a648)) | (~c1_1(a648)))),
% 2.31/2.57 inference(rewrite,[status(thm)],[])).
% 2.31/2.57 tff(806,plain,
% 2.31/2.57 ((hskp41 | (~ndr1_0) | c2_1(a648) | (~c3_1(a648)) | (~c1_1(a648)) | c2_1(a648) | (~c1_1(a648)) | (~c0_1(a648))) <=> (hskp41 | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c3_1(a648)) | (~c1_1(a648)))),
% 2.31/2.57 inference(rewrite,[status(thm)],[])).
% 2.31/2.57 tff(807,plain,
% 2.31/2.57 (((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | (~ndr1_0) | c2_1(a648) | (~c3_1(a648)) | (~c1_1(a648)) | c2_1(a648) | (~c1_1(a648)) | (~c0_1(a648)))) <=> ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c3_1(a648)) | (~c1_1(a648))))),
% 2.31/2.57 inference(monotonicity,[status(thm)],[806])).
% 2.31/2.57 tff(808,plain,
% 2.31/2.57 (((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | (~ndr1_0) | c2_1(a648) | (~c3_1(a648)) | (~c1_1(a648)) | c2_1(a648) | (~c1_1(a648)) | (~c0_1(a648)))) <=> ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp41 | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c3_1(a648)) | (~c1_1(a648)))),
% 2.31/2.57 inference(transitivity,[status(thm)],[807, 805])).
% 2.31/2.57 tff(809,plain,
% 2.31/2.57 ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | (~ndr1_0) | c2_1(a648) | (~c3_1(a648)) | (~c1_1(a648)) | c2_1(a648) | (~c1_1(a648)) | (~c0_1(a648)))),
% 2.31/2.57 inference(quant_inst,[status(thm)],[])).
% 2.31/2.57 tff(810,plain,
% 2.31/2.57 ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp41 | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c3_1(a648)) | (~c1_1(a648))),
% 2.31/2.57 inference(modus_ponens,[status(thm)],[809, 808])).
% 2.31/2.57 tff(811,plain,
% 2.31/2.57 (hskp41 | (~c1_1(a648))),
% 2.31/2.57 inference(unit_resolution,[status(thm)],[810, 87, 804, 803, 802, 299])).
% 2.31/2.57 tff(812,plain,
% 2.31/2.57 (~c1_1(a648)),
% 2.31/2.57 inference(unit_resolution,[status(thm)],[811, 97])).
% 2.31/2.57 tff(813,plain,
% 2.31/2.57 (^[V: $i, U: $i] : refl((hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))),
% 2.31/2.57 inference(bind,[status(th)],[])).
% 2.31/2.57 tff(814,plain,
% 2.31/2.57 (![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.31/2.57 inference(quant_intro,[status(thm)],[813])).
% 2.31/2.57 tff(815,plain,
% 2.31/2.57 (![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.31/2.57 inference(rewrite,[status(thm)],[])).
% 2.31/2.57 tff(816,plain,
% 2.31/2.57 (^[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))) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)))), (((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V))))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V)))), ((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V))))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp42) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp42))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | hskp42) <=> (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp42) <=> (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))))),
% 2.31/2.57 inference(bind,[status(th)],[])).
% 2.31/2.57 tff(817,plain,
% 2.31/2.57 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp42) <=> ![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.31/2.57 inference(quant_intro,[status(thm)],[816])).
% 2.31/2.57 tff(818,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | hskp42)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause303')).
% 2.31/2.57 tff(819,plain,
% 2.31/2.57 (![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.31/2.57 inference(modus_ponens,[status(thm)],[818, 817])).
% 2.31/2.57 tff(820,plain,
% 2.31/2.57 (![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.31/2.57 inference(modus_ponens,[status(thm)],[819, 815])).
% 2.31/2.57 tff(821,plain,(
% 2.31/2.57 ![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.31/2.57 inference(skolemize,[status(sab)],[820])).
% 2.31/2.58 tff(822,plain,
% 2.31/2.58 (![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))),
% 2.31/2.58 inference(modus_ponens,[status(thm)],[821, 814])).
% 2.31/2.58 tff(823,plain,
% 2.31/2.58 (((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c3_1(a648)))) <=> ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp58 | hskp41 | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c3_1(a648)))),
% 2.31/2.58 inference(rewrite,[status(thm)],[])).
% 2.31/2.58 tff(824,plain,
% 2.31/2.58 ((hskp58 | hskp41 | (~ndr1_0) | c2_1(a648) | (~c3_1(a648)) | (~c0_1(a648))) <=> (hskp58 | hskp41 | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c3_1(a648)))),
% 2.31/2.58 inference(rewrite,[status(thm)],[])).
% 2.31/2.58 tff(825,plain,
% 2.31/2.58 (((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | (~ndr1_0) | c2_1(a648) | (~c3_1(a648)) | (~c0_1(a648)))) <=> ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c3_1(a648))))),
% 2.31/2.58 inference(monotonicity,[status(thm)],[824])).
% 2.31/2.58 tff(826,plain,
% 2.31/2.58 (((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | (~ndr1_0) | c2_1(a648) | (~c3_1(a648)) | (~c0_1(a648)))) <=> ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp58 | hskp41 | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c3_1(a648)))),
% 2.31/2.58 inference(transitivity,[status(thm)],[825, 823])).
% 2.31/2.58 tff(827,plain,
% 2.31/2.58 ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | (~ndr1_0) | c2_1(a648) | (~c3_1(a648)) | (~c0_1(a648)))),
% 2.31/2.58 inference(quant_inst,[status(thm)],[])).
% 2.31/2.58 tff(828,plain,
% 2.31/2.58 ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp58 | hskp41 | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | (~c3_1(a648))),
% 2.31/2.58 inference(modus_ponens,[status(thm)],[827, 826])).
% 2.31/2.58 tff(829,plain,
% 2.31/2.58 (hskp58 | hskp41),
% 2.31/2.58 inference(unit_resolution,[status(thm)],[828, 87, 804, 803, 802, 107])).
% 2.31/2.58 tff(830,plain,
% 2.31/2.58 (hskp58),
% 2.31/2.58 inference(unit_resolution,[status(thm)],[829, 97])).
% 2.31/2.58 tff(831,plain,
% 2.31/2.58 (~c1_1(a663)),
% 2.31/2.58 inference(unit_resolution,[status(thm)],[41, 830])).
% 2.31/2.58 tff(832,plain,
% 2.31/2.58 (~c0_1(a663)),
% 2.31/2.58 inference(unit_resolution,[status(thm)],[47, 830])).
% 2.31/2.58 tff(833,plain,
% 2.31/2.58 (c3_1(a663)),
% 2.31/2.58 inference(unit_resolution,[status(thm)],[55, 830])).
% 2.31/2.58 tff(834,plain,
% 2.31/2.58 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | c0_1(a663) | c1_1(a663) | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | c1_1(a648) | (~c3_1(a663)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c0_1(a663) | c1_1(a663) | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | c1_1(a648) | (~c3_1(a663)))),
% 2.31/2.58 inference(rewrite,[status(thm)],[])).
% 2.31/2.58 tff(835,plain,
% 2.31/2.58 ((hskp42 | (~ndr1_0) | c1_1(a648) | c2_1(a648) | (~c0_1(a648)) | c1_1(a663) | c0_1(a663) | (~c3_1(a663))) <=> (hskp42 | c0_1(a663) | c1_1(a663) | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | c1_1(a648) | (~c3_1(a663)))),
% 2.31/2.58 inference(rewrite,[status(thm)],[])).
% 2.31/2.58 tff(836,plain,
% 2.31/2.58 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a648) | c2_1(a648) | (~c0_1(a648)) | c1_1(a663) | c0_1(a663) | (~c3_1(a663)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | c0_1(a663) | c1_1(a663) | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | c1_1(a648) | (~c3_1(a663))))),
% 2.31/2.58 inference(monotonicity,[status(thm)],[835])).
% 2.31/2.58 tff(837,plain,
% 2.31/2.58 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a648) | c2_1(a648) | (~c0_1(a648)) | c1_1(a663) | c0_1(a663) | (~c3_1(a663)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c0_1(a663) | c1_1(a663) | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | c1_1(a648) | (~c3_1(a663)))),
% 2.31/2.58 inference(transitivity,[status(thm)],[836, 834])).
% 2.31/2.58 tff(838,plain,
% 2.31/2.58 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a648) | c2_1(a648) | (~c0_1(a648)) | c1_1(a663) | c0_1(a663) | (~c3_1(a663)))),
% 2.31/2.58 inference(quant_inst,[status(thm)],[])).
% 2.31/2.58 tff(839,plain,
% 2.31/2.58 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c0_1(a663) | c1_1(a663) | c2_1(a648) | (~ndr1_0) | (~c0_1(a648)) | c1_1(a648) | (~c3_1(a663))),
% 2.31/2.58 inference(modus_ponens,[status(thm)],[838, 837])).
% 2.31/2.58 tff(840,plain,
% 2.31/2.58 (hskp42),
% 2.31/2.58 inference(unit_resolution,[status(thm)],[839, 87, 833, 803, 832, 831, 802, 822, 812])).
% 2.31/2.58 tff(841,plain,
% 2.31/2.58 (((~hskp42) | (~c2_1(a618))) <=> ((~hskp42) | (~c2_1(a618)))),
% 2.31/2.58 inference(rewrite,[status(thm)],[])).
% 2.31/2.58 tff(842,plain,
% 2.31/2.58 (((~c2_1(a618)) | (~hskp42)) <=> ((~hskp42) | (~c2_1(a618)))),
% 2.31/2.58 inference(rewrite,[status(thm)],[])).
% 2.31/2.58 tff(843,axiom,((~c2_1(a618)) | (~hskp42)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause201')).
% 2.31/2.58 tff(844,plain,
% 2.31/2.58 ((~hskp42) | (~c2_1(a618))),
% 2.31/2.58 inference(modus_ponens,[status(thm)],[843, 842])).
% 2.31/2.58 tff(845,plain,
% 2.31/2.58 ((~hskp42) | (~c2_1(a618))),
% 2.31/2.58 inference(modus_ponens,[status(thm)],[844, 841])).
% 2.31/2.58 tff(846,plain,
% 2.31/2.58 (~c2_1(a618)),
% 2.31/2.58 inference(unit_resolution,[status(thm)],[845, 840])).
% 2.31/2.58 tff(847,plain,
% 2.31/2.58 (^[V: $i, U: $i] : refl((hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))),
% 2.31/2.58 inference(bind,[status(th)],[])).
% 2.31/2.58 tff(848,plain,
% 2.31/2.58 (![V: $i, U: $i] : (hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 2.31/2.58 inference(quant_intro,[status(thm)],[847])).
% 2.31/2.58 tff(849,plain,
% 2.31/2.58 (![V: $i, U: $i] : (hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 2.31/2.58 inference(rewrite,[status(thm)],[])).
% 2.31/2.58 tff(850,plain,
% 2.31/2.58 (^[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)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c3_1(V)))), ((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c3_1(V))))), (((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c3_1(V))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c3_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) | c0_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) | c0_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) | c0_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) | c0_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) | c0_1(U)) | c1_1(V)) | hskp55) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp55))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp55) <=> (hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) | c0_1(U)) | c1_1(V)) | hskp55) <=> (hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))))),
% 2.31/2.58 inference(bind,[status(th)],[])).
% 2.31/2.58 tff(851,plain,
% 2.31/2.58 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) | c0_1(U)) | c1_1(V)) | hskp55) <=> ![V: $i, U: $i] : (hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 2.31/2.58 inference(quant_intro,[status(thm)],[850])).
% 2.31/2.58 tff(852,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c0_1(V))) | c1_1(U)) | c0_1(U)) | c1_1(V)) | hskp55)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause313')).
% 2.31/2.58 tff(853,plain,
% 2.31/2.58 (![V: $i, U: $i] : (hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 2.31/2.58 inference(modus_ponens,[status(thm)],[852, 851])).
% 2.31/2.58 tff(854,plain,
% 2.31/2.58 (![V: $i, U: $i] : (hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 2.31/2.58 inference(modus_ponens,[status(thm)],[853, 849])).
% 2.31/2.58 tff(855,plain,(
% 2.31/2.58 ![V: $i, U: $i] : (hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 2.31/2.58 inference(skolemize,[status(sab)],[854])).
% 2.31/2.58 tff(856,plain,
% 2.31/2.58 (![V: $i, U: $i] : (hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 2.31/2.58 inference(modus_ponens,[status(thm)],[855, 848])).
% 2.31/2.58 tff(857,plain,
% 2.31/2.58 (((~![V: $i, U: $i] : (hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp55 | c0_1(a663) | c1_1(a663) | (~ndr1_0) | (~c0_1(a648)) | (~c3_1(a648)) | c1_1(a648) | (~c3_1(a663)))) <=> ((~![V: $i, U: $i] : (hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp55 | c0_1(a663) | c1_1(a663) | (~ndr1_0) | (~c0_1(a648)) | (~c3_1(a648)) | c1_1(a648) | (~c3_1(a663)))),
% 2.31/2.58 inference(rewrite,[status(thm)],[])).
% 2.31/2.58 tff(858,plain,
% 2.31/2.58 ((hskp55 | (~ndr1_0) | c1_1(a663) | c0_1(a663) | (~c3_1(a663)) | c1_1(a648) | (~c3_1(a648)) | (~c0_1(a648))) <=> (hskp55 | c0_1(a663) | c1_1(a663) | (~ndr1_0) | (~c0_1(a648)) | (~c3_1(a648)) | c1_1(a648) | (~c3_1(a663)))),
% 2.31/2.58 inference(rewrite,[status(thm)],[])).
% 2.31/2.58 tff(859,plain,
% 2.31/2.58 (((~![V: $i, U: $i] : (hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp55 | (~ndr1_0) | c1_1(a663) | c0_1(a663) | (~c3_1(a663)) | c1_1(a648) | (~c3_1(a648)) | (~c0_1(a648)))) <=> ((~![V: $i, U: $i] : (hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp55 | c0_1(a663) | c1_1(a663) | (~ndr1_0) | (~c0_1(a648)) | (~c3_1(a648)) | c1_1(a648) | (~c3_1(a663))))),
% 2.31/2.58 inference(monotonicity,[status(thm)],[858])).
% 2.31/2.58 tff(860,plain,
% 2.31/2.58 (((~![V: $i, U: $i] : (hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp55 | (~ndr1_0) | c1_1(a663) | c0_1(a663) | (~c3_1(a663)) | c1_1(a648) | (~c3_1(a648)) | (~c0_1(a648)))) <=> ((~![V: $i, U: $i] : (hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp55 | c0_1(a663) | c1_1(a663) | (~ndr1_0) | (~c0_1(a648)) | (~c3_1(a648)) | c1_1(a648) | (~c3_1(a663)))),
% 2.31/2.58 inference(transitivity,[status(thm)],[859, 857])).
% 2.31/2.58 tff(861,plain,
% 2.31/2.58 ((~![V: $i, U: $i] : (hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp55 | (~ndr1_0) | c1_1(a663) | c0_1(a663) | (~c3_1(a663)) | c1_1(a648) | (~c3_1(a648)) | (~c0_1(a648)))),
% 2.31/2.58 inference(quant_inst,[status(thm)],[])).
% 2.31/2.58 tff(862,plain,
% 2.31/2.58 ((~![V: $i, U: $i] : (hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp55 | c0_1(a663) | c1_1(a663) | (~ndr1_0) | (~c0_1(a648)) | (~c3_1(a648)) | c1_1(a648) | (~c3_1(a663))),
% 2.31/2.58 inference(modus_ponens,[status(thm)],[861, 860])).
% 2.31/2.58 tff(863,plain,
% 2.31/2.58 (hskp55),
% 2.31/2.58 inference(unit_resolution,[status(thm)],[862, 87, 833, 804, 803, 832, 831, 856, 812])).
% 2.31/2.58 tff(864,plain,
% 2.31/2.58 (((~hskp55) | (~c2_1(a653))) <=> ((~hskp55) | (~c2_1(a653)))),
% 2.31/2.58 inference(rewrite,[status(thm)],[])).
% 2.31/2.58 tff(865,plain,
% 2.31/2.58 (((~c2_1(a653)) | (~hskp55)) <=> ((~hskp55) | (~c2_1(a653)))),
% 2.31/2.58 inference(rewrite,[status(thm)],[])).
% 2.31/2.58 tff(866,axiom,((~c2_1(a653)) | (~hskp55)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause185')).
% 2.31/2.58 tff(867,plain,
% 2.31/2.58 ((~hskp55) | (~c2_1(a653))),
% 2.31/2.58 inference(modus_ponens,[status(thm)],[866, 865])).
% 2.31/2.58 tff(868,plain,
% 2.31/2.58 ((~hskp55) | (~c2_1(a653))),
% 2.31/2.58 inference(modus_ponens,[status(thm)],[867, 864])).
% 2.31/2.58 tff(869,plain,
% 2.31/2.58 (~c2_1(a653)),
% 2.31/2.58 inference(unit_resolution,[status(thm)],[868, 863])).
% 2.31/2.58 tff(870,plain,
% 2.31/2.58 (((~hskp42) | c1_1(a618)) <=> ((~hskp42) | c1_1(a618))),
% 2.31/2.58 inference(rewrite,[status(thm)],[])).
% 2.31/2.58 tff(871,axiom,((~hskp42) | c1_1(a618)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause118')).
% 2.31/2.58 tff(872,plain,
% 2.31/2.58 ((~hskp42) | c1_1(a618)),
% 2.31/2.58 inference(modus_ponens,[status(thm)],[871, 870])).
% 2.31/2.58 tff(873,plain,
% 2.31/2.58 ((~hskp42) | c1_1(a618)),
% 2.31/2.58 inference(modus_ponens,[status(thm)],[872, 870])).
% 2.31/2.58 tff(874,plain,
% 2.31/2.58 ((~hskp42) | c1_1(a618)),
% 2.31/2.58 inference(modus_ponens,[status(thm)],[873, 870])).
% 2.31/2.58 tff(875,plain,
% 2.31/2.58 ((~hskp42) | c1_1(a618)),
% 2.31/2.58 inference(modus_ponens,[status(thm)],[874, 870])).
% 2.31/2.58 tff(876,plain,
% 2.31/2.58 ((~hskp42) | c1_1(a618)),
% 2.31/2.58 inference(modus_ponens,[status(thm)],[875, 870])).
% 2.31/2.58 tff(877,plain,
% 2.31/2.58 (c1_1(a618)),
% 2.31/2.58 inference(unit_resolution,[status(thm)],[876, 840])).
% 2.31/2.58 tff(878,plain,
% 2.31/2.58 (((~hskp55) | c1_1(a653)) <=> ((~hskp55) | c1_1(a653))),
% 2.31/2.58 inference(rewrite,[status(thm)],[])).
% 2.31/2.58 tff(879,axiom,((~hskp55) | c1_1(a653)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause96')).
% 2.31/2.58 tff(880,plain,
% 2.31/2.58 ((~hskp55) | c1_1(a653)),
% 2.31/2.58 inference(modus_ponens,[status(thm)],[879, 878])).
% 2.31/2.58 tff(881,plain,
% 2.31/2.58 ((~hskp55) | c1_1(a653)),
% 2.31/2.58 inference(modus_ponens,[status(thm)],[880, 878])).
% 2.31/2.58 tff(882,plain,
% 2.31/2.58 ((~hskp55) | c1_1(a653)),
% 2.31/2.58 inference(modus_ponens,[status(thm)],[881, 878])).
% 2.31/2.58 tff(883,plain,
% 2.31/2.58 ((~hskp55) | c1_1(a653)),
% 2.31/2.58 inference(modus_ponens,[status(thm)],[882, 878])).
% 2.31/2.58 tff(884,plain,
% 2.31/2.58 ((~hskp55) | c1_1(a653)),
% 2.31/2.58 inference(modus_ponens,[status(thm)],[883, 878])).
% 2.31/2.58 tff(885,plain,
% 2.31/2.58 (c1_1(a653)),
% 2.31/2.58 inference(unit_resolution,[status(thm)],[884, 863])).
% 2.31/2.58 tff(886,plain,
% 2.31/2.58 (((~hskp55) | c3_1(a653)) <=> ((~hskp55) | c3_1(a653))),
% 2.31/2.58 inference(rewrite,[status(thm)],[])).
% 2.31/2.58 tff(887,axiom,((~hskp55) | c3_1(a653)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause95')).
% 2.31/2.58 tff(888,plain,
% 2.31/2.58 ((~hskp55) | c3_1(a653)),
% 2.31/2.58 inference(modus_ponens,[status(thm)],[887, 886])).
% 2.31/2.58 tff(889,plain,
% 2.31/2.58 ((~hskp55) | c3_1(a653)),
% 2.31/2.58 inference(modus_ponens,[status(thm)],[888, 886])).
% 2.31/2.58 tff(890,plain,
% 2.31/2.58 ((~hskp55) | c3_1(a653)),
% 2.31/2.58 inference(modus_ponens,[status(thm)],[889, 886])).
% 2.31/2.58 tff(891,plain,
% 2.31/2.58 ((~hskp55) | c3_1(a653)),
% 2.31/2.58 inference(modus_ponens,[status(thm)],[890, 886])).
% 2.31/2.58 tff(892,plain,
% 2.31/2.58 ((~hskp55) | c3_1(a653)),
% 2.31/2.58 inference(modus_ponens,[status(thm)],[891, 886])).
% 2.31/2.58 tff(893,plain,
% 2.31/2.58 (c3_1(a653)),
% 2.31/2.58 inference(unit_resolution,[status(thm)],[892, 863])).
% 2.31/2.58 tff(894,plain,
% 2.31/2.58 (((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | c2_1(a653) | c2_1(a618) | (~ndr1_0) | (~c1_1(a618)) | (~c0_1(a618)) | (~c3_1(a653)) | (~c1_1(a653)))) <=> ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp41 | c2_1(a653) | c2_1(a618) | (~ndr1_0) | (~c1_1(a618)) | (~c0_1(a618)) | (~c3_1(a653)) | (~c1_1(a653)))),
% 2.31/2.58 inference(rewrite,[status(thm)],[])).
% 2.31/2.58 tff(895,plain,
% 2.31/2.58 ((hskp41 | (~ndr1_0) | c2_1(a653) | (~c3_1(a653)) | (~c1_1(a653)) | c2_1(a618) | (~c1_1(a618)) | (~c0_1(a618))) <=> (hskp41 | c2_1(a653) | c2_1(a618) | (~ndr1_0) | (~c1_1(a618)) | (~c0_1(a618)) | (~c3_1(a653)) | (~c1_1(a653)))),
% 2.31/2.58 inference(rewrite,[status(thm)],[])).
% 2.31/2.58 tff(896,plain,
% 2.31/2.58 (((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | (~ndr1_0) | c2_1(a653) | (~c3_1(a653)) | (~c1_1(a653)) | c2_1(a618) | (~c1_1(a618)) | (~c0_1(a618)))) <=> ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | c2_1(a653) | c2_1(a618) | (~ndr1_0) | (~c1_1(a618)) | (~c0_1(a618)) | (~c3_1(a653)) | (~c1_1(a653))))),
% 2.31/2.58 inference(monotonicity,[status(thm)],[895])).
% 2.31/2.58 tff(897,plain,
% 2.31/2.58 (((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | (~ndr1_0) | c2_1(a653) | (~c3_1(a653)) | (~c1_1(a653)) | c2_1(a618) | (~c1_1(a618)) | (~c0_1(a618)))) <=> ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp41 | c2_1(a653) | c2_1(a618) | (~ndr1_0) | (~c1_1(a618)) | (~c0_1(a618)) | (~c3_1(a653)) | (~c1_1(a653)))),
% 2.31/2.58 inference(transitivity,[status(thm)],[896, 894])).
% 2.31/2.58 tff(898,plain,
% 2.31/2.58 ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | (~ndr1_0) | c2_1(a653) | (~c3_1(a653)) | (~c1_1(a653)) | c2_1(a618) | (~c1_1(a618)) | (~c0_1(a618)))),
% 2.31/2.58 inference(quant_inst,[status(thm)],[])).
% 2.31/2.58 tff(899,plain,
% 2.31/2.58 ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp41 | c2_1(a653) | c2_1(a618) | (~ndr1_0) | (~c1_1(a618)) | (~c0_1(a618)) | (~c3_1(a653)) | (~c1_1(a653))),
% 2.31/2.58 inference(modus_ponens,[status(thm)],[898, 897])).
% 2.31/2.58 tff(900,plain,
% 2.31/2.58 (~c0_1(a618)),
% 2.31/2.58 inference(unit_resolution,[status(thm)],[899, 87, 97, 893, 885, 877, 869, 846, 299])).
% 2.31/2.58 tff(901,plain,
% 2.31/2.58 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)))),
% 2.31/2.58 inference(bind,[status(th)],[])).
% 2.31/2.58 tff(902,plain,
% 2.31/2.58 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 2.31/2.58 inference(quant_intro,[status(thm)],[901])).
% 2.31/2.58 tff(903,plain,
% 2.31/2.58 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 2.31/2.58 inference(rewrite,[status(thm)],[])).
% 2.31/2.58 tff(904,plain,
% 2.31/2.58 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)))), (((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))))), ((((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | (~c3_1(V))) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), ((((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | (~c3_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), (((((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | (~c3_1(V))) | (~c0_1(V))) | c3_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W))), (((((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | (~c3_1(V))) | (~c0_1(V))) | c3_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W)))), ((((((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | (~c3_1(V))) | (~c0_1(V))) | c3_1(W)) | c0_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W)) | c0_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | c3_1(W)) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W))), ((((((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | (~c3_1(V))) | (~c0_1(V))) | c3_1(W)) | c0_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W)))), (((((((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | (~c3_1(V))) | (~c0_1(V))) | c3_1(W)) | c0_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | c0_1(W) | c3_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))), (((((((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | (~c3_1(V))) | (~c0_1(V))) | c3_1(W)) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)))), ((((((((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | (~c3_1(V))) | (~c0_1(V))) | c3_1(W)) | c0_1(W)) | c2_1(W)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))), ((((((((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | (~c3_1(V))) | (~c0_1(V))) | c3_1(W)) | c0_1(W)) | c2_1(W)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)))), (((((((((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | (~c3_1(V))) | (~c0_1(V))) | c3_1(W)) | c0_1(W)) | c2_1(W)) | c1_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))), (((((((((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | (~c3_1(V))) | (~c0_1(V))) | c3_1(W)) | c0_1(W)) | c2_1(W)) | c1_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))))),
% 2.31/2.58 inference(bind,[status(th)],[])).
% 2.31/2.58 tff(905,plain,
% 2.31/2.58 (![W: $i, V: $i, U: $i] : ((((((((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | (~c3_1(V))) | (~c0_1(V))) | c3_1(W)) | c0_1(W)) | c2_1(W)) | c1_1(U)) | c2_1(V)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 2.31/2.58 inference(quant_intro,[status(thm)],[904])).
% 2.31/2.58 tff(906,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~ndr1_0) | (~c3_1(U))) | (~c0_1(U))) | (~c3_1(V))) | (~c0_1(V))) | c3_1(W)) | c0_1(W)) | c2_1(W)) | c1_1(U)) | c2_1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause322')).
% 2.31/2.58 tff(907,plain,
% 2.31/2.58 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 2.31/2.58 inference(modus_ponens,[status(thm)],[906, 905])).
% 2.31/2.58 tff(908,plain,
% 2.31/2.58 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 2.31/2.58 inference(modus_ponens,[status(thm)],[907, 903])).
% 2.31/2.58 tff(909,plain,(
% 2.31/2.58 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 2.31/2.58 inference(skolemize,[status(sab)],[908])).
% 2.31/2.58 tff(910,plain,
% 2.31/2.58 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))),
% 2.31/2.58 inference(modus_ponens,[status(thm)],[909, 902])).
% 2.31/2.58 tff(911,plain,
% 2.31/2.58 (((~hskp42) | (~c3_1(a618))) <=> ((~hskp42) | (~c3_1(a618)))),
% 2.31/2.58 inference(rewrite,[status(thm)],[])).
% 2.31/2.58 tff(912,plain,
% 2.31/2.58 (((~c3_1(a618)) | (~hskp42)) <=> ((~hskp42) | (~c3_1(a618)))),
% 2.31/2.58 inference(rewrite,[status(thm)],[])).
% 2.31/2.58 tff(913,axiom,((~c3_1(a618)) | (~hskp42)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause202')).
% 2.31/2.58 tff(914,plain,
% 2.31/2.58 ((~hskp42) | (~c3_1(a618))),
% 2.31/2.58 inference(modus_ponens,[status(thm)],[913, 912])).
% 2.31/2.58 tff(915,plain,
% 2.31/2.58 ((~hskp42) | (~c3_1(a618))),
% 2.31/2.58 inference(modus_ponens,[status(thm)],[914, 911])).
% 2.31/2.58 tff(916,plain,
% 2.31/2.58 (~c3_1(a618)),
% 2.31/2.58 inference(unit_resolution,[status(thm)],[915, 840])).
% 2.31/2.58 tff(917,plain,
% 2.31/2.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a648) | c2_1(a618) | c3_1(a618) | (~ndr1_0) | c0_1(a618) | (~c0_1(a648)) | (~c3_1(a648)) | c1_1(a648))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a648) | c2_1(a618) | c3_1(a618) | (~ndr1_0) | c0_1(a618) | (~c0_1(a648)) | (~c3_1(a648)) | c1_1(a648))),
% 2.31/2.58 inference(rewrite,[status(thm)],[])).
% 2.31/2.58 tff(918,plain,
% 2.31/2.58 (((~ndr1_0) | c1_1(a648) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a648) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a618) | c0_1(a618) | c3_1(a618)) <=> (c2_1(a648) | c2_1(a618) | c3_1(a618) | (~ndr1_0) | c0_1(a618) | (~c0_1(a648)) | (~c3_1(a648)) | c1_1(a648))),
% 2.31/2.58 inference(rewrite,[status(thm)],[])).
% 2.31/2.58 tff(919,plain,
% 2.31/2.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a648) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a648) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a618) | c0_1(a618) | c3_1(a618))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a648) | c2_1(a618) | c3_1(a618) | (~ndr1_0) | c0_1(a618) | (~c0_1(a648)) | (~c3_1(a648)) | c1_1(a648)))),
% 2.31/2.58 inference(monotonicity,[status(thm)],[918])).
% 2.31/2.58 tff(920,plain,
% 2.31/2.58 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a648) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a648) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a618) | c0_1(a618) | c3_1(a618))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a648) | c2_1(a618) | c3_1(a618) | (~ndr1_0) | c0_1(a618) | (~c0_1(a648)) | (~c3_1(a648)) | c1_1(a648))),
% 2.31/2.58 inference(transitivity,[status(thm)],[919, 917])).
% 2.31/2.58 tff(921,plain,
% 2.31/2.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a648) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a648) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a618) | c0_1(a618) | c3_1(a618))),
% 2.31/2.58 inference(quant_inst,[status(thm)],[])).
% 2.31/2.58 tff(922,plain,
% 2.31/2.58 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a648) | c2_1(a618) | c3_1(a618) | (~ndr1_0) | c0_1(a618) | (~c0_1(a648)) | (~c3_1(a648)) | c1_1(a648)),
% 2.31/2.58 inference(modus_ponens,[status(thm)],[921, 920])).
% 2.31/2.58 tff(923,plain,
% 2.31/2.58 ($false),
% 2.31/2.58 inference(unit_resolution,[status(thm)],[922, 87, 804, 803, 802, 846, 916, 910, 900, 812])).
% 2.31/2.58 tff(924,plain,(hskp41 | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a648)), inference(lemma,lemma(discharge,[]))).
% 2.31/2.58 tff(925,plain,
% 2.31/2.58 (hskp41),
% 2.31/2.58 inference(unit_resolution,[status(thm)],[924, 793, 801, 785])).
% 2.31/2.58 tff(926,plain,
% 2.31/2.58 (c2_1(a617)),
% 2.31/2.58 inference(unit_resolution,[status(thm)],[496, 925])).
% 2.31/2.58 tff(927,plain,
% 2.31/2.58 (c3_1(a617)),
% 2.31/2.58 inference(unit_resolution,[status(thm)],[471, 925])).
% 2.31/2.58 tff(928,plain,
% 2.31/2.58 (^[U: $i] : refl((hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))),
% 2.31/2.58 inference(bind,[status(th)],[])).
% 2.31/2.58 tff(929,plain,
% 2.31/2.58 (![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 2.31/2.58 inference(quant_intro,[status(thm)],[928])).
% 2.31/2.58 tff(930,plain,
% 2.31/2.58 (![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 2.31/2.58 inference(rewrite,[status(thm)],[])).
% 2.31/2.58 tff(931,plain,
% 2.31/2.58 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp3) <=> (((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp3))), rewrite((((~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp3) <=> (hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp3) | hskp29) <=> ((hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp29))), rewrite(((hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U))) | hskp29) <=> (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp3) | hskp29) <=> (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))))),
% 2.31/2.58 inference(bind,[status(th)],[])).
% 2.31/2.58 tff(932,plain,
% 2.31/2.58 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp3) | hskp29) <=> ![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 2.31/2.58 inference(quant_intro,[status(thm)],[931])).
% 2.31/2.58 tff(933,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp3) | hskp29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause288')).
% 2.31/2.58 tff(934,plain,
% 2.31/2.58 (![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 2.31/2.58 inference(modus_ponens,[status(thm)],[933, 932])).
% 2.31/2.58 tff(935,plain,
% 2.31/2.58 (![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 2.31/2.58 inference(modus_ponens,[status(thm)],[934, 930])).
% 2.31/2.58 tff(936,plain,(
% 2.31/2.58 ![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 2.31/2.58 inference(skolemize,[status(sab)],[935])).
% 2.31/2.58 tff(937,plain,
% 2.31/2.58 (![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))),
% 2.31/2.58 inference(modus_ponens,[status(thm)],[936, 929])).
% 2.31/2.58 tff(938,assumption,(~c0_1(a617)), introduced(assumption)).
% 2.31/2.58 tff(939,plain,
% 2.31/2.58 (~hskp65),
% 2.31/2.58 inference(unit_resolution,[status(thm)],[265, 256, 257])).
% 2.31/2.58 tff(940,plain,
% 2.31/2.58 (hskp66),
% 2.31/2.58 inference(unit_resolution,[status(thm)],[85, 939, 24])).
% 2.31/2.58 tff(941,plain,
% 2.31/2.58 (~c2_1(a675)),
% 2.31/2.58 inference(unit_resolution,[status(thm)],[272, 940])).
% 2.31/2.58 tff(942,plain,
% 2.31/2.58 (c3_1(a675)),
% 2.31/2.58 inference(unit_resolution,[status(thm)],[280, 940])).
% 2.31/2.58 tff(943,assumption,(~c3_1(a603)), introduced(assumption)).
% 2.31/2.58 tff(944,plain,
% 2.31/2.58 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W))) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W))))),
% 2.31/2.58 inference(bind,[status(th)],[])).
% 2.31/2.58 tff(945,plain,
% 2.31/2.58 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))),
% 2.31/2.58 inference(quant_intro,[status(thm)],[944])).
% 2.31/2.58 tff(946,plain,
% 2.31/2.58 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))),
% 2.31/2.58 inference(rewrite,[status(thm)],[])).
% 2.31/2.58 tff(947,plain,
% 2.31/2.58 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c3_1(W))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(W)) | (~c3_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(W)) | (~c3_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | (~c0_1(W))) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(W)) | (~c3_1(W))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(W)) | (~c3_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(W)) | (~c3_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | (~c0_1(W))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(W)) | (~c3_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | (~c0_1(W))) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(W)) | (~c3_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(W)) | (~c3_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(W)) | (~c3_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | (~c0_1(W))) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(W)) | (~c3_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | (~c0_1(W))) | c3_1(U)) | c0_1(V)) | c2_1(W)) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(W)) | (~c3_1(W))) | c2_1(W)))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | (~c0_1(W)) | (~c3_1(W))) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | (~c0_1(W))) | c3_1(U)) | c0_1(V)) | c2_1(W)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))))),
% 2.31/2.58 inference(bind,[status(th)],[])).
% 2.31/2.58 tff(948,plain,
% 2.31/2.58 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | (~c0_1(W))) | c3_1(U)) | c0_1(V)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))),
% 2.31/2.58 inference(quant_intro,[status(thm)],[947])).
% 2.31/2.58 tff(949,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c3_1(V))) | (~c3_1(W))) | (~c0_1(W))) | c3_1(U)) | c0_1(V)) | c2_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause327')).
% 2.31/2.58 tff(950,plain,
% 2.31/2.58 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))),
% 2.31/2.58 inference(modus_ponens,[status(thm)],[949, 948])).
% 2.31/2.58 tff(951,plain,
% 2.31/2.58 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))),
% 2.31/2.58 inference(modus_ponens,[status(thm)],[950, 946])).
% 2.31/2.58 tff(952,plain,(
% 2.31/2.58 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))),
% 2.31/2.58 inference(skolemize,[status(sab)],[951])).
% 2.31/2.58 tff(953,plain,
% 2.31/2.58 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))),
% 2.31/2.58 inference(modus_ponens,[status(thm)],[952, 945])).
% 2.31/2.58 tff(954,plain,
% 2.31/2.58 (hskp41),
% 2.31/2.58 inference(unit_resolution,[status(thm)],[924, 803, 804, 802])).
% 2.31/2.58 tff(955,plain,
% 2.31/2.58 (~c1_1(a617)),
% 2.31/2.58 inference(unit_resolution,[status(thm)],[463, 954])).
% 2.31/2.58 tff(956,plain,
% 2.31/2.58 (c3_1(a617)),
% 2.31/2.58 inference(unit_resolution,[status(thm)],[471, 954])).
% 2.31/2.58 tff(957,plain,
% 2.31/2.58 (c2_1(a617)),
% 2.31/2.58 inference(unit_resolution,[status(thm)],[496, 954])).
% 2.31/2.58 tff(958,assumption,(c0_1(a635)), introduced(assumption)).
% 2.31/2.58 tff(959,assumption,(~c1_1(a635)), introduced(assumption)).
% 2.31/2.58 tff(960,plain,
% 2.31/2.58 (hskp41),
% 2.31/2.58 inference(unit_resolution,[status(thm)],[924, 804, 803, 802])).
% 2.31/2.58 tff(961,plain,
% 2.31/2.58 (~c1_1(a617)),
% 2.31/2.58 inference(unit_resolution,[status(thm)],[463, 960])).
% 2.31/2.58 tff(962,assumption,(~c2_1(a635)), introduced(assumption)).
% 2.31/2.58 tff(963,plain,
% 2.31/2.58 (c3_1(a617)),
% 2.31/2.59 inference(unit_resolution,[status(thm)],[471, 960])).
% 2.31/2.59 tff(964,plain,
% 2.31/2.59 (c2_1(a617)),
% 2.31/2.59 inference(unit_resolution,[status(thm)],[496, 960])).
% 2.31/2.59 tff(965,plain,
% 2.31/2.59 (hskp15 | hskp14 | (~c0_1(a617))),
% 2.31/2.59 inference(unit_resolution,[status(thm)],[552, 87, 964, 961, 232])).
% 2.31/2.59 tff(966,plain,
% 2.31/2.59 (~c0_1(a617)),
% 2.31/2.59 inference(unit_resolution,[status(thm)],[965, 257, 256])).
% 2.31/2.59 tff(967,plain,
% 2.31/2.59 (^[V: $i, U: $i] : refl((hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))))),
% 2.31/2.59 inference(bind,[status(th)],[])).
% 2.31/2.59 tff(968,plain,
% 2.31/2.59 (![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 2.31/2.59 inference(quant_intro,[status(thm)],[967])).
% 2.31/2.59 tff(969,plain,
% 2.31/2.59 (![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 2.31/2.59 inference(rewrite,[status(thm)],[])).
% 2.31/2.59 tff(970,plain,
% 2.31/2.59 (^[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))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp45) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp45))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V))) | hskp45) <=> (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp45) <=> (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))))),
% 2.31/2.59 inference(bind,[status(th)],[])).
% 2.31/2.59 tff(971,plain,
% 2.31/2.59 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp45) <=> ![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 2.31/2.59 inference(quant_intro,[status(thm)],[970])).
% 2.31/2.59 tff(972,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | hskp45)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause308')).
% 2.31/2.59 tff(973,plain,
% 2.31/2.59 (![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 2.31/2.59 inference(modus_ponens,[status(thm)],[972, 971])).
% 2.31/2.59 tff(974,plain,
% 2.31/2.59 (![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 2.31/2.59 inference(modus_ponens,[status(thm)],[973, 969])).
% 2.31/2.59 tff(975,plain,(
% 2.31/2.59 ![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 2.31/2.59 inference(skolemize,[status(sab)],[974])).
% 2.31/2.59 tff(976,plain,
% 2.31/2.59 (![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))),
% 2.31/2.59 inference(modus_ponens,[status(thm)],[975, 968])).
% 2.31/2.59 tff(977,plain,
% 2.31/2.59 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | c1_1(a617) | c1_1(a635) | c2_1(a635) | (~ndr1_0) | (~c0_1(a635)) | c0_1(a617) | (~c3_1(a617)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c1_1(a617) | c1_1(a635) | c2_1(a635) | (~ndr1_0) | (~c0_1(a635)) | c0_1(a617) | (~c3_1(a617)))),
% 2.31/2.59 inference(rewrite,[status(thm)],[])).
% 2.31/2.59 tff(978,plain,
% 2.31/2.59 ((hskp42 | (~ndr1_0) | c1_1(a635) | c2_1(a635) | (~c0_1(a635)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617))) <=> (hskp42 | c1_1(a617) | c1_1(a635) | c2_1(a635) | (~ndr1_0) | (~c0_1(a635)) | c0_1(a617) | (~c3_1(a617)))),
% 2.31/2.59 inference(rewrite,[status(thm)],[])).
% 2.31/2.59 tff(979,plain,
% 2.31/2.59 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a635) | c2_1(a635) | (~c0_1(a635)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | c1_1(a617) | c1_1(a635) | c2_1(a635) | (~ndr1_0) | (~c0_1(a635)) | c0_1(a617) | (~c3_1(a617))))),
% 2.31/2.59 inference(monotonicity,[status(thm)],[978])).
% 2.31/2.59 tff(980,plain,
% 2.31/2.59 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a635) | c2_1(a635) | (~c0_1(a635)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c1_1(a617) | c1_1(a635) | c2_1(a635) | (~ndr1_0) | (~c0_1(a635)) | c0_1(a617) | (~c3_1(a617)))),
% 2.31/2.59 inference(transitivity,[status(thm)],[979, 977])).
% 2.31/2.59 tff(981,plain,
% 2.31/2.59 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a635) | c2_1(a635) | (~c0_1(a635)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)))),
% 2.31/2.59 inference(quant_inst,[status(thm)],[])).
% 2.31/2.59 tff(982,plain,
% 2.31/2.59 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c1_1(a617) | c1_1(a635) | c2_1(a635) | (~ndr1_0) | (~c0_1(a635)) | c0_1(a617) | (~c3_1(a617))),
% 2.31/2.59 inference(modus_ponens,[status(thm)],[981, 980])).
% 2.31/2.59 tff(983,plain,
% 2.31/2.59 (hskp42 | (~c0_1(a635)) | c0_1(a617)),
% 2.31/2.59 inference(unit_resolution,[status(thm)],[982, 87, 648, 647, 959, 962, 822])).
% 2.31/2.59 tff(984,plain,
% 2.31/2.59 (hskp42),
% 2.31/2.59 inference(unit_resolution,[status(thm)],[983, 938, 958])).
% 2.31/2.59 tff(985,plain,
% 2.31/2.59 (~c3_1(a618)),
% 2.31/2.59 inference(unit_resolution,[status(thm)],[915, 984])).
% 2.31/2.59 tff(986,plain,
% 2.31/2.59 (~c2_1(a618)),
% 2.31/2.59 inference(unit_resolution,[status(thm)],[845, 984])).
% 2.31/2.59 tff(987,plain,
% 2.31/2.59 (c1_1(a618)),
% 2.31/2.59 inference(unit_resolution,[status(thm)],[876, 984])).
% 2.31/2.59 tff(988,assumption,(~hskp45), introduced(assumption)).
% 2.31/2.59 tff(989,plain,
% 2.31/2.59 (((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp45 | c2_1(a618) | c3_1(a618) | (~ndr1_0) | (~c1_1(a618)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))) <=> ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp45 | c2_1(a618) | c3_1(a618) | (~ndr1_0) | (~c1_1(a618)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 2.31/2.59 inference(rewrite,[status(thm)],[])).
% 2.31/2.59 tff(990,plain,
% 2.31/2.59 ((hskp45 | (~ndr1_0) | c3_1(a618) | c2_1(a618) | (~c1_1(a618)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617))) <=> (hskp45 | c2_1(a618) | c3_1(a618) | (~ndr1_0) | (~c1_1(a618)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 2.31/2.59 inference(rewrite,[status(thm)],[])).
% 2.31/2.59 tff(991,plain,
% 2.31/2.59 (((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp45 | (~ndr1_0) | c3_1(a618) | c2_1(a618) | (~c1_1(a618)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))) <=> ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp45 | c2_1(a618) | c3_1(a618) | (~ndr1_0) | (~c1_1(a618)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617))))),
% 2.31/2.59 inference(monotonicity,[status(thm)],[990])).
% 2.31/2.59 tff(992,plain,
% 2.31/2.59 (((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp45 | (~ndr1_0) | c3_1(a618) | c2_1(a618) | (~c1_1(a618)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))) <=> ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp45 | c2_1(a618) | c3_1(a618) | (~ndr1_0) | (~c1_1(a618)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 2.31/2.59 inference(transitivity,[status(thm)],[991, 989])).
% 2.31/2.59 tff(993,plain,
% 2.31/2.59 ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp45 | (~ndr1_0) | c3_1(a618) | c2_1(a618) | (~c1_1(a618)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 2.31/2.59 inference(quant_inst,[status(thm)],[])).
% 2.31/2.59 tff(994,plain,
% 2.31/2.59 ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp45 | c2_1(a618) | c3_1(a618) | (~ndr1_0) | (~c1_1(a618)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617))),
% 2.31/2.59 inference(modus_ponens,[status(thm)],[993, 992])).
% 2.31/2.59 tff(995,plain,
% 2.31/2.59 ($false),
% 2.31/2.59 inference(unit_resolution,[status(thm)],[994, 87, 988, 987, 649, 648, 986, 985, 976, 938])).
% 2.31/2.59 tff(996,plain,(c0_1(a617) | hskp45 | (~c2_1(a617)) | (~c3_1(a617)) | (~c0_1(a635)) | c1_1(a617) | c1_1(a635) | c2_1(a635)), inference(lemma,lemma(discharge,[]))).
% 2.31/2.59 tff(997,plain,
% 2.31/2.59 (hskp45),
% 2.31/2.59 inference(unit_resolution,[status(thm)],[996, 966, 964, 963, 962, 961, 959, 958])).
% 2.31/2.59 tff(998,plain,
% 2.31/2.59 (((~hskp45) | (~c0_1(a623))) <=> ((~hskp45) | (~c0_1(a623)))),
% 2.31/2.59 inference(rewrite,[status(thm)],[])).
% 2.31/2.59 tff(999,plain,
% 2.31/2.59 (((~c0_1(a623)) | (~hskp45)) <=> ((~hskp45) | (~c0_1(a623)))),
% 2.31/2.59 inference(rewrite,[status(thm)],[])).
% 2.31/2.59 tff(1000,axiom,((~c0_1(a623)) | (~hskp45)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause197')).
% 2.31/2.59 tff(1001,plain,
% 2.31/2.59 ((~hskp45) | (~c0_1(a623))),
% 2.31/2.59 inference(modus_ponens,[status(thm)],[1000, 999])).
% 2.31/2.59 tff(1002,plain,
% 2.31/2.59 ((~hskp45) | (~c0_1(a623))),
% 2.31/2.59 inference(modus_ponens,[status(thm)],[1001, 998])).
% 2.31/2.59 tff(1003,plain,
% 2.31/2.59 (~c0_1(a623)),
% 2.31/2.59 inference(unit_resolution,[status(thm)],[1002, 997])).
% 2.31/2.59 tff(1004,plain,
% 2.31/2.59 (((~hskp45) | c3_1(a623)) <=> ((~hskp45) | c3_1(a623))),
% 2.31/2.59 inference(rewrite,[status(thm)],[])).
% 2.31/2.59 tff(1005,axiom,((~hskp45) | c3_1(a623)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause113')).
% 2.31/2.59 tff(1006,plain,
% 2.31/2.59 ((~hskp45) | c3_1(a623)),
% 2.31/2.59 inference(modus_ponens,[status(thm)],[1005, 1004])).
% 2.31/2.59 tff(1007,plain,
% 2.31/2.59 ((~hskp45) | c3_1(a623)),
% 2.31/2.59 inference(modus_ponens,[status(thm)],[1006, 1004])).
% 2.31/2.59 tff(1008,plain,
% 2.31/2.59 ((~hskp45) | c3_1(a623)),
% 2.31/2.59 inference(modus_ponens,[status(thm)],[1007, 1004])).
% 2.42/2.59 tff(1009,plain,
% 2.42/2.59 ((~hskp45) | c3_1(a623)),
% 2.42/2.59 inference(modus_ponens,[status(thm)],[1008, 1004])).
% 2.42/2.59 tff(1010,plain,
% 2.42/2.59 ((~hskp45) | c3_1(a623)),
% 2.42/2.59 inference(modus_ponens,[status(thm)],[1009, 1004])).
% 2.42/2.59 tff(1011,plain,
% 2.42/2.59 (c3_1(a623)),
% 2.42/2.59 inference(unit_resolution,[status(thm)],[1010, 997])).
% 2.42/2.59 tff(1012,plain,
% 2.42/2.59 (((~hskp45) | c2_1(a623)) <=> ((~hskp45) | c2_1(a623))),
% 2.42/2.59 inference(rewrite,[status(thm)],[])).
% 2.42/2.59 tff(1013,axiom,((~hskp45) | c2_1(a623)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause114')).
% 2.42/2.59 tff(1014,plain,
% 2.42/2.59 ((~hskp45) | c2_1(a623)),
% 2.42/2.59 inference(modus_ponens,[status(thm)],[1013, 1012])).
% 2.42/2.59 tff(1015,plain,
% 2.42/2.59 ((~hskp45) | c2_1(a623)),
% 2.42/2.59 inference(modus_ponens,[status(thm)],[1014, 1012])).
% 2.42/2.59 tff(1016,plain,
% 2.42/2.59 ((~hskp45) | c2_1(a623)),
% 2.42/2.59 inference(modus_ponens,[status(thm)],[1015, 1012])).
% 2.42/2.59 tff(1017,plain,
% 2.42/2.59 ((~hskp45) | c2_1(a623)),
% 2.42/2.59 inference(modus_ponens,[status(thm)],[1016, 1012])).
% 2.42/2.59 tff(1018,plain,
% 2.42/2.59 ((~hskp45) | c2_1(a623)),
% 2.42/2.59 inference(modus_ponens,[status(thm)],[1017, 1012])).
% 2.42/2.59 tff(1019,plain,
% 2.42/2.59 (c2_1(a623)),
% 2.42/2.59 inference(unit_resolution,[status(thm)],[1018, 997])).
% 2.42/2.59 tff(1020,assumption,(hskp9), introduced(assumption)).
% 2.42/2.59 tff(1021,plain,
% 2.42/2.59 (((~hskp9) | (~c3_1(a613))) <=> ((~hskp9) | (~c3_1(a613)))),
% 2.42/2.59 inference(rewrite,[status(thm)],[])).
% 2.42/2.59 tff(1022,plain,
% 2.42/2.59 (((~c3_1(a613)) | (~hskp9)) <=> ((~hskp9) | (~c3_1(a613)))),
% 2.42/2.59 inference(rewrite,[status(thm)],[])).
% 2.42/2.59 tff(1023,axiom,((~c3_1(a613)) | (~hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause258')).
% 2.42/2.59 tff(1024,plain,
% 2.42/2.59 ((~hskp9) | (~c3_1(a613))),
% 2.42/2.59 inference(modus_ponens,[status(thm)],[1023, 1022])).
% 2.42/2.59 tff(1025,plain,
% 2.42/2.59 ((~hskp9) | (~c3_1(a613))),
% 2.42/2.59 inference(modus_ponens,[status(thm)],[1024, 1021])).
% 2.42/2.59 tff(1026,plain,
% 2.42/2.59 (~c3_1(a613)),
% 2.42/2.59 inference(unit_resolution,[status(thm)],[1025, 1020])).
% 2.42/2.59 tff(1027,assumption,(~c0_1(a623)), introduced(assumption)).
% 2.42/2.59 tff(1028,plain,
% 2.42/2.59 (((~hskp9) | c2_1(a613)) <=> ((~hskp9) | c2_1(a613))),
% 2.42/2.59 inference(rewrite,[status(thm)],[])).
% 2.42/2.59 tff(1029,axiom,((~hskp9) | c2_1(a613)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause161')).
% 2.42/2.59 tff(1030,plain,
% 2.42/2.59 ((~hskp9) | c2_1(a613)),
% 2.42/2.59 inference(modus_ponens,[status(thm)],[1029, 1028])).
% 2.42/2.59 tff(1031,plain,
% 2.42/2.59 ((~hskp9) | c2_1(a613)),
% 2.42/2.59 inference(modus_ponens,[status(thm)],[1030, 1028])).
% 2.42/2.59 tff(1032,plain,
% 2.42/2.59 ((~hskp9) | c2_1(a613)),
% 2.42/2.59 inference(modus_ponens,[status(thm)],[1031, 1028])).
% 2.42/2.59 tff(1033,plain,
% 2.42/2.59 ((~hskp9) | c2_1(a613)),
% 2.42/2.59 inference(modus_ponens,[status(thm)],[1032, 1028])).
% 2.42/2.59 tff(1034,plain,
% 2.42/2.59 ((~hskp9) | c2_1(a613)),
% 2.42/2.59 inference(modus_ponens,[status(thm)],[1033, 1028])).
% 2.42/2.59 tff(1035,plain,
% 2.42/2.59 (c2_1(a613)),
% 2.42/2.59 inference(unit_resolution,[status(thm)],[1034, 1020])).
% 2.42/2.59 tff(1036,plain,
% 2.42/2.59 (((~hskp9) | c1_1(a613)) <=> ((~hskp9) | c1_1(a613))),
% 2.42/2.59 inference(rewrite,[status(thm)],[])).
% 2.42/2.59 tff(1037,axiom,((~hskp9) | c1_1(a613)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause160')).
% 2.42/2.59 tff(1038,plain,
% 2.42/2.59 ((~hskp9) | c1_1(a613)),
% 2.42/2.59 inference(modus_ponens,[status(thm)],[1037, 1036])).
% 2.42/2.59 tff(1039,plain,
% 2.42/2.59 ((~hskp9) | c1_1(a613)),
% 2.42/2.59 inference(modus_ponens,[status(thm)],[1038, 1036])).
% 2.42/2.59 tff(1040,plain,
% 2.42/2.59 ((~hskp9) | c1_1(a613)),
% 2.42/2.59 inference(modus_ponens,[status(thm)],[1039, 1036])).
% 2.42/2.59 tff(1041,plain,
% 2.42/2.59 ((~hskp9) | c1_1(a613)),
% 2.42/2.59 inference(modus_ponens,[status(thm)],[1040, 1036])).
% 2.42/2.59 tff(1042,plain,
% 2.42/2.59 ((~hskp9) | c1_1(a613)),
% 2.42/2.59 inference(modus_ponens,[status(thm)],[1041, 1036])).
% 2.42/2.59 tff(1043,plain,
% 2.42/2.59 (c1_1(a613)),
% 2.42/2.59 inference(unit_resolution,[status(thm)],[1042, 1020])).
% 2.42/2.59 tff(1044,assumption,(c2_1(a623)), introduced(assumption)).
% 2.42/2.59 tff(1045,assumption,(c3_1(a623)), introduced(assumption)).
% 2.42/2.59 tff(1046,plain,
% 2.42/2.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | (c2_1(a648) | c0_1(a623) | c3_1(a613) | (~ndr1_0) | (~c1_1(a613)) | (~c2_1(a613)) | (~c2_1(a623)) | (~c3_1(a623)) | (~c0_1(a648)) | (~c3_1(a648)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c2_1(a648) | c0_1(a623) | c3_1(a613) | (~ndr1_0) | (~c1_1(a613)) | (~c2_1(a613)) | (~c2_1(a623)) | (~c3_1(a623)) | (~c0_1(a648)) | (~c3_1(a648)))),
% 2.42/2.59 inference(rewrite,[status(thm)],[])).
% 2.42/2.59 tff(1047,plain,
% 2.42/2.59 (((~ndr1_0) | c3_1(a613) | (~c1_1(a613)) | (~c2_1(a613)) | c0_1(a623) | (~c2_1(a623)) | (~c3_1(a623)) | c2_1(a648) | (~c0_1(a648)) | (~c3_1(a648))) <=> (c2_1(a648) | c0_1(a623) | c3_1(a613) | (~ndr1_0) | (~c1_1(a613)) | (~c2_1(a613)) | (~c2_1(a623)) | (~c3_1(a623)) | (~c0_1(a648)) | (~c3_1(a648)))),
% 2.42/2.59 inference(rewrite,[status(thm)],[])).
% 2.42/2.59 tff(1048,plain,
% 2.42/2.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a613) | (~c1_1(a613)) | (~c2_1(a613)) | c0_1(a623) | (~c2_1(a623)) | (~c3_1(a623)) | c2_1(a648) | (~c0_1(a648)) | (~c3_1(a648)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | (c2_1(a648) | c0_1(a623) | c3_1(a613) | (~ndr1_0) | (~c1_1(a613)) | (~c2_1(a613)) | (~c2_1(a623)) | (~c3_1(a623)) | (~c0_1(a648)) | (~c3_1(a648))))),
% 2.42/2.59 inference(monotonicity,[status(thm)],[1047])).
% 2.42/2.59 tff(1049,plain,
% 2.42/2.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a613) | (~c1_1(a613)) | (~c2_1(a613)) | c0_1(a623) | (~c2_1(a623)) | (~c3_1(a623)) | c2_1(a648) | (~c0_1(a648)) | (~c3_1(a648)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c2_1(a648) | c0_1(a623) | c3_1(a613) | (~ndr1_0) | (~c1_1(a613)) | (~c2_1(a613)) | (~c2_1(a623)) | (~c3_1(a623)) | (~c0_1(a648)) | (~c3_1(a648)))),
% 2.42/2.59 inference(transitivity,[status(thm)],[1048, 1046])).
% 2.42/2.59 tff(1050,plain,
% 2.42/2.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a613) | (~c1_1(a613)) | (~c2_1(a613)) | c0_1(a623) | (~c2_1(a623)) | (~c3_1(a623)) | c2_1(a648) | (~c0_1(a648)) | (~c3_1(a648)))),
% 2.42/2.59 inference(quant_inst,[status(thm)],[])).
% 2.42/2.59 tff(1051,plain,
% 2.42/2.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c2_1(a648) | c0_1(a623) | c3_1(a613) | (~ndr1_0) | (~c1_1(a613)) | (~c2_1(a613)) | (~c2_1(a623)) | (~c3_1(a623)) | (~c0_1(a648)) | (~c3_1(a648))),
% 2.42/2.59 inference(modus_ponens,[status(thm)],[1050, 1049])).
% 2.42/2.59 tff(1052,plain,
% 2.42/2.59 ($false),
% 2.42/2.59 inference(unit_resolution,[status(thm)],[1051, 87, 804, 803, 1045, 1044, 1043, 1035, 802, 1027, 1026, 953])).
% 2.42/2.59 tff(1053,plain,((~hskp9) | (~c3_1(a648)) | (~c0_1(a648)) | (~c3_1(a623)) | (~c2_1(a623)) | c2_1(a648) | c0_1(a623)), inference(lemma,lemma(discharge,[]))).
% 2.42/2.59 tff(1054,plain,
% 2.42/2.59 (~hskp9),
% 2.42/2.59 inference(unit_resolution,[status(thm)],[1053, 1019, 804, 803, 1011, 802, 1003])).
% 2.42/2.59 tff(1055,plain,
% 2.42/2.59 ((hskp17 | hskp16 | hskp9) <=> (hskp17 | hskp16 | hskp9)),
% 2.42/2.59 inference(rewrite,[status(thm)],[])).
% 2.42/2.59 tff(1056,plain,
% 2.42/2.59 (((hskp16 | hskp17) | hskp9) <=> (hskp17 | hskp16 | hskp9)),
% 2.42/2.59 inference(rewrite,[status(thm)],[])).
% 2.42/2.59 tff(1057,axiom,((hskp16 | hskp17) | hskp9), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause71')).
% 2.42/2.59 tff(1058,plain,
% 2.42/2.59 (hskp17 | hskp16 | hskp9),
% 2.42/2.59 inference(modus_ponens,[status(thm)],[1057, 1056])).
% 2.42/2.59 tff(1059,plain,
% 2.42/2.59 (hskp17 | hskp16 | hskp9),
% 2.42/2.59 inference(modus_ponens,[status(thm)],[1058, 1055])).
% 2.42/2.59 tff(1060,plain,
% 2.42/2.59 (hskp17 | hskp16 | hskp9),
% 2.42/2.59 inference(modus_ponens,[status(thm)],[1059, 1055])).
% 2.42/2.59 tff(1061,plain,
% 2.42/2.59 (hskp17 | hskp16 | hskp9),
% 2.42/2.59 inference(modus_ponens,[status(thm)],[1060, 1055])).
% 2.42/2.59 tff(1062,plain,
% 2.42/2.59 (hskp17 | hskp16 | hskp9),
% 2.42/2.59 inference(modus_ponens,[status(thm)],[1061, 1055])).
% 2.42/2.59 tff(1063,plain,
% 2.42/2.59 (hskp16),
% 2.42/2.59 inference(unit_resolution,[status(thm)],[1062, 1054, 12])).
% 2.42/2.59 tff(1064,plain,
% 2.42/2.59 (((~hskp16) | (~c3_1(a627))) <=> ((~hskp16) | (~c3_1(a627)))),
% 2.42/2.59 inference(rewrite,[status(thm)],[])).
% 2.42/2.59 tff(1065,plain,
% 2.42/2.59 (((~c3_1(a627)) | (~hskp16)) <=> ((~hskp16) | (~c3_1(a627)))),
% 2.42/2.59 inference(rewrite,[status(thm)],[])).
% 2.42/2.59 tff(1066,axiom,((~c3_1(a627)) | (~hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause244')).
% 2.42/2.59 tff(1067,plain,
% 2.42/2.59 ((~hskp16) | (~c3_1(a627))),
% 2.42/2.59 inference(modus_ponens,[status(thm)],[1066, 1065])).
% 2.42/2.59 tff(1068,plain,
% 2.42/2.59 ((~hskp16) | (~c3_1(a627))),
% 2.42/2.59 inference(modus_ponens,[status(thm)],[1067, 1064])).
% 2.42/2.59 tff(1069,plain,
% 2.42/2.59 (~c3_1(a627)),
% 2.42/2.59 inference(unit_resolution,[status(thm)],[1068, 1063])).
% 2.42/2.59 tff(1070,plain,
% 2.42/2.59 (((~hskp16) | c2_1(a627)) <=> ((~hskp16) | c2_1(a627))),
% 2.42/2.59 inference(rewrite,[status(thm)],[])).
% 2.42/2.59 tff(1071,axiom,((~hskp16) | c2_1(a627)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause153')).
% 2.42/2.59 tff(1072,plain,
% 2.42/2.59 ((~hskp16) | c2_1(a627)),
% 2.42/2.59 inference(modus_ponens,[status(thm)],[1071, 1070])).
% 2.42/2.59 tff(1073,plain,
% 2.42/2.59 ((~hskp16) | c2_1(a627)),
% 2.42/2.59 inference(modus_ponens,[status(thm)],[1072, 1070])).
% 2.42/2.59 tff(1074,plain,
% 2.42/2.59 ((~hskp16) | c2_1(a627)),
% 2.42/2.59 inference(modus_ponens,[status(thm)],[1073, 1070])).
% 2.42/2.59 tff(1075,plain,
% 2.42/2.59 ((~hskp16) | c2_1(a627)),
% 2.42/2.59 inference(modus_ponens,[status(thm)],[1074, 1070])).
% 2.42/2.59 tff(1076,plain,
% 2.42/2.59 ((~hskp16) | c2_1(a627)),
% 2.42/2.59 inference(modus_ponens,[status(thm)],[1075, 1070])).
% 2.42/2.59 tff(1077,plain,
% 2.42/2.59 (c2_1(a627)),
% 2.42/2.59 inference(unit_resolution,[status(thm)],[1076, 1063])).
% 2.42/2.59 tff(1078,plain,
% 2.42/2.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | (c2_1(a648) | c0_1(a623) | c3_1(a627) | (~ndr1_0) | (~c2_1(a623)) | (~c3_1(a623)) | (~c2_1(a627)) | (~c1_1(a627)) | (~c0_1(a648)) | (~c3_1(a648)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c2_1(a648) | c0_1(a623) | c3_1(a627) | (~ndr1_0) | (~c2_1(a623)) | (~c3_1(a623)) | (~c2_1(a627)) | (~c1_1(a627)) | (~c0_1(a648)) | (~c3_1(a648)))),
% 2.42/2.59 inference(rewrite,[status(thm)],[])).
% 2.42/2.59 tff(1079,plain,
% 2.42/2.59 (((~ndr1_0) | c3_1(a627) | (~c1_1(a627)) | (~c2_1(a627)) | c0_1(a623) | (~c2_1(a623)) | (~c3_1(a623)) | c2_1(a648) | (~c0_1(a648)) | (~c3_1(a648))) <=> (c2_1(a648) | c0_1(a623) | c3_1(a627) | (~ndr1_0) | (~c2_1(a623)) | (~c3_1(a623)) | (~c2_1(a627)) | (~c1_1(a627)) | (~c0_1(a648)) | (~c3_1(a648)))),
% 2.42/2.59 inference(rewrite,[status(thm)],[])).
% 2.42/2.59 tff(1080,plain,
% 2.42/2.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a627) | (~c1_1(a627)) | (~c2_1(a627)) | c0_1(a623) | (~c2_1(a623)) | (~c3_1(a623)) | c2_1(a648) | (~c0_1(a648)) | (~c3_1(a648)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | (c2_1(a648) | c0_1(a623) | c3_1(a627) | (~ndr1_0) | (~c2_1(a623)) | (~c3_1(a623)) | (~c2_1(a627)) | (~c1_1(a627)) | (~c0_1(a648)) | (~c3_1(a648))))),
% 2.42/2.59 inference(monotonicity,[status(thm)],[1079])).
% 2.42/2.59 tff(1081,plain,
% 2.42/2.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a627) | (~c1_1(a627)) | (~c2_1(a627)) | c0_1(a623) | (~c2_1(a623)) | (~c3_1(a623)) | c2_1(a648) | (~c0_1(a648)) | (~c3_1(a648)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c2_1(a648) | c0_1(a623) | c3_1(a627) | (~ndr1_0) | (~c2_1(a623)) | (~c3_1(a623)) | (~c2_1(a627)) | (~c1_1(a627)) | (~c0_1(a648)) | (~c3_1(a648)))),
% 2.42/2.59 inference(transitivity,[status(thm)],[1080, 1078])).
% 2.42/2.59 tff(1082,plain,
% 2.42/2.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a627) | (~c1_1(a627)) | (~c2_1(a627)) | c0_1(a623) | (~c2_1(a623)) | (~c3_1(a623)) | c2_1(a648) | (~c0_1(a648)) | (~c3_1(a648)))),
% 2.42/2.59 inference(quant_inst,[status(thm)],[])).
% 2.42/2.59 tff(1083,plain,
% 2.42/2.59 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c2_1(a648) | c0_1(a623) | c3_1(a627) | (~ndr1_0) | (~c2_1(a623)) | (~c3_1(a623)) | (~c2_1(a627)) | (~c1_1(a627)) | (~c0_1(a648)) | (~c3_1(a648))),
% 2.42/2.59 inference(modus_ponens,[status(thm)],[1082, 1081])).
% 2.42/2.59 tff(1084,plain,
% 2.42/2.59 (~c1_1(a627)),
% 2.42/2.59 inference(unit_resolution,[status(thm)],[1083, 87, 804, 803, 1011, 1019, 1077, 802, 1003, 1069, 953])).
% 2.42/2.59 tff(1085,plain,
% 2.42/2.59 (((~hskp16) | c0_1(a627)) <=> ((~hskp16) | c0_1(a627))),
% 2.42/2.59 inference(rewrite,[status(thm)],[])).
% 2.42/2.59 tff(1086,axiom,((~hskp16) | c0_1(a627)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause154')).
% 2.42/2.59 tff(1087,plain,
% 2.42/2.59 ((~hskp16) | c0_1(a627)),
% 2.42/2.59 inference(modus_ponens,[status(thm)],[1086, 1085])).
% 2.42/2.59 tff(1088,plain,
% 2.42/2.59 ((~hskp16) | c0_1(a627)),
% 2.42/2.59 inference(modus_ponens,[status(thm)],[1087, 1085])).
% 2.42/2.59 tff(1089,plain,
% 2.42/2.59 ((~hskp16) | c0_1(a627)),
% 2.42/2.59 inference(modus_ponens,[status(thm)],[1088, 1085])).
% 2.42/2.59 tff(1090,plain,
% 2.42/2.59 ((~hskp16) | c0_1(a627)),
% 2.42/2.59 inference(modus_ponens,[status(thm)],[1089, 1085])).
% 2.42/2.59 tff(1091,plain,
% 2.42/2.59 ((~hskp16) | c0_1(a627)),
% 2.42/2.59 inference(modus_ponens,[status(thm)],[1090, 1085])).
% 2.42/2.59 tff(1092,plain,
% 2.42/2.59 (c0_1(a627)),
% 2.42/2.59 inference(unit_resolution,[status(thm)],[1091, 1063])).
% 2.42/2.59 tff(1093,plain,
% 2.42/2.59 (((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp15 | hskp14 | (~ndr1_0) | (~c2_1(a627)) | (~c0_1(a627)) | c1_1(a627))) <=> ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp15 | hskp14 | (~ndr1_0) | (~c2_1(a627)) | (~c0_1(a627)) | c1_1(a627))),
% 2.42/2.59 inference(rewrite,[status(thm)],[])).
% 2.42/2.59 tff(1094,plain,
% 2.42/2.59 ((hskp15 | hskp14 | (~ndr1_0) | c1_1(a627) | (~c0_1(a627)) | (~c2_1(a627))) <=> (hskp15 | hskp14 | (~ndr1_0) | (~c2_1(a627)) | (~c0_1(a627)) | c1_1(a627))),
% 2.42/2.59 inference(rewrite,[status(thm)],[])).
% 2.42/2.59 tff(1095,plain,
% 2.42/2.59 (((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp15 | hskp14 | (~ndr1_0) | c1_1(a627) | (~c0_1(a627)) | (~c2_1(a627)))) <=> ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp15 | hskp14 | (~ndr1_0) | (~c2_1(a627)) | (~c0_1(a627)) | c1_1(a627)))),
% 2.42/2.59 inference(monotonicity,[status(thm)],[1094])).
% 2.42/2.59 tff(1096,plain,
% 2.42/2.59 (((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp15 | hskp14 | (~ndr1_0) | c1_1(a627) | (~c0_1(a627)) | (~c2_1(a627)))) <=> ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp15 | hskp14 | (~ndr1_0) | (~c2_1(a627)) | (~c0_1(a627)) | c1_1(a627))),
% 2.42/2.59 inference(transitivity,[status(thm)],[1095, 1093])).
% 2.42/2.59 tff(1097,plain,
% 2.42/2.59 ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp15 | hskp14 | (~ndr1_0) | c1_1(a627) | (~c0_1(a627)) | (~c2_1(a627)))),
% 2.42/2.59 inference(quant_inst,[status(thm)],[])).
% 2.42/2.59 tff(1098,plain,
% 2.42/2.59 ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp15 | hskp14 | (~ndr1_0) | (~c2_1(a627)) | (~c0_1(a627)) | c1_1(a627)),
% 2.42/2.59 inference(modus_ponens,[status(thm)],[1097, 1096])).
% 2.42/2.59 tff(1099,plain,
% 2.42/2.59 ($false),
% 2.42/2.59 inference(unit_resolution,[status(thm)],[1098, 87, 257, 256, 1077, 1092, 232, 1084])).
% 2.42/2.59 tff(1100,plain,(hskp15 | hskp14 | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a648) | hskp17 | c2_1(a635) | c1_1(a635) | (~c0_1(a635))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.59 tff(1101,plain,
% 2.42/2.59 (~c0_1(a635)),
% 2.42/2.59 inference(unit_resolution,[status(thm)],[1100, 614, 804, 803, 802, 12, 257, 620, 256])).
% 2.42/2.59 tff(1102,plain,
% 2.42/2.59 (hskp15 | hskp14 | (~c0_1(a617))),
% 2.42/2.59 inference(unit_resolution,[status(thm)],[552, 87, 957, 955, 232])).
% 2.42/2.59 tff(1103,plain,
% 2.42/2.59 (~c0_1(a617)),
% 2.42/2.59 inference(unit_resolution,[status(thm)],[1102, 256, 257])).
% 2.42/2.59 tff(1104,plain,
% 2.42/2.59 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)))),
% 2.42/2.59 inference(bind,[status(th)],[])).
% 2.42/2.59 tff(1105,plain,
% 2.42/2.59 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 2.42/2.59 inference(quant_intro,[status(thm)],[1104])).
% 2.42/2.59 tff(1106,plain,
% 2.42/2.59 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 2.42/2.59 inference(rewrite,[status(thm)],[])).
% 2.42/2.59 tff(1107,plain,
% 2.42/2.59 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~c2_1(U))) <=> ((~c3_1(U)) | (~c2_1(U)))), ((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)))), ((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))))), (((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)))), (((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))))), ((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V)))), ((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))))), (((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))), ((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))))), (((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | c3_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V))) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W))), (((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W)))), ((((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c3_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c3_1(W))), ((((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c3_1(W)))), (((((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(W)) | c1_1(W)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c3_1(W)) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c3_1(W)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))), (((((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(W)) | c1_1(W)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))))),
% 2.42/2.59 inference(bind,[status(th)],[])).
% 2.42/2.59 tff(1108,plain,
% 2.42/2.59 (![W: $i, V: $i, U: $i] : ((((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(W)) | c1_1(W)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 2.42/2.59 inference(quant_intro,[status(thm)],[1107])).
% 2.42/2.59 tff(1109,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c3_1(U)) | (~c2_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(W)) | c1_1(W)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause321')).
% 2.42/2.59 tff(1110,plain,
% 2.42/2.59 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 2.42/2.59 inference(modus_ponens,[status(thm)],[1109, 1108])).
% 2.42/2.59 tff(1111,plain,
% 2.42/2.59 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 2.42/2.59 inference(modus_ponens,[status(thm)],[1110, 1106])).
% 2.42/2.59 tff(1112,plain,(
% 2.42/2.59 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 2.42/2.59 inference(skolemize,[status(sab)],[1111])).
% 2.42/2.59 tff(1113,plain,
% 2.42/2.59 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))),
% 2.42/2.59 inference(modus_ponens,[status(thm)],[1112, 1105])).
% 2.42/2.59 tff(1114,plain,
% 2.42/2.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a617) | c1_1(a635) | c3_1(a635) | (~ndr1_0) | c0_1(a635) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a617) | c1_1(a635) | c3_1(a635) | (~ndr1_0) | c0_1(a635) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 2.42/2.59 inference(rewrite,[status(thm)],[])).
% 2.42/2.59 tff(1115,plain,
% 2.42/2.59 (((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)) | c1_1(a635) | c0_1(a635) | c3_1(a635)) <=> (c1_1(a617) | c1_1(a635) | c3_1(a635) | (~ndr1_0) | c0_1(a635) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 2.42/2.59 inference(rewrite,[status(thm)],[])).
% 2.42/2.59 tff(1116,plain,
% 2.42/2.59 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)) | c1_1(a635) | c0_1(a635) | c3_1(a635))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a617) | c1_1(a635) | c3_1(a635) | (~ndr1_0) | c0_1(a635) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617))))),
% 2.42/2.60 inference(monotonicity,[status(thm)],[1115])).
% 2.42/2.60 tff(1117,plain,
% 2.42/2.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)) | c1_1(a635) | c0_1(a635) | c3_1(a635))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a617) | c1_1(a635) | c3_1(a635) | (~ndr1_0) | c0_1(a635) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 2.42/2.60 inference(transitivity,[status(thm)],[1116, 1114])).
% 2.42/2.60 tff(1118,plain,
% 2.42/2.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)) | c1_1(a635) | c0_1(a635) | c3_1(a635))),
% 2.42/2.60 inference(quant_inst,[status(thm)],[])).
% 2.42/2.60 tff(1119,plain,
% 2.42/2.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a617) | c1_1(a635) | c3_1(a635) | (~ndr1_0) | c0_1(a635) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617))),
% 2.42/2.60 inference(modus_ponens,[status(thm)],[1118, 1117])).
% 2.42/2.60 tff(1120,plain,
% 2.42/2.60 ($false),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[1119, 87, 957, 956, 955, 620, 608, 1113, 1103, 1101])).
% 2.42/2.60 tff(1121,plain,((~hskp20) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a648) | hskp17 | hskp15 | hskp14), inference(lemma,lemma(discharge,[]))).
% 2.42/2.60 tff(1122,plain,
% 2.42/2.60 (~hskp20),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[1121, 256, 803, 802, 12, 257, 804])).
% 2.42/2.60 tff(1123,plain,
% 2.42/2.60 (hskp15 | hskp14 | (~c0_1(a617))),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[552, 87, 649, 647, 232])).
% 2.42/2.60 tff(1124,plain,
% 2.42/2.60 (~c0_1(a617)),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[1123, 256, 257])).
% 2.42/2.60 tff(1125,assumption,(~c1_1(a603)), introduced(assumption)).
% 2.42/2.60 tff(1126,plain,
% 2.42/2.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a603) | c1_1(a617) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a603) | c1_1(a617) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 2.42/2.60 inference(rewrite,[status(thm)],[])).
% 2.42/2.60 tff(1127,plain,
% 2.42/2.60 (((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)) | c1_1(a603) | c0_1(a603) | c3_1(a603)) <=> (c0_1(a603) | c1_1(a617) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 2.42/2.60 inference(rewrite,[status(thm)],[])).
% 2.42/2.60 tff(1128,plain,
% 2.42/2.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)) | c1_1(a603) | c0_1(a603) | c3_1(a603))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a603) | c1_1(a617) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617))))),
% 2.42/2.60 inference(monotonicity,[status(thm)],[1127])).
% 2.42/2.60 tff(1129,plain,
% 2.42/2.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)) | c1_1(a603) | c0_1(a603) | c3_1(a603))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a603) | c1_1(a617) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 2.42/2.60 inference(transitivity,[status(thm)],[1128, 1126])).
% 2.42/2.60 tff(1130,plain,
% 2.42/2.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)) | c1_1(a603) | c0_1(a603) | c3_1(a603))),
% 2.42/2.60 inference(quant_inst,[status(thm)],[])).
% 2.42/2.60 tff(1131,plain,
% 2.42/2.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a603) | c1_1(a617) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617))),
% 2.42/2.60 inference(modus_ponens,[status(thm)],[1130, 1129])).
% 2.42/2.60 tff(1132,plain,
% 2.42/2.60 (c0_1(a603)),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[1131, 87, 649, 648, 647, 1125, 943, 1113, 1124])).
% 2.42/2.60 tff(1133,plain,
% 2.42/2.60 (((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp15 | hskp14 | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)))) <=> ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp15 | hskp14 | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)))),
% 2.42/2.60 inference(rewrite,[status(thm)],[])).
% 2.42/2.60 tff(1134,plain,
% 2.42/2.60 ((hskp15 | hskp14 | (~ndr1_0) | c1_1(a603) | (~c0_1(a603)) | (~c2_1(a603))) <=> (hskp15 | hskp14 | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)))),
% 2.42/2.60 inference(rewrite,[status(thm)],[])).
% 2.42/2.60 tff(1135,plain,
% 2.42/2.60 (((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp15 | hskp14 | (~ndr1_0) | c1_1(a603) | (~c0_1(a603)) | (~c2_1(a603)))) <=> ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp15 | hskp14 | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603))))),
% 2.42/2.60 inference(monotonicity,[status(thm)],[1134])).
% 2.42/2.60 tff(1136,plain,
% 2.42/2.60 (((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp15 | hskp14 | (~ndr1_0) | c1_1(a603) | (~c0_1(a603)) | (~c2_1(a603)))) <=> ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp15 | hskp14 | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)))),
% 2.42/2.60 inference(transitivity,[status(thm)],[1135, 1133])).
% 2.42/2.60 tff(1137,plain,
% 2.42/2.60 ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp15 | hskp14 | (~ndr1_0) | c1_1(a603) | (~c0_1(a603)) | (~c2_1(a603)))),
% 2.42/2.60 inference(quant_inst,[status(thm)],[])).
% 2.42/2.60 tff(1138,plain,
% 2.42/2.60 ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp15 | hskp14 | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603))),
% 2.42/2.60 inference(modus_ponens,[status(thm)],[1137, 1136])).
% 2.42/2.60 tff(1139,plain,
% 2.42/2.60 (~c2_1(a603)),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[1138, 87, 257, 256, 1132, 1125, 232])).
% 2.42/2.60 tff(1140,plain,
% 2.42/2.60 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | c1_1(a617) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c2_1(a617)) | (~c3_1(a617)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp20 | c1_1(a617) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c2_1(a617)) | (~c3_1(a617)))),
% 2.42/2.60 inference(rewrite,[status(thm)],[])).
% 2.42/2.60 tff(1141,plain,
% 2.42/2.60 ((hskp20 | (~ndr1_0) | c3_1(a603) | c2_1(a603) | (~c0_1(a603)) | c1_1(a617) | (~c2_1(a617)) | (~c3_1(a617))) <=> (hskp20 | c1_1(a617) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c2_1(a617)) | (~c3_1(a617)))),
% 2.42/2.60 inference(rewrite,[status(thm)],[])).
% 2.42/2.60 tff(1142,plain,
% 2.42/2.60 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a603) | c2_1(a603) | (~c0_1(a603)) | c1_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | c1_1(a617) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c2_1(a617)) | (~c3_1(a617))))),
% 2.42/2.60 inference(monotonicity,[status(thm)],[1141])).
% 2.42/2.60 tff(1143,plain,
% 2.42/2.60 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a603) | c2_1(a603) | (~c0_1(a603)) | c1_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp20 | c1_1(a617) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c2_1(a617)) | (~c3_1(a617)))),
% 2.42/2.60 inference(transitivity,[status(thm)],[1142, 1140])).
% 2.42/2.60 tff(1144,plain,
% 2.42/2.60 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a603) | c2_1(a603) | (~c0_1(a603)) | c1_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 2.42/2.60 inference(quant_inst,[status(thm)],[])).
% 2.42/2.60 tff(1145,plain,
% 2.42/2.60 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp20 | c1_1(a617) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c2_1(a617)) | (~c3_1(a617))),
% 2.42/2.60 inference(modus_ponens,[status(thm)],[1144, 1143])).
% 2.42/2.60 tff(1146,plain,
% 2.42/2.60 (hskp20 | c2_1(a603) | (~c0_1(a603))),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[1145, 87, 649, 648, 647, 943, 660])).
% 2.42/2.60 tff(1147,plain,
% 2.42/2.60 ($false),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[1146, 1139, 1132, 646])).
% 2.42/2.60 tff(1148,plain,(c1_1(a603) | hskp20 | (~c2_1(a617)) | (~c3_1(a617)) | c1_1(a617) | c3_1(a603) | hskp15 | hskp14), inference(lemma,lemma(discharge,[]))).
% 2.42/2.60 tff(1149,plain,
% 2.42/2.60 (c1_1(a603)),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[1148, 1122, 957, 956, 955, 943, 257, 256])).
% 2.42/2.60 tff(1150,plain,
% 2.42/2.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | (c2_1(a648) | (~c1_1(a603)) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)) | (~c0_1(a648)) | (~c3_1(a648)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c2_1(a648) | (~c1_1(a603)) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)) | (~c0_1(a648)) | (~c3_1(a648)))),
% 2.42/2.60 inference(rewrite,[status(thm)],[])).
% 2.42/2.60 tff(1151,plain,
% 2.42/2.60 (((~ndr1_0) | c3_1(a603) | (~c1_1(a603)) | (~c2_1(a603)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)) | c2_1(a648) | (~c0_1(a648)) | (~c3_1(a648))) <=> (c2_1(a648) | (~c1_1(a603)) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)) | (~c0_1(a648)) | (~c3_1(a648)))),
% 2.42/2.60 inference(rewrite,[status(thm)],[])).
% 2.42/2.60 tff(1152,plain,
% 2.42/2.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c1_1(a603)) | (~c2_1(a603)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)) | c2_1(a648) | (~c0_1(a648)) | (~c3_1(a648)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | (c2_1(a648) | (~c1_1(a603)) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)) | (~c0_1(a648)) | (~c3_1(a648))))),
% 2.42/2.60 inference(monotonicity,[status(thm)],[1151])).
% 2.42/2.60 tff(1153,plain,
% 2.42/2.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c1_1(a603)) | (~c2_1(a603)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)) | c2_1(a648) | (~c0_1(a648)) | (~c3_1(a648)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c2_1(a648) | (~c1_1(a603)) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)) | (~c0_1(a648)) | (~c3_1(a648)))),
% 2.42/2.60 inference(transitivity,[status(thm)],[1152, 1150])).
% 2.43/2.60 tff(1154,plain,
% 2.43/2.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a603) | (~c1_1(a603)) | (~c2_1(a603)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)) | c2_1(a648) | (~c0_1(a648)) | (~c3_1(a648)))),
% 2.43/2.60 inference(quant_inst,[status(thm)],[])).
% 2.43/2.60 tff(1155,plain,
% 2.43/2.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c2_1(a648) | (~c1_1(a603)) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)) | (~c0_1(a648)) | (~c3_1(a648))),
% 2.43/2.60 inference(modus_ponens,[status(thm)],[1154, 1153])).
% 2.43/2.60 tff(1156,plain,
% 2.43/2.60 ((~c1_1(a603)) | (~c2_1(a603))),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[1155, 87, 804, 803, 957, 956, 802, 943, 953, 1103])).
% 2.43/2.60 tff(1157,plain,
% 2.43/2.60 (~c2_1(a603)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[1156, 1149])).
% 2.43/2.60 tff(1158,plain,
% 2.43/2.60 (((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp45 | (~c1_1(a603)) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))) <=> ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp45 | (~c1_1(a603)) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 2.43/2.60 inference(rewrite,[status(thm)],[])).
% 2.43/2.60 tff(1159,plain,
% 2.43/2.60 ((hskp45 | (~ndr1_0) | c3_1(a603) | c2_1(a603) | (~c1_1(a603)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617))) <=> (hskp45 | (~c1_1(a603)) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 2.43/2.60 inference(rewrite,[status(thm)],[])).
% 2.43/2.60 tff(1160,plain,
% 2.43/2.60 (((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp45 | (~ndr1_0) | c3_1(a603) | c2_1(a603) | (~c1_1(a603)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))) <=> ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp45 | (~c1_1(a603)) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617))))),
% 2.43/2.60 inference(monotonicity,[status(thm)],[1159])).
% 2.43/2.60 tff(1161,plain,
% 2.43/2.60 (((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp45 | (~ndr1_0) | c3_1(a603) | c2_1(a603) | (~c1_1(a603)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))) <=> ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp45 | (~c1_1(a603)) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 2.43/2.60 inference(transitivity,[status(thm)],[1160, 1158])).
% 2.43/2.60 tff(1162,plain,
% 2.43/2.60 ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp45 | (~ndr1_0) | c3_1(a603) | c2_1(a603) | (~c1_1(a603)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 2.43/2.60 inference(quant_inst,[status(thm)],[])).
% 2.43/2.60 tff(1163,plain,
% 2.43/2.60 ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp45 | (~c1_1(a603)) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617))),
% 2.43/2.60 inference(modus_ponens,[status(thm)],[1162, 1161])).
% 2.43/2.60 tff(1164,plain,
% 2.43/2.60 (hskp45 | (~c1_1(a603)) | c2_1(a603)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[1163, 87, 957, 956, 943, 976, 1103])).
% 2.43/2.60 tff(1165,plain,
% 2.43/2.60 (hskp45),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[1164, 1149, 1157])).
% 2.43/2.60 tff(1166,plain,
% 2.43/2.60 (~c0_1(a623)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[1002, 1165])).
% 2.43/2.60 tff(1167,plain,
% 2.43/2.60 (c3_1(a623)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[1010, 1165])).
% 2.43/2.60 tff(1168,plain,
% 2.43/2.60 (c2_1(a623)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[1018, 1165])).
% 2.43/2.60 tff(1169,plain,
% 2.43/2.60 (~hskp9),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[1053, 1168, 804, 803, 1167, 802, 1166])).
% 2.43/2.60 tff(1170,plain,
% 2.43/2.60 (hskp16),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[1062, 1169, 12])).
% 2.43/2.60 tff(1171,plain,
% 2.43/2.60 (~c3_1(a627)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[1068, 1170])).
% 2.43/2.60 tff(1172,plain,
% 2.43/2.60 (c2_1(a627)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[1076, 1170])).
% 2.43/2.60 tff(1173,plain,
% 2.43/2.60 (~c1_1(a627)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[1083, 87, 804, 803, 1167, 1168, 1172, 802, 1166, 1171, 953])).
% 2.43/2.60 tff(1174,plain,
% 2.43/2.60 (c0_1(a627)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[1091, 1170])).
% 2.43/2.60 tff(1175,plain,
% 2.43/2.60 ($false),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[1098, 87, 257, 256, 1172, 1174, 232, 1173])).
% 2.43/2.60 tff(1176,plain,(hskp14 | hskp15 | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a648) | hskp17 | c3_1(a603)), inference(lemma,lemma(discharge,[]))).
% 2.43/2.60 tff(1177,plain,
% 2.43/2.60 (hskp14),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[1176, 943, 804, 803, 802, 12, 257])).
% 2.43/2.60 tff(1178,plain,
% 2.43/2.60 (c3_1(a624)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[199, 1177])).
% 2.43/2.60 tff(1179,plain,
% 2.43/2.60 (~c2_1(a624)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[191, 1177])).
% 2.43/2.60 tff(1180,plain,
% 2.43/2.60 (~c1_1(a624)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[212, 1177])).
% 2.43/2.60 tff(1181,plain,
% 2.43/2.60 (~hskp37),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[757, 635, 649, 647, 694, 693, 703, 648, 646])).
% 2.43/2.60 tff(1182,plain,
% 2.43/2.60 (hskp37 | hskp5 | (~c0_1(a617))),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[529, 87, 649, 648, 521])).
% 2.43/2.60 tff(1183,plain,
% 2.43/2.60 (hskp5),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[1182, 1181, 635])).
% 2.43/2.60 tff(1184,plain,
% 2.43/2.60 (~c3_1(a606)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[574, 1183])).
% 2.43/2.60 tff(1185,plain,
% 2.43/2.60 (~c0_1(a606)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[580, 1183])).
% 2.43/2.60 tff(1186,plain,
% 2.43/2.60 (c2_1(a606)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[588, 1183])).
% 2.43/2.60 tff(1187,plain,
% 2.43/2.60 (hskp54),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[764, 87, 1181, 1186, 1185, 1184, 372])).
% 2.43/2.60 tff(1188,plain,
% 2.43/2.60 (~c0_1(a651)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[425, 1187])).
% 2.43/2.60 tff(1189,plain,
% 2.43/2.60 (c2_1(a651)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[433, 1187])).
% 2.43/2.60 tff(1190,plain,
% 2.43/2.60 (c3_1(a651)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[448, 1187])).
% 2.43/2.60 tff(1191,plain,
% 2.43/2.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c0_1(a651) | c1_1(a617) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | (~c3_1(a624)) | (~c2_1(a617)) | (~c0_1(a617)) | (~c2_1(a651)) | (~c3_1(a651)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a651) | c1_1(a617) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | (~c3_1(a624)) | (~c2_1(a617)) | (~c0_1(a617)) | (~c2_1(a651)) | (~c3_1(a651)))),
% 2.43/2.60 inference(rewrite,[status(thm)],[])).
% 2.43/2.60 tff(1192,plain,
% 2.43/2.60 (((~ndr1_0) | c0_1(a651) | (~c3_1(a651)) | (~c2_1(a651)) | c1_1(a617) | (~c2_1(a617)) | (~c0_1(a617)) | c2_1(a624) | c1_1(a624) | (~c3_1(a624))) <=> (c0_1(a651) | c1_1(a617) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | (~c3_1(a624)) | (~c2_1(a617)) | (~c0_1(a617)) | (~c2_1(a651)) | (~c3_1(a651)))),
% 2.43/2.60 inference(rewrite,[status(thm)],[])).
% 2.43/2.60 tff(1193,plain,
% 2.43/2.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a651) | (~c3_1(a651)) | (~c2_1(a651)) | c1_1(a617) | (~c2_1(a617)) | (~c0_1(a617)) | c2_1(a624) | c1_1(a624) | (~c3_1(a624)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c0_1(a651) | c1_1(a617) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | (~c3_1(a624)) | (~c2_1(a617)) | (~c0_1(a617)) | (~c2_1(a651)) | (~c3_1(a651))))),
% 2.43/2.60 inference(monotonicity,[status(thm)],[1192])).
% 2.43/2.60 tff(1194,plain,
% 2.43/2.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a651) | (~c3_1(a651)) | (~c2_1(a651)) | c1_1(a617) | (~c2_1(a617)) | (~c0_1(a617)) | c2_1(a624) | c1_1(a624) | (~c3_1(a624)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a651) | c1_1(a617) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | (~c3_1(a624)) | (~c2_1(a617)) | (~c0_1(a617)) | (~c2_1(a651)) | (~c3_1(a651)))),
% 2.43/2.60 inference(transitivity,[status(thm)],[1193, 1191])).
% 2.43/2.60 tff(1195,plain,
% 2.43/2.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a651) | (~c3_1(a651)) | (~c2_1(a651)) | c1_1(a617) | (~c2_1(a617)) | (~c0_1(a617)) | c2_1(a624) | c1_1(a624) | (~c3_1(a624)))),
% 2.43/2.60 inference(quant_inst,[status(thm)],[])).
% 2.43/2.60 tff(1196,plain,
% 2.43/2.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c0_1(a651) | c1_1(a617) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | (~c3_1(a624)) | (~c2_1(a617)) | (~c0_1(a617)) | (~c2_1(a651)) | (~c3_1(a651))),
% 2.43/2.60 inference(modus_ponens,[status(thm)],[1195, 1194])).
% 2.43/2.60 tff(1197,plain,
% 2.43/2.60 ($false),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[1196, 87, 1190, 1189, 649, 703, 1188, 647, 694, 693, 645, 635])).
% 2.43/2.60 tff(1198,plain,((~c0_1(a617)) | (~c2_1(a617)) | (~c3_1(a624)) | c1_1(a617) | c1_1(a624) | c2_1(a624) | (~c3_1(a617)) | hskp20), inference(lemma,lemma(discharge,[]))).
% 2.43/2.60 tff(1199,plain,
% 2.43/2.60 (~c0_1(a617)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[1198, 646, 703, 955, 694, 693, 956, 957])).
% 2.43/2.60 tff(1200,plain,
% 2.43/2.60 (c0_1(a603) | c0_1(a617)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[1131, 87, 649, 648, 647, 1125, 943, 1113])).
% 2.43/2.60 tff(1201,plain,
% 2.43/2.60 (c0_1(a603)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[1200, 938])).
% 2.43/2.60 tff(1202,plain,
% 2.43/2.60 (c2_1(a603)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[1146, 1201, 646])).
% 2.43/2.60 tff(1203,plain,
% 2.43/2.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a624) | c2_1(a624) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | (~c3_1(a624)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a624) | c2_1(a624) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | (~c3_1(a624)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 2.43/2.60 inference(rewrite,[status(thm)],[])).
% 2.43/2.60 tff(1204,plain,
% 2.43/2.60 (((~ndr1_0) | c0_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c2_1(a624) | c1_1(a624) | (~c3_1(a624))) <=> (c1_1(a624) | c2_1(a624) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | (~c3_1(a624)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 2.43/2.60 inference(rewrite,[status(thm)],[])).
% 2.43/2.60 tff(1205,plain,
% 2.43/2.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c2_1(a624) | c1_1(a624) | (~c3_1(a624)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a624) | c2_1(a624) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | (~c3_1(a624)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617))))),
% 2.43/2.60 inference(monotonicity,[status(thm)],[1204])).
% 2.43/2.60 tff(1206,plain,
% 2.43/2.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c2_1(a624) | c1_1(a624) | (~c3_1(a624)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a624) | c2_1(a624) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | (~c3_1(a624)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 2.43/2.60 inference(transitivity,[status(thm)],[1205, 1203])).
% 2.43/2.60 tff(1207,plain,
% 2.43/2.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a603) | (~c2_1(a603)) | (~c0_1(a603)) | c2_1(a624) | c1_1(a624) | (~c3_1(a624)))),
% 2.43/2.60 inference(quant_inst,[status(thm)],[])).
% 2.43/2.60 tff(1208,plain,
% 2.43/2.60 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a624) | c2_1(a624) | c1_1(a603) | (~ndr1_0) | (~c2_1(a603)) | (~c0_1(a603)) | (~c3_1(a624)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617))),
% 2.43/2.60 inference(modus_ponens,[status(thm)],[1207, 1206])).
% 2.43/2.60 tff(1209,plain,
% 2.43/2.60 ($false),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[1208, 87, 649, 648, 703, 1201, 694, 693, 1125, 645, 1202, 938])).
% 2.43/2.60 tff(1210,plain,(c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)) | (~c3_1(a624)) | c1_1(a624) | c2_1(a624) | c1_1(a603) | hskp20 | c1_1(a617) | c3_1(a603)), inference(lemma,lemma(discharge,[]))).
% 2.43/2.60 tff(1211,plain,
% 2.43/2.60 (c1_1(a603)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[1210, 1199, 956, 703, 694, 693, 957, 646, 955, 943])).
% 2.43/2.60 tff(1212,plain,
% 2.43/2.60 (~c2_1(a603)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[1155, 87, 804, 803, 957, 956, 802, 1211, 943, 953, 1199])).
% 2.43/2.60 tff(1213,plain,
% 2.43/2.60 (hskp45),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[1163, 87, 957, 956, 1211, 943, 976, 1212, 1199])).
% 2.43/2.60 tff(1214,plain,
% 2.43/2.60 (~c0_1(a623)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[1002, 1213])).
% 2.43/2.60 tff(1215,plain,
% 2.43/2.60 (c3_1(a623)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[1010, 1213])).
% 2.43/2.60 tff(1216,plain,
% 2.43/2.60 (c2_1(a623)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[1018, 1213])).
% 2.43/2.60 tff(1217,plain,
% 2.43/2.60 (~hskp9),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[1053, 1216, 804, 803, 1215, 802, 1214])).
% 2.43/2.60 tff(1218,plain,
% 2.43/2.60 (hskp16),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[1062, 1217, 12])).
% 2.43/2.60 tff(1219,plain,
% 2.43/2.60 (~c3_1(a627)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[1068, 1218])).
% 2.43/2.60 tff(1220,plain,
% 2.43/2.60 (c2_1(a627)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[1076, 1218])).
% 2.43/2.60 tff(1221,plain,
% 2.43/2.60 (~c1_1(a627)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[1083, 87, 804, 803, 1215, 1216, 1220, 802, 1214, 1219, 953])).
% 2.43/2.60 tff(1222,plain,
% 2.43/2.60 (hskp20 | c2_1(a603) | (~c0_1(a603))),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[1145, 87, 957, 956, 955, 943, 660])).
% 2.43/2.60 tff(1223,plain,
% 2.43/2.60 (~c0_1(a603)),
% 2.43/2.60 inference(unit_resolution,[status(thm)],[1222, 1212, 646])).
% 2.43/2.60 tff(1224,plain,
% 2.43/2.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a603) | c2_1(a648) | c1_1(a624) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a624)) | (~c3_1(a624)) | (~c0_1(a648)) | (~c3_1(a648)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a603) | c2_1(a648) | c1_1(a624) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a624)) | (~c3_1(a624)) | (~c0_1(a648)) | (~c3_1(a648)))),
% 2.43/2.60 inference(rewrite,[status(thm)],[])).
% 2.43/2.60 tff(1225,plain,
% 2.43/2.60 (((~ndr1_0) | c1_1(a624) | (~c3_1(a624)) | (~c0_1(a624)) | c2_1(a648) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a603) | c0_1(a603) | c3_1(a603)) <=> (c0_1(a603) | c2_1(a648) | c1_1(a624) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a624)) | (~c3_1(a624)) | (~c0_1(a648)) | (~c3_1(a648)))),
% 2.43/2.60 inference(rewrite,[status(thm)],[])).
% 2.43/2.60 tff(1226,plain,
% 2.43/2.60 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a624) | (~c3_1(a624)) | (~c0_1(a624)) | c2_1(a648) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a603) | c0_1(a603) | c3_1(a603))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a603) | c2_1(a648) | c1_1(a624) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a624)) | (~c3_1(a624)) | (~c0_1(a648)) | (~c3_1(a648))))),
% 2.43/2.61 inference(monotonicity,[status(thm)],[1225])).
% 2.43/2.61 tff(1227,plain,
% 2.43/2.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a624) | (~c3_1(a624)) | (~c0_1(a624)) | c2_1(a648) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a603) | c0_1(a603) | c3_1(a603))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a603) | c2_1(a648) | c1_1(a624) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a624)) | (~c3_1(a624)) | (~c0_1(a648)) | (~c3_1(a648)))),
% 2.43/2.61 inference(transitivity,[status(thm)],[1226, 1224])).
% 2.43/2.61 tff(1228,plain,
% 2.43/2.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a624) | (~c3_1(a624)) | (~c0_1(a624)) | c2_1(a648) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a603) | c0_1(a603) | c3_1(a603))),
% 2.43/2.61 inference(quant_inst,[status(thm)],[])).
% 2.43/2.61 tff(1229,plain,
% 2.43/2.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a603) | c2_1(a648) | c1_1(a624) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a624)) | (~c3_1(a624)) | (~c0_1(a648)) | (~c3_1(a648))),
% 2.43/2.61 inference(modus_ponens,[status(thm)],[1228, 1227])).
% 2.43/2.61 tff(1230,plain,
% 2.43/2.61 (~c0_1(a624)),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[1229, 87, 804, 803, 703, 1223, 802, 694, 943, 910, 1212])).
% 2.43/2.61 tff(1231,plain,
% 2.43/2.61 (^[V: $i, U: $i] : refl((hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))))),
% 2.43/2.61 inference(bind,[status(th)],[])).
% 2.43/2.61 tff(1232,plain,
% 2.43/2.61 (![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 2.43/2.61 inference(quant_intro,[status(thm)],[1231])).
% 2.43/2.61 tff(1233,plain,
% 2.43/2.61 (![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 2.43/2.61 inference(rewrite,[status(thm)],[])).
% 2.43/2.61 tff(1234,plain,
% 2.43/2.61 (^[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))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | (~c3_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c2_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | (~c3_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c2_1(V) | (~c3_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_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) | (~c3_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c2_1(V)) | c1_1(V)) | hskp56) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) | hskp56))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V))) | hskp56) <=> (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c2_1(V)) | c1_1(V)) | hskp56) <=> (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))))),
% 2.43/2.61 inference(bind,[status(th)],[])).
% 2.43/2.61 tff(1235,plain,
% 2.43/2.61 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c2_1(V)) | c1_1(V)) | hskp56) <=> ![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 2.43/2.61 inference(quant_intro,[status(thm)],[1234])).
% 2.43/2.61 tff(1236,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c2_1(U)) | c3_1(U)) | c2_1(V)) | c1_1(V)) | hskp56)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause306')).
% 2.43/2.61 tff(1237,plain,
% 2.43/2.61 (![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 2.43/2.61 inference(modus_ponens,[status(thm)],[1236, 1235])).
% 2.43/2.61 tff(1238,plain,
% 2.43/2.61 (![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 2.43/2.61 inference(modus_ponens,[status(thm)],[1237, 1233])).
% 2.43/2.61 tff(1239,plain,(
% 2.43/2.61 ![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 2.43/2.61 inference(skolemize,[status(sab)],[1238])).
% 2.43/2.61 tff(1240,plain,
% 2.43/2.61 (![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))),
% 2.43/2.61 inference(modus_ponens,[status(thm)],[1239, 1232])).
% 2.43/2.61 tff(1241,plain,
% 2.43/2.61 (((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp56 | c1_1(a624) | c2_1(a624) | (~c1_1(a603)) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c3_1(a624)))) <=> ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp56 | c1_1(a624) | c2_1(a624) | (~c1_1(a603)) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c3_1(a624)))),
% 2.43/2.61 inference(rewrite,[status(thm)],[])).
% 2.43/2.61 tff(1242,plain,
% 2.43/2.61 ((hskp56 | (~ndr1_0) | c3_1(a603) | c2_1(a603) | (~c1_1(a603)) | c1_1(a624) | c2_1(a624) | (~c3_1(a624))) <=> (hskp56 | c1_1(a624) | c2_1(a624) | (~c1_1(a603)) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c3_1(a624)))),
% 2.43/2.61 inference(rewrite,[status(thm)],[])).
% 2.43/2.61 tff(1243,plain,
% 2.43/2.61 (((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp56 | (~ndr1_0) | c3_1(a603) | c2_1(a603) | (~c1_1(a603)) | c1_1(a624) | c2_1(a624) | (~c3_1(a624)))) <=> ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp56 | c1_1(a624) | c2_1(a624) | (~c1_1(a603)) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c3_1(a624))))),
% 2.43/2.61 inference(monotonicity,[status(thm)],[1242])).
% 2.43/2.61 tff(1244,plain,
% 2.43/2.61 (((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp56 | (~ndr1_0) | c3_1(a603) | c2_1(a603) | (~c1_1(a603)) | c1_1(a624) | c2_1(a624) | (~c3_1(a624)))) <=> ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp56 | c1_1(a624) | c2_1(a624) | (~c1_1(a603)) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c3_1(a624)))),
% 2.43/2.61 inference(transitivity,[status(thm)],[1243, 1241])).
% 2.43/2.61 tff(1245,plain,
% 2.43/2.61 ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp56 | (~ndr1_0) | c3_1(a603) | c2_1(a603) | (~c1_1(a603)) | c1_1(a624) | c2_1(a624) | (~c3_1(a624)))),
% 2.43/2.61 inference(quant_inst,[status(thm)],[])).
% 2.43/2.61 tff(1246,plain,
% 2.43/2.61 ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp56 | c1_1(a624) | c2_1(a624) | (~c1_1(a603)) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c3_1(a624))),
% 2.43/2.61 inference(modus_ponens,[status(thm)],[1245, 1244])).
% 2.43/2.61 tff(1247,plain,
% 2.43/2.61 (hskp56 | (~c1_1(a603)) | c2_1(a603)),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[1246, 87, 703, 694, 693, 943, 1240])).
% 2.43/2.61 tff(1248,plain,
% 2.43/2.61 (hskp56),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[1247, 1212, 1211])).
% 2.43/2.61 tff(1249,plain,
% 2.43/2.61 (((~hskp56) | (~c1_1(a658))) <=> ((~hskp56) | (~c1_1(a658)))),
% 2.43/2.61 inference(rewrite,[status(thm)],[])).
% 2.43/2.61 tff(1250,plain,
% 2.43/2.61 (((~c1_1(a658)) | (~hskp56)) <=> ((~hskp56) | (~c1_1(a658)))),
% 2.43/2.61 inference(rewrite,[status(thm)],[])).
% 2.43/2.61 tff(1251,axiom,((~c1_1(a658)) | (~hskp56)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause184')).
% 2.43/2.61 tff(1252,plain,
% 2.43/2.61 ((~hskp56) | (~c1_1(a658))),
% 2.43/2.61 inference(modus_ponens,[status(thm)],[1251, 1250])).
% 2.43/2.61 tff(1253,plain,
% 2.43/2.61 ((~hskp56) | (~c1_1(a658))),
% 2.43/2.61 inference(modus_ponens,[status(thm)],[1252, 1249])).
% 2.43/2.61 tff(1254,plain,
% 2.43/2.61 (~c1_1(a658)),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[1253, 1248])).
% 2.43/2.61 tff(1255,plain,
% 2.43/2.61 (((~hskp56) | c3_1(a658)) <=> ((~hskp56) | c3_1(a658))),
% 2.43/2.61 inference(rewrite,[status(thm)],[])).
% 2.43/2.61 tff(1256,axiom,((~hskp56) | c3_1(a658)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause94')).
% 2.43/2.61 tff(1257,plain,
% 2.43/2.61 ((~hskp56) | c3_1(a658)),
% 2.43/2.61 inference(modus_ponens,[status(thm)],[1256, 1255])).
% 2.43/2.61 tff(1258,plain,
% 2.43/2.61 ((~hskp56) | c3_1(a658)),
% 2.43/2.61 inference(modus_ponens,[status(thm)],[1257, 1255])).
% 2.43/2.61 tff(1259,plain,
% 2.43/2.61 ((~hskp56) | c3_1(a658)),
% 2.43/2.61 inference(modus_ponens,[status(thm)],[1258, 1255])).
% 2.43/2.61 tff(1260,plain,
% 2.43/2.61 ((~hskp56) | c3_1(a658)),
% 2.43/2.61 inference(modus_ponens,[status(thm)],[1259, 1255])).
% 2.43/2.61 tff(1261,plain,
% 2.43/2.61 ((~hskp56) | c3_1(a658)),
% 2.43/2.61 inference(modus_ponens,[status(thm)],[1260, 1255])).
% 2.43/2.61 tff(1262,plain,
% 2.43/2.61 (c3_1(a658)),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[1261, 1248])).
% 2.43/2.61 tff(1263,plain,
% 2.43/2.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a603) | c1_1(a658) | c2_1(a648) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a658)) | (~c3_1(a658)) | (~c0_1(a648)) | (~c3_1(a648)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a603) | c1_1(a658) | c2_1(a648) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a658)) | (~c3_1(a658)) | (~c0_1(a648)) | (~c3_1(a648)))),
% 2.43/2.61 inference(rewrite,[status(thm)],[])).
% 2.43/2.61 tff(1264,plain,
% 2.43/2.61 (((~ndr1_0) | c1_1(a658) | (~c3_1(a658)) | (~c0_1(a658)) | c2_1(a648) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a603) | c0_1(a603) | c3_1(a603)) <=> (c0_1(a603) | c1_1(a658) | c2_1(a648) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a658)) | (~c3_1(a658)) | (~c0_1(a648)) | (~c3_1(a648)))),
% 2.43/2.61 inference(rewrite,[status(thm)],[])).
% 2.43/2.61 tff(1265,plain,
% 2.43/2.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a658) | (~c3_1(a658)) | (~c0_1(a658)) | c2_1(a648) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a603) | c0_1(a603) | c3_1(a603))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a603) | c1_1(a658) | c2_1(a648) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a658)) | (~c3_1(a658)) | (~c0_1(a648)) | (~c3_1(a648))))),
% 2.43/2.61 inference(monotonicity,[status(thm)],[1264])).
% 2.43/2.61 tff(1266,plain,
% 2.43/2.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a658) | (~c3_1(a658)) | (~c0_1(a658)) | c2_1(a648) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a603) | c0_1(a603) | c3_1(a603))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a603) | c1_1(a658) | c2_1(a648) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a658)) | (~c3_1(a658)) | (~c0_1(a648)) | (~c3_1(a648)))),
% 2.43/2.61 inference(transitivity,[status(thm)],[1265, 1263])).
% 2.43/2.61 tff(1267,plain,
% 2.43/2.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a658) | (~c3_1(a658)) | (~c0_1(a658)) | c2_1(a648) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a603) | c0_1(a603) | c3_1(a603))),
% 2.43/2.61 inference(quant_inst,[status(thm)],[])).
% 2.43/2.61 tff(1268,plain,
% 2.43/2.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c0_1(a603) | c1_1(a658) | c2_1(a648) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a658)) | (~c3_1(a658)) | (~c0_1(a648)) | (~c3_1(a648))),
% 2.43/2.61 inference(modus_ponens,[status(thm)],[1267, 1266])).
% 2.43/2.61 tff(1269,plain,
% 2.43/2.61 (~c0_1(a658)),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[1268, 87, 1262, 804, 803, 1223, 1254, 802, 943, 910, 1212])).
% 2.43/2.61 tff(1270,plain,
% 2.43/2.61 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 2.43/2.61 inference(bind,[status(th)],[])).
% 2.43/2.61 tff(1271,plain,
% 2.43/2.61 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 2.43/2.61 inference(quant_intro,[status(thm)],[1270])).
% 2.43/2.61 tff(1272,plain,
% 2.43/2.61 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 2.43/2.61 inference(rewrite,[status(thm)],[])).
% 2.43/2.61 tff(1273,plain,
% 2.43/2.61 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)))), (((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | c0_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c2_1(V))) | c0_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | c0_1(W))), (((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | c0_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | c0_1(W)))), ((((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | c1_1(W) | c0_1(W))), ((((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | c1_1(W) | c0_1(W)))), (((((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))), ((((((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | c0_1(W)) | c1_1(W)) | c2_1(W)) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))), ((((((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | c0_1(W)) | c1_1(W)) | c2_1(W)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))), (((((((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | c0_1(W)) | c1_1(W)) | c2_1(W)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | c0_1(W)) | c1_1(W)) | c2_1(W)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))), ((((((((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | c0_1(W)) | c1_1(W)) | c2_1(W)) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))), ((((((((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | c0_1(W)) | c1_1(W)) | c2_1(W)) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)))), (((((((((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | c0_1(W)) | c1_1(W)) | c2_1(W)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) | c1_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | c0_1(W)) | c1_1(W)) | c2_1(W)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 2.43/2.61 inference(bind,[status(th)],[])).
% 2.43/2.61 tff(1274,plain,
% 2.43/2.61 (![W: $i, V: $i, U: $i] : ((((((((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | c0_1(W)) | c1_1(W)) | c2_1(W)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 2.43/2.61 inference(quant_intro,[status(thm)],[1273])).
% 2.43/2.61 tff(1275,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~ndr1_0) | (~c2_1(U))) | (~c2_1(V))) | c0_1(W)) | c1_1(W)) | c2_1(W)) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c1_1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause320')).
% 2.43/2.61 tff(1276,plain,
% 2.43/2.61 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 2.43/2.61 inference(modus_ponens,[status(thm)],[1275, 1274])).
% 2.43/2.61 tff(1277,plain,
% 2.43/2.61 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 2.43/2.61 inference(modus_ponens,[status(thm)],[1276, 1272])).
% 2.43/2.61 tff(1278,plain,(
% 2.43/2.61 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 2.43/2.61 inference(skolemize,[status(sab)],[1277])).
% 2.43/2.61 tff(1279,plain,
% 2.43/2.61 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))),
% 2.43/2.61 inference(modus_ponens,[status(thm)],[1278, 1271])).
% 2.43/2.61 tff(1280,plain,
% 2.43/2.61 (((~hskp56) | c2_1(a658)) <=> ((~hskp56) | c2_1(a658))),
% 2.43/2.61 inference(rewrite,[status(thm)],[])).
% 2.43/2.61 tff(1281,axiom,((~hskp56) | c2_1(a658)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause93')).
% 2.43/2.61 tff(1282,plain,
% 2.43/2.61 ((~hskp56) | c2_1(a658)),
% 2.43/2.61 inference(modus_ponens,[status(thm)],[1281, 1280])).
% 2.43/2.61 tff(1283,plain,
% 2.43/2.61 ((~hskp56) | c2_1(a658)),
% 2.43/2.61 inference(modus_ponens,[status(thm)],[1282, 1280])).
% 2.43/2.61 tff(1284,plain,
% 2.43/2.61 ((~hskp56) | c2_1(a658)),
% 2.43/2.61 inference(modus_ponens,[status(thm)],[1283, 1280])).
% 2.43/2.61 tff(1285,plain,
% 2.43/2.61 ((~hskp56) | c2_1(a658)),
% 2.43/2.61 inference(modus_ponens,[status(thm)],[1284, 1280])).
% 2.43/2.61 tff(1286,plain,
% 2.43/2.61 ((~hskp56) | c2_1(a658)),
% 2.43/2.61 inference(modus_ponens,[status(thm)],[1285, 1280])).
% 2.43/2.61 tff(1287,plain,
% 2.43/2.61 (c2_1(a658)),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[1286, 1248])).
% 2.43/2.61 tff(1288,plain,
% 2.43/2.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a658) | c3_1(a627) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | c0_1(a624) | c0_1(a658) | (~c2_1(a658)) | (~c2_1(a627)) | c1_1(a627))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a658) | c3_1(a627) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | c0_1(a624) | c0_1(a658) | (~c2_1(a658)) | (~c2_1(a627)) | c1_1(a627))),
% 2.43/2.61 inference(rewrite,[status(thm)],[])).
% 2.43/2.61 tff(1289,plain,
% 2.43/2.61 (((~ndr1_0) | c3_1(a627) | c1_1(a627) | (~c2_1(a627)) | c1_1(a658) | c0_1(a658) | (~c2_1(a658)) | c2_1(a624) | c1_1(a624) | c0_1(a624)) <=> (c1_1(a658) | c3_1(a627) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | c0_1(a624) | c0_1(a658) | (~c2_1(a658)) | (~c2_1(a627)) | c1_1(a627))),
% 2.43/2.61 inference(rewrite,[status(thm)],[])).
% 2.43/2.61 tff(1290,plain,
% 2.43/2.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a627) | c1_1(a627) | (~c2_1(a627)) | c1_1(a658) | c0_1(a658) | (~c2_1(a658)) | c2_1(a624) | c1_1(a624) | c0_1(a624))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a658) | c3_1(a627) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | c0_1(a624) | c0_1(a658) | (~c2_1(a658)) | (~c2_1(a627)) | c1_1(a627)))),
% 2.43/2.61 inference(monotonicity,[status(thm)],[1289])).
% 2.43/2.61 tff(1291,plain,
% 2.43/2.61 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a627) | c1_1(a627) | (~c2_1(a627)) | c1_1(a658) | c0_1(a658) | (~c2_1(a658)) | c2_1(a624) | c1_1(a624) | c0_1(a624))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a658) | c3_1(a627) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | c0_1(a624) | c0_1(a658) | (~c2_1(a658)) | (~c2_1(a627)) | c1_1(a627))),
% 2.43/2.61 inference(transitivity,[status(thm)],[1290, 1288])).
% 2.43/2.61 tff(1292,plain,
% 2.43/2.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a627) | c1_1(a627) | (~c2_1(a627)) | c1_1(a658) | c0_1(a658) | (~c2_1(a658)) | c2_1(a624) | c1_1(a624) | c0_1(a624))),
% 2.43/2.61 inference(quant_inst,[status(thm)],[])).
% 2.43/2.61 tff(1293,plain,
% 2.43/2.61 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a658) | c3_1(a627) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | c0_1(a624) | c0_1(a658) | (~c2_1(a658)) | (~c2_1(a627)) | c1_1(a627)),
% 2.43/2.61 inference(modus_ponens,[status(thm)],[1292, 1291])).
% 2.43/2.61 tff(1294,plain,
% 2.43/2.61 ($false),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[1293, 87, 1287, 1220, 1254, 1219, 694, 693, 1279, 1269, 1230, 1221])).
% 2.43/2.61 tff(1295,plain,(hskp20 | c1_1(a624) | c2_1(a624) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a648) | (~c3_1(a624)) | c3_1(a603) | hskp17), inference(lemma,lemma(discharge,[]))).
% 2.43/2.61 tff(1296,plain,
% 2.43/2.61 (hskp20),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[1295, 1180, 1179, 804, 803, 802, 1178, 943, 12])).
% 2.43/2.61 tff(1297,plain,
% 2.43/2.61 (~c2_1(a635)),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[613, 1296])).
% 2.43/2.61 tff(1298,plain,
% 2.43/2.61 (~c1_1(a635)),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[619, 1296])).
% 2.43/2.61 tff(1299,plain,
% 2.43/2.61 (~c3_1(a635)),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[607, 1296])).
% 2.43/2.61 tff(1300,plain,
% 2.43/2.61 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | (c1_1(a635) | c2_1(a635) | c3_1(a635) | (~ndr1_0) | c0_1(a635))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | c1_1(a635) | c2_1(a635) | c3_1(a635) | (~ndr1_0) | c0_1(a635))),
% 2.43/2.61 inference(rewrite,[status(thm)],[])).
% 2.43/2.61 tff(1301,plain,
% 2.43/2.61 (((~ndr1_0) | c3_1(a635) | c2_1(a635) | c0_1(a635) | c1_1(a635) | c3_1(a635) | c0_1(a635)) <=> (c1_1(a635) | c2_1(a635) | c3_1(a635) | (~ndr1_0) | c0_1(a635))),
% 2.43/2.61 inference(rewrite,[status(thm)],[])).
% 2.43/2.61 tff(1302,plain,
% 2.43/2.61 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | ((~ndr1_0) | c3_1(a635) | c2_1(a635) | c0_1(a635) | c1_1(a635) | c3_1(a635) | c0_1(a635))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | (c1_1(a635) | c2_1(a635) | c3_1(a635) | (~ndr1_0) | c0_1(a635)))),
% 2.43/2.61 inference(monotonicity,[status(thm)],[1301])).
% 2.43/2.61 tff(1303,plain,
% 2.43/2.61 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | ((~ndr1_0) | c3_1(a635) | c2_1(a635) | c0_1(a635) | c1_1(a635) | c3_1(a635) | c0_1(a635))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | c1_1(a635) | c2_1(a635) | c3_1(a635) | (~ndr1_0) | c0_1(a635))),
% 2.43/2.61 inference(transitivity,[status(thm)],[1302, 1300])).
% 2.43/2.61 tff(1304,plain,
% 2.43/2.61 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | ((~ndr1_0) | c3_1(a635) | c2_1(a635) | c0_1(a635) | c1_1(a635) | c3_1(a635) | c0_1(a635))),
% 2.43/2.61 inference(quant_inst,[status(thm)],[])).
% 2.43/2.61 tff(1305,plain,
% 2.43/2.61 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | c1_1(a635) | c2_1(a635) | c3_1(a635) | (~ndr1_0) | c0_1(a635)),
% 2.43/2.61 inference(modus_ponens,[status(thm)],[1304, 1303])).
% 2.43/2.61 tff(1306,plain,
% 2.43/2.61 (c0_1(a635)),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[1305, 87, 1298, 1297, 1299, 170])).
% 2.43/2.61 tff(1307,plain,
% 2.43/2.61 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a648) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | (~c3_1(a624)) | (~c0_1(a648)) | (~c1_1(a648)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a648) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | (~c3_1(a624)) | (~c0_1(a648)) | (~c1_1(a648)))),
% 2.43/2.61 inference(rewrite,[status(thm)],[])).
% 2.43/2.61 tff(1308,plain,
% 2.43/2.61 ((hskp5 | (~ndr1_0) | c1_1(a624) | c2_1(a624) | (~c3_1(a624)) | c2_1(a648) | (~c1_1(a648)) | (~c0_1(a648))) <=> (hskp5 | c2_1(a648) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | (~c3_1(a624)) | (~c0_1(a648)) | (~c1_1(a648)))),
% 2.43/2.61 inference(rewrite,[status(thm)],[])).
% 2.43/2.61 tff(1309,plain,
% 2.43/2.61 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a624) | c2_1(a624) | (~c3_1(a624)) | c2_1(a648) | (~c1_1(a648)) | (~c0_1(a648)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a648) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | (~c3_1(a624)) | (~c0_1(a648)) | (~c1_1(a648))))),
% 2.43/2.61 inference(monotonicity,[status(thm)],[1308])).
% 2.43/2.61 tff(1310,plain,
% 2.43/2.61 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a624) | c2_1(a624) | (~c3_1(a624)) | c2_1(a648) | (~c1_1(a648)) | (~c0_1(a648)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a648) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | (~c3_1(a624)) | (~c0_1(a648)) | (~c1_1(a648)))),
% 2.43/2.61 inference(transitivity,[status(thm)],[1309, 1307])).
% 2.43/2.61 tff(1311,plain,
% 2.43/2.61 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a624) | c2_1(a624) | (~c3_1(a624)) | c2_1(a648) | (~c1_1(a648)) | (~c0_1(a648)))),
% 2.43/2.61 inference(quant_inst,[status(thm)],[])).
% 2.43/2.61 tff(1312,plain,
% 2.43/2.61 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a648) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | (~c3_1(a624)) | (~c0_1(a648)) | (~c1_1(a648))),
% 2.43/2.61 inference(modus_ponens,[status(thm)],[1311, 1310])).
% 2.43/2.61 tff(1313,plain,
% 2.43/2.61 (~c1_1(a648)),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[1312, 87, 523, 803, 200, 802, 213, 192, 507])).
% 2.43/2.61 tff(1314,plain,
% 2.43/2.61 ($false),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[545, 395, 403, 523, 186, 387])).
% 2.43/2.61 tff(1315,plain,((~hskp37) | hskp5 | (~hskp14)), inference(lemma,lemma(discharge,[]))).
% 2.43/2.61 tff(1316,plain,
% 2.43/2.61 (~hskp37),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[1315, 186, 523])).
% 2.43/2.61 tff(1317,plain,
% 2.43/2.61 (hskp37 | (~c0_1(a617))),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[529, 87, 523, 964, 963, 521])).
% 2.43/2.61 tff(1318,plain,
% 2.43/2.61 (~c0_1(a617)),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[1317, 1316])).
% 2.43/2.61 tff(1319,plain,
% 2.43/2.61 (hskp42 | (~c0_1(a635)) | c0_1(a617)),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[982, 87, 963, 961, 959, 962, 822])).
% 2.43/2.61 tff(1320,plain,
% 2.43/2.61 (hskp42),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[1319, 1318, 958])).
% 2.43/2.61 tff(1321,plain,
% 2.43/2.61 (~c3_1(a618)),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[915, 1320])).
% 2.43/2.61 tff(1322,plain,
% 2.43/2.61 (~c2_1(a618)),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[845, 1320])).
% 2.43/2.61 tff(1323,plain,
% 2.43/2.61 (c0_1(a618)),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[922, 87, 804, 803, 802, 1322, 1321, 910, 1313])).
% 2.43/2.61 tff(1324,plain,
% 2.43/2.61 (c1_1(a618)),
% 2.43/2.61 inference(unit_resolution,[status(thm)],[876, 1320])).
% 2.43/2.61 tff(1325,plain,
% 2.43/2.61 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a618) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | (~c3_1(a624)) | (~c1_1(a618)) | (~c0_1(a618)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a618) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | (~c3_1(a624)) | (~c1_1(a618)) | (~c0_1(a618)))),
% 2.43/2.61 inference(rewrite,[status(thm)],[])).
% 2.43/2.61 tff(1326,plain,
% 2.43/2.61 ((hskp5 | (~ndr1_0) | c1_1(a624) | c2_1(a624) | (~c3_1(a624)) | c2_1(a618) | (~c1_1(a618)) | (~c0_1(a618))) <=> (hskp5 | c2_1(a618) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | (~c3_1(a624)) | (~c1_1(a618)) | (~c0_1(a618)))),
% 2.43/2.61 inference(rewrite,[status(thm)],[])).
% 2.43/2.61 tff(1327,plain,
% 2.43/2.61 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a624) | c2_1(a624) | (~c3_1(a624)) | c2_1(a618) | (~c1_1(a618)) | (~c0_1(a618)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a618) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | (~c3_1(a624)) | (~c1_1(a618)) | (~c0_1(a618))))),
% 2.43/2.61 inference(monotonicity,[status(thm)],[1326])).
% 2.43/2.61 tff(1328,plain,
% 2.43/2.61 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a624) | c2_1(a624) | (~c3_1(a624)) | c2_1(a618) | (~c1_1(a618)) | (~c0_1(a618)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a618) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | (~c3_1(a624)) | (~c1_1(a618)) | (~c0_1(a618)))),
% 2.43/2.61 inference(transitivity,[status(thm)],[1327, 1325])).
% 2.43/2.61 tff(1329,plain,
% 2.43/2.61 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a624) | c2_1(a624) | (~c3_1(a624)) | c2_1(a618) | (~c1_1(a618)) | (~c0_1(a618)))),
% 2.43/2.61 inference(quant_inst,[status(thm)],[])).
% 2.43/2.61 tff(1330,plain,
% 2.43/2.61 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a618) | c1_1(a624) | c2_1(a624) | (~ndr1_0) | (~c3_1(a624)) | (~c1_1(a618)) | (~c0_1(a618))),
% 2.43/2.62 inference(modus_ponens,[status(thm)],[1329, 1328])).
% 2.43/2.62 tff(1331,plain,
% 2.43/2.62 ($false),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[1330, 87, 523, 1324, 200, 1322, 213, 192, 507, 1323])).
% 2.43/2.62 tff(1332,plain,((~hskp14) | hskp5 | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a648) | (~c0_1(a635)) | c1_1(a635) | c2_1(a635)), inference(lemma,lemma(discharge,[]))).
% 2.43/2.62 tff(1333,plain,
% 2.43/2.62 (hskp5),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[1332, 1306, 804, 803, 802, 1177, 1298, 1297])).
% 2.43/2.62 tff(1334,plain,
% 2.43/2.62 (~c3_1(a606)),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[574, 1333])).
% 2.43/2.62 tff(1335,plain,
% 2.43/2.62 (c2_1(a606)),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[588, 1333])).
% 2.43/2.62 tff(1336,plain,
% 2.43/2.62 (~c0_1(a606)),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[580, 1333])).
% 2.43/2.62 tff(1337,plain,
% 2.43/2.62 ($false),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[629, 1336, 1335, 1296, 1334])).
% 2.43/2.62 tff(1338,plain,(c3_1(a603) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a648) | hskp17 | hskp15), inference(lemma,lemma(discharge,[]))).
% 2.43/2.62 tff(1339,plain,
% 2.43/2.62 (c3_1(a603)),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[1338, 257, 793, 785, 12, 801])).
% 2.43/2.62 tff(1340,plain,
% 2.43/2.62 (((~hskp3) | (~c3_1(a603))) <=> ((~hskp3) | (~c3_1(a603)))),
% 2.43/2.62 inference(rewrite,[status(thm)],[])).
% 2.43/2.62 tff(1341,plain,
% 2.43/2.62 (((~c3_1(a603)) | (~hskp3)) <=> ((~hskp3) | (~c3_1(a603)))),
% 2.43/2.62 inference(rewrite,[status(thm)],[])).
% 2.43/2.62 tff(1342,axiom,((~c3_1(a603)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause271')).
% 2.43/2.62 tff(1343,plain,
% 2.43/2.62 ((~hskp3) | (~c3_1(a603))),
% 2.43/2.62 inference(modus_ponens,[status(thm)],[1342, 1341])).
% 2.43/2.62 tff(1344,plain,
% 2.43/2.62 ((~hskp3) | (~c3_1(a603))),
% 2.43/2.62 inference(modus_ponens,[status(thm)],[1343, 1340])).
% 2.43/2.62 tff(1345,plain,
% 2.43/2.62 (~hskp3),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[1344, 1339])).
% 2.43/2.62 tff(1346,plain,
% 2.43/2.62 (~c1_1(a617)),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[463, 925])).
% 2.43/2.62 tff(1347,assumption,(hskp29), introduced(assumption)).
% 2.43/2.62 tff(1348,plain,
% 2.43/2.62 (((~hskp29) | (~c0_1(a660))) <=> ((~hskp29) | (~c0_1(a660)))),
% 2.43/2.62 inference(rewrite,[status(thm)],[])).
% 2.43/2.62 tff(1349,plain,
% 2.43/2.62 (((~c0_1(a660)) | (~hskp29)) <=> ((~hskp29) | (~c0_1(a660)))),
% 2.43/2.62 inference(rewrite,[status(thm)],[])).
% 2.43/2.62 tff(1350,axiom,((~c0_1(a660)) | (~hskp29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause219')).
% 2.43/2.62 tff(1351,plain,
% 2.43/2.62 ((~hskp29) | (~c0_1(a660))),
% 2.43/2.62 inference(modus_ponens,[status(thm)],[1350, 1349])).
% 2.43/2.62 tff(1352,plain,
% 2.43/2.62 ((~hskp29) | (~c0_1(a660))),
% 2.43/2.62 inference(modus_ponens,[status(thm)],[1351, 1348])).
% 2.43/2.62 tff(1353,plain,
% 2.43/2.62 (~c0_1(a660)),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[1352, 1347])).
% 2.43/2.62 tff(1354,plain,
% 2.43/2.62 (((~hskp29) | (~c3_1(a660))) <=> ((~hskp29) | (~c3_1(a660)))),
% 2.43/2.62 inference(rewrite,[status(thm)],[])).
% 2.43/2.62 tff(1355,plain,
% 2.43/2.62 (((~c3_1(a660)) | (~hskp29)) <=> ((~hskp29) | (~c3_1(a660)))),
% 2.43/2.62 inference(rewrite,[status(thm)],[])).
% 2.43/2.62 tff(1356,axiom,((~c3_1(a660)) | (~hskp29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause218')).
% 2.43/2.62 tff(1357,plain,
% 2.43/2.62 ((~hskp29) | (~c3_1(a660))),
% 2.43/2.62 inference(modus_ponens,[status(thm)],[1356, 1355])).
% 2.43/2.62 tff(1358,plain,
% 2.43/2.62 ((~hskp29) | (~c3_1(a660))),
% 2.43/2.62 inference(modus_ponens,[status(thm)],[1357, 1354])).
% 2.43/2.62 tff(1359,plain,
% 2.43/2.62 (~c3_1(a660)),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[1358, 1347])).
% 2.43/2.62 tff(1360,plain,
% 2.43/2.62 (((~hskp29) | (~c1_1(a660))) <=> ((~hskp29) | (~c1_1(a660)))),
% 2.43/2.62 inference(rewrite,[status(thm)],[])).
% 2.43/2.62 tff(1361,plain,
% 2.43/2.62 (((~c1_1(a660)) | (~hskp29)) <=> ((~hskp29) | (~c1_1(a660)))),
% 2.43/2.62 inference(rewrite,[status(thm)],[])).
% 2.43/2.62 tff(1362,axiom,((~c1_1(a660)) | (~hskp29)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause217')).
% 2.43/2.62 tff(1363,plain,
% 2.43/2.62 ((~hskp29) | (~c1_1(a660))),
% 2.43/2.62 inference(modus_ponens,[status(thm)],[1362, 1361])).
% 2.43/2.62 tff(1364,plain,
% 2.43/2.62 ((~hskp29) | (~c1_1(a660))),
% 2.43/2.62 inference(modus_ponens,[status(thm)],[1363, 1360])).
% 2.43/2.62 tff(1365,plain,
% 2.43/2.62 (~c1_1(a660)),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[1364, 1347])).
% 2.43/2.62 tff(1366,plain,
% 2.43/2.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a617) | c1_1(a660) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a617) | c1_1(a660) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 2.43/2.62 inference(rewrite,[status(thm)],[])).
% 2.43/2.62 tff(1367,plain,
% 2.43/2.62 (((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)) | c1_1(a660) | c0_1(a660) | c3_1(a660)) <=> (c1_1(a617) | c1_1(a660) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 2.43/2.62 inference(rewrite,[status(thm)],[])).
% 2.43/2.62 tff(1368,plain,
% 2.43/2.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)) | c1_1(a660) | c0_1(a660) | c3_1(a660))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a617) | c1_1(a660) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617))))),
% 2.43/2.62 inference(monotonicity,[status(thm)],[1367])).
% 2.43/2.62 tff(1369,plain,
% 2.43/2.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)) | c1_1(a660) | c0_1(a660) | c3_1(a660))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a617) | c1_1(a660) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 2.43/2.62 inference(transitivity,[status(thm)],[1368, 1366])).
% 2.43/2.62 tff(1370,plain,
% 2.43/2.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)) | c1_1(a660) | c0_1(a660) | c3_1(a660))),
% 2.43/2.62 inference(quant_inst,[status(thm)],[])).
% 2.43/2.62 tff(1371,plain,
% 2.43/2.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a617) | c1_1(a660) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617))),
% 2.43/2.62 inference(modus_ponens,[status(thm)],[1370, 1369])).
% 2.43/2.62 tff(1372,plain,
% 2.43/2.62 ($false),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[1371, 87, 649, 648, 647, 1365, 1359, 1353, 1113, 938])).
% 2.43/2.62 tff(1373,plain,((~hskp29) | (~c2_1(a617)) | (~c3_1(a617)) | c1_1(a617) | c0_1(a617)), inference(lemma,lemma(discharge,[]))).
% 2.43/2.62 tff(1374,plain,
% 2.43/2.62 (~hskp29),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[1373, 938, 927, 1346, 926])).
% 2.43/2.62 tff(1375,plain,
% 2.43/2.62 (((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | c2_1(a675) | (~ndr1_0) | c0_1(a675) | (~c3_1(a675)))) <=> ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp29 | hskp3 | c2_1(a675) | (~ndr1_0) | c0_1(a675) | (~c3_1(a675)))),
% 2.43/2.62 inference(rewrite,[status(thm)],[])).
% 2.43/2.62 tff(1376,plain,
% 2.43/2.62 ((hskp29 | hskp3 | (~ndr1_0) | c2_1(a675) | c0_1(a675) | (~c3_1(a675))) <=> (hskp29 | hskp3 | c2_1(a675) | (~ndr1_0) | c0_1(a675) | (~c3_1(a675)))),
% 2.43/2.62 inference(rewrite,[status(thm)],[])).
% 2.43/2.62 tff(1377,plain,
% 2.43/2.62 (((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | (~ndr1_0) | c2_1(a675) | c0_1(a675) | (~c3_1(a675)))) <=> ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | c2_1(a675) | (~ndr1_0) | c0_1(a675) | (~c3_1(a675))))),
% 2.43/2.62 inference(monotonicity,[status(thm)],[1376])).
% 2.43/2.62 tff(1378,plain,
% 2.43/2.62 (((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | (~ndr1_0) | c2_1(a675) | c0_1(a675) | (~c3_1(a675)))) <=> ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp29 | hskp3 | c2_1(a675) | (~ndr1_0) | c0_1(a675) | (~c3_1(a675)))),
% 2.43/2.62 inference(transitivity,[status(thm)],[1377, 1375])).
% 2.43/2.62 tff(1379,plain,
% 2.43/2.62 ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | (~ndr1_0) | c2_1(a675) | c0_1(a675) | (~c3_1(a675)))),
% 2.43/2.62 inference(quant_inst,[status(thm)],[])).
% 2.43/2.62 tff(1380,plain,
% 2.43/2.62 ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp29 | hskp3 | c2_1(a675) | (~ndr1_0) | c0_1(a675) | (~c3_1(a675))),
% 2.43/2.62 inference(modus_ponens,[status(thm)],[1379, 1378])).
% 2.43/2.62 tff(1381,plain,
% 2.43/2.62 (c0_1(a675)),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[1380, 87, 1374, 1345, 942, 941, 937])).
% 2.43/2.62 tff(1382,plain,
% 2.43/2.62 (c1_1(a675)),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[288, 940])).
% 2.43/2.62 tff(1383,plain,
% 2.43/2.62 (((~![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp6 | (~ndr1_0) | (~c1_1(a675)) | (~c3_1(a675)) | (~c0_1(a675)))) <=> ((~![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp6 | (~ndr1_0) | (~c1_1(a675)) | (~c3_1(a675)) | (~c0_1(a675)))),
% 2.43/2.62 inference(rewrite,[status(thm)],[])).
% 2.43/2.62 tff(1384,plain,
% 2.43/2.62 ((hskp6 | (~ndr1_0) | (~c3_1(a675)) | (~c1_1(a675)) | (~c0_1(a675))) <=> (hskp6 | (~ndr1_0) | (~c1_1(a675)) | (~c3_1(a675)) | (~c0_1(a675)))),
% 2.43/2.62 inference(rewrite,[status(thm)],[])).
% 2.43/2.62 tff(1385,plain,
% 2.43/2.62 (((~![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp6 | (~ndr1_0) | (~c3_1(a675)) | (~c1_1(a675)) | (~c0_1(a675)))) <=> ((~![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp6 | (~ndr1_0) | (~c1_1(a675)) | (~c3_1(a675)) | (~c0_1(a675))))),
% 2.43/2.62 inference(monotonicity,[status(thm)],[1384])).
% 2.43/2.62 tff(1386,plain,
% 2.43/2.62 (((~![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp6 | (~ndr1_0) | (~c3_1(a675)) | (~c1_1(a675)) | (~c0_1(a675)))) <=> ((~![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp6 | (~ndr1_0) | (~c1_1(a675)) | (~c3_1(a675)) | (~c0_1(a675)))),
% 2.43/2.62 inference(transitivity,[status(thm)],[1385, 1383])).
% 2.43/2.62 tff(1387,plain,
% 2.43/2.62 ((~![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp6 | (~ndr1_0) | (~c3_1(a675)) | (~c1_1(a675)) | (~c0_1(a675)))),
% 2.43/2.62 inference(quant_inst,[status(thm)],[])).
% 2.43/2.62 tff(1388,plain,
% 2.43/2.62 ((~![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp6 | (~ndr1_0) | (~c1_1(a675)) | (~c3_1(a675)) | (~c0_1(a675))),
% 2.43/2.62 inference(modus_ponens,[status(thm)],[1387, 1386])).
% 2.43/2.62 tff(1389,plain,
% 2.43/2.62 (hskp6 | (~c0_1(a675))),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[1388, 87, 1382, 942, 679])).
% 2.43/2.62 tff(1390,plain,
% 2.43/2.62 (hskp6),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[1389, 1381])).
% 2.43/2.62 tff(1391,plain,
% 2.43/2.62 (((~hskp6) | (~c1_1(a609))) <=> ((~hskp6) | (~c1_1(a609)))),
% 2.43/2.62 inference(rewrite,[status(thm)],[])).
% 2.43/2.62 tff(1392,plain,
% 2.43/2.62 (((~c1_1(a609)) | (~hskp6)) <=> ((~hskp6) | (~c1_1(a609)))),
% 2.43/2.62 inference(rewrite,[status(thm)],[])).
% 2.43/2.62 tff(1393,axiom,((~c1_1(a609)) | (~hskp6)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause264')).
% 2.43/2.62 tff(1394,plain,
% 2.43/2.62 ((~hskp6) | (~c1_1(a609))),
% 2.43/2.62 inference(modus_ponens,[status(thm)],[1393, 1392])).
% 2.43/2.62 tff(1395,plain,
% 2.43/2.62 ((~hskp6) | (~c1_1(a609))),
% 2.43/2.62 inference(modus_ponens,[status(thm)],[1394, 1391])).
% 2.43/2.62 tff(1396,plain,
% 2.43/2.62 (~c1_1(a609)),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[1395, 1390])).
% 2.43/2.62 tff(1397,plain,
% 2.43/2.62 (~c0_1(a609)),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[691, 1390])).
% 2.43/2.62 tff(1398,plain,
% 2.43/2.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a617) | c0_1(a609) | c1_1(a609) | (~ndr1_0) | c3_1(a609) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a617) | c0_1(a609) | c1_1(a609) | (~ndr1_0) | c3_1(a609) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 2.43/2.62 inference(rewrite,[status(thm)],[])).
% 2.43/2.62 tff(1399,plain,
% 2.43/2.62 (((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)) | c1_1(a609) | c0_1(a609) | c3_1(a609)) <=> (c1_1(a617) | c0_1(a609) | c1_1(a609) | (~ndr1_0) | c3_1(a609) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 2.43/2.62 inference(rewrite,[status(thm)],[])).
% 2.43/2.62 tff(1400,plain,
% 2.43/2.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)) | c1_1(a609) | c0_1(a609) | c3_1(a609))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a617) | c0_1(a609) | c1_1(a609) | (~ndr1_0) | c3_1(a609) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617))))),
% 2.43/2.62 inference(monotonicity,[status(thm)],[1399])).
% 2.43/2.62 tff(1401,plain,
% 2.43/2.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)) | c1_1(a609) | c0_1(a609) | c3_1(a609))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a617) | c0_1(a609) | c1_1(a609) | (~ndr1_0) | c3_1(a609) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 2.43/2.62 inference(transitivity,[status(thm)],[1400, 1398])).
% 2.43/2.62 tff(1402,plain,
% 2.43/2.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)) | c1_1(a609) | c0_1(a609) | c3_1(a609))),
% 2.43/2.62 inference(quant_inst,[status(thm)],[])).
% 2.43/2.62 tff(1403,plain,
% 2.43/2.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a617) | c0_1(a609) | c1_1(a609) | (~ndr1_0) | c3_1(a609) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617))),
% 2.43/2.62 inference(modus_ponens,[status(thm)],[1402, 1401])).
% 2.43/2.62 tff(1404,plain,
% 2.43/2.62 (c3_1(a609)),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[1403, 87, 926, 927, 1346, 1397, 1396, 1113, 938])).
% 2.43/2.62 tff(1405,plain,
% 2.43/2.62 (c2_1(a609)),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[701, 1390])).
% 2.43/2.62 tff(1406,assumption,(c0_1(a675)), introduced(assumption)).
% 2.43/2.62 tff(1407,assumption,(c3_1(a609)), introduced(assumption)).
% 2.43/2.62 tff(1408,assumption,(~c0_1(a609)), introduced(assumption)).
% 2.43/2.62 tff(1409,assumption,(c2_1(a609)), introduced(assumption)).
% 2.43/2.62 tff(1410,plain,
% 2.43/2.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | (c2_1(a675) | c3_1(a613) | c0_1(a609) | (~ndr1_0) | (~c3_1(a675)) | (~c0_1(a675)) | (~c3_1(a609)) | (~c2_1(a609)) | (~c1_1(a613)) | (~c2_1(a613)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c2_1(a675) | c3_1(a613) | c0_1(a609) | (~ndr1_0) | (~c3_1(a675)) | (~c0_1(a675)) | (~c3_1(a609)) | (~c2_1(a609)) | (~c1_1(a613)) | (~c2_1(a613)))),
% 2.43/2.62 inference(rewrite,[status(thm)],[])).
% 2.43/2.62 tff(1411,plain,
% 2.43/2.62 (((~ndr1_0) | c3_1(a613) | (~c1_1(a613)) | (~c2_1(a613)) | c0_1(a609) | (~c2_1(a609)) | (~c3_1(a609)) | c2_1(a675) | (~c0_1(a675)) | (~c3_1(a675))) <=> (c2_1(a675) | c3_1(a613) | c0_1(a609) | (~ndr1_0) | (~c3_1(a675)) | (~c0_1(a675)) | (~c3_1(a609)) | (~c2_1(a609)) | (~c1_1(a613)) | (~c2_1(a613)))),
% 2.43/2.62 inference(rewrite,[status(thm)],[])).
% 2.43/2.62 tff(1412,plain,
% 2.43/2.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a613) | (~c1_1(a613)) | (~c2_1(a613)) | c0_1(a609) | (~c2_1(a609)) | (~c3_1(a609)) | c2_1(a675) | (~c0_1(a675)) | (~c3_1(a675)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | (c2_1(a675) | c3_1(a613) | c0_1(a609) | (~ndr1_0) | (~c3_1(a675)) | (~c0_1(a675)) | (~c3_1(a609)) | (~c2_1(a609)) | (~c1_1(a613)) | (~c2_1(a613))))),
% 2.43/2.62 inference(monotonicity,[status(thm)],[1411])).
% 2.43/2.62 tff(1413,plain,
% 2.43/2.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a613) | (~c1_1(a613)) | (~c2_1(a613)) | c0_1(a609) | (~c2_1(a609)) | (~c3_1(a609)) | c2_1(a675) | (~c0_1(a675)) | (~c3_1(a675)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c2_1(a675) | c3_1(a613) | c0_1(a609) | (~ndr1_0) | (~c3_1(a675)) | (~c0_1(a675)) | (~c3_1(a609)) | (~c2_1(a609)) | (~c1_1(a613)) | (~c2_1(a613)))),
% 2.43/2.62 inference(transitivity,[status(thm)],[1412, 1410])).
% 2.43/2.62 tff(1414,plain,
% 2.43/2.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a613) | (~c1_1(a613)) | (~c2_1(a613)) | c0_1(a609) | (~c2_1(a609)) | (~c3_1(a609)) | c2_1(a675) | (~c0_1(a675)) | (~c3_1(a675)))),
% 2.43/2.62 inference(quant_inst,[status(thm)],[])).
% 2.43/2.62 tff(1415,plain,
% 2.43/2.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c2_1(a675) | c3_1(a613) | c0_1(a609) | (~ndr1_0) | (~c3_1(a675)) | (~c0_1(a675)) | (~c3_1(a609)) | (~c2_1(a609)) | (~c1_1(a613)) | (~c2_1(a613))),
% 2.43/2.62 inference(modus_ponens,[status(thm)],[1414, 1413])).
% 2.43/2.62 tff(1416,plain,
% 2.43/2.62 ($false),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[1415, 87, 324, 1043, 1035, 1409, 307, 1026, 1408, 953, 1407, 1406])).
% 2.43/2.62 tff(1417,plain,((~hskp9) | (~c3_1(a675)) | (~c2_1(a609)) | c2_1(a675) | c0_1(a609) | (~c3_1(a609)) | (~c0_1(a675))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.62 tff(1418,plain,
% 2.43/2.62 (~hskp9),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[1417, 942, 1405, 941, 1397, 1404, 1381])).
% 2.43/2.62 tff(1419,plain,
% 2.43/2.62 (hskp16),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[1062, 1418, 12])).
% 2.43/2.62 tff(1420,plain,
% 2.43/2.62 (c0_1(a627)),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[1091, 1419])).
% 2.43/2.62 tff(1421,plain,
% 2.43/2.62 (c2_1(a627)),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[1076, 1419])).
% 2.43/2.62 tff(1422,plain,
% 2.43/2.62 (c1_1(a627)),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[1098, 87, 257, 256, 1421, 1420, 232])).
% 2.43/2.62 tff(1423,plain,
% 2.43/2.62 (~c3_1(a627)),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[1068, 1419])).
% 2.43/2.62 tff(1424,plain,
% 2.43/2.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | (c2_1(a675) | c3_1(a627) | c0_1(a609) | (~ndr1_0) | (~c3_1(a675)) | (~c0_1(a675)) | (~c3_1(a609)) | (~c2_1(a609)) | (~c2_1(a627)) | (~c1_1(a627)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c2_1(a675) | c3_1(a627) | c0_1(a609) | (~ndr1_0) | (~c3_1(a675)) | (~c0_1(a675)) | (~c3_1(a609)) | (~c2_1(a609)) | (~c2_1(a627)) | (~c1_1(a627)))),
% 2.43/2.62 inference(rewrite,[status(thm)],[])).
% 2.43/2.62 tff(1425,plain,
% 2.43/2.62 (((~ndr1_0) | c3_1(a627) | (~c1_1(a627)) | (~c2_1(a627)) | c0_1(a609) | (~c2_1(a609)) | (~c3_1(a609)) | c2_1(a675) | (~c0_1(a675)) | (~c3_1(a675))) <=> (c2_1(a675) | c3_1(a627) | c0_1(a609) | (~ndr1_0) | (~c3_1(a675)) | (~c0_1(a675)) | (~c3_1(a609)) | (~c2_1(a609)) | (~c2_1(a627)) | (~c1_1(a627)))),
% 2.43/2.62 inference(rewrite,[status(thm)],[])).
% 2.43/2.62 tff(1426,plain,
% 2.43/2.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a627) | (~c1_1(a627)) | (~c2_1(a627)) | c0_1(a609) | (~c2_1(a609)) | (~c3_1(a609)) | c2_1(a675) | (~c0_1(a675)) | (~c3_1(a675)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | (c2_1(a675) | c3_1(a627) | c0_1(a609) | (~ndr1_0) | (~c3_1(a675)) | (~c0_1(a675)) | (~c3_1(a609)) | (~c2_1(a609)) | (~c2_1(a627)) | (~c1_1(a627))))),
% 2.43/2.62 inference(monotonicity,[status(thm)],[1425])).
% 2.43/2.62 tff(1427,plain,
% 2.43/2.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a627) | (~c1_1(a627)) | (~c2_1(a627)) | c0_1(a609) | (~c2_1(a609)) | (~c3_1(a609)) | c2_1(a675) | (~c0_1(a675)) | (~c3_1(a675)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c2_1(a675) | c3_1(a627) | c0_1(a609) | (~ndr1_0) | (~c3_1(a675)) | (~c0_1(a675)) | (~c3_1(a609)) | (~c2_1(a609)) | (~c2_1(a627)) | (~c1_1(a627)))),
% 2.43/2.62 inference(transitivity,[status(thm)],[1426, 1424])).
% 2.43/2.62 tff(1428,plain,
% 2.43/2.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a627) | (~c1_1(a627)) | (~c2_1(a627)) | c0_1(a609) | (~c2_1(a609)) | (~c3_1(a609)) | c2_1(a675) | (~c0_1(a675)) | (~c3_1(a675)))),
% 2.43/2.62 inference(quant_inst,[status(thm)],[])).
% 2.43/2.62 tff(1429,plain,
% 2.43/2.62 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c2_1(a675) | c3_1(a627) | c0_1(a609) | (~ndr1_0) | (~c3_1(a675)) | (~c0_1(a675)) | (~c3_1(a609)) | (~c2_1(a609)) | (~c2_1(a627)) | (~c1_1(a627))),
% 2.43/2.62 inference(modus_ponens,[status(thm)],[1428, 1427])).
% 2.43/2.62 tff(1430,plain,
% 2.43/2.62 ($false),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[1429, 87, 942, 1421, 1405, 941, 1423, 1397, 953, 1404, 1381, 1422])).
% 2.43/2.62 tff(1431,plain,(hskp14 | hskp15 | hskp17 | c0_1(a617) | hskp64), inference(lemma,lemma(discharge,[]))).
% 2.43/2.62 tff(1432,plain,
% 2.43/2.62 (hskp14),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[1431, 938, 12, 257, 24])).
% 2.43/2.62 tff(1433,plain,
% 2.43/2.62 (~c2_1(a624)),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[191, 1432])).
% 2.43/2.62 tff(1434,plain,
% 2.43/2.62 (c3_1(a624)),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[199, 1432])).
% 2.43/2.62 tff(1435,plain,
% 2.43/2.62 (((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | c2_1(a624) | (~ndr1_0) | c0_1(a624) | (~c3_1(a624)))) <=> ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp29 | hskp3 | c2_1(a624) | (~ndr1_0) | c0_1(a624) | (~c3_1(a624)))),
% 2.43/2.62 inference(rewrite,[status(thm)],[])).
% 2.43/2.62 tff(1436,plain,
% 2.43/2.62 ((hskp29 | hskp3 | (~ndr1_0) | c2_1(a624) | c0_1(a624) | (~c3_1(a624))) <=> (hskp29 | hskp3 | c2_1(a624) | (~ndr1_0) | c0_1(a624) | (~c3_1(a624)))),
% 2.43/2.62 inference(rewrite,[status(thm)],[])).
% 2.43/2.62 tff(1437,plain,
% 2.43/2.62 (((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | (~ndr1_0) | c2_1(a624) | c0_1(a624) | (~c3_1(a624)))) <=> ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | c2_1(a624) | (~ndr1_0) | c0_1(a624) | (~c3_1(a624))))),
% 2.43/2.62 inference(monotonicity,[status(thm)],[1436])).
% 2.43/2.62 tff(1438,plain,
% 2.43/2.62 (((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | (~ndr1_0) | c2_1(a624) | c0_1(a624) | (~c3_1(a624)))) <=> ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp29 | hskp3 | c2_1(a624) | (~ndr1_0) | c0_1(a624) | (~c3_1(a624)))),
% 2.43/2.62 inference(transitivity,[status(thm)],[1437, 1435])).
% 2.43/2.62 tff(1439,plain,
% 2.43/2.62 ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | (~ndr1_0) | c2_1(a624) | c0_1(a624) | (~c3_1(a624)))),
% 2.43/2.62 inference(quant_inst,[status(thm)],[])).
% 2.43/2.62 tff(1440,plain,
% 2.43/2.62 ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp29 | hskp3 | c2_1(a624) | (~ndr1_0) | c0_1(a624) | (~c3_1(a624))),
% 2.43/2.62 inference(modus_ponens,[status(thm)],[1439, 1438])).
% 2.43/2.62 tff(1441,plain,
% 2.43/2.62 (c0_1(a624)),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[1440, 87, 1374, 1345, 1434, 1433, 937])).
% 2.43/2.62 tff(1442,plain,
% 2.43/2.62 (~c1_1(a624)),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[212, 1432])).
% 2.43/2.62 tff(1443,plain,
% 2.43/2.62 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W))) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W))))),
% 2.43/2.62 inference(bind,[status(th)],[])).
% 2.43/2.62 tff(1444,plain,
% 2.43/2.62 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 2.43/2.62 inference(quant_intro,[status(thm)],[1443])).
% 2.43/2.62 tff(1445,plain,
% 2.43/2.62 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 2.43/2.62 inference(rewrite,[status(thm)],[])).
% 2.43/2.62 tff(1446,plain,
% 2.43/2.62 (^[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) | (~c3_1(U)) | (~c2_1(U)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)))), (((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c2_1(W)))), ((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c2_1(W))))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c2_1(W))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c2_1(W))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W)))), (((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | (~c1_1(W))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W)))), ((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | (~c1_1(W))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | (~c1_1(W))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W)))), (((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | (~c1_1(W))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | (~c1_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W)))), ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | (~c1_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | (~c1_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | (~c1_1(W)) | (~c2_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))), (((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | (~c1_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))))),
% 2.43/2.62 inference(bind,[status(th)],[])).
% 2.43/2.62 tff(1447,plain,
% 2.43/2.62 (![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | (~c1_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 2.43/2.62 inference(quant_intro,[status(thm)],[1446])).
% 2.43/2.62 tff(1448,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c2_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c2_1(W))) | (~c1_1(W))) | c1_1(U)) | c1_1(V)) | c0_1(V)) | c0_1(W))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause326')).
% 2.43/2.62 tff(1449,plain,
% 2.43/2.62 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 2.43/2.62 inference(modus_ponens,[status(thm)],[1448, 1447])).
% 2.43/2.62 tff(1450,plain,
% 2.43/2.62 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 2.43/2.62 inference(modus_ponens,[status(thm)],[1449, 1445])).
% 2.43/2.62 tff(1451,plain,(
% 2.43/2.62 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 2.43/2.62 inference(skolemize,[status(sab)],[1450])).
% 2.43/2.62 tff(1452,plain,
% 2.43/2.62 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))),
% 2.43/2.62 inference(modus_ponens,[status(thm)],[1451, 1444])).
% 2.43/2.62 tff(1453,assumption,(hskp57), introduced(assumption)).
% 2.43/2.62 tff(1454,plain,
% 2.43/2.62 (~c0_1(a662)),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[732, 1453])).
% 2.43/2.62 tff(1455,plain,
% 2.43/2.62 (c2_1(a662)),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[740, 1453])).
% 2.43/2.62 tff(1456,plain,
% 2.43/2.62 (c1_1(a662)),
% 2.43/2.62 inference(unit_resolution,[status(thm)],[748, 1453])).
% 2.43/2.62 tff(1457,plain,
% 2.43/2.62 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a662) | c1_1(a617) | (~ndr1_0) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)) | (~c2_1(a662)) | (~c1_1(a662)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a662) | c1_1(a617) | (~ndr1_0) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)) | (~c2_1(a662)) | (~c1_1(a662)))),
% 2.43/2.62 inference(rewrite,[status(thm)],[])).
% 2.43/2.62 tff(1458,plain,
% 2.43/2.62 (((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)) | c0_1(a662) | (~c1_1(a662)) | (~c2_1(a662))) <=> (c0_1(a662) | c1_1(a617) | (~ndr1_0) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)) | (~c2_1(a662)) | (~c1_1(a662)))),
% 2.43/2.63 inference(rewrite,[status(thm)],[])).
% 2.43/2.63 tff(1459,plain,
% 2.43/2.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)) | c0_1(a662) | (~c1_1(a662)) | (~c2_1(a662)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a662) | c1_1(a617) | (~ndr1_0) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)) | (~c2_1(a662)) | (~c1_1(a662))))),
% 2.43/2.63 inference(monotonicity,[status(thm)],[1458])).
% 2.43/2.63 tff(1460,plain,
% 2.43/2.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)) | c0_1(a662) | (~c1_1(a662)) | (~c2_1(a662)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a662) | c1_1(a617) | (~ndr1_0) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)) | (~c2_1(a662)) | (~c1_1(a662)))),
% 2.43/2.63 inference(transitivity,[status(thm)],[1459, 1457])).
% 2.43/2.63 tff(1461,plain,
% 2.43/2.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)) | c0_1(a662) | (~c1_1(a662)) | (~c2_1(a662)))),
% 2.43/2.63 inference(quant_inst,[status(thm)],[])).
% 2.43/2.63 tff(1462,plain,
% 2.43/2.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a662) | c1_1(a617) | (~ndr1_0) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)) | (~c2_1(a662)) | (~c1_1(a662))),
% 2.43/2.63 inference(modus_ponens,[status(thm)],[1461, 1460])).
% 2.43/2.63 tff(1463,plain,
% 2.43/2.63 ($false),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[1462, 87, 1456, 1455, 649, 648, 1454, 647, 1452, 938])).
% 2.43/2.63 tff(1464,plain,((~hskp57) | (~c2_1(a617)) | (~c3_1(a617)) | c1_1(a617) | c0_1(a617)), inference(lemma,lemma(discharge,[]))).
% 2.43/2.63 tff(1465,plain,
% 2.43/2.63 (~hskp57),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[1464, 938, 927, 1346, 926])).
% 2.43/2.63 tff(1466,plain,
% 2.43/2.63 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | c1_1(a624) | (~ndr1_0) | (~c0_1(a624)) | (~c3_1(a624)) | (~c0_1(a648)) | (~c3_1(a648)) | (~c1_1(a648)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | c1_1(a624) | (~ndr1_0) | (~c0_1(a624)) | (~c3_1(a624)) | (~c0_1(a648)) | (~c3_1(a648)) | (~c1_1(a648)))),
% 2.43/2.63 inference(rewrite,[status(thm)],[])).
% 2.43/2.63 tff(1467,plain,
% 2.43/2.63 ((hskp57 | (~ndr1_0) | (~c3_1(a648)) | (~c1_1(a648)) | (~c0_1(a648)) | c1_1(a624) | (~c3_1(a624)) | (~c0_1(a624))) <=> (hskp57 | c1_1(a624) | (~ndr1_0) | (~c0_1(a624)) | (~c3_1(a624)) | (~c0_1(a648)) | (~c3_1(a648)) | (~c1_1(a648)))),
% 2.43/2.63 inference(rewrite,[status(thm)],[])).
% 2.43/2.63 tff(1468,plain,
% 2.43/2.63 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | (~c3_1(a648)) | (~c1_1(a648)) | (~c0_1(a648)) | c1_1(a624) | (~c3_1(a624)) | (~c0_1(a624)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | c1_1(a624) | (~ndr1_0) | (~c0_1(a624)) | (~c3_1(a624)) | (~c0_1(a648)) | (~c3_1(a648)) | (~c1_1(a648))))),
% 2.43/2.63 inference(monotonicity,[status(thm)],[1467])).
% 2.43/2.63 tff(1469,plain,
% 2.43/2.63 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | (~c3_1(a648)) | (~c1_1(a648)) | (~c0_1(a648)) | c1_1(a624) | (~c3_1(a624)) | (~c0_1(a624)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | c1_1(a624) | (~ndr1_0) | (~c0_1(a624)) | (~c3_1(a624)) | (~c0_1(a648)) | (~c3_1(a648)) | (~c1_1(a648)))),
% 2.43/2.63 inference(transitivity,[status(thm)],[1468, 1466])).
% 2.43/2.63 tff(1470,plain,
% 2.43/2.63 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | (~c3_1(a648)) | (~c1_1(a648)) | (~c0_1(a648)) | c1_1(a624) | (~c3_1(a624)) | (~c0_1(a624)))),
% 2.43/2.63 inference(quant_inst,[status(thm)],[])).
% 2.43/2.63 tff(1471,plain,
% 2.43/2.63 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | c1_1(a624) | (~ndr1_0) | (~c0_1(a624)) | (~c3_1(a624)) | (~c0_1(a648)) | (~c3_1(a648)) | (~c1_1(a648))),
% 2.43/2.63 inference(modus_ponens,[status(thm)],[1470, 1469])).
% 2.43/2.63 tff(1472,plain,
% 2.43/2.63 (~c1_1(a648)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[1471, 87, 1465, 801, 793, 1434, 1442, 720, 1441])).
% 2.43/2.63 tff(1473,plain,
% 2.43/2.63 (((~![V: $i, U: $i] : (hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp55 | c1_1(a617) | c1_1(a624) | (~ndr1_0) | (~c0_1(a624)) | (~c3_1(a624)) | c0_1(a617) | (~c3_1(a617)))) <=> ((~![V: $i, U: $i] : (hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp55 | c1_1(a617) | c1_1(a624) | (~ndr1_0) | (~c0_1(a624)) | (~c3_1(a624)) | c0_1(a617) | (~c3_1(a617)))),
% 2.43/2.63 inference(rewrite,[status(thm)],[])).
% 2.43/2.63 tff(1474,plain,
% 2.43/2.63 ((hskp55 | (~ndr1_0) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)) | c1_1(a624) | (~c3_1(a624)) | (~c0_1(a624))) <=> (hskp55 | c1_1(a617) | c1_1(a624) | (~ndr1_0) | (~c0_1(a624)) | (~c3_1(a624)) | c0_1(a617) | (~c3_1(a617)))),
% 2.43/2.63 inference(rewrite,[status(thm)],[])).
% 2.43/2.63 tff(1475,plain,
% 2.43/2.63 (((~![V: $i, U: $i] : (hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp55 | (~ndr1_0) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)) | c1_1(a624) | (~c3_1(a624)) | (~c0_1(a624)))) <=> ((~![V: $i, U: $i] : (hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp55 | c1_1(a617) | c1_1(a624) | (~ndr1_0) | (~c0_1(a624)) | (~c3_1(a624)) | c0_1(a617) | (~c3_1(a617))))),
% 2.43/2.63 inference(monotonicity,[status(thm)],[1474])).
% 2.43/2.63 tff(1476,plain,
% 2.43/2.63 (((~![V: $i, U: $i] : (hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp55 | (~ndr1_0) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)) | c1_1(a624) | (~c3_1(a624)) | (~c0_1(a624)))) <=> ((~![V: $i, U: $i] : (hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp55 | c1_1(a617) | c1_1(a624) | (~ndr1_0) | (~c0_1(a624)) | (~c3_1(a624)) | c0_1(a617) | (~c3_1(a617)))),
% 2.43/2.63 inference(transitivity,[status(thm)],[1475, 1473])).
% 2.43/2.63 tff(1477,plain,
% 2.43/2.63 ((~![V: $i, U: $i] : (hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp55 | (~ndr1_0) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)) | c1_1(a624) | (~c3_1(a624)) | (~c0_1(a624)))),
% 2.43/2.63 inference(quant_inst,[status(thm)],[])).
% 2.43/2.63 tff(1478,plain,
% 2.43/2.63 ((~![V: $i, U: $i] : (hskp55 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp55 | c1_1(a617) | c1_1(a624) | (~ndr1_0) | (~c0_1(a624)) | (~c3_1(a624)) | c0_1(a617) | (~c3_1(a617))),
% 2.43/2.63 inference(modus_ponens,[status(thm)],[1477, 1476])).
% 2.43/2.63 tff(1479,plain,
% 2.43/2.63 (hskp55),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[1478, 87, 927, 1434, 1346, 1442, 856, 938, 1441])).
% 2.43/2.63 tff(1480,plain,
% 2.43/2.63 (c1_1(a653)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[884, 1479])).
% 2.43/2.63 tff(1481,plain,
% 2.43/2.63 (c3_1(a653)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[892, 1479])).
% 2.43/2.63 tff(1482,plain,
% 2.43/2.63 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | (~c0_1(a648)) | (~c3_1(a648)) | c1_1(a648) | (~c0_1(a653)) | (~c3_1(a653)) | (~c1_1(a653)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | (~ndr1_0) | (~c0_1(a648)) | (~c3_1(a648)) | c1_1(a648) | (~c0_1(a653)) | (~c3_1(a653)) | (~c1_1(a653)))),
% 2.43/2.63 inference(rewrite,[status(thm)],[])).
% 2.43/2.63 tff(1483,plain,
% 2.43/2.63 ((hskp57 | (~ndr1_0) | (~c3_1(a653)) | (~c1_1(a653)) | (~c0_1(a653)) | c1_1(a648) | (~c3_1(a648)) | (~c0_1(a648))) <=> (hskp57 | (~ndr1_0) | (~c0_1(a648)) | (~c3_1(a648)) | c1_1(a648) | (~c0_1(a653)) | (~c3_1(a653)) | (~c1_1(a653)))),
% 2.43/2.63 inference(rewrite,[status(thm)],[])).
% 2.43/2.63 tff(1484,plain,
% 2.43/2.63 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | (~c3_1(a653)) | (~c1_1(a653)) | (~c0_1(a653)) | c1_1(a648) | (~c3_1(a648)) | (~c0_1(a648)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | (~c0_1(a648)) | (~c3_1(a648)) | c1_1(a648) | (~c0_1(a653)) | (~c3_1(a653)) | (~c1_1(a653))))),
% 2.43/2.63 inference(monotonicity,[status(thm)],[1483])).
% 2.43/2.63 tff(1485,plain,
% 2.43/2.63 (((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | (~c3_1(a653)) | (~c1_1(a653)) | (~c0_1(a653)) | c1_1(a648) | (~c3_1(a648)) | (~c0_1(a648)))) <=> ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | (~ndr1_0) | (~c0_1(a648)) | (~c3_1(a648)) | c1_1(a648) | (~c0_1(a653)) | (~c3_1(a653)) | (~c1_1(a653)))),
% 2.43/2.63 inference(transitivity,[status(thm)],[1484, 1482])).
% 2.43/2.63 tff(1486,plain,
% 2.43/2.63 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp57 | (~ndr1_0) | (~c3_1(a653)) | (~c1_1(a653)) | (~c0_1(a653)) | c1_1(a648) | (~c3_1(a648)) | (~c0_1(a648)))),
% 2.43/2.63 inference(quant_inst,[status(thm)],[])).
% 2.43/2.63 tff(1487,plain,
% 2.43/2.63 ((~![V: $i, U: $i] : (hskp57 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp57 | (~ndr1_0) | (~c0_1(a648)) | (~c3_1(a648)) | c1_1(a648) | (~c0_1(a653)) | (~c3_1(a653)) | (~c1_1(a653))),
% 2.43/2.63 inference(modus_ponens,[status(thm)],[1486, 1485])).
% 2.43/2.63 tff(1488,plain,
% 2.43/2.63 (~c0_1(a653)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[1487, 87, 1465, 1481, 1480, 801, 793, 720, 1472])).
% 2.43/2.63 tff(1489,plain,
% 2.43/2.63 (~c2_1(a653)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[868, 1479])).
% 2.43/2.63 tff(1490,plain,
% 2.43/2.63 (((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | c2_1(a653) | (~ndr1_0) | c0_1(a653) | (~c3_1(a653)))) <=> ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp29 | hskp3 | c2_1(a653) | (~ndr1_0) | c0_1(a653) | (~c3_1(a653)))),
% 2.43/2.63 inference(rewrite,[status(thm)],[])).
% 2.43/2.63 tff(1491,plain,
% 2.43/2.63 ((hskp29 | hskp3 | (~ndr1_0) | c2_1(a653) | c0_1(a653) | (~c3_1(a653))) <=> (hskp29 | hskp3 | c2_1(a653) | (~ndr1_0) | c0_1(a653) | (~c3_1(a653)))),
% 2.43/2.63 inference(rewrite,[status(thm)],[])).
% 2.43/2.63 tff(1492,plain,
% 2.43/2.63 (((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | (~ndr1_0) | c2_1(a653) | c0_1(a653) | (~c3_1(a653)))) <=> ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | c2_1(a653) | (~ndr1_0) | c0_1(a653) | (~c3_1(a653))))),
% 2.43/2.63 inference(monotonicity,[status(thm)],[1491])).
% 2.43/2.63 tff(1493,plain,
% 2.43/2.63 (((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | (~ndr1_0) | c2_1(a653) | c0_1(a653) | (~c3_1(a653)))) <=> ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp29 | hskp3 | c2_1(a653) | (~ndr1_0) | c0_1(a653) | (~c3_1(a653)))),
% 2.43/2.63 inference(transitivity,[status(thm)],[1492, 1490])).
% 2.43/2.63 tff(1494,plain,
% 2.43/2.63 ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | (~ndr1_0) | c2_1(a653) | c0_1(a653) | (~c3_1(a653)))),
% 2.43/2.63 inference(quant_inst,[status(thm)],[])).
% 2.43/2.63 tff(1495,plain,
% 2.43/2.63 ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp29 | hskp3 | c2_1(a653) | (~ndr1_0) | c0_1(a653) | (~c3_1(a653))),
% 2.43/2.63 inference(modus_ponens,[status(thm)],[1494, 1493])).
% 2.43/2.63 tff(1496,plain,
% 2.43/2.63 ($false),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[1495, 87, 1374, 1345, 1481, 1489, 937, 1488])).
% 2.43/2.63 tff(1497,plain,(c0_1(a617) | hskp17 | hskp15 | hskp64), inference(lemma,lemma(discharge,[]))).
% 2.43/2.63 tff(1498,plain,
% 2.43/2.63 (c0_1(a617)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[1497, 257, 12, 24])).
% 2.43/2.63 tff(1499,plain,
% 2.43/2.63 (hskp15 | hskp14 | (~c0_1(a617))),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[552, 87, 926, 1346, 232])).
% 2.43/2.63 tff(1500,plain,
% 2.43/2.63 (hskp14),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[1499, 1498, 257])).
% 2.43/2.63 tff(1501,plain,
% 2.43/2.63 (~c2_1(a624)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[191, 1500])).
% 2.43/2.63 tff(1502,plain,
% 2.43/2.63 (~c1_1(a624)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[212, 1500])).
% 2.43/2.63 tff(1503,plain,
% 2.43/2.63 (c3_1(a624)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[199, 1500])).
% 2.43/2.63 tff(1504,plain,
% 2.43/2.63 (hskp20),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[1198, 1503, 1498, 1346, 1502, 1501, 927, 926])).
% 2.43/2.63 tff(1505,plain,
% 2.43/2.63 (~c2_1(a635)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[613, 1504])).
% 2.43/2.63 tff(1506,plain,
% 2.43/2.63 (~c1_1(a635)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[619, 1504])).
% 2.43/2.63 tff(1507,plain,
% 2.43/2.63 (~c3_1(a635)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[607, 1504])).
% 2.43/2.63 tff(1508,plain,
% 2.43/2.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a648) | c1_1(a617) | c2_1(a635) | c3_1(a635) | (~ndr1_0) | c0_1(a635) | (~c3_1(a617)) | (~c0_1(a617)) | (~c0_1(a648)) | (~c3_1(a648)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a648) | c1_1(a617) | c2_1(a635) | c3_1(a635) | (~ndr1_0) | c0_1(a635) | (~c3_1(a617)) | (~c0_1(a617)) | (~c0_1(a648)) | (~c3_1(a648)))),
% 2.43/2.63 inference(rewrite,[status(thm)],[])).
% 2.43/2.63 tff(1509,plain,
% 2.43/2.63 (((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c0_1(a617)) | c2_1(a648) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a635) | c0_1(a635) | c3_1(a635)) <=> (c2_1(a648) | c1_1(a617) | c2_1(a635) | c3_1(a635) | (~ndr1_0) | c0_1(a635) | (~c3_1(a617)) | (~c0_1(a617)) | (~c0_1(a648)) | (~c3_1(a648)))),
% 2.43/2.63 inference(rewrite,[status(thm)],[])).
% 2.43/2.63 tff(1510,plain,
% 2.43/2.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c0_1(a617)) | c2_1(a648) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a635) | c0_1(a635) | c3_1(a635))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a648) | c1_1(a617) | c2_1(a635) | c3_1(a635) | (~ndr1_0) | c0_1(a635) | (~c3_1(a617)) | (~c0_1(a617)) | (~c0_1(a648)) | (~c3_1(a648))))),
% 2.43/2.63 inference(monotonicity,[status(thm)],[1509])).
% 2.43/2.63 tff(1511,plain,
% 2.43/2.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c0_1(a617)) | c2_1(a648) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a635) | c0_1(a635) | c3_1(a635))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a648) | c1_1(a617) | c2_1(a635) | c3_1(a635) | (~ndr1_0) | c0_1(a635) | (~c3_1(a617)) | (~c0_1(a617)) | (~c0_1(a648)) | (~c3_1(a648)))),
% 2.43/2.63 inference(transitivity,[status(thm)],[1510, 1508])).
% 2.43/2.63 tff(1512,plain,
% 2.43/2.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c0_1(a617)) | c2_1(a648) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a635) | c0_1(a635) | c3_1(a635))),
% 2.43/2.63 inference(quant_inst,[status(thm)],[])).
% 2.43/2.63 tff(1513,plain,
% 2.43/2.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a648) | c1_1(a617) | c2_1(a635) | c3_1(a635) | (~ndr1_0) | c0_1(a635) | (~c3_1(a617)) | (~c0_1(a617)) | (~c0_1(a648)) | (~c3_1(a648))),
% 2.43/2.63 inference(modus_ponens,[status(thm)],[1512, 1511])).
% 2.43/2.63 tff(1514,plain,
% 2.43/2.63 (c0_1(a635)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[1513, 87, 801, 793, 927, 785, 1346, 1505, 1507, 910, 1498])).
% 2.43/2.63 tff(1515,plain,
% 2.43/2.63 (hskp5),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[1332, 1514, 801, 793, 785, 1500, 1506, 1505])).
% 2.43/2.63 tff(1516,plain,
% 2.43/2.63 (~c3_1(a606)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[574, 1515])).
% 2.43/2.63 tff(1517,plain,
% 2.43/2.63 (c2_1(a606)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[588, 1515])).
% 2.43/2.63 tff(1518,plain,
% 2.43/2.63 (~c0_1(a606)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[580, 1515])).
% 2.43/2.63 tff(1519,plain,
% 2.43/2.63 ($false),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[629, 1518, 1517, 1504, 1516])).
% 2.43/2.63 tff(1520,plain,(hskp15 | hskp17 | hskp64), inference(lemma,lemma(discharge,[]))).
% 2.43/2.63 tff(1521,plain,
% 2.43/2.63 (hskp15),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[1520, 24, 12])).
% 2.43/2.63 tff(1522,plain,
% 2.43/2.63 (~c0_1(a625)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[146, 1521])).
% 2.43/2.63 tff(1523,plain,
% 2.43/2.63 (~c1_1(a625)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[152, 1521])).
% 2.43/2.63 tff(1524,plain,
% 2.43/2.63 (~c2_1(a625)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[175, 1521])).
% 2.43/2.63 tff(1525,assumption,(~c0_1(a625)), introduced(assumption)).
% 2.43/2.63 tff(1526,assumption,(~c1_1(a625)), introduced(assumption)).
% 2.43/2.63 tff(1527,plain,
% 2.43/2.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a617) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | c3_1(a625) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a617) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | c3_1(a625) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 2.43/2.63 inference(rewrite,[status(thm)],[])).
% 2.43/2.63 tff(1528,plain,
% 2.43/2.63 (((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)) | c1_1(a625) | c0_1(a625) | c3_1(a625)) <=> (c1_1(a617) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | c3_1(a625) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 2.43/2.63 inference(rewrite,[status(thm)],[])).
% 2.43/2.63 tff(1529,plain,
% 2.43/2.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)) | c1_1(a625) | c0_1(a625) | c3_1(a625))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a617) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | c3_1(a625) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617))))),
% 2.43/2.63 inference(monotonicity,[status(thm)],[1528])).
% 2.43/2.63 tff(1530,plain,
% 2.43/2.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)) | c1_1(a625) | c0_1(a625) | c3_1(a625))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a617) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | c3_1(a625) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 2.43/2.63 inference(transitivity,[status(thm)],[1529, 1527])).
% 2.43/2.63 tff(1531,plain,
% 2.43/2.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)) | c1_1(a625) | c0_1(a625) | c3_1(a625))),
% 2.43/2.63 inference(quant_inst,[status(thm)],[])).
% 2.43/2.63 tff(1532,plain,
% 2.43/2.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a617) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | c3_1(a625) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617))),
% 2.43/2.63 inference(modus_ponens,[status(thm)],[1531, 1530])).
% 2.43/2.63 tff(1533,plain,
% 2.43/2.63 (c3_1(a625) | c0_1(a617)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[1532, 87, 957, 956, 955, 1526, 1525, 1113])).
% 2.43/2.63 tff(1534,plain,
% 2.43/2.63 (c3_1(a625)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[1533, 938])).
% 2.43/2.63 tff(1535,plain,
% 2.43/2.63 (~hskp29),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[1373, 938, 956, 955, 957])).
% 2.43/2.63 tff(1536,assumption,(~c2_1(a625)), introduced(assumption)).
% 2.43/2.63 tff(1537,plain,
% 2.43/2.63 (((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | c2_1(a625) | c0_1(a625) | (~ndr1_0) | (~c3_1(a625)))) <=> ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp29 | hskp3 | c2_1(a625) | c0_1(a625) | (~ndr1_0) | (~c3_1(a625)))),
% 2.43/2.63 inference(rewrite,[status(thm)],[])).
% 2.43/2.63 tff(1538,plain,
% 2.43/2.63 ((hskp29 | hskp3 | (~ndr1_0) | c2_1(a625) | c0_1(a625) | (~c3_1(a625))) <=> (hskp29 | hskp3 | c2_1(a625) | c0_1(a625) | (~ndr1_0) | (~c3_1(a625)))),
% 2.43/2.63 inference(rewrite,[status(thm)],[])).
% 2.43/2.63 tff(1539,plain,
% 2.43/2.63 (((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | (~ndr1_0) | c2_1(a625) | c0_1(a625) | (~c3_1(a625)))) <=> ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | c2_1(a625) | c0_1(a625) | (~ndr1_0) | (~c3_1(a625))))),
% 2.43/2.63 inference(monotonicity,[status(thm)],[1538])).
% 2.43/2.63 tff(1540,plain,
% 2.43/2.63 (((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | (~ndr1_0) | c2_1(a625) | c0_1(a625) | (~c3_1(a625)))) <=> ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp29 | hskp3 | c2_1(a625) | c0_1(a625) | (~ndr1_0) | (~c3_1(a625)))),
% 2.43/2.63 inference(transitivity,[status(thm)],[1539, 1537])).
% 2.43/2.63 tff(1541,plain,
% 2.43/2.63 ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | (~ndr1_0) | c2_1(a625) | c0_1(a625) | (~c3_1(a625)))),
% 2.43/2.63 inference(quant_inst,[status(thm)],[])).
% 2.43/2.63 tff(1542,plain,
% 2.43/2.63 ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp29 | hskp3 | c2_1(a625) | c0_1(a625) | (~ndr1_0) | (~c3_1(a625))),
% 2.43/2.63 inference(modus_ponens,[status(thm)],[1541, 1540])).
% 2.43/2.63 tff(1543,plain,
% 2.43/2.63 (hskp29 | hskp3 | (~c3_1(a625))),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[1542, 87, 1536, 1525, 937])).
% 2.43/2.63 tff(1544,plain,
% 2.43/2.63 (hskp3),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[1543, 1535, 1534])).
% 2.43/2.63 tff(1545,plain,
% 2.43/2.63 (~c3_1(a603)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[1344, 1544])).
% 2.43/2.63 tff(1546,plain,
% 2.43/2.63 (((~hskp3) | (~c1_1(a603))) <=> ((~hskp3) | (~c1_1(a603)))),
% 2.43/2.63 inference(rewrite,[status(thm)],[])).
% 2.43/2.63 tff(1547,plain,
% 2.43/2.63 (((~c1_1(a603)) | (~hskp3)) <=> ((~hskp3) | (~c1_1(a603)))),
% 2.43/2.63 inference(rewrite,[status(thm)],[])).
% 2.43/2.63 tff(1548,axiom,((~c1_1(a603)) | (~hskp3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause270')).
% 2.43/2.63 tff(1549,plain,
% 2.43/2.63 ((~hskp3) | (~c1_1(a603))),
% 2.43/2.63 inference(modus_ponens,[status(thm)],[1548, 1547])).
% 2.43/2.63 tff(1550,plain,
% 2.43/2.63 ((~hskp3) | (~c1_1(a603))),
% 2.43/2.63 inference(modus_ponens,[status(thm)],[1549, 1546])).
% 2.43/2.63 tff(1551,plain,
% 2.43/2.63 (~c1_1(a603)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[1550, 1544])).
% 2.43/2.63 tff(1552,plain,
% 2.43/2.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a617) | c2_1(a625) | c1_1(a625) | c0_1(a625) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a617) | (~c2_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a617) | c2_1(a625) | c1_1(a625) | c0_1(a625) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a617) | (~c2_1(a617)))),
% 2.43/2.63 inference(rewrite,[status(thm)],[])).
% 2.43/2.63 tff(1553,plain,
% 2.43/2.63 (((~ndr1_0) | c3_1(a603) | c1_1(a603) | (~c2_1(a603)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)) | c2_1(a625) | c1_1(a625) | c0_1(a625)) <=> (c1_1(a617) | c2_1(a625) | c1_1(a625) | c0_1(a625) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a617) | (~c2_1(a617)))),
% 2.43/2.63 inference(rewrite,[status(thm)],[])).
% 2.43/2.63 tff(1554,plain,
% 2.43/2.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a603) | c1_1(a603) | (~c2_1(a603)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)) | c2_1(a625) | c1_1(a625) | c0_1(a625))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a617) | c2_1(a625) | c1_1(a625) | c0_1(a625) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a617) | (~c2_1(a617))))),
% 2.43/2.63 inference(monotonicity,[status(thm)],[1553])).
% 2.43/2.63 tff(1555,plain,
% 2.43/2.63 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a603) | c1_1(a603) | (~c2_1(a603)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)) | c2_1(a625) | c1_1(a625) | c0_1(a625))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a617) | c2_1(a625) | c1_1(a625) | c0_1(a625) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a617) | (~c2_1(a617)))),
% 2.43/2.63 inference(transitivity,[status(thm)],[1554, 1552])).
% 2.43/2.63 tff(1556,plain,
% 2.43/2.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a603) | c1_1(a603) | (~c2_1(a603)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)) | c2_1(a625) | c1_1(a625) | c0_1(a625))),
% 2.43/2.63 inference(quant_inst,[status(thm)],[])).
% 2.43/2.63 tff(1557,plain,
% 2.43/2.63 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a617) | c2_1(a625) | c1_1(a625) | c0_1(a625) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a617) | (~c2_1(a617))),
% 2.43/2.63 inference(modus_ponens,[status(thm)],[1556, 1555])).
% 2.43/2.63 tff(1558,plain,
% 2.43/2.63 (~c2_1(a603)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[1557, 87, 957, 955, 1536, 1526, 1525, 1551, 1545, 1279, 938])).
% 2.43/2.63 tff(1559,plain,
% 2.43/2.63 (((~hskp3) | c0_1(a603)) <=> ((~hskp3) | c0_1(a603))),
% 2.43/2.63 inference(rewrite,[status(thm)],[])).
% 2.43/2.63 tff(1560,axiom,((~hskp3) | c0_1(a603)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause166')).
% 2.43/2.63 tff(1561,plain,
% 2.43/2.63 ((~hskp3) | c0_1(a603)),
% 2.43/2.63 inference(modus_ponens,[status(thm)],[1560, 1559])).
% 2.43/2.63 tff(1562,plain,
% 2.43/2.63 ((~hskp3) | c0_1(a603)),
% 2.43/2.63 inference(modus_ponens,[status(thm)],[1561, 1559])).
% 2.43/2.63 tff(1563,plain,
% 2.43/2.63 ((~hskp3) | c0_1(a603)),
% 2.43/2.63 inference(modus_ponens,[status(thm)],[1562, 1559])).
% 2.43/2.63 tff(1564,plain,
% 2.43/2.63 ((~hskp3) | c0_1(a603)),
% 2.43/2.63 inference(modus_ponens,[status(thm)],[1563, 1559])).
% 2.43/2.63 tff(1565,plain,
% 2.43/2.63 ((~hskp3) | c0_1(a603)),
% 2.43/2.63 inference(modus_ponens,[status(thm)],[1564, 1559])).
% 2.43/2.63 tff(1566,plain,
% 2.43/2.63 (c0_1(a603)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[1565, 1544])).
% 2.43/2.63 tff(1567,plain,
% 2.43/2.63 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | c1_1(a617) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | c0_1(a617) | (~c3_1(a617)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c1_1(a617) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | c0_1(a617) | (~c3_1(a617)))),
% 2.43/2.63 inference(rewrite,[status(thm)],[])).
% 2.43/2.63 tff(1568,plain,
% 2.43/2.63 ((hskp42 | (~ndr1_0) | c1_1(a603) | c2_1(a603) | (~c0_1(a603)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617))) <=> (hskp42 | c1_1(a617) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | c0_1(a617) | (~c3_1(a617)))),
% 2.43/2.63 inference(rewrite,[status(thm)],[])).
% 2.43/2.63 tff(1569,plain,
% 2.43/2.63 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a603) | c2_1(a603) | (~c0_1(a603)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | c1_1(a617) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | c0_1(a617) | (~c3_1(a617))))),
% 2.43/2.63 inference(monotonicity,[status(thm)],[1568])).
% 2.43/2.63 tff(1570,plain,
% 2.43/2.63 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a603) | c2_1(a603) | (~c0_1(a603)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c1_1(a617) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | c0_1(a617) | (~c3_1(a617)))),
% 2.43/2.63 inference(transitivity,[status(thm)],[1569, 1567])).
% 2.43/2.63 tff(1571,plain,
% 2.43/2.63 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a603) | c2_1(a603) | (~c0_1(a603)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)))),
% 2.43/2.63 inference(quant_inst,[status(thm)],[])).
% 2.43/2.63 tff(1572,plain,
% 2.43/2.63 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c1_1(a617) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | c0_1(a617) | (~c3_1(a617))),
% 2.43/2.63 inference(modus_ponens,[status(thm)],[1571, 1570])).
% 2.43/2.63 tff(1573,plain,
% 2.43/2.63 (hskp42),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[1572, 87, 956, 1566, 955, 1551, 822, 1558, 938])).
% 2.43/2.63 tff(1574,plain,
% 2.43/2.63 (~c3_1(a618)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[915, 1573])).
% 2.43/2.63 tff(1575,plain,
% 2.43/2.63 (~c2_1(a618)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[845, 1573])).
% 2.43/2.63 tff(1576,plain,
% 2.43/2.63 (c1_1(a618)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[876, 1573])).
% 2.43/2.63 tff(1577,plain,
% 2.43/2.63 (hskp45),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[994, 87, 1576, 957, 956, 1575, 1574, 976, 938])).
% 2.43/2.63 tff(1578,plain,
% 2.43/2.63 (~c0_1(a623)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[1002, 1577])).
% 2.43/2.63 tff(1579,plain,
% 2.43/2.63 (c3_1(a623)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[1010, 1577])).
% 2.43/2.63 tff(1580,plain,
% 2.43/2.63 (c2_1(a623)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[1018, 1577])).
% 2.43/2.63 tff(1581,plain,
% 2.43/2.63 (~hskp9),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[1053, 1580, 804, 803, 1579, 802, 1578])).
% 2.43/2.63 tff(1582,plain,
% 2.43/2.63 (hskp16),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[1062, 1581, 12])).
% 2.43/2.63 tff(1583,plain,
% 2.43/2.63 (~c3_1(a627)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[1068, 1582])).
% 2.43/2.63 tff(1584,plain,
% 2.43/2.63 (c2_1(a627)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[1076, 1582])).
% 2.43/2.63 tff(1585,plain,
% 2.43/2.63 (~c1_1(a627)),
% 2.43/2.63 inference(unit_resolution,[status(thm)],[1083, 87, 804, 803, 1579, 1580, 1584, 802, 1578, 1583, 953])).
% 2.43/2.63 tff(1586,plain,
% 2.43/2.63 (((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp56 | c2_1(a618) | c3_1(a618) | c2_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c1_1(a618)))) <=> ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp56 | c2_1(a618) | c3_1(a618) | c2_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c1_1(a618)))),
% 2.43/2.63 inference(rewrite,[status(thm)],[])).
% 2.43/2.63 tff(1587,plain,
% 2.43/2.63 ((hskp56 | (~ndr1_0) | c3_1(a618) | c2_1(a618) | (~c1_1(a618)) | c1_1(a625) | c2_1(a625) | (~c3_1(a625))) <=> (hskp56 | c2_1(a618) | c3_1(a618) | c2_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c1_1(a618)))),
% 2.43/2.63 inference(rewrite,[status(thm)],[])).
% 2.43/2.63 tff(1588,plain,
% 2.43/2.63 (((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp56 | (~ndr1_0) | c3_1(a618) | c2_1(a618) | (~c1_1(a618)) | c1_1(a625) | c2_1(a625) | (~c3_1(a625)))) <=> ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp56 | c2_1(a618) | c3_1(a618) | c2_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c1_1(a618))))),
% 2.43/2.64 inference(monotonicity,[status(thm)],[1587])).
% 2.43/2.64 tff(1589,plain,
% 2.43/2.64 (((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp56 | (~ndr1_0) | c3_1(a618) | c2_1(a618) | (~c1_1(a618)) | c1_1(a625) | c2_1(a625) | (~c3_1(a625)))) <=> ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp56 | c2_1(a618) | c3_1(a618) | c2_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c1_1(a618)))),
% 2.43/2.64 inference(transitivity,[status(thm)],[1588, 1586])).
% 2.43/2.64 tff(1590,plain,
% 2.43/2.64 ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp56 | (~ndr1_0) | c3_1(a618) | c2_1(a618) | (~c1_1(a618)) | c1_1(a625) | c2_1(a625) | (~c3_1(a625)))),
% 2.43/2.64 inference(quant_inst,[status(thm)],[])).
% 2.43/2.64 tff(1591,plain,
% 2.43/2.64 ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp56 | c2_1(a618) | c3_1(a618) | c2_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c1_1(a618))),
% 2.43/2.64 inference(modus_ponens,[status(thm)],[1590, 1589])).
% 2.43/2.64 tff(1592,plain,
% 2.43/2.64 (hskp56),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[1591, 87, 1576, 1575, 1574, 1536, 1526, 1240, 1534])).
% 2.43/2.64 tff(1593,plain,
% 2.43/2.64 (~c1_1(a658)),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[1253, 1592])).
% 2.43/2.64 tff(1594,plain,
% 2.43/2.64 (c2_1(a658)),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[1286, 1592])).
% 2.43/2.64 tff(1595,plain,
% 2.43/2.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a658) | c0_1(a623) | c2_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c0_1(a658)) | (~c2_1(a658)) | (~c2_1(a623)) | (~c3_1(a623)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a658) | c0_1(a623) | c2_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c0_1(a658)) | (~c2_1(a658)) | (~c2_1(a623)) | (~c3_1(a623)))),
% 2.43/2.64 inference(rewrite,[status(thm)],[])).
% 2.43/2.64 tff(1596,plain,
% 2.43/2.64 (((~ndr1_0) | c0_1(a623) | (~c3_1(a623)) | (~c2_1(a623)) | c1_1(a658) | (~c2_1(a658)) | (~c0_1(a658)) | c2_1(a625) | c1_1(a625) | (~c3_1(a625))) <=> (c1_1(a658) | c0_1(a623) | c2_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c0_1(a658)) | (~c2_1(a658)) | (~c2_1(a623)) | (~c3_1(a623)))),
% 2.43/2.64 inference(rewrite,[status(thm)],[])).
% 2.43/2.64 tff(1597,plain,
% 2.43/2.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a623) | (~c3_1(a623)) | (~c2_1(a623)) | c1_1(a658) | (~c2_1(a658)) | (~c0_1(a658)) | c2_1(a625) | c1_1(a625) | (~c3_1(a625)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a658) | c0_1(a623) | c2_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c0_1(a658)) | (~c2_1(a658)) | (~c2_1(a623)) | (~c3_1(a623))))),
% 2.43/2.64 inference(monotonicity,[status(thm)],[1596])).
% 2.43/2.64 tff(1598,plain,
% 2.43/2.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a623) | (~c3_1(a623)) | (~c2_1(a623)) | c1_1(a658) | (~c2_1(a658)) | (~c0_1(a658)) | c2_1(a625) | c1_1(a625) | (~c3_1(a625)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a658) | c0_1(a623) | c2_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c0_1(a658)) | (~c2_1(a658)) | (~c2_1(a623)) | (~c3_1(a623)))),
% 2.43/2.64 inference(transitivity,[status(thm)],[1597, 1595])).
% 2.43/2.64 tff(1599,plain,
% 2.43/2.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a623) | (~c3_1(a623)) | (~c2_1(a623)) | c1_1(a658) | (~c2_1(a658)) | (~c0_1(a658)) | c2_1(a625) | c1_1(a625) | (~c3_1(a625)))),
% 2.43/2.64 inference(quant_inst,[status(thm)],[])).
% 2.43/2.64 tff(1600,plain,
% 2.43/2.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a658) | c0_1(a623) | c2_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c0_1(a658)) | (~c2_1(a658)) | (~c2_1(a623)) | (~c3_1(a623))),
% 2.43/2.64 inference(modus_ponens,[status(thm)],[1599, 1598])).
% 2.43/2.64 tff(1601,plain,
% 2.43/2.64 (~c0_1(a658)),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[1600, 87, 1594, 1579, 1580, 1593, 1578, 1536, 1526, 645, 1534])).
% 2.43/2.64 tff(1602,plain,
% 2.43/2.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a658) | c3_1(a627) | c2_1(a625) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | c0_1(a658) | (~c2_1(a658)) | (~c2_1(a627)) | c1_1(a627))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a658) | c3_1(a627) | c2_1(a625) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | c0_1(a658) | (~c2_1(a658)) | (~c2_1(a627)) | c1_1(a627))),
% 2.43/2.64 inference(rewrite,[status(thm)],[])).
% 2.43/2.64 tff(1603,plain,
% 2.43/2.64 (((~ndr1_0) | c3_1(a627) | c1_1(a627) | (~c2_1(a627)) | c1_1(a658) | c0_1(a658) | (~c2_1(a658)) | c2_1(a625) | c1_1(a625) | c0_1(a625)) <=> (c1_1(a658) | c3_1(a627) | c2_1(a625) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | c0_1(a658) | (~c2_1(a658)) | (~c2_1(a627)) | c1_1(a627))),
% 2.43/2.64 inference(rewrite,[status(thm)],[])).
% 2.43/2.64 tff(1604,plain,
% 2.43/2.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a627) | c1_1(a627) | (~c2_1(a627)) | c1_1(a658) | c0_1(a658) | (~c2_1(a658)) | c2_1(a625) | c1_1(a625) | c0_1(a625))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a658) | c3_1(a627) | c2_1(a625) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | c0_1(a658) | (~c2_1(a658)) | (~c2_1(a627)) | c1_1(a627)))),
% 2.43/2.64 inference(monotonicity,[status(thm)],[1603])).
% 2.43/2.64 tff(1605,plain,
% 2.43/2.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a627) | c1_1(a627) | (~c2_1(a627)) | c1_1(a658) | c0_1(a658) | (~c2_1(a658)) | c2_1(a625) | c1_1(a625) | c0_1(a625))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a658) | c3_1(a627) | c2_1(a625) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | c0_1(a658) | (~c2_1(a658)) | (~c2_1(a627)) | c1_1(a627))),
% 2.43/2.64 inference(transitivity,[status(thm)],[1604, 1602])).
% 2.43/2.64 tff(1606,plain,
% 2.43/2.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a627) | c1_1(a627) | (~c2_1(a627)) | c1_1(a658) | c0_1(a658) | (~c2_1(a658)) | c2_1(a625) | c1_1(a625) | c0_1(a625))),
% 2.43/2.64 inference(quant_inst,[status(thm)],[])).
% 2.43/2.64 tff(1607,plain,
% 2.43/2.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a658) | c3_1(a627) | c2_1(a625) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | c0_1(a658) | (~c2_1(a658)) | (~c2_1(a627)) | c1_1(a627)),
% 2.43/2.64 inference(modus_ponens,[status(thm)],[1606, 1605])).
% 2.43/2.64 tff(1608,plain,
% 2.43/2.64 ($false),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[1607, 87, 1594, 1584, 1593, 1583, 1536, 1526, 1525, 1279, 1601, 1585])).
% 2.43/2.64 tff(1609,plain,(c0_1(a617) | c2_1(a625) | c1_1(a625) | c0_1(a625) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a648) | hskp17), inference(lemma,lemma(discharge,[]))).
% 2.43/2.64 tff(1610,plain,
% 2.43/2.64 (c0_1(a617)),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[1609, 1524, 1523, 1522, 801, 793, 785, 12])).
% 2.43/2.64 tff(1611,plain,
% 2.43/2.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a648) | c1_1(a617) | c2_1(a625) | c0_1(a625) | (~ndr1_0) | c3_1(a625) | (~c3_1(a617)) | (~c0_1(a617)) | (~c0_1(a648)) | (~c3_1(a648)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a648) | c1_1(a617) | c2_1(a625) | c0_1(a625) | (~ndr1_0) | c3_1(a625) | (~c3_1(a617)) | (~c0_1(a617)) | (~c0_1(a648)) | (~c3_1(a648)))),
% 2.43/2.64 inference(rewrite,[status(thm)],[])).
% 2.43/2.64 tff(1612,plain,
% 2.43/2.64 (((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c0_1(a617)) | c2_1(a648) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a625) | c0_1(a625) | c3_1(a625)) <=> (c2_1(a648) | c1_1(a617) | c2_1(a625) | c0_1(a625) | (~ndr1_0) | c3_1(a625) | (~c3_1(a617)) | (~c0_1(a617)) | (~c0_1(a648)) | (~c3_1(a648)))),
% 2.43/2.64 inference(rewrite,[status(thm)],[])).
% 2.43/2.64 tff(1613,plain,
% 2.43/2.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c0_1(a617)) | c2_1(a648) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a625) | c0_1(a625) | c3_1(a625))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a648) | c1_1(a617) | c2_1(a625) | c0_1(a625) | (~ndr1_0) | c3_1(a625) | (~c3_1(a617)) | (~c0_1(a617)) | (~c0_1(a648)) | (~c3_1(a648))))),
% 2.43/2.64 inference(monotonicity,[status(thm)],[1612])).
% 2.43/2.64 tff(1614,plain,
% 2.43/2.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c0_1(a617)) | c2_1(a648) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a625) | c0_1(a625) | c3_1(a625))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a648) | c1_1(a617) | c2_1(a625) | c0_1(a625) | (~ndr1_0) | c3_1(a625) | (~c3_1(a617)) | (~c0_1(a617)) | (~c0_1(a648)) | (~c3_1(a648)))),
% 2.43/2.64 inference(transitivity,[status(thm)],[1613, 1611])).
% 2.43/2.64 tff(1615,plain,
% 2.43/2.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c0_1(a617)) | c2_1(a648) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a625) | c0_1(a625) | c3_1(a625))),
% 2.43/2.64 inference(quant_inst,[status(thm)],[])).
% 2.43/2.64 tff(1616,plain,
% 2.43/2.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a648) | c1_1(a617) | c2_1(a625) | c0_1(a625) | (~ndr1_0) | c3_1(a625) | (~c3_1(a617)) | (~c0_1(a617)) | (~c0_1(a648)) | (~c3_1(a648))),
% 2.43/2.64 inference(modus_ponens,[status(thm)],[1615, 1614])).
% 2.43/2.64 tff(1617,plain,
% 2.43/2.64 (c3_1(a625) | (~c0_1(a617))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[1616, 87, 801, 793, 927, 785, 1346, 1524, 1522, 910])).
% 2.43/2.64 tff(1618,plain,
% 2.43/2.64 (c3_1(a625)),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[1617, 1610])).
% 2.43/2.64 tff(1619,assumption,(c3_1(a625)), introduced(assumption)).
% 2.43/2.64 tff(1620,plain,
% 2.43/2.64 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a648) | c2_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c0_1(a648)) | (~c1_1(a648)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a648) | c2_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c0_1(a648)) | (~c1_1(a648)))),
% 2.43/2.64 inference(rewrite,[status(thm)],[])).
% 2.43/2.64 tff(1621,plain,
% 2.43/2.64 ((hskp5 | (~ndr1_0) | c1_1(a625) | c2_1(a625) | (~c3_1(a625)) | c2_1(a648) | (~c1_1(a648)) | (~c0_1(a648))) <=> (hskp5 | c2_1(a648) | c2_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c0_1(a648)) | (~c1_1(a648)))),
% 2.43/2.64 inference(rewrite,[status(thm)],[])).
% 2.43/2.64 tff(1622,plain,
% 2.43/2.64 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a625) | c2_1(a625) | (~c3_1(a625)) | c2_1(a648) | (~c1_1(a648)) | (~c0_1(a648)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a648) | c2_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c0_1(a648)) | (~c1_1(a648))))),
% 2.43/2.64 inference(monotonicity,[status(thm)],[1621])).
% 2.43/2.64 tff(1623,plain,
% 2.43/2.64 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a625) | c2_1(a625) | (~c3_1(a625)) | c2_1(a648) | (~c1_1(a648)) | (~c0_1(a648)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a648) | c2_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c0_1(a648)) | (~c1_1(a648)))),
% 2.43/2.64 inference(transitivity,[status(thm)],[1622, 1620])).
% 2.43/2.64 tff(1624,plain,
% 2.43/2.64 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a625) | c2_1(a625) | (~c3_1(a625)) | c2_1(a648) | (~c1_1(a648)) | (~c0_1(a648)))),
% 2.43/2.64 inference(quant_inst,[status(thm)],[])).
% 2.43/2.64 tff(1625,plain,
% 2.43/2.64 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a648) | c2_1(a625) | c1_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c0_1(a648)) | (~c1_1(a648))),
% 2.43/2.64 inference(modus_ponens,[status(thm)],[1624, 1623])).
% 2.43/2.64 tff(1626,plain,
% 2.43/2.64 (hskp5 | (~c3_1(a625)) | (~c1_1(a648))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[1625, 87, 803, 802, 1536, 1526, 507])).
% 2.43/2.64 tff(1627,plain,
% 2.43/2.64 (~c1_1(a648)),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[1626, 523, 1619])).
% 2.43/2.64 tff(1628,plain,
% 2.43/2.64 (hskp37 | hskp5 | (~c0_1(a617))),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[529, 87, 957, 956, 521])).
% 2.43/2.64 tff(1629,plain,
% 2.43/2.64 (hskp37),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[1628, 523, 635])).
% 2.43/2.64 tff(1630,plain,
% 2.43/2.64 (~c2_1(a607)),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[386, 1629])).
% 2.43/2.64 tff(1631,plain,
% 2.43/2.64 (c0_1(a607)),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[394, 1629])).
% 2.43/2.64 tff(1632,plain,
% 2.43/2.64 (c1_1(a607)),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[402, 1629])).
% 2.43/2.64 tff(1633,plain,
% 2.43/2.64 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a648) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c1_1(a607)) | (~c3_1(a648)) | c1_1(a648))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a648) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c1_1(a607)) | (~c3_1(a648)) | c1_1(a648))),
% 2.43/2.64 inference(rewrite,[status(thm)],[])).
% 2.43/2.64 tff(1634,plain,
% 2.43/2.64 ((hskp5 | (~ndr1_0) | c1_1(a648) | c2_1(a648) | (~c3_1(a648)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607))) <=> (hskp5 | c2_1(a648) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c1_1(a607)) | (~c3_1(a648)) | c1_1(a648))),
% 2.43/2.64 inference(rewrite,[status(thm)],[])).
% 2.43/2.64 tff(1635,plain,
% 2.43/2.64 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a648) | c2_1(a648) | (~c3_1(a648)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a648) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c1_1(a607)) | (~c3_1(a648)) | c1_1(a648)))),
% 2.43/2.64 inference(monotonicity,[status(thm)],[1634])).
% 2.43/2.64 tff(1636,plain,
% 2.43/2.64 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a648) | c2_1(a648) | (~c3_1(a648)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a648) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c1_1(a607)) | (~c3_1(a648)) | c1_1(a648))),
% 2.43/2.64 inference(transitivity,[status(thm)],[1635, 1633])).
% 2.43/2.64 tff(1637,plain,
% 2.43/2.64 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a648) | c2_1(a648) | (~c3_1(a648)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))),
% 2.43/2.64 inference(quant_inst,[status(thm)],[])).
% 2.43/2.64 tff(1638,plain,
% 2.43/2.64 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a648) | c2_1(a607) | (~ndr1_0) | (~c0_1(a607)) | (~c1_1(a607)) | (~c3_1(a648)) | c1_1(a648)),
% 2.43/2.64 inference(modus_ponens,[status(thm)],[1637, 1636])).
% 2.43/2.64 tff(1639,plain,
% 2.43/2.64 ($false),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[1638, 87, 523, 804, 1632, 1631, 802, 1630, 507, 1627])).
% 2.43/2.64 tff(1640,plain,(hskp5 | (~c3_1(a648)) | c2_1(a648) | (~c3_1(a625)) | (~c0_1(a648)) | c2_1(a625) | c1_1(a625) | (~c0_1(a617))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.64 tff(1641,plain,
% 2.43/2.64 (hskp5),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[1640, 801, 785, 1618, 793, 1524, 1523, 1610])).
% 2.43/2.64 tff(1642,plain,
% 2.43/2.64 (~c3_1(a606)),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[574, 1641])).
% 2.43/2.64 tff(1643,plain,
% 2.43/2.64 (~c0_1(a606)),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[580, 1641])).
% 2.43/2.64 tff(1644,plain,
% 2.43/2.64 (c2_1(a606)),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[588, 1641])).
% 2.43/2.64 tff(1645,plain,
% 2.43/2.64 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (c0_1(a606) | c3_1(a606) | (~ndr1_0) | (~c2_1(a606)) | (~c1_1(a606)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | c0_1(a606) | c3_1(a606) | (~ndr1_0) | (~c2_1(a606)) | (~c1_1(a606)))),
% 2.43/2.64 inference(rewrite,[status(thm)],[])).
% 2.43/2.64 tff(1646,plain,
% 2.43/2.64 (((~ndr1_0) | c3_1(a606) | c0_1(a606) | (~c2_1(a606)) | c0_1(a606) | (~c2_1(a606)) | (~c1_1(a606))) <=> (c0_1(a606) | c3_1(a606) | (~ndr1_0) | (~c2_1(a606)) | (~c1_1(a606)))),
% 2.43/2.64 inference(rewrite,[status(thm)],[])).
% 2.43/2.64 tff(1647,plain,
% 2.43/2.64 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c3_1(a606) | c0_1(a606) | (~c2_1(a606)) | c0_1(a606) | (~c2_1(a606)) | (~c1_1(a606)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (c0_1(a606) | c3_1(a606) | (~ndr1_0) | (~c2_1(a606)) | (~c1_1(a606))))),
% 2.43/2.64 inference(monotonicity,[status(thm)],[1646])).
% 2.43/2.64 tff(1648,plain,
% 2.43/2.64 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c3_1(a606) | c0_1(a606) | (~c2_1(a606)) | c0_1(a606) | (~c2_1(a606)) | (~c1_1(a606)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | c0_1(a606) | c3_1(a606) | (~ndr1_0) | (~c2_1(a606)) | (~c1_1(a606)))),
% 2.43/2.64 inference(transitivity,[status(thm)],[1647, 1645])).
% 2.43/2.64 tff(1649,plain,
% 2.43/2.64 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c3_1(a606) | c0_1(a606) | (~c2_1(a606)) | c0_1(a606) | (~c2_1(a606)) | (~c1_1(a606)))),
% 2.43/2.64 inference(quant_inst,[status(thm)],[])).
% 2.43/2.64 tff(1650,plain,
% 2.43/2.64 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | c0_1(a606) | c3_1(a606) | (~ndr1_0) | (~c2_1(a606)) | (~c1_1(a606))),
% 2.43/2.64 inference(modus_ponens,[status(thm)],[1649, 1648])).
% 2.43/2.64 tff(1651,plain,
% 2.43/2.64 (~c1_1(a606)),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[1650, 87, 1644, 1643, 1642, 23])).
% 2.43/2.64 tff(1652,plain,
% 2.43/2.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a617) | c1_1(a625) | c0_1(a625) | c0_1(a606) | c3_1(a606) | (~ndr1_0) | c1_1(a606) | (~c3_1(a625)) | (~c2_1(a617)) | (~c3_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a617) | c1_1(a625) | c0_1(a625) | c0_1(a606) | c3_1(a606) | (~ndr1_0) | c1_1(a606) | (~c3_1(a625)) | (~c2_1(a617)) | (~c3_1(a617)))),
% 2.43/2.64 inference(rewrite,[status(thm)],[])).
% 2.43/2.64 tff(1653,plain,
% 2.43/2.64 (((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a625) | c0_1(a625) | (~c3_1(a625)) | c1_1(a606) | c0_1(a606) | c3_1(a606)) <=> (c1_1(a617) | c1_1(a625) | c0_1(a625) | c0_1(a606) | c3_1(a606) | (~ndr1_0) | c1_1(a606) | (~c3_1(a625)) | (~c2_1(a617)) | (~c3_1(a617)))),
% 2.43/2.64 inference(rewrite,[status(thm)],[])).
% 2.43/2.64 tff(1654,plain,
% 2.43/2.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a625) | c0_1(a625) | (~c3_1(a625)) | c1_1(a606) | c0_1(a606) | c3_1(a606))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a617) | c1_1(a625) | c0_1(a625) | c0_1(a606) | c3_1(a606) | (~ndr1_0) | c1_1(a606) | (~c3_1(a625)) | (~c2_1(a617)) | (~c3_1(a617))))),
% 2.43/2.64 inference(monotonicity,[status(thm)],[1653])).
% 2.43/2.64 tff(1655,plain,
% 2.43/2.64 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a625) | c0_1(a625) | (~c3_1(a625)) | c1_1(a606) | c0_1(a606) | c3_1(a606))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a617) | c1_1(a625) | c0_1(a625) | c0_1(a606) | c3_1(a606) | (~ndr1_0) | c1_1(a606) | (~c3_1(a625)) | (~c2_1(a617)) | (~c3_1(a617)))),
% 2.43/2.64 inference(transitivity,[status(thm)],[1654, 1652])).
% 2.43/2.64 tff(1656,plain,
% 2.43/2.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a625) | c0_1(a625) | (~c3_1(a625)) | c1_1(a606) | c0_1(a606) | c3_1(a606))),
% 2.43/2.64 inference(quant_inst,[status(thm)],[])).
% 2.43/2.64 tff(1657,plain,
% 2.43/2.64 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a617) | c1_1(a625) | c0_1(a625) | c0_1(a606) | c3_1(a606) | (~ndr1_0) | c1_1(a606) | (~c3_1(a625)) | (~c2_1(a617)) | (~c3_1(a617))),
% 2.43/2.64 inference(modus_ponens,[status(thm)],[1656, 1655])).
% 2.43/2.64 tff(1658,plain,
% 2.43/2.64 ($false),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[1657, 87, 926, 927, 1346, 1523, 1522, 1643, 1642, 1113, 1618, 1651])).
% 2.43/2.64 tff(1659,plain,(hskp64 | hskp17), inference(lemma,lemma(discharge,[]))).
% 2.43/2.64 tff(1660,plain,
% 2.43/2.64 (hskp64),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[1659, 12])).
% 2.43/2.64 tff(1661,plain,
% 2.43/2.64 (((~hskp64) | c3_1(a673)) <=> ((~hskp64) | c3_1(a673))),
% 2.43/2.64 inference(rewrite,[status(thm)],[])).
% 2.43/2.64 tff(1662,axiom,((~hskp64) | c3_1(a673)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause80')).
% 2.43/2.64 tff(1663,plain,
% 2.43/2.64 ((~hskp64) | c3_1(a673)),
% 2.43/2.64 inference(modus_ponens,[status(thm)],[1662, 1661])).
% 2.43/2.64 tff(1664,plain,
% 2.43/2.64 ((~hskp64) | c3_1(a673)),
% 2.43/2.64 inference(modus_ponens,[status(thm)],[1663, 1661])).
% 2.43/2.64 tff(1665,plain,
% 2.43/2.64 ((~hskp64) | c3_1(a673)),
% 2.43/2.64 inference(modus_ponens,[status(thm)],[1664, 1661])).
% 2.43/2.64 tff(1666,plain,
% 2.43/2.64 ((~hskp64) | c3_1(a673)),
% 2.43/2.64 inference(modus_ponens,[status(thm)],[1665, 1661])).
% 2.43/2.64 tff(1667,plain,
% 2.43/2.64 ((~hskp64) | c3_1(a673)),
% 2.43/2.64 inference(modus_ponens,[status(thm)],[1666, 1661])).
% 2.43/2.64 tff(1668,plain,
% 2.43/2.64 (c3_1(a673)),
% 2.43/2.64 inference(unit_resolution,[status(thm)],[1667, 1660])).
% 2.43/2.64 tff(1669,plain,
% 2.43/2.64 (^[V: $i, U: $i] : refl((hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))),
% 2.43/2.64 inference(bind,[status(th)],[])).
% 2.43/2.64 tff(1670,plain,
% 2.43/2.64 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 2.43/2.64 inference(quant_intro,[status(thm)],[1669])).
% 2.43/2.64 tff(1671,plain,
% 2.43/2.64 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 2.43/2.64 inference(rewrite,[status(thm)],[])).
% 2.43/2.64 tff(1672,plain,
% 2.43/2.64 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~c0_1(U))) <=> ((~c0_1(U)) | (~c2_1(U)))), ((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> (((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)))), ((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))))), (((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)))), (((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V))))), ((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V)))), ((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V))))), (((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V)))), (((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V))))), ((((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c2_1(V) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | c0_1(V)) | hskp16) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp16))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp16) <=> (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | c0_1(V)) | hskp16) <=> (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))))),
% 2.43/2.64 inference(bind,[status(th)],[])).
% 2.43/2.64 tff(1673,plain,
% 2.43/2.64 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | c0_1(V)) | hskp16) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 2.43/2.64 inference(quant_intro,[status(thm)],[1672])).
% 2.43/2.64 tff(1674,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~c0_1(U))) | (~ndr1_0)) | (~c3_1(V))) | c3_1(U)) | c2_1(V)) | c0_1(V)) | hskp16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause310')).
% 2.43/2.64 tff(1675,plain,
% 2.43/2.64 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 2.43/2.64 inference(modus_ponens,[status(thm)],[1674, 1673])).
% 2.43/2.64 tff(1676,plain,
% 2.43/2.64 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 2.43/2.64 inference(modus_ponens,[status(thm)],[1675, 1671])).
% 2.43/2.64 tff(1677,plain,(
% 2.43/2.64 ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 2.43/2.64 inference(skolemize,[status(sab)],[1676])).
% 2.43/2.64 tff(1678,plain,
% 2.43/2.64 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 2.43/2.64 inference(modus_ponens,[status(thm)],[1677, 1670])).
% 2.43/2.64 tff(1679,plain,
% 2.43/2.64 (^[V: $i, U: $i] : refl((hskp51 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | c0_1(V)) <=> (hskp51 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | c0_1(V)))),
% 2.43/2.64 inference(bind,[status(th)],[])).
% 2.43/2.64 tff(1680,plain,
% 2.43/2.64 (![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))),
% 2.43/2.64 inference(quant_intro,[status(thm)],[1679])).
% 2.43/2.64 tff(1681,plain,
% 2.43/2.64 (![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))),
% 2.43/2.64 inference(rewrite,[status(thm)],[])).
% 2.43/2.64 tff(1682,plain,
% 2.43/2.64 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | c1_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U))) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c1_1(V)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V)) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c1_1(V)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c1_1(V)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c1_1(V)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | c0_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c1_1(V)) | c0_1(V)) | c3_1(V)) | hskp51) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | c0_1(V)) | hskp51))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | c0_1(V)) | hskp51) <=> (hskp51 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c1_1(V)) | c0_1(V)) | c3_1(V)) | hskp51) <=> (hskp51 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))))),
% 2.43/2.64 inference(bind,[status(th)],[])).
% 2.43/2.64 tff(1683,plain,
% 2.43/2.64 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c1_1(V)) | c0_1(V)) | c3_1(V)) | hskp51) <=> ![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))),
% 2.43/2.64 inference(quant_intro,[status(thm)],[1682])).
% 2.43/2.64 tff(1684,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c0_1(U)) | c1_1(V)) | c0_1(V)) | c3_1(V)) | hskp51)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause304')).
% 2.43/2.65 tff(1685,plain,
% 2.43/2.65 (![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))),
% 2.43/2.65 inference(modus_ponens,[status(thm)],[1684, 1683])).
% 2.43/2.65 tff(1686,plain,
% 2.43/2.65 (![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))),
% 2.43/2.65 inference(modus_ponens,[status(thm)],[1685, 1681])).
% 2.43/2.65 tff(1687,plain,(
% 2.43/2.65 ![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))),
% 2.43/2.65 inference(skolemize,[status(sab)],[1686])).
% 2.43/2.65 tff(1688,plain,
% 2.43/2.65 (![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))),
% 2.43/2.65 inference(modus_ponens,[status(thm)],[1687, 1680])).
% 2.43/2.65 tff(1689,plain,
% 2.43/2.65 (((~hskp64) | (~c0_1(a673))) <=> ((~hskp64) | (~c0_1(a673)))),
% 2.43/2.65 inference(rewrite,[status(thm)],[])).
% 2.43/2.65 tff(1690,plain,
% 2.43/2.65 (((~c0_1(a673)) | (~hskp64)) <=> ((~hskp64) | (~c0_1(a673)))),
% 2.43/2.65 inference(rewrite,[status(thm)],[])).
% 2.43/2.65 tff(1691,axiom,((~c0_1(a673)) | (~hskp64)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause173')).
% 2.43/2.65 tff(1692,plain,
% 2.43/2.65 ((~hskp64) | (~c0_1(a673))),
% 2.43/2.65 inference(modus_ponens,[status(thm)],[1691, 1690])).
% 2.43/2.65 tff(1693,plain,
% 2.43/2.65 ((~hskp64) | (~c0_1(a673))),
% 2.43/2.65 inference(modus_ponens,[status(thm)],[1692, 1689])).
% 2.43/2.65 tff(1694,plain,
% 2.43/2.65 (~c0_1(a673)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[1693, 1660])).
% 2.43/2.65 tff(1695,plain,
% 2.43/2.65 (((~hskp64) | c1_1(a673)) <=> ((~hskp64) | c1_1(a673))),
% 2.43/2.65 inference(rewrite,[status(thm)],[])).
% 2.43/2.65 tff(1696,axiom,((~hskp64) | c1_1(a673)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause81')).
% 2.43/2.65 tff(1697,plain,
% 2.43/2.65 ((~hskp64) | c1_1(a673)),
% 2.43/2.65 inference(modus_ponens,[status(thm)],[1696, 1695])).
% 2.43/2.65 tff(1698,plain,
% 2.43/2.65 ((~hskp64) | c1_1(a673)),
% 2.43/2.65 inference(modus_ponens,[status(thm)],[1697, 1695])).
% 2.43/2.65 tff(1699,plain,
% 2.43/2.65 ((~hskp64) | c1_1(a673)),
% 2.43/2.65 inference(modus_ponens,[status(thm)],[1698, 1695])).
% 2.43/2.65 tff(1700,plain,
% 2.43/2.65 ((~hskp64) | c1_1(a673)),
% 2.43/2.65 inference(modus_ponens,[status(thm)],[1699, 1695])).
% 2.43/2.65 tff(1701,plain,
% 2.43/2.65 ((~hskp64) | c1_1(a673)),
% 2.43/2.65 inference(modus_ponens,[status(thm)],[1700, 1695])).
% 2.43/2.65 tff(1702,plain,
% 2.43/2.65 (c1_1(a673)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[1701, 1660])).
% 2.43/2.65 tff(1703,plain,
% 2.43/2.65 (((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | (hskp51 | c0_1(a673) | c1_1(a660) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | (~c3_1(a673)) | (~c1_1(a673)))) <=> ((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | hskp51 | c0_1(a673) | c1_1(a660) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | (~c3_1(a673)) | (~c1_1(a673)))),
% 2.43/2.65 inference(rewrite,[status(thm)],[])).
% 2.43/2.65 tff(1704,plain,
% 2.43/2.65 ((hskp51 | (~ndr1_0) | c0_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c1_1(a660) | c3_1(a660) | c0_1(a660)) <=> (hskp51 | c0_1(a673) | c1_1(a660) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | (~c3_1(a673)) | (~c1_1(a673)))),
% 2.43/2.65 inference(rewrite,[status(thm)],[])).
% 2.43/2.65 tff(1705,plain,
% 2.43/2.65 (((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | (hskp51 | (~ndr1_0) | c0_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c1_1(a660) | c3_1(a660) | c0_1(a660))) <=> ((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | (hskp51 | c0_1(a673) | c1_1(a660) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | (~c3_1(a673)) | (~c1_1(a673))))),
% 2.43/2.65 inference(monotonicity,[status(thm)],[1704])).
% 2.43/2.65 tff(1706,plain,
% 2.43/2.65 (((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | (hskp51 | (~ndr1_0) | c0_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c1_1(a660) | c3_1(a660) | c0_1(a660))) <=> ((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | hskp51 | c0_1(a673) | c1_1(a660) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | (~c3_1(a673)) | (~c1_1(a673)))),
% 2.43/2.65 inference(transitivity,[status(thm)],[1705, 1703])).
% 2.43/2.65 tff(1707,plain,
% 2.43/2.65 ((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | (hskp51 | (~ndr1_0) | c0_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c1_1(a660) | c3_1(a660) | c0_1(a660))),
% 2.43/2.65 inference(quant_inst,[status(thm)],[])).
% 2.43/2.65 tff(1708,plain,
% 2.43/2.65 ((~![V: $i, U: $i] : (hskp51 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | hskp51 | c0_1(a673) | c1_1(a660) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | (~c3_1(a673)) | (~c1_1(a673))),
% 2.43/2.65 inference(modus_ponens,[status(thm)],[1707, 1706])).
% 2.43/2.65 tff(1709,plain,
% 2.43/2.65 (hskp51),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[1708, 87, 1668, 1702, 1694, 1365, 1359, 1353, 1688])).
% 2.43/2.65 tff(1710,plain,
% 2.43/2.65 (((~hskp51) | (~c3_1(a644))) <=> ((~hskp51) | (~c3_1(a644)))),
% 2.43/2.65 inference(rewrite,[status(thm)],[])).
% 2.43/2.65 tff(1711,plain,
% 2.43/2.65 (((~c3_1(a644)) | (~hskp51)) <=> ((~hskp51) | (~c3_1(a644)))),
% 2.43/2.65 inference(rewrite,[status(thm)],[])).
% 2.43/2.65 tff(1712,axiom,((~c3_1(a644)) | (~hskp51)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause190')).
% 2.43/2.65 tff(1713,plain,
% 2.43/2.65 ((~hskp51) | (~c3_1(a644))),
% 2.43/2.65 inference(modus_ponens,[status(thm)],[1712, 1711])).
% 2.43/2.65 tff(1714,plain,
% 2.43/2.65 ((~hskp51) | (~c3_1(a644))),
% 2.43/2.65 inference(modus_ponens,[status(thm)],[1713, 1710])).
% 2.43/2.65 tff(1715,plain,
% 2.43/2.65 (~c3_1(a644)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[1714, 1709])).
% 2.43/2.65 tff(1716,plain,
% 2.43/2.65 (((~hskp51) | c0_1(a644)) <=> ((~hskp51) | c0_1(a644))),
% 2.43/2.65 inference(rewrite,[status(thm)],[])).
% 2.43/2.65 tff(1717,axiom,((~hskp51) | c0_1(a644)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause103')).
% 2.43/2.65 tff(1718,plain,
% 2.43/2.65 ((~hskp51) | c0_1(a644)),
% 2.43/2.65 inference(modus_ponens,[status(thm)],[1717, 1716])).
% 2.43/2.65 tff(1719,plain,
% 2.43/2.65 ((~hskp51) | c0_1(a644)),
% 2.43/2.65 inference(modus_ponens,[status(thm)],[1718, 1716])).
% 2.43/2.65 tff(1720,plain,
% 2.43/2.65 ((~hskp51) | c0_1(a644)),
% 2.43/2.65 inference(modus_ponens,[status(thm)],[1719, 1716])).
% 2.43/2.65 tff(1721,plain,
% 2.43/2.65 ((~hskp51) | c0_1(a644)),
% 2.43/2.65 inference(modus_ponens,[status(thm)],[1720, 1716])).
% 2.43/2.65 tff(1722,plain,
% 2.43/2.65 ((~hskp51) | c0_1(a644)),
% 2.43/2.65 inference(modus_ponens,[status(thm)],[1721, 1716])).
% 2.43/2.65 tff(1723,plain,
% 2.43/2.65 (c0_1(a644)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[1722, 1709])).
% 2.43/2.65 tff(1724,plain,
% 2.43/2.65 (((~hskp51) | c2_1(a644)) <=> ((~hskp51) | c2_1(a644))),
% 2.43/2.65 inference(rewrite,[status(thm)],[])).
% 2.43/2.65 tff(1725,axiom,((~hskp51) | c2_1(a644)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause102')).
% 2.43/2.65 tff(1726,plain,
% 2.43/2.65 ((~hskp51) | c2_1(a644)),
% 2.43/2.65 inference(modus_ponens,[status(thm)],[1725, 1724])).
% 2.43/2.65 tff(1727,plain,
% 2.43/2.65 ((~hskp51) | c2_1(a644)),
% 2.43/2.65 inference(modus_ponens,[status(thm)],[1726, 1724])).
% 2.43/2.65 tff(1728,plain,
% 2.43/2.65 ((~hskp51) | c2_1(a644)),
% 2.43/2.65 inference(modus_ponens,[status(thm)],[1727, 1724])).
% 2.43/2.65 tff(1729,plain,
% 2.43/2.65 ((~hskp51) | c2_1(a644)),
% 2.43/2.65 inference(modus_ponens,[status(thm)],[1728, 1724])).
% 2.43/2.65 tff(1730,plain,
% 2.43/2.65 ((~hskp51) | c2_1(a644)),
% 2.43/2.65 inference(modus_ponens,[status(thm)],[1729, 1724])).
% 2.43/2.65 tff(1731,plain,
% 2.43/2.65 (c2_1(a644)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[1730, 1709])).
% 2.43/2.65 tff(1732,plain,
% 2.43/2.65 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp16 | c0_1(a673) | c3_1(a644) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c2_1(a644)) | (~c0_1(a644)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp16 | c0_1(a673) | c3_1(a644) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c2_1(a644)) | (~c0_1(a644)))),
% 2.43/2.65 inference(rewrite,[status(thm)],[])).
% 2.43/2.65 tff(1733,plain,
% 2.43/2.65 ((hskp16 | (~ndr1_0) | c3_1(a644) | (~c0_1(a644)) | (~c2_1(a644)) | c0_1(a673) | c2_1(a673) | (~c3_1(a673))) <=> (hskp16 | c0_1(a673) | c3_1(a644) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c2_1(a644)) | (~c0_1(a644)))),
% 2.43/2.65 inference(rewrite,[status(thm)],[])).
% 2.43/2.65 tff(1734,plain,
% 2.43/2.65 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a644) | (~c0_1(a644)) | (~c2_1(a644)) | c0_1(a673) | c2_1(a673) | (~c3_1(a673)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp16 | c0_1(a673) | c3_1(a644) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c2_1(a644)) | (~c0_1(a644))))),
% 2.43/2.65 inference(monotonicity,[status(thm)],[1733])).
% 2.43/2.65 tff(1735,plain,
% 2.43/2.65 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a644) | (~c0_1(a644)) | (~c2_1(a644)) | c0_1(a673) | c2_1(a673) | (~c3_1(a673)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp16 | c0_1(a673) | c3_1(a644) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c2_1(a644)) | (~c0_1(a644)))),
% 2.43/2.65 inference(transitivity,[status(thm)],[1734, 1732])).
% 2.43/2.65 tff(1736,plain,
% 2.43/2.65 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a644) | (~c0_1(a644)) | (~c2_1(a644)) | c0_1(a673) | c2_1(a673) | (~c3_1(a673)))),
% 2.43/2.65 inference(quant_inst,[status(thm)],[])).
% 2.43/2.65 tff(1737,plain,
% 2.43/2.65 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp16 | c0_1(a673) | c3_1(a644) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c2_1(a644)) | (~c0_1(a644))),
% 2.43/2.65 inference(modus_ponens,[status(thm)],[1736, 1735])).
% 2.43/2.65 tff(1738,plain,
% 2.43/2.65 (hskp16),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[1737, 87, 1668, 1731, 1723, 1694, 1715, 1678, 13])).
% 2.43/2.65 tff(1739,assumption,(hskp53), introduced(assumption)).
% 2.43/2.65 tff(1740,plain,
% 2.43/2.65 (~c2_1(a648)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[784, 1739])).
% 2.43/2.65 tff(1741,plain,
% 2.43/2.65 (c3_1(a648)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[800, 1739])).
% 2.43/2.65 tff(1742,plain,
% 2.43/2.65 (c0_1(a648)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[792, 1739])).
% 2.43/2.65 tff(1743,plain,
% 2.43/2.65 ($false),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[924, 1742, 1741, 97, 1740])).
% 2.43/2.65 tff(1744,plain,((~hskp53) | hskp41), inference(lemma,lemma(discharge,[]))).
% 2.43/2.65 tff(1745,plain,
% 2.43/2.65 (~hskp53),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[1744, 97])).
% 2.43/2.65 tff(1746,plain,
% 2.43/2.65 (~hskp58),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[95, 1745, 12])).
% 2.43/2.65 tff(1747,plain,
% 2.43/2.65 (~hskp33),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[139, 1746, 97])).
% 2.43/2.65 tff(1748,plain,
% 2.43/2.65 (~hskp15),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[184, 1745, 12])).
% 2.43/2.65 tff(1749,plain,
% 2.43/2.65 (~hskp33),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[139, 96, 97])).
% 2.43/2.65 tff(1750,assumption,(~hskp61), introduced(assumption)).
% 2.43/2.65 tff(1751,assumption,(c1_1(a673)), introduced(assumption)).
% 2.43/2.65 tff(1752,assumption,(c3_1(a673)), introduced(assumption)).
% 2.43/2.65 tff(1753,plain,
% 2.43/2.65 (((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | c2_1(a669) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | (~c0_1(a669)) | (~c1_1(a669)))) <=> ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp41 | c2_1(a669) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | (~c0_1(a669)) | (~c1_1(a669)))),
% 2.43/2.65 inference(rewrite,[status(thm)],[])).
% 2.43/2.65 tff(1754,plain,
% 2.43/2.65 ((hskp41 | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c2_1(a669) | (~c1_1(a669)) | (~c0_1(a669))) <=> (hskp41 | c2_1(a669) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | (~c0_1(a669)) | (~c1_1(a669)))),
% 2.43/2.65 inference(rewrite,[status(thm)],[])).
% 2.43/2.65 tff(1755,plain,
% 2.43/2.65 (((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c2_1(a669) | (~c1_1(a669)) | (~c0_1(a669)))) <=> ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | c2_1(a669) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | (~c0_1(a669)) | (~c1_1(a669))))),
% 2.43/2.65 inference(monotonicity,[status(thm)],[1754])).
% 2.43/2.65 tff(1756,plain,
% 2.43/2.65 (((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c2_1(a669) | (~c1_1(a669)) | (~c0_1(a669)))) <=> ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp41 | c2_1(a669) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | (~c0_1(a669)) | (~c1_1(a669)))),
% 2.43/2.65 inference(transitivity,[status(thm)],[1755, 1753])).
% 2.43/2.65 tff(1757,plain,
% 2.43/2.65 ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c2_1(a669) | (~c1_1(a669)) | (~c0_1(a669)))),
% 2.43/2.65 inference(quant_inst,[status(thm)],[])).
% 2.43/2.65 tff(1758,plain,
% 2.43/2.65 ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp41 | c2_1(a669) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | (~c0_1(a669)) | (~c1_1(a669))),
% 2.43/2.65 inference(modus_ponens,[status(thm)],[1757, 1756])).
% 2.43/2.65 tff(1759,plain,
% 2.43/2.65 ($false),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[1758, 87, 97, 1752, 1751, 323, 315, 306, 299, 13])).
% 2.43/2.65 tff(1760,plain,((~hskp60) | hskp41 | (~c3_1(a673)) | (~c1_1(a673)) | c2_1(a673)), inference(lemma,lemma(discharge,[]))).
% 2.43/2.65 tff(1761,plain,
% 2.43/2.65 (~hskp60),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[1760, 97, 1752, 1751, 13])).
% 2.43/2.65 tff(1762,plain,
% 2.43/2.65 (hskp33),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[342, 1761, 1750])).
% 2.43/2.65 tff(1763,plain,
% 2.43/2.65 (~c2_1(a599)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[113, 1762])).
% 2.43/2.65 tff(1764,plain,
% 2.43/2.65 (c3_1(a599)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[121, 1762])).
% 2.43/2.65 tff(1765,plain,
% 2.43/2.65 (c0_1(a599)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[129, 1762])).
% 2.43/2.65 tff(1766,plain,
% 2.43/2.65 ($false),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[137, 87, 131, 97, 1765, 1764, 1763, 107])).
% 2.43/2.65 tff(1767,plain,(hskp41 | hskp58 | hskp61 | (~c3_1(a673)) | (~c1_1(a673)) | c2_1(a673)), inference(lemma,lemma(discharge,[]))).
% 2.43/2.65 tff(1768,plain,
% 2.43/2.65 (hskp61),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[1767, 13, 1668, 97, 1702, 96])).
% 2.43/2.65 tff(1769,plain,
% 2.43/2.65 (~c0_1(a670)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[348, 1768])).
% 2.43/2.65 tff(1770,plain,
% 2.43/2.65 (~c1_1(a670)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[354, 1768])).
% 2.43/2.65 tff(1771,plain,
% 2.43/2.65 (~c3_1(a670)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[361, 87, 35, 12, 1770, 1769, 34])).
% 2.43/2.65 tff(1772,assumption,(hskp3), introduced(assumption)).
% 2.43/2.65 tff(1773,plain,
% 2.43/2.65 (c0_1(a603)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[1565, 1772])).
% 2.43/2.65 tff(1774,assumption,(~c2_1(a603)), introduced(assumption)).
% 2.43/2.65 tff(1775,assumption,(hskp61), introduced(assumption)).
% 2.43/2.65 tff(1776,plain,
% 2.43/2.65 (~c0_1(a670)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[348, 1775])).
% 2.43/2.65 tff(1777,plain,
% 2.43/2.65 (~c1_1(a670)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[354, 1775])).
% 2.43/2.65 tff(1778,plain,
% 2.43/2.65 (~c3_1(a670)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[361, 87, 35, 12, 1777, 1776, 34])).
% 2.43/2.65 tff(1779,plain,
% 2.43/2.65 (c2_1(a670)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[379, 1775])).
% 2.43/2.65 tff(1780,plain,
% 2.43/2.65 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (c0_1(a670) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c2_1(a670)) | c3_1(a670))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | c0_1(a670) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c2_1(a670)) | c3_1(a670))),
% 2.43/2.65 inference(rewrite,[status(thm)],[])).
% 2.43/2.65 tff(1781,plain,
% 2.43/2.65 (((~ndr1_0) | c3_1(a670) | c0_1(a670) | (~c2_1(a670)) | c1_1(a603) | c3_1(a603) | c2_1(a603)) <=> (c0_1(a670) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c2_1(a670)) | c3_1(a670))),
% 2.43/2.65 inference(rewrite,[status(thm)],[])).
% 2.43/2.65 tff(1782,plain,
% 2.43/2.65 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | ((~ndr1_0) | c3_1(a670) | c0_1(a670) | (~c2_1(a670)) | c1_1(a603) | c3_1(a603) | c2_1(a603))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (c0_1(a670) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c2_1(a670)) | c3_1(a670)))),
% 2.43/2.65 inference(monotonicity,[status(thm)],[1781])).
% 2.43/2.65 tff(1783,plain,
% 2.43/2.65 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | ((~ndr1_0) | c3_1(a670) | c0_1(a670) | (~c2_1(a670)) | c1_1(a603) | c3_1(a603) | c2_1(a603))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | c0_1(a670) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c2_1(a670)) | c3_1(a670))),
% 2.43/2.65 inference(transitivity,[status(thm)],[1782, 1780])).
% 2.43/2.65 tff(1784,plain,
% 2.43/2.65 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | ((~ndr1_0) | c3_1(a670) | c0_1(a670) | (~c2_1(a670)) | c1_1(a603) | c3_1(a603) | c2_1(a603))),
% 2.43/2.65 inference(quant_inst,[status(thm)],[])).
% 2.43/2.65 tff(1785,plain,
% 2.43/2.65 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | c0_1(a670) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c2_1(a670)) | c3_1(a670)),
% 2.43/2.65 inference(modus_ponens,[status(thm)],[1784, 1783])).
% 2.43/2.65 tff(1786,plain,
% 2.43/2.65 ($false),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[1785, 87, 1779, 1776, 1125, 943, 599, 1774, 1778])).
% 2.43/2.65 tff(1787,plain,((~hskp61) | c1_1(a603) | c3_1(a603) | c2_1(a603) | hskp53 | hskp17), inference(lemma,lemma(discharge,[]))).
% 2.43/2.65 tff(1788,plain,
% 2.43/2.65 (c1_1(a603)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[1787, 1768, 12, 943, 35, 1774])).
% 2.43/2.65 tff(1789,assumption,(c0_1(a603)), introduced(assumption)).
% 2.43/2.65 tff(1790,plain,
% 2.43/2.65 (((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | (~c1_1(a603)) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c2_1(a603) | (~c0_1(a603)))) <=> ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp41 | (~c1_1(a603)) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c2_1(a603) | (~c0_1(a603)))),
% 2.43/2.65 inference(rewrite,[status(thm)],[])).
% 2.43/2.65 tff(1791,plain,
% 2.43/2.65 ((hskp41 | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c2_1(a603) | (~c1_1(a603)) | (~c0_1(a603))) <=> (hskp41 | (~c1_1(a603)) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c2_1(a603) | (~c0_1(a603)))),
% 2.43/2.65 inference(rewrite,[status(thm)],[])).
% 2.43/2.65 tff(1792,plain,
% 2.43/2.65 (((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c2_1(a603) | (~c1_1(a603)) | (~c0_1(a603)))) <=> ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | (~c1_1(a603)) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c2_1(a603) | (~c0_1(a603))))),
% 2.43/2.65 inference(monotonicity,[status(thm)],[1791])).
% 2.43/2.65 tff(1793,plain,
% 2.43/2.65 (((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c2_1(a603) | (~c1_1(a603)) | (~c0_1(a603)))) <=> ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp41 | (~c1_1(a603)) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c2_1(a603) | (~c0_1(a603)))),
% 2.43/2.65 inference(transitivity,[status(thm)],[1792, 1790])).
% 2.43/2.65 tff(1794,plain,
% 2.43/2.65 ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c2_1(a603) | (~c1_1(a603)) | (~c0_1(a603)))),
% 2.43/2.65 inference(quant_inst,[status(thm)],[])).
% 2.43/2.65 tff(1795,plain,
% 2.43/2.65 ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp41 | (~c1_1(a603)) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c2_1(a603) | (~c0_1(a603))),
% 2.43/2.65 inference(modus_ponens,[status(thm)],[1794, 1793])).
% 2.43/2.65 tff(1796,plain,
% 2.43/2.65 ($false),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[1795, 87, 97, 1668, 1702, 1789, 1788, 299, 13, 1774])).
% 2.43/2.65 tff(1797,plain,(c2_1(a673) | hskp41 | (~c0_1(a603)) | c2_1(a603) | hskp17 | c3_1(a603) | hskp53), inference(lemma,lemma(discharge,[]))).
% 2.43/2.65 tff(1798,plain,
% 2.43/2.65 (c2_1(a603)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[1797, 1773, 97, 13, 12, 943, 35])).
% 2.43/2.65 tff(1799,plain,
% 2.43/2.65 (~c1_1(a603)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[1550, 1772])).
% 2.43/2.65 tff(1800,plain,
% 2.43/2.65 (~hskp14),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[221, 35, 12, 97])).
% 2.43/2.65 tff(1801,plain,
% 2.43/2.65 ($false),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[1138, 87, 257, 1800, 1773, 1799, 232, 1798])).
% 2.43/2.65 tff(1802,plain,((~hskp3) | hskp15 | hskp41 | c2_1(a673) | hskp17 | c3_1(a603) | hskp53), inference(lemma,lemma(discharge,[]))).
% 2.43/2.65 tff(1803,plain,
% 2.43/2.65 (~hskp3),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[1802, 13, 97, 257, 12, 943, 35])).
% 2.43/2.65 tff(1804,plain,
% 2.43/2.65 (((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | c0_1(a673) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)))) <=> ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp29 | hskp3 | c0_1(a673) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)))),
% 2.43/2.65 inference(rewrite,[status(thm)],[])).
% 2.43/2.65 tff(1805,plain,
% 2.43/2.65 ((hskp29 | hskp3 | (~ndr1_0) | c2_1(a673) | c0_1(a673) | (~c3_1(a673))) <=> (hskp29 | hskp3 | c0_1(a673) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)))),
% 2.43/2.65 inference(rewrite,[status(thm)],[])).
% 2.43/2.65 tff(1806,plain,
% 2.43/2.65 (((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | (~ndr1_0) | c2_1(a673) | c0_1(a673) | (~c3_1(a673)))) <=> ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | c0_1(a673) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673))))),
% 2.43/2.65 inference(monotonicity,[status(thm)],[1805])).
% 2.43/2.65 tff(1807,plain,
% 2.43/2.65 (((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | (~ndr1_0) | c2_1(a673) | c0_1(a673) | (~c3_1(a673)))) <=> ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp29 | hskp3 | c0_1(a673) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)))),
% 2.43/2.65 inference(transitivity,[status(thm)],[1806, 1804])).
% 2.43/2.65 tff(1808,plain,
% 2.43/2.65 ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | (~ndr1_0) | c2_1(a673) | c0_1(a673) | (~c3_1(a673)))),
% 2.43/2.65 inference(quant_inst,[status(thm)],[])).
% 2.43/2.65 tff(1809,plain,
% 2.43/2.65 ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp29 | hskp3 | c0_1(a673) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673))),
% 2.43/2.65 inference(modus_ponens,[status(thm)],[1808, 1807])).
% 2.43/2.65 tff(1810,plain,
% 2.43/2.65 (hskp29 | hskp3 | c2_1(a673)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[1809, 87, 1668, 1694, 937])).
% 2.43/2.65 tff(1811,plain,
% 2.43/2.65 (hskp29),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[1810, 1803, 13])).
% 2.43/2.65 tff(1812,plain,
% 2.43/2.65 (~c3_1(a660)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[1358, 1811])).
% 2.43/2.65 tff(1813,plain,
% 2.43/2.65 (~c0_1(a660)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[1352, 1811])).
% 2.43/2.65 tff(1814,plain,
% 2.43/2.65 (~c1_1(a660)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[1364, 1811])).
% 2.43/2.65 tff(1815,plain,
% 2.43/2.65 (c2_1(a670)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[379, 1768])).
% 2.43/2.65 tff(1816,plain,
% 2.43/2.65 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (c0_1(a670) | c1_1(a660) | c3_1(a660) | (~ndr1_0) | c2_1(a660) | (~c2_1(a670)) | c3_1(a670))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | c0_1(a670) | c1_1(a660) | c3_1(a660) | (~ndr1_0) | c2_1(a660) | (~c2_1(a670)) | c3_1(a670))),
% 2.43/2.65 inference(rewrite,[status(thm)],[])).
% 2.43/2.65 tff(1817,plain,
% 2.43/2.65 (((~ndr1_0) | c3_1(a670) | c0_1(a670) | (~c2_1(a670)) | c1_1(a660) | c3_1(a660) | c2_1(a660)) <=> (c0_1(a670) | c1_1(a660) | c3_1(a660) | (~ndr1_0) | c2_1(a660) | (~c2_1(a670)) | c3_1(a670))),
% 2.43/2.65 inference(rewrite,[status(thm)],[])).
% 2.43/2.65 tff(1818,plain,
% 2.43/2.65 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | ((~ndr1_0) | c3_1(a670) | c0_1(a670) | (~c2_1(a670)) | c1_1(a660) | c3_1(a660) | c2_1(a660))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (c0_1(a670) | c1_1(a660) | c3_1(a660) | (~ndr1_0) | c2_1(a660) | (~c2_1(a670)) | c3_1(a670)))),
% 2.43/2.65 inference(monotonicity,[status(thm)],[1817])).
% 2.43/2.65 tff(1819,plain,
% 2.43/2.65 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | ((~ndr1_0) | c3_1(a670) | c0_1(a670) | (~c2_1(a670)) | c1_1(a660) | c3_1(a660) | c2_1(a660))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | c0_1(a670) | c1_1(a660) | c3_1(a660) | (~ndr1_0) | c2_1(a660) | (~c2_1(a670)) | c3_1(a670))),
% 2.43/2.65 inference(transitivity,[status(thm)],[1818, 1816])).
% 2.43/2.65 tff(1820,plain,
% 2.43/2.65 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | ((~ndr1_0) | c3_1(a670) | c0_1(a670) | (~c2_1(a670)) | c1_1(a660) | c3_1(a660) | c2_1(a660))),
% 2.43/2.65 inference(quant_inst,[status(thm)],[])).
% 2.43/2.65 tff(1821,plain,
% 2.43/2.65 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | c0_1(a670) | c1_1(a660) | c3_1(a660) | (~ndr1_0) | c2_1(a660) | (~c2_1(a670)) | c3_1(a670)),
% 2.43/2.65 inference(modus_ponens,[status(thm)],[1820, 1819])).
% 2.43/2.65 tff(1822,plain,
% 2.43/2.65 (c2_1(a660)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[1821, 87, 1815, 1769, 1814, 1812, 599, 1771])).
% 2.43/2.65 tff(1823,assumption,(hskp54), introduced(assumption)).
% 2.43/2.65 tff(1824,plain,
% 2.43/2.65 (~c0_1(a651)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[425, 1823])).
% 2.43/2.65 tff(1825,plain,
% 2.43/2.65 (c3_1(a651)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[448, 1823])).
% 2.43/2.65 tff(1826,plain,
% 2.43/2.65 (c1_1(a651)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[455, 87, 35, 12, 1825, 1824, 34])).
% 2.43/2.65 tff(1827,assumption,(c2_1(a660)), introduced(assumption)).
% 2.43/2.65 tff(1828,assumption,(~c0_1(a660)), introduced(assumption)).
% 2.43/2.65 tff(1829,assumption,(~c3_1(a660)), introduced(assumption)).
% 2.43/2.65 tff(1830,plain,
% 2.43/2.65 (c2_1(a651)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[433, 1823])).
% 2.43/2.65 tff(1831,plain,
% 2.43/2.65 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (c0_1(a651) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | (~c2_1(a660)) | (~c2_1(a651)) | (~c1_1(a651)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | c0_1(a651) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | (~c2_1(a660)) | (~c2_1(a651)) | (~c1_1(a651)))),
% 2.43/2.65 inference(rewrite,[status(thm)],[])).
% 2.43/2.65 tff(1832,plain,
% 2.43/2.65 (((~ndr1_0) | c3_1(a660) | c0_1(a660) | (~c2_1(a660)) | c0_1(a651) | (~c2_1(a651)) | (~c1_1(a651))) <=> (c0_1(a651) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | (~c2_1(a660)) | (~c2_1(a651)) | (~c1_1(a651)))),
% 2.43/2.65 inference(rewrite,[status(thm)],[])).
% 2.43/2.65 tff(1833,plain,
% 2.43/2.65 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c3_1(a660) | c0_1(a660) | (~c2_1(a660)) | c0_1(a651) | (~c2_1(a651)) | (~c1_1(a651)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (c0_1(a651) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | (~c2_1(a660)) | (~c2_1(a651)) | (~c1_1(a651))))),
% 2.43/2.65 inference(monotonicity,[status(thm)],[1832])).
% 2.43/2.65 tff(1834,plain,
% 2.43/2.65 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c3_1(a660) | c0_1(a660) | (~c2_1(a660)) | c0_1(a651) | (~c2_1(a651)) | (~c1_1(a651)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | c0_1(a651) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | (~c2_1(a660)) | (~c2_1(a651)) | (~c1_1(a651)))),
% 2.43/2.65 inference(transitivity,[status(thm)],[1833, 1831])).
% 2.43/2.65 tff(1835,plain,
% 2.43/2.65 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c3_1(a660) | c0_1(a660) | (~c2_1(a660)) | c0_1(a651) | (~c2_1(a651)) | (~c1_1(a651)))),
% 2.43/2.65 inference(quant_inst,[status(thm)],[])).
% 2.43/2.65 tff(1836,plain,
% 2.43/2.65 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | c0_1(a651) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | (~c2_1(a660)) | (~c2_1(a651)) | (~c1_1(a651))),
% 2.43/2.65 inference(modus_ponens,[status(thm)],[1835, 1834])).
% 2.43/2.65 tff(1837,plain,
% 2.43/2.65 ($false),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[1836, 87, 1830, 1824, 1829, 1828, 23, 1827, 1826])).
% 2.43/2.65 tff(1838,plain,((~hskp54) | c3_1(a660) | c0_1(a660) | (~c2_1(a660)) | hskp53 | hskp17), inference(lemma,lemma(discharge,[]))).
% 2.43/2.65 tff(1839,plain,
% 2.43/2.65 (~hskp54),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[1838, 1822, 35, 1813, 1812, 12])).
% 2.43/2.65 tff(1840,plain,
% 2.43/2.65 (hskp54 | hskp37 | c3_1(a670)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[418, 87, 1815, 1769, 372])).
% 2.43/2.65 tff(1841,plain,
% 2.43/2.65 (hskp37),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[1840, 1839, 1771])).
% 2.43/2.65 tff(1842,plain,
% 2.43/2.65 (~c2_1(a607)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[386, 1841])).
% 2.43/2.65 tff(1843,plain,
% 2.43/2.65 (c0_1(a607)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[394, 1841])).
% 2.43/2.65 tff(1844,plain,
% 2.43/2.65 (c1_1(a607)),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[402, 1841])).
% 2.43/2.65 tff(1845,plain,
% 2.43/2.65 (((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | c2_1(a607) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | (~c0_1(a607)) | (~c1_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp41 | c2_1(a607) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | (~c0_1(a607)) | (~c1_1(a607)))),
% 2.43/2.65 inference(rewrite,[status(thm)],[])).
% 2.43/2.65 tff(1846,plain,
% 2.43/2.65 ((hskp41 | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607))) <=> (hskp41 | c2_1(a607) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | (~c0_1(a607)) | (~c1_1(a607)))),
% 2.43/2.65 inference(rewrite,[status(thm)],[])).
% 2.43/2.65 tff(1847,plain,
% 2.43/2.65 (((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | c2_1(a607) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | (~c0_1(a607)) | (~c1_1(a607))))),
% 2.43/2.65 inference(monotonicity,[status(thm)],[1846])).
% 2.43/2.65 tff(1848,plain,
% 2.43/2.65 (((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp41 | c2_1(a607) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | (~c0_1(a607)) | (~c1_1(a607)))),
% 2.43/2.65 inference(transitivity,[status(thm)],[1847, 1845])).
% 2.43/2.65 tff(1849,plain,
% 2.43/2.65 ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))),
% 2.43/2.65 inference(quant_inst,[status(thm)],[])).
% 2.43/2.65 tff(1850,plain,
% 2.43/2.65 ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp41 | c2_1(a607) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | (~c0_1(a607)) | (~c1_1(a607))),
% 2.43/2.65 inference(modus_ponens,[status(thm)],[1849, 1848])).
% 2.43/2.65 tff(1851,plain,
% 2.43/2.65 ($false),
% 2.43/2.65 inference(unit_resolution,[status(thm)],[1850, 87, 97, 1668, 1702, 1844, 1843, 1842, 299, 13])).
% 2.43/2.65 tff(1852,plain,(c2_1(a673) | hskp41 | hskp53 | hskp17 | hskp15 | c3_1(a603)), inference(lemma,lemma(discharge,[]))).
% 2.43/2.65 tff(1853,plain,
% 2.43/2.66 (c2_1(a673)),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[1852, 35, 97, 12, 257, 943])).
% 2.43/2.66 tff(1854,assumption,(c2_1(a673)), introduced(assumption)).
% 2.43/2.66 tff(1855,assumption,(~c0_1(a673)), introduced(assumption)).
% 2.43/2.66 tff(1856,plain,
% 2.43/2.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a673) | c1_1(a670) | c0_1(a670) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a670)) | (~c3_1(a670)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a673) | c1_1(a670) | c0_1(a670) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a670)) | (~c3_1(a670)))),
% 2.43/2.66 inference(rewrite,[status(thm)],[])).
% 2.43/2.66 tff(1857,plain,
% 2.43/2.66 (((~ndr1_0) | c1_1(a670) | (~c3_1(a670)) | (~c2_1(a670)) | c1_1(a670) | c0_1(a670) | (~c2_1(a670)) | c0_1(a673) | (~c1_1(a673)) | (~c2_1(a673))) <=> (c0_1(a673) | c1_1(a670) | c0_1(a670) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a670)) | (~c3_1(a670)))),
% 2.43/2.66 inference(rewrite,[status(thm)],[])).
% 2.43/2.66 tff(1858,plain,
% 2.43/2.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a670) | (~c3_1(a670)) | (~c2_1(a670)) | c1_1(a670) | c0_1(a670) | (~c2_1(a670)) | c0_1(a673) | (~c1_1(a673)) | (~c2_1(a673)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a673) | c1_1(a670) | c0_1(a670) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a670)) | (~c3_1(a670))))),
% 2.43/2.66 inference(monotonicity,[status(thm)],[1857])).
% 2.43/2.66 tff(1859,plain,
% 2.43/2.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a670) | (~c3_1(a670)) | (~c2_1(a670)) | c1_1(a670) | c0_1(a670) | (~c2_1(a670)) | c0_1(a673) | (~c1_1(a673)) | (~c2_1(a673)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a673) | c1_1(a670) | c0_1(a670) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a670)) | (~c3_1(a670)))),
% 2.43/2.66 inference(transitivity,[status(thm)],[1858, 1856])).
% 2.43/2.66 tff(1860,plain,
% 2.43/2.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a670) | (~c3_1(a670)) | (~c2_1(a670)) | c1_1(a670) | c0_1(a670) | (~c2_1(a670)) | c0_1(a673) | (~c1_1(a673)) | (~c2_1(a673)))),
% 2.43/2.66 inference(quant_inst,[status(thm)],[])).
% 2.43/2.66 tff(1861,plain,
% 2.43/2.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a673) | c1_1(a670) | c0_1(a670) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a670)) | (~c3_1(a670))),
% 2.43/2.66 inference(modus_ponens,[status(thm)],[1860, 1859])).
% 2.43/2.66 tff(1862,plain,
% 2.43/2.66 (~c3_1(a670)),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[1861, 87, 1751, 1779, 1855, 1777, 1776, 1452, 1854])).
% 2.43/2.66 tff(1863,plain,
% 2.43/2.66 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (c0_1(a673) | c0_1(a670) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a670)) | c3_1(a670))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | c0_1(a673) | c0_1(a670) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a670)) | c3_1(a670))),
% 2.43/2.66 inference(rewrite,[status(thm)],[])).
% 2.43/2.66 tff(1864,plain,
% 2.43/2.66 (((~ndr1_0) | c3_1(a670) | c0_1(a670) | (~c2_1(a670)) | c0_1(a673) | (~c2_1(a673)) | (~c1_1(a673))) <=> (c0_1(a673) | c0_1(a670) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a670)) | c3_1(a670))),
% 2.43/2.66 inference(rewrite,[status(thm)],[])).
% 2.43/2.66 tff(1865,plain,
% 2.43/2.66 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c3_1(a670) | c0_1(a670) | (~c2_1(a670)) | c0_1(a673) | (~c2_1(a673)) | (~c1_1(a673)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (c0_1(a673) | c0_1(a670) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a670)) | c3_1(a670)))),
% 2.43/2.66 inference(monotonicity,[status(thm)],[1864])).
% 2.43/2.66 tff(1866,plain,
% 2.43/2.66 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c3_1(a670) | c0_1(a670) | (~c2_1(a670)) | c0_1(a673) | (~c2_1(a673)) | (~c1_1(a673)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | c0_1(a673) | c0_1(a670) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a670)) | c3_1(a670))),
% 2.43/2.66 inference(transitivity,[status(thm)],[1865, 1863])).
% 2.43/2.66 tff(1867,plain,
% 2.43/2.66 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c3_1(a670) | c0_1(a670) | (~c2_1(a670)) | c0_1(a673) | (~c2_1(a673)) | (~c1_1(a673)))),
% 2.43/2.66 inference(quant_inst,[status(thm)],[])).
% 2.43/2.66 tff(1868,plain,
% 2.43/2.66 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | c0_1(a673) | c0_1(a670) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a670)) | c3_1(a670)),
% 2.43/2.66 inference(modus_ponens,[status(thm)],[1867, 1866])).
% 2.43/2.66 tff(1869,plain,
% 2.43/2.66 ($false),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[1868, 87, 1751, 1779, 1855, 1776, 23, 1854, 1862])).
% 2.43/2.66 tff(1870,plain,((~hskp61) | (~c1_1(a673)) | c0_1(a673) | (~c2_1(a673))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.66 tff(1871,plain,
% 2.43/2.66 (~hskp61),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[1870, 1853, 1694, 1702])).
% 2.43/2.66 tff(1872,plain,
% 2.43/2.66 (hskp60),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[342, 1871, 1749])).
% 2.43/2.66 tff(1873,plain,
% 2.43/2.66 (~c2_1(a669)),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[305, 1872])).
% 2.43/2.66 tff(1874,plain,
% 2.43/2.66 (c0_1(a669)),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[322, 1872])).
% 2.43/2.66 tff(1875,assumption,(hskp62), introduced(assumption)).
% 2.43/2.66 tff(1876,plain,
% 2.43/2.66 (((~hskp62) | c0_1(a671)) <=> ((~hskp62) | c0_1(a671))),
% 2.43/2.66 inference(rewrite,[status(thm)],[])).
% 2.43/2.66 tff(1877,axiom,((~hskp62) | c0_1(a671)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause84')).
% 2.43/2.66 tff(1878,plain,
% 2.43/2.66 ((~hskp62) | c0_1(a671)),
% 2.43/2.66 inference(modus_ponens,[status(thm)],[1877, 1876])).
% 2.43/2.66 tff(1879,plain,
% 2.43/2.66 ((~hskp62) | c0_1(a671)),
% 2.43/2.66 inference(modus_ponens,[status(thm)],[1878, 1876])).
% 2.43/2.66 tff(1880,plain,
% 2.43/2.66 ((~hskp62) | c0_1(a671)),
% 2.43/2.66 inference(modus_ponens,[status(thm)],[1879, 1876])).
% 2.43/2.66 tff(1881,plain,
% 2.43/2.66 ((~hskp62) | c0_1(a671)),
% 2.43/2.66 inference(modus_ponens,[status(thm)],[1880, 1876])).
% 2.43/2.66 tff(1882,plain,
% 2.43/2.66 ((~hskp62) | c0_1(a671)),
% 2.43/2.66 inference(modus_ponens,[status(thm)],[1881, 1876])).
% 2.43/2.66 tff(1883,plain,
% 2.43/2.66 (c0_1(a671)),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[1882, 1875])).
% 2.43/2.66 tff(1884,plain,
% 2.43/2.66 (((~hskp62) | c3_1(a671)) <=> ((~hskp62) | c3_1(a671))),
% 2.43/2.66 inference(rewrite,[status(thm)],[])).
% 2.43/2.66 tff(1885,axiom,((~hskp62) | c3_1(a671)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause83')).
% 2.43/2.66 tff(1886,plain,
% 2.43/2.66 ((~hskp62) | c3_1(a671)),
% 2.43/2.66 inference(modus_ponens,[status(thm)],[1885, 1884])).
% 2.43/2.66 tff(1887,plain,
% 2.43/2.66 ((~hskp62) | c3_1(a671)),
% 2.43/2.66 inference(modus_ponens,[status(thm)],[1886, 1884])).
% 2.43/2.66 tff(1888,plain,
% 2.43/2.66 ((~hskp62) | c3_1(a671)),
% 2.43/2.66 inference(modus_ponens,[status(thm)],[1887, 1884])).
% 2.43/2.66 tff(1889,plain,
% 2.43/2.66 ((~hskp62) | c3_1(a671)),
% 2.43/2.66 inference(modus_ponens,[status(thm)],[1888, 1884])).
% 2.43/2.66 tff(1890,plain,
% 2.43/2.66 ((~hskp62) | c3_1(a671)),
% 2.43/2.66 inference(modus_ponens,[status(thm)],[1889, 1884])).
% 2.43/2.66 tff(1891,plain,
% 2.43/2.66 (c3_1(a671)),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[1890, 1875])).
% 2.43/2.66 tff(1892,plain,
% 2.43/2.66 (((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | (~ndr1_0) | (~c3_1(a671)) | c2_1(a671) | (~c0_1(a671)))) <=> ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp58 | hskp41 | (~ndr1_0) | (~c3_1(a671)) | c2_1(a671) | (~c0_1(a671)))),
% 2.43/2.66 inference(rewrite,[status(thm)],[])).
% 2.43/2.66 tff(1893,plain,
% 2.43/2.66 ((hskp58 | hskp41 | (~ndr1_0) | c2_1(a671) | (~c3_1(a671)) | (~c0_1(a671))) <=> (hskp58 | hskp41 | (~ndr1_0) | (~c3_1(a671)) | c2_1(a671) | (~c0_1(a671)))),
% 2.43/2.66 inference(rewrite,[status(thm)],[])).
% 2.43/2.66 tff(1894,plain,
% 2.43/2.66 (((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | (~ndr1_0) | c2_1(a671) | (~c3_1(a671)) | (~c0_1(a671)))) <=> ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | (~ndr1_0) | (~c3_1(a671)) | c2_1(a671) | (~c0_1(a671))))),
% 2.43/2.66 inference(monotonicity,[status(thm)],[1893])).
% 2.43/2.66 tff(1895,plain,
% 2.43/2.66 (((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | (~ndr1_0) | c2_1(a671) | (~c3_1(a671)) | (~c0_1(a671)))) <=> ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp58 | hskp41 | (~ndr1_0) | (~c3_1(a671)) | c2_1(a671) | (~c0_1(a671)))),
% 2.43/2.66 inference(transitivity,[status(thm)],[1894, 1892])).
% 2.43/2.66 tff(1896,plain,
% 2.43/2.66 ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | (~ndr1_0) | c2_1(a671) | (~c3_1(a671)) | (~c0_1(a671)))),
% 2.43/2.66 inference(quant_inst,[status(thm)],[])).
% 2.43/2.66 tff(1897,plain,
% 2.43/2.66 ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp58 | hskp41 | (~ndr1_0) | (~c3_1(a671)) | c2_1(a671) | (~c0_1(a671))),
% 2.43/2.66 inference(modus_ponens,[status(thm)],[1896, 1895])).
% 2.43/2.66 tff(1898,plain,
% 2.43/2.66 (c2_1(a671)),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[1897, 87, 131, 97, 1891, 1883, 107])).
% 2.43/2.66 tff(1899,plain,
% 2.43/2.66 (((~hskp62) | (~c1_1(a671))) <=> ((~hskp62) | (~c1_1(a671)))),
% 2.43/2.66 inference(rewrite,[status(thm)],[])).
% 2.43/2.66 tff(1900,plain,
% 2.43/2.66 (((~c1_1(a671)) | (~hskp62)) <=> ((~hskp62) | (~c1_1(a671)))),
% 2.43/2.66 inference(rewrite,[status(thm)],[])).
% 2.43/2.66 tff(1901,axiom,((~c1_1(a671)) | (~hskp62)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause176')).
% 2.43/2.66 tff(1902,plain,
% 2.43/2.66 ((~hskp62) | (~c1_1(a671))),
% 2.43/2.66 inference(modus_ponens,[status(thm)],[1901, 1900])).
% 2.43/2.66 tff(1903,plain,
% 2.43/2.66 ((~hskp62) | (~c1_1(a671))),
% 2.43/2.66 inference(modus_ponens,[status(thm)],[1902, 1899])).
% 2.43/2.66 tff(1904,plain,
% 2.43/2.66 (~c1_1(a671)),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[1903, 1875])).
% 2.43/2.66 tff(1905,plain,
% 2.43/2.66 (((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp15 | hskp14 | c1_1(a671) | (~ndr1_0) | (~c2_1(a671)) | (~c0_1(a671)))) <=> ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp15 | hskp14 | c1_1(a671) | (~ndr1_0) | (~c2_1(a671)) | (~c0_1(a671)))),
% 2.43/2.66 inference(rewrite,[status(thm)],[])).
% 2.43/2.66 tff(1906,plain,
% 2.43/2.66 ((hskp15 | hskp14 | (~ndr1_0) | c1_1(a671) | (~c0_1(a671)) | (~c2_1(a671))) <=> (hskp15 | hskp14 | c1_1(a671) | (~ndr1_0) | (~c2_1(a671)) | (~c0_1(a671)))),
% 2.43/2.66 inference(rewrite,[status(thm)],[])).
% 2.43/2.66 tff(1907,plain,
% 2.43/2.66 (((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp15 | hskp14 | (~ndr1_0) | c1_1(a671) | (~c0_1(a671)) | (~c2_1(a671)))) <=> ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp15 | hskp14 | c1_1(a671) | (~ndr1_0) | (~c2_1(a671)) | (~c0_1(a671))))),
% 2.43/2.66 inference(monotonicity,[status(thm)],[1906])).
% 2.43/2.66 tff(1908,plain,
% 2.43/2.66 (((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp15 | hskp14 | (~ndr1_0) | c1_1(a671) | (~c0_1(a671)) | (~c2_1(a671)))) <=> ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp15 | hskp14 | c1_1(a671) | (~ndr1_0) | (~c2_1(a671)) | (~c0_1(a671)))),
% 2.43/2.66 inference(transitivity,[status(thm)],[1907, 1905])).
% 2.43/2.66 tff(1909,plain,
% 2.43/2.66 ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | (hskp15 | hskp14 | (~ndr1_0) | c1_1(a671) | (~c0_1(a671)) | (~c2_1(a671)))),
% 2.43/2.66 inference(quant_inst,[status(thm)],[])).
% 2.43/2.66 tff(1910,plain,
% 2.43/2.66 ((~![U: $i] : (hskp15 | hskp14 | (~ndr1_0) | c1_1(U) | (~c0_1(U)) | (~c2_1(U)))) | hskp15 | hskp14 | c1_1(a671) | (~ndr1_0) | (~c2_1(a671)) | (~c0_1(a671))),
% 2.43/2.66 inference(modus_ponens,[status(thm)],[1909, 1908])).
% 2.43/2.66 tff(1911,plain,
% 2.43/2.66 ($false),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[1910, 87, 257, 256, 1883, 1904, 232, 1898])).
% 2.43/2.66 tff(1912,plain,((~hskp62) | hskp15 | hskp14 | hskp58 | hskp41), inference(lemma,lemma(discharge,[]))).
% 2.43/2.66 tff(1913,plain,
% 2.43/2.66 (~hskp62),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[1912, 1800, 257, 96, 97])).
% 2.43/2.66 tff(1914,plain,
% 2.43/2.66 (~c2_1(a603)),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[1138, 87, 257, 1800, 1773, 1799, 232])).
% 2.43/2.66 tff(1915,assumption,(~hskp9), introduced(assumption)).
% 2.43/2.66 tff(1916,plain,
% 2.43/2.66 (hskp16),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[1062, 1915, 12])).
% 2.43/2.66 tff(1917,plain,
% 2.43/2.66 (c0_1(a627)),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[1091, 1916])).
% 2.43/2.66 tff(1918,plain,
% 2.43/2.66 (c2_1(a627)),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[1076, 1916])).
% 2.43/2.66 tff(1919,plain,
% 2.43/2.66 (c1_1(a627)),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[1098, 87, 257, 256, 1918, 1917, 232])).
% 2.43/2.66 tff(1920,plain,
% 2.43/2.66 (^[U: $i] : refl((hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) <=> (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)))),
% 2.43/2.66 inference(bind,[status(th)],[])).
% 2.43/2.66 tff(1921,plain,
% 2.43/2.66 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) <=> ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 2.43/2.66 inference(quant_intro,[status(thm)],[1920])).
% 2.43/2.66 tff(1922,plain,
% 2.43/2.66 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) <=> ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 2.43/2.66 inference(rewrite,[status(thm)],[])).
% 2.43/2.66 tff(1923,plain,
% 2.43/2.66 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U))), ((((~ndr1_0) | c2_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c2_1(U)) | c1_1(U)))), rewrite((((~ndr1_0) | c2_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U))), ((((~ndr1_0) | c2_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U)))), (((((~ndr1_0) | c2_1(U)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))), (((((~ndr1_0) | c2_1(U)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)))), ((((((~ndr1_0) | c2_1(U)) | c1_1(U)) | c3_1(U)) | hskp8) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) | hskp8))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))), ((((((~ndr1_0) | c2_1(U)) | c1_1(U)) | c3_1(U)) | hskp8) <=> (hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)))), (((((((~ndr1_0) | c2_1(U)) | c1_1(U)) | c3_1(U)) | hskp8) | hskp9) <=> ((hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) | hskp9))), rewrite(((hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) | hskp9) <=> (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))), (((((((~ndr1_0) | c2_1(U)) | c1_1(U)) | c3_1(U)) | hskp8) | hskp9) <=> (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))))),
% 2.43/2.66 inference(bind,[status(th)],[])).
% 2.43/2.66 tff(1924,plain,
% 2.43/2.66 (![U: $i] : ((((((~ndr1_0) | c2_1(U)) | c1_1(U)) | c3_1(U)) | hskp8) | hskp9) <=> ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 2.43/2.66 inference(quant_intro,[status(thm)],[1923])).
% 2.43/2.66 tff(1925,axiom,(![U: $i] : ((((((~ndr1_0) | c2_1(U)) | c1_1(U)) | c3_1(U)) | hskp8) | hskp9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause277')).
% 2.43/2.66 tff(1926,plain,
% 2.43/2.66 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 2.43/2.66 inference(modus_ponens,[status(thm)],[1925, 1924])).
% 2.43/2.66 tff(1927,plain,
% 2.43/2.66 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 2.43/2.66 inference(modus_ponens,[status(thm)],[1926, 1922])).
% 2.43/2.66 tff(1928,plain,(
% 2.43/2.66 ![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 2.43/2.66 inference(skolemize,[status(sab)],[1927])).
% 2.43/2.66 tff(1929,plain,
% 2.43/2.66 (![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 2.43/2.66 inference(modus_ponens,[status(thm)],[1928, 1921])).
% 2.43/2.66 tff(1930,plain,
% 2.43/2.66 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp9 | hskp8 | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp9 | hskp8 | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603))),
% 2.43/2.66 inference(rewrite,[status(thm)],[])).
% 2.43/2.66 tff(1931,plain,
% 2.43/2.66 ((hskp9 | hskp8 | (~ndr1_0) | c3_1(a603) | c1_1(a603) | c2_1(a603)) <=> (hskp9 | hskp8 | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603))),
% 2.43/2.66 inference(rewrite,[status(thm)],[])).
% 2.43/2.66 tff(1932,plain,
% 2.43/2.66 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp9 | hskp8 | (~ndr1_0) | c3_1(a603) | c1_1(a603) | c2_1(a603))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp9 | hskp8 | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603)))),
% 2.43/2.66 inference(monotonicity,[status(thm)],[1931])).
% 2.43/2.66 tff(1933,plain,
% 2.43/2.66 (((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp9 | hskp8 | (~ndr1_0) | c3_1(a603) | c1_1(a603) | c2_1(a603))) <=> ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp9 | hskp8 | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603))),
% 2.43/2.66 inference(transitivity,[status(thm)],[1932, 1930])).
% 2.43/2.66 tff(1934,plain,
% 2.43/2.66 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp9 | hskp8 | (~ndr1_0) | c3_1(a603) | c1_1(a603) | c2_1(a603))),
% 2.43/2.66 inference(quant_inst,[status(thm)],[])).
% 2.43/2.66 tff(1935,plain,
% 2.43/2.66 ((~![U: $i] : (hskp9 | hskp8 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp9 | hskp8 | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603)),
% 2.43/2.66 inference(modus_ponens,[status(thm)],[1934, 1933])).
% 2.43/2.66 tff(1936,plain,
% 2.43/2.66 (hskp9 | hskp8 | c1_1(a603) | c2_1(a603)),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[1935, 87, 943, 1929])).
% 2.43/2.66 tff(1937,plain,
% 2.43/2.66 (hskp8),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[1936, 1915, 1125, 1774])).
% 2.43/2.66 tff(1938,plain,
% 2.43/2.66 (((~hskp8) | (~c2_1(a612))) <=> ((~hskp8) | (~c2_1(a612)))),
% 2.43/2.66 inference(rewrite,[status(thm)],[])).
% 2.43/2.66 tff(1939,plain,
% 2.43/2.66 (((~c2_1(a612)) | (~hskp8)) <=> ((~hskp8) | (~c2_1(a612)))),
% 2.43/2.66 inference(rewrite,[status(thm)],[])).
% 2.43/2.66 tff(1940,axiom,((~c2_1(a612)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause259')).
% 2.43/2.66 tff(1941,plain,
% 2.43/2.66 ((~hskp8) | (~c2_1(a612))),
% 2.43/2.66 inference(modus_ponens,[status(thm)],[1940, 1939])).
% 2.43/2.66 tff(1942,plain,
% 2.43/2.66 ((~hskp8) | (~c2_1(a612))),
% 2.43/2.66 inference(modus_ponens,[status(thm)],[1941, 1938])).
% 2.43/2.66 tff(1943,plain,
% 2.43/2.66 (~c2_1(a612)),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[1942, 1937])).
% 2.43/2.66 tff(1944,plain,
% 2.43/2.66 (~c3_1(a627)),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[1068, 1916])).
% 2.43/2.66 tff(1945,plain,
% 2.43/2.66 (((~hskp8) | c3_1(a612)) <=> ((~hskp8) | c3_1(a612))),
% 2.43/2.66 inference(rewrite,[status(thm)],[])).
% 2.43/2.66 tff(1946,axiom,((~hskp8) | c3_1(a612)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause162')).
% 2.43/2.66 tff(1947,plain,
% 2.43/2.66 ((~hskp8) | c3_1(a612)),
% 2.43/2.66 inference(modus_ponens,[status(thm)],[1946, 1945])).
% 2.43/2.66 tff(1948,plain,
% 2.43/2.66 ((~hskp8) | c3_1(a612)),
% 2.43/2.66 inference(modus_ponens,[status(thm)],[1947, 1945])).
% 2.43/2.66 tff(1949,plain,
% 2.43/2.66 ((~hskp8) | c3_1(a612)),
% 2.43/2.66 inference(modus_ponens,[status(thm)],[1948, 1945])).
% 2.43/2.66 tff(1950,plain,
% 2.43/2.66 ((~hskp8) | c3_1(a612)),
% 2.43/2.66 inference(modus_ponens,[status(thm)],[1949, 1945])).
% 2.43/2.66 tff(1951,plain,
% 2.43/2.66 ((~hskp8) | c3_1(a612)),
% 2.43/2.66 inference(modus_ponens,[status(thm)],[1950, 1945])).
% 2.43/2.66 tff(1952,plain,
% 2.43/2.66 (c3_1(a612)),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[1951, 1937])).
% 2.43/2.66 tff(1953,plain,
% 2.43/2.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | (c0_1(a673) | c3_1(a627) | c2_1(a612) | (~ndr1_0) | (~c3_1(a673)) | (~c2_1(a673)) | (~c3_1(a612)) | (~c0_1(a612)) | (~c2_1(a627)) | (~c1_1(a627)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c0_1(a673) | c3_1(a627) | c2_1(a612) | (~ndr1_0) | (~c3_1(a673)) | (~c2_1(a673)) | (~c3_1(a612)) | (~c0_1(a612)) | (~c2_1(a627)) | (~c1_1(a627)))),
% 2.43/2.66 inference(rewrite,[status(thm)],[])).
% 2.43/2.66 tff(1954,plain,
% 2.43/2.66 (((~ndr1_0) | c3_1(a627) | (~c1_1(a627)) | (~c2_1(a627)) | c0_1(a673) | (~c2_1(a673)) | (~c3_1(a673)) | c2_1(a612) | (~c0_1(a612)) | (~c3_1(a612))) <=> (c0_1(a673) | c3_1(a627) | c2_1(a612) | (~ndr1_0) | (~c3_1(a673)) | (~c2_1(a673)) | (~c3_1(a612)) | (~c0_1(a612)) | (~c2_1(a627)) | (~c1_1(a627)))),
% 2.43/2.66 inference(rewrite,[status(thm)],[])).
% 2.43/2.66 tff(1955,plain,
% 2.43/2.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a627) | (~c1_1(a627)) | (~c2_1(a627)) | c0_1(a673) | (~c2_1(a673)) | (~c3_1(a673)) | c2_1(a612) | (~c0_1(a612)) | (~c3_1(a612)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | (c0_1(a673) | c3_1(a627) | c2_1(a612) | (~ndr1_0) | (~c3_1(a673)) | (~c2_1(a673)) | (~c3_1(a612)) | (~c0_1(a612)) | (~c2_1(a627)) | (~c1_1(a627))))),
% 2.43/2.66 inference(monotonicity,[status(thm)],[1954])).
% 2.43/2.66 tff(1956,plain,
% 2.43/2.66 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a627) | (~c1_1(a627)) | (~c2_1(a627)) | c0_1(a673) | (~c2_1(a673)) | (~c3_1(a673)) | c2_1(a612) | (~c0_1(a612)) | (~c3_1(a612)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c0_1(a673) | c3_1(a627) | c2_1(a612) | (~ndr1_0) | (~c3_1(a673)) | (~c2_1(a673)) | (~c3_1(a612)) | (~c0_1(a612)) | (~c2_1(a627)) | (~c1_1(a627)))),
% 2.43/2.66 inference(transitivity,[status(thm)],[1955, 1953])).
% 2.43/2.66 tff(1957,plain,
% 2.43/2.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a627) | (~c1_1(a627)) | (~c2_1(a627)) | c0_1(a673) | (~c2_1(a673)) | (~c3_1(a673)) | c2_1(a612) | (~c0_1(a612)) | (~c3_1(a612)))),
% 2.43/2.66 inference(quant_inst,[status(thm)],[])).
% 2.43/2.66 tff(1958,plain,
% 2.43/2.66 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c0_1(a673) | c3_1(a627) | c2_1(a612) | (~ndr1_0) | (~c3_1(a673)) | (~c2_1(a673)) | (~c3_1(a612)) | (~c0_1(a612)) | (~c2_1(a627)) | (~c1_1(a627))),
% 2.43/2.66 inference(modus_ponens,[status(thm)],[1957, 1956])).
% 2.43/2.66 tff(1959,plain,
% 2.43/2.66 (~c0_1(a612)),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[1958, 87, 1752, 1918, 1952, 1855, 1944, 1943, 953, 1854, 1919])).
% 2.43/2.66 tff(1960,plain,
% 2.43/2.66 (((~hskp8) | (~c1_1(a612))) <=> ((~hskp8) | (~c1_1(a612)))),
% 2.43/2.66 inference(rewrite,[status(thm)],[])).
% 2.43/2.66 tff(1961,plain,
% 2.43/2.66 (((~c1_1(a612)) | (~hskp8)) <=> ((~hskp8) | (~c1_1(a612)))),
% 2.43/2.66 inference(rewrite,[status(thm)],[])).
% 2.43/2.66 tff(1962,axiom,((~c1_1(a612)) | (~hskp8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause260')).
% 2.43/2.66 tff(1963,plain,
% 2.43/2.66 ((~hskp8) | (~c1_1(a612))),
% 2.43/2.66 inference(modus_ponens,[status(thm)],[1962, 1961])).
% 2.43/2.66 tff(1964,plain,
% 2.43/2.66 ((~hskp8) | (~c1_1(a612))),
% 2.43/2.66 inference(modus_ponens,[status(thm)],[1963, 1960])).
% 2.43/2.66 tff(1965,plain,
% 2.43/2.66 (~c1_1(a612)),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[1964, 1937])).
% 2.43/2.66 tff(1966,plain,
% 2.43/2.66 (((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | c1_1(a612) | (~ndr1_0) | (~c3_1(a612)) | c0_1(a612))) <=> ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp53 | hskp17 | c1_1(a612) | (~ndr1_0) | (~c3_1(a612)) | c0_1(a612))),
% 2.43/2.66 inference(rewrite,[status(thm)],[])).
% 2.43/2.66 tff(1967,plain,
% 2.43/2.66 ((hskp53 | hskp17 | (~ndr1_0) | c1_1(a612) | c0_1(a612) | (~c3_1(a612))) <=> (hskp53 | hskp17 | c1_1(a612) | (~ndr1_0) | (~c3_1(a612)) | c0_1(a612))),
% 2.43/2.66 inference(rewrite,[status(thm)],[])).
% 2.43/2.66 tff(1968,plain,
% 2.43/2.66 (((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | (~ndr1_0) | c1_1(a612) | c0_1(a612) | (~c3_1(a612)))) <=> ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | c1_1(a612) | (~ndr1_0) | (~c3_1(a612)) | c0_1(a612)))),
% 2.43/2.66 inference(monotonicity,[status(thm)],[1967])).
% 2.43/2.66 tff(1969,plain,
% 2.43/2.66 (((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | (~ndr1_0) | c1_1(a612) | c0_1(a612) | (~c3_1(a612)))) <=> ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp53 | hskp17 | c1_1(a612) | (~ndr1_0) | (~c3_1(a612)) | c0_1(a612))),
% 2.43/2.66 inference(transitivity,[status(thm)],[1968, 1966])).
% 2.43/2.66 tff(1970,plain,
% 2.43/2.66 ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | (~ndr1_0) | c1_1(a612) | c0_1(a612) | (~c3_1(a612)))),
% 2.43/2.66 inference(quant_inst,[status(thm)],[])).
% 2.43/2.66 tff(1971,plain,
% 2.43/2.66 ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp53 | hskp17 | c1_1(a612) | (~ndr1_0) | (~c3_1(a612)) | c0_1(a612)),
% 2.43/2.66 inference(modus_ponens,[status(thm)],[1970, 1969])).
% 2.43/2.66 tff(1972,plain,
% 2.43/2.66 ($false),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[1971, 87, 35, 12, 1952, 1965, 34, 1959])).
% 2.43/2.66 tff(1973,plain,(hskp9 | hskp53 | hskp17 | (~c3_1(a673)) | c0_1(a673) | (~c2_1(a673)) | hskp15 | hskp14 | c1_1(a603) | c2_1(a603) | c3_1(a603)), inference(lemma,lemma(discharge,[]))).
% 2.43/2.66 tff(1974,plain,
% 2.43/2.66 (hskp9),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[1973, 1914, 12, 1668, 1694, 943, 257, 1800, 1853, 1799, 35])).
% 2.43/2.66 tff(1975,plain,
% 2.43/2.66 (~hskp41),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[568, 35, 12, 523])).
% 2.43/2.66 tff(1976,plain,
% 2.43/2.66 (~hskp61),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[1787, 1774, 943, 1125, 35, 12])).
% 2.43/2.66 tff(1977,plain,
% 2.43/2.66 (c2_1(a673)),
% 2.43/2.66 inference(unit_resolution,[status(thm)],[1767, 1976, 1975, 1752, 1751, 96])).
% 2.43/2.66 tff(1978,assumption,(c0_1(a613)), introduced(assumption)).
% 2.43/2.66 tff(1979,assumption,(~c3_1(a613)), introduced(assumption)).
% 2.43/2.66 tff(1980,assumption,(c2_1(a613)), introduced(assumption)).
% 2.43/2.66 tff(1981,assumption,(c1_1(a613)), introduced(assumption)).
% 2.43/2.66 tff(1982,plain,
% 2.43/2.66 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W))))),
% 2.43/2.66 inference(bind,[status(th)],[])).
% 2.43/2.66 tff(1983,plain,
% 2.43/2.66 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))),
% 2.43/2.66 inference(quant_intro,[status(thm)],[1982])).
% 2.43/2.66 tff(1984,plain,
% 2.43/2.66 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))),
% 2.43/2.66 inference(rewrite,[status(thm)],[])).
% 2.43/2.66 tff(1985,plain,
% 2.43/2.66 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~c0_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)))), ((((~c3_1(U)) | (~c0_1(U))) | (~c2_1(U))) <=> (((~c3_1(U)) | (~c0_1(U))) | (~c2_1(U))))), rewrite((((~c3_1(U)) | (~c0_1(U))) | (~c2_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), ((((~c3_1(U)) | (~c0_1(U))) | (~c2_1(U))) <=> ((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))))), (((((~c3_1(U)) | (~c0_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))), (((((~c3_1(U)) | (~c0_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))))), ((((((~c3_1(U)) | (~c0_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)))), ((((((~c3_1(U)) | (~c0_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V))))), (((((((~c3_1(U)) | (~c0_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c3_1(U)) | (~c0_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c3_1(U)) | (~c0_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W)))), ((((((((~c3_1(U)) | (~c0_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))))), (((((((((~c3_1(U)) | (~c0_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | (~c2_1(W))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c2_1(W))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c2_1(W)))), (((((((((~c3_1(U)) | (~c0_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | (~c2_1(W))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c2_1(W))))), ((((((((((~c3_1(U)) | (~c0_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | (~c2_1(W))) | (~c0_1(W))) | (~c1_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c2_1(W))) | (~c1_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c2_1(W))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))), ((((((((((~c3_1(U)) | (~c0_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | (~c2_1(W))) | (~c0_1(W))) | (~c1_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W))))), (((((((((((~c3_1(U)) | (~c0_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | (~c2_1(W))) | (~c0_1(W))) | (~c1_1(W))) | c3_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))), (((((((((((~c3_1(U)) | (~c0_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | (~c2_1(W))) | (~c0_1(W))) | (~c1_1(W))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))))),
% 2.43/2.66 inference(bind,[status(th)],[])).
% 2.43/2.66 tff(1986,plain,
% 2.43/2.66 (![W: $i, V: $i, U: $i] : ((((((((((~c3_1(U)) | (~c0_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | (~c2_1(W))) | (~c0_1(W))) | (~c1_1(W))) | c3_1(V)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))),
% 2.43/2.67 inference(quant_intro,[status(thm)],[1985])).
% 2.43/2.67 tff(1987,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c3_1(U)) | (~c0_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c2_1(V))) | (~c0_1(V))) | (~c2_1(W))) | (~c0_1(W))) | (~c1_1(W))) | c3_1(V))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause328')).
% 2.43/2.67 tff(1988,plain,
% 2.43/2.67 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))),
% 2.43/2.67 inference(modus_ponens,[status(thm)],[1987, 1986])).
% 2.43/2.67 tff(1989,plain,
% 2.43/2.67 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))),
% 2.43/2.67 inference(modus_ponens,[status(thm)],[1988, 1984])).
% 2.43/2.67 tff(1990,plain,(
% 2.43/2.67 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))),
% 2.43/2.67 inference(skolemize,[status(sab)],[1989])).
% 2.43/2.67 tff(1991,plain,
% 2.43/2.67 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))),
% 2.43/2.67 inference(modus_ponens,[status(thm)],[1990, 1983])).
% 2.43/2.67 tff(1992,plain,
% 2.43/2.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))) | (c3_1(a613) | (~ndr1_0) | (~c1_1(a613)) | (~c2_1(a613)) | (~c0_1(a613)) | (~c3_1(a671)) | (~c2_1(a671)) | (~c0_1(a671)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))) | c3_1(a613) | (~ndr1_0) | (~c1_1(a613)) | (~c2_1(a613)) | (~c0_1(a613)) | (~c3_1(a671)) | (~c2_1(a671)) | (~c0_1(a671)))),
% 2.43/2.67 inference(rewrite,[status(thm)],[])).
% 2.43/2.67 tff(1993,plain,
% 2.43/2.67 (((~ndr1_0) | (~c3_1(a671)) | (~c0_1(a671)) | (~c2_1(a671)) | c3_1(a613) | (~c2_1(a613)) | (~c0_1(a613)) | (~c0_1(a613)) | (~c1_1(a613)) | (~c2_1(a613))) <=> (c3_1(a613) | (~ndr1_0) | (~c1_1(a613)) | (~c2_1(a613)) | (~c0_1(a613)) | (~c3_1(a671)) | (~c2_1(a671)) | (~c0_1(a671)))),
% 2.43/2.67 inference(rewrite,[status(thm)],[])).
% 2.43/2.67 tff(1994,plain,
% 2.43/2.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a671)) | (~c0_1(a671)) | (~c2_1(a671)) | c3_1(a613) | (~c2_1(a613)) | (~c0_1(a613)) | (~c0_1(a613)) | (~c1_1(a613)) | (~c2_1(a613)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))) | (c3_1(a613) | (~ndr1_0) | (~c1_1(a613)) | (~c2_1(a613)) | (~c0_1(a613)) | (~c3_1(a671)) | (~c2_1(a671)) | (~c0_1(a671))))),
% 2.43/2.67 inference(monotonicity,[status(thm)],[1993])).
% 2.43/2.67 tff(1995,plain,
% 2.43/2.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a671)) | (~c0_1(a671)) | (~c2_1(a671)) | c3_1(a613) | (~c2_1(a613)) | (~c0_1(a613)) | (~c0_1(a613)) | (~c1_1(a613)) | (~c2_1(a613)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))) | c3_1(a613) | (~ndr1_0) | (~c1_1(a613)) | (~c2_1(a613)) | (~c0_1(a613)) | (~c3_1(a671)) | (~c2_1(a671)) | (~c0_1(a671)))),
% 2.43/2.67 inference(transitivity,[status(thm)],[1994, 1992])).
% 2.43/2.67 tff(1996,plain,
% 2.43/2.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a671)) | (~c0_1(a671)) | (~c2_1(a671)) | c3_1(a613) | (~c2_1(a613)) | (~c0_1(a613)) | (~c0_1(a613)) | (~c1_1(a613)) | (~c2_1(a613)))),
% 2.43/2.67 inference(quant_inst,[status(thm)],[])).
% 2.43/2.67 tff(1997,plain,
% 2.43/2.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))) | c3_1(a613) | (~ndr1_0) | (~c1_1(a613)) | (~c2_1(a613)) | (~c0_1(a613)) | (~c3_1(a671)) | (~c2_1(a671)) | (~c0_1(a671))),
% 2.43/2.67 inference(modus_ponens,[status(thm)],[1996, 1995])).
% 2.43/2.67 tff(1998,plain,
% 2.43/2.67 (~c2_1(a671)),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[1997, 87, 1891, 1883, 1981, 1980, 1979, 1991, 1978])).
% 2.43/2.67 tff(1999,assumption,(~c2_1(a669)), introduced(assumption)).
% 2.43/2.67 tff(2000,assumption,(c1_1(a669)), introduced(assumption)).
% 2.43/2.67 tff(2001,assumption,(c0_1(a669)), introduced(assumption)).
% 2.43/2.67 tff(2002,plain,
% 2.43/2.67 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c1_1(a671) | c2_1(a669) | (~ndr1_0) | (~c0_1(a669)) | (~c1_1(a669)) | (~c3_1(a671)) | c2_1(a671))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c1_1(a671) | c2_1(a669) | (~ndr1_0) | (~c0_1(a669)) | (~c1_1(a669)) | (~c3_1(a671)) | c2_1(a671))),
% 2.43/2.67 inference(rewrite,[status(thm)],[])).
% 2.43/2.67 tff(2003,plain,
% 2.43/2.67 ((hskp5 | (~ndr1_0) | c1_1(a671) | c2_1(a671) | (~c3_1(a671)) | c2_1(a669) | (~c1_1(a669)) | (~c0_1(a669))) <=> (hskp5 | c1_1(a671) | c2_1(a669) | (~ndr1_0) | (~c0_1(a669)) | (~c1_1(a669)) | (~c3_1(a671)) | c2_1(a671))),
% 2.43/2.67 inference(rewrite,[status(thm)],[])).
% 2.43/2.67 tff(2004,plain,
% 2.43/2.67 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a671) | c2_1(a671) | (~c3_1(a671)) | c2_1(a669) | (~c1_1(a669)) | (~c0_1(a669)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c1_1(a671) | c2_1(a669) | (~ndr1_0) | (~c0_1(a669)) | (~c1_1(a669)) | (~c3_1(a671)) | c2_1(a671)))),
% 2.43/2.67 inference(monotonicity,[status(thm)],[2003])).
% 2.43/2.67 tff(2005,plain,
% 2.43/2.67 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a671) | c2_1(a671) | (~c3_1(a671)) | c2_1(a669) | (~c1_1(a669)) | (~c0_1(a669)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c1_1(a671) | c2_1(a669) | (~ndr1_0) | (~c0_1(a669)) | (~c1_1(a669)) | (~c3_1(a671)) | c2_1(a671))),
% 2.43/2.67 inference(transitivity,[status(thm)],[2004, 2002])).
% 2.43/2.67 tff(2006,plain,
% 2.43/2.67 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a671) | c2_1(a671) | (~c3_1(a671)) | c2_1(a669) | (~c1_1(a669)) | (~c0_1(a669)))),
% 2.43/2.67 inference(quant_inst,[status(thm)],[])).
% 2.43/2.67 tff(2007,plain,
% 2.43/2.67 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c1_1(a671) | c2_1(a669) | (~ndr1_0) | (~c0_1(a669)) | (~c1_1(a669)) | (~c3_1(a671)) | c2_1(a671)),
% 2.43/2.67 inference(modus_ponens,[status(thm)],[2006, 2005])).
% 2.43/2.67 tff(2008,plain,
% 2.43/2.67 ($false),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[2007, 87, 523, 1891, 2001, 2000, 1904, 1999, 507, 1998])).
% 2.43/2.67 tff(2009,plain,((~hskp62) | hskp5 | (~c0_1(a669)) | (~c1_1(a669)) | c2_1(a669) | (~c1_1(a613)) | (~c2_1(a613)) | c3_1(a613) | (~c0_1(a613))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.67 tff(2010,plain,
% 2.43/2.67 (~hskp62),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[2009, 323, 523, 315, 306, 1981, 1980, 1979, 1978])).
% 2.43/2.67 tff(2011,plain,
% 2.43/2.67 (^[U: $i] : refl((hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) <=> (hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)))),
% 2.43/2.67 inference(bind,[status(th)],[])).
% 2.43/2.67 tff(2012,plain,
% 2.43/2.67 (![U: $i] : (hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) <=> ![U: $i] : (hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 2.43/2.67 inference(quant_intro,[status(thm)],[2011])).
% 2.43/2.67 tff(2013,plain,
% 2.43/2.67 (![U: $i] : (hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) <=> ![U: $i] : (hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 2.43/2.67 inference(rewrite,[status(thm)],[])).
% 2.43/2.67 tff(2014,plain,
% 2.43/2.67 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ndr1_0) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U)) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U))), ((((~ndr1_0) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U)))), (((((~ndr1_0) | c1_1(U)) | c3_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U)) | c2_1(U)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))), (((((~ndr1_0) | c1_1(U)) | c3_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)))), ((((((~ndr1_0) | c1_1(U)) | c3_1(U)) | c2_1(U)) | hskp62) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) | hskp62))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) | hskp62) <=> (hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))), ((((((~ndr1_0) | c1_1(U)) | c3_1(U)) | c2_1(U)) | hskp62) <=> (hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)))), (((((((~ndr1_0) | c1_1(U)) | c3_1(U)) | c2_1(U)) | hskp62) | hskp63) <=> ((hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) | hskp63))), rewrite(((hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U)) | hskp63) <=> (hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))), (((((((~ndr1_0) | c1_1(U)) | c3_1(U)) | c2_1(U)) | hskp62) | hskp63) <=> (hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))))),
% 2.43/2.67 inference(bind,[status(th)],[])).
% 2.43/2.67 tff(2015,plain,
% 2.43/2.67 (![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c3_1(U)) | c2_1(U)) | hskp62) | hskp63) <=> ![U: $i] : (hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 2.43/2.67 inference(quant_intro,[status(thm)],[2014])).
% 2.43/2.67 tff(2016,axiom,(![U: $i] : ((((((~ndr1_0) | c1_1(U)) | c3_1(U)) | c2_1(U)) | hskp62) | hskp63)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause279')).
% 2.43/2.67 tff(2017,plain,
% 2.43/2.67 (![U: $i] : (hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 2.43/2.67 inference(modus_ponens,[status(thm)],[2016, 2015])).
% 2.43/2.67 tff(2018,plain,
% 2.43/2.67 (![U: $i] : (hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 2.43/2.67 inference(modus_ponens,[status(thm)],[2017, 2013])).
% 2.43/2.67 tff(2019,plain,(
% 2.43/2.67 ![U: $i] : (hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 2.43/2.67 inference(skolemize,[status(sab)],[2018])).
% 2.43/2.67 tff(2020,plain,
% 2.43/2.67 (![U: $i] : (hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))),
% 2.43/2.67 inference(modus_ponens,[status(thm)],[2019, 2012])).
% 2.43/2.67 tff(2021,plain,
% 2.43/2.67 (((~![U: $i] : (hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp63 | hskp62 | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603))) <=> ((~![U: $i] : (hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp63 | hskp62 | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603))),
% 2.43/2.67 inference(rewrite,[status(thm)],[])).
% 2.43/2.67 tff(2022,plain,
% 2.43/2.67 ((hskp63 | hskp62 | (~ndr1_0) | c3_1(a603) | c1_1(a603) | c2_1(a603)) <=> (hskp63 | hskp62 | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603))),
% 2.43/2.67 inference(rewrite,[status(thm)],[])).
% 2.43/2.67 tff(2023,plain,
% 2.43/2.67 (((~![U: $i] : (hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp63 | hskp62 | (~ndr1_0) | c3_1(a603) | c1_1(a603) | c2_1(a603))) <=> ((~![U: $i] : (hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp63 | hskp62 | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603)))),
% 2.43/2.67 inference(monotonicity,[status(thm)],[2022])).
% 2.43/2.67 tff(2024,plain,
% 2.43/2.67 (((~![U: $i] : (hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp63 | hskp62 | (~ndr1_0) | c3_1(a603) | c1_1(a603) | c2_1(a603))) <=> ((~![U: $i] : (hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp63 | hskp62 | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603))),
% 2.43/2.67 inference(transitivity,[status(thm)],[2023, 2021])).
% 2.43/2.67 tff(2025,plain,
% 2.43/2.67 ((~![U: $i] : (hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp63 | hskp62 | (~ndr1_0) | c3_1(a603) | c1_1(a603) | c2_1(a603))),
% 2.43/2.67 inference(quant_inst,[status(thm)],[])).
% 2.43/2.67 tff(2026,plain,
% 2.43/2.67 ((~![U: $i] : (hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp63 | hskp62 | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603)),
% 2.43/2.67 inference(modus_ponens,[status(thm)],[2025, 2024])).
% 2.43/2.67 tff(2027,plain,
% 2.43/2.67 (hskp63 | hskp62 | c1_1(a603) | c2_1(a603)),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[2026, 87, 943, 2020])).
% 2.43/2.67 tff(2028,plain,
% 2.43/2.67 (hskp63),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[2027, 2010, 1125, 1774])).
% 2.43/2.67 tff(2029,plain,
% 2.43/2.67 (((~hskp63) | (~c0_1(a672))) <=> ((~hskp63) | (~c0_1(a672)))),
% 2.43/2.67 inference(rewrite,[status(thm)],[])).
% 2.43/2.67 tff(2030,plain,
% 2.43/2.67 (((~c0_1(a672)) | (~hskp63)) <=> ((~hskp63) | (~c0_1(a672)))),
% 2.43/2.67 inference(rewrite,[status(thm)],[])).
% 2.43/2.67 tff(2031,axiom,((~c0_1(a672)) | (~hskp63)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause174')).
% 2.43/2.67 tff(2032,plain,
% 2.43/2.67 ((~hskp63) | (~c0_1(a672))),
% 2.43/2.67 inference(modus_ponens,[status(thm)],[2031, 2030])).
% 2.43/2.67 tff(2033,plain,
% 2.43/2.67 ((~hskp63) | (~c0_1(a672))),
% 2.43/2.67 inference(modus_ponens,[status(thm)],[2032, 2029])).
% 2.43/2.67 tff(2034,plain,
% 2.43/2.67 (~c0_1(a672)),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[2033, 2028])).
% 2.43/2.67 tff(2035,plain,
% 2.43/2.67 (((~hskp63) | c3_1(a672)) <=> ((~hskp63) | c3_1(a672))),
% 2.43/2.67 inference(rewrite,[status(thm)],[])).
% 2.43/2.67 tff(2036,axiom,((~hskp63) | c3_1(a672)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause82')).
% 2.43/2.67 tff(2037,plain,
% 2.43/2.67 ((~hskp63) | c3_1(a672)),
% 2.43/2.67 inference(modus_ponens,[status(thm)],[2036, 2035])).
% 2.43/2.67 tff(2038,plain,
% 2.43/2.67 ((~hskp63) | c3_1(a672)),
% 2.43/2.67 inference(modus_ponens,[status(thm)],[2037, 2035])).
% 2.43/2.67 tff(2039,plain,
% 2.43/2.67 ((~hskp63) | c3_1(a672)),
% 2.43/2.67 inference(modus_ponens,[status(thm)],[2038, 2035])).
% 2.43/2.67 tff(2040,plain,
% 2.43/2.67 ((~hskp63) | c3_1(a672)),
% 2.43/2.67 inference(modus_ponens,[status(thm)],[2039, 2035])).
% 2.43/2.67 tff(2041,plain,
% 2.43/2.67 ((~hskp63) | c3_1(a672)),
% 2.43/2.67 inference(modus_ponens,[status(thm)],[2040, 2035])).
% 2.43/2.67 tff(2042,plain,
% 2.43/2.67 (c3_1(a672)),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[2041, 2028])).
% 2.43/2.67 tff(2043,plain,
% 2.43/2.67 (((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | c0_1(a672) | (~ndr1_0) | (~c3_1(a672)) | c1_1(a672))) <=> ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp53 | hskp17 | c0_1(a672) | (~ndr1_0) | (~c3_1(a672)) | c1_1(a672))),
% 2.43/2.67 inference(rewrite,[status(thm)],[])).
% 2.43/2.67 tff(2044,plain,
% 2.43/2.67 ((hskp53 | hskp17 | (~ndr1_0) | c1_1(a672) | c0_1(a672) | (~c3_1(a672))) <=> (hskp53 | hskp17 | c0_1(a672) | (~ndr1_0) | (~c3_1(a672)) | c1_1(a672))),
% 2.43/2.67 inference(rewrite,[status(thm)],[])).
% 2.43/2.67 tff(2045,plain,
% 2.43/2.67 (((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | (~ndr1_0) | c1_1(a672) | c0_1(a672) | (~c3_1(a672)))) <=> ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | c0_1(a672) | (~ndr1_0) | (~c3_1(a672)) | c1_1(a672)))),
% 2.43/2.67 inference(monotonicity,[status(thm)],[2044])).
% 2.43/2.67 tff(2046,plain,
% 2.43/2.67 (((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | (~ndr1_0) | c1_1(a672) | c0_1(a672) | (~c3_1(a672)))) <=> ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp53 | hskp17 | c0_1(a672) | (~ndr1_0) | (~c3_1(a672)) | c1_1(a672))),
% 2.43/2.67 inference(transitivity,[status(thm)],[2045, 2043])).
% 2.43/2.67 tff(2047,plain,
% 2.43/2.67 ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp53 | hskp17 | (~ndr1_0) | c1_1(a672) | c0_1(a672) | (~c3_1(a672)))),
% 2.43/2.67 inference(quant_inst,[status(thm)],[])).
% 2.43/2.67 tff(2048,plain,
% 2.43/2.67 ((~![U: $i] : (hskp53 | hskp17 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))) | hskp53 | hskp17 | c0_1(a672) | (~ndr1_0) | (~c3_1(a672)) | c1_1(a672)),
% 2.43/2.67 inference(modus_ponens,[status(thm)],[2047, 2046])).
% 2.43/2.67 tff(2049,plain,
% 2.43/2.67 (c1_1(a672)),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[2048, 87, 35, 12, 2042, 2034, 34])).
% 2.43/2.67 tff(2050,plain,
% 2.43/2.67 (((~hskp63) | (~c2_1(a672))) <=> ((~hskp63) | (~c2_1(a672)))),
% 2.43/2.67 inference(rewrite,[status(thm)],[])).
% 2.43/2.67 tff(2051,plain,
% 2.43/2.67 (((~c2_1(a672)) | (~hskp63)) <=> ((~hskp63) | (~c2_1(a672)))),
% 2.43/2.67 inference(rewrite,[status(thm)],[])).
% 2.43/2.67 tff(2052,axiom,((~c2_1(a672)) | (~hskp63)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause175')).
% 2.43/2.67 tff(2053,plain,
% 2.43/2.67 ((~hskp63) | (~c2_1(a672))),
% 2.43/2.67 inference(modus_ponens,[status(thm)],[2052, 2051])).
% 2.43/2.67 tff(2054,plain,
% 2.43/2.67 ((~hskp63) | (~c2_1(a672))),
% 2.43/2.67 inference(modus_ponens,[status(thm)],[2053, 2050])).
% 2.43/2.67 tff(2055,plain,
% 2.43/2.67 (~c2_1(a672)),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[2054, 2028])).
% 2.43/2.67 tff(2056,plain,
% 2.43/2.67 (((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | c2_1(a672) | c2_1(a669) | (~ndr1_0) | (~c0_1(a669)) | (~c1_1(a669)) | (~c3_1(a672)) | (~c1_1(a672)))) <=> ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp41 | c2_1(a672) | c2_1(a669) | (~ndr1_0) | (~c0_1(a669)) | (~c1_1(a669)) | (~c3_1(a672)) | (~c1_1(a672)))),
% 2.43/2.67 inference(rewrite,[status(thm)],[])).
% 2.43/2.67 tff(2057,plain,
% 2.43/2.67 ((hskp41 | (~ndr1_0) | c2_1(a672) | (~c3_1(a672)) | (~c1_1(a672)) | c2_1(a669) | (~c1_1(a669)) | (~c0_1(a669))) <=> (hskp41 | c2_1(a672) | c2_1(a669) | (~ndr1_0) | (~c0_1(a669)) | (~c1_1(a669)) | (~c3_1(a672)) | (~c1_1(a672)))),
% 2.43/2.67 inference(rewrite,[status(thm)],[])).
% 2.43/2.67 tff(2058,plain,
% 2.43/2.67 (((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | (~ndr1_0) | c2_1(a672) | (~c3_1(a672)) | (~c1_1(a672)) | c2_1(a669) | (~c1_1(a669)) | (~c0_1(a669)))) <=> ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | c2_1(a672) | c2_1(a669) | (~ndr1_0) | (~c0_1(a669)) | (~c1_1(a669)) | (~c3_1(a672)) | (~c1_1(a672))))),
% 2.43/2.67 inference(monotonicity,[status(thm)],[2057])).
% 2.43/2.67 tff(2059,plain,
% 2.43/2.67 (((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | (~ndr1_0) | c2_1(a672) | (~c3_1(a672)) | (~c1_1(a672)) | c2_1(a669) | (~c1_1(a669)) | (~c0_1(a669)))) <=> ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp41 | c2_1(a672) | c2_1(a669) | (~ndr1_0) | (~c0_1(a669)) | (~c1_1(a669)) | (~c3_1(a672)) | (~c1_1(a672)))),
% 2.43/2.67 inference(transitivity,[status(thm)],[2058, 2056])).
% 2.43/2.67 tff(2060,plain,
% 2.43/2.67 ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp41 | (~ndr1_0) | c2_1(a672) | (~c3_1(a672)) | (~c1_1(a672)) | c2_1(a669) | (~c1_1(a669)) | (~c0_1(a669)))),
% 2.43/2.67 inference(quant_inst,[status(thm)],[])).
% 2.43/2.67 tff(2061,plain,
% 2.43/2.67 ((~![V: $i, U: $i] : (hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp41 | c2_1(a672) | c2_1(a669) | (~ndr1_0) | (~c0_1(a669)) | (~c1_1(a669)) | (~c3_1(a672)) | (~c1_1(a672))),
% 2.43/2.67 inference(modus_ponens,[status(thm)],[2060, 2059])).
% 2.43/2.67 tff(2062,plain,
% 2.43/2.67 ($false),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[2061, 87, 97, 2042, 323, 315, 2055, 306, 299, 2049])).
% 2.43/2.67 tff(2063,plain,((~hskp60) | hskp41 | hskp53 | hskp17 | c1_1(a603) | c2_1(a603) | c3_1(a603) | hskp5 | (~c1_1(a613)) | (~c2_1(a613)) | c3_1(a613) | (~c0_1(a613))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.67 tff(2064,plain,
% 2.43/2.67 (~c0_1(a613)),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[2063, 1043, 35, 12, 1125, 1774, 943, 523, 300, 1035, 1026, 97])).
% 2.43/2.67 tff(2065,plain,
% 2.43/2.67 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (c0_1(a673) | c3_1(a613) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a613)) | c0_1(a613))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | c0_1(a673) | c3_1(a613) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a613)) | c0_1(a613))),
% 2.43/2.67 inference(rewrite,[status(thm)],[])).
% 2.43/2.67 tff(2066,plain,
% 2.43/2.67 (((~ndr1_0) | c3_1(a613) | c0_1(a613) | (~c2_1(a613)) | c0_1(a673) | (~c2_1(a673)) | (~c1_1(a673))) <=> (c0_1(a673) | c3_1(a613) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a613)) | c0_1(a613))),
% 2.43/2.67 inference(rewrite,[status(thm)],[])).
% 2.43/2.67 tff(2067,plain,
% 2.43/2.67 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c3_1(a613) | c0_1(a613) | (~c2_1(a613)) | c0_1(a673) | (~c2_1(a673)) | (~c1_1(a673)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (c0_1(a673) | c3_1(a613) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a613)) | c0_1(a613)))),
% 2.43/2.67 inference(monotonicity,[status(thm)],[2066])).
% 2.43/2.67 tff(2068,plain,
% 2.43/2.67 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c3_1(a613) | c0_1(a613) | (~c2_1(a613)) | c0_1(a673) | (~c2_1(a673)) | (~c1_1(a673)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | c0_1(a673) | c3_1(a613) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a613)) | c0_1(a613))),
% 2.43/2.67 inference(transitivity,[status(thm)],[2067, 2065])).
% 2.43/2.67 tff(2069,plain,
% 2.43/2.67 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c3_1(a613) | c0_1(a613) | (~c2_1(a613)) | c0_1(a673) | (~c2_1(a673)) | (~c1_1(a673)))),
% 2.43/2.67 inference(quant_inst,[status(thm)],[])).
% 2.43/2.67 tff(2070,plain,
% 2.43/2.67 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | c0_1(a673) | c3_1(a613) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a613)) | c0_1(a613)),
% 2.43/2.67 inference(modus_ponens,[status(thm)],[2069, 2068])).
% 2.43/2.67 tff(2071,plain,
% 2.43/2.67 ($false),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[2070, 87, 1751, 1035, 1855, 1026, 23, 1854, 2064])).
% 2.43/2.67 tff(2072,plain,((~hskp9) | (~c1_1(a673)) | c0_1(a673) | (~c2_1(a673)) | hskp53 | hskp17 | c1_1(a603) | c2_1(a603) | c3_1(a603) | hskp5 | (~hskp60) | hskp41), inference(lemma,lemma(discharge,[]))).
% 2.43/2.67 tff(2073,plain,
% 2.43/2.67 (~hskp60),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[2072, 1020, 1855, 1977, 35, 12, 1125, 1774, 943, 523, 1751, 1975])).
% 2.43/2.67 tff(2074,plain,
% 2.43/2.67 (hskp33),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[342, 2073, 1976])).
% 2.43/2.67 tff(2075,plain,
% 2.43/2.67 (~c2_1(a599)),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[113, 2074])).
% 2.43/2.67 tff(2076,plain,
% 2.43/2.67 (c3_1(a599)),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[121, 2074])).
% 2.43/2.67 tff(2077,plain,
% 2.43/2.67 (c0_1(a599)),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[129, 2074])).
% 2.43/2.67 tff(2078,plain,
% 2.43/2.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | (c0_1(a673) | c2_1(a599) | c3_1(a613) | (~ndr1_0) | (~c3_1(a673)) | (~c2_1(a673)) | (~c1_1(a613)) | (~c2_1(a613)) | (~c0_1(a599)) | (~c3_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c0_1(a673) | c2_1(a599) | c3_1(a613) | (~ndr1_0) | (~c3_1(a673)) | (~c2_1(a673)) | (~c1_1(a613)) | (~c2_1(a613)) | (~c0_1(a599)) | (~c3_1(a599)))),
% 2.43/2.67 inference(rewrite,[status(thm)],[])).
% 2.43/2.67 tff(2079,plain,
% 2.43/2.67 (((~ndr1_0) | c3_1(a613) | (~c1_1(a613)) | (~c2_1(a613)) | c0_1(a673) | (~c2_1(a673)) | (~c3_1(a673)) | c2_1(a599) | (~c0_1(a599)) | (~c3_1(a599))) <=> (c0_1(a673) | c2_1(a599) | c3_1(a613) | (~ndr1_0) | (~c3_1(a673)) | (~c2_1(a673)) | (~c1_1(a613)) | (~c2_1(a613)) | (~c0_1(a599)) | (~c3_1(a599)))),
% 2.43/2.67 inference(rewrite,[status(thm)],[])).
% 2.43/2.67 tff(2080,plain,
% 2.43/2.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a613) | (~c1_1(a613)) | (~c2_1(a613)) | c0_1(a673) | (~c2_1(a673)) | (~c3_1(a673)) | c2_1(a599) | (~c0_1(a599)) | (~c3_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | (c0_1(a673) | c2_1(a599) | c3_1(a613) | (~ndr1_0) | (~c3_1(a673)) | (~c2_1(a673)) | (~c1_1(a613)) | (~c2_1(a613)) | (~c0_1(a599)) | (~c3_1(a599))))),
% 2.43/2.67 inference(monotonicity,[status(thm)],[2079])).
% 2.43/2.67 tff(2081,plain,
% 2.43/2.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a613) | (~c1_1(a613)) | (~c2_1(a613)) | c0_1(a673) | (~c2_1(a673)) | (~c3_1(a673)) | c2_1(a599) | (~c0_1(a599)) | (~c3_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c0_1(a673) | c2_1(a599) | c3_1(a613) | (~ndr1_0) | (~c3_1(a673)) | (~c2_1(a673)) | (~c1_1(a613)) | (~c2_1(a613)) | (~c0_1(a599)) | (~c3_1(a599)))),
% 2.43/2.67 inference(transitivity,[status(thm)],[2080, 2078])).
% 2.43/2.67 tff(2082,plain,
% 2.43/2.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a613) | (~c1_1(a613)) | (~c2_1(a613)) | c0_1(a673) | (~c2_1(a673)) | (~c3_1(a673)) | c2_1(a599) | (~c0_1(a599)) | (~c3_1(a599)))),
% 2.43/2.67 inference(quant_inst,[status(thm)],[])).
% 2.43/2.67 tff(2083,plain,
% 2.43/2.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c0_1(a673) | c2_1(a599) | c3_1(a613) | (~ndr1_0) | (~c3_1(a673)) | (~c2_1(a673)) | (~c1_1(a613)) | (~c2_1(a613)) | (~c0_1(a599)) | (~c3_1(a599))),
% 2.43/2.67 inference(modus_ponens,[status(thm)],[2082, 2081])).
% 2.43/2.67 tff(2084,plain,
% 2.43/2.67 ($false),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[2083, 87, 1752, 2077, 2076, 1043, 1035, 1855, 2075, 1026, 953, 1977])).
% 2.43/2.67 tff(2085,plain,((~hskp9) | (~c3_1(a673)) | c0_1(a673) | hskp53 | hskp17 | c1_1(a603) | c2_1(a603) | c3_1(a603) | hskp5 | (~c1_1(a673))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.67 tff(2086,plain,
% 2.43/2.67 (hskp5),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[2085, 1914, 1702, 1694, 12, 35, 1799, 943, 1974, 1668])).
% 2.43/2.67 tff(2087,plain,
% 2.43/2.67 (~c0_1(a606)),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[580, 2086])).
% 2.43/2.67 tff(2088,plain,
% 2.43/2.67 (~c3_1(a606)),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[574, 2086])).
% 2.43/2.67 tff(2089,plain,
% 2.43/2.67 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (c0_1(a606) | c3_1(a606) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c2_1(a606)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | c0_1(a606) | c3_1(a606) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c2_1(a606)))),
% 2.43/2.67 inference(rewrite,[status(thm)],[])).
% 2.43/2.67 tff(2090,plain,
% 2.43/2.67 (((~ndr1_0) | c3_1(a606) | c0_1(a606) | (~c2_1(a606)) | c1_1(a603) | c3_1(a603) | c2_1(a603)) <=> (c0_1(a606) | c3_1(a606) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c2_1(a606)))),
% 2.43/2.67 inference(rewrite,[status(thm)],[])).
% 2.43/2.67 tff(2091,plain,
% 2.43/2.67 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | ((~ndr1_0) | c3_1(a606) | c0_1(a606) | (~c2_1(a606)) | c1_1(a603) | c3_1(a603) | c2_1(a603))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (c0_1(a606) | c3_1(a606) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c2_1(a606))))),
% 2.43/2.67 inference(monotonicity,[status(thm)],[2090])).
% 2.43/2.67 tff(2092,plain,
% 2.43/2.67 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | ((~ndr1_0) | c3_1(a606) | c0_1(a606) | (~c2_1(a606)) | c1_1(a603) | c3_1(a603) | c2_1(a603))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | c0_1(a606) | c3_1(a606) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c2_1(a606)))),
% 2.43/2.67 inference(transitivity,[status(thm)],[2091, 2089])).
% 2.43/2.67 tff(2093,plain,
% 2.43/2.67 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | ((~ndr1_0) | c3_1(a606) | c0_1(a606) | (~c2_1(a606)) | c1_1(a603) | c3_1(a603) | c2_1(a603))),
% 2.43/2.67 inference(quant_inst,[status(thm)],[])).
% 2.43/2.67 tff(2094,plain,
% 2.43/2.67 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | c0_1(a606) | c3_1(a606) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c2_1(a606))),
% 2.43/2.67 inference(modus_ponens,[status(thm)],[2093, 2092])).
% 2.43/2.67 tff(2095,plain,
% 2.43/2.67 (c0_1(a606) | c2_1(a603) | (~c2_1(a606))),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[2094, 87, 600, 1125, 943, 599])).
% 2.43/2.67 tff(2096,plain,
% 2.43/2.67 (~c2_1(a606)),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[2095, 1774, 601])).
% 2.43/2.67 tff(2097,assumption,(hskp8), introduced(assumption)).
% 2.43/2.67 tff(2098,plain,
% 2.43/2.67 (~c1_1(a612)),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[1964, 2097])).
% 2.43/2.67 tff(2099,plain,
% 2.43/2.67 (~c2_1(a612)),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[1942, 2097])).
% 2.43/2.67 tff(2100,assumption,(~c2_1(a606)), introduced(assumption)).
% 2.43/2.67 tff(2101,plain,
% 2.43/2.67 (c3_1(a612)),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[1951, 2097])).
% 2.43/2.67 tff(2102,plain,
% 2.43/2.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a606) | c2_1(a612) | c1_1(a612) | c0_1(a606) | c3_1(a606) | (~ndr1_0) | (~c3_1(a612)) | (~c0_1(a612)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a606) | c2_1(a612) | c1_1(a612) | c0_1(a606) | c3_1(a606) | (~ndr1_0) | (~c3_1(a612)) | (~c0_1(a612)))),
% 2.43/2.67 inference(rewrite,[status(thm)],[])).
% 2.43/2.67 tff(2103,plain,
% 2.43/2.67 (((~ndr1_0) | c1_1(a612) | (~c3_1(a612)) | (~c0_1(a612)) | c2_1(a612) | (~c3_1(a612)) | (~c0_1(a612)) | c2_1(a606) | c0_1(a606) | c3_1(a606)) <=> (c2_1(a606) | c2_1(a612) | c1_1(a612) | c0_1(a606) | c3_1(a606) | (~ndr1_0) | (~c3_1(a612)) | (~c0_1(a612)))),
% 2.43/2.67 inference(rewrite,[status(thm)],[])).
% 2.43/2.67 tff(2104,plain,
% 2.43/2.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a612) | (~c3_1(a612)) | (~c0_1(a612)) | c2_1(a612) | (~c3_1(a612)) | (~c0_1(a612)) | c2_1(a606) | c0_1(a606) | c3_1(a606))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a606) | c2_1(a612) | c1_1(a612) | c0_1(a606) | c3_1(a606) | (~ndr1_0) | (~c3_1(a612)) | (~c0_1(a612))))),
% 2.43/2.67 inference(monotonicity,[status(thm)],[2103])).
% 2.43/2.67 tff(2105,plain,
% 2.43/2.67 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a612) | (~c3_1(a612)) | (~c0_1(a612)) | c2_1(a612) | (~c3_1(a612)) | (~c0_1(a612)) | c2_1(a606) | c0_1(a606) | c3_1(a606))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a606) | c2_1(a612) | c1_1(a612) | c0_1(a606) | c3_1(a606) | (~ndr1_0) | (~c3_1(a612)) | (~c0_1(a612)))),
% 2.43/2.67 inference(transitivity,[status(thm)],[2104, 2102])).
% 2.43/2.67 tff(2106,plain,
% 2.43/2.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a612) | (~c3_1(a612)) | (~c0_1(a612)) | c2_1(a612) | (~c3_1(a612)) | (~c0_1(a612)) | c2_1(a606) | c0_1(a606) | c3_1(a606))),
% 2.43/2.67 inference(quant_inst,[status(thm)],[])).
% 2.43/2.67 tff(2107,plain,
% 2.43/2.67 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a606) | c2_1(a612) | c1_1(a612) | c0_1(a606) | c3_1(a606) | (~ndr1_0) | (~c3_1(a612)) | (~c0_1(a612))),
% 2.43/2.67 inference(modus_ponens,[status(thm)],[2106, 2105])).
% 2.43/2.67 tff(2108,plain,
% 2.43/2.67 (~c0_1(a612)),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[2107, 87, 2101, 2100, 2099, 2098, 601, 600, 910])).
% 2.43/2.67 tff(2109,plain,
% 2.43/2.67 ($false),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[1971, 87, 35, 12, 2101, 2098, 34, 2108])).
% 2.43/2.67 tff(2110,plain,((~hskp8) | hskp53 | hskp17 | c2_1(a606) | c0_1(a606) | c3_1(a606)), inference(lemma,lemma(discharge,[]))).
% 2.43/2.67 tff(2111,plain,
% 2.43/2.67 (~hskp8),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[2110, 35, 12, 2096, 601, 600])).
% 2.43/2.67 tff(2112,plain,
% 2.43/2.67 (hskp9),
% 2.43/2.67 inference(unit_resolution,[status(thm)],[1936, 2111, 1125, 1774])).
% 2.43/2.67 tff(2113,plain,
% 2.43/2.68 (~c3_1(a613)),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[1025, 2112])).
% 2.43/2.68 tff(2114,plain,
% 2.43/2.68 (c2_1(a613)),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[1034, 2112])).
% 2.43/2.68 tff(2115,plain,
% 2.43/2.68 (~hskp5),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[588, 2096])).
% 2.43/2.68 tff(2116,plain,
% 2.43/2.68 (c1_1(a613)),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[1042, 2112])).
% 2.43/2.68 tff(2117,plain,
% 2.43/2.68 (~c0_1(a613)),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[2063, 2116, 300, 12, 1125, 1774, 943, 2115, 35, 2114, 2113, 97])).
% 2.43/2.68 tff(2118,plain,
% 2.43/2.68 ($false),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[2070, 87, 1751, 2114, 1855, 2113, 23, 1854, 2117])).
% 2.43/2.68 tff(2119,plain,(hskp53 | (~c1_1(a673)) | c0_1(a673) | (~c2_1(a673)) | (~hskp60) | hskp17 | c1_1(a603) | c2_1(a603) | c3_1(a603) | hskp41 | c0_1(a606) | c3_1(a606)), inference(lemma,lemma(discharge,[]))).
% 2.43/2.68 tff(2120,plain,
% 2.43/2.68 ($false),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[2119, 2088, 2087, 1694, 1702, 35, 12, 1853, 1799, 943, 97, 1914, 1872])).
% 2.43/2.68 tff(2121,plain,((~hskp3) | hskp53 | hskp17 | c3_1(a603) | hskp41 | hskp15), inference(lemma,lemma(discharge,[]))).
% 2.43/2.68 tff(2122,plain,
% 2.43/2.68 (~hskp3),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[2121, 35, 12, 943, 97, 257])).
% 2.43/2.68 tff(2123,assumption,(~hskp3), introduced(assumption)).
% 2.43/2.68 tff(2124,assumption,(~hskp29), introduced(assumption)).
% 2.43/2.68 tff(2125,assumption,(hskp25), introduced(assumption)).
% 2.43/2.68 tff(2126,plain,
% 2.43/2.68 (((~hskp25) | (~c0_1(a646))) <=> ((~hskp25) | (~c0_1(a646)))),
% 2.43/2.68 inference(rewrite,[status(thm)],[])).
% 2.43/2.68 tff(2127,plain,
% 2.43/2.68 (((~c0_1(a646)) | (~hskp25)) <=> ((~hskp25) | (~c0_1(a646)))),
% 2.43/2.68 inference(rewrite,[status(thm)],[])).
% 2.43/2.68 tff(2128,axiom,((~c0_1(a646)) | (~hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause228')).
% 2.43/2.68 tff(2129,plain,
% 2.43/2.68 ((~hskp25) | (~c0_1(a646))),
% 2.43/2.68 inference(modus_ponens,[status(thm)],[2128, 2127])).
% 2.43/2.68 tff(2130,plain,
% 2.43/2.68 ((~hskp25) | (~c0_1(a646))),
% 2.43/2.68 inference(modus_ponens,[status(thm)],[2129, 2126])).
% 2.43/2.68 tff(2131,plain,
% 2.43/2.68 (~c0_1(a646)),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[2130, 2125])).
% 2.43/2.68 tff(2132,plain,
% 2.43/2.68 (((~hskp25) | (~c2_1(a646))) <=> ((~hskp25) | (~c2_1(a646)))),
% 2.43/2.68 inference(rewrite,[status(thm)],[])).
% 2.43/2.68 tff(2133,plain,
% 2.43/2.68 (((~c2_1(a646)) | (~hskp25)) <=> ((~hskp25) | (~c2_1(a646)))),
% 2.43/2.68 inference(rewrite,[status(thm)],[])).
% 2.43/2.68 tff(2134,axiom,((~c2_1(a646)) | (~hskp25)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause227')).
% 2.43/2.68 tff(2135,plain,
% 2.43/2.68 ((~hskp25) | (~c2_1(a646))),
% 2.43/2.68 inference(modus_ponens,[status(thm)],[2134, 2133])).
% 2.43/2.68 tff(2136,plain,
% 2.43/2.68 ((~hskp25) | (~c2_1(a646))),
% 2.43/2.68 inference(modus_ponens,[status(thm)],[2135, 2132])).
% 2.43/2.68 tff(2137,plain,
% 2.43/2.68 (~c2_1(a646)),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[2136, 2125])).
% 2.43/2.68 tff(2138,plain,
% 2.43/2.68 (((~hskp25) | c3_1(a646)) <=> ((~hskp25) | c3_1(a646))),
% 2.43/2.68 inference(rewrite,[status(thm)],[])).
% 2.43/2.68 tff(2139,axiom,((~hskp25) | c3_1(a646)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause143')).
% 2.43/2.68 tff(2140,plain,
% 2.43/2.68 ((~hskp25) | c3_1(a646)),
% 2.43/2.68 inference(modus_ponens,[status(thm)],[2139, 2138])).
% 2.43/2.68 tff(2141,plain,
% 2.43/2.68 ((~hskp25) | c3_1(a646)),
% 2.43/2.68 inference(modus_ponens,[status(thm)],[2140, 2138])).
% 2.43/2.68 tff(2142,plain,
% 2.43/2.68 ((~hskp25) | c3_1(a646)),
% 2.43/2.68 inference(modus_ponens,[status(thm)],[2141, 2138])).
% 2.43/2.68 tff(2143,plain,
% 2.43/2.68 ((~hskp25) | c3_1(a646)),
% 2.43/2.68 inference(modus_ponens,[status(thm)],[2142, 2138])).
% 2.43/2.68 tff(2144,plain,
% 2.43/2.68 ((~hskp25) | c3_1(a646)),
% 2.43/2.68 inference(modus_ponens,[status(thm)],[2143, 2138])).
% 2.43/2.68 tff(2145,plain,
% 2.43/2.68 (c3_1(a646)),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[2144, 2125])).
% 2.43/2.68 tff(2146,plain,
% 2.43/2.68 (((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | c2_1(a646) | c0_1(a646) | (~ndr1_0) | (~c3_1(a646)))) <=> ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp29 | hskp3 | c2_1(a646) | c0_1(a646) | (~ndr1_0) | (~c3_1(a646)))),
% 2.43/2.68 inference(rewrite,[status(thm)],[])).
% 2.43/2.68 tff(2147,plain,
% 2.43/2.68 ((hskp29 | hskp3 | (~ndr1_0) | c2_1(a646) | c0_1(a646) | (~c3_1(a646))) <=> (hskp29 | hskp3 | c2_1(a646) | c0_1(a646) | (~ndr1_0) | (~c3_1(a646)))),
% 2.43/2.68 inference(rewrite,[status(thm)],[])).
% 2.43/2.68 tff(2148,plain,
% 2.43/2.68 (((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | (~ndr1_0) | c2_1(a646) | c0_1(a646) | (~c3_1(a646)))) <=> ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | c2_1(a646) | c0_1(a646) | (~ndr1_0) | (~c3_1(a646))))),
% 2.43/2.68 inference(monotonicity,[status(thm)],[2147])).
% 2.43/2.68 tff(2149,plain,
% 2.43/2.68 (((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | (~ndr1_0) | c2_1(a646) | c0_1(a646) | (~c3_1(a646)))) <=> ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp29 | hskp3 | c2_1(a646) | c0_1(a646) | (~ndr1_0) | (~c3_1(a646)))),
% 2.43/2.68 inference(transitivity,[status(thm)],[2148, 2146])).
% 2.43/2.68 tff(2150,plain,
% 2.43/2.68 ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | (~ndr1_0) | c2_1(a646) | c0_1(a646) | (~c3_1(a646)))),
% 2.43/2.68 inference(quant_inst,[status(thm)],[])).
% 2.43/2.68 tff(2151,plain,
% 2.43/2.68 ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp29 | hskp3 | c2_1(a646) | c0_1(a646) | (~ndr1_0) | (~c3_1(a646))),
% 2.43/2.68 inference(modus_ponens,[status(thm)],[2150, 2149])).
% 2.43/2.68 tff(2152,plain,
% 2.43/2.68 ($false),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[2151, 87, 2124, 2123, 2145, 2137, 2131, 937])).
% 2.43/2.68 tff(2153,plain,((~hskp25) | hskp29 | hskp3), inference(lemma,lemma(discharge,[]))).
% 2.43/2.68 tff(2154,plain,
% 2.43/2.68 (~hskp25),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[2153, 2124, 2123])).
% 2.43/2.68 tff(2155,plain,
% 2.43/2.68 (((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | c2_1(a669) | (~ndr1_0) | (~c0_1(a669)) | (~c3_1(a669)))) <=> ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp58 | hskp41 | c2_1(a669) | (~ndr1_0) | (~c0_1(a669)) | (~c3_1(a669)))),
% 2.43/2.68 inference(rewrite,[status(thm)],[])).
% 2.43/2.68 tff(2156,plain,
% 2.43/2.68 ((hskp58 | hskp41 | (~ndr1_0) | c2_1(a669) | (~c3_1(a669)) | (~c0_1(a669))) <=> (hskp58 | hskp41 | c2_1(a669) | (~ndr1_0) | (~c0_1(a669)) | (~c3_1(a669)))),
% 2.43/2.68 inference(rewrite,[status(thm)],[])).
% 2.43/2.68 tff(2157,plain,
% 2.43/2.68 (((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | (~ndr1_0) | c2_1(a669) | (~c3_1(a669)) | (~c0_1(a669)))) <=> ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | c2_1(a669) | (~ndr1_0) | (~c0_1(a669)) | (~c3_1(a669))))),
% 2.43/2.68 inference(monotonicity,[status(thm)],[2156])).
% 2.43/2.68 tff(2158,plain,
% 2.43/2.68 (((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | (~ndr1_0) | c2_1(a669) | (~c3_1(a669)) | (~c0_1(a669)))) <=> ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp58 | hskp41 | c2_1(a669) | (~ndr1_0) | (~c0_1(a669)) | (~c3_1(a669)))),
% 2.43/2.68 inference(transitivity,[status(thm)],[2157, 2155])).
% 2.43/2.68 tff(2159,plain,
% 2.43/2.68 ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | (~ndr1_0) | c2_1(a669) | (~c3_1(a669)) | (~c0_1(a669)))),
% 2.43/2.68 inference(quant_inst,[status(thm)],[])).
% 2.43/2.68 tff(2160,plain,
% 2.43/2.68 ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp58 | hskp41 | c2_1(a669) | (~ndr1_0) | (~c0_1(a669)) | (~c3_1(a669))),
% 2.43/2.68 inference(modus_ponens,[status(thm)],[2159, 2158])).
% 2.43/2.68 tff(2161,plain,
% 2.43/2.68 (~c3_1(a669)),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[2160, 87, 131, 97, 2001, 1999, 107])).
% 2.43/2.68 tff(2162,plain,
% 2.43/2.68 (^[U: $i] : refl((hskp52 | hskp25 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> (hskp52 | hskp25 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))),
% 2.43/2.68 inference(bind,[status(th)],[])).
% 2.43/2.68 tff(2163,plain,
% 2.43/2.68 (![U: $i] : (hskp52 | hskp25 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp52 | hskp25 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 2.43/2.68 inference(quant_intro,[status(thm)],[2162])).
% 2.43/2.68 tff(2164,plain,
% 2.43/2.68 (![U: $i] : (hskp52 | hskp25 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp52 | hskp25 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 2.43/2.68 inference(rewrite,[status(thm)],[])).
% 2.43/2.68 tff(2165,plain,
% 2.43/2.68 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c3_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c3_1(U) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c3_1(U) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c3_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c3_1(U)) | c2_1(U)) | hskp25) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp25))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp25) <=> (hskp25 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c3_1(U)) | c2_1(U)) | hskp25) <=> (hskp25 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c3_1(U)) | c2_1(U)) | hskp25) | hskp52) <=> ((hskp25 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp52))), rewrite(((hskp25 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp52) <=> (hskp52 | hskp25 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c3_1(U)) | c2_1(U)) | hskp25) | hskp52) <=> (hskp52 | hskp25 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))))),
% 2.43/2.68 inference(bind,[status(th)],[])).
% 2.43/2.68 tff(2166,plain,
% 2.43/2.68 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c3_1(U)) | c2_1(U)) | hskp25) | hskp52) <=> ![U: $i] : (hskp52 | hskp25 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 2.43/2.68 inference(quant_intro,[status(thm)],[2165])).
% 2.43/2.68 tff(2167,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c3_1(U)) | c2_1(U)) | hskp25) | hskp52)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause284')).
% 2.43/2.68 tff(2168,plain,
% 2.43/2.68 (![U: $i] : (hskp52 | hskp25 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 2.43/2.68 inference(modus_ponens,[status(thm)],[2167, 2166])).
% 2.43/2.68 tff(2169,plain,
% 2.43/2.68 (![U: $i] : (hskp52 | hskp25 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 2.43/2.68 inference(modus_ponens,[status(thm)],[2168, 2164])).
% 2.43/2.68 tff(2170,plain,(
% 2.43/2.68 ![U: $i] : (hskp52 | hskp25 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 2.43/2.68 inference(skolemize,[status(sab)],[2169])).
% 2.43/2.68 tff(2171,plain,
% 2.43/2.68 (![U: $i] : (hskp52 | hskp25 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 2.43/2.68 inference(modus_ponens,[status(thm)],[2170, 2163])).
% 2.43/2.68 tff(2172,plain,
% 2.43/2.68 (((~![U: $i] : (hskp52 | hskp25 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp52 | hskp25 | c2_1(a669) | (~ndr1_0) | (~c0_1(a669)) | c3_1(a669))) <=> ((~![U: $i] : (hskp52 | hskp25 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp52 | hskp25 | c2_1(a669) | (~ndr1_0) | (~c0_1(a669)) | c3_1(a669))),
% 2.43/2.68 inference(rewrite,[status(thm)],[])).
% 2.43/2.68 tff(2173,plain,
% 2.43/2.68 ((hskp52 | hskp25 | (~ndr1_0) | c3_1(a669) | c2_1(a669) | (~c0_1(a669))) <=> (hskp52 | hskp25 | c2_1(a669) | (~ndr1_0) | (~c0_1(a669)) | c3_1(a669))),
% 2.43/2.68 inference(rewrite,[status(thm)],[])).
% 2.43/2.68 tff(2174,plain,
% 2.43/2.68 (((~![U: $i] : (hskp52 | hskp25 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp52 | hskp25 | (~ndr1_0) | c3_1(a669) | c2_1(a669) | (~c0_1(a669)))) <=> ((~![U: $i] : (hskp52 | hskp25 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp52 | hskp25 | c2_1(a669) | (~ndr1_0) | (~c0_1(a669)) | c3_1(a669)))),
% 2.43/2.68 inference(monotonicity,[status(thm)],[2173])).
% 2.43/2.68 tff(2175,plain,
% 2.43/2.68 (((~![U: $i] : (hskp52 | hskp25 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp52 | hskp25 | (~ndr1_0) | c3_1(a669) | c2_1(a669) | (~c0_1(a669)))) <=> ((~![U: $i] : (hskp52 | hskp25 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp52 | hskp25 | c2_1(a669) | (~ndr1_0) | (~c0_1(a669)) | c3_1(a669))),
% 2.43/2.68 inference(transitivity,[status(thm)],[2174, 2172])).
% 2.43/2.68 tff(2176,plain,
% 2.43/2.68 ((~![U: $i] : (hskp52 | hskp25 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp52 | hskp25 | (~ndr1_0) | c3_1(a669) | c2_1(a669) | (~c0_1(a669)))),
% 2.43/2.68 inference(quant_inst,[status(thm)],[])).
% 2.43/2.68 tff(2177,plain,
% 2.43/2.68 ((~![U: $i] : (hskp52 | hskp25 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp52 | hskp25 | c2_1(a669) | (~ndr1_0) | (~c0_1(a669)) | c3_1(a669)),
% 2.43/2.68 inference(modus_ponens,[status(thm)],[2176, 2175])).
% 2.43/2.68 tff(2178,plain,
% 2.43/2.68 (hskp52 | hskp25),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[2177, 87, 2001, 1999, 2171, 2161])).
% 2.43/2.68 tff(2179,plain,
% 2.43/2.68 (hskp52),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[2178, 2154])).
% 2.43/2.68 tff(2180,plain,
% 2.43/2.68 (((~hskp52) | (~c2_1(a647))) <=> ((~hskp52) | (~c2_1(a647)))),
% 2.43/2.68 inference(rewrite,[status(thm)],[])).
% 2.43/2.68 tff(2181,plain,
% 2.43/2.68 (((~c2_1(a647)) | (~hskp52)) <=> ((~hskp52) | (~c2_1(a647)))),
% 2.43/2.68 inference(rewrite,[status(thm)],[])).
% 2.43/2.68 tff(2182,axiom,((~c2_1(a647)) | (~hskp52)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause188')).
% 2.43/2.68 tff(2183,plain,
% 2.43/2.68 ((~hskp52) | (~c2_1(a647))),
% 2.43/2.68 inference(modus_ponens,[status(thm)],[2182, 2181])).
% 2.43/2.68 tff(2184,plain,
% 2.43/2.68 ((~hskp52) | (~c2_1(a647))),
% 2.43/2.68 inference(modus_ponens,[status(thm)],[2183, 2180])).
% 2.43/2.68 tff(2185,plain,
% 2.43/2.68 (~c2_1(a647)),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[2184, 2179])).
% 2.43/2.68 tff(2186,plain,
% 2.43/2.68 (((~hskp52) | c0_1(a647)) <=> ((~hskp52) | c0_1(a647))),
% 2.43/2.68 inference(rewrite,[status(thm)],[])).
% 2.43/2.68 tff(2187,axiom,((~hskp52) | c0_1(a647)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause101')).
% 2.43/2.68 tff(2188,plain,
% 2.43/2.68 ((~hskp52) | c0_1(a647)),
% 2.43/2.68 inference(modus_ponens,[status(thm)],[2187, 2186])).
% 2.43/2.68 tff(2189,plain,
% 2.43/2.68 ((~hskp52) | c0_1(a647)),
% 2.43/2.68 inference(modus_ponens,[status(thm)],[2188, 2186])).
% 2.43/2.68 tff(2190,plain,
% 2.43/2.68 ((~hskp52) | c0_1(a647)),
% 2.43/2.68 inference(modus_ponens,[status(thm)],[2189, 2186])).
% 2.43/2.68 tff(2191,plain,
% 2.43/2.68 ((~hskp52) | c0_1(a647)),
% 2.43/2.68 inference(modus_ponens,[status(thm)],[2190, 2186])).
% 2.43/2.68 tff(2192,plain,
% 2.43/2.68 ((~hskp52) | c0_1(a647)),
% 2.43/2.68 inference(modus_ponens,[status(thm)],[2191, 2186])).
% 2.43/2.68 tff(2193,plain,
% 2.43/2.68 (c0_1(a647)),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[2192, 2179])).
% 2.43/2.68 tff(2194,plain,
% 2.43/2.68 (((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | c2_1(a647) | (~ndr1_0) | (~c3_1(a647)) | (~c0_1(a647)))) <=> ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp58 | hskp41 | c2_1(a647) | (~ndr1_0) | (~c3_1(a647)) | (~c0_1(a647)))),
% 2.43/2.68 inference(rewrite,[status(thm)],[])).
% 2.43/2.68 tff(2195,plain,
% 2.43/2.68 ((hskp58 | hskp41 | (~ndr1_0) | c2_1(a647) | (~c3_1(a647)) | (~c0_1(a647))) <=> (hskp58 | hskp41 | c2_1(a647) | (~ndr1_0) | (~c3_1(a647)) | (~c0_1(a647)))),
% 2.43/2.68 inference(rewrite,[status(thm)],[])).
% 2.43/2.68 tff(2196,plain,
% 2.43/2.68 (((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | (~ndr1_0) | c2_1(a647) | (~c3_1(a647)) | (~c0_1(a647)))) <=> ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | c2_1(a647) | (~ndr1_0) | (~c3_1(a647)) | (~c0_1(a647))))),
% 2.43/2.68 inference(monotonicity,[status(thm)],[2195])).
% 2.43/2.68 tff(2197,plain,
% 2.43/2.68 (((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | (~ndr1_0) | c2_1(a647) | (~c3_1(a647)) | (~c0_1(a647)))) <=> ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp58 | hskp41 | c2_1(a647) | (~ndr1_0) | (~c3_1(a647)) | (~c0_1(a647)))),
% 2.43/2.68 inference(transitivity,[status(thm)],[2196, 2194])).
% 2.43/2.68 tff(2198,plain,
% 2.43/2.68 ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | (~ndr1_0) | c2_1(a647) | (~c3_1(a647)) | (~c0_1(a647)))),
% 2.43/2.68 inference(quant_inst,[status(thm)],[])).
% 2.43/2.68 tff(2199,plain,
% 2.43/2.68 ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp58 | hskp41 | c2_1(a647) | (~ndr1_0) | (~c3_1(a647)) | (~c0_1(a647))),
% 2.43/2.68 inference(modus_ponens,[status(thm)],[2198, 2197])).
% 2.43/2.68 tff(2200,plain,
% 2.43/2.68 (~c3_1(a647)),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[2199, 87, 131, 97, 2193, 2185, 107])).
% 2.43/2.68 tff(2201,plain,
% 2.43/2.68 (((~hskp52) | (~c1_1(a647))) <=> ((~hskp52) | (~c1_1(a647)))),
% 2.43/2.68 inference(rewrite,[status(thm)],[])).
% 2.43/2.68 tff(2202,plain,
% 2.43/2.68 (((~c1_1(a647)) | (~hskp52)) <=> ((~hskp52) | (~c1_1(a647)))),
% 2.43/2.68 inference(rewrite,[status(thm)],[])).
% 2.43/2.68 tff(2203,axiom,((~c1_1(a647)) | (~hskp52)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause189')).
% 2.43/2.68 tff(2204,plain,
% 2.43/2.68 ((~hskp52) | (~c1_1(a647))),
% 2.43/2.68 inference(modus_ponens,[status(thm)],[2203, 2202])).
% 2.43/2.68 tff(2205,plain,
% 2.43/2.68 ((~hskp52) | (~c1_1(a647))),
% 2.43/2.68 inference(modus_ponens,[status(thm)],[2204, 2201])).
% 2.43/2.68 tff(2206,plain,
% 2.43/2.68 (~c1_1(a647)),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[2205, 2179])).
% 2.43/2.68 tff(2207,assumption,(~hskp62), introduced(assumption)).
% 2.43/2.68 tff(2208,plain,
% 2.43/2.68 (((~![U: $i] : (hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp63 | hskp62 | c2_1(a647) | c1_1(a647) | (~ndr1_0) | c3_1(a647))) <=> ((~![U: $i] : (hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp63 | hskp62 | c2_1(a647) | c1_1(a647) | (~ndr1_0) | c3_1(a647))),
% 2.43/2.68 inference(rewrite,[status(thm)],[])).
% 2.43/2.68 tff(2209,plain,
% 2.43/2.68 ((hskp63 | hskp62 | (~ndr1_0) | c3_1(a647) | c1_1(a647) | c2_1(a647)) <=> (hskp63 | hskp62 | c2_1(a647) | c1_1(a647) | (~ndr1_0) | c3_1(a647))),
% 2.43/2.68 inference(rewrite,[status(thm)],[])).
% 2.43/2.68 tff(2210,plain,
% 2.43/2.68 (((~![U: $i] : (hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp63 | hskp62 | (~ndr1_0) | c3_1(a647) | c1_1(a647) | c2_1(a647))) <=> ((~![U: $i] : (hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp63 | hskp62 | c2_1(a647) | c1_1(a647) | (~ndr1_0) | c3_1(a647)))),
% 2.43/2.68 inference(monotonicity,[status(thm)],[2209])).
% 2.43/2.68 tff(2211,plain,
% 2.43/2.68 (((~![U: $i] : (hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp63 | hskp62 | (~ndr1_0) | c3_1(a647) | c1_1(a647) | c2_1(a647))) <=> ((~![U: $i] : (hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp63 | hskp62 | c2_1(a647) | c1_1(a647) | (~ndr1_0) | c3_1(a647))),
% 2.43/2.68 inference(transitivity,[status(thm)],[2210, 2208])).
% 2.43/2.68 tff(2212,plain,
% 2.43/2.68 ((~![U: $i] : (hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | (hskp63 | hskp62 | (~ndr1_0) | c3_1(a647) | c1_1(a647) | c2_1(a647))),
% 2.43/2.68 inference(quant_inst,[status(thm)],[])).
% 2.43/2.68 tff(2213,plain,
% 2.43/2.68 ((~![U: $i] : (hskp63 | hskp62 | (~ndr1_0) | c3_1(U) | c1_1(U) | c2_1(U))) | hskp63 | hskp62 | c2_1(a647) | c1_1(a647) | (~ndr1_0) | c3_1(a647)),
% 2.43/2.68 inference(modus_ponens,[status(thm)],[2212, 2211])).
% 2.43/2.68 tff(2214,plain,
% 2.43/2.68 (hskp63),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[2213, 87, 2207, 2185, 2206, 2020, 2200])).
% 2.43/2.68 tff(2215,plain,
% 2.43/2.68 (~c2_1(a672)),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[2054, 2214])).
% 2.43/2.68 tff(2216,plain,
% 2.43/2.68 (~c0_1(a672)),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[2033, 2214])).
% 2.43/2.68 tff(2217,plain,
% 2.43/2.68 (c3_1(a672)),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[2041, 2214])).
% 2.43/2.68 tff(2218,plain,
% 2.43/2.68 (((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | c0_1(a672) | c2_1(a672) | (~ndr1_0) | (~c3_1(a672)))) <=> ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp29 | hskp3 | c0_1(a672) | c2_1(a672) | (~ndr1_0) | (~c3_1(a672)))),
% 2.43/2.68 inference(rewrite,[status(thm)],[])).
% 2.43/2.68 tff(2219,plain,
% 2.43/2.68 ((hskp29 | hskp3 | (~ndr1_0) | c2_1(a672) | c0_1(a672) | (~c3_1(a672))) <=> (hskp29 | hskp3 | c0_1(a672) | c2_1(a672) | (~ndr1_0) | (~c3_1(a672)))),
% 2.43/2.68 inference(rewrite,[status(thm)],[])).
% 2.43/2.68 tff(2220,plain,
% 2.43/2.68 (((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | (~ndr1_0) | c2_1(a672) | c0_1(a672) | (~c3_1(a672)))) <=> ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | c0_1(a672) | c2_1(a672) | (~ndr1_0) | (~c3_1(a672))))),
% 2.43/2.68 inference(monotonicity,[status(thm)],[2219])).
% 2.43/2.68 tff(2221,plain,
% 2.43/2.68 (((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | (~ndr1_0) | c2_1(a672) | c0_1(a672) | (~c3_1(a672)))) <=> ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp29 | hskp3 | c0_1(a672) | c2_1(a672) | (~ndr1_0) | (~c3_1(a672)))),
% 2.43/2.68 inference(transitivity,[status(thm)],[2220, 2218])).
% 2.43/2.68 tff(2222,plain,
% 2.43/2.68 ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | (~ndr1_0) | c2_1(a672) | c0_1(a672) | (~c3_1(a672)))),
% 2.43/2.68 inference(quant_inst,[status(thm)],[])).
% 2.43/2.68 tff(2223,plain,
% 2.43/2.68 ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp29 | hskp3 | c0_1(a672) | c2_1(a672) | (~ndr1_0) | (~c3_1(a672))),
% 2.43/2.68 inference(modus_ponens,[status(thm)],[2222, 2221])).
% 2.43/2.68 tff(2224,plain,
% 2.43/2.68 ($false),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[2223, 87, 2124, 2123, 2217, 2216, 2215, 937])).
% 2.43/2.68 tff(2225,plain,(hskp29 | hskp3 | hskp62 | hskp58 | hskp41 | (~c0_1(a669)) | c2_1(a669)), inference(lemma,lemma(discharge,[]))).
% 2.43/2.68 tff(2226,plain,
% 2.43/2.68 (hskp29),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[2225, 2122, 1913, 96, 97, 1874, 1873])).
% 2.43/2.68 tff(2227,plain,
% 2.43/2.68 (~c0_1(a660)),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[1352, 2226])).
% 2.43/2.68 tff(2228,plain,
% 2.43/2.68 (~c3_1(a660)),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[1358, 2226])).
% 2.43/2.68 tff(2229,plain,
% 2.43/2.68 (~c1_1(a660)),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[1364, 2226])).
% 2.43/2.68 tff(2230,plain,
% 2.43/2.68 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | (c1_1(a660) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | c2_1(a660))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | c1_1(a660) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | c2_1(a660))),
% 2.43/2.68 inference(rewrite,[status(thm)],[])).
% 2.43/2.68 tff(2231,plain,
% 2.43/2.68 (((~ndr1_0) | c3_1(a660) | c2_1(a660) | c0_1(a660) | c1_1(a660) | c3_1(a660) | c0_1(a660)) <=> (c1_1(a660) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | c2_1(a660))),
% 2.43/2.68 inference(rewrite,[status(thm)],[])).
% 2.43/2.68 tff(2232,plain,
% 2.43/2.68 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | ((~ndr1_0) | c3_1(a660) | c2_1(a660) | c0_1(a660) | c1_1(a660) | c3_1(a660) | c0_1(a660))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | (c1_1(a660) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | c2_1(a660)))),
% 2.43/2.68 inference(monotonicity,[status(thm)],[2231])).
% 2.43/2.68 tff(2233,plain,
% 2.43/2.68 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | ((~ndr1_0) | c3_1(a660) | c2_1(a660) | c0_1(a660) | c1_1(a660) | c3_1(a660) | c0_1(a660))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | c1_1(a660) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | c2_1(a660))),
% 2.43/2.68 inference(transitivity,[status(thm)],[2232, 2230])).
% 2.43/2.68 tff(2234,plain,
% 2.43/2.68 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | ((~ndr1_0) | c3_1(a660) | c2_1(a660) | c0_1(a660) | c1_1(a660) | c3_1(a660) | c0_1(a660))),
% 2.43/2.68 inference(quant_inst,[status(thm)],[])).
% 2.43/2.68 tff(2235,plain,
% 2.43/2.68 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | c1_1(a660) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | c2_1(a660)),
% 2.43/2.68 inference(modus_ponens,[status(thm)],[2234, 2233])).
% 2.43/2.68 tff(2236,plain,
% 2.43/2.68 (c2_1(a660)),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[2235, 87, 2229, 2228, 2227, 170])).
% 2.43/2.68 tff(2237,plain,
% 2.43/2.68 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (c0_1(a673) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a660)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | c0_1(a673) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a660)))),
% 2.43/2.68 inference(rewrite,[status(thm)],[])).
% 2.43/2.68 tff(2238,plain,
% 2.43/2.68 (((~ndr1_0) | c3_1(a660) | c0_1(a660) | (~c2_1(a660)) | c0_1(a673) | (~c2_1(a673)) | (~c1_1(a673))) <=> (c0_1(a673) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a660)))),
% 2.43/2.68 inference(rewrite,[status(thm)],[])).
% 2.43/2.68 tff(2239,plain,
% 2.43/2.68 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c3_1(a660) | c0_1(a660) | (~c2_1(a660)) | c0_1(a673) | (~c2_1(a673)) | (~c1_1(a673)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (c0_1(a673) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a660))))),
% 2.43/2.68 inference(monotonicity,[status(thm)],[2238])).
% 2.43/2.68 tff(2240,plain,
% 2.43/2.68 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c3_1(a660) | c0_1(a660) | (~c2_1(a660)) | c0_1(a673) | (~c2_1(a673)) | (~c1_1(a673)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | c0_1(a673) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a660)))),
% 2.43/2.68 inference(transitivity,[status(thm)],[2239, 2237])).
% 2.43/2.68 tff(2241,plain,
% 2.43/2.68 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | ((~ndr1_0) | c3_1(a660) | c0_1(a660) | (~c2_1(a660)) | c0_1(a673) | (~c2_1(a673)) | (~c1_1(a673)))),
% 2.43/2.68 inference(quant_inst,[status(thm)],[])).
% 2.43/2.68 tff(2242,plain,
% 2.43/2.68 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | c0_1(a673) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a660))),
% 2.43/2.68 inference(modus_ponens,[status(thm)],[2241, 2240])).
% 2.43/2.68 tff(2243,plain,
% 2.43/2.68 ($false),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[2242, 87, 1702, 1694, 2228, 2227, 23, 1853, 2236])).
% 2.43/2.68 tff(2244,plain,(hskp53 | hskp41 | hskp17 | c3_1(a603) | hskp15), inference(lemma,lemma(discharge,[]))).
% 2.43/2.68 tff(2245,plain,
% 2.43/2.68 (c3_1(a603)),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[2244, 1745, 12, 97, 1748])).
% 2.43/2.68 tff(2246,plain,
% 2.43/2.68 (~hskp3),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[1344, 2245])).
% 2.43/2.68 tff(2247,plain,
% 2.43/2.68 (hskp29),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[1810, 13, 2246])).
% 2.43/2.68 tff(2248,plain,
% 2.43/2.68 (~c0_1(a660)),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[1352, 2247])).
% 2.43/2.68 tff(2249,plain,
% 2.43/2.68 (~c3_1(a660)),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[1358, 2247])).
% 2.43/2.68 tff(2250,plain,
% 2.43/2.68 (~c1_1(a660)),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[1364, 2247])).
% 2.43/2.68 tff(2251,plain,
% 2.43/2.68 (hskp61),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[1767, 13, 1668, 97, 1702, 1746])).
% 2.43/2.68 tff(2252,plain,
% 2.43/2.68 (~c0_1(a670)),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[348, 2251])).
% 2.43/2.68 tff(2253,plain,
% 2.43/2.68 (~c1_1(a670)),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[354, 2251])).
% 2.43/2.68 tff(2254,plain,
% 2.43/2.68 (c2_1(a670)),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[379, 2251])).
% 2.43/2.68 tff(2255,plain,
% 2.43/2.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a670) | c0_1(a670) | c1_1(a660) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | (~c2_1(a670)) | (~c3_1(a670)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a670) | c0_1(a670) | c1_1(a660) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | (~c2_1(a670)) | (~c3_1(a670)))),
% 2.43/2.68 inference(rewrite,[status(thm)],[])).
% 2.43/2.68 tff(2256,plain,
% 2.43/2.68 (((~ndr1_0) | c1_1(a670) | (~c3_1(a670)) | (~c2_1(a670)) | c1_1(a670) | c0_1(a670) | (~c3_1(a670)) | c1_1(a660) | c0_1(a660) | c3_1(a660)) <=> (c1_1(a670) | c0_1(a670) | c1_1(a660) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | (~c2_1(a670)) | (~c3_1(a670)))),
% 2.43/2.68 inference(rewrite,[status(thm)],[])).
% 2.43/2.68 tff(2257,plain,
% 2.43/2.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a670) | (~c3_1(a670)) | (~c2_1(a670)) | c1_1(a670) | c0_1(a670) | (~c3_1(a670)) | c1_1(a660) | c0_1(a660) | c3_1(a660))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a670) | c0_1(a670) | c1_1(a660) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | (~c2_1(a670)) | (~c3_1(a670))))),
% 2.43/2.68 inference(monotonicity,[status(thm)],[2256])).
% 2.43/2.68 tff(2258,plain,
% 2.43/2.68 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a670) | (~c3_1(a670)) | (~c2_1(a670)) | c1_1(a670) | c0_1(a670) | (~c3_1(a670)) | c1_1(a660) | c0_1(a660) | c3_1(a660))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a670) | c0_1(a670) | c1_1(a660) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | (~c2_1(a670)) | (~c3_1(a670)))),
% 2.43/2.68 inference(transitivity,[status(thm)],[2257, 2255])).
% 2.43/2.68 tff(2259,plain,
% 2.43/2.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a670) | (~c3_1(a670)) | (~c2_1(a670)) | c1_1(a670) | c0_1(a670) | (~c3_1(a670)) | c1_1(a660) | c0_1(a660) | c3_1(a660))),
% 2.43/2.68 inference(quant_inst,[status(thm)],[])).
% 2.43/2.68 tff(2260,plain,
% 2.43/2.68 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a670) | c0_1(a670) | c1_1(a660) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | (~c2_1(a670)) | (~c3_1(a670))),
% 2.43/2.68 inference(modus_ponens,[status(thm)],[2259, 2258])).
% 2.43/2.68 tff(2261,plain,
% 2.43/2.68 (~c3_1(a670)),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[2260, 87, 2254, 2253, 2252, 2250, 2249, 2248, 1113])).
% 2.43/2.68 tff(2262,plain,
% 2.43/2.68 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | (c1_1(a670) | c0_1(a670) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | c2_1(a660) | c3_1(a670))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | c1_1(a670) | c0_1(a670) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | c2_1(a660) | c3_1(a670))),
% 2.43/2.68 inference(rewrite,[status(thm)],[])).
% 2.43/2.68 tff(2263,plain,
% 2.43/2.68 (((~ndr1_0) | c3_1(a660) | c2_1(a660) | c0_1(a660) | c1_1(a670) | c3_1(a670) | c0_1(a670)) <=> (c1_1(a670) | c0_1(a670) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | c2_1(a660) | c3_1(a670))),
% 2.43/2.68 inference(rewrite,[status(thm)],[])).
% 2.43/2.68 tff(2264,plain,
% 2.43/2.68 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | ((~ndr1_0) | c3_1(a660) | c2_1(a660) | c0_1(a660) | c1_1(a670) | c3_1(a670) | c0_1(a670))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | (c1_1(a670) | c0_1(a670) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | c2_1(a660) | c3_1(a670)))),
% 2.43/2.68 inference(monotonicity,[status(thm)],[2263])).
% 2.43/2.68 tff(2265,plain,
% 2.43/2.68 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | ((~ndr1_0) | c3_1(a660) | c2_1(a660) | c0_1(a660) | c1_1(a670) | c3_1(a670) | c0_1(a670))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | c1_1(a670) | c0_1(a670) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | c2_1(a660) | c3_1(a670))),
% 2.43/2.68 inference(transitivity,[status(thm)],[2264, 2262])).
% 2.43/2.68 tff(2266,plain,
% 2.43/2.68 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | ((~ndr1_0) | c3_1(a660) | c2_1(a660) | c0_1(a660) | c1_1(a670) | c3_1(a670) | c0_1(a670))),
% 2.43/2.68 inference(quant_inst,[status(thm)],[])).
% 2.43/2.68 tff(2267,plain,
% 2.43/2.68 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | c1_1(a670) | c0_1(a670) | c3_1(a660) | c0_1(a660) | (~ndr1_0) | c2_1(a660) | c3_1(a670)),
% 2.43/2.68 inference(modus_ponens,[status(thm)],[2266, 2265])).
% 2.43/2.68 tff(2268,plain,
% 2.43/2.68 (c2_1(a660)),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[2267, 87, 2253, 2252, 2249, 2248, 170, 2261])).
% 2.43/2.68 tff(2269,plain,
% 2.43/2.68 (~hskp54),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[1838, 2268, 1745, 2248, 2249, 12])).
% 2.43/2.68 tff(2270,plain,
% 2.43/2.68 (hskp54 | hskp37 | c3_1(a670)),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[418, 87, 2254, 2252, 372])).
% 2.43/2.68 tff(2271,plain,
% 2.43/2.68 (hskp37),
% 2.43/2.68 inference(unit_resolution,[status(thm)],[2270, 2269, 2261])).
% 2.43/2.68 tff(2272,plain,
% 2.43/2.68 (~c2_1(a607)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[386, 2271])).
% 2.43/2.69 tff(2273,plain,
% 2.43/2.69 (c0_1(a607)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[394, 2271])).
% 2.43/2.69 tff(2274,plain,
% 2.43/2.69 (c1_1(a607)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[402, 2271])).
% 2.43/2.69 tff(2275,plain,
% 2.43/2.69 ($false),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[1850, 87, 97, 1668, 1702, 2274, 2273, 2272, 299, 13])).
% 2.43/2.69 tff(2276,plain,(c2_1(a673) | hskp41 | hskp17), inference(lemma,lemma(discharge,[]))).
% 2.43/2.69 tff(2277,plain,
% 2.43/2.69 (c2_1(a673)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[2276, 97, 12])).
% 2.43/2.69 tff(2278,plain,
% 2.43/2.69 (~hskp61),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[1870, 2277, 1694, 1702])).
% 2.43/2.69 tff(2279,plain,
% 2.43/2.69 (hskp60),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[342, 2278, 1747])).
% 2.43/2.69 tff(2280,plain,
% 2.43/2.69 (~c2_1(a669)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[305, 2279])).
% 2.43/2.69 tff(2281,plain,
% 2.43/2.69 (~hskp14),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[221, 1745, 12, 97])).
% 2.43/2.69 tff(2282,plain,
% 2.43/2.69 (~hskp62),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[1912, 2281, 1748, 1746, 97])).
% 2.43/2.69 tff(2283,plain,
% 2.43/2.69 (c0_1(a669)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[322, 2279])).
% 2.43/2.69 tff(2284,plain,
% 2.43/2.69 (hskp29),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[2225, 2283, 2282, 1746, 97, 2246, 2280])).
% 2.43/2.69 tff(2285,plain,
% 2.43/2.69 (~c0_1(a660)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[1352, 2284])).
% 2.43/2.69 tff(2286,plain,
% 2.43/2.69 (~c3_1(a660)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[1358, 2284])).
% 2.43/2.69 tff(2287,plain,
% 2.43/2.69 (~c1_1(a660)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[1364, 2284])).
% 2.43/2.69 tff(2288,plain,
% 2.43/2.69 (c2_1(a660)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[2235, 87, 2287, 2286, 2285, 170])).
% 2.43/2.69 tff(2289,plain,
% 2.43/2.69 ($false),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[2242, 87, 1702, 1694, 2286, 2285, 23, 2277, 2288])).
% 2.43/2.69 tff(2290,plain,(hskp41 | hskp17), inference(lemma,lemma(discharge,[]))).
% 2.43/2.69 tff(2291,plain,
% 2.43/2.69 (hskp41),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[2290, 12])).
% 2.43/2.69 tff(2292,plain,
% 2.43/2.69 (c2_1(a617)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[496, 2291])).
% 2.43/2.69 tff(2293,plain,
% 2.43/2.69 (~c1_1(a617)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[463, 2291])).
% 2.43/2.69 tff(2294,plain,
% 2.43/2.69 (c3_1(a617)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[471, 2291])).
% 2.43/2.69 tff(2295,plain,
% 2.43/2.69 (c0_1(a617)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[1373, 1347, 2294, 2293, 2292])).
% 2.43/2.69 tff(2296,plain,
% 2.43/2.69 (c2_1(a660)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[2235, 87, 1365, 1359, 1353, 170])).
% 2.43/2.69 tff(2297,plain,
% 2.43/2.69 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (c3_1(a660) | c0_1(a660) | c1_1(a635) | c2_1(a635) | c3_1(a635) | (~ndr1_0) | (~c2_1(a660)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | c3_1(a660) | c0_1(a660) | c1_1(a635) | c2_1(a635) | c3_1(a635) | (~ndr1_0) | (~c2_1(a660)))),
% 2.43/2.69 inference(rewrite,[status(thm)],[])).
% 2.43/2.69 tff(2298,plain,
% 2.43/2.69 (((~ndr1_0) | c3_1(a660) | c0_1(a660) | (~c2_1(a660)) | c1_1(a635) | c3_1(a635) | c2_1(a635)) <=> (c3_1(a660) | c0_1(a660) | c1_1(a635) | c2_1(a635) | c3_1(a635) | (~ndr1_0) | (~c2_1(a660)))),
% 2.43/2.69 inference(rewrite,[status(thm)],[])).
% 2.43/2.69 tff(2299,plain,
% 2.43/2.69 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | ((~ndr1_0) | c3_1(a660) | c0_1(a660) | (~c2_1(a660)) | c1_1(a635) | c3_1(a635) | c2_1(a635))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (c3_1(a660) | c0_1(a660) | c1_1(a635) | c2_1(a635) | c3_1(a635) | (~ndr1_0) | (~c2_1(a660))))),
% 2.43/2.69 inference(monotonicity,[status(thm)],[2298])).
% 2.43/2.69 tff(2300,plain,
% 2.43/2.69 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | ((~ndr1_0) | c3_1(a660) | c0_1(a660) | (~c2_1(a660)) | c1_1(a635) | c3_1(a635) | c2_1(a635))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | c3_1(a660) | c0_1(a660) | c1_1(a635) | c2_1(a635) | c3_1(a635) | (~ndr1_0) | (~c2_1(a660)))),
% 2.43/2.69 inference(transitivity,[status(thm)],[2299, 2297])).
% 2.43/2.69 tff(2301,plain,
% 2.43/2.69 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | ((~ndr1_0) | c3_1(a660) | c0_1(a660) | (~c2_1(a660)) | c1_1(a635) | c3_1(a635) | c2_1(a635))),
% 2.43/2.69 inference(quant_inst,[status(thm)],[])).
% 2.43/2.69 tff(2302,plain,
% 2.43/2.69 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | c3_1(a660) | c0_1(a660) | c1_1(a635) | c2_1(a635) | c3_1(a635) | (~ndr1_0) | (~c2_1(a660))),
% 2.43/2.69 inference(modus_ponens,[status(thm)],[2301, 2300])).
% 2.43/2.69 tff(2303,plain,
% 2.43/2.69 ($false),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[2302, 87, 1829, 1828, 620, 614, 608, 599, 1827])).
% 2.43/2.69 tff(2304,plain,((~hskp20) | c3_1(a660) | c0_1(a660) | (~c2_1(a660))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.69 tff(2305,plain,
% 2.43/2.69 (~hskp20),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[2304, 1359, 1353, 2296])).
% 2.43/2.69 tff(2306,plain,
% 2.43/2.69 ($false),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[1198, 213, 200, 635, 647, 646, 192, 648, 649])).
% 2.43/2.69 tff(2307,plain,((~hskp14) | (~c0_1(a617)) | c1_1(a617) | hskp20 | (~c3_1(a617)) | (~c2_1(a617))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.69 tff(2308,plain,
% 2.43/2.69 (~hskp14),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[2307, 2295, 2293, 2305, 2294, 2292])).
% 2.43/2.69 tff(2309,plain,
% 2.43/2.69 (hskp15 | hskp14 | (~c0_1(a617))),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[552, 87, 2292, 2293, 232])).
% 2.43/2.69 tff(2310,plain,
% 2.43/2.69 (hskp15),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[2309, 2308, 2295])).
% 2.43/2.69 tff(2311,plain,
% 2.43/2.69 (hskp53),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[184, 2310, 12])).
% 2.43/2.69 tff(2312,plain,
% 2.43/2.69 (c3_1(a648)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[800, 2311])).
% 2.43/2.69 tff(2313,plain,
% 2.43/2.69 (c0_1(a648)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[792, 2311])).
% 2.43/2.69 tff(2314,plain,
% 2.43/2.69 (~c2_1(a648)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[784, 2311])).
% 2.43/2.69 tff(2315,assumption,(~hskp38), introduced(assumption)).
% 2.43/2.69 tff(2316,plain,
% 2.43/2.69 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp38 | c0_1(a673) | c2_1(a625) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | (~c3_1(a673)) | (~c1_1(a673)))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp38 | c0_1(a673) | c2_1(a625) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | (~c3_1(a673)) | (~c1_1(a673)))),
% 2.43/2.69 inference(rewrite,[status(thm)],[])).
% 2.43/2.69 tff(2317,plain,
% 2.43/2.69 ((hskp38 | (~ndr1_0) | c0_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c1_1(a625) | c0_1(a625) | c2_1(a625)) <=> (hskp38 | c0_1(a673) | c2_1(a625) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | (~c3_1(a673)) | (~c1_1(a673)))),
% 2.43/2.69 inference(rewrite,[status(thm)],[])).
% 2.43/2.69 tff(2318,plain,
% 2.43/2.69 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp38 | (~ndr1_0) | c0_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c1_1(a625) | c0_1(a625) | c2_1(a625))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp38 | c0_1(a673) | c2_1(a625) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | (~c3_1(a673)) | (~c1_1(a673))))),
% 2.43/2.69 inference(monotonicity,[status(thm)],[2317])).
% 2.43/2.69 tff(2319,plain,
% 2.43/2.69 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp38 | (~ndr1_0) | c0_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c1_1(a625) | c0_1(a625) | c2_1(a625))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp38 | c0_1(a673) | c2_1(a625) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | (~c3_1(a673)) | (~c1_1(a673)))),
% 2.43/2.69 inference(transitivity,[status(thm)],[2318, 2316])).
% 2.43/2.69 tff(2320,plain,
% 2.43/2.69 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp38 | (~ndr1_0) | c0_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c1_1(a625) | c0_1(a625) | c2_1(a625))),
% 2.43/2.69 inference(quant_inst,[status(thm)],[])).
% 2.43/2.69 tff(2321,plain,
% 2.43/2.69 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp38 | c0_1(a673) | c2_1(a625) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | (~c3_1(a673)) | (~c1_1(a673))),
% 2.43/2.69 inference(modus_ponens,[status(thm)],[2320, 2319])).
% 2.43/2.69 tff(2322,plain,
% 2.43/2.69 ($false),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[2321, 87, 2315, 1752, 1751, 1855, 1536, 1526, 1525, 11])).
% 2.43/2.69 tff(2323,plain,(c1_1(a625) | hskp38 | (~c3_1(a673)) | (~c1_1(a673)) | c0_1(a673) | c2_1(a625) | c0_1(a625)), inference(lemma,lemma(discharge,[]))).
% 2.43/2.69 tff(2324,plain,
% 2.43/2.69 ($false),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[2323, 147, 153, 1752, 1751, 1855, 2315, 1536])).
% 2.43/2.69 tff(2325,plain,((~hskp15) | (~c3_1(a673)) | (~c1_1(a673)) | c0_1(a673) | hskp38 | c2_1(a625)), inference(lemma,lemma(discharge,[]))).
% 2.43/2.69 tff(2326,plain,
% 2.43/2.69 ($false),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[2325, 176, 141, 1751, 1855, 2315, 1752])).
% 2.43/2.69 tff(2327,plain,((~hskp15) | (~c1_1(a673)) | c0_1(a673) | hskp38 | (~c3_1(a673))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.69 tff(2328,plain,
% 2.43/2.69 (hskp38),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[2327, 141, 1855, 1751, 1752])).
% 2.43/2.69 tff(2329,assumption,(hskp38), introduced(assumption)).
% 2.43/2.69 tff(2330,plain,
% 2.43/2.69 (((~hskp38) | c0_1(a608)) <=> ((~hskp38) | c0_1(a608))),
% 2.43/2.69 inference(rewrite,[status(thm)],[])).
% 2.43/2.69 tff(2331,axiom,((~hskp38) | c0_1(a608)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause128')).
% 2.43/2.69 tff(2332,plain,
% 2.43/2.69 ((~hskp38) | c0_1(a608)),
% 2.43/2.69 inference(modus_ponens,[status(thm)],[2331, 2330])).
% 2.43/2.69 tff(2333,plain,
% 2.43/2.69 ((~hskp38) | c0_1(a608)),
% 2.43/2.69 inference(modus_ponens,[status(thm)],[2332, 2330])).
% 2.43/2.69 tff(2334,plain,
% 2.43/2.69 ((~hskp38) | c0_1(a608)),
% 2.43/2.69 inference(modus_ponens,[status(thm)],[2333, 2330])).
% 2.43/2.69 tff(2335,plain,
% 2.43/2.69 ((~hskp38) | c0_1(a608)),
% 2.43/2.69 inference(modus_ponens,[status(thm)],[2334, 2330])).
% 2.43/2.69 tff(2336,plain,
% 2.43/2.69 ((~hskp38) | c0_1(a608)),
% 2.43/2.69 inference(modus_ponens,[status(thm)],[2335, 2330])).
% 2.43/2.69 tff(2337,plain,
% 2.43/2.69 (c0_1(a608)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[2336, 2329])).
% 2.43/2.69 tff(2338,plain,
% 2.43/2.69 (((~hskp38) | c3_1(a608)) <=> ((~hskp38) | c3_1(a608))),
% 2.43/2.69 inference(rewrite,[status(thm)],[])).
% 2.43/2.69 tff(2339,axiom,((~hskp38) | c3_1(a608)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause127')).
% 2.43/2.69 tff(2340,plain,
% 2.43/2.69 ((~hskp38) | c3_1(a608)),
% 2.43/2.69 inference(modus_ponens,[status(thm)],[2339, 2338])).
% 2.43/2.69 tff(2341,plain,
% 2.43/2.69 ((~hskp38) | c3_1(a608)),
% 2.43/2.69 inference(modus_ponens,[status(thm)],[2340, 2338])).
% 2.43/2.69 tff(2342,plain,
% 2.43/2.69 ((~hskp38) | c3_1(a608)),
% 2.43/2.69 inference(modus_ponens,[status(thm)],[2341, 2338])).
% 2.43/2.69 tff(2343,plain,
% 2.43/2.69 ((~hskp38) | c3_1(a608)),
% 2.43/2.69 inference(modus_ponens,[status(thm)],[2342, 2338])).
% 2.43/2.69 tff(2344,plain,
% 2.43/2.69 ((~hskp38) | c3_1(a608)),
% 2.43/2.69 inference(modus_ponens,[status(thm)],[2343, 2338])).
% 2.43/2.69 tff(2345,plain,
% 2.43/2.69 (c3_1(a608)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[2344, 2329])).
% 2.43/2.69 tff(2346,plain,
% 2.43/2.69 (((~hskp38) | c1_1(a608)) <=> ((~hskp38) | c1_1(a608))),
% 2.43/2.69 inference(rewrite,[status(thm)],[])).
% 2.43/2.69 tff(2347,axiom,((~hskp38) | c1_1(a608)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause126')).
% 2.43/2.69 tff(2348,plain,
% 2.43/2.69 ((~hskp38) | c1_1(a608)),
% 2.43/2.69 inference(modus_ponens,[status(thm)],[2347, 2346])).
% 2.43/2.69 tff(2349,plain,
% 2.43/2.69 ((~hskp38) | c1_1(a608)),
% 2.43/2.69 inference(modus_ponens,[status(thm)],[2348, 2346])).
% 2.43/2.69 tff(2350,plain,
% 2.43/2.69 ((~hskp38) | c1_1(a608)),
% 2.43/2.69 inference(modus_ponens,[status(thm)],[2349, 2346])).
% 2.43/2.69 tff(2351,plain,
% 2.43/2.69 ((~hskp38) | c1_1(a608)),
% 2.43/2.69 inference(modus_ponens,[status(thm)],[2350, 2346])).
% 2.43/2.69 tff(2352,plain,
% 2.43/2.69 ((~hskp38) | c1_1(a608)),
% 2.43/2.69 inference(modus_ponens,[status(thm)],[2351, 2346])).
% 2.43/2.69 tff(2353,plain,
% 2.43/2.69 (c1_1(a608)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[2352, 2329])).
% 2.43/2.69 tff(2354,assumption,(~hskp6), introduced(assumption)).
% 2.43/2.69 tff(2355,plain,
% 2.43/2.69 (((~![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp6 | (~ndr1_0) | (~c3_1(a608)) | (~c1_1(a608)) | (~c0_1(a608)))) <=> ((~![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp6 | (~ndr1_0) | (~c3_1(a608)) | (~c1_1(a608)) | (~c0_1(a608)))),
% 2.43/2.69 inference(rewrite,[status(thm)],[])).
% 2.43/2.69 tff(2356,plain,
% 2.43/2.69 ((~![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp6 | (~ndr1_0) | (~c3_1(a608)) | (~c1_1(a608)) | (~c0_1(a608)))),
% 2.43/2.69 inference(quant_inst,[status(thm)],[])).
% 2.43/2.69 tff(2357,plain,
% 2.43/2.69 ((~![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp6 | (~ndr1_0) | (~c3_1(a608)) | (~c1_1(a608)) | (~c0_1(a608))),
% 2.43/2.69 inference(modus_ponens,[status(thm)],[2356, 2355])).
% 2.43/2.69 tff(2358,plain,
% 2.43/2.69 ($false),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[2357, 87, 2354, 2353, 2345, 2337, 679])).
% 2.43/2.69 tff(2359,plain,((~hskp38) | hskp6), inference(lemma,lemma(discharge,[]))).
% 2.43/2.69 tff(2360,plain,
% 2.43/2.69 (hskp6),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[2359, 2328])).
% 2.43/2.69 tff(2361,plain,
% 2.43/2.69 (c2_1(a609)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[701, 2360])).
% 2.43/2.69 tff(2362,assumption,(hskp16), introduced(assumption)).
% 2.43/2.69 tff(2363,plain,
% 2.43/2.69 (~c0_1(a609)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[691, 2360])).
% 2.43/2.69 tff(2364,plain,
% 2.43/2.69 (~c1_1(a609)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[1395, 2360])).
% 2.43/2.69 tff(2365,assumption,(~c1_1(a609)), introduced(assumption)).
% 2.43/2.69 tff(2366,plain,
% 2.43/2.69 (~c3_1(a627)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[1068, 2362])).
% 2.43/2.69 tff(2367,plain,
% 2.43/2.69 (c2_1(a627)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[1076, 2362])).
% 2.43/2.69 tff(2368,plain,
% 2.43/2.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a627) | c2_1(a625) | c1_1(a625) | c0_1(a625) | c0_1(a609) | c1_1(a609) | (~ndr1_0) | (~c2_1(a609)) | (~c2_1(a627)) | c1_1(a627))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a627) | c2_1(a625) | c1_1(a625) | c0_1(a625) | c0_1(a609) | c1_1(a609) | (~ndr1_0) | (~c2_1(a609)) | (~c2_1(a627)) | c1_1(a627))),
% 2.43/2.69 inference(rewrite,[status(thm)],[])).
% 2.43/2.69 tff(2369,plain,
% 2.43/2.69 (((~ndr1_0) | c3_1(a627) | c1_1(a627) | (~c2_1(a627)) | c1_1(a609) | c0_1(a609) | (~c2_1(a609)) | c2_1(a625) | c1_1(a625) | c0_1(a625)) <=> (c3_1(a627) | c2_1(a625) | c1_1(a625) | c0_1(a625) | c0_1(a609) | c1_1(a609) | (~ndr1_0) | (~c2_1(a609)) | (~c2_1(a627)) | c1_1(a627))),
% 2.43/2.69 inference(rewrite,[status(thm)],[])).
% 2.43/2.69 tff(2370,plain,
% 2.43/2.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a627) | c1_1(a627) | (~c2_1(a627)) | c1_1(a609) | c0_1(a609) | (~c2_1(a609)) | c2_1(a625) | c1_1(a625) | c0_1(a625))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a627) | c2_1(a625) | c1_1(a625) | c0_1(a625) | c0_1(a609) | c1_1(a609) | (~ndr1_0) | (~c2_1(a609)) | (~c2_1(a627)) | c1_1(a627)))),
% 2.43/2.69 inference(monotonicity,[status(thm)],[2369])).
% 2.43/2.69 tff(2371,plain,
% 2.43/2.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a627) | c1_1(a627) | (~c2_1(a627)) | c1_1(a609) | c0_1(a609) | (~c2_1(a609)) | c2_1(a625) | c1_1(a625) | c0_1(a625))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a627) | c2_1(a625) | c1_1(a625) | c0_1(a625) | c0_1(a609) | c1_1(a609) | (~ndr1_0) | (~c2_1(a609)) | (~c2_1(a627)) | c1_1(a627))),
% 2.43/2.69 inference(transitivity,[status(thm)],[2370, 2368])).
% 2.43/2.69 tff(2372,plain,
% 2.43/2.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a627) | c1_1(a627) | (~c2_1(a627)) | c1_1(a609) | c0_1(a609) | (~c2_1(a609)) | c2_1(a625) | c1_1(a625) | c0_1(a625))),
% 2.43/2.69 inference(quant_inst,[status(thm)],[])).
% 2.43/2.69 tff(2373,plain,
% 2.43/2.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a627) | c2_1(a625) | c1_1(a625) | c0_1(a625) | c0_1(a609) | c1_1(a609) | (~ndr1_0) | (~c2_1(a609)) | (~c2_1(a627)) | c1_1(a627)),
% 2.43/2.69 inference(modus_ponens,[status(thm)],[2372, 2371])).
% 2.43/2.69 tff(2374,plain,
% 2.43/2.69 (c1_1(a627)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[2373, 87, 2367, 1409, 2366, 1536, 1526, 1525, 1408, 2365, 1279])).
% 2.43/2.69 tff(2375,plain,
% 2.43/2.69 (c0_1(a627)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[1091, 2362])).
% 2.43/2.69 tff(2376,plain,
% 2.43/2.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))) | (c3_1(a627) | (~ndr1_0) | (~c2_1(a627)) | (~c0_1(a627)) | (~c1_1(a627)) | (~c2_1(a617)) | (~c3_1(a617)) | (~c0_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))) | c3_1(a627) | (~ndr1_0) | (~c2_1(a627)) | (~c0_1(a627)) | (~c1_1(a627)) | (~c2_1(a617)) | (~c3_1(a617)) | (~c0_1(a617)))),
% 2.43/2.69 inference(rewrite,[status(thm)],[])).
% 2.43/2.69 tff(2377,plain,
% 2.43/2.69 (((~ndr1_0) | (~c3_1(a617)) | (~c0_1(a617)) | (~c2_1(a617)) | c3_1(a627) | (~c2_1(a627)) | (~c0_1(a627)) | (~c0_1(a627)) | (~c1_1(a627)) | (~c2_1(a627))) <=> (c3_1(a627) | (~ndr1_0) | (~c2_1(a627)) | (~c0_1(a627)) | (~c1_1(a627)) | (~c2_1(a617)) | (~c3_1(a617)) | (~c0_1(a617)))),
% 2.43/2.69 inference(rewrite,[status(thm)],[])).
% 2.43/2.69 tff(2378,plain,
% 2.43/2.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a617)) | (~c0_1(a617)) | (~c2_1(a617)) | c3_1(a627) | (~c2_1(a627)) | (~c0_1(a627)) | (~c0_1(a627)) | (~c1_1(a627)) | (~c2_1(a627)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))) | (c3_1(a627) | (~ndr1_0) | (~c2_1(a627)) | (~c0_1(a627)) | (~c1_1(a627)) | (~c2_1(a617)) | (~c3_1(a617)) | (~c0_1(a617))))),
% 2.43/2.69 inference(monotonicity,[status(thm)],[2377])).
% 2.43/2.69 tff(2379,plain,
% 2.43/2.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a617)) | (~c0_1(a617)) | (~c2_1(a617)) | c3_1(a627) | (~c2_1(a627)) | (~c0_1(a627)) | (~c0_1(a627)) | (~c1_1(a627)) | (~c2_1(a627)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))) | c3_1(a627) | (~ndr1_0) | (~c2_1(a627)) | (~c0_1(a627)) | (~c1_1(a627)) | (~c2_1(a617)) | (~c3_1(a617)) | (~c0_1(a617)))),
% 2.43/2.69 inference(transitivity,[status(thm)],[2378, 2376])).
% 2.43/2.69 tff(2380,plain,
% 2.43/2.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a617)) | (~c0_1(a617)) | (~c2_1(a617)) | c3_1(a627) | (~c2_1(a627)) | (~c0_1(a627)) | (~c0_1(a627)) | (~c1_1(a627)) | (~c2_1(a627)))),
% 2.43/2.69 inference(quant_inst,[status(thm)],[])).
% 2.43/2.69 tff(2381,plain,
% 2.43/2.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))) | c3_1(a627) | (~ndr1_0) | (~c2_1(a627)) | (~c0_1(a627)) | (~c1_1(a627)) | (~c2_1(a617)) | (~c3_1(a617)) | (~c0_1(a617))),
% 2.43/2.69 inference(modus_ponens,[status(thm)],[2380, 2379])).
% 2.43/2.69 tff(2382,plain,
% 2.43/2.69 ((~c1_1(a627)) | (~c0_1(a617))),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[2381, 87, 964, 963, 2367, 2375, 2366, 1991])).
% 2.43/2.69 tff(2383,plain,
% 2.43/2.69 (~c0_1(a617)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[2382, 2374])).
% 2.43/2.69 tff(2384,plain,
% 2.43/2.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | (c2_1(a648) | c3_1(a627) | c0_1(a609) | (~ndr1_0) | (~c3_1(a609)) | (~c2_1(a609)) | (~c2_1(a627)) | (~c1_1(a627)) | (~c0_1(a648)) | (~c3_1(a648)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c2_1(a648) | c3_1(a627) | c0_1(a609) | (~ndr1_0) | (~c3_1(a609)) | (~c2_1(a609)) | (~c2_1(a627)) | (~c1_1(a627)) | (~c0_1(a648)) | (~c3_1(a648)))),
% 2.43/2.69 inference(rewrite,[status(thm)],[])).
% 2.43/2.69 tff(2385,plain,
% 2.43/2.69 (((~ndr1_0) | c3_1(a627) | (~c1_1(a627)) | (~c2_1(a627)) | c0_1(a609) | (~c2_1(a609)) | (~c3_1(a609)) | c2_1(a648) | (~c0_1(a648)) | (~c3_1(a648))) <=> (c2_1(a648) | c3_1(a627) | c0_1(a609) | (~ndr1_0) | (~c3_1(a609)) | (~c2_1(a609)) | (~c2_1(a627)) | (~c1_1(a627)) | (~c0_1(a648)) | (~c3_1(a648)))),
% 2.43/2.69 inference(rewrite,[status(thm)],[])).
% 2.43/2.69 tff(2386,plain,
% 2.43/2.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a627) | (~c1_1(a627)) | (~c2_1(a627)) | c0_1(a609) | (~c2_1(a609)) | (~c3_1(a609)) | c2_1(a648) | (~c0_1(a648)) | (~c3_1(a648)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | (c2_1(a648) | c3_1(a627) | c0_1(a609) | (~ndr1_0) | (~c3_1(a609)) | (~c2_1(a609)) | (~c2_1(a627)) | (~c1_1(a627)) | (~c0_1(a648)) | (~c3_1(a648))))),
% 2.43/2.69 inference(monotonicity,[status(thm)],[2385])).
% 2.43/2.69 tff(2387,plain,
% 2.43/2.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a627) | (~c1_1(a627)) | (~c2_1(a627)) | c0_1(a609) | (~c2_1(a609)) | (~c3_1(a609)) | c2_1(a648) | (~c0_1(a648)) | (~c3_1(a648)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c2_1(a648) | c3_1(a627) | c0_1(a609) | (~ndr1_0) | (~c3_1(a609)) | (~c2_1(a609)) | (~c2_1(a627)) | (~c1_1(a627)) | (~c0_1(a648)) | (~c3_1(a648)))),
% 2.43/2.69 inference(transitivity,[status(thm)],[2386, 2384])).
% 2.43/2.69 tff(2388,plain,
% 2.43/2.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a627) | (~c1_1(a627)) | (~c2_1(a627)) | c0_1(a609) | (~c2_1(a609)) | (~c3_1(a609)) | c2_1(a648) | (~c0_1(a648)) | (~c3_1(a648)))),
% 2.43/2.69 inference(quant_inst,[status(thm)],[])).
% 2.43/2.69 tff(2389,plain,
% 2.43/2.69 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c2_1(a648) | c3_1(a627) | c0_1(a609) | (~ndr1_0) | (~c3_1(a609)) | (~c2_1(a609)) | (~c2_1(a627)) | (~c1_1(a627)) | (~c0_1(a648)) | (~c3_1(a648))),
% 2.43/2.69 inference(modus_ponens,[status(thm)],[2388, 2387])).
% 2.43/2.69 tff(2390,plain,
% 2.43/2.69 ((~c3_1(a609)) | (~c1_1(a627))),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[2389, 87, 804, 803, 2367, 1409, 802, 2366, 1408, 953])).
% 2.43/2.69 tff(2391,plain,
% 2.43/2.69 (~c3_1(a609)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[2390, 2374])).
% 2.43/2.69 tff(2392,plain,
% 2.43/2.69 (c3_1(a609) | c0_1(a617)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[1403, 87, 964, 963, 961, 1408, 2365, 1113])).
% 2.43/2.69 tff(2393,plain,
% 2.43/2.69 ($false),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[2392, 2391, 2383])).
% 2.43/2.69 tff(2394,plain,((~hskp16) | c0_1(a609) | c1_1(a609) | (~c3_1(a648)) | (~c0_1(a648)) | (~c2_1(a609)) | c2_1(a648) | c2_1(a625) | c1_1(a625) | c0_1(a625)), inference(lemma,lemma(discharge,[]))).
% 2.43/2.69 tff(2395,plain,
% 2.43/2.69 ($false),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[2394, 2364, 2363, 2362, 804, 803, 2361, 802, 176, 153, 147])).
% 2.43/2.69 tff(2396,plain,((~hskp15) | (~hskp16) | (~c3_1(a648)) | (~c0_1(a648)) | c2_1(a648) | c0_1(a673) | (~c1_1(a673)) | (~c3_1(a673))), inference(lemma,lemma(discharge,[]))).
% 2.43/2.69 tff(2397,plain,
% 2.43/2.69 ($false),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[2396, 2314, 2313, 1702, 1694, 2310, 2312, 1738, 1668])).
% 2.43/2.69 tff(2398,plain,((~hskp29) | hskp17 | c2_1(a673)), inference(lemma,lemma(discharge,[]))).
% 2.43/2.69 tff(2399,plain,
% 2.43/2.69 (~hskp29),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[2398, 13, 12])).
% 2.43/2.69 tff(2400,plain,
% 2.43/2.69 (hskp3),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[1810, 2399, 13])).
% 2.43/2.69 tff(2401,plain,
% 2.43/2.69 (~c3_1(a603)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[1344, 2400])).
% 2.43/2.69 tff(2402,assumption,(~hskp16), introduced(assumption)).
% 2.43/2.69 tff(2403,plain,
% 2.43/2.69 (c0_1(a603)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[1565, 2400])).
% 2.43/2.69 tff(2404,plain,
% 2.43/2.69 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp16 | c0_1(a673) | c3_1(a603) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c2_1(a603)) | (~c0_1(a603)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp16 | c0_1(a673) | c3_1(a603) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c2_1(a603)) | (~c0_1(a603)))),
% 2.43/2.69 inference(rewrite,[status(thm)],[])).
% 2.43/2.69 tff(2405,plain,
% 2.43/2.69 ((hskp16 | (~ndr1_0) | c3_1(a603) | (~c0_1(a603)) | (~c2_1(a603)) | c0_1(a673) | c2_1(a673) | (~c3_1(a673))) <=> (hskp16 | c0_1(a673) | c3_1(a603) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c2_1(a603)) | (~c0_1(a603)))),
% 2.43/2.69 inference(rewrite,[status(thm)],[])).
% 2.43/2.69 tff(2406,plain,
% 2.43/2.69 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a603) | (~c0_1(a603)) | (~c2_1(a603)) | c0_1(a673) | c2_1(a673) | (~c3_1(a673)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp16 | c0_1(a673) | c3_1(a603) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c2_1(a603)) | (~c0_1(a603))))),
% 2.43/2.69 inference(monotonicity,[status(thm)],[2405])).
% 2.43/2.69 tff(2407,plain,
% 2.43/2.69 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a603) | (~c0_1(a603)) | (~c2_1(a603)) | c0_1(a673) | c2_1(a673) | (~c3_1(a673)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp16 | c0_1(a673) | c3_1(a603) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c2_1(a603)) | (~c0_1(a603)))),
% 2.43/2.69 inference(transitivity,[status(thm)],[2406, 2404])).
% 2.43/2.69 tff(2408,plain,
% 2.43/2.69 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a603) | (~c0_1(a603)) | (~c2_1(a603)) | c0_1(a673) | c2_1(a673) | (~c3_1(a673)))),
% 2.43/2.69 inference(quant_inst,[status(thm)],[])).
% 2.43/2.69 tff(2409,plain,
% 2.43/2.69 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp16 | c0_1(a673) | c3_1(a603) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c2_1(a603)) | (~c0_1(a603))),
% 2.43/2.69 inference(modus_ponens,[status(thm)],[2408, 2407])).
% 2.43/2.69 tff(2410,plain,
% 2.43/2.69 (hskp16 | (~c2_1(a603))),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[2409, 87, 1668, 2403, 1694, 2401, 1678, 13])).
% 2.43/2.69 tff(2411,plain,
% 2.43/2.69 (~c2_1(a603)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[2410, 2402])).
% 2.43/2.69 tff(2412,plain,
% 2.43/2.69 (hskp20 | c2_1(a603)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[1145, 87, 2292, 2294, 2403, 2293, 2401, 660])).
% 2.43/2.69 tff(2413,plain,
% 2.43/2.69 (hskp20),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[2412, 2411])).
% 2.43/2.69 tff(2414,plain,
% 2.43/2.69 (~c1_1(a635)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[619, 2413])).
% 2.43/2.69 tff(2415,plain,
% 2.43/2.69 (~c2_1(a635)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[613, 2413])).
% 2.43/2.69 tff(2416,plain,
% 2.43/2.69 (~c3_1(a635)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[607, 2413])).
% 2.43/2.69 tff(2417,plain,
% 2.43/2.69 (hskp9),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[1062, 2402, 12])).
% 2.43/2.69 tff(2418,plain,
% 2.43/2.69 (~c3_1(a613)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[1025, 2417])).
% 2.43/2.69 tff(2419,plain,
% 2.43/2.69 (c2_1(a613)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[1034, 2417])).
% 2.43/2.69 tff(2420,plain,
% 2.43/2.69 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp16 | c0_1(a673) | c3_1(a613) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c2_1(a613)) | (~c0_1(a613)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp16 | c0_1(a673) | c3_1(a613) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c2_1(a613)) | (~c0_1(a613)))),
% 2.43/2.69 inference(rewrite,[status(thm)],[])).
% 2.43/2.69 tff(2421,plain,
% 2.43/2.69 ((hskp16 | (~ndr1_0) | c3_1(a613) | (~c0_1(a613)) | (~c2_1(a613)) | c0_1(a673) | c2_1(a673) | (~c3_1(a673))) <=> (hskp16 | c0_1(a673) | c3_1(a613) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c2_1(a613)) | (~c0_1(a613)))),
% 2.43/2.69 inference(rewrite,[status(thm)],[])).
% 2.43/2.69 tff(2422,plain,
% 2.43/2.69 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a613) | (~c0_1(a613)) | (~c2_1(a613)) | c0_1(a673) | c2_1(a673) | (~c3_1(a673)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp16 | c0_1(a673) | c3_1(a613) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c2_1(a613)) | (~c0_1(a613))))),
% 2.43/2.69 inference(monotonicity,[status(thm)],[2421])).
% 2.43/2.69 tff(2423,plain,
% 2.43/2.69 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a613) | (~c0_1(a613)) | (~c2_1(a613)) | c0_1(a673) | c2_1(a673) | (~c3_1(a673)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp16 | c0_1(a673) | c3_1(a613) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c2_1(a613)) | (~c0_1(a613)))),
% 2.43/2.69 inference(transitivity,[status(thm)],[2422, 2420])).
% 2.43/2.69 tff(2424,plain,
% 2.43/2.69 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a613) | (~c0_1(a613)) | (~c2_1(a613)) | c0_1(a673) | c2_1(a673) | (~c3_1(a673)))),
% 2.43/2.69 inference(quant_inst,[status(thm)],[])).
% 2.43/2.69 tff(2425,plain,
% 2.43/2.69 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | (~c0_1(U)) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp16 | c0_1(a673) | c3_1(a613) | (~ndr1_0) | c2_1(a673) | (~c3_1(a673)) | (~c2_1(a613)) | (~c0_1(a613))),
% 2.43/2.69 inference(modus_ponens,[status(thm)],[2424, 2423])).
% 2.43/2.69 tff(2426,plain,
% 2.43/2.69 (~c0_1(a613)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[2425, 87, 2402, 1752, 2419, 1855, 2418, 1678, 13])).
% 2.43/2.69 tff(2427,assumption,(~c3_1(a635)), introduced(assumption)).
% 2.43/2.69 tff(2428,plain,
% 2.43/2.69 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (c1_1(a635) | c2_1(a635) | c3_1(a635) | c3_1(a613) | (~ndr1_0) | (~c2_1(a613)) | c0_1(a613))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | c1_1(a635) | c2_1(a635) | c3_1(a635) | c3_1(a613) | (~ndr1_0) | (~c2_1(a613)) | c0_1(a613))),
% 2.43/2.69 inference(rewrite,[status(thm)],[])).
% 2.43/2.69 tff(2429,plain,
% 2.43/2.69 (((~ndr1_0) | c3_1(a613) | c0_1(a613) | (~c2_1(a613)) | c1_1(a635) | c3_1(a635) | c2_1(a635)) <=> (c1_1(a635) | c2_1(a635) | c3_1(a635) | c3_1(a613) | (~ndr1_0) | (~c2_1(a613)) | c0_1(a613))),
% 2.43/2.69 inference(rewrite,[status(thm)],[])).
% 2.43/2.69 tff(2430,plain,
% 2.43/2.69 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | ((~ndr1_0) | c3_1(a613) | c0_1(a613) | (~c2_1(a613)) | c1_1(a635) | c3_1(a635) | c2_1(a635))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | (c1_1(a635) | c2_1(a635) | c3_1(a635) | c3_1(a613) | (~ndr1_0) | (~c2_1(a613)) | c0_1(a613)))),
% 2.43/2.69 inference(monotonicity,[status(thm)],[2429])).
% 2.43/2.69 tff(2431,plain,
% 2.43/2.69 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | ((~ndr1_0) | c3_1(a613) | c0_1(a613) | (~c2_1(a613)) | c1_1(a635) | c3_1(a635) | c2_1(a635))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | c1_1(a635) | c2_1(a635) | c3_1(a635) | c3_1(a613) | (~ndr1_0) | (~c2_1(a613)) | c0_1(a613))),
% 2.43/2.69 inference(transitivity,[status(thm)],[2430, 2428])).
% 2.43/2.69 tff(2432,plain,
% 2.43/2.69 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | ((~ndr1_0) | c3_1(a613) | c0_1(a613) | (~c2_1(a613)) | c1_1(a635) | c3_1(a635) | c2_1(a635))),
% 2.43/2.69 inference(quant_inst,[status(thm)],[])).
% 2.43/2.69 tff(2433,plain,
% 2.43/2.69 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)) | c1_1(V) | c3_1(V) | c2_1(V))) | c1_1(a635) | c2_1(a635) | c3_1(a635) | c3_1(a613) | (~ndr1_0) | (~c2_1(a613)) | c0_1(a613)),
% 2.43/2.69 inference(modus_ponens,[status(thm)],[2432, 2431])).
% 2.43/2.69 tff(2434,plain,
% 2.43/2.69 ($false),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[2433, 87, 2419, 959, 962, 2427, 2418, 599, 2426])).
% 2.43/2.69 tff(2435,plain,(hskp16 | c1_1(a635) | c2_1(a635) | c3_1(a635) | (~c3_1(a673)) | c0_1(a673) | c2_1(a673) | hskp17), inference(lemma,lemma(discharge,[]))).
% 2.43/2.69 tff(2436,plain,
% 2.43/2.69 ($false),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[2435, 2416, 2415, 12, 1668, 13, 1694, 2402, 2414])).
% 2.43/2.69 tff(2437,plain,(hskp16 | hskp17 | c2_1(a673)), inference(lemma,lemma(discharge,[]))).
% 2.43/2.69 tff(2438,plain,
% 2.43/2.69 (hskp16),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[2437, 13, 12])).
% 2.43/2.69 tff(2439,plain,
% 2.43/2.69 (hskp53),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[184, 141, 12])).
% 2.43/2.69 tff(2440,plain,
% 2.43/2.69 (c0_1(a648)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[792, 2439])).
% 2.43/2.69 tff(2441,plain,
% 2.43/2.69 (c3_1(a648)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[800, 2439])).
% 2.43/2.69 tff(2442,plain,
% 2.43/2.69 (~c2_1(a648)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[784, 2439])).
% 2.43/2.69 tff(2443,plain,
% 2.43/2.69 ($false),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[2396, 2442, 2441, 1702, 1694, 2362, 141, 2440, 1668])).
% 2.43/2.69 tff(2444,plain,((~hskp15) | (~hskp16) | hskp17), inference(lemma,lemma(discharge,[]))).
% 2.43/2.69 tff(2445,plain,
% 2.43/2.69 (~hskp15),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[2444, 2438, 12])).
% 2.43/2.69 tff(2446,plain,
% 2.43/2.69 (hskp53),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[555, 257, 12, 2291, 256])).
% 2.43/2.69 tff(2447,plain,
% 2.43/2.69 (~c2_1(a648)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[784, 2446])).
% 2.43/2.69 tff(2448,plain,
% 2.43/2.69 (c3_1(a648)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[800, 2446])).
% 2.43/2.69 tff(2449,plain,
% 2.43/2.69 (c0_1(a648)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[792, 2446])).
% 2.43/2.69 tff(2450,plain,
% 2.43/2.69 ($false),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[1176, 2449, 2448, 257, 943, 2447, 12, 256])).
% 2.43/2.69 tff(2451,plain,(hskp15 | c3_1(a603) | hskp17 | hskp14), inference(lemma,lemma(discharge,[]))).
% 2.43/2.69 tff(2452,plain,
% 2.43/2.69 (hskp14),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[2451, 2445, 12, 2401])).
% 2.43/2.69 tff(2453,plain,
% 2.43/2.69 (hskp5),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[568, 35, 12, 2291])).
% 2.43/2.69 tff(2454,plain,
% 2.43/2.69 (~c3_1(a606)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[574, 2453])).
% 2.43/2.69 tff(2455,plain,
% 2.43/2.69 (hskp53 | c0_1(a617)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[478, 87, 12, 2294, 2293, 34])).
% 2.43/2.69 tff(2456,plain,
% 2.43/2.69 (c0_1(a617)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[2455, 35])).
% 2.43/2.69 tff(2457,plain,
% 2.43/2.69 (hskp20),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[2307, 2456, 2293, 186, 2294, 2292])).
% 2.43/2.69 tff(2458,plain,
% 2.43/2.69 (c2_1(a606)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[588, 2453])).
% 2.43/2.69 tff(2459,plain,
% 2.43/2.69 (~c0_1(a606)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[580, 2453])).
% 2.43/2.69 tff(2460,plain,
% 2.43/2.69 ($false),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[629, 2459, 2458, 2457, 2454])).
% 2.43/2.69 tff(2461,plain,(hskp53 | (~hskp14) | hskp17), inference(lemma,lemma(discharge,[]))).
% 2.43/2.69 tff(2462,plain,
% 2.43/2.69 (hskp53),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[2461, 2452, 12])).
% 2.43/2.69 tff(2463,plain,
% 2.43/2.69 (c3_1(a648)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[800, 2462])).
% 2.43/2.69 tff(2464,plain,
% 2.43/2.69 (c0_1(a648)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[792, 2462])).
% 2.43/2.69 tff(2465,plain,
% 2.43/2.69 (~c2_1(a648)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[784, 2462])).
% 2.43/2.69 tff(2466,plain,
% 2.43/2.69 ($false),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[1338, 2465, 2464, 2445, 2401, 12, 2463])).
% 2.43/2.69 tff(2467,plain,(c2_1(a673) | hskp17), inference(lemma,lemma(discharge,[]))).
% 2.43/2.69 tff(2468,plain,
% 2.43/2.69 (c2_1(a673)),
% 2.43/2.69 inference(unit_resolution,[status(thm)],[2467, 12])).
% 2.43/2.69 tff(2469,plain,
% 2.43/2.69 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a673) | c1_1(a617) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a673) | c1_1(a617) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 2.43/2.70 inference(rewrite,[status(thm)],[])).
% 2.43/2.70 tff(2470,plain,
% 2.43/2.70 (((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)) | c0_1(a673) | (~c1_1(a673)) | (~c2_1(a673))) <=> (c0_1(a673) | c1_1(a617) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 2.43/2.70 inference(rewrite,[status(thm)],[])).
% 2.43/2.70 tff(2471,plain,
% 2.43/2.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)) | c0_1(a673) | (~c1_1(a673)) | (~c2_1(a673)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | (c0_1(a673) | c1_1(a617) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617))))),
% 2.43/2.70 inference(monotonicity,[status(thm)],[2470])).
% 2.43/2.70 tff(2472,plain,
% 2.43/2.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)) | c0_1(a673) | (~c1_1(a673)) | (~c2_1(a673)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a673) | c1_1(a617) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617)))),
% 2.43/2.70 inference(transitivity,[status(thm)],[2471, 2469])).
% 2.43/2.70 tff(2473,plain,
% 2.43/2.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a617) | c0_1(a617) | (~c2_1(a617)) | c0_1(a673) | (~c1_1(a673)) | (~c2_1(a673)))),
% 2.43/2.70 inference(quant_inst,[status(thm)],[])).
% 2.43/2.70 tff(2474,plain,
% 2.43/2.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c0_1(W) | (~c1_1(W)) | (~c2_1(W)))) | c0_1(a673) | c1_1(a617) | (~ndr1_0) | (~c1_1(a673)) | (~c2_1(a673)) | c0_1(a617) | (~c2_1(a617)) | (~c3_1(a617))),
% 2.43/2.70 inference(modus_ponens,[status(thm)],[2473, 2472])).
% 2.43/2.70 tff(2475,plain,
% 2.43/2.70 ((~c2_1(a673)) | c0_1(a617)),
% 2.43/2.70 inference(unit_resolution,[status(thm)],[2474, 87, 1702, 2292, 2294, 1694, 2293, 1452])).
% 2.43/2.70 tff(2476,plain,
% 2.43/2.70 (c0_1(a617)),
% 2.43/2.70 inference(unit_resolution,[status(thm)],[2475, 2468])).
% 2.43/2.70 tff(2477,plain,
% 2.43/2.70 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (c1_1(a617) | (~ndr1_0) | (~c3_1(a673)) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a617)) | (~c0_1(a617)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | c1_1(a617) | (~ndr1_0) | (~c3_1(a673)) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a617)) | (~c0_1(a617)))),
% 2.43/2.70 inference(rewrite,[status(thm)],[])).
% 2.43/2.70 tff(2478,plain,
% 2.43/2.70 (((~ndr1_0) | (~c3_1(a673)) | (~c1_1(a673)) | (~c2_1(a673)) | c1_1(a617) | (~c2_1(a617)) | (~c0_1(a617))) <=> (c1_1(a617) | (~ndr1_0) | (~c3_1(a673)) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a617)) | (~c0_1(a617)))),
% 2.43/2.70 inference(rewrite,[status(thm)],[])).
% 2.43/2.70 tff(2479,plain,
% 2.43/2.70 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | ((~ndr1_0) | (~c3_1(a673)) | (~c1_1(a673)) | (~c2_1(a673)) | c1_1(a617) | (~c2_1(a617)) | (~c0_1(a617)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (c1_1(a617) | (~ndr1_0) | (~c3_1(a673)) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a617)) | (~c0_1(a617))))),
% 2.43/2.70 inference(monotonicity,[status(thm)],[2478])).
% 2.43/2.70 tff(2480,plain,
% 2.43/2.70 (((~![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | ((~ndr1_0) | (~c3_1(a673)) | (~c1_1(a673)) | (~c2_1(a673)) | c1_1(a617) | (~c2_1(a617)) | (~c0_1(a617)))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | c1_1(a617) | (~ndr1_0) | (~c3_1(a673)) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a617)) | (~c0_1(a617)))),
% 2.43/2.70 inference(transitivity,[status(thm)],[2479, 2477])).
% 2.43/2.70 tff(2481,plain,
% 2.43/2.70 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | ((~ndr1_0) | (~c3_1(a673)) | (~c1_1(a673)) | (~c2_1(a673)) | c1_1(a617) | (~c2_1(a617)) | (~c0_1(a617)))),
% 2.43/2.70 inference(quant_inst,[status(thm)],[])).
% 2.43/2.70 tff(2482,plain,
% 2.43/2.70 ((~![V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | c1_1(a617) | (~ndr1_0) | (~c3_1(a673)) | (~c1_1(a673)) | (~c2_1(a673)) | (~c2_1(a617)) | (~c0_1(a617))),
% 2.43/2.70 inference(modus_ponens,[status(thm)],[2481, 2480])).
% 2.43/2.70 tff(2483,plain,
% 2.43/2.70 ((~c2_1(a673)) | (~c0_1(a617))),
% 2.43/2.70 inference(unit_resolution,[status(thm)],[2482, 87, 1668, 1702, 2292, 2293, 489])).
% 2.43/2.70 tff(2484,plain,
% 2.43/2.70 ($false),
% 2.43/2.70 inference(unit_resolution,[status(thm)],[2483, 2476, 2468])).
% 2.43/2.70 tff(2485,plain,(hskp17), inference(lemma,lemma(discharge,[]))).
% 2.43/2.70 tff(2486,plain,
% 2.43/2.70 (((~hskp17) | (~c1_1(a628))) <=> ((~hskp17) | (~c1_1(a628)))),
% 2.43/2.70 inference(rewrite,[status(thm)],[])).
% 2.43/2.70 tff(2487,plain,
% 2.43/2.70 (((~c1_1(a628)) | (~hskp17)) <=> ((~hskp17) | (~c1_1(a628)))),
% 2.43/2.70 inference(rewrite,[status(thm)],[])).
% 2.43/2.70 tff(2488,axiom,((~c1_1(a628)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause243')).
% 2.43/2.70 tff(2489,plain,
% 2.43/2.70 ((~hskp17) | (~c1_1(a628))),
% 2.43/2.70 inference(modus_ponens,[status(thm)],[2488, 2487])).
% 2.43/2.70 tff(2490,plain,
% 2.43/2.70 ((~hskp17) | (~c1_1(a628))),
% 2.43/2.70 inference(modus_ponens,[status(thm)],[2489, 2486])).
% 2.43/2.70 tff(2491,plain,
% 2.43/2.70 (~c1_1(a628)),
% 2.43/2.70 inference(unit_resolution,[status(thm)],[2490, 2485])).
% 2.43/2.70 tff(2492,plain,
% 2.43/2.70 (((~hskp17) | (~c2_1(a628))) <=> ((~hskp17) | (~c2_1(a628)))),
% 2.43/2.70 inference(rewrite,[status(thm)],[])).
% 2.43/2.70 tff(2493,plain,
% 2.43/2.70 (((~c2_1(a628)) | (~hskp17)) <=> ((~hskp17) | (~c2_1(a628)))),
% 2.43/2.70 inference(rewrite,[status(thm)],[])).
% 2.43/2.70 tff(2494,axiom,((~c2_1(a628)) | (~hskp17)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause242')).
% 2.43/2.70 tff(2495,plain,
% 2.43/2.70 ((~hskp17) | (~c2_1(a628))),
% 2.43/2.70 inference(modus_ponens,[status(thm)],[2494, 2493])).
% 2.43/2.70 tff(2496,plain,
% 2.43/2.70 ((~hskp17) | (~c2_1(a628))),
% 2.43/2.70 inference(modus_ponens,[status(thm)],[2495, 2492])).
% 2.43/2.70 tff(2497,plain,
% 2.43/2.70 (~c2_1(a628)),
% 2.43/2.70 inference(unit_resolution,[status(thm)],[2496, 2485])).
% 2.43/2.70 tff(2498,assumption,(hskp5), introduced(assumption)).
% 2.43/2.70 tff(2499,plain,
% 2.43/2.70 (~c3_1(a606)),
% 2.43/2.70 inference(unit_resolution,[status(thm)],[574, 2498])).
% 2.43/2.70 tff(2500,plain,
% 2.43/2.70 (~c0_1(a606)),
% 2.43/2.70 inference(unit_resolution,[status(thm)],[580, 2498])).
% 2.43/2.70 tff(2501,plain,
% 2.43/2.70 (c2_1(a606)),
% 2.43/2.70 inference(unit_resolution,[status(thm)],[588, 2498])).
% 2.43/2.70 tff(2502,plain,
% 2.43/2.70 (~c1_1(a606)),
% 2.43/2.70 inference(unit_resolution,[status(thm)],[1650, 87, 2501, 2500, 2499, 23])).
% 2.43/2.70 tff(2503,plain,
% 2.43/2.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a628) | c1_1(a628) | c0_1(a606) | c3_1(a606) | (~ndr1_0) | c1_1(a606) | (~c2_1(a606)) | c0_1(a628))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a628) | c1_1(a628) | c0_1(a606) | c3_1(a606) | (~ndr1_0) | c1_1(a606) | (~c2_1(a606)) | c0_1(a628))),
% 2.43/2.70 inference(rewrite,[status(thm)],[])).
% 2.43/2.70 tff(2504,plain,
% 2.43/2.70 (((~ndr1_0) | c3_1(a606) | c1_1(a606) | (~c2_1(a606)) | c1_1(a606) | c0_1(a606) | (~c2_1(a606)) | c2_1(a628) | c1_1(a628) | c0_1(a628)) <=> (c2_1(a628) | c1_1(a628) | c0_1(a606) | c3_1(a606) | (~ndr1_0) | c1_1(a606) | (~c2_1(a606)) | c0_1(a628))),
% 2.43/2.70 inference(rewrite,[status(thm)],[])).
% 2.43/2.70 tff(2505,plain,
% 2.43/2.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a606) | c1_1(a606) | (~c2_1(a606)) | c1_1(a606) | c0_1(a606) | (~c2_1(a606)) | c2_1(a628) | c1_1(a628) | c0_1(a628))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a628) | c1_1(a628) | c0_1(a606) | c3_1(a606) | (~ndr1_0) | c1_1(a606) | (~c2_1(a606)) | c0_1(a628)))),
% 2.43/2.70 inference(monotonicity,[status(thm)],[2504])).
% 2.43/2.70 tff(2506,plain,
% 2.43/2.70 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a606) | c1_1(a606) | (~c2_1(a606)) | c1_1(a606) | c0_1(a606) | (~c2_1(a606)) | c2_1(a628) | c1_1(a628) | c0_1(a628))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a628) | c1_1(a628) | c0_1(a606) | c3_1(a606) | (~ndr1_0) | c1_1(a606) | (~c2_1(a606)) | c0_1(a628))),
% 2.43/2.70 inference(transitivity,[status(thm)],[2505, 2503])).
% 2.43/2.70 tff(2507,plain,
% 2.43/2.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a606) | c1_1(a606) | (~c2_1(a606)) | c1_1(a606) | c0_1(a606) | (~c2_1(a606)) | c2_1(a628) | c1_1(a628) | c0_1(a628))),
% 2.43/2.70 inference(quant_inst,[status(thm)],[])).
% 2.43/2.70 tff(2508,plain,
% 2.43/2.70 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a628) | c1_1(a628) | c0_1(a606) | c3_1(a606) | (~ndr1_0) | c1_1(a606) | (~c2_1(a606)) | c0_1(a628)),
% 2.43/2.70 inference(modus_ponens,[status(thm)],[2507, 2506])).
% 2.43/2.70 tff(2509,plain,
% 2.43/2.70 ($false),
% 2.43/2.70 inference(unit_resolution,[status(thm)],[2508, 87, 2501, 2497, 2491, 2500, 2499, 1279, 1, 2502])).
% 2.43/2.70 tff(2510,plain,((~hskp5) | c0_1(a628)), inference(lemma,lemma(discharge,[]))).
% 2.43/2.70 tff(2511,plain,
% 2.43/2.70 (~hskp5),
% 2.43/2.70 inference(unit_resolution,[status(thm)],[2510, 1])).
% 2.43/2.70 tff(2512,plain,
% 2.43/2.70 (((~hskp17) | c3_1(a628)) <=> ((~hskp17) | c3_1(a628))),
% 2.43/2.70 inference(rewrite,[status(thm)],[])).
% 2.43/2.70 tff(2513,axiom,((~hskp17) | c3_1(a628)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause152')).
% 2.43/2.70 tff(2514,plain,
% 2.43/2.70 ((~hskp17) | c3_1(a628)),
% 2.43/2.70 inference(modus_ponens,[status(thm)],[2513, 2512])).
% 2.43/2.70 tff(2515,plain,
% 2.43/2.70 ((~hskp17) | c3_1(a628)),
% 2.43/2.70 inference(modus_ponens,[status(thm)],[2514, 2512])).
% 2.43/2.70 tff(2516,plain,
% 2.43/2.70 ((~hskp17) | c3_1(a628)),
% 2.43/2.70 inference(modus_ponens,[status(thm)],[2515, 2512])).
% 2.43/2.70 tff(2517,plain,
% 2.43/2.70 ((~hskp17) | c3_1(a628)),
% 2.43/2.70 inference(modus_ponens,[status(thm)],[2516, 2512])).
% 2.43/2.70 tff(2518,plain,
% 2.43/2.70 ((~hskp17) | c3_1(a628)),
% 2.43/2.70 inference(modus_ponens,[status(thm)],[2517, 2512])).
% 2.43/2.70 tff(2519,plain,
% 2.43/2.70 (c3_1(a628)),
% 2.43/2.70 inference(unit_resolution,[status(thm)],[2518, 2485])).
% 2.43/2.70 tff(2520,plain,
% 2.43/2.70 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a669) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c3_1(a628)) | (~c0_1(a669)) | (~c1_1(a669)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a669) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c3_1(a628)) | (~c0_1(a669)) | (~c1_1(a669)))),
% 2.43/2.70 inference(rewrite,[status(thm)],[])).
% 2.43/2.70 tff(2521,plain,
% 2.43/2.70 ((hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a669) | (~c1_1(a669)) | (~c0_1(a669))) <=> (hskp5 | c2_1(a669) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c3_1(a628)) | (~c0_1(a669)) | (~c1_1(a669)))),
% 2.43/2.70 inference(rewrite,[status(thm)],[])).
% 2.43/2.70 tff(2522,plain,
% 2.43/2.70 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a669) | (~c1_1(a669)) | (~c0_1(a669)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a669) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c3_1(a628)) | (~c0_1(a669)) | (~c1_1(a669))))),
% 2.53/2.70 inference(monotonicity,[status(thm)],[2521])).
% 2.53/2.70 tff(2523,plain,
% 2.53/2.70 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a669) | (~c1_1(a669)) | (~c0_1(a669)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a669) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c3_1(a628)) | (~c0_1(a669)) | (~c1_1(a669)))),
% 2.53/2.70 inference(transitivity,[status(thm)],[2522, 2520])).
% 2.53/2.70 tff(2524,plain,
% 2.53/2.70 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a669) | (~c1_1(a669)) | (~c0_1(a669)))),
% 2.53/2.70 inference(quant_inst,[status(thm)],[])).
% 2.53/2.70 tff(2525,plain,
% 2.53/2.70 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a669) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c3_1(a628)) | (~c0_1(a669)) | (~c1_1(a669))),
% 2.53/2.70 inference(modus_ponens,[status(thm)],[2524, 2523])).
% 2.53/2.70 tff(2526,plain,
% 2.53/2.70 ($false),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[2525, 87, 523, 323, 315, 2519, 306, 2497, 2491, 507])).
% 2.53/2.70 tff(2527,plain,((~hskp60) | hskp5), inference(lemma,lemma(discharge,[]))).
% 2.53/2.70 tff(2528,plain,
% 2.53/2.70 (~hskp60),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[2527, 2511])).
% 2.53/2.70 tff(2529,assumption,(~c1_1(a658)), introduced(assumption)).
% 2.53/2.70 tff(2530,assumption,(~c2_1(a658)), introduced(assumption)).
% 2.53/2.70 tff(2531,plain,
% 2.53/2.70 (~hskp56),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[1286, 2530])).
% 2.53/2.70 tff(2532,assumption,(hskp42), introduced(assumption)).
% 2.53/2.70 tff(2533,plain,
% 2.53/2.70 (~c3_1(a618)),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[915, 2532])).
% 2.53/2.70 tff(2534,assumption,(~hskp56), introduced(assumption)).
% 2.53/2.70 tff(2535,plain,
% 2.53/2.70 (c1_1(a618)),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[876, 2532])).
% 2.53/2.70 tff(2536,plain,
% 2.53/2.70 (~c2_1(a618)),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[845, 2532])).
% 2.53/2.70 tff(2537,assumption,(hskp17), introduced(assumption)).
% 2.53/2.70 tff(2538,plain,
% 2.53/2.70 (~c1_1(a628)),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[2490, 2537])).
% 2.53/2.70 tff(2539,plain,
% 2.53/2.70 (~c2_1(a628)),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[2496, 2537])).
% 2.53/2.70 tff(2540,assumption,(~c3_1(a618)), introduced(assumption)).
% 2.53/2.70 tff(2541,assumption,(~c2_1(a618)), introduced(assumption)).
% 2.53/2.70 tff(2542,plain,
% 2.53/2.70 (c3_1(a628)),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[2518, 2537])).
% 2.53/2.70 tff(2543,assumption,(c1_1(a618)), introduced(assumption)).
% 2.53/2.70 tff(2544,plain,
% 2.53/2.70 (((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp56 | c2_1(a618) | c3_1(a618) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c1_1(a618)) | (~c3_1(a628)))) <=> ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp56 | c2_1(a618) | c3_1(a618) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c1_1(a618)) | (~c3_1(a628)))),
% 2.53/2.70 inference(rewrite,[status(thm)],[])).
% 2.53/2.70 tff(2545,plain,
% 2.53/2.70 ((hskp56 | (~ndr1_0) | c3_1(a618) | c2_1(a618) | (~c1_1(a618)) | c1_1(a628) | c2_1(a628) | (~c3_1(a628))) <=> (hskp56 | c2_1(a618) | c3_1(a618) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c1_1(a618)) | (~c3_1(a628)))),
% 2.53/2.70 inference(rewrite,[status(thm)],[])).
% 2.53/2.70 tff(2546,plain,
% 2.53/2.70 (((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp56 | (~ndr1_0) | c3_1(a618) | c2_1(a618) | (~c1_1(a618)) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)))) <=> ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp56 | c2_1(a618) | c3_1(a618) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c1_1(a618)) | (~c3_1(a628))))),
% 2.53/2.70 inference(monotonicity,[status(thm)],[2545])).
% 2.53/2.70 tff(2547,plain,
% 2.53/2.70 (((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp56 | (~ndr1_0) | c3_1(a618) | c2_1(a618) | (~c1_1(a618)) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)))) <=> ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp56 | c2_1(a618) | c3_1(a618) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c1_1(a618)) | (~c3_1(a628)))),
% 2.53/2.70 inference(transitivity,[status(thm)],[2546, 2544])).
% 2.53/2.70 tff(2548,plain,
% 2.53/2.70 ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp56 | (~ndr1_0) | c3_1(a618) | c2_1(a618) | (~c1_1(a618)) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)))),
% 2.53/2.70 inference(quant_inst,[status(thm)],[])).
% 2.53/2.70 tff(2549,plain,
% 2.53/2.70 ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp56 | c2_1(a618) | c3_1(a618) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c1_1(a618)) | (~c3_1(a628))),
% 2.53/2.70 inference(modus_ponens,[status(thm)],[2548, 2547])).
% 2.53/2.70 tff(2550,plain,
% 2.53/2.70 ($false),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[2549, 87, 2534, 2543, 2542, 2541, 2540, 2539, 2538, 1240])).
% 2.53/2.70 tff(2551,plain,((~hskp17) | hskp56 | (~c1_1(a618)) | c2_1(a618) | c3_1(a618)), inference(lemma,lemma(discharge,[]))).
% 2.53/2.70 tff(2552,plain,
% 2.53/2.70 (hskp56 | (~c1_1(a618)) | c2_1(a618) | c3_1(a618)),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[2551, 2485])).
% 2.53/2.70 tff(2553,plain,
% 2.53/2.70 ($false),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[2552, 2536, 2535, 2534, 2533])).
% 2.53/2.70 tff(2554,plain,((~hskp42) | hskp56), inference(lemma,lemma(discharge,[]))).
% 2.53/2.70 tff(2555,plain,
% 2.53/2.70 (~hskp42),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[2554, 2531])).
% 2.53/2.70 tff(2556,plain,
% 2.53/2.70 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | c2_1(a658) | c1_1(a658) | c1_1(a628) | (~ndr1_0) | (~c0_1(a658)) | c0_1(a628) | (~c3_1(a628)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c2_1(a658) | c1_1(a658) | c1_1(a628) | (~ndr1_0) | (~c0_1(a658)) | c0_1(a628) | (~c3_1(a628)))),
% 2.53/2.70 inference(rewrite,[status(thm)],[])).
% 2.53/2.70 tff(2557,plain,
% 2.53/2.70 ((hskp42 | (~ndr1_0) | c1_1(a658) | c2_1(a658) | (~c0_1(a658)) | c1_1(a628) | c0_1(a628) | (~c3_1(a628))) <=> (hskp42 | c2_1(a658) | c1_1(a658) | c1_1(a628) | (~ndr1_0) | (~c0_1(a658)) | c0_1(a628) | (~c3_1(a628)))),
% 2.53/2.70 inference(rewrite,[status(thm)],[])).
% 2.53/2.70 tff(2558,plain,
% 2.53/2.70 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a658) | c2_1(a658) | (~c0_1(a658)) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | c2_1(a658) | c1_1(a658) | c1_1(a628) | (~ndr1_0) | (~c0_1(a658)) | c0_1(a628) | (~c3_1(a628))))),
% 2.53/2.70 inference(monotonicity,[status(thm)],[2557])).
% 2.53/2.70 tff(2559,plain,
% 2.53/2.70 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a658) | c2_1(a658) | (~c0_1(a658)) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c2_1(a658) | c1_1(a658) | c1_1(a628) | (~ndr1_0) | (~c0_1(a658)) | c0_1(a628) | (~c3_1(a628)))),
% 2.53/2.70 inference(transitivity,[status(thm)],[2558, 2556])).
% 2.53/2.70 tff(2560,plain,
% 2.53/2.70 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a658) | c2_1(a658) | (~c0_1(a658)) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)))),
% 2.53/2.70 inference(quant_inst,[status(thm)],[])).
% 2.53/2.70 tff(2561,plain,
% 2.53/2.70 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c2_1(a658) | c1_1(a658) | c1_1(a628) | (~ndr1_0) | (~c0_1(a658)) | c0_1(a628) | (~c3_1(a628))),
% 2.53/2.70 inference(modus_ponens,[status(thm)],[2560, 2559])).
% 2.53/2.70 tff(2562,plain,
% 2.53/2.70 (hskp42 | c2_1(a658) | (~c0_1(a658))),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[2561, 87, 2519, 2529, 2491, 822, 1])).
% 2.53/2.70 tff(2563,plain,
% 2.53/2.70 (~c0_1(a658)),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[2562, 2555, 2530])).
% 2.53/2.70 tff(2564,plain,
% 2.53/2.70 (~hskp42),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[2554, 2534])).
% 2.53/2.70 tff(2565,plain,
% 2.53/2.70 (((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp56 | c2_1(a628) | c1_1(a628) | (~c1_1(a603)) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c3_1(a628)))) <=> ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp56 | c2_1(a628) | c1_1(a628) | (~c1_1(a603)) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c3_1(a628)))),
% 2.53/2.70 inference(rewrite,[status(thm)],[])).
% 2.53/2.70 tff(2566,plain,
% 2.53/2.70 ((hskp56 | (~ndr1_0) | c3_1(a603) | c2_1(a603) | (~c1_1(a603)) | c1_1(a628) | c2_1(a628) | (~c3_1(a628))) <=> (hskp56 | c2_1(a628) | c1_1(a628) | (~c1_1(a603)) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c3_1(a628)))),
% 2.53/2.70 inference(rewrite,[status(thm)],[])).
% 2.53/2.70 tff(2567,plain,
% 2.53/2.70 (((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp56 | (~ndr1_0) | c3_1(a603) | c2_1(a603) | (~c1_1(a603)) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)))) <=> ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp56 | c2_1(a628) | c1_1(a628) | (~c1_1(a603)) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c3_1(a628))))),
% 2.53/2.70 inference(monotonicity,[status(thm)],[2566])).
% 2.53/2.70 tff(2568,plain,
% 2.53/2.70 (((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp56 | (~ndr1_0) | c3_1(a603) | c2_1(a603) | (~c1_1(a603)) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)))) <=> ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp56 | c2_1(a628) | c1_1(a628) | (~c1_1(a603)) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c3_1(a628)))),
% 2.53/2.70 inference(transitivity,[status(thm)],[2567, 2565])).
% 2.53/2.70 tff(2569,plain,
% 2.53/2.70 ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp56 | (~ndr1_0) | c3_1(a603) | c2_1(a603) | (~c1_1(a603)) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)))),
% 2.53/2.70 inference(quant_inst,[status(thm)],[])).
% 2.53/2.70 tff(2570,plain,
% 2.53/2.70 ((~![V: $i, U: $i] : (hskp56 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)))) | hskp56 | c2_1(a628) | c1_1(a628) | (~c1_1(a603)) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c3_1(a628))),
% 2.53/2.70 inference(modus_ponens,[status(thm)],[2569, 2568])).
% 2.53/2.70 tff(2571,plain,
% 2.53/2.70 (hskp56 | (~c1_1(a603)) | c2_1(a603)),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[2570, 87, 2519, 2497, 2491, 943, 1240])).
% 2.53/2.70 tff(2572,plain,
% 2.53/2.70 (~c1_1(a603)),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[2571, 2534, 1774])).
% 2.53/2.70 tff(2573,plain,
% 2.53/2.70 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | (c0_1(a603) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | c0_1(a603) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603))),
% 2.53/2.70 inference(rewrite,[status(thm)],[])).
% 2.53/2.70 tff(2574,plain,
% 2.53/2.70 (((~ndr1_0) | c3_1(a603) | c2_1(a603) | c0_1(a603) | c1_1(a603) | c3_1(a603) | c0_1(a603)) <=> (c0_1(a603) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603))),
% 2.53/2.70 inference(rewrite,[status(thm)],[])).
% 2.53/2.70 tff(2575,plain,
% 2.53/2.70 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | ((~ndr1_0) | c3_1(a603) | c2_1(a603) | c0_1(a603) | c1_1(a603) | c3_1(a603) | c0_1(a603))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | (c0_1(a603) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603)))),
% 2.53/2.70 inference(monotonicity,[status(thm)],[2574])).
% 2.53/2.70 tff(2576,plain,
% 2.53/2.70 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | ((~ndr1_0) | c3_1(a603) | c2_1(a603) | c0_1(a603) | c1_1(a603) | c3_1(a603) | c0_1(a603))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | c0_1(a603) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603))),
% 2.53/2.70 inference(transitivity,[status(thm)],[2575, 2573])).
% 2.53/2.70 tff(2577,plain,
% 2.53/2.70 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | ((~ndr1_0) | c3_1(a603) | c2_1(a603) | c0_1(a603) | c1_1(a603) | c3_1(a603) | c0_1(a603))),
% 2.53/2.70 inference(quant_inst,[status(thm)],[])).
% 2.53/2.70 tff(2578,plain,
% 2.53/2.70 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | c0_1(a603) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c2_1(a603)),
% 2.53/2.70 inference(modus_ponens,[status(thm)],[2577, 2576])).
% 2.53/2.70 tff(2579,plain,
% 2.53/2.70 (c0_1(a603)),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[2578, 87, 2572, 943, 170, 1774])).
% 2.53/2.70 tff(2580,plain,
% 2.53/2.70 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | c1_1(a628) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | c0_1(a628) | (~c3_1(a628)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c1_1(a628) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | c0_1(a628) | (~c3_1(a628)))),
% 2.53/2.70 inference(rewrite,[status(thm)],[])).
% 2.53/2.70 tff(2581,plain,
% 2.53/2.70 ((hskp42 | (~ndr1_0) | c1_1(a603) | c2_1(a603) | (~c0_1(a603)) | c1_1(a628) | c0_1(a628) | (~c3_1(a628))) <=> (hskp42 | c1_1(a628) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | c0_1(a628) | (~c3_1(a628)))),
% 2.53/2.70 inference(rewrite,[status(thm)],[])).
% 2.53/2.70 tff(2582,plain,
% 2.53/2.70 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a603) | c2_1(a603) | (~c0_1(a603)) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | c1_1(a628) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | c0_1(a628) | (~c3_1(a628))))),
% 2.53/2.70 inference(monotonicity,[status(thm)],[2581])).
% 2.53/2.70 tff(2583,plain,
% 2.53/2.70 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a603) | c2_1(a603) | (~c0_1(a603)) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c1_1(a628) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | c0_1(a628) | (~c3_1(a628)))),
% 2.53/2.70 inference(transitivity,[status(thm)],[2582, 2580])).
% 2.53/2.70 tff(2584,plain,
% 2.53/2.70 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a603) | c2_1(a603) | (~c0_1(a603)) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)))),
% 2.53/2.70 inference(quant_inst,[status(thm)],[])).
% 2.53/2.70 tff(2585,plain,
% 2.53/2.70 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c1_1(a628) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | c0_1(a628) | (~c3_1(a628))),
% 2.53/2.70 inference(modus_ponens,[status(thm)],[2584, 2583])).
% 2.53/2.70 tff(2586,plain,
% 2.53/2.70 ((~c0_1(a603)) | c0_1(a628)),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[2585, 87, 2564, 2519, 2491, 2572, 822, 1774])).
% 2.53/2.70 tff(2587,plain,
% 2.53/2.70 (c0_1(a628)),
% 2.53/2.70 inference(unit_resolution,[status(thm)],[2586, 2579])).
% 2.53/2.70 tff(2588,plain,
% 2.53/2.70 (((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | c2_1(a628) | (~ndr1_0) | (~c0_1(a628)) | (~c3_1(a628)))) <=> ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp58 | hskp41 | c2_1(a628) | (~ndr1_0) | (~c0_1(a628)) | (~c3_1(a628)))),
% 2.53/2.70 inference(rewrite,[status(thm)],[])).
% 2.53/2.70 tff(2589,plain,
% 2.53/2.70 ((hskp58 | hskp41 | (~ndr1_0) | c2_1(a628) | (~c3_1(a628)) | (~c0_1(a628))) <=> (hskp58 | hskp41 | c2_1(a628) | (~ndr1_0) | (~c0_1(a628)) | (~c3_1(a628)))),
% 2.53/2.70 inference(rewrite,[status(thm)],[])).
% 2.53/2.71 tff(2590,plain,
% 2.53/2.71 (((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | (~ndr1_0) | c2_1(a628) | (~c3_1(a628)) | (~c0_1(a628)))) <=> ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | c2_1(a628) | (~ndr1_0) | (~c0_1(a628)) | (~c3_1(a628))))),
% 2.53/2.71 inference(monotonicity,[status(thm)],[2589])).
% 2.53/2.71 tff(2591,plain,
% 2.53/2.71 (((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | (~ndr1_0) | c2_1(a628) | (~c3_1(a628)) | (~c0_1(a628)))) <=> ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp58 | hskp41 | c2_1(a628) | (~ndr1_0) | (~c0_1(a628)) | (~c3_1(a628)))),
% 2.53/2.71 inference(transitivity,[status(thm)],[2590, 2588])).
% 2.53/2.71 tff(2592,plain,
% 2.53/2.71 ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp58 | hskp41 | (~ndr1_0) | c2_1(a628) | (~c3_1(a628)) | (~c0_1(a628)))),
% 2.53/2.71 inference(quant_inst,[status(thm)],[])).
% 2.53/2.71 tff(2593,plain,
% 2.53/2.71 ((~![U: $i] : (hskp58 | hskp41 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp58 | hskp41 | c2_1(a628) | (~ndr1_0) | (~c0_1(a628)) | (~c3_1(a628))),
% 2.53/2.71 inference(modus_ponens,[status(thm)],[2592, 2591])).
% 2.53/2.71 tff(2594,plain,
% 2.53/2.71 (hskp58 | hskp41 | (~c0_1(a628))),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[2593, 87, 2519, 2497, 107])).
% 2.53/2.71 tff(2595,plain,
% 2.53/2.71 (hskp58),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[2594, 2587, 97])).
% 2.53/2.71 tff(2596,plain,
% 2.53/2.71 (~c1_1(a663)),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[41, 2595])).
% 2.53/2.71 tff(2597,plain,
% 2.53/2.71 (~c0_1(a663)),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[47, 2595])).
% 2.53/2.71 tff(2598,plain,
% 2.53/2.71 (c3_1(a663)),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[55, 2595])).
% 2.53/2.71 tff(2599,plain,
% 2.53/2.71 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | c0_1(a663) | c1_1(a663) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c0_1(a628)) | (~c3_1(a663)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c0_1(a663) | c1_1(a663) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c0_1(a628)) | (~c3_1(a663)))),
% 2.53/2.71 inference(rewrite,[status(thm)],[])).
% 2.53/2.71 tff(2600,plain,
% 2.53/2.71 ((hskp42 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c0_1(a628)) | c1_1(a663) | c0_1(a663) | (~c3_1(a663))) <=> (hskp42 | c0_1(a663) | c1_1(a663) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c0_1(a628)) | (~c3_1(a663)))),
% 2.53/2.71 inference(rewrite,[status(thm)],[])).
% 2.53/2.71 tff(2601,plain,
% 2.53/2.71 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c0_1(a628)) | c1_1(a663) | c0_1(a663) | (~c3_1(a663)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | c0_1(a663) | c1_1(a663) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c0_1(a628)) | (~c3_1(a663))))),
% 2.53/2.71 inference(monotonicity,[status(thm)],[2600])).
% 2.53/2.71 tff(2602,plain,
% 2.53/2.71 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c0_1(a628)) | c1_1(a663) | c0_1(a663) | (~c3_1(a663)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c0_1(a663) | c1_1(a663) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c0_1(a628)) | (~c3_1(a663)))),
% 2.53/2.71 inference(transitivity,[status(thm)],[2601, 2599])).
% 2.53/2.71 tff(2603,plain,
% 2.53/2.71 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c0_1(a628)) | c1_1(a663) | c0_1(a663) | (~c3_1(a663)))),
% 2.53/2.71 inference(quant_inst,[status(thm)],[])).
% 2.53/2.71 tff(2604,plain,
% 2.53/2.71 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c0_1(a663) | c1_1(a663) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c0_1(a628)) | (~c3_1(a663))),
% 2.53/2.71 inference(modus_ponens,[status(thm)],[2603, 2602])).
% 2.53/2.71 tff(2605,plain,
% 2.53/2.71 ($false),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[2604, 87, 2564, 2598, 2597, 2596, 2497, 2491, 822, 2587])).
% 2.53/2.71 tff(2606,plain,(hskp56 | hskp41 | c2_1(a603) | c3_1(a603)), inference(lemma,lemma(discharge,[]))).
% 2.53/2.71 tff(2607,plain,
% 2.53/2.71 (hskp41),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[2606, 1774, 2534, 943])).
% 2.53/2.71 tff(2608,plain,
% 2.53/2.71 (~c1_1(a617)),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[463, 2607])).
% 2.53/2.71 tff(2609,assumption,(~c0_1(a658)), introduced(assumption)).
% 2.53/2.71 tff(2610,plain,
% 2.53/2.71 (c2_1(a617)),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[496, 2607])).
% 2.53/2.71 tff(2611,plain,
% 2.53/2.71 (c3_1(a617)),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[471, 2607])).
% 2.53/2.71 tff(2612,assumption,(c1_1(a603)), introduced(assumption)).
% 2.53/2.71 tff(2613,plain,
% 2.53/2.71 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a628) | c1_1(a628) | (~c1_1(a603)) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c3_1(a628)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a628) | c1_1(a628) | (~c1_1(a603)) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c3_1(a628)))),
% 2.53/2.71 inference(rewrite,[status(thm)],[])).
% 2.53/2.71 tff(2614,plain,
% 2.53/2.71 ((hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a603) | (~c1_1(a603)) | (~c0_1(a603))) <=> (hskp5 | c2_1(a628) | c1_1(a628) | (~c1_1(a603)) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c3_1(a628)))),
% 2.53/2.71 inference(rewrite,[status(thm)],[])).
% 2.53/2.71 tff(2615,plain,
% 2.53/2.71 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a603) | (~c1_1(a603)) | (~c0_1(a603)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a628) | c1_1(a628) | (~c1_1(a603)) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c3_1(a628))))),
% 2.53/2.71 inference(monotonicity,[status(thm)],[2614])).
% 2.53/2.71 tff(2616,plain,
% 2.53/2.71 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a603) | (~c1_1(a603)) | (~c0_1(a603)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a628) | c1_1(a628) | (~c1_1(a603)) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c3_1(a628)))),
% 2.53/2.71 inference(transitivity,[status(thm)],[2615, 2613])).
% 2.53/2.71 tff(2617,plain,
% 2.53/2.71 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a603) | (~c1_1(a603)) | (~c0_1(a603)))),
% 2.53/2.71 inference(quant_inst,[status(thm)],[])).
% 2.53/2.71 tff(2618,plain,
% 2.53/2.71 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a628) | c1_1(a628) | (~c1_1(a603)) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c3_1(a628))),
% 2.53/2.71 inference(modus_ponens,[status(thm)],[2617, 2616])).
% 2.53/2.71 tff(2619,plain,
% 2.53/2.71 ((~c1_1(a603)) | (~c0_1(a603))),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[2618, 87, 2511, 2519, 2497, 2491, 507, 1774])).
% 2.53/2.71 tff(2620,plain,
% 2.53/2.71 (~c0_1(a603)),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[2619, 2612])).
% 2.53/2.71 tff(2621,plain,
% 2.53/2.71 (~hskp3),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[1550, 2612])).
% 2.53/2.71 tff(2622,plain,
% 2.53/2.71 (((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | c2_1(a628) | (~ndr1_0) | c0_1(a628) | (~c3_1(a628)))) <=> ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp29 | hskp3 | c2_1(a628) | (~ndr1_0) | c0_1(a628) | (~c3_1(a628)))),
% 2.53/2.71 inference(rewrite,[status(thm)],[])).
% 2.53/2.71 tff(2623,plain,
% 2.53/2.71 ((hskp29 | hskp3 | (~ndr1_0) | c2_1(a628) | c0_1(a628) | (~c3_1(a628))) <=> (hskp29 | hskp3 | c2_1(a628) | (~ndr1_0) | c0_1(a628) | (~c3_1(a628)))),
% 2.53/2.71 inference(rewrite,[status(thm)],[])).
% 2.53/2.71 tff(2624,plain,
% 2.53/2.71 (((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | (~ndr1_0) | c2_1(a628) | c0_1(a628) | (~c3_1(a628)))) <=> ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | c2_1(a628) | (~ndr1_0) | c0_1(a628) | (~c3_1(a628))))),
% 2.53/2.71 inference(monotonicity,[status(thm)],[2623])).
% 2.53/2.71 tff(2625,plain,
% 2.53/2.71 (((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | (~ndr1_0) | c2_1(a628) | c0_1(a628) | (~c3_1(a628)))) <=> ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp29 | hskp3 | c2_1(a628) | (~ndr1_0) | c0_1(a628) | (~c3_1(a628)))),
% 2.53/2.71 inference(transitivity,[status(thm)],[2624, 2622])).
% 2.53/2.71 tff(2626,plain,
% 2.53/2.71 ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | (hskp29 | hskp3 | (~ndr1_0) | c2_1(a628) | c0_1(a628) | (~c3_1(a628)))),
% 2.53/2.71 inference(quant_inst,[status(thm)],[])).
% 2.53/2.71 tff(2627,plain,
% 2.53/2.71 ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c2_1(U) | c0_1(U) | (~c3_1(U)))) | hskp29 | hskp3 | c2_1(a628) | (~ndr1_0) | c0_1(a628) | (~c3_1(a628))),
% 2.53/2.71 inference(modus_ponens,[status(thm)],[2626, 2625])).
% 2.53/2.71 tff(2628,plain,
% 2.53/2.71 (hskp29 | hskp3 | c0_1(a628)),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[2627, 87, 2519, 2497, 937])).
% 2.53/2.71 tff(2629,plain,
% 2.53/2.71 (hskp29),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[2628, 2621, 1])).
% 2.53/2.71 tff(2630,assumption,(~c0_1(a603)), introduced(assumption)).
% 2.53/2.71 tff(2631,plain,
% 2.53/2.71 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | (c0_1(a603) | c1_1(a660) | c3_1(a660) | c0_1(a660) | c3_1(a603) | (~ndr1_0) | c2_1(a603))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | c0_1(a603) | c1_1(a660) | c3_1(a660) | c0_1(a660) | c3_1(a603) | (~ndr1_0) | c2_1(a603))),
% 2.53/2.71 inference(rewrite,[status(thm)],[])).
% 2.53/2.71 tff(2632,plain,
% 2.53/2.71 (((~ndr1_0) | c3_1(a603) | c2_1(a603) | c0_1(a603) | c1_1(a660) | c3_1(a660) | c0_1(a660)) <=> (c0_1(a603) | c1_1(a660) | c3_1(a660) | c0_1(a660) | c3_1(a603) | (~ndr1_0) | c2_1(a603))),
% 2.53/2.71 inference(rewrite,[status(thm)],[])).
% 2.53/2.71 tff(2633,plain,
% 2.53/2.71 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | ((~ndr1_0) | c3_1(a603) | c2_1(a603) | c0_1(a603) | c1_1(a660) | c3_1(a660) | c0_1(a660))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | (c0_1(a603) | c1_1(a660) | c3_1(a660) | c0_1(a660) | c3_1(a603) | (~ndr1_0) | c2_1(a603)))),
% 2.53/2.71 inference(monotonicity,[status(thm)],[2632])).
% 2.53/2.71 tff(2634,plain,
% 2.53/2.71 (((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | ((~ndr1_0) | c3_1(a603) | c2_1(a603) | c0_1(a603) | c1_1(a660) | c3_1(a660) | c0_1(a660))) <=> ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | c0_1(a603) | c1_1(a660) | c3_1(a660) | c0_1(a660) | c3_1(a603) | (~ndr1_0) | c2_1(a603))),
% 2.53/2.71 inference(transitivity,[status(thm)],[2633, 2631])).
% 2.53/2.71 tff(2635,plain,
% 2.53/2.71 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | ((~ndr1_0) | c3_1(a603) | c2_1(a603) | c0_1(a603) | c1_1(a660) | c3_1(a660) | c0_1(a660))),
% 2.53/2.71 inference(quant_inst,[status(thm)],[])).
% 2.53/2.71 tff(2636,plain,
% 2.53/2.71 ((~![V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c2_1(U) | c0_1(U) | c1_1(V) | c3_1(V) | c0_1(V))) | c0_1(a603) | c1_1(a660) | c3_1(a660) | c0_1(a660) | c3_1(a603) | (~ndr1_0) | c2_1(a603)),
% 2.53/2.71 inference(modus_ponens,[status(thm)],[2635, 2634])).
% 2.53/2.71 tff(2637,plain,
% 2.53/2.71 ($false),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[2636, 87, 2630, 1365, 1359, 1353, 943, 170, 1774])).
% 2.53/2.71 tff(2638,plain,((~hskp29) | c0_1(a603) | c3_1(a603) | c2_1(a603)), inference(lemma,lemma(discharge,[]))).
% 2.53/2.71 tff(2639,plain,
% 2.53/2.71 ($false),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[2638, 2629, 2620, 943, 1774])).
% 2.53/2.71 tff(2640,plain,((~c1_1(a603)) | c3_1(a603) | c2_1(a603) | c0_1(a628)), inference(lemma,lemma(discharge,[]))).
% 2.53/2.71 tff(2641,plain,
% 2.53/2.71 (~c1_1(a603)),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[2640, 1774, 1, 943])).
% 2.53/2.71 tff(2642,assumption,(~hskp42), introduced(assumption)).
% 2.53/2.71 tff(2643,plain,
% 2.53/2.71 (^[V: $i, U: $i] : refl((hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V)) <=> (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V)))),
% 2.53/2.71 inference(bind,[status(th)],[])).
% 2.53/2.71 tff(2644,plain,
% 2.53/2.71 (![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))),
% 2.53/2.71 inference(quant_intro,[status(thm)],[2643])).
% 2.53/2.71 tff(2645,plain,
% 2.53/2.71 (![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))),
% 2.53/2.71 inference(rewrite,[status(thm)],[])).
% 2.53/2.71 tff(2646,plain,
% 2.53/2.71 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ndr1_0) | (~c3_1(U))) | c3_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c3_1(V))), (((((~ndr1_0) | (~c3_1(U))) | c3_1(V)) | c0_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | c3_1(V)) | c0_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c3_1(V)) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c3_1(V) | c0_1(V))), (((((~ndr1_0) | (~c3_1(U))) | c3_1(V)) | c0_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c3_1(V) | c0_1(V)))), ((((((~ndr1_0) | (~c3_1(U))) | c3_1(V)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | c3_1(V) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c3_1(V) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))), ((((((~ndr1_0) | (~c3_1(U))) | c3_1(V)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V)))), (((((((~ndr1_0) | (~c3_1(U))) | c3_1(V)) | c0_1(V)) | c1_1(V)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V)) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))), (((((((~ndr1_0) | (~c3_1(U))) | c3_1(V)) | c0_1(V)) | c1_1(V)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V)))), ((((((((~ndr1_0) | (~c3_1(U))) | c3_1(V)) | c0_1(V)) | c1_1(V)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V)) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))), ((((((((~ndr1_0) | (~c3_1(U))) | c3_1(V)) | c0_1(V)) | c1_1(V)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V)))), (((((((((~ndr1_0) | (~c3_1(U))) | c3_1(V)) | c0_1(V)) | c1_1(V)) | c0_1(U)) | c1_1(U)) | hskp42) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V)) | hskp42))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V)) | hskp42) <=> (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))), (((((((((~ndr1_0) | (~c3_1(U))) | c3_1(V)) | c0_1(V)) | c1_1(V)) | c0_1(U)) | c1_1(U)) | hskp42) <=> (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))))),
% 2.53/2.71 inference(bind,[status(th)],[])).
% 2.53/2.71 tff(2647,plain,
% 2.53/2.71 (![V: $i, U: $i] : ((((((((~ndr1_0) | (~c3_1(U))) | c3_1(V)) | c0_1(V)) | c1_1(V)) | c0_1(U)) | c1_1(U)) | hskp42) <=> ![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))),
% 2.53/2.71 inference(quant_intro,[status(thm)],[2646])).
% 2.53/2.71 tff(2648,axiom,(![V: $i, U: $i] : ((((((((~ndr1_0) | (~c3_1(U))) | c3_1(V)) | c0_1(V)) | c1_1(V)) | c0_1(U)) | c1_1(U)) | hskp42)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause300')).
% 2.53/2.71 tff(2649,plain,
% 2.53/2.71 (![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))),
% 2.53/2.71 inference(modus_ponens,[status(thm)],[2648, 2647])).
% 2.53/2.71 tff(2650,plain,
% 2.53/2.71 (![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))),
% 2.53/2.71 inference(modus_ponens,[status(thm)],[2649, 2645])).
% 2.53/2.71 tff(2651,plain,(
% 2.53/2.71 ![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))),
% 2.53/2.71 inference(skolemize,[status(sab)],[2650])).
% 2.53/2.71 tff(2652,plain,
% 2.53/2.71 (![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))),
% 2.53/2.71 inference(modus_ponens,[status(thm)],[2651, 2644])).
% 2.53/2.71 tff(2653,plain,
% 2.53/2.71 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | (hskp42 | c3_1(a658) | c1_1(a658) | c1_1(a628) | (~ndr1_0) | c0_1(a658) | c0_1(a628) | (~c3_1(a628)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | hskp42 | c3_1(a658) | c1_1(a658) | c1_1(a628) | (~ndr1_0) | c0_1(a658) | c0_1(a628) | (~c3_1(a628)))),
% 2.53/2.71 inference(rewrite,[status(thm)],[])).
% 2.53/2.71 tff(2654,plain,
% 2.53/2.71 ((hskp42 | (~ndr1_0) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)) | c1_1(a658) | c3_1(a658) | c0_1(a658)) <=> (hskp42 | c3_1(a658) | c1_1(a658) | c1_1(a628) | (~ndr1_0) | c0_1(a658) | c0_1(a628) | (~c3_1(a628)))),
% 2.53/2.71 inference(rewrite,[status(thm)],[])).
% 2.53/2.71 tff(2655,plain,
% 2.53/2.71 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | (hskp42 | (~ndr1_0) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)) | c1_1(a658) | c3_1(a658) | c0_1(a658))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | (hskp42 | c3_1(a658) | c1_1(a658) | c1_1(a628) | (~ndr1_0) | c0_1(a658) | c0_1(a628) | (~c3_1(a628))))),
% 2.53/2.71 inference(monotonicity,[status(thm)],[2654])).
% 2.53/2.71 tff(2656,plain,
% 2.53/2.71 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | (hskp42 | (~ndr1_0) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)) | c1_1(a658) | c3_1(a658) | c0_1(a658))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | hskp42 | c3_1(a658) | c1_1(a658) | c1_1(a628) | (~ndr1_0) | c0_1(a658) | c0_1(a628) | (~c3_1(a628)))),
% 2.53/2.71 inference(transitivity,[status(thm)],[2655, 2653])).
% 2.53/2.71 tff(2657,plain,
% 2.53/2.71 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | (hskp42 | (~ndr1_0) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)) | c1_1(a658) | c3_1(a658) | c0_1(a658))),
% 2.53/2.71 inference(quant_inst,[status(thm)],[])).
% 2.53/2.71 tff(2658,plain,
% 2.53/2.71 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | hskp42 | c3_1(a658) | c1_1(a658) | c1_1(a628) | (~ndr1_0) | c0_1(a658) | c0_1(a628) | (~c3_1(a628))),
% 2.53/2.71 inference(modus_ponens,[status(thm)],[2657, 2656])).
% 2.53/2.71 tff(2659,plain,
% 2.53/2.71 (hskp42 | c3_1(a658) | c0_1(a658)),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[2658, 87, 2519, 2529, 2491, 2652, 1])).
% 2.53/2.71 tff(2660,plain,
% 2.53/2.71 (c3_1(a658)),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[2659, 2642, 2609])).
% 2.53/2.71 tff(2661,plain,
% 2.53/2.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a603) | c1_1(a658) | c1_1(a617) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c0_1(a658) | (~c3_1(a658)) | (~c2_1(a617)) | (~c3_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a603) | c1_1(a658) | c1_1(a617) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c0_1(a658) | (~c3_1(a658)) | (~c2_1(a617)) | (~c3_1(a617)))),
% 2.53/2.71 inference(rewrite,[status(thm)],[])).
% 2.53/2.71 tff(2662,plain,
% 2.53/2.71 (((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a658) | c0_1(a658) | (~c3_1(a658)) | c1_1(a603) | c0_1(a603) | c3_1(a603)) <=> (c0_1(a603) | c1_1(a658) | c1_1(a617) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c0_1(a658) | (~c3_1(a658)) | (~c2_1(a617)) | (~c3_1(a617)))),
% 2.53/2.71 inference(rewrite,[status(thm)],[])).
% 2.53/2.71 tff(2663,plain,
% 2.53/2.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a658) | c0_1(a658) | (~c3_1(a658)) | c1_1(a603) | c0_1(a603) | c3_1(a603))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c0_1(a603) | c1_1(a658) | c1_1(a617) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c0_1(a658) | (~c3_1(a658)) | (~c2_1(a617)) | (~c3_1(a617))))),
% 2.53/2.71 inference(monotonicity,[status(thm)],[2662])).
% 2.53/2.71 tff(2664,plain,
% 2.53/2.71 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a658) | c0_1(a658) | (~c3_1(a658)) | c1_1(a603) | c0_1(a603) | c3_1(a603))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a603) | c1_1(a658) | c1_1(a617) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c0_1(a658) | (~c3_1(a658)) | (~c2_1(a617)) | (~c3_1(a617)))),
% 2.53/2.71 inference(transitivity,[status(thm)],[2663, 2661])).
% 2.53/2.71 tff(2665,plain,
% 2.53/2.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c2_1(a617)) | c1_1(a658) | c0_1(a658) | (~c3_1(a658)) | c1_1(a603) | c0_1(a603) | c3_1(a603))),
% 2.53/2.71 inference(quant_inst,[status(thm)],[])).
% 2.53/2.71 tff(2666,plain,
% 2.53/2.71 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c0_1(a603) | c1_1(a658) | c1_1(a617) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | c0_1(a658) | (~c3_1(a658)) | (~c2_1(a617)) | (~c3_1(a617))),
% 2.53/2.71 inference(modus_ponens,[status(thm)],[2665, 2664])).
% 2.53/2.71 tff(2667,plain,
% 2.53/2.71 (c0_1(a603)),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[2666, 87, 2660, 649, 648, 2529, 647, 2641, 943, 1113, 2609])).
% 2.53/2.71 tff(2668,plain,
% 2.53/2.71 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | c1_1(a658) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | c0_1(a658) | (~c3_1(a658)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c1_1(a658) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | c0_1(a658) | (~c3_1(a658)))),
% 2.53/2.71 inference(rewrite,[status(thm)],[])).
% 2.53/2.71 tff(2669,plain,
% 2.53/2.71 ((hskp42 | (~ndr1_0) | c1_1(a603) | c2_1(a603) | (~c0_1(a603)) | c1_1(a658) | c0_1(a658) | (~c3_1(a658))) <=> (hskp42 | c1_1(a658) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | c0_1(a658) | (~c3_1(a658)))),
% 2.53/2.71 inference(rewrite,[status(thm)],[])).
% 2.53/2.71 tff(2670,plain,
% 2.53/2.71 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a603) | c2_1(a603) | (~c0_1(a603)) | c1_1(a658) | c0_1(a658) | (~c3_1(a658)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | c1_1(a658) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | c0_1(a658) | (~c3_1(a658))))),
% 2.53/2.71 inference(monotonicity,[status(thm)],[2669])).
% 2.53/2.71 tff(2671,plain,
% 2.53/2.71 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a603) | c2_1(a603) | (~c0_1(a603)) | c1_1(a658) | c0_1(a658) | (~c3_1(a658)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c1_1(a658) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | c0_1(a658) | (~c3_1(a658)))),
% 2.53/2.71 inference(transitivity,[status(thm)],[2670, 2668])).
% 2.53/2.71 tff(2672,plain,
% 2.53/2.71 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a603) | c2_1(a603) | (~c0_1(a603)) | c1_1(a658) | c0_1(a658) | (~c3_1(a658)))),
% 2.53/2.71 inference(quant_inst,[status(thm)],[])).
% 2.53/2.71 tff(2673,plain,
% 2.53/2.71 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c1_1(a658) | c1_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | c0_1(a658) | (~c3_1(a658))),
% 2.53/2.71 inference(modus_ponens,[status(thm)],[2672, 2671])).
% 2.53/2.71 tff(2674,plain,
% 2.53/2.71 ($false),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[2673, 87, 2642, 2660, 2667, 2529, 2641, 822, 1774, 2609])).
% 2.53/2.71 tff(2675,plain,(c2_1(a603) | hskp42 | c1_1(a658) | c0_1(a658) | (~c2_1(a617)) | (~c3_1(a617)) | c1_1(a617) | c3_1(a603) | c0_1(a628)), inference(lemma,lemma(discharge,[]))).
% 2.53/2.71 tff(2676,plain,
% 2.53/2.71 ($false),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[2675, 2611, 2610, 2529, 943, 2609, 1774, 2608, 2564, 1])).
% 2.53/2.71 tff(2677,plain,(c2_1(a603) | c1_1(a658) | c3_1(a603) | c0_1(a658) | c0_1(a628) | hskp56), inference(lemma,lemma(discharge,[]))).
% 2.53/2.71 tff(2678,plain,
% 2.53/2.71 (c2_1(a603)),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[2677, 2563, 943, 2529, 1, 2531])).
% 2.53/2.71 tff(2679,plain,
% 2.53/2.71 (c3_1(a658)),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[2659, 2555, 2563])).
% 2.53/2.71 tff(2680,assumption,(c3_1(a658)), introduced(assumption)).
% 2.53/2.71 tff(2681,plain,
% 2.53/2.71 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a658) | c1_1(a658) | c2_1(a599) | (~ndr1_0) | (~c3_1(a658)) | (~c0_1(a599)) | (~c1_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a658) | c1_1(a658) | c2_1(a599) | (~ndr1_0) | (~c3_1(a658)) | (~c0_1(a599)) | (~c1_1(a599)))),
% 2.53/2.71 inference(rewrite,[status(thm)],[])).
% 2.53/2.71 tff(2682,plain,
% 2.53/2.71 ((hskp5 | (~ndr1_0) | c1_1(a658) | c2_1(a658) | (~c3_1(a658)) | c2_1(a599) | (~c1_1(a599)) | (~c0_1(a599))) <=> (hskp5 | c2_1(a658) | c1_1(a658) | c2_1(a599) | (~ndr1_0) | (~c3_1(a658)) | (~c0_1(a599)) | (~c1_1(a599)))),
% 2.53/2.71 inference(rewrite,[status(thm)],[])).
% 2.53/2.71 tff(2683,plain,
% 2.53/2.71 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a658) | c2_1(a658) | (~c3_1(a658)) | c2_1(a599) | (~c1_1(a599)) | (~c0_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a658) | c1_1(a658) | c2_1(a599) | (~ndr1_0) | (~c3_1(a658)) | (~c0_1(a599)) | (~c1_1(a599))))),
% 2.53/2.71 inference(monotonicity,[status(thm)],[2682])).
% 2.53/2.71 tff(2684,plain,
% 2.53/2.71 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a658) | c2_1(a658) | (~c3_1(a658)) | c2_1(a599) | (~c1_1(a599)) | (~c0_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a658) | c1_1(a658) | c2_1(a599) | (~ndr1_0) | (~c3_1(a658)) | (~c0_1(a599)) | (~c1_1(a599)))),
% 2.53/2.71 inference(transitivity,[status(thm)],[2683, 2681])).
% 2.53/2.71 tff(2685,plain,
% 2.53/2.71 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a658) | c2_1(a658) | (~c3_1(a658)) | c2_1(a599) | (~c1_1(a599)) | (~c0_1(a599)))),
% 2.53/2.71 inference(quant_inst,[status(thm)],[])).
% 2.53/2.71 tff(2686,plain,
% 2.53/2.71 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a658) | c1_1(a658) | c2_1(a599) | (~ndr1_0) | (~c3_1(a658)) | (~c0_1(a599)) | (~c1_1(a599))),
% 2.53/2.71 inference(modus_ponens,[status(thm)],[2685, 2684])).
% 2.53/2.71 tff(2687,plain,
% 2.53/2.71 (~c1_1(a599)),
% 2.53/2.71 inference(unit_resolution,[status(thm)],[2686, 87, 523, 2530, 2680, 130, 2529, 114, 507])).
% 2.53/2.71 tff(2688,plain,
% 2.53/2.71 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | c1_1(a658) | c2_1(a599) | (~ndr1_0) | c0_1(a658) | (~c3_1(a658)) | (~c0_1(a599)) | c1_1(a599))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c1_1(a658) | c2_1(a599) | (~ndr1_0) | c0_1(a658) | (~c3_1(a658)) | (~c0_1(a599)) | c1_1(a599))),
% 2.53/2.72 inference(rewrite,[status(thm)],[])).
% 2.53/2.72 tff(2689,plain,
% 2.53/2.72 ((hskp42 | (~ndr1_0) | c1_1(a599) | c2_1(a599) | (~c0_1(a599)) | c1_1(a658) | c0_1(a658) | (~c3_1(a658))) <=> (hskp42 | c1_1(a658) | c2_1(a599) | (~ndr1_0) | c0_1(a658) | (~c3_1(a658)) | (~c0_1(a599)) | c1_1(a599))),
% 2.53/2.72 inference(rewrite,[status(thm)],[])).
% 2.53/2.72 tff(2690,plain,
% 2.53/2.72 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a599) | c2_1(a599) | (~c0_1(a599)) | c1_1(a658) | c0_1(a658) | (~c3_1(a658)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | c1_1(a658) | c2_1(a599) | (~ndr1_0) | c0_1(a658) | (~c3_1(a658)) | (~c0_1(a599)) | c1_1(a599)))),
% 2.53/2.72 inference(monotonicity,[status(thm)],[2689])).
% 2.53/2.72 tff(2691,plain,
% 2.53/2.72 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a599) | c2_1(a599) | (~c0_1(a599)) | c1_1(a658) | c0_1(a658) | (~c3_1(a658)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c1_1(a658) | c2_1(a599) | (~ndr1_0) | c0_1(a658) | (~c3_1(a658)) | (~c0_1(a599)) | c1_1(a599))),
% 2.53/2.72 inference(transitivity,[status(thm)],[2690, 2688])).
% 2.53/2.72 tff(2692,plain,
% 2.53/2.72 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a599) | c2_1(a599) | (~c0_1(a599)) | c1_1(a658) | c0_1(a658) | (~c3_1(a658)))),
% 2.53/2.72 inference(quant_inst,[status(thm)],[])).
% 2.53/2.72 tff(2693,plain,
% 2.53/2.72 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c1_1(a658) | c2_1(a599) | (~ndr1_0) | c0_1(a658) | (~c3_1(a658)) | (~c0_1(a599)) | c1_1(a599)),
% 2.53/2.72 inference(modus_ponens,[status(thm)],[2692, 2691])).
% 2.53/2.72 tff(2694,plain,
% 2.53/2.72 ($false),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[2693, 87, 2555, 2680, 130, 2529, 114, 822, 2609, 2687])).
% 2.53/2.72 tff(2695,plain,((~hskp33) | (~c3_1(a658)) | c1_1(a658) | c0_1(a658) | hskp5 | c2_1(a658)), inference(lemma,lemma(discharge,[]))).
% 2.53/2.72 tff(2696,plain,
% 2.53/2.72 (~hskp33),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[2695, 2679, 2529, 2563, 2511, 2530])).
% 2.53/2.72 tff(2697,plain,
% 2.53/2.72 (hskp61),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[342, 2696, 2528])).
% 2.53/2.72 tff(2698,assumption,(c2_1(a603)), introduced(assumption)).
% 2.53/2.72 tff(2699,plain,
% 2.53/2.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a670) | c0_1(a670) | c2_1(a628) | c1_1(a628) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a628) | (~c2_1(a670)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a670) | c0_1(a670) | c2_1(a628) | c1_1(a628) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a628) | (~c2_1(a670)))),
% 2.53/2.72 inference(rewrite,[status(thm)],[])).
% 2.53/2.72 tff(2700,plain,
% 2.53/2.72 (((~ndr1_0) | c3_1(a603) | c1_1(a603) | (~c2_1(a603)) | c1_1(a670) | c0_1(a670) | (~c2_1(a670)) | c2_1(a628) | c1_1(a628) | c0_1(a628)) <=> (c1_1(a670) | c0_1(a670) | c2_1(a628) | c1_1(a628) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a628) | (~c2_1(a670)))),
% 2.53/2.72 inference(rewrite,[status(thm)],[])).
% 2.53/2.72 tff(2701,plain,
% 2.53/2.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a603) | c1_1(a603) | (~c2_1(a603)) | c1_1(a670) | c0_1(a670) | (~c2_1(a670)) | c2_1(a628) | c1_1(a628) | c0_1(a628))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a670) | c0_1(a670) | c2_1(a628) | c1_1(a628) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a628) | (~c2_1(a670))))),
% 2.53/2.72 inference(monotonicity,[status(thm)],[2700])).
% 2.53/2.72 tff(2702,plain,
% 2.53/2.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a603) | c1_1(a603) | (~c2_1(a603)) | c1_1(a670) | c0_1(a670) | (~c2_1(a670)) | c2_1(a628) | c1_1(a628) | c0_1(a628))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a670) | c0_1(a670) | c2_1(a628) | c1_1(a628) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a628) | (~c2_1(a670)))),
% 2.53/2.72 inference(transitivity,[status(thm)],[2701, 2699])).
% 2.53/2.72 tff(2703,plain,
% 2.53/2.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a603) | c1_1(a603) | (~c2_1(a603)) | c1_1(a670) | c0_1(a670) | (~c2_1(a670)) | c2_1(a628) | c1_1(a628) | c0_1(a628))),
% 2.53/2.72 inference(quant_inst,[status(thm)],[])).
% 2.53/2.72 tff(2704,plain,
% 2.53/2.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a670) | c0_1(a670) | c2_1(a628) | c1_1(a628) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a628) | (~c2_1(a670))),
% 2.53/2.72 inference(modus_ponens,[status(thm)],[2703, 2702])).
% 2.53/2.72 tff(2705,plain,
% 2.53/2.72 ($false),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[2704, 87, 1779, 1777, 1776, 2497, 2491, 1125, 943, 1279, 2698, 1])).
% 2.53/2.72 tff(2706,plain,((~hskp61) | c1_1(a603) | c3_1(a603) | (~c2_1(a603)) | c0_1(a628)), inference(lemma,lemma(discharge,[]))).
% 2.53/2.72 tff(2707,plain,
% 2.53/2.72 (c1_1(a603)),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[2706, 2697, 2678, 943, 1])).
% 2.53/2.72 tff(2708,plain,
% 2.53/2.72 (~hskp3),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[1550, 2707])).
% 2.53/2.72 tff(2709,plain,
% 2.53/2.72 (hskp29),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[2628, 2708, 1])).
% 2.53/2.72 tff(2710,plain,
% 2.53/2.72 (~c0_1(a660)),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[1352, 2709])).
% 2.53/2.72 tff(2711,plain,
% 2.53/2.72 (~c3_1(a660)),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[1358, 2709])).
% 2.53/2.72 tff(2712,plain,
% 2.53/2.72 (~c1_1(a660)),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[1364, 2709])).
% 2.53/2.72 tff(2713,plain,
% 2.53/2.72 (~c0_1(a670)),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[348, 2697])).
% 2.53/2.72 tff(2714,plain,
% 2.53/2.72 (~c1_1(a670)),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[354, 2697])).
% 2.53/2.72 tff(2715,plain,
% 2.53/2.72 (c2_1(a670)),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[379, 2697])).
% 2.53/2.72 tff(2716,plain,
% 2.53/2.72 (~c3_1(a670)),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[2260, 87, 2715, 2714, 2713, 2712, 2711, 2710, 1113])).
% 2.53/2.72 tff(2717,plain,
% 2.53/2.72 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | (hskp42 | c1_1(a670) | c0_1(a670) | c1_1(a658) | (~ndr1_0) | c0_1(a658) | (~c3_1(a658)) | c3_1(a670))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | hskp42 | c1_1(a670) | c0_1(a670) | c1_1(a658) | (~ndr1_0) | c0_1(a658) | (~c3_1(a658)) | c3_1(a670))),
% 2.53/2.72 inference(rewrite,[status(thm)],[])).
% 2.53/2.72 tff(2718,plain,
% 2.53/2.72 ((hskp42 | (~ndr1_0) | c1_1(a658) | c0_1(a658) | (~c3_1(a658)) | c1_1(a670) | c3_1(a670) | c0_1(a670)) <=> (hskp42 | c1_1(a670) | c0_1(a670) | c1_1(a658) | (~ndr1_0) | c0_1(a658) | (~c3_1(a658)) | c3_1(a670))),
% 2.53/2.72 inference(rewrite,[status(thm)],[])).
% 2.53/2.72 tff(2719,plain,
% 2.53/2.72 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | (hskp42 | (~ndr1_0) | c1_1(a658) | c0_1(a658) | (~c3_1(a658)) | c1_1(a670) | c3_1(a670) | c0_1(a670))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | (hskp42 | c1_1(a670) | c0_1(a670) | c1_1(a658) | (~ndr1_0) | c0_1(a658) | (~c3_1(a658)) | c3_1(a670)))),
% 2.53/2.72 inference(monotonicity,[status(thm)],[2718])).
% 2.53/2.72 tff(2720,plain,
% 2.53/2.72 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | (hskp42 | (~ndr1_0) | c1_1(a658) | c0_1(a658) | (~c3_1(a658)) | c1_1(a670) | c3_1(a670) | c0_1(a670))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | hskp42 | c1_1(a670) | c0_1(a670) | c1_1(a658) | (~ndr1_0) | c0_1(a658) | (~c3_1(a658)) | c3_1(a670))),
% 2.53/2.72 inference(transitivity,[status(thm)],[2719, 2717])).
% 2.53/2.72 tff(2721,plain,
% 2.53/2.72 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | (hskp42 | (~ndr1_0) | c1_1(a658) | c0_1(a658) | (~c3_1(a658)) | c1_1(a670) | c3_1(a670) | c0_1(a670))),
% 2.53/2.72 inference(quant_inst,[status(thm)],[])).
% 2.53/2.72 tff(2722,plain,
% 2.53/2.72 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | hskp42 | c1_1(a670) | c0_1(a670) | c1_1(a658) | (~ndr1_0) | c0_1(a658) | (~c3_1(a658)) | c3_1(a670)),
% 2.53/2.72 inference(modus_ponens,[status(thm)],[2721, 2720])).
% 2.53/2.72 tff(2723,plain,
% 2.53/2.72 ($false),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[2722, 87, 2555, 2679, 2714, 2713, 2529, 2652, 2563, 2716])).
% 2.53/2.72 tff(2724,plain,(c2_1(a658) | c1_1(a658) | c0_1(a628) | c3_1(a603)), inference(lemma,lemma(discharge,[]))).
% 2.53/2.72 tff(2725,plain,
% 2.53/2.72 (c3_1(a603)),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[2724, 2530, 1, 2529])).
% 2.53/2.72 tff(2726,plain,
% 2.53/2.72 (~hskp3),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[1344, 2725])).
% 2.53/2.72 tff(2727,plain,
% 2.53/2.72 (hskp29),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[2628, 2726, 1])).
% 2.53/2.72 tff(2728,plain,
% 2.53/2.72 (~c3_1(a660)),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[1358, 2727])).
% 2.53/2.72 tff(2729,plain,
% 2.53/2.72 (~c1_1(a660)),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[1364, 2727])).
% 2.53/2.72 tff(2730,plain,
% 2.53/2.72 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a599) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c3_1(a628)) | (~c0_1(a599)) | (~c1_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a599) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c3_1(a628)) | (~c0_1(a599)) | (~c1_1(a599)))),
% 2.53/2.72 inference(rewrite,[status(thm)],[])).
% 2.53/2.72 tff(2731,plain,
% 2.53/2.72 ((hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a599) | (~c1_1(a599)) | (~c0_1(a599))) <=> (hskp5 | c2_1(a599) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c3_1(a628)) | (~c0_1(a599)) | (~c1_1(a599)))),
% 2.53/2.72 inference(rewrite,[status(thm)],[])).
% 2.53/2.72 tff(2732,plain,
% 2.53/2.72 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a599) | (~c1_1(a599)) | (~c0_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a599) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c3_1(a628)) | (~c0_1(a599)) | (~c1_1(a599))))),
% 2.53/2.72 inference(monotonicity,[status(thm)],[2731])).
% 2.53/2.72 tff(2733,plain,
% 2.53/2.72 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a599) | (~c1_1(a599)) | (~c0_1(a599)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a599) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c3_1(a628)) | (~c0_1(a599)) | (~c1_1(a599)))),
% 2.53/2.72 inference(transitivity,[status(thm)],[2732, 2730])).
% 2.53/2.72 tff(2734,plain,
% 2.53/2.72 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a599) | (~c1_1(a599)) | (~c0_1(a599)))),
% 2.53/2.72 inference(quant_inst,[status(thm)],[])).
% 2.53/2.72 tff(2735,plain,
% 2.53/2.72 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a599) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c3_1(a628)) | (~c0_1(a599)) | (~c1_1(a599))),
% 2.53/2.72 inference(modus_ponens,[status(thm)],[2734, 2733])).
% 2.53/2.72 tff(2736,plain,
% 2.53/2.72 (~c1_1(a599)),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[2735, 87, 2511, 130, 2519, 114, 2497, 2491, 507])).
% 2.53/2.72 tff(2737,plain,
% 2.53/2.72 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | c2_1(a599) | c1_1(a628) | (~ndr1_0) | c0_1(a628) | (~c3_1(a628)) | (~c0_1(a599)) | c1_1(a599))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c2_1(a599) | c1_1(a628) | (~ndr1_0) | c0_1(a628) | (~c3_1(a628)) | (~c0_1(a599)) | c1_1(a599))),
% 2.53/2.72 inference(rewrite,[status(thm)],[])).
% 2.53/2.72 tff(2738,plain,
% 2.53/2.72 ((hskp42 | (~ndr1_0) | c1_1(a599) | c2_1(a599) | (~c0_1(a599)) | c1_1(a628) | c0_1(a628) | (~c3_1(a628))) <=> (hskp42 | c2_1(a599) | c1_1(a628) | (~ndr1_0) | c0_1(a628) | (~c3_1(a628)) | (~c0_1(a599)) | c1_1(a599))),
% 2.53/2.72 inference(rewrite,[status(thm)],[])).
% 2.53/2.72 tff(2739,plain,
% 2.53/2.72 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a599) | c2_1(a599) | (~c0_1(a599)) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | c2_1(a599) | c1_1(a628) | (~ndr1_0) | c0_1(a628) | (~c3_1(a628)) | (~c0_1(a599)) | c1_1(a599)))),
% 2.53/2.72 inference(monotonicity,[status(thm)],[2738])).
% 2.53/2.72 tff(2740,plain,
% 2.53/2.72 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a599) | c2_1(a599) | (~c0_1(a599)) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c2_1(a599) | c1_1(a628) | (~ndr1_0) | c0_1(a628) | (~c3_1(a628)) | (~c0_1(a599)) | c1_1(a599))),
% 2.53/2.72 inference(transitivity,[status(thm)],[2739, 2737])).
% 2.53/2.72 tff(2741,plain,
% 2.53/2.72 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a599) | c2_1(a599) | (~c0_1(a599)) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)))),
% 2.53/2.72 inference(quant_inst,[status(thm)],[])).
% 2.53/2.72 tff(2742,plain,
% 2.53/2.72 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c2_1(a599) | c1_1(a628) | (~ndr1_0) | c0_1(a628) | (~c3_1(a628)) | (~c0_1(a599)) | c1_1(a599)),
% 2.53/2.72 inference(modus_ponens,[status(thm)],[2741, 2740])).
% 2.53/2.72 tff(2743,plain,
% 2.53/2.72 ($false),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[2742, 87, 2642, 130, 2519, 114, 2491, 822, 1, 2736])).
% 2.53/2.72 tff(2744,plain,((~hskp33) | hskp42 | c0_1(a628)), inference(lemma,lemma(discharge,[]))).
% 2.53/2.72 tff(2745,plain,
% 2.53/2.72 (~hskp33),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[2744, 2555, 1])).
% 2.53/2.72 tff(2746,plain,
% 2.53/2.72 (hskp61),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[342, 2745, 2528])).
% 2.53/2.72 tff(2747,plain,
% 2.53/2.72 (~c0_1(a670)),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[348, 2746])).
% 2.53/2.72 tff(2748,plain,
% 2.53/2.72 (~c1_1(a670)),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[354, 2746])).
% 2.53/2.72 tff(2749,plain,
% 2.53/2.72 (c2_1(a670)),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[379, 2746])).
% 2.53/2.72 tff(2750,plain,
% 2.53/2.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a658) | c1_1(a670) | c0_1(a670) | c1_1(a658) | c1_1(a660) | c3_1(a660) | (~ndr1_0) | c0_1(a658) | (~c2_1(a660)) | (~c2_1(a670)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a658) | c1_1(a670) | c0_1(a670) | c1_1(a658) | c1_1(a660) | c3_1(a660) | (~ndr1_0) | c0_1(a658) | (~c2_1(a660)) | (~c2_1(a670)))),
% 2.53/2.72 inference(rewrite,[status(thm)],[])).
% 2.53/2.72 tff(2751,plain,
% 2.53/2.72 (((~ndr1_0) | c3_1(a660) | c1_1(a660) | (~c2_1(a660)) | c1_1(a670) | c0_1(a670) | (~c2_1(a670)) | c2_1(a658) | c1_1(a658) | c0_1(a658)) <=> (c2_1(a658) | c1_1(a670) | c0_1(a670) | c1_1(a658) | c1_1(a660) | c3_1(a660) | (~ndr1_0) | c0_1(a658) | (~c2_1(a660)) | (~c2_1(a670)))),
% 2.53/2.72 inference(rewrite,[status(thm)],[])).
% 2.53/2.72 tff(2752,plain,
% 2.53/2.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a660) | c1_1(a660) | (~c2_1(a660)) | c1_1(a670) | c0_1(a670) | (~c2_1(a670)) | c2_1(a658) | c1_1(a658) | c0_1(a658))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a658) | c1_1(a670) | c0_1(a670) | c1_1(a658) | c1_1(a660) | c3_1(a660) | (~ndr1_0) | c0_1(a658) | (~c2_1(a660)) | (~c2_1(a670))))),
% 2.53/2.72 inference(monotonicity,[status(thm)],[2751])).
% 2.53/2.72 tff(2753,plain,
% 2.53/2.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a660) | c1_1(a660) | (~c2_1(a660)) | c1_1(a670) | c0_1(a670) | (~c2_1(a670)) | c2_1(a658) | c1_1(a658) | c0_1(a658))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a658) | c1_1(a670) | c0_1(a670) | c1_1(a658) | c1_1(a660) | c3_1(a660) | (~ndr1_0) | c0_1(a658) | (~c2_1(a660)) | (~c2_1(a670)))),
% 2.53/2.72 inference(transitivity,[status(thm)],[2752, 2750])).
% 2.53/2.72 tff(2754,plain,
% 2.53/2.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a660) | c1_1(a660) | (~c2_1(a660)) | c1_1(a670) | c0_1(a670) | (~c2_1(a670)) | c2_1(a658) | c1_1(a658) | c0_1(a658))),
% 2.53/2.72 inference(quant_inst,[status(thm)],[])).
% 2.53/2.72 tff(2755,plain,
% 2.53/2.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a658) | c1_1(a670) | c0_1(a670) | c1_1(a658) | c1_1(a660) | c3_1(a660) | (~ndr1_0) | c0_1(a658) | (~c2_1(a660)) | (~c2_1(a670))),
% 2.53/2.72 inference(modus_ponens,[status(thm)],[2754, 2753])).
% 2.53/2.72 tff(2756,plain,
% 2.53/2.72 (~c2_1(a660)),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[2755, 87, 2749, 2530, 2748, 2747, 2529, 2729, 2728, 1279, 2563])).
% 2.53/2.72 tff(2757,plain,
% 2.53/2.72 (~c0_1(a660)),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[1352, 2727])).
% 2.53/2.72 tff(2758,plain,
% 2.53/2.72 ($false),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[2235, 87, 2729, 2728, 2757, 170, 2756])).
% 2.53/2.72 tff(2759,plain,(c2_1(a658) | c1_1(a658) | c0_1(a628)), inference(lemma,lemma(discharge,[]))).
% 2.53/2.72 tff(2760,plain,
% 2.53/2.72 (c2_1(a658)),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[2759, 2529, 1])).
% 2.53/2.72 tff(2761,assumption,(~c3_1(a658)), introduced(assumption)).
% 2.53/2.72 tff(2762,plain,
% 2.53/2.72 (~hskp56),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[1261, 2761])).
% 2.53/2.72 tff(2763,plain,
% 2.53/2.72 (~hskp42),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[2554, 2762])).
% 2.53/2.72 tff(2764,plain,
% 2.53/2.72 (~hskp33),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[2744, 2763, 1])).
% 2.53/2.72 tff(2765,plain,
% 2.53/2.72 (hskp61),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[342, 2764, 2528])).
% 2.53/2.72 tff(2766,plain,
% 2.53/2.72 (~c0_1(a670)),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[348, 2765])).
% 2.53/2.72 tff(2767,plain,
% 2.53/2.72 (~c1_1(a670)),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[354, 2765])).
% 2.53/2.72 tff(2768,assumption,(c2_1(a658)), introduced(assumption)).
% 2.53/2.72 tff(2769,plain,
% 2.53/2.72 (c2_1(a670)),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[379, 2765])).
% 2.53/2.72 tff(2770,plain,
% 2.53/2.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a658) | c1_1(a670) | c0_1(a670) | c1_1(a658) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c2_1(a658)) | c0_1(a628) | (~c2_1(a670)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a658) | c1_1(a670) | c0_1(a670) | c1_1(a658) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c2_1(a658)) | c0_1(a628) | (~c2_1(a670)))),
% 2.53/2.72 inference(rewrite,[status(thm)],[])).
% 2.53/2.72 tff(2771,plain,
% 2.53/2.72 (((~ndr1_0) | c3_1(a658) | c1_1(a658) | (~c2_1(a658)) | c1_1(a670) | c0_1(a670) | (~c2_1(a670)) | c2_1(a628) | c1_1(a628) | c0_1(a628)) <=> (c3_1(a658) | c1_1(a670) | c0_1(a670) | c1_1(a658) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c2_1(a658)) | c0_1(a628) | (~c2_1(a670)))),
% 2.53/2.72 inference(rewrite,[status(thm)],[])).
% 2.53/2.72 tff(2772,plain,
% 2.53/2.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a658) | c1_1(a658) | (~c2_1(a658)) | c1_1(a670) | c0_1(a670) | (~c2_1(a670)) | c2_1(a628) | c1_1(a628) | c0_1(a628))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a658) | c1_1(a670) | c0_1(a670) | c1_1(a658) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c2_1(a658)) | c0_1(a628) | (~c2_1(a670))))),
% 2.53/2.72 inference(monotonicity,[status(thm)],[2771])).
% 2.53/2.72 tff(2773,plain,
% 2.53/2.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a658) | c1_1(a658) | (~c2_1(a658)) | c1_1(a670) | c0_1(a670) | (~c2_1(a670)) | c2_1(a628) | c1_1(a628) | c0_1(a628))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a658) | c1_1(a670) | c0_1(a670) | c1_1(a658) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c2_1(a658)) | c0_1(a628) | (~c2_1(a670)))),
% 2.53/2.72 inference(transitivity,[status(thm)],[2772, 2770])).
% 2.53/2.72 tff(2774,plain,
% 2.53/2.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a658) | c1_1(a658) | (~c2_1(a658)) | c1_1(a670) | c0_1(a670) | (~c2_1(a670)) | c2_1(a628) | c1_1(a628) | c0_1(a628))),
% 2.53/2.72 inference(quant_inst,[status(thm)],[])).
% 2.53/2.72 tff(2775,plain,
% 2.53/2.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a658) | c1_1(a670) | c0_1(a670) | c1_1(a658) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c2_1(a658)) | c0_1(a628) | (~c2_1(a670))),
% 2.53/2.72 inference(modus_ponens,[status(thm)],[2774, 2773])).
% 2.53/2.72 tff(2776,plain,
% 2.53/2.72 ($false),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[2775, 87, 2769, 2768, 2761, 2767, 2766, 2529, 2497, 2491, 1279, 1])).
% 2.53/2.72 tff(2777,plain,(c3_1(a658) | (~c2_1(a658)) | c1_1(a658) | c0_1(a628)), inference(lemma,lemma(discharge,[]))).
% 2.53/2.72 tff(2778,plain,
% 2.53/2.72 (c3_1(a658)),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[2777, 2760, 2529, 1])).
% 2.53/2.72 tff(2779,plain,
% 2.53/2.72 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a607) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c3_1(a628)) | (~c0_1(a607)) | (~c1_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a607) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c3_1(a628)) | (~c0_1(a607)) | (~c1_1(a607)))),
% 2.53/2.72 inference(rewrite,[status(thm)],[])).
% 2.53/2.72 tff(2780,plain,
% 2.53/2.72 ((hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607))) <=> (hskp5 | c2_1(a607) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c3_1(a628)) | (~c0_1(a607)) | (~c1_1(a607)))),
% 2.53/2.72 inference(rewrite,[status(thm)],[])).
% 2.53/2.72 tff(2781,plain,
% 2.53/2.72 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a607) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c3_1(a628)) | (~c0_1(a607)) | (~c1_1(a607))))),
% 2.53/2.72 inference(monotonicity,[status(thm)],[2780])).
% 2.53/2.72 tff(2782,plain,
% 2.53/2.72 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a607) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c3_1(a628)) | (~c0_1(a607)) | (~c1_1(a607)))),
% 2.53/2.72 inference(transitivity,[status(thm)],[2781, 2779])).
% 2.53/2.72 tff(2783,plain,
% 2.53/2.72 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a607) | (~c1_1(a607)) | (~c0_1(a607)))),
% 2.53/2.72 inference(quant_inst,[status(thm)],[])).
% 2.53/2.72 tff(2784,plain,
% 2.53/2.72 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a607) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c3_1(a628)) | (~c0_1(a607)) | (~c1_1(a607))),
% 2.53/2.72 inference(modus_ponens,[status(thm)],[2783, 2782])).
% 2.53/2.72 tff(2785,plain,
% 2.53/2.72 ($false),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[2784, 87, 523, 403, 395, 2519, 387, 2497, 2491, 507])).
% 2.53/2.72 tff(2786,plain,((~hskp37) | hskp5), inference(lemma,lemma(discharge,[]))).
% 2.53/2.72 tff(2787,plain,
% 2.53/2.72 (~hskp37),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[2786, 2511])).
% 2.53/2.72 tff(2788,plain,
% 2.53/2.72 (((~![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp37 | hskp5 | (~ndr1_0) | (~c0_1(a658)) | (~c2_1(a658)) | (~c3_1(a658)))) <=> ((~![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp37 | hskp5 | (~ndr1_0) | (~c0_1(a658)) | (~c2_1(a658)) | (~c3_1(a658)))),
% 2.53/2.72 inference(rewrite,[status(thm)],[])).
% 2.53/2.72 tff(2789,plain,
% 2.53/2.72 ((hskp37 | hskp5 | (~ndr1_0) | (~c3_1(a658)) | (~c0_1(a658)) | (~c2_1(a658))) <=> (hskp37 | hskp5 | (~ndr1_0) | (~c0_1(a658)) | (~c2_1(a658)) | (~c3_1(a658)))),
% 2.53/2.72 inference(rewrite,[status(thm)],[])).
% 2.53/2.72 tff(2790,plain,
% 2.53/2.72 (((~![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(a658)) | (~c0_1(a658)) | (~c2_1(a658)))) <=> ((~![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp37 | hskp5 | (~ndr1_0) | (~c0_1(a658)) | (~c2_1(a658)) | (~c3_1(a658))))),
% 2.53/2.72 inference(monotonicity,[status(thm)],[2789])).
% 2.53/2.72 tff(2791,plain,
% 2.53/2.72 (((~![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(a658)) | (~c0_1(a658)) | (~c2_1(a658)))) <=> ((~![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp37 | hskp5 | (~ndr1_0) | (~c0_1(a658)) | (~c2_1(a658)) | (~c3_1(a658)))),
% 2.53/2.72 inference(transitivity,[status(thm)],[2790, 2788])).
% 2.53/2.72 tff(2792,plain,
% 2.53/2.72 ((~![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(a658)) | (~c0_1(a658)) | (~c2_1(a658)))),
% 2.53/2.72 inference(quant_inst,[status(thm)],[])).
% 2.53/2.72 tff(2793,plain,
% 2.53/2.72 ((~![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp37 | hskp5 | (~ndr1_0) | (~c0_1(a658)) | (~c2_1(a658)) | (~c3_1(a658))),
% 2.53/2.72 inference(modus_ponens,[status(thm)],[2792, 2791])).
% 2.53/2.72 tff(2794,plain,
% 2.53/2.72 (~c0_1(a658)),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[2793, 87, 2787, 2511, 2760, 2778, 521])).
% 2.53/2.72 tff(2795,plain,
% 2.53/2.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a658) | c1_1(a660) | c3_1(a660) | c0_1(a660) | c1_1(a628) | (~ndr1_0) | (~c2_1(a658)) | (~c3_1(a658)) | c0_1(a628) | (~c3_1(a628)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a658) | c1_1(a660) | c3_1(a660) | c0_1(a660) | c1_1(a628) | (~ndr1_0) | (~c2_1(a658)) | (~c3_1(a658)) | c0_1(a628) | (~c3_1(a628)))),
% 2.53/2.72 inference(rewrite,[status(thm)],[])).
% 2.53/2.72 tff(2796,plain,
% 2.53/2.72 (((~ndr1_0) | c1_1(a658) | (~c3_1(a658)) | (~c2_1(a658)) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)) | c1_1(a660) | c0_1(a660) | c3_1(a660)) <=> (c1_1(a658) | c1_1(a660) | c3_1(a660) | c0_1(a660) | c1_1(a628) | (~ndr1_0) | (~c2_1(a658)) | (~c3_1(a658)) | c0_1(a628) | (~c3_1(a628)))),
% 2.53/2.72 inference(rewrite,[status(thm)],[])).
% 2.53/2.72 tff(2797,plain,
% 2.53/2.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a658) | (~c3_1(a658)) | (~c2_1(a658)) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)) | c1_1(a660) | c0_1(a660) | c3_1(a660))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a658) | c1_1(a660) | c3_1(a660) | c0_1(a660) | c1_1(a628) | (~ndr1_0) | (~c2_1(a658)) | (~c3_1(a658)) | c0_1(a628) | (~c3_1(a628))))),
% 2.53/2.72 inference(monotonicity,[status(thm)],[2796])).
% 2.53/2.72 tff(2798,plain,
% 2.53/2.72 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a658) | (~c3_1(a658)) | (~c2_1(a658)) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)) | c1_1(a660) | c0_1(a660) | c3_1(a660))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a658) | c1_1(a660) | c3_1(a660) | c0_1(a660) | c1_1(a628) | (~ndr1_0) | (~c2_1(a658)) | (~c3_1(a658)) | c0_1(a628) | (~c3_1(a628)))),
% 2.53/2.72 inference(transitivity,[status(thm)],[2797, 2795])).
% 2.53/2.72 tff(2799,plain,
% 2.53/2.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a658) | (~c3_1(a658)) | (~c2_1(a658)) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)) | c1_1(a660) | c0_1(a660) | c3_1(a660))),
% 2.53/2.72 inference(quant_inst,[status(thm)],[])).
% 2.53/2.72 tff(2800,plain,
% 2.53/2.72 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a658) | c1_1(a660) | c3_1(a660) | c0_1(a660) | c1_1(a628) | (~ndr1_0) | (~c2_1(a658)) | (~c3_1(a658)) | c0_1(a628) | (~c3_1(a628))),
% 2.53/2.72 inference(modus_ponens,[status(thm)],[2799, 2798])).
% 2.53/2.72 tff(2801,plain,
% 2.53/2.72 ($false),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[2800, 87, 2768, 2680, 2519, 2529, 1365, 1359, 1353, 2491, 1113, 1])).
% 2.53/2.72 tff(2802,plain,((~hskp29) | (~c2_1(a658)) | (~c3_1(a658)) | c1_1(a658) | c0_1(a628)), inference(lemma,lemma(discharge,[]))).
% 2.53/2.72 tff(2803,plain,
% 2.53/2.72 (~hskp29),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[2802, 2760, 2778, 2529, 1])).
% 2.53/2.72 tff(2804,plain,
% 2.53/2.72 (hskp3),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[2628, 2803, 1])).
% 2.53/2.72 tff(2805,plain,
% 2.53/2.72 (~c3_1(a603)),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[1344, 2804])).
% 2.53/2.72 tff(2806,plain,
% 2.53/2.72 (c0_1(a603)),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[2578, 87, 2641, 943, 170, 1774])).
% 2.53/2.72 tff(2807,plain,
% 2.53/2.72 (hskp42 | (~c0_1(a603))),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[2585, 87, 2519, 2491, 2641, 822, 1774, 1])).
% 2.53/2.72 tff(2808,plain,
% 2.53/2.72 (hskp42),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[2807, 2806])).
% 2.53/2.72 tff(2809,plain,
% 2.53/2.72 (hskp56),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[2554, 2808])).
% 2.53/2.72 tff(2810,plain,
% 2.53/2.72 (c3_1(a658)),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[1261, 2809])).
% 2.53/2.72 tff(2811,plain,
% 2.53/2.72 (~c3_1(a618)),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[915, 2808])).
% 2.53/2.72 tff(2812,plain,
% 2.53/2.72 (~c2_1(a618)),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[845, 2808])).
% 2.53/2.72 tff(2813,plain,
% 2.53/2.72 (c2_1(a658)),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[2724, 943, 1, 2529])).
% 2.53/2.72 tff(2814,plain,
% 2.53/2.72 (c1_1(a618)),
% 2.53/2.72 inference(unit_resolution,[status(thm)],[876, 2808])).
% 2.53/2.72 tff(2815,plain,
% 2.53/2.72 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a618) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c1_1(a618)) | (~c0_1(a618)) | (~c3_1(a628)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a618) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c1_1(a618)) | (~c0_1(a618)) | (~c3_1(a628)))),
% 2.53/2.72 inference(rewrite,[status(thm)],[])).
% 2.53/2.72 tff(2816,plain,
% 2.53/2.72 ((hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a618) | (~c1_1(a618)) | (~c0_1(a618))) <=> (hskp5 | c2_1(a618) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c1_1(a618)) | (~c0_1(a618)) | (~c3_1(a628)))),
% 2.53/2.73 inference(rewrite,[status(thm)],[])).
% 2.53/2.73 tff(2817,plain,
% 2.53/2.73 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a618) | (~c1_1(a618)) | (~c0_1(a618)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a618) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c1_1(a618)) | (~c0_1(a618)) | (~c3_1(a628))))),
% 2.53/2.73 inference(monotonicity,[status(thm)],[2816])).
% 2.53/2.73 tff(2818,plain,
% 2.53/2.73 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a618) | (~c1_1(a618)) | (~c0_1(a618)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a618) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c1_1(a618)) | (~c0_1(a618)) | (~c3_1(a628)))),
% 2.53/2.73 inference(transitivity,[status(thm)],[2817, 2815])).
% 2.53/2.73 tff(2819,plain,
% 2.53/2.73 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a618) | (~c1_1(a618)) | (~c0_1(a618)))),
% 2.53/2.73 inference(quant_inst,[status(thm)],[])).
% 2.53/2.73 tff(2820,plain,
% 2.53/2.73 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a618) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c1_1(a618)) | (~c0_1(a618)) | (~c3_1(a628))),
% 2.53/2.73 inference(modus_ponens,[status(thm)],[2819, 2818])).
% 2.53/2.73 tff(2821,plain,
% 2.53/2.73 (~c0_1(a618)),
% 2.53/2.73 inference(unit_resolution,[status(thm)],[2820, 87, 2511, 2814, 2519, 2812, 2497, 2491, 507])).
% 2.53/2.73 tff(2822,assumption,(~c0_1(a618)), introduced(assumption)).
% 2.53/2.73 tff(2823,assumption,(c3_1(a670)), introduced(assumption)).
% 2.53/2.73 tff(2824,assumption,(~c0_1(a670)), introduced(assumption)).
% 2.53/2.73 tff(2825,assumption,(c2_1(a670)), introduced(assumption)).
% 2.53/2.73 tff(2826,plain,
% 2.53/2.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a674) | c0_1(a670) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c0_1(a674)) | (~c2_1(a674)) | (~c3_1(a628)) | (~c2_1(a670)) | (~c3_1(a670)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a674) | c0_1(a670) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c0_1(a674)) | (~c2_1(a674)) | (~c3_1(a628)) | (~c2_1(a670)) | (~c3_1(a670)))),
% 2.53/2.73 inference(rewrite,[status(thm)],[])).
% 2.53/2.73 tff(2827,plain,
% 2.53/2.73 (((~ndr1_0) | c0_1(a670) | (~c3_1(a670)) | (~c2_1(a670)) | c1_1(a674) | (~c2_1(a674)) | (~c0_1(a674)) | c2_1(a628) | c1_1(a628) | (~c3_1(a628))) <=> (c1_1(a674) | c0_1(a670) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c0_1(a674)) | (~c2_1(a674)) | (~c3_1(a628)) | (~c2_1(a670)) | (~c3_1(a670)))),
% 2.53/2.73 inference(rewrite,[status(thm)],[])).
% 2.53/2.73 tff(2828,plain,
% 2.53/2.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a670) | (~c3_1(a670)) | (~c2_1(a670)) | c1_1(a674) | (~c2_1(a674)) | (~c0_1(a674)) | c2_1(a628) | c1_1(a628) | (~c3_1(a628)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a674) | c0_1(a670) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c0_1(a674)) | (~c2_1(a674)) | (~c3_1(a628)) | (~c2_1(a670)) | (~c3_1(a670))))),
% 2.53/2.73 inference(monotonicity,[status(thm)],[2827])).
% 2.53/2.73 tff(2829,plain,
% 2.53/2.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a670) | (~c3_1(a670)) | (~c2_1(a670)) | c1_1(a674) | (~c2_1(a674)) | (~c0_1(a674)) | c2_1(a628) | c1_1(a628) | (~c3_1(a628)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a674) | c0_1(a670) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c0_1(a674)) | (~c2_1(a674)) | (~c3_1(a628)) | (~c2_1(a670)) | (~c3_1(a670)))),
% 2.53/2.73 inference(transitivity,[status(thm)],[2828, 2826])).
% 2.53/2.73 tff(2830,plain,
% 2.53/2.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a670) | (~c3_1(a670)) | (~c2_1(a670)) | c1_1(a674) | (~c2_1(a674)) | (~c0_1(a674)) | c2_1(a628) | c1_1(a628) | (~c3_1(a628)))),
% 2.53/2.73 inference(quant_inst,[status(thm)],[])).
% 2.53/2.73 tff(2831,plain,
% 2.53/2.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a674) | c0_1(a670) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c0_1(a674)) | (~c2_1(a674)) | (~c3_1(a628)) | (~c2_1(a670)) | (~c3_1(a670))),
% 2.53/2.73 inference(modus_ponens,[status(thm)],[2830, 2829])).
% 2.53/2.73 tff(2832,plain,
% 2.53/2.73 ($false),
% 2.53/2.73 inference(unit_resolution,[status(thm)],[2831, 87, 255, 247, 2825, 2519, 239, 2824, 2497, 2491, 645, 2823])).
% 2.53/2.73 tff(2833,plain,((~hskp65) | (~c2_1(a670)) | c0_1(a670) | (~c3_1(a670))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.73 tff(2834,plain,
% 2.53/2.73 (~c3_1(a670)),
% 2.53/2.73 inference(unit_resolution,[status(thm)],[2833, 1779, 233, 1776])).
% 2.53/2.73 tff(2835,plain,
% 2.53/2.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a670) | c0_1(a670) | c1_1(a658) | c1_1(a628) | (~ndr1_0) | (~c2_1(a658)) | (~c3_1(a658)) | c0_1(a628) | (~c3_1(a628)) | c3_1(a670))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a670) | c0_1(a670) | c1_1(a658) | c1_1(a628) | (~ndr1_0) | (~c2_1(a658)) | (~c3_1(a658)) | c0_1(a628) | (~c3_1(a628)) | c3_1(a670))),
% 2.53/2.73 inference(rewrite,[status(thm)],[])).
% 2.53/2.73 tff(2836,plain,
% 2.53/2.73 (((~ndr1_0) | c1_1(a658) | (~c3_1(a658)) | (~c2_1(a658)) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)) | c1_1(a670) | c0_1(a670) | c3_1(a670)) <=> (c1_1(a670) | c0_1(a670) | c1_1(a658) | c1_1(a628) | (~ndr1_0) | (~c2_1(a658)) | (~c3_1(a658)) | c0_1(a628) | (~c3_1(a628)) | c3_1(a670))),
% 2.53/2.73 inference(rewrite,[status(thm)],[])).
% 2.53/2.73 tff(2837,plain,
% 2.53/2.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a658) | (~c3_1(a658)) | (~c2_1(a658)) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)) | c1_1(a670) | c0_1(a670) | c3_1(a670))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a670) | c0_1(a670) | c1_1(a658) | c1_1(a628) | (~ndr1_0) | (~c2_1(a658)) | (~c3_1(a658)) | c0_1(a628) | (~c3_1(a628)) | c3_1(a670)))),
% 2.53/2.73 inference(monotonicity,[status(thm)],[2836])).
% 2.53/2.73 tff(2838,plain,
% 2.53/2.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a658) | (~c3_1(a658)) | (~c2_1(a658)) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)) | c1_1(a670) | c0_1(a670) | c3_1(a670))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a670) | c0_1(a670) | c1_1(a658) | c1_1(a628) | (~ndr1_0) | (~c2_1(a658)) | (~c3_1(a658)) | c0_1(a628) | (~c3_1(a628)) | c3_1(a670))),
% 2.53/2.73 inference(transitivity,[status(thm)],[2837, 2835])).
% 2.53/2.73 tff(2839,plain,
% 2.53/2.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a658) | (~c3_1(a658)) | (~c2_1(a658)) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)) | c1_1(a670) | c0_1(a670) | c3_1(a670))),
% 2.53/2.73 inference(quant_inst,[status(thm)],[])).
% 2.53/2.73 tff(2840,plain,
% 2.53/2.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a670) | c0_1(a670) | c1_1(a658) | c1_1(a628) | (~ndr1_0) | (~c2_1(a658)) | (~c3_1(a658)) | c0_1(a628) | (~c3_1(a628)) | c3_1(a670)),
% 2.53/2.73 inference(modus_ponens,[status(thm)],[2839, 2838])).
% 2.53/2.73 tff(2841,plain,
% 2.53/2.73 ($false),
% 2.53/2.73 inference(unit_resolution,[status(thm)],[2840, 87, 2768, 2680, 2519, 1777, 1776, 2529, 2491, 1113, 2834, 1])).
% 2.53/2.73 tff(2842,plain,((~hskp61) | (~c2_1(a658)) | (~c3_1(a658)) | c1_1(a658) | c0_1(a628) | (~hskp65)), inference(lemma,lemma(discharge,[]))).
% 2.53/2.73 tff(2843,plain,
% 2.53/2.73 (~hskp61),
% 2.53/2.73 inference(unit_resolution,[status(thm)],[2842, 233, 2680, 2529, 1, 2768])).
% 2.53/2.73 tff(2844,plain,
% 2.53/2.73 (hskp33),
% 2.53/2.73 inference(unit_resolution,[status(thm)],[342, 2843, 2528])).
% 2.53/2.73 tff(2845,plain,
% 2.53/2.73 (~c2_1(a599)),
% 2.53/2.73 inference(unit_resolution,[status(thm)],[113, 2844])).
% 2.53/2.73 tff(2846,plain,
% 2.53/2.73 (c3_1(a599)),
% 2.53/2.73 inference(unit_resolution,[status(thm)],[121, 2844])).
% 2.53/2.73 tff(2847,plain,
% 2.53/2.73 (c0_1(a599)),
% 2.53/2.73 inference(unit_resolution,[status(thm)],[129, 2844])).
% 2.53/2.73 tff(2848,plain,
% 2.53/2.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a658) | c2_1(a618) | c3_1(a618) | c2_1(a599) | (~ndr1_0) | c0_1(a618) | (~c0_1(a658)) | (~c3_1(a658)) | (~c0_1(a599)) | (~c3_1(a599)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a658) | c2_1(a618) | c3_1(a618) | c2_1(a599) | (~ndr1_0) | c0_1(a618) | (~c0_1(a658)) | (~c3_1(a658)) | (~c0_1(a599)) | (~c3_1(a599)))),
% 2.53/2.73 inference(rewrite,[status(thm)],[])).
% 2.53/2.73 tff(2849,plain,
% 2.53/2.73 (((~ndr1_0) | c1_1(a658) | (~c3_1(a658)) | (~c0_1(a658)) | c2_1(a599) | (~c3_1(a599)) | (~c0_1(a599)) | c2_1(a618) | c0_1(a618) | c3_1(a618)) <=> (c1_1(a658) | c2_1(a618) | c3_1(a618) | c2_1(a599) | (~ndr1_0) | c0_1(a618) | (~c0_1(a658)) | (~c3_1(a658)) | (~c0_1(a599)) | (~c3_1(a599)))),
% 2.53/2.73 inference(rewrite,[status(thm)],[])).
% 2.53/2.73 tff(2850,plain,
% 2.53/2.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a658) | (~c3_1(a658)) | (~c0_1(a658)) | c2_1(a599) | (~c3_1(a599)) | (~c0_1(a599)) | c2_1(a618) | c0_1(a618) | c3_1(a618))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a658) | c2_1(a618) | c3_1(a618) | c2_1(a599) | (~ndr1_0) | c0_1(a618) | (~c0_1(a658)) | (~c3_1(a658)) | (~c0_1(a599)) | (~c3_1(a599))))),
% 2.53/2.73 inference(monotonicity,[status(thm)],[2849])).
% 2.53/2.73 tff(2851,plain,
% 2.53/2.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a658) | (~c3_1(a658)) | (~c0_1(a658)) | c2_1(a599) | (~c3_1(a599)) | (~c0_1(a599)) | c2_1(a618) | c0_1(a618) | c3_1(a618))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a658) | c2_1(a618) | c3_1(a618) | c2_1(a599) | (~ndr1_0) | c0_1(a618) | (~c0_1(a658)) | (~c3_1(a658)) | (~c0_1(a599)) | (~c3_1(a599)))),
% 2.53/2.73 inference(transitivity,[status(thm)],[2850, 2848])).
% 2.53/2.73 tff(2852,plain,
% 2.53/2.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a658) | (~c3_1(a658)) | (~c0_1(a658)) | c2_1(a599) | (~c3_1(a599)) | (~c0_1(a599)) | c2_1(a618) | c0_1(a618) | c3_1(a618))),
% 2.53/2.73 inference(quant_inst,[status(thm)],[])).
% 2.53/2.73 tff(2853,plain,
% 2.53/2.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a658) | c2_1(a618) | c3_1(a618) | c2_1(a599) | (~ndr1_0) | c0_1(a618) | (~c0_1(a658)) | (~c3_1(a658)) | (~c0_1(a599)) | (~c3_1(a599))),
% 2.53/2.73 inference(modus_ponens,[status(thm)],[2852, 2851])).
% 2.53/2.73 tff(2854,plain,
% 2.53/2.73 (~c0_1(a658)),
% 2.53/2.73 inference(unit_resolution,[status(thm)],[2853, 87, 2680, 2847, 2846, 2529, 2541, 2540, 2845, 910, 2822])).
% 2.53/2.73 tff(2855,plain,
% 2.53/2.73 (((~![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp6 | (~ndr1_0) | (~c0_1(a599)) | (~c3_1(a599)) | (~c1_1(a599)))) <=> ((~![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp6 | (~ndr1_0) | (~c0_1(a599)) | (~c3_1(a599)) | (~c1_1(a599)))),
% 2.53/2.73 inference(rewrite,[status(thm)],[])).
% 2.53/2.73 tff(2856,plain,
% 2.53/2.73 ((hskp6 | (~ndr1_0) | (~c3_1(a599)) | (~c1_1(a599)) | (~c0_1(a599))) <=> (hskp6 | (~ndr1_0) | (~c0_1(a599)) | (~c3_1(a599)) | (~c1_1(a599)))),
% 2.53/2.73 inference(rewrite,[status(thm)],[])).
% 2.53/2.73 tff(2857,plain,
% 2.53/2.73 (((~![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp6 | (~ndr1_0) | (~c3_1(a599)) | (~c1_1(a599)) | (~c0_1(a599)))) <=> ((~![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp6 | (~ndr1_0) | (~c0_1(a599)) | (~c3_1(a599)) | (~c1_1(a599))))),
% 2.53/2.73 inference(monotonicity,[status(thm)],[2856])).
% 2.53/2.73 tff(2858,plain,
% 2.53/2.73 (((~![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp6 | (~ndr1_0) | (~c3_1(a599)) | (~c1_1(a599)) | (~c0_1(a599)))) <=> ((~![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp6 | (~ndr1_0) | (~c0_1(a599)) | (~c3_1(a599)) | (~c1_1(a599)))),
% 2.53/2.73 inference(transitivity,[status(thm)],[2857, 2855])).
% 2.53/2.73 tff(2859,plain,
% 2.53/2.73 ((~![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp6 | (~ndr1_0) | (~c3_1(a599)) | (~c1_1(a599)) | (~c0_1(a599)))),
% 2.53/2.73 inference(quant_inst,[status(thm)],[])).
% 2.53/2.73 tff(2860,plain,
% 2.53/2.73 ((~![U: $i] : (hskp6 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp6 | (~ndr1_0) | (~c0_1(a599)) | (~c3_1(a599)) | (~c1_1(a599))),
% 2.53/2.73 inference(modus_ponens,[status(thm)],[2859, 2858])).
% 2.53/2.73 tff(2861,plain,
% 2.53/2.73 (~c1_1(a599)),
% 2.53/2.73 inference(unit_resolution,[status(thm)],[2860, 87, 2354, 130, 122, 679])).
% 2.53/2.73 tff(2862,plain,
% 2.53/2.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a618) | c3_1(a618) | c2_1(a599) | (~ndr1_0) | c0_1(a618) | (~c0_1(a599)) | (~c3_1(a599)) | c1_1(a599))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a618) | c3_1(a618) | c2_1(a599) | (~ndr1_0) | c0_1(a618) | (~c0_1(a599)) | (~c3_1(a599)) | c1_1(a599))),
% 2.53/2.73 inference(rewrite,[status(thm)],[])).
% 2.53/2.73 tff(2863,plain,
% 2.53/2.73 (((~ndr1_0) | c1_1(a599) | (~c3_1(a599)) | (~c0_1(a599)) | c2_1(a599) | (~c3_1(a599)) | (~c0_1(a599)) | c2_1(a618) | c0_1(a618) | c3_1(a618)) <=> (c2_1(a618) | c3_1(a618) | c2_1(a599) | (~ndr1_0) | c0_1(a618) | (~c0_1(a599)) | (~c3_1(a599)) | c1_1(a599))),
% 2.53/2.73 inference(rewrite,[status(thm)],[])).
% 2.53/2.73 tff(2864,plain,
% 2.53/2.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c3_1(a599)) | (~c0_1(a599)) | c2_1(a599) | (~c3_1(a599)) | (~c0_1(a599)) | c2_1(a618) | c0_1(a618) | c3_1(a618))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a618) | c3_1(a618) | c2_1(a599) | (~ndr1_0) | c0_1(a618) | (~c0_1(a599)) | (~c3_1(a599)) | c1_1(a599)))),
% 2.53/2.73 inference(monotonicity,[status(thm)],[2863])).
% 2.53/2.73 tff(2865,plain,
% 2.53/2.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c3_1(a599)) | (~c0_1(a599)) | c2_1(a599) | (~c3_1(a599)) | (~c0_1(a599)) | c2_1(a618) | c0_1(a618) | c3_1(a618))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a618) | c3_1(a618) | c2_1(a599) | (~ndr1_0) | c0_1(a618) | (~c0_1(a599)) | (~c3_1(a599)) | c1_1(a599))),
% 2.53/2.73 inference(transitivity,[status(thm)],[2864, 2862])).
% 2.53/2.73 tff(2866,plain,
% 2.53/2.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a599) | (~c3_1(a599)) | (~c0_1(a599)) | c2_1(a599) | (~c3_1(a599)) | (~c0_1(a599)) | c2_1(a618) | c0_1(a618) | c3_1(a618))),
% 2.53/2.73 inference(quant_inst,[status(thm)],[])).
% 2.53/2.73 tff(2867,plain,
% 2.53/2.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a618) | c3_1(a618) | c2_1(a599) | (~ndr1_0) | c0_1(a618) | (~c0_1(a599)) | (~c3_1(a599)) | c1_1(a599)),
% 2.53/2.73 inference(modus_ponens,[status(thm)],[2866, 2865])).
% 2.53/2.73 tff(2868,plain,
% 2.53/2.73 ($false),
% 2.53/2.73 inference(unit_resolution,[status(thm)],[2867, 87, 130, 122, 2541, 2540, 114, 910, 2822, 2861])).
% 2.53/2.73 tff(2869,plain,((~hskp33) | c2_1(a618) | c3_1(a618) | c0_1(a618) | hskp6), inference(lemma,lemma(discharge,[]))).
% 2.53/2.73 tff(2870,plain,
% 2.53/2.73 (hskp6),
% 2.53/2.73 inference(unit_resolution,[status(thm)],[2869, 2844, 2540, 2822, 2541])).
% 2.53/2.73 tff(2871,plain,
% 2.53/2.73 (~c0_1(a609)),
% 2.53/2.73 inference(unit_resolution,[status(thm)],[691, 2870])).
% 2.53/2.73 tff(2872,plain,
% 2.53/2.73 (c2_1(a609)),
% 2.53/2.73 inference(unit_resolution,[status(thm)],[701, 2870])).
% 2.53/2.73 tff(2873,plain,
% 2.53/2.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a674) | c2_1(a628) | c1_1(a628) | c0_1(a609) | (~ndr1_0) | (~c3_1(a609)) | (~c2_1(a609)) | (~c0_1(a674)) | (~c2_1(a674)) | (~c3_1(a628)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a674) | c2_1(a628) | c1_1(a628) | c0_1(a609) | (~ndr1_0) | (~c3_1(a609)) | (~c2_1(a609)) | (~c0_1(a674)) | (~c2_1(a674)) | (~c3_1(a628)))),
% 2.53/2.73 inference(rewrite,[status(thm)],[])).
% 2.53/2.73 tff(2874,plain,
% 2.53/2.73 (((~ndr1_0) | c0_1(a609) | (~c3_1(a609)) | (~c2_1(a609)) | c1_1(a674) | (~c2_1(a674)) | (~c0_1(a674)) | c2_1(a628) | c1_1(a628) | (~c3_1(a628))) <=> (c1_1(a674) | c2_1(a628) | c1_1(a628) | c0_1(a609) | (~ndr1_0) | (~c3_1(a609)) | (~c2_1(a609)) | (~c0_1(a674)) | (~c2_1(a674)) | (~c3_1(a628)))),
% 2.53/2.73 inference(rewrite,[status(thm)],[])).
% 2.53/2.73 tff(2875,plain,
% 2.53/2.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a609) | (~c3_1(a609)) | (~c2_1(a609)) | c1_1(a674) | (~c2_1(a674)) | (~c0_1(a674)) | c2_1(a628) | c1_1(a628) | (~c3_1(a628)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | (c1_1(a674) | c2_1(a628) | c1_1(a628) | c0_1(a609) | (~ndr1_0) | (~c3_1(a609)) | (~c2_1(a609)) | (~c0_1(a674)) | (~c2_1(a674)) | (~c3_1(a628))))),
% 2.53/2.73 inference(monotonicity,[status(thm)],[2874])).
% 2.53/2.73 tff(2876,plain,
% 2.53/2.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a609) | (~c3_1(a609)) | (~c2_1(a609)) | c1_1(a674) | (~c2_1(a674)) | (~c0_1(a674)) | c2_1(a628) | c1_1(a628) | (~c3_1(a628)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a674) | c2_1(a628) | c1_1(a628) | c0_1(a609) | (~ndr1_0) | (~c3_1(a609)) | (~c2_1(a609)) | (~c0_1(a674)) | (~c2_1(a674)) | (~c3_1(a628)))),
% 2.53/2.73 inference(transitivity,[status(thm)],[2875, 2873])).
% 2.53/2.73 tff(2877,plain,
% 2.53/2.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | ((~ndr1_0) | c0_1(a609) | (~c3_1(a609)) | (~c2_1(a609)) | c1_1(a674) | (~c2_1(a674)) | (~c0_1(a674)) | c2_1(a628) | c1_1(a628) | (~c3_1(a628)))),
% 2.53/2.73 inference(quant_inst,[status(thm)],[])).
% 2.53/2.73 tff(2878,plain,
% 2.53/2.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)) | c2_1(W) | c1_1(W) | (~c3_1(W)))) | c1_1(a674) | c2_1(a628) | c1_1(a628) | c0_1(a609) | (~ndr1_0) | (~c3_1(a609)) | (~c2_1(a609)) | (~c0_1(a674)) | (~c2_1(a674)) | (~c3_1(a628))),
% 2.53/2.73 inference(modus_ponens,[status(thm)],[2877, 2876])).
% 2.53/2.73 tff(2879,plain,
% 2.53/2.73 (~c3_1(a609)),
% 2.53/2.73 inference(unit_resolution,[status(thm)],[2878, 87, 255, 247, 2519, 2872, 239, 2497, 2491, 2871, 645])).
% 2.53/2.73 tff(2880,plain,
% 2.53/2.73 (~c1_1(a609)),
% 2.53/2.73 inference(unit_resolution,[status(thm)],[1395, 2870])).
% 2.53/2.73 tff(2881,plain,
% 2.53/2.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a658) | c0_1(a609) | c1_1(a609) | (~ndr1_0) | c3_1(a609) | c0_1(a658) | (~c2_1(a658)) | (~c3_1(a658)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a658) | c0_1(a609) | c1_1(a609) | (~ndr1_0) | c3_1(a609) | c0_1(a658) | (~c2_1(a658)) | (~c3_1(a658)))),
% 2.53/2.73 inference(rewrite,[status(thm)],[])).
% 2.53/2.73 tff(2882,plain,
% 2.53/2.73 (((~ndr1_0) | c1_1(a658) | (~c3_1(a658)) | (~c2_1(a658)) | c1_1(a658) | c0_1(a658) | (~c3_1(a658)) | c1_1(a609) | c0_1(a609) | c3_1(a609)) <=> (c1_1(a658) | c0_1(a609) | c1_1(a609) | (~ndr1_0) | c3_1(a609) | c0_1(a658) | (~c2_1(a658)) | (~c3_1(a658)))),
% 2.53/2.73 inference(rewrite,[status(thm)],[])).
% 2.53/2.73 tff(2883,plain,
% 2.53/2.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a658) | (~c3_1(a658)) | (~c2_1(a658)) | c1_1(a658) | c0_1(a658) | (~c3_1(a658)) | c1_1(a609) | c0_1(a609) | c3_1(a609))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a658) | c0_1(a609) | c1_1(a609) | (~ndr1_0) | c3_1(a609) | c0_1(a658) | (~c2_1(a658)) | (~c3_1(a658))))),
% 2.53/2.73 inference(monotonicity,[status(thm)],[2882])).
% 2.53/2.73 tff(2884,plain,
% 2.53/2.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a658) | (~c3_1(a658)) | (~c2_1(a658)) | c1_1(a658) | c0_1(a658) | (~c3_1(a658)) | c1_1(a609) | c0_1(a609) | c3_1(a609))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a658) | c0_1(a609) | c1_1(a609) | (~ndr1_0) | c3_1(a609) | c0_1(a658) | (~c2_1(a658)) | (~c3_1(a658)))),
% 2.53/2.73 inference(transitivity,[status(thm)],[2883, 2881])).
% 2.53/2.73 tff(2885,plain,
% 2.53/2.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a658) | (~c3_1(a658)) | (~c2_1(a658)) | c1_1(a658) | c0_1(a658) | (~c3_1(a658)) | c1_1(a609) | c0_1(a609) | c3_1(a609))),
% 2.53/2.73 inference(quant_inst,[status(thm)],[])).
% 2.53/2.73 tff(2886,plain,
% 2.53/2.73 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a658) | c0_1(a609) | c1_1(a609) | (~ndr1_0) | c3_1(a609) | c0_1(a658) | (~c2_1(a658)) | (~c3_1(a658))),
% 2.53/2.73 inference(modus_ponens,[status(thm)],[2885, 2884])).
% 2.53/2.73 tff(2887,plain,
% 2.53/2.73 ($false),
% 2.53/2.73 inference(unit_resolution,[status(thm)],[2886, 87, 2768, 2680, 2529, 2871, 2880, 1113, 2879, 2854])).
% 2.53/2.73 tff(2888,plain,((~hskp65) | (~c2_1(a658)) | (~c3_1(a658)) | c1_1(a658) | c2_1(a618) | c3_1(a618) | c0_1(a618) | c0_1(a628)), inference(lemma,lemma(discharge,[]))).
% 2.53/2.73 tff(2889,plain,
% 2.53/2.73 (~hskp65),
% 2.53/2.73 inference(unit_resolution,[status(thm)],[2888, 2821, 2813, 2529, 2812, 2811, 2810, 1])).
% 2.53/2.73 tff(2890,plain,
% 2.53/2.73 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | c1_1(a658) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c2_1(a658)) | (~c3_1(a658)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp20 | c1_1(a658) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c2_1(a658)) | (~c3_1(a658)))),
% 2.53/2.73 inference(rewrite,[status(thm)],[])).
% 2.53/2.73 tff(2891,plain,
% 2.53/2.73 ((hskp20 | (~ndr1_0) | c3_1(a603) | c2_1(a603) | (~c0_1(a603)) | c1_1(a658) | (~c2_1(a658)) | (~c3_1(a658))) <=> (hskp20 | c1_1(a658) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c2_1(a658)) | (~c3_1(a658)))),
% 2.53/2.73 inference(rewrite,[status(thm)],[])).
% 2.53/2.73 tff(2892,plain,
% 2.53/2.73 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a603) | c2_1(a603) | (~c0_1(a603)) | c1_1(a658) | (~c2_1(a658)) | (~c3_1(a658)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | c1_1(a658) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c2_1(a658)) | (~c3_1(a658))))),
% 2.53/2.73 inference(monotonicity,[status(thm)],[2891])).
% 2.53/2.73 tff(2893,plain,
% 2.53/2.73 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a603) | c2_1(a603) | (~c0_1(a603)) | c1_1(a658) | (~c2_1(a658)) | (~c3_1(a658)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp20 | c1_1(a658) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c2_1(a658)) | (~c3_1(a658)))),
% 2.53/2.73 inference(transitivity,[status(thm)],[2892, 2890])).
% 2.53/2.73 tff(2894,plain,
% 2.53/2.73 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a603) | c2_1(a603) | (~c0_1(a603)) | c1_1(a658) | (~c2_1(a658)) | (~c3_1(a658)))),
% 2.53/2.73 inference(quant_inst,[status(thm)],[])).
% 2.53/2.73 tff(2895,plain,
% 2.53/2.73 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp20 | c1_1(a658) | c3_1(a603) | (~ndr1_0) | c2_1(a603) | (~c0_1(a603)) | (~c2_1(a658)) | (~c3_1(a658))),
% 2.53/2.73 inference(modus_ponens,[status(thm)],[2894, 2893])).
% 2.53/2.73 tff(2896,plain,
% 2.53/2.73 (hskp20 | c2_1(a603) | (~c0_1(a603)) | (~c2_1(a658)) | (~c3_1(a658))),
% 2.53/2.73 inference(unit_resolution,[status(thm)],[2895, 87, 2529, 943, 660])).
% 2.53/2.73 tff(2897,plain,
% 2.53/2.73 (hskp20),
% 2.53/2.73 inference(unit_resolution,[status(thm)],[2896, 2810, 2813, 2806, 1774])).
% 2.53/2.73 tff(2898,plain,
% 2.53/2.73 (~c3_1(a635)),
% 2.53/2.73 inference(unit_resolution,[status(thm)],[607, 2897])).
% 2.53/2.73 tff(2899,plain,
% 2.53/2.73 (~c1_1(a635)),
% 2.53/2.73 inference(unit_resolution,[status(thm)],[619, 2897])).
% 2.53/2.73 tff(2900,plain,
% 2.53/2.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a658) | c1_1(a635) | c3_1(a635) | c1_1(a628) | (~ndr1_0) | c0_1(a635) | (~c2_1(a658)) | (~c3_1(a658)) | c0_1(a628) | (~c3_1(a628)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a658) | c1_1(a635) | c3_1(a635) | c1_1(a628) | (~ndr1_0) | c0_1(a635) | (~c2_1(a658)) | (~c3_1(a658)) | c0_1(a628) | (~c3_1(a628)))),
% 2.53/2.73 inference(rewrite,[status(thm)],[])).
% 2.53/2.73 tff(2901,plain,
% 2.53/2.73 (((~ndr1_0) | c1_1(a658) | (~c3_1(a658)) | (~c2_1(a658)) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)) | c1_1(a635) | c0_1(a635) | c3_1(a635)) <=> (c1_1(a658) | c1_1(a635) | c3_1(a635) | c1_1(a628) | (~ndr1_0) | c0_1(a635) | (~c2_1(a658)) | (~c3_1(a658)) | c0_1(a628) | (~c3_1(a628)))),
% 2.53/2.73 inference(rewrite,[status(thm)],[])).
% 2.53/2.73 tff(2902,plain,
% 2.53/2.73 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a658) | (~c3_1(a658)) | (~c2_1(a658)) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)) | c1_1(a635) | c0_1(a635) | c3_1(a635))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a658) | c1_1(a635) | c3_1(a635) | c1_1(a628) | (~ndr1_0) | c0_1(a635) | (~c2_1(a658)) | (~c3_1(a658)) | c0_1(a628) | (~c3_1(a628))))),
% 2.53/2.74 inference(monotonicity,[status(thm)],[2901])).
% 2.53/2.74 tff(2903,plain,
% 2.53/2.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a658) | (~c3_1(a658)) | (~c2_1(a658)) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)) | c1_1(a635) | c0_1(a635) | c3_1(a635))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a658) | c1_1(a635) | c3_1(a635) | c1_1(a628) | (~ndr1_0) | c0_1(a635) | (~c2_1(a658)) | (~c3_1(a658)) | c0_1(a628) | (~c3_1(a628)))),
% 2.53/2.74 inference(transitivity,[status(thm)],[2902, 2900])).
% 2.53/2.74 tff(2904,plain,
% 2.53/2.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a658) | (~c3_1(a658)) | (~c2_1(a658)) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)) | c1_1(a635) | c0_1(a635) | c3_1(a635))),
% 2.53/2.74 inference(quant_inst,[status(thm)],[])).
% 2.53/2.74 tff(2905,plain,
% 2.53/2.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a658) | c1_1(a635) | c3_1(a635) | c1_1(a628) | (~ndr1_0) | c0_1(a635) | (~c2_1(a658)) | (~c3_1(a658)) | c0_1(a628) | (~c3_1(a628))),
% 2.53/2.74 inference(modus_ponens,[status(thm)],[2904, 2903])).
% 2.53/2.74 tff(2906,plain,
% 2.53/2.74 (c0_1(a635)),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[2905, 87, 2813, 2810, 2519, 2529, 2899, 2898, 2491, 1113, 1])).
% 2.53/2.74 tff(2907,plain,
% 2.53/2.74 (~c2_1(a635)),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[613, 2897])).
% 2.53/2.74 tff(2908,plain,
% 2.53/2.74 (hskp6),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[2359, 2329])).
% 2.53/2.74 tff(2909,plain,
% 2.53/2.74 (~c1_1(a609)),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[1395, 2908])).
% 2.53/2.74 tff(2910,plain,
% 2.53/2.74 (~c0_1(a609)),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[691, 2908])).
% 2.53/2.74 tff(2911,plain,
% 2.53/2.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a658) | c1_1(a628) | c0_1(a609) | c1_1(a609) | (~ndr1_0) | c3_1(a609) | (~c2_1(a658)) | (~c3_1(a658)) | c0_1(a628) | (~c3_1(a628)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a658) | c1_1(a628) | c0_1(a609) | c1_1(a609) | (~ndr1_0) | c3_1(a609) | (~c2_1(a658)) | (~c3_1(a658)) | c0_1(a628) | (~c3_1(a628)))),
% 2.53/2.74 inference(rewrite,[status(thm)],[])).
% 2.53/2.74 tff(2912,plain,
% 2.53/2.74 (((~ndr1_0) | c1_1(a658) | (~c3_1(a658)) | (~c2_1(a658)) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)) | c1_1(a609) | c0_1(a609) | c3_1(a609)) <=> (c1_1(a658) | c1_1(a628) | c0_1(a609) | c1_1(a609) | (~ndr1_0) | c3_1(a609) | (~c2_1(a658)) | (~c3_1(a658)) | c0_1(a628) | (~c3_1(a628)))),
% 2.53/2.74 inference(rewrite,[status(thm)],[])).
% 2.53/2.74 tff(2913,plain,
% 2.53/2.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a658) | (~c3_1(a658)) | (~c2_1(a658)) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)) | c1_1(a609) | c0_1(a609) | c3_1(a609))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a658) | c1_1(a628) | c0_1(a609) | c1_1(a609) | (~ndr1_0) | c3_1(a609) | (~c2_1(a658)) | (~c3_1(a658)) | c0_1(a628) | (~c3_1(a628))))),
% 2.53/2.74 inference(monotonicity,[status(thm)],[2912])).
% 2.53/2.74 tff(2914,plain,
% 2.53/2.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a658) | (~c3_1(a658)) | (~c2_1(a658)) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)) | c1_1(a609) | c0_1(a609) | c3_1(a609))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a658) | c1_1(a628) | c0_1(a609) | c1_1(a609) | (~ndr1_0) | c3_1(a609) | (~c2_1(a658)) | (~c3_1(a658)) | c0_1(a628) | (~c3_1(a628)))),
% 2.53/2.74 inference(transitivity,[status(thm)],[2913, 2911])).
% 2.53/2.74 tff(2915,plain,
% 2.53/2.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a658) | (~c3_1(a658)) | (~c2_1(a658)) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)) | c1_1(a609) | c0_1(a609) | c3_1(a609))),
% 2.53/2.74 inference(quant_inst,[status(thm)],[])).
% 2.53/2.74 tff(2916,plain,
% 2.53/2.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)) | c1_1(W) | c0_1(W) | c3_1(W))) | c1_1(a658) | c1_1(a628) | c0_1(a609) | c1_1(a609) | (~ndr1_0) | c3_1(a609) | (~c2_1(a658)) | (~c3_1(a658)) | c0_1(a628) | (~c3_1(a628))),
% 2.53/2.74 inference(modus_ponens,[status(thm)],[2915, 2914])).
% 2.53/2.74 tff(2917,plain,
% 2.53/2.74 (c3_1(a609)),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[2916, 87, 2768, 2680, 2519, 2529, 2491, 2910, 2909, 1113, 1])).
% 2.53/2.74 tff(2918,plain,
% 2.53/2.74 (c2_1(a609)),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[701, 2908])).
% 2.53/2.74 tff(2919,plain,
% 2.53/2.74 (((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp45 | c2_1(a618) | c3_1(a618) | c0_1(a609) | (~ndr1_0) | (~c3_1(a609)) | (~c2_1(a609)) | (~c1_1(a618)))) <=> ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp45 | c2_1(a618) | c3_1(a618) | c0_1(a609) | (~ndr1_0) | (~c3_1(a609)) | (~c2_1(a609)) | (~c1_1(a618)))),
% 2.53/2.74 inference(rewrite,[status(thm)],[])).
% 2.53/2.74 tff(2920,plain,
% 2.53/2.74 ((hskp45 | (~ndr1_0) | c3_1(a618) | c2_1(a618) | (~c1_1(a618)) | c0_1(a609) | (~c2_1(a609)) | (~c3_1(a609))) <=> (hskp45 | c2_1(a618) | c3_1(a618) | c0_1(a609) | (~ndr1_0) | (~c3_1(a609)) | (~c2_1(a609)) | (~c1_1(a618)))),
% 2.53/2.74 inference(rewrite,[status(thm)],[])).
% 2.53/2.74 tff(2921,plain,
% 2.53/2.74 (((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp45 | (~ndr1_0) | c3_1(a618) | c2_1(a618) | (~c1_1(a618)) | c0_1(a609) | (~c2_1(a609)) | (~c3_1(a609)))) <=> ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp45 | c2_1(a618) | c3_1(a618) | c0_1(a609) | (~ndr1_0) | (~c3_1(a609)) | (~c2_1(a609)) | (~c1_1(a618))))),
% 2.53/2.74 inference(monotonicity,[status(thm)],[2920])).
% 2.53/2.74 tff(2922,plain,
% 2.53/2.74 (((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp45 | (~ndr1_0) | c3_1(a618) | c2_1(a618) | (~c1_1(a618)) | c0_1(a609) | (~c2_1(a609)) | (~c3_1(a609)))) <=> ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp45 | c2_1(a618) | c3_1(a618) | c0_1(a609) | (~ndr1_0) | (~c3_1(a609)) | (~c2_1(a609)) | (~c1_1(a618)))),
% 2.53/2.74 inference(transitivity,[status(thm)],[2921, 2919])).
% 2.53/2.74 tff(2923,plain,
% 2.53/2.74 ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp45 | (~ndr1_0) | c3_1(a618) | c2_1(a618) | (~c1_1(a618)) | c0_1(a609) | (~c2_1(a609)) | (~c3_1(a609)))),
% 2.53/2.74 inference(quant_inst,[status(thm)],[])).
% 2.53/2.74 tff(2924,plain,
% 2.53/2.74 ((~![V: $i, U: $i] : (hskp45 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp45 | c2_1(a618) | c3_1(a618) | c0_1(a609) | (~ndr1_0) | (~c3_1(a609)) | (~c2_1(a609)) | (~c1_1(a618))),
% 2.53/2.74 inference(modus_ponens,[status(thm)],[2923, 2922])).
% 2.53/2.74 tff(2925,plain,
% 2.53/2.74 (hskp45),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[2924, 87, 2543, 2918, 2541, 2540, 2910, 976, 2917])).
% 2.53/2.74 tff(2926,plain,
% 2.53/2.74 (c3_1(a623)),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[1010, 2925])).
% 2.53/2.74 tff(2927,plain,
% 2.53/2.74 (^[V: $i, U: $i] : refl((hskp36 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> (hskp36 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))))),
% 2.53/2.74 inference(bind,[status(th)],[])).
% 2.53/2.74 tff(2928,plain,
% 2.53/2.74 (![V: $i, U: $i] : (hskp36 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp36 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 2.53/2.74 inference(quant_intro,[status(thm)],[2927])).
% 2.53/2.74 tff(2929,plain,
% 2.53/2.74 (![V: $i, U: $i] : (hskp36 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp36 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 2.53/2.74 inference(rewrite,[status(thm)],[])).
% 2.53/2.74 tff(2930,plain,
% 2.53/2.74 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | hskp36) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) | hskp36))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) | hskp36) <=> (hskp36 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | hskp36) <=> (hskp36 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))))),
% 2.53/2.74 inference(bind,[status(th)],[])).
% 2.53/2.74 tff(2931,plain,
% 2.53/2.74 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | hskp36) <=> ![V: $i, U: $i] : (hskp36 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 2.53/2.74 inference(quant_intro,[status(thm)],[2930])).
% 2.53/2.74 tff(2932,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | hskp36)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause315')).
% 2.53/2.74 tff(2933,plain,
% 2.53/2.74 (![V: $i, U: $i] : (hskp36 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 2.53/2.74 inference(modus_ponens,[status(thm)],[2932, 2931])).
% 2.53/2.74 tff(2934,plain,
% 2.53/2.74 (![V: $i, U: $i] : (hskp36 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 2.53/2.74 inference(modus_ponens,[status(thm)],[2933, 2929])).
% 2.53/2.74 tff(2935,plain,(
% 2.53/2.74 ![V: $i, U: $i] : (hskp36 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 2.53/2.74 inference(skolemize,[status(sab)],[2934])).
% 2.53/2.74 tff(2936,plain,
% 2.53/2.74 (![V: $i, U: $i] : (hskp36 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 2.53/2.74 inference(modus_ponens,[status(thm)],[2935, 2928])).
% 2.53/2.74 tff(2937,plain,
% 2.53/2.74 (((~![V: $i, U: $i] : (hskp36 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp36 | c1_1(a635) | c2_1(a635) | (~ndr1_0) | (~c3_1(a608)) | (~c1_1(a608)) | (~c0_1(a608)) | (~c0_1(a635)))) <=> ((~![V: $i, U: $i] : (hskp36 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp36 | c1_1(a635) | c2_1(a635) | (~ndr1_0) | (~c3_1(a608)) | (~c1_1(a608)) | (~c0_1(a608)) | (~c0_1(a635)))),
% 2.53/2.74 inference(rewrite,[status(thm)],[])).
% 2.53/2.74 tff(2938,plain,
% 2.53/2.74 ((hskp36 | (~ndr1_0) | (~c3_1(a608)) | (~c1_1(a608)) | (~c0_1(a608)) | c1_1(a635) | c2_1(a635) | (~c0_1(a635))) <=> (hskp36 | c1_1(a635) | c2_1(a635) | (~ndr1_0) | (~c3_1(a608)) | (~c1_1(a608)) | (~c0_1(a608)) | (~c0_1(a635)))),
% 2.53/2.74 inference(rewrite,[status(thm)],[])).
% 2.53/2.74 tff(2939,plain,
% 2.53/2.74 (((~![V: $i, U: $i] : (hskp36 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp36 | (~ndr1_0) | (~c3_1(a608)) | (~c1_1(a608)) | (~c0_1(a608)) | c1_1(a635) | c2_1(a635) | (~c0_1(a635)))) <=> ((~![V: $i, U: $i] : (hskp36 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp36 | c1_1(a635) | c2_1(a635) | (~ndr1_0) | (~c3_1(a608)) | (~c1_1(a608)) | (~c0_1(a608)) | (~c0_1(a635))))),
% 2.53/2.74 inference(monotonicity,[status(thm)],[2938])).
% 2.53/2.74 tff(2940,plain,
% 2.53/2.74 (((~![V: $i, U: $i] : (hskp36 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp36 | (~ndr1_0) | (~c3_1(a608)) | (~c1_1(a608)) | (~c0_1(a608)) | c1_1(a635) | c2_1(a635) | (~c0_1(a635)))) <=> ((~![V: $i, U: $i] : (hskp36 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp36 | c1_1(a635) | c2_1(a635) | (~ndr1_0) | (~c3_1(a608)) | (~c1_1(a608)) | (~c0_1(a608)) | (~c0_1(a635)))),
% 2.53/2.74 inference(transitivity,[status(thm)],[2939, 2937])).
% 2.53/2.74 tff(2941,plain,
% 2.53/2.74 ((~![V: $i, U: $i] : (hskp36 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp36 | (~ndr1_0) | (~c3_1(a608)) | (~c1_1(a608)) | (~c0_1(a608)) | c1_1(a635) | c2_1(a635) | (~c0_1(a635)))),
% 2.53/2.74 inference(quant_inst,[status(thm)],[])).
% 2.53/2.74 tff(2942,plain,
% 2.53/2.74 ((~![V: $i, U: $i] : (hskp36 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp36 | c1_1(a635) | c2_1(a635) | (~ndr1_0) | (~c3_1(a608)) | (~c1_1(a608)) | (~c0_1(a608)) | (~c0_1(a635))),
% 2.53/2.74 inference(modus_ponens,[status(thm)],[2941, 2940])).
% 2.53/2.74 tff(2943,plain,
% 2.53/2.74 (hskp36),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[2942, 87, 2353, 2345, 2337, 959, 962, 2936, 958])).
% 2.53/2.74 tff(2944,plain,
% 2.53/2.74 (((~hskp36) | (~c3_1(a605))) <=> ((~hskp36) | (~c3_1(a605)))),
% 2.53/2.74 inference(rewrite,[status(thm)],[])).
% 2.53/2.74 tff(2945,plain,
% 2.53/2.74 (((~c3_1(a605)) | (~hskp36)) <=> ((~hskp36) | (~c3_1(a605)))),
% 2.53/2.74 inference(rewrite,[status(thm)],[])).
% 2.53/2.74 tff(2946,axiom,((~c3_1(a605)) | (~hskp36)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause206')).
% 2.53/2.74 tff(2947,plain,
% 2.53/2.74 ((~hskp36) | (~c3_1(a605))),
% 2.53/2.74 inference(modus_ponens,[status(thm)],[2946, 2945])).
% 2.53/2.74 tff(2948,plain,
% 2.53/2.74 ((~hskp36) | (~c3_1(a605))),
% 2.53/2.74 inference(modus_ponens,[status(thm)],[2947, 2944])).
% 2.53/2.74 tff(2949,plain,
% 2.53/2.74 (~c3_1(a605)),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[2948, 2943])).
% 2.53/2.74 tff(2950,plain,
% 2.53/2.74 (~c0_1(a623)),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[1002, 2925])).
% 2.53/2.74 tff(2951,plain,
% 2.53/2.74 (((~hskp36) | c1_1(a605)) <=> ((~hskp36) | c1_1(a605))),
% 2.53/2.74 inference(rewrite,[status(thm)],[])).
% 2.53/2.74 tff(2952,axiom,((~hskp36) | c1_1(a605)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause131')).
% 2.53/2.74 tff(2953,plain,
% 2.53/2.74 ((~hskp36) | c1_1(a605)),
% 2.53/2.74 inference(modus_ponens,[status(thm)],[2952, 2951])).
% 2.53/2.74 tff(2954,plain,
% 2.53/2.74 ((~hskp36) | c1_1(a605)),
% 2.53/2.74 inference(modus_ponens,[status(thm)],[2953, 2951])).
% 2.53/2.74 tff(2955,plain,
% 2.53/2.74 ((~hskp36) | c1_1(a605)),
% 2.53/2.74 inference(modus_ponens,[status(thm)],[2954, 2951])).
% 2.53/2.74 tff(2956,plain,
% 2.53/2.74 ((~hskp36) | c1_1(a605)),
% 2.53/2.74 inference(modus_ponens,[status(thm)],[2955, 2951])).
% 2.53/2.74 tff(2957,plain,
% 2.53/2.74 ((~hskp36) | c1_1(a605)),
% 2.53/2.74 inference(modus_ponens,[status(thm)],[2956, 2951])).
% 2.53/2.74 tff(2958,plain,
% 2.53/2.74 (c1_1(a605)),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[2957, 2943])).
% 2.53/2.74 tff(2959,plain,
% 2.53/2.74 (c2_1(a623)),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[1018, 2925])).
% 2.53/2.74 tff(2960,plain,
% 2.53/2.74 (((~hskp36) | c0_1(a605)) <=> ((~hskp36) | c0_1(a605))),
% 2.53/2.74 inference(rewrite,[status(thm)],[])).
% 2.53/2.74 tff(2961,axiom,((~hskp36) | c0_1(a605)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause132')).
% 2.53/2.74 tff(2962,plain,
% 2.53/2.74 ((~hskp36) | c0_1(a605)),
% 2.53/2.74 inference(modus_ponens,[status(thm)],[2961, 2960])).
% 2.53/2.74 tff(2963,plain,
% 2.53/2.74 ((~hskp36) | c0_1(a605)),
% 2.53/2.74 inference(modus_ponens,[status(thm)],[2962, 2960])).
% 2.53/2.74 tff(2964,plain,
% 2.53/2.74 ((~hskp36) | c0_1(a605)),
% 2.53/2.74 inference(modus_ponens,[status(thm)],[2963, 2960])).
% 2.53/2.74 tff(2965,plain,
% 2.53/2.74 ((~hskp36) | c0_1(a605)),
% 2.53/2.74 inference(modus_ponens,[status(thm)],[2964, 2960])).
% 2.53/2.74 tff(2966,plain,
% 2.53/2.74 ((~hskp36) | c0_1(a605)),
% 2.53/2.74 inference(modus_ponens,[status(thm)],[2965, 2960])).
% 2.53/2.74 tff(2967,plain,
% 2.53/2.74 (c0_1(a605)),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[2966, 2943])).
% 2.53/2.74 tff(2968,assumption,(~c2_1(a605)), introduced(assumption)).
% 2.53/2.74 tff(2969,assumption,(~c1_1(a628)), introduced(assumption)).
% 2.53/2.74 tff(2970,assumption,(~c2_1(a628)), introduced(assumption)).
% 2.53/2.74 tff(2971,assumption,(c3_1(a628)), introduced(assumption)).
% 2.53/2.74 tff(2972,assumption,(c0_1(a605)), introduced(assumption)).
% 2.53/2.74 tff(2973,assumption,(c1_1(a605)), introduced(assumption)).
% 2.53/2.74 tff(2974,plain,
% 2.53/2.74 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a628) | c1_1(a628) | (~ndr1_0) | c2_1(a605) | (~c0_1(a605)) | (~c1_1(a605)) | (~c3_1(a628)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a628) | c1_1(a628) | (~ndr1_0) | c2_1(a605) | (~c0_1(a605)) | (~c1_1(a605)) | (~c3_1(a628)))),
% 2.53/2.74 inference(rewrite,[status(thm)],[])).
% 2.53/2.74 tff(2975,plain,
% 2.53/2.74 ((hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a605) | (~c1_1(a605)) | (~c0_1(a605))) <=> (hskp5 | c2_1(a628) | c1_1(a628) | (~ndr1_0) | c2_1(a605) | (~c0_1(a605)) | (~c1_1(a605)) | (~c3_1(a628)))),
% 2.53/2.74 inference(rewrite,[status(thm)],[])).
% 2.53/2.74 tff(2976,plain,
% 2.53/2.74 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a605) | (~c1_1(a605)) | (~c0_1(a605)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a628) | c1_1(a628) | (~ndr1_0) | c2_1(a605) | (~c0_1(a605)) | (~c1_1(a605)) | (~c3_1(a628))))),
% 2.53/2.74 inference(monotonicity,[status(thm)],[2975])).
% 2.53/2.74 tff(2977,plain,
% 2.53/2.74 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a605) | (~c1_1(a605)) | (~c0_1(a605)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a628) | c1_1(a628) | (~ndr1_0) | c2_1(a605) | (~c0_1(a605)) | (~c1_1(a605)) | (~c3_1(a628)))),
% 2.53/2.74 inference(transitivity,[status(thm)],[2976, 2974])).
% 2.53/2.74 tff(2978,plain,
% 2.53/2.74 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a605) | (~c1_1(a605)) | (~c0_1(a605)))),
% 2.53/2.74 inference(quant_inst,[status(thm)],[])).
% 2.53/2.74 tff(2979,plain,
% 2.53/2.74 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a628) | c1_1(a628) | (~ndr1_0) | c2_1(a605) | (~c0_1(a605)) | (~c1_1(a605)) | (~c3_1(a628))),
% 2.53/2.74 inference(modus_ponens,[status(thm)],[2978, 2977])).
% 2.53/2.74 tff(2980,plain,
% 2.53/2.74 ($false),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[2979, 87, 523, 2973, 2972, 2971, 2970, 2969, 507, 2968])).
% 2.53/2.74 tff(2981,plain,(c2_1(a605) | hskp5 | (~c1_1(a605)) | (~c0_1(a605)) | (~c3_1(a628)) | c2_1(a628) | c1_1(a628)), inference(lemma,lemma(discharge,[]))).
% 2.53/2.74 tff(2982,plain,
% 2.53/2.74 (c2_1(a605) | hskp5 | (~c1_1(a605)) | (~c0_1(a605))),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[2981, 2491, 2519, 2497])).
% 2.53/2.74 tff(2983,plain,
% 2.53/2.74 (c2_1(a605)),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[2982, 2958, 2511, 2967])).
% 2.53/2.74 tff(2984,assumption,(c2_1(a605)), introduced(assumption)).
% 2.53/2.74 tff(2985,assumption,(~c3_1(a605)), introduced(assumption)).
% 2.53/2.74 tff(2986,assumption,(c0_1(a608)), introduced(assumption)).
% 2.53/2.74 tff(2987,assumption,(c3_1(a608)), introduced(assumption)).
% 2.53/2.74 tff(2988,plain,
% 2.53/2.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))) | (c3_1(a605) | (~ndr1_0) | (~c3_1(a608)) | (~c0_1(a608)) | (~c2_1(a608)) | (~c2_1(a605)) | (~c0_1(a605)) | (~c1_1(a605)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))) | c3_1(a605) | (~ndr1_0) | (~c3_1(a608)) | (~c0_1(a608)) | (~c2_1(a608)) | (~c2_1(a605)) | (~c0_1(a605)) | (~c1_1(a605)))),
% 2.53/2.74 inference(rewrite,[status(thm)],[])).
% 2.53/2.74 tff(2989,plain,
% 2.53/2.74 (((~ndr1_0) | (~c3_1(a608)) | (~c0_1(a608)) | (~c2_1(a608)) | c3_1(a605) | (~c2_1(a605)) | (~c0_1(a605)) | (~c0_1(a605)) | (~c1_1(a605)) | (~c2_1(a605))) <=> (c3_1(a605) | (~ndr1_0) | (~c3_1(a608)) | (~c0_1(a608)) | (~c2_1(a608)) | (~c2_1(a605)) | (~c0_1(a605)) | (~c1_1(a605)))),
% 2.53/2.74 inference(rewrite,[status(thm)],[])).
% 2.53/2.74 tff(2990,plain,
% 2.53/2.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a608)) | (~c0_1(a608)) | (~c2_1(a608)) | c3_1(a605) | (~c2_1(a605)) | (~c0_1(a605)) | (~c0_1(a605)) | (~c1_1(a605)) | (~c2_1(a605)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))) | (c3_1(a605) | (~ndr1_0) | (~c3_1(a608)) | (~c0_1(a608)) | (~c2_1(a608)) | (~c2_1(a605)) | (~c0_1(a605)) | (~c1_1(a605))))),
% 2.53/2.74 inference(monotonicity,[status(thm)],[2989])).
% 2.53/2.74 tff(2991,plain,
% 2.53/2.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a608)) | (~c0_1(a608)) | (~c2_1(a608)) | c3_1(a605) | (~c2_1(a605)) | (~c0_1(a605)) | (~c0_1(a605)) | (~c1_1(a605)) | (~c2_1(a605)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))) | c3_1(a605) | (~ndr1_0) | (~c3_1(a608)) | (~c0_1(a608)) | (~c2_1(a608)) | (~c2_1(a605)) | (~c0_1(a605)) | (~c1_1(a605)))),
% 2.53/2.74 inference(transitivity,[status(thm)],[2990, 2988])).
% 2.53/2.74 tff(2992,plain,
% 2.53/2.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))) | ((~ndr1_0) | (~c3_1(a608)) | (~c0_1(a608)) | (~c2_1(a608)) | c3_1(a605) | (~c2_1(a605)) | (~c0_1(a605)) | (~c0_1(a605)) | (~c1_1(a605)) | (~c2_1(a605)))),
% 2.53/2.74 inference(quant_inst,[status(thm)],[])).
% 2.53/2.74 tff(2993,plain,
% 2.53/2.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)) | c3_1(V) | (~c2_1(V)) | (~c0_1(V)) | (~c0_1(W)) | (~c1_1(W)) | (~c2_1(W)))) | c3_1(a605) | (~ndr1_0) | (~c3_1(a608)) | (~c0_1(a608)) | (~c2_1(a608)) | (~c2_1(a605)) | (~c0_1(a605)) | (~c1_1(a605))),
% 2.53/2.74 inference(modus_ponens,[status(thm)],[2992, 2991])).
% 2.53/2.74 tff(2994,plain,
% 2.53/2.74 ((~c2_1(a608)) | (~c2_1(a605))),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[2993, 87, 2987, 2986, 2973, 2972, 2985, 1991])).
% 2.53/2.74 tff(2995,plain,
% 2.53/2.74 (~c2_1(a608)),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[2994, 2984])).
% 2.53/2.74 tff(2996,plain,
% 2.53/2.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | (c0_1(a623) | c3_1(a605) | (~ndr1_0) | c2_1(a608) | (~c3_1(a608)) | (~c0_1(a608)) | (~c2_1(a605)) | (~c1_1(a605)) | (~c2_1(a623)) | (~c3_1(a623)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c0_1(a623) | c3_1(a605) | (~ndr1_0) | c2_1(a608) | (~c3_1(a608)) | (~c0_1(a608)) | (~c2_1(a605)) | (~c1_1(a605)) | (~c2_1(a623)) | (~c3_1(a623)))),
% 2.53/2.74 inference(rewrite,[status(thm)],[])).
% 2.53/2.74 tff(2997,plain,
% 2.53/2.74 (((~ndr1_0) | c3_1(a605) | (~c1_1(a605)) | (~c2_1(a605)) | c0_1(a623) | (~c2_1(a623)) | (~c3_1(a623)) | c2_1(a608) | (~c0_1(a608)) | (~c3_1(a608))) <=> (c0_1(a623) | c3_1(a605) | (~ndr1_0) | c2_1(a608) | (~c3_1(a608)) | (~c0_1(a608)) | (~c2_1(a605)) | (~c1_1(a605)) | (~c2_1(a623)) | (~c3_1(a623)))),
% 2.53/2.74 inference(rewrite,[status(thm)],[])).
% 2.53/2.74 tff(2998,plain,
% 2.53/2.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a605) | (~c1_1(a605)) | (~c2_1(a605)) | c0_1(a623) | (~c2_1(a623)) | (~c3_1(a623)) | c2_1(a608) | (~c0_1(a608)) | (~c3_1(a608)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | (c0_1(a623) | c3_1(a605) | (~ndr1_0) | c2_1(a608) | (~c3_1(a608)) | (~c0_1(a608)) | (~c2_1(a605)) | (~c1_1(a605)) | (~c2_1(a623)) | (~c3_1(a623))))),
% 2.53/2.74 inference(monotonicity,[status(thm)],[2997])).
% 2.53/2.74 tff(2999,plain,
% 2.53/2.74 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a605) | (~c1_1(a605)) | (~c2_1(a605)) | c0_1(a623) | (~c2_1(a623)) | (~c3_1(a623)) | c2_1(a608) | (~c0_1(a608)) | (~c3_1(a608)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c0_1(a623) | c3_1(a605) | (~ndr1_0) | c2_1(a608) | (~c3_1(a608)) | (~c0_1(a608)) | (~c2_1(a605)) | (~c1_1(a605)) | (~c2_1(a623)) | (~c3_1(a623)))),
% 2.53/2.74 inference(transitivity,[status(thm)],[2998, 2996])).
% 2.53/2.74 tff(3000,plain,
% 2.53/2.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c3_1(a605) | (~c1_1(a605)) | (~c2_1(a605)) | c0_1(a623) | (~c2_1(a623)) | (~c3_1(a623)) | c2_1(a608) | (~c0_1(a608)) | (~c3_1(a608)))),
% 2.53/2.74 inference(quant_inst,[status(thm)],[])).
% 2.53/2.74 tff(3001,plain,
% 2.53/2.74 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c2_1(U)) | c0_1(V) | (~c2_1(V)) | (~c3_1(V)) | c2_1(W) | (~c0_1(W)) | (~c3_1(W)))) | c0_1(a623) | c3_1(a605) | (~ndr1_0) | c2_1(a608) | (~c3_1(a608)) | (~c0_1(a608)) | (~c2_1(a605)) | (~c1_1(a605)) | (~c2_1(a623)) | (~c3_1(a623))),
% 2.53/2.74 inference(modus_ponens,[status(thm)],[3000, 2999])).
% 2.53/2.74 tff(3002,plain,
% 2.53/2.74 ($false),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[3001, 87, 1045, 1044, 2987, 2986, 2973, 1027, 2985, 953, 2995, 2984])).
% 2.53/2.74 tff(3003,plain,((~c2_1(a605)) | (~c3_1(a623)) | (~c2_1(a623)) | (~c3_1(a608)) | (~c0_1(a608)) | (~c1_1(a605)) | c0_1(a623) | c3_1(a605) | (~c0_1(a605))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.74 tff(3004,plain,
% 2.53/2.74 ($false),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[3003, 2983, 2967, 2959, 2345, 2337, 2958, 2950, 2949, 2926])).
% 2.53/2.74 tff(3005,plain,((~hskp38) | (~c1_1(a618)) | c2_1(a618) | c3_1(a618) | c1_1(a635) | c2_1(a635) | (~c0_1(a635)) | (~c2_1(a658)) | (~c3_1(a658)) | c1_1(a658) | c0_1(a628)), inference(lemma,lemma(discharge,[]))).
% 2.53/2.74 tff(3006,plain,
% 2.53/2.74 (~hskp38),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[3005, 2814, 2812, 2811, 2899, 2907, 2906, 2813, 2810, 2529, 1])).
% 2.53/2.74 tff(3007,assumption,(hskp66), introduced(assumption)).
% 2.53/2.74 tff(3008,plain,
% 2.53/2.74 (~c2_1(a675)),
% 2.53/2.74 inference(unit_resolution,[status(thm)],[272, 3007])).
% 2.53/2.75 tff(3009,plain,
% 2.53/2.75 (c1_1(a675)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[288, 3007])).
% 2.53/2.75 tff(3010,plain,
% 2.53/2.75 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a675) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c1_1(a675)) | (~c0_1(a675)) | (~c3_1(a628)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a675) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c1_1(a675)) | (~c0_1(a675)) | (~c3_1(a628)))),
% 2.53/2.75 inference(rewrite,[status(thm)],[])).
% 2.53/2.75 tff(3011,plain,
% 2.53/2.75 ((hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a675) | (~c1_1(a675)) | (~c0_1(a675))) <=> (hskp5 | c2_1(a675) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c1_1(a675)) | (~c0_1(a675)) | (~c3_1(a628)))),
% 2.53/2.75 inference(rewrite,[status(thm)],[])).
% 2.53/2.75 tff(3012,plain,
% 2.53/2.75 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a675) | (~c1_1(a675)) | (~c0_1(a675)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a675) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c1_1(a675)) | (~c0_1(a675)) | (~c3_1(a628))))),
% 2.53/2.75 inference(monotonicity,[status(thm)],[3011])).
% 2.53/2.75 tff(3013,plain,
% 2.53/2.75 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a675) | (~c1_1(a675)) | (~c0_1(a675)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a675) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c1_1(a675)) | (~c0_1(a675)) | (~c3_1(a628)))),
% 2.53/2.75 inference(transitivity,[status(thm)],[3012, 3010])).
% 2.53/2.75 tff(3014,plain,
% 2.53/2.75 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a675) | (~c1_1(a675)) | (~c0_1(a675)))),
% 2.53/2.75 inference(quant_inst,[status(thm)],[])).
% 2.53/2.75 tff(3015,plain,
% 2.53/2.75 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a675) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c1_1(a675)) | (~c0_1(a675)) | (~c3_1(a628))),
% 2.53/2.75 inference(modus_ponens,[status(thm)],[3014, 3013])).
% 2.53/2.75 tff(3016,plain,
% 2.53/2.75 (~c0_1(a675)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[3015, 87, 2511, 3009, 2519, 3008, 2497, 2491, 507])).
% 2.53/2.75 tff(3017,plain,
% 2.53/2.75 (c3_1(a675)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[280, 3007])).
% 2.53/2.75 tff(3018,plain,
% 2.53/2.75 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp38 | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c1_1(a675)) | c0_1(a675) | (~c3_1(a675)) | c0_1(a628))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp38 | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c1_1(a675)) | c0_1(a675) | (~c3_1(a675)) | c0_1(a628))),
% 2.53/2.75 inference(rewrite,[status(thm)],[])).
% 2.53/2.75 tff(3019,plain,
% 2.53/2.75 ((hskp38 | (~ndr1_0) | c0_1(a675) | (~c3_1(a675)) | (~c1_1(a675)) | c1_1(a628) | c0_1(a628) | c2_1(a628)) <=> (hskp38 | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c1_1(a675)) | c0_1(a675) | (~c3_1(a675)) | c0_1(a628))),
% 2.53/2.75 inference(rewrite,[status(thm)],[])).
% 2.53/2.75 tff(3020,plain,
% 2.53/2.75 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp38 | (~ndr1_0) | c0_1(a675) | (~c3_1(a675)) | (~c1_1(a675)) | c1_1(a628) | c0_1(a628) | c2_1(a628))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp38 | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c1_1(a675)) | c0_1(a675) | (~c3_1(a675)) | c0_1(a628)))),
% 2.53/2.75 inference(monotonicity,[status(thm)],[3019])).
% 2.53/2.75 tff(3021,plain,
% 2.53/2.75 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp38 | (~ndr1_0) | c0_1(a675) | (~c3_1(a675)) | (~c1_1(a675)) | c1_1(a628) | c0_1(a628) | c2_1(a628))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp38 | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c1_1(a675)) | c0_1(a675) | (~c3_1(a675)) | c0_1(a628))),
% 2.53/2.75 inference(transitivity,[status(thm)],[3020, 3018])).
% 2.53/2.75 tff(3022,plain,
% 2.53/2.75 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp38 | (~ndr1_0) | c0_1(a675) | (~c3_1(a675)) | (~c1_1(a675)) | c1_1(a628) | c0_1(a628) | c2_1(a628))),
% 2.53/2.75 inference(quant_inst,[status(thm)],[])).
% 2.53/2.75 tff(3023,plain,
% 2.53/2.75 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp38 | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c1_1(a675)) | c0_1(a675) | (~c3_1(a675)) | c0_1(a628)),
% 2.53/2.75 inference(modus_ponens,[status(thm)],[3022, 3021])).
% 2.53/2.75 tff(3024,plain,
% 2.53/2.75 ($false),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[3023, 87, 2315, 3009, 3017, 2497, 2491, 11, 3016, 1])).
% 2.53/2.75 tff(3025,plain,((~hskp66) | hskp38 | c0_1(a628)), inference(lemma,lemma(discharge,[]))).
% 2.53/2.75 tff(3026,plain,
% 2.53/2.75 (~hskp66),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[3025, 3006, 1])).
% 2.53/2.75 tff(3027,plain,
% 2.53/2.75 (hskp64),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[85, 3026, 2889])).
% 2.53/2.75 tff(3028,plain,
% 2.53/2.75 (~c0_1(a673)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[1693, 3027])).
% 2.53/2.75 tff(3029,plain,
% 2.53/2.75 (c3_1(a673)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[1667, 3027])).
% 2.53/2.75 tff(3030,plain,
% 2.53/2.75 (c1_1(a673)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[1701, 3027])).
% 2.53/2.75 tff(3031,plain,
% 2.53/2.75 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp38 | c0_1(a673) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c3_1(a673)) | (~c1_1(a673)) | c0_1(a628))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp38 | c0_1(a673) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c3_1(a673)) | (~c1_1(a673)) | c0_1(a628))),
% 2.53/2.75 inference(rewrite,[status(thm)],[])).
% 2.53/2.75 tff(3032,plain,
% 2.53/2.75 ((hskp38 | (~ndr1_0) | c0_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c1_1(a628) | c0_1(a628) | c2_1(a628)) <=> (hskp38 | c0_1(a673) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c3_1(a673)) | (~c1_1(a673)) | c0_1(a628))),
% 2.53/2.75 inference(rewrite,[status(thm)],[])).
% 2.53/2.75 tff(3033,plain,
% 2.53/2.75 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp38 | (~ndr1_0) | c0_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c1_1(a628) | c0_1(a628) | c2_1(a628))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp38 | c0_1(a673) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c3_1(a673)) | (~c1_1(a673)) | c0_1(a628)))),
% 2.53/2.75 inference(monotonicity,[status(thm)],[3032])).
% 2.53/2.75 tff(3034,plain,
% 2.53/2.75 (((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp38 | (~ndr1_0) | c0_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c1_1(a628) | c0_1(a628) | c2_1(a628))) <=> ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp38 | c0_1(a673) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c3_1(a673)) | (~c1_1(a673)) | c0_1(a628))),
% 2.53/2.75 inference(transitivity,[status(thm)],[3033, 3031])).
% 2.53/2.75 tff(3035,plain,
% 2.53/2.75 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | (hskp38 | (~ndr1_0) | c0_1(a673) | (~c3_1(a673)) | (~c1_1(a673)) | c1_1(a628) | c0_1(a628) | c2_1(a628))),
% 2.53/2.75 inference(quant_inst,[status(thm)],[])).
% 2.53/2.75 tff(3036,plain,
% 2.53/2.75 ((~![V: $i, U: $i] : (hskp38 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c0_1(V) | c2_1(V))) | hskp38 | c0_1(a673) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c3_1(a673)) | (~c1_1(a673)) | c0_1(a628)),
% 2.53/2.75 inference(modus_ponens,[status(thm)],[3035, 3034])).
% 2.53/2.75 tff(3037,plain,
% 2.53/2.75 (hskp38 | (~c3_1(a673)) | (~c1_1(a673)) | c0_1(a628)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[3036, 87, 1855, 2497, 2491, 11])).
% 2.53/2.75 tff(3038,plain,
% 2.53/2.75 (hskp38),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[3037, 1, 1751, 1752])).
% 2.53/2.75 tff(3039,plain,
% 2.53/2.75 (hskp6),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[2359, 3038])).
% 2.53/2.75 tff(3040,plain,
% 2.53/2.75 (~c1_1(a609)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[1395, 3039])).
% 2.53/2.75 tff(3041,plain,
% 2.53/2.75 (~c0_1(a609)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[691, 3039])).
% 2.53/2.75 tff(3042,plain,
% 2.53/2.75 (c3_1(a609)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[2916, 87, 2768, 2680, 2519, 2529, 2491, 3041, 3040, 1113, 1])).
% 2.53/2.75 tff(3043,plain,
% 2.53/2.75 (hskp42 | (~c0_1(a603)) | c0_1(a628)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[2585, 87, 2519, 2491, 1125, 822, 1774])).
% 2.53/2.75 tff(3044,plain,
% 2.53/2.75 (hskp42),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[3043, 1, 1789])).
% 2.53/2.75 tff(3045,plain,
% 2.53/2.75 (~c3_1(a618)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[915, 3044])).
% 2.53/2.75 tff(3046,plain,
% 2.53/2.75 (~c2_1(a618)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[845, 3044])).
% 2.53/2.75 tff(3047,plain,
% 2.53/2.75 (c2_1(a609)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[701, 3039])).
% 2.53/2.75 tff(3048,plain,
% 2.53/2.75 (c1_1(a618)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[876, 3044])).
% 2.53/2.75 tff(3049,plain,
% 2.53/2.75 (hskp45),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[2924, 87, 3048, 3047, 3046, 3045, 3041, 976, 3042])).
% 2.53/2.75 tff(3050,plain,
% 2.53/2.75 (c3_1(a623)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[1010, 3049])).
% 2.53/2.75 tff(3051,plain,
% 2.53/2.75 (c0_1(a608)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[2336, 3038])).
% 2.53/2.75 tff(3052,plain,
% 2.53/2.75 (c3_1(a608)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[2344, 3038])).
% 2.53/2.75 tff(3053,plain,
% 2.53/2.75 (c1_1(a608)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[2352, 3038])).
% 2.53/2.75 tff(3054,plain,
% 2.53/2.75 (hskp36),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[2942, 87, 3053, 3052, 3051, 959, 962, 2936, 958])).
% 2.53/2.75 tff(3055,plain,
% 2.53/2.75 (~c3_1(a605)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[2948, 3054])).
% 2.53/2.75 tff(3056,plain,
% 2.53/2.75 (~c0_1(a623)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[1002, 3049])).
% 2.53/2.75 tff(3057,plain,
% 2.53/2.75 (c1_1(a605)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[2957, 3054])).
% 2.53/2.75 tff(3058,plain,
% 2.53/2.75 (c2_1(a623)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[1018, 3049])).
% 2.53/2.75 tff(3059,plain,
% 2.53/2.75 (c0_1(a605)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[2966, 3054])).
% 2.53/2.75 tff(3060,plain,
% 2.53/2.75 (c2_1(a605)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[2982, 3057, 2511, 3059])).
% 2.53/2.75 tff(3061,plain,
% 2.53/2.75 ($false),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[3003, 3060, 3059, 3058, 3052, 3051, 3057, 3056, 3055, 3050])).
% 2.53/2.75 tff(3062,plain,(c0_1(a628) | c1_1(a635) | c2_1(a635) | (~c0_1(a635)) | (~c2_1(a658)) | (~c3_1(a658)) | c1_1(a658) | (~c0_1(a603)) | c1_1(a603) | c2_1(a603) | (~c1_1(a673)) | (~c3_1(a673)) | c0_1(a673)), inference(lemma,lemma(discharge,[]))).
% 2.53/2.75 tff(3063,plain,
% 2.53/2.75 ($false),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[3062, 3030, 3029, 2899, 1, 2813, 2810, 2529, 2806, 2641, 1774, 2906, 2907, 3028])).
% 2.53/2.75 tff(3064,plain,(c2_1(a603) | c0_1(a628) | c1_1(a658) | c3_1(a603)), inference(lemma,lemma(discharge,[]))).
% 2.53/2.75 tff(3065,plain,
% 2.53/2.75 (c2_1(a603)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[3064, 2805, 2529, 1])).
% 2.53/2.75 tff(3066,plain,
% 2.53/2.75 (~c1_1(a603)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[1550, 2804])).
% 2.53/2.75 tff(3067,plain,
% 2.53/2.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a658) | c2_1(a628) | c1_1(a628) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a658) | (~c2_1(a658)) | c0_1(a628))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a658) | c2_1(a628) | c1_1(a628) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a658) | (~c2_1(a658)) | c0_1(a628))),
% 2.53/2.75 inference(rewrite,[status(thm)],[])).
% 2.53/2.75 tff(3068,plain,
% 2.53/2.75 (((~ndr1_0) | c3_1(a603) | c1_1(a603) | (~c2_1(a603)) | c1_1(a658) | c0_1(a658) | (~c2_1(a658)) | c2_1(a628) | c1_1(a628) | c0_1(a628)) <=> (c1_1(a658) | c2_1(a628) | c1_1(a628) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a658) | (~c2_1(a658)) | c0_1(a628))),
% 2.53/2.75 inference(rewrite,[status(thm)],[])).
% 2.53/2.75 tff(3069,plain,
% 2.53/2.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a603) | c1_1(a603) | (~c2_1(a603)) | c1_1(a658) | c0_1(a658) | (~c2_1(a658)) | c2_1(a628) | c1_1(a628) | c0_1(a628))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a658) | c2_1(a628) | c1_1(a628) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a658) | (~c2_1(a658)) | c0_1(a628)))),
% 2.53/2.75 inference(monotonicity,[status(thm)],[3068])).
% 2.53/2.75 tff(3070,plain,
% 2.53/2.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a603) | c1_1(a603) | (~c2_1(a603)) | c1_1(a658) | c0_1(a658) | (~c2_1(a658)) | c2_1(a628) | c1_1(a628) | c0_1(a628))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a658) | c2_1(a628) | c1_1(a628) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a658) | (~c2_1(a658)) | c0_1(a628))),
% 2.53/2.75 inference(transitivity,[status(thm)],[3069, 3067])).
% 2.53/2.75 tff(3071,plain,
% 2.53/2.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c3_1(a603) | c1_1(a603) | (~c2_1(a603)) | c1_1(a658) | c0_1(a658) | (~c2_1(a658)) | c2_1(a628) | c1_1(a628) | c0_1(a628))),
% 2.53/2.75 inference(quant_inst,[status(thm)],[])).
% 2.53/2.75 tff(3072,plain,
% 2.53/2.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c1_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a658) | c2_1(a628) | c1_1(a628) | c1_1(a603) | c3_1(a603) | (~ndr1_0) | (~c2_1(a603)) | c0_1(a658) | (~c2_1(a658)) | c0_1(a628)),
% 2.53/2.75 inference(modus_ponens,[status(thm)],[3071, 3070])).
% 2.53/2.75 tff(3073,plain,
% 2.53/2.75 ($false),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[3072, 87, 2760, 2529, 2497, 2491, 3066, 2805, 1279, 3065, 2794, 1])).
% 2.53/2.75 tff(3074,plain,(c1_1(a658) | c0_1(a628)), inference(lemma,lemma(discharge,[]))).
% 2.53/2.75 tff(3075,plain,
% 2.53/2.75 (c1_1(a658)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[3074, 1])).
% 2.53/2.75 tff(3076,plain,
% 2.53/2.75 (~hskp56),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[1253, 3075])).
% 2.53/2.75 tff(3077,plain,
% 2.53/2.75 (~hskp42),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[2554, 3076])).
% 2.53/2.75 tff(3078,plain,
% 2.53/2.75 (~hskp33),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[2744, 3077, 1])).
% 2.53/2.75 tff(3079,plain,
% 2.53/2.75 (hskp61),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[342, 3078, 2528])).
% 2.53/2.75 tff(3080,plain,
% 2.53/2.75 (~c0_1(a670)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[348, 3079])).
% 2.53/2.75 tff(3081,plain,
% 2.53/2.75 (c2_1(a670)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[379, 3079])).
% 2.53/2.75 tff(3082,plain,
% 2.53/2.75 (~c1_1(a670)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[354, 3079])).
% 2.53/2.75 tff(3083,plain,
% 2.53/2.75 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | (hskp42 | c1_1(a670) | c0_1(a670) | c1_1(a628) | (~ndr1_0) | c0_1(a628) | (~c3_1(a628)) | c3_1(a670))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | hskp42 | c1_1(a670) | c0_1(a670) | c1_1(a628) | (~ndr1_0) | c0_1(a628) | (~c3_1(a628)) | c3_1(a670))),
% 2.53/2.75 inference(rewrite,[status(thm)],[])).
% 2.53/2.75 tff(3084,plain,
% 2.53/2.75 ((hskp42 | (~ndr1_0) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)) | c1_1(a670) | c3_1(a670) | c0_1(a670)) <=> (hskp42 | c1_1(a670) | c0_1(a670) | c1_1(a628) | (~ndr1_0) | c0_1(a628) | (~c3_1(a628)) | c3_1(a670))),
% 2.53/2.75 inference(rewrite,[status(thm)],[])).
% 2.53/2.75 tff(3085,plain,
% 2.53/2.75 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | (hskp42 | (~ndr1_0) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)) | c1_1(a670) | c3_1(a670) | c0_1(a670))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | (hskp42 | c1_1(a670) | c0_1(a670) | c1_1(a628) | (~ndr1_0) | c0_1(a628) | (~c3_1(a628)) | c3_1(a670)))),
% 2.53/2.75 inference(monotonicity,[status(thm)],[3084])).
% 2.53/2.75 tff(3086,plain,
% 2.53/2.75 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | (hskp42 | (~ndr1_0) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)) | c1_1(a670) | c3_1(a670) | c0_1(a670))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | hskp42 | c1_1(a670) | c0_1(a670) | c1_1(a628) | (~ndr1_0) | c0_1(a628) | (~c3_1(a628)) | c3_1(a670))),
% 2.53/2.75 inference(transitivity,[status(thm)],[3085, 3083])).
% 2.53/2.75 tff(3087,plain,
% 2.53/2.75 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | (hskp42 | (~ndr1_0) | c1_1(a628) | c0_1(a628) | (~c3_1(a628)) | c1_1(a670) | c3_1(a670) | c0_1(a670))),
% 2.53/2.75 inference(quant_inst,[status(thm)],[])).
% 2.53/2.75 tff(3088,plain,
% 2.53/2.75 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c3_1(V) | c0_1(V))) | hskp42 | c1_1(a670) | c0_1(a670) | c1_1(a628) | (~ndr1_0) | c0_1(a628) | (~c3_1(a628)) | c3_1(a670)),
% 2.53/2.75 inference(modus_ponens,[status(thm)],[3087, 3086])).
% 2.53/2.75 tff(3089,plain,
% 2.53/2.75 (c3_1(a670)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[3088, 87, 3077, 2519, 3082, 3080, 2491, 2652, 1])).
% 2.53/2.75 tff(3090,plain,
% 2.53/2.75 (~hskp65),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[2833, 3089, 3081, 3080])).
% 2.53/2.75 tff(3091,plain,
% 2.53/2.75 (~hskp37),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[2786, 523])).
% 2.53/2.75 tff(3092,plain,
% 2.53/2.75 (((~![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(a608)) | (~c0_1(a608)) | (~c2_1(a608)))) <=> ((~![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp37 | hskp5 | (~ndr1_0) | (~c3_1(a608)) | (~c0_1(a608)) | (~c2_1(a608)))),
% 2.53/2.75 inference(rewrite,[status(thm)],[])).
% 2.53/2.75 tff(3093,plain,
% 2.53/2.75 ((~![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(a608)) | (~c0_1(a608)) | (~c2_1(a608)))),
% 2.53/2.75 inference(quant_inst,[status(thm)],[])).
% 2.53/2.75 tff(3094,plain,
% 2.53/2.75 ((~![U: $i] : (hskp37 | hskp5 | (~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(U)))) | hskp37 | hskp5 | (~ndr1_0) | (~c3_1(a608)) | (~c0_1(a608)) | (~c2_1(a608))),
% 2.53/2.75 inference(modus_ponens,[status(thm)],[3093, 3092])).
% 2.53/2.75 tff(3095,plain,
% 2.53/2.75 (~c2_1(a608)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[3094, 87, 3091, 523, 2345, 2337, 521])).
% 2.53/2.75 tff(3096,plain,
% 2.53/2.75 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a628) | c1_1(a628) | (~ndr1_0) | c2_1(a608) | (~c1_1(a608)) | (~c0_1(a608)) | (~c3_1(a628)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a628) | c1_1(a628) | (~ndr1_0) | c2_1(a608) | (~c1_1(a608)) | (~c0_1(a608)) | (~c3_1(a628)))),
% 2.53/2.75 inference(rewrite,[status(thm)],[])).
% 2.53/2.75 tff(3097,plain,
% 2.53/2.75 ((hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a608) | (~c1_1(a608)) | (~c0_1(a608))) <=> (hskp5 | c2_1(a628) | c1_1(a628) | (~ndr1_0) | c2_1(a608) | (~c1_1(a608)) | (~c0_1(a608)) | (~c3_1(a628)))),
% 2.53/2.75 inference(rewrite,[status(thm)],[])).
% 2.53/2.75 tff(3098,plain,
% 2.53/2.75 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a608) | (~c1_1(a608)) | (~c0_1(a608)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | c2_1(a628) | c1_1(a628) | (~ndr1_0) | c2_1(a608) | (~c1_1(a608)) | (~c0_1(a608)) | (~c3_1(a628))))),
% 2.53/2.75 inference(monotonicity,[status(thm)],[3097])).
% 2.53/2.75 tff(3099,plain,
% 2.53/2.75 (((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a608) | (~c1_1(a608)) | (~c0_1(a608)))) <=> ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a628) | c1_1(a628) | (~ndr1_0) | c2_1(a608) | (~c1_1(a608)) | (~c0_1(a608)) | (~c3_1(a628)))),
% 2.53/2.75 inference(transitivity,[status(thm)],[3098, 3096])).
% 2.53/2.75 tff(3100,plain,
% 2.53/2.75 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp5 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c3_1(a628)) | c2_1(a608) | (~c1_1(a608)) | (~c0_1(a608)))),
% 2.53/2.75 inference(quant_inst,[status(thm)],[])).
% 2.53/2.75 tff(3101,plain,
% 2.53/2.75 ((~![V: $i, U: $i] : (hskp5 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c3_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp5 | c2_1(a628) | c1_1(a628) | (~ndr1_0) | c2_1(a608) | (~c1_1(a608)) | (~c0_1(a608)) | (~c3_1(a628))),
% 2.53/2.75 inference(modus_ponens,[status(thm)],[3100, 3099])).
% 2.53/2.75 tff(3102,plain,
% 2.53/2.75 ($false),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[3101, 87, 523, 2353, 2337, 2519, 2497, 2491, 507, 3095])).
% 2.53/2.75 tff(3103,plain,((~hskp38) | hskp5), inference(lemma,lemma(discharge,[]))).
% 2.53/2.75 tff(3104,plain,
% 2.53/2.75 (~hskp38),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[3103, 2511])).
% 2.53/2.75 tff(3105,plain,
% 2.53/2.75 (~hskp66),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[3025, 3104, 1])).
% 2.53/2.75 tff(3106,plain,
% 2.53/2.75 (hskp64),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[85, 3105, 3090])).
% 2.53/2.75 tff(3107,plain,
% 2.53/2.75 (~c0_1(a673)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[1693, 3106])).
% 2.53/2.75 tff(3108,plain,
% 2.53/2.75 (c1_1(a673)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[1701, 3106])).
% 2.53/2.75 tff(3109,plain,
% 2.53/2.75 (c3_1(a673)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[1667, 3106])).
% 2.53/2.75 tff(3110,plain,
% 2.53/2.75 ($false),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[3036, 87, 3104, 3109, 3108, 3107, 2497, 2491, 11, 1])).
% 2.53/2.75 tff(3111,plain,(c0_1(a628)), inference(lemma,lemma(discharge,[]))).
% 2.53/2.75 tff(3112,assumption,(c0_1(a628)), introduced(assumption)).
% 2.53/2.75 tff(3113,plain,
% 2.53/2.75 (hskp58),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[2594, 3112, 97])).
% 2.53/2.75 tff(3114,plain,
% 2.53/2.75 (~c1_1(a663)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[41, 3113])).
% 2.53/2.75 tff(3115,plain,
% 2.53/2.75 (~c0_1(a663)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[47, 3113])).
% 2.53/2.75 tff(3116,plain,
% 2.53/2.75 (c3_1(a663)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[55, 3113])).
% 2.53/2.75 tff(3117,plain,
% 2.53/2.75 ($false),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[2604, 87, 2642, 3116, 3115, 3114, 2497, 2491, 822, 3112])).
% 2.53/2.75 tff(3118,plain,((~c0_1(a628)) | hskp42 | hskp41), inference(lemma,lemma(discharge,[]))).
% 2.53/2.75 tff(3119,plain,
% 2.53/2.75 (hskp41),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[3118, 2642, 3111])).
% 2.53/2.75 tff(3120,plain,
% 2.53/2.75 (~c1_1(a617)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[463, 3119])).
% 2.53/2.75 tff(3121,plain,
% 2.53/2.75 (c3_1(a617)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[471, 3119])).
% 2.53/2.75 tff(3122,plain,
% 2.53/2.75 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | c1_1(a617) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c0_1(a628)) | c0_1(a617) | (~c3_1(a617)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c1_1(a617) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c0_1(a628)) | c0_1(a617) | (~c3_1(a617)))),
% 2.53/2.75 inference(rewrite,[status(thm)],[])).
% 2.53/2.75 tff(3123,plain,
% 2.53/2.75 ((hskp42 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c0_1(a628)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617))) <=> (hskp42 | c1_1(a617) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c0_1(a628)) | c0_1(a617) | (~c3_1(a617)))),
% 2.53/2.75 inference(rewrite,[status(thm)],[])).
% 2.53/2.75 tff(3124,plain,
% 2.53/2.75 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c0_1(a628)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | c1_1(a617) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c0_1(a628)) | c0_1(a617) | (~c3_1(a617))))),
% 2.53/2.75 inference(monotonicity,[status(thm)],[3123])).
% 2.53/2.75 tff(3125,plain,
% 2.53/2.75 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c0_1(a628)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c1_1(a617) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c0_1(a628)) | c0_1(a617) | (~c3_1(a617)))),
% 2.53/2.75 inference(transitivity,[status(thm)],[3124, 3122])).
% 2.53/2.75 tff(3126,plain,
% 2.53/2.75 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c0_1(a628)) | c1_1(a617) | c0_1(a617) | (~c3_1(a617)))),
% 2.53/2.75 inference(quant_inst,[status(thm)],[])).
% 2.53/2.75 tff(3127,plain,
% 2.53/2.75 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c1_1(a617) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | (~c0_1(a628)) | c0_1(a617) | (~c3_1(a617))),
% 2.53/2.75 inference(modus_ponens,[status(thm)],[3126, 3125])).
% 2.53/2.75 tff(3128,plain,
% 2.53/2.75 (c0_1(a617)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[3127, 87, 2642, 3121, 3120, 2497, 2491, 822, 3111])).
% 2.53/2.75 tff(3129,plain,
% 2.53/2.75 (c2_1(a617)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[496, 3119])).
% 2.53/2.75 tff(3130,plain,
% 2.53/2.75 ($false),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[1182, 3091, 523, 635])).
% 2.53/2.75 tff(3131,plain,(hskp5 | (~c0_1(a617)) | (~c2_1(a617)) | (~c3_1(a617))), inference(lemma,lemma(discharge,[]))).
% 2.53/2.75 tff(3132,plain,
% 2.53/2.75 (hskp5),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[3131, 3128, 3129, 3121])).
% 2.53/2.75 tff(3133,plain,
% 2.53/2.75 (~c3_1(a606)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[574, 3132])).
% 2.53/2.75 tff(3134,plain,
% 2.53/2.75 (c2_1(a606)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[588, 3132])).
% 2.53/2.75 tff(3135,plain,
% 2.53/2.75 (~c0_1(a606)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[580, 3132])).
% 2.53/2.75 tff(3136,plain,
% 2.53/2.75 (~hskp20),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[629, 3135, 3134, 3133])).
% 2.53/2.75 tff(3137,plain,
% 2.53/2.75 (~hskp14),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[2307, 3136, 3128, 3120, 3121, 3129])).
% 2.53/2.75 tff(3138,plain,
% 2.53/2.75 (hskp15 | hskp14 | (~c0_1(a617))),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[552, 87, 3129, 3120, 232])).
% 2.53/2.75 tff(3139,plain,
% 2.53/2.75 (hskp15),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[3138, 3137, 3128])).
% 2.53/2.75 tff(3140,plain,
% 2.53/2.75 (~c0_1(a625)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[146, 3139])).
% 2.53/2.75 tff(3141,plain,
% 2.53/2.75 (~c2_1(a625)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[175, 3139])).
% 2.53/2.75 tff(3142,plain,
% 2.53/2.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a617) | c2_1(a628) | c2_1(a625) | c0_1(a625) | (~ndr1_0) | c3_1(a625) | (~c0_1(a628)) | (~c3_1(a628)) | (~c3_1(a617)) | (~c0_1(a617)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a617) | c2_1(a628) | c2_1(a625) | c0_1(a625) | (~ndr1_0) | c3_1(a625) | (~c0_1(a628)) | (~c3_1(a628)) | (~c3_1(a617)) | (~c0_1(a617)))),
% 2.53/2.75 inference(rewrite,[status(thm)],[])).
% 2.53/2.75 tff(3143,plain,
% 2.53/2.75 (((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c0_1(a617)) | c2_1(a628) | (~c3_1(a628)) | (~c0_1(a628)) | c2_1(a625) | c0_1(a625) | c3_1(a625)) <=> (c1_1(a617) | c2_1(a628) | c2_1(a625) | c0_1(a625) | (~ndr1_0) | c3_1(a625) | (~c0_1(a628)) | (~c3_1(a628)) | (~c3_1(a617)) | (~c0_1(a617)))),
% 2.53/2.75 inference(rewrite,[status(thm)],[])).
% 2.53/2.75 tff(3144,plain,
% 2.53/2.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c0_1(a617)) | c2_1(a628) | (~c3_1(a628)) | (~c0_1(a628)) | c2_1(a625) | c0_1(a625) | c3_1(a625))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c1_1(a617) | c2_1(a628) | c2_1(a625) | c0_1(a625) | (~ndr1_0) | c3_1(a625) | (~c0_1(a628)) | (~c3_1(a628)) | (~c3_1(a617)) | (~c0_1(a617))))),
% 2.53/2.75 inference(monotonicity,[status(thm)],[3143])).
% 2.53/2.75 tff(3145,plain,
% 2.53/2.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c0_1(a617)) | c2_1(a628) | (~c3_1(a628)) | (~c0_1(a628)) | c2_1(a625) | c0_1(a625) | c3_1(a625))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a617) | c2_1(a628) | c2_1(a625) | c0_1(a625) | (~ndr1_0) | c3_1(a625) | (~c0_1(a628)) | (~c3_1(a628)) | (~c3_1(a617)) | (~c0_1(a617)))),
% 2.53/2.75 inference(transitivity,[status(thm)],[3144, 3142])).
% 2.53/2.75 tff(3146,plain,
% 2.53/2.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a617) | (~c3_1(a617)) | (~c0_1(a617)) | c2_1(a628) | (~c3_1(a628)) | (~c0_1(a628)) | c2_1(a625) | c0_1(a625) | c3_1(a625))),
% 2.53/2.75 inference(quant_inst,[status(thm)],[])).
% 2.53/2.75 tff(3147,plain,
% 2.53/2.75 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c1_1(a617) | c2_1(a628) | c2_1(a625) | c0_1(a625) | (~ndr1_0) | c3_1(a625) | (~c0_1(a628)) | (~c3_1(a628)) | (~c3_1(a617)) | (~c0_1(a617))),
% 2.53/2.75 inference(modus_ponens,[status(thm)],[3146, 3145])).
% 2.53/2.75 tff(3148,plain,
% 2.53/2.75 (c3_1(a625)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[3147, 87, 3121, 2519, 3120, 2497, 3141, 3140, 910, 3128, 3111])).
% 2.53/2.75 tff(3149,plain,
% 2.53/2.75 (~c1_1(a625)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[152, 3139])).
% 2.53/2.75 tff(3150,plain,
% 2.53/2.75 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | c2_1(a628) | c1_1(a628) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c0_1(a628)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c2_1(a628) | c1_1(a628) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c0_1(a628)))),
% 2.53/2.75 inference(rewrite,[status(thm)],[])).
% 2.53/2.75 tff(3151,plain,
% 2.53/2.75 ((hskp42 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c0_1(a628)) | c1_1(a625) | c0_1(a625) | (~c3_1(a625))) <=> (hskp42 | c2_1(a628) | c1_1(a628) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c0_1(a628)))),
% 2.53/2.75 inference(rewrite,[status(thm)],[])).
% 2.53/2.75 tff(3152,plain,
% 2.53/2.75 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c0_1(a628)) | c1_1(a625) | c0_1(a625) | (~c3_1(a625)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | c2_1(a628) | c1_1(a628) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c0_1(a628))))),
% 2.53/2.75 inference(monotonicity,[status(thm)],[3151])).
% 2.53/2.75 tff(3153,plain,
% 2.53/2.75 (((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c0_1(a628)) | c1_1(a625) | c0_1(a625) | (~c3_1(a625)))) <=> ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c2_1(a628) | c1_1(a628) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c0_1(a628)))),
% 2.53/2.75 inference(transitivity,[status(thm)],[3152, 3150])).
% 2.53/2.75 tff(3154,plain,
% 2.53/2.75 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | (hskp42 | (~ndr1_0) | c1_1(a628) | c2_1(a628) | (~c0_1(a628)) | c1_1(a625) | c0_1(a625) | (~c3_1(a625)))),
% 2.53/2.75 inference(quant_inst,[status(thm)],[])).
% 2.53/2.75 tff(3155,plain,
% 2.53/2.75 ((~![V: $i, U: $i] : (hskp42 | (~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V) | (~c3_1(V)))) | hskp42 | c2_1(a628) | c1_1(a628) | c1_1(a625) | c0_1(a625) | (~ndr1_0) | (~c3_1(a625)) | (~c0_1(a628))),
% 2.53/2.75 inference(modus_ponens,[status(thm)],[3154, 3153])).
% 2.53/2.75 tff(3156,plain,
% 2.53/2.75 ($false),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[3155, 87, 2642, 2497, 2491, 3149, 3140, 822, 3148, 3111])).
% 2.53/2.75 tff(3157,plain,(hskp42), inference(lemma,lemma(discharge,[]))).
% 2.53/2.75 tff(3158,plain,
% 2.53/2.75 (~c3_1(a618)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[915, 3157])).
% 2.53/2.75 tff(3159,plain,
% 2.53/2.75 (~c2_1(a618)),
% 2.53/2.75 inference(unit_resolution,[status(thm)],[845, 3157])).
% 2.53/2.75 tff(3160,plain,
% 2.53/2.75 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a618) | c3_1(a618) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | c0_1(a618) | (~c0_1(a628)) | (~c3_1(a628)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a618) | c3_1(a618) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | c0_1(a618) | (~c0_1(a628)) | (~c3_1(a628)))),
% 2.53/2.76 inference(rewrite,[status(thm)],[])).
% 2.53/2.76 tff(3161,plain,
% 2.53/2.76 (((~ndr1_0) | c1_1(a628) | (~c3_1(a628)) | (~c0_1(a628)) | c2_1(a628) | (~c3_1(a628)) | (~c0_1(a628)) | c2_1(a618) | c0_1(a618) | c3_1(a618)) <=> (c2_1(a618) | c3_1(a618) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | c0_1(a618) | (~c0_1(a628)) | (~c3_1(a628)))),
% 2.53/2.76 inference(rewrite,[status(thm)],[])).
% 2.53/2.76 tff(3162,plain,
% 2.53/2.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a628) | (~c3_1(a628)) | (~c0_1(a628)) | c2_1(a628) | (~c3_1(a628)) | (~c0_1(a628)) | c2_1(a618) | c0_1(a618) | c3_1(a618))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | (c2_1(a618) | c3_1(a618) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | c0_1(a618) | (~c0_1(a628)) | (~c3_1(a628))))),
% 2.53/2.76 inference(monotonicity,[status(thm)],[3161])).
% 2.53/2.76 tff(3163,plain,
% 2.53/2.76 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a628) | (~c3_1(a628)) | (~c0_1(a628)) | c2_1(a628) | (~c3_1(a628)) | (~c0_1(a628)) | c2_1(a618) | c0_1(a618) | c3_1(a618))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a618) | c3_1(a618) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | c0_1(a618) | (~c0_1(a628)) | (~c3_1(a628)))),
% 2.53/2.76 inference(transitivity,[status(thm)],[3162, 3160])).
% 2.53/2.76 tff(3164,plain,
% 2.53/2.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | ((~ndr1_0) | c1_1(a628) | (~c3_1(a628)) | (~c0_1(a628)) | c2_1(a628) | (~c3_1(a628)) | (~c0_1(a628)) | c2_1(a618) | c0_1(a618) | c3_1(a618))),
% 2.53/2.76 inference(quant_inst,[status(thm)],[])).
% 2.53/2.76 tff(3165,plain,
% 2.53/2.76 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c2_1(W) | c0_1(W) | c3_1(W))) | c2_1(a618) | c3_1(a618) | c2_1(a628) | c1_1(a628) | (~ndr1_0) | c0_1(a618) | (~c0_1(a628)) | (~c3_1(a628))),
% 2.53/2.76 inference(modus_ponens,[status(thm)],[3164, 3163])).
% 2.53/2.76 tff(3166,plain,
% 2.53/2.76 (c0_1(a618)),
% 2.53/2.76 inference(unit_resolution,[status(thm)],[3165, 87, 2519, 3159, 3158, 2497, 2491, 910, 3111])).
% 2.53/2.76 tff(3167,plain,
% 2.53/2.76 (c1_1(a618)),
% 2.53/2.76 inference(unit_resolution,[status(thm)],[876, 3157])).
% 2.53/2.76 tff(3168,plain,
% 2.53/2.76 (hskp5),
% 2.53/2.76 inference(unit_resolution,[status(thm)],[2820, 87, 3167, 2519, 3159, 2497, 2491, 507, 3166])).
% 2.53/2.76 tff(3169,plain,
% 2.53/2.76 (~c3_1(a606)),
% 2.53/2.76 inference(unit_resolution,[status(thm)],[574, 3168])).
% 2.53/2.76 tff(3170,plain,
% 2.53/2.76 (c2_1(a606)),
% 2.53/2.76 inference(unit_resolution,[status(thm)],[588, 3168])).
% 2.53/2.76 tff(3171,plain,
% 2.53/2.76 (hskp56),
% 2.53/2.76 inference(unit_resolution,[status(thm)],[2554, 3157])).
% 2.53/2.76 tff(3172,plain,
% 2.53/2.76 (~c1_1(a658)),
% 2.53/2.76 inference(unit_resolution,[status(thm)],[1253, 3171])).
% 2.53/2.76 tff(3173,plain,
% 2.53/2.76 (c3_1(a658)),
% 2.53/2.76 inference(unit_resolution,[status(thm)],[1261, 3171])).
% 2.53/2.76 tff(3174,plain,
% 2.53/2.76 (c2_1(a658)),
% 2.53/2.76 inference(unit_resolution,[status(thm)],[1286, 3171])).
% 2.53/2.76 tff(3175,plain,
% 2.53/2.76 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | c1_1(a658) | c2_1(a618) | c3_1(a618) | (~ndr1_0) | (~c0_1(a618)) | (~c2_1(a658)) | (~c3_1(a658)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp20 | c1_1(a658) | c2_1(a618) | c3_1(a618) | (~ndr1_0) | (~c0_1(a618)) | (~c2_1(a658)) | (~c3_1(a658)))),
% 2.53/2.76 inference(rewrite,[status(thm)],[])).
% 2.53/2.76 tff(3176,plain,
% 2.53/2.76 ((hskp20 | (~ndr1_0) | c3_1(a618) | c2_1(a618) | (~c0_1(a618)) | c1_1(a658) | (~c2_1(a658)) | (~c3_1(a658))) <=> (hskp20 | c1_1(a658) | c2_1(a618) | c3_1(a618) | (~ndr1_0) | (~c0_1(a618)) | (~c2_1(a658)) | (~c3_1(a658)))),
% 2.53/2.76 inference(rewrite,[status(thm)],[])).
% 2.53/2.76 tff(3177,plain,
% 2.53/2.76 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a618) | c2_1(a618) | (~c0_1(a618)) | c1_1(a658) | (~c2_1(a658)) | (~c3_1(a658)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | c1_1(a658) | c2_1(a618) | c3_1(a618) | (~ndr1_0) | (~c0_1(a618)) | (~c2_1(a658)) | (~c3_1(a658))))),
% 2.53/2.76 inference(monotonicity,[status(thm)],[3176])).
% 2.53/2.76 tff(3178,plain,
% 2.53/2.76 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a618) | c2_1(a618) | (~c0_1(a618)) | c1_1(a658) | (~c2_1(a658)) | (~c3_1(a658)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp20 | c1_1(a658) | c2_1(a618) | c3_1(a618) | (~ndr1_0) | (~c0_1(a618)) | (~c2_1(a658)) | (~c3_1(a658)))),
% 2.53/2.76 inference(transitivity,[status(thm)],[3177, 3175])).
% 2.53/2.76 tff(3179,plain,
% 2.53/2.76 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | (hskp20 | (~ndr1_0) | c3_1(a618) | c2_1(a618) | (~c0_1(a618)) | c1_1(a658) | (~c2_1(a658)) | (~c3_1(a658)))),
% 2.53/2.76 inference(quant_inst,[status(thm)],[])).
% 2.53/2.76 tff(3180,plain,
% 2.53/2.76 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)) | (~c3_1(V)))) | hskp20 | c1_1(a658) | c2_1(a618) | c3_1(a618) | (~ndr1_0) | (~c0_1(a618)) | (~c2_1(a658)) | (~c3_1(a658))),
% 2.53/2.76 inference(modus_ponens,[status(thm)],[3179, 3178])).
% 2.53/2.76 tff(3181,plain,
% 2.53/2.76 (hskp20 | (~c0_1(a618))),
% 2.53/2.76 inference(unit_resolution,[status(thm)],[3180, 87, 3174, 3173, 3172, 3159, 3158, 660])).
% 2.53/2.76 tff(3182,plain,
% 2.53/2.76 (hskp20),
% 2.53/2.76 inference(unit_resolution,[status(thm)],[3181, 3166])).
% 2.53/2.76 tff(3183,plain,
% 2.53/2.76 (~c0_1(a606)),
% 2.53/2.76 inference(unit_resolution,[status(thm)],[580, 3168])).
% 2.53/2.76 tff(3184,plain,
% 2.53/2.76 ($false),
% 2.53/2.76 inference(unit_resolution,[status(thm)],[629, 3183, 3182, 3170, 3169])).
% 2.53/2.76 % SZS output end Proof
% 2.53/2.77 % E exiting
%------------------------------------------------------------------------------