%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN067-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:38:07 AM UTC 2025
% Result : Unsatisfiable 0.49s 0.71s
% Output : Proof 0.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYN067-1 : TPTP v9.0.0. Released v1.0.0.
% 0.03/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n008.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 12:27:33 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.49/0.71 % SZS status Unsatisfiable
% 0.49/0.71 % SZS output start Proof
% 0.49/0.71 tff(big_p_type, type, (
% 0.49/0.71 big_p: $i > $o)).
% 0.49/0.71 tff(f6_type, type, (
% 0.49/0.71 f6: $i > $i)).
% 0.49/0.71 tff(c4_type, type, (
% 0.49/0.71 c4: $i)).
% 0.49/0.71 tff(f2_type, type, (
% 0.49/0.71 f2: $i > $i)).
% 0.49/0.71 tff(c2_type, type, (
% 0.49/0.71 c2: $i)).
% 0.49/0.71 tff(c1_type, type, (
% 0.49/0.71 c1: $i)).
% 0.49/0.71 tff(big_r_type, type, (
% 0.49/0.71 big_r: ( $i * $i ) > $o)).
% 0.49/0.71 tff(f1_type, type, (
% 0.49/0.71 f1: $i > $i)).
% 0.49/0.71 tff(c3_type, type, (
% 0.49/0.71 c3: $i)).
% 0.49/0.71 tff(f4_type, type, (
% 0.49/0.71 f4: $i > $i)).
% 0.49/0.71 tff(a_type, type, (
% 0.49/0.71 a: $i)).
% 0.49/0.71 tff(f3_type, type, (
% 0.49/0.71 f3: $i > $i)).
% 0.49/0.71 tff(f5_type, type, (
% 0.49/0.71 f5: $i > $i)).
% 0.49/0.71 tff(1,assumption,(~big_p(f6(c2))), introduced(assumption)).
% 0.49/0.71 tff(2,assumption,(~big_p(c1)), introduced(assumption)).
% 0.49/0.71 tff(3,assumption,(~big_r(c4, f1(c4))), introduced(assumption)).
% 0.49/0.71 tff(4,assumption,(~big_p(c4)), introduced(assumption)).
% 0.49/0.71 tff(5,plain,
% 0.49/0.71 (big_p(a) <=> big_p(a)),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(6,plain,
% 0.49/0.71 ((big_p(a) | big_p(a)) <=> big_p(a)),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(7,plain,
% 0.49/0.71 (((big_p(a) | big_p(a)) | big_p(a)) <=> (big_p(a) | big_p(a))),
% 0.49/0.71 inference(monotonicity,[status(thm)],[6])).
% 0.49/0.71 tff(8,plain,
% 0.49/0.71 (((big_p(a) | big_p(a)) | big_p(a)) <=> big_p(a)),
% 0.49/0.71 inference(transitivity,[status(thm)],[7, 6])).
% 0.49/0.71 tff(9,axiom,((big_p(a) | big_p(a)) | big_p(a)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_37')).
% 0.49/0.71 tff(10,plain,
% 0.49/0.71 (big_p(a)),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.49/0.71 tff(11,plain,
% 0.49/0.71 (big_p(a)),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.49/0.71 tff(12,plain,
% 0.49/0.71 (^[X7: $i, X1: $i] : refl(((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7))) <=> ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7))))),
% 0.49/0.71 inference(bind,[status(th)],[])).
% 0.49/0.71 tff(13,plain,
% 0.49/0.71 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7))) <=> ![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))),
% 0.49/0.71 inference(quant_intro,[status(thm)],[12])).
% 0.49/0.71 tff(14,plain,
% 0.49/0.71 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7))) <=> ![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(15,plain,
% 0.49/0.71 (^[X7: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~big_p(a)) | big_p(X7)) <=> ((~big_p(a)) | big_p(X7))), ((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) <=> (((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))))), rewrite((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)))), ((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))))), (((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) <=> (((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))) | (~big_p(a))))), rewrite((((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)))), (((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))))), ((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) <=> (((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))) | big_p(X1)))), rewrite((((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))), ((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7))))), (((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) | big_p(f4(X1))) <=> (((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7))) | big_p(f4(X1))))), rewrite((((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7))) | big_p(f4(X1))) <=> ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))), (((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) | big_p(f4(X1))) <=> ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))))),
% 0.49/0.71 inference(bind,[status(th)],[])).
% 0.49/0.71 tff(16,plain,
% 0.49/0.71 (![X7: $i, X1: $i] : ((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) | big_p(f4(X1))) <=> ![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))),
% 0.49/0.71 inference(quant_intro,[status(thm)],[15])).
% 0.49/0.71 tff(17,axiom,(![X7: $i, X1: $i] : ((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) | big_p(f4(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_7')).
% 0.49/0.71 tff(18,plain,
% 0.49/0.71 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.49/0.71 tff(19,plain,
% 0.49/0.71 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.49/0.71 tff(20,plain,(
% 0.49/0.71 ![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))),
% 0.49/0.71 inference(skolemize,[status(sab)],[19])).
% 0.49/0.71 tff(21,plain,
% 0.49/0.71 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.49/0.71 tff(22,plain,
% 0.49/0.71 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c4) | big_r(c4, f1(c4)) | big_p(f4(c4)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | (~big_p(a)) | big_p(c4) | big_r(c4, f1(c4)) | big_p(f4(c4)))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(23,plain,
% 0.49/0.71 (((~big_p(a)) | big_p(f4(c4)) | big_p(c4) | big_p(c4) | big_r(c4, f1(c4))) <=> ((~big_p(a)) | big_p(c4) | big_r(c4, f1(c4)) | big_p(f4(c4)))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(24,plain,
% 0.49/0.71 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(f4(c4)) | big_p(c4) | big_p(c4) | big_r(c4, f1(c4)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c4) | big_r(c4, f1(c4)) | big_p(f4(c4))))),
% 0.49/0.71 inference(monotonicity,[status(thm)],[23])).
% 0.49/0.71 tff(25,plain,
% 0.49/0.71 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(f4(c4)) | big_p(c4) | big_p(c4) | big_r(c4, f1(c4)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | (~big_p(a)) | big_p(c4) | big_r(c4, f1(c4)) | big_p(f4(c4)))),
% 0.49/0.71 inference(transitivity,[status(thm)],[24, 22])).
% 0.49/0.71 tff(26,plain,
% 0.49/0.71 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(f4(c4)) | big_p(c4) | big_p(c4) | big_r(c4, f1(c4)))),
% 0.49/0.71 inference(quant_inst,[status(thm)],[])).
% 0.49/0.71 tff(27,plain,
% 0.49/0.71 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | (~big_p(a)) | big_p(c4) | big_r(c4, f1(c4)) | big_p(f4(c4))),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.49/0.71 tff(28,plain,
% 0.49/0.71 (big_p(f4(c4))),
% 0.49/0.71 inference(unit_resolution,[status(thm)],[27, 21, 11, 4, 3])).
% 0.49/0.71 tff(29,plain,
% 0.49/0.71 (^[X7: $i, X1: $i] : refl(((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7))) <=> ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7))))),
% 0.49/0.71 inference(bind,[status(th)],[])).
% 0.49/0.71 tff(30,plain,
% 0.49/0.71 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7))) <=> ![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))),
% 0.49/0.71 inference(quant_intro,[status(thm)],[29])).
% 0.49/0.71 tff(31,plain,
% 0.49/0.71 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7))) <=> ![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(32,plain,
% 0.49/0.71 (^[X7: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~big_p(a)) | big_p(X7)) <=> ((~big_p(a)) | big_p(X7))), ((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) <=> (((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))))), rewrite((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)))), ((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))))), (((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) <=> (((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))) | (~big_p(a))))), rewrite((((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)))), (((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))))), ((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) <=> (((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))) | big_p(X1)))), rewrite((((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))), ((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7))))), (((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) | big_r(f3(X1), f4(X1))) <=> (((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7))) | big_r(f3(X1), f4(X1))))), rewrite((((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7))) | big_r(f3(X1), f4(X1))) <=> ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))), (((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) | big_r(f3(X1), f4(X1))) <=> ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))))),
% 0.49/0.71 inference(bind,[status(th)],[])).
% 0.49/0.71 tff(33,plain,
% 0.49/0.71 (![X7: $i, X1: $i] : ((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) | big_r(f3(X1), f4(X1))) <=> ![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))),
% 0.49/0.71 inference(quant_intro,[status(thm)],[32])).
% 0.49/0.71 tff(34,axiom,(![X7: $i, X1: $i] : ((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) | big_r(f3(X1), f4(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_9')).
% 0.49/0.71 tff(35,plain,
% 0.49/0.71 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.49/0.71 tff(36,plain,
% 0.49/0.71 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.49/0.71 tff(37,plain,(
% 0.49/0.71 ![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))),
% 0.49/0.71 inference(skolemize,[status(sab)],[36])).
% 0.49/0.71 tff(38,plain,
% 0.49/0.71 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))),
% 0.49/0.71 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.49/0.71 tff(39,plain,
% 0.49/0.71 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c4) | big_r(f3(c4), f4(c4)) | big_r(c4, f1(c4)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))) | (~big_p(a)) | big_p(c4) | big_r(f3(c4), f4(c4)) | big_r(c4, f1(c4)))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(40,plain,
% 0.49/0.71 (((~big_p(a)) | big_p(c4) | big_p(c4) | big_r(f3(c4), f4(c4)) | big_r(c4, f1(c4))) <=> ((~big_p(a)) | big_p(c4) | big_r(f3(c4), f4(c4)) | big_r(c4, f1(c4)))),
% 0.49/0.71 inference(rewrite,[status(thm)],[])).
% 0.49/0.71 tff(41,plain,
% 0.49/0.71 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c4) | big_p(c4) | big_r(f3(c4), f4(c4)) | big_r(c4, f1(c4)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c4) | big_r(f3(c4), f4(c4)) | big_r(c4, f1(c4))))),
% 0.49/0.71 inference(monotonicity,[status(thm)],[40])).
% 0.49/0.71 tff(42,plain,
% 0.49/0.71 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c4) | big_p(c4) | big_r(f3(c4), f4(c4)) | big_r(c4, f1(c4)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))) | (~big_p(a)) | big_p(c4) | big_r(f3(c4), f4(c4)) | big_r(c4, f1(c4)))),
% 0.49/0.72 inference(transitivity,[status(thm)],[41, 39])).
% 0.49/0.72 tff(43,plain,
% 0.49/0.72 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c4) | big_p(c4) | big_r(f3(c4), f4(c4)) | big_r(c4, f1(c4)))),
% 0.49/0.72 inference(quant_inst,[status(thm)],[])).
% 0.49/0.72 tff(44,plain,
% 0.49/0.72 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))) | (~big_p(a)) | big_p(c4) | big_r(f3(c4), f4(c4)) | big_r(c4, f1(c4))),
% 0.49/0.72 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.49/0.72 tff(45,plain,
% 0.49/0.72 (big_r(f3(c4), f4(c4)) | big_r(c4, f1(c4))),
% 0.49/0.72 inference(unit_resolution,[status(thm)],[44, 38, 11, 4])).
% 0.49/0.72 tff(46,plain,
% 0.49/0.72 (big_r(f3(c4), f4(c4))),
% 0.49/0.72 inference(unit_resolution,[status(thm)],[45, 3])).
% 0.49/0.72 tff(47,assumption,(~big_r(c4, f3(c4))), introduced(assumption)).
% 0.49/0.72 tff(48,plain,
% 0.49/0.72 (^[X7: $i, X1: $i] : refl(((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1))) <=> ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1))))),
% 0.49/0.72 inference(bind,[status(th)],[])).
% 0.49/0.72 tff(49,plain,
% 0.49/0.72 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1))) <=> ![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))),
% 0.49/0.72 inference(quant_intro,[status(thm)],[48])).
% 0.49/0.72 tff(50,plain,
% 0.49/0.72 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1))) <=> ![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))),
% 0.49/0.72 inference(rewrite,[status(thm)],[])).
% 0.49/0.72 tff(51,plain,
% 0.49/0.72 (^[X7: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~big_p(a)) | big_p(X7)) <=> ((~big_p(a)) | big_p(X7))), ((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) <=> (((~big_p(a)) | big_p(X7)) | big_p(f2(X7))))), rewrite((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7))), ((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7)))), (((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) <=> (((~big_p(a)) | big_p(f2(X7)) | big_p(X7)) | (~big_p(a))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | big_p(X7)) | (~big_p(a))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7))), (((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7)))), ((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) <=> (((~big_p(a)) | big_p(f2(X7)) | big_p(X7)) | big_p(X1)))), rewrite((((~big_p(a)) | big_p(f2(X7)) | big_p(X7)) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))), ((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7)))), (((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(X1, f3(X1))) <=> (((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7)) | big_r(X1, f3(X1))))), rewrite((((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7)) | big_r(X1, f3(X1))) <=> ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))), (((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(X1, f3(X1))) <=> ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))))),
% 0.49/0.72 inference(bind,[status(th)],[])).
% 0.49/0.72 tff(52,plain,
% 0.49/0.72 (![X7: $i, X1: $i] : ((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(X1, f3(X1))) <=> ![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))),
% 0.49/0.72 inference(quant_intro,[status(thm)],[51])).
% 0.49/0.72 tff(53,axiom,(![X7: $i, X1: $i] : ((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(X1, f3(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_2')).
% 0.49/0.72 tff(54,plain,
% 0.49/0.72 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))),
% 0.49/0.72 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.49/0.72 tff(55,plain,
% 0.49/0.72 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))),
% 0.49/0.72 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.49/0.72 tff(56,plain,(
% 0.49/0.72 ![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))),
% 0.49/0.72 inference(skolemize,[status(sab)],[55])).
% 0.49/0.72 tff(57,plain,
% 0.49/0.72 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))),
% 0.49/0.72 inference(modus_ponens,[status(thm)],[56, 49])).
% 0.49/0.72 tff(58,plain,
% 0.49/0.72 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))) | ((~big_p(a)) | big_p(c4) | big_r(c4, f3(c4)) | big_p(f2(c4)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))) | (~big_p(a)) | big_p(c4) | big_r(c4, f3(c4)) | big_p(f2(c4)))),
% 0.49/0.72 inference(rewrite,[status(thm)],[])).
% 0.49/0.72 tff(59,plain,
% 0.49/0.72 (((~big_p(a)) | big_p(c4) | big_p(f2(c4)) | big_p(c4) | big_r(c4, f3(c4))) <=> ((~big_p(a)) | big_p(c4) | big_r(c4, f3(c4)) | big_p(f2(c4)))),
% 0.49/0.72 inference(rewrite,[status(thm)],[])).
% 0.49/0.72 tff(60,plain,
% 0.49/0.72 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))) | ((~big_p(a)) | big_p(c4) | big_p(f2(c4)) | big_p(c4) | big_r(c4, f3(c4)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))) | ((~big_p(a)) | big_p(c4) | big_r(c4, f3(c4)) | big_p(f2(c4))))),
% 0.49/0.72 inference(monotonicity,[status(thm)],[59])).
% 0.49/0.72 tff(61,plain,
% 0.49/0.72 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))) | ((~big_p(a)) | big_p(c4) | big_p(f2(c4)) | big_p(c4) | big_r(c4, f3(c4)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))) | (~big_p(a)) | big_p(c4) | big_r(c4, f3(c4)) | big_p(f2(c4)))),
% 0.49/0.72 inference(transitivity,[status(thm)],[60, 58])).
% 0.49/0.72 tff(62,plain,
% 0.49/0.72 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))) | ((~big_p(a)) | big_p(c4) | big_p(f2(c4)) | big_p(c4) | big_r(c4, f3(c4)))),
% 0.49/0.72 inference(quant_inst,[status(thm)],[])).
% 0.49/0.72 tff(63,plain,
% 0.49/0.72 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))) | (~big_p(a)) | big_p(c4) | big_r(c4, f3(c4)) | big_p(f2(c4))),
% 0.49/0.72 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.49/0.72 tff(64,plain,
% 0.49/0.72 (big_p(f2(c4))),
% 0.49/0.72 inference(unit_resolution,[status(thm)],[63, 57, 11, 4, 47])).
% 0.49/0.72 tff(65,assumption,(~big_r(c2, c1)), introduced(assumption)).
% 0.49/0.72 tff(66,plain,
% 0.49/0.72 (^[X7: $i, X1: $i] : refl(((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7))) <=> ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7))))),
% 0.49/0.72 inference(bind,[status(th)],[])).
% 0.49/0.72 tff(67,plain,
% 0.49/0.72 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7))) <=> ![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))),
% 0.49/0.72 inference(quant_intro,[status(thm)],[66])).
% 0.49/0.72 tff(68,plain,
% 0.49/0.72 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7))) <=> ![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))),
% 0.49/0.72 inference(rewrite,[status(thm)],[])).
% 0.49/0.72 tff(69,plain,
% 0.49/0.72 (^[X7: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~big_p(a)) | big_p(X7)) <=> ((~big_p(a)) | big_p(X7))), ((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) <=> (((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))))), rewrite((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)))), ((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))))), (((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) <=> (((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))) | (~big_p(a))))), rewrite((((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)))), (((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))))), ((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) <=> (((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))) | big_p(X1)))), rewrite((((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))), ((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7))))), (((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) | big_r(X1, f3(X1))) <=> (((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7))) | big_r(X1, f3(X1))))), rewrite((((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7))) | big_r(X1, f3(X1))) <=> ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))), (((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) | big_r(X1, f3(X1))) <=> ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))))),
% 0.49/0.72 inference(bind,[status(th)],[])).
% 0.49/0.72 tff(70,plain,
% 0.49/0.72 (![X7: $i, X1: $i] : ((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) | big_r(X1, f3(X1))) <=> ![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))),
% 0.49/0.72 inference(quant_intro,[status(thm)],[69])).
% 0.49/0.72 tff(71,axiom,(![X7: $i, X1: $i] : ((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) | big_r(X1, f3(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_8')).
% 0.49/0.72 tff(72,plain,
% 0.49/0.72 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))),
% 0.49/0.72 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.49/0.72 tff(73,plain,
% 0.49/0.72 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))),
% 0.49/0.72 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.49/0.72 tff(74,plain,(
% 0.49/0.72 ![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))),
% 0.49/0.72 inference(skolemize,[status(sab)],[73])).
% 0.49/0.72 tff(75,plain,
% 0.49/0.72 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))),
% 0.49/0.72 inference(modus_ponens,[status(thm)],[74, 67])).
% 0.49/0.72 tff(76,plain,
% 0.49/0.72 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c4) | big_r(c4, f3(c4)) | big_r(c4, f1(c4)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))) | (~big_p(a)) | big_p(c4) | big_r(c4, f3(c4)) | big_r(c4, f1(c4)))),
% 0.49/0.72 inference(rewrite,[status(thm)],[])).
% 0.49/0.72 tff(77,plain,
% 0.49/0.72 (((~big_p(a)) | big_p(c4) | big_p(c4) | big_r(c4, f3(c4)) | big_r(c4, f1(c4))) <=> ((~big_p(a)) | big_p(c4) | big_r(c4, f3(c4)) | big_r(c4, f1(c4)))),
% 0.49/0.72 inference(rewrite,[status(thm)],[])).
% 0.49/0.72 tff(78,plain,
% 0.49/0.72 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c4) | big_p(c4) | big_r(c4, f3(c4)) | big_r(c4, f1(c4)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c4) | big_r(c4, f3(c4)) | big_r(c4, f1(c4))))),
% 0.49/0.72 inference(monotonicity,[status(thm)],[77])).
% 0.49/0.72 tff(79,plain,
% 0.49/0.72 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c4) | big_p(c4) | big_r(c4, f3(c4)) | big_r(c4, f1(c4)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))) | (~big_p(a)) | big_p(c4) | big_r(c4, f3(c4)) | big_r(c4, f1(c4)))),
% 0.49/0.72 inference(transitivity,[status(thm)],[78, 76])).
% 0.49/0.72 tff(80,plain,
% 0.49/0.72 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c4) | big_p(c4) | big_r(c4, f3(c4)) | big_r(c4, f1(c4)))),
% 0.56/0.72 inference(quant_inst,[status(thm)],[])).
% 0.56/0.72 tff(81,plain,
% 0.56/0.72 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))) | (~big_p(a)) | big_p(c4) | big_r(c4, f3(c4)) | big_r(c4, f1(c4))),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.56/0.72 tff(82,plain,
% 0.56/0.72 (big_r(c4, f3(c4)) | big_r(c4, f1(c4))),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[81, 75, 11, 4])).
% 0.56/0.72 tff(83,plain,
% 0.56/0.72 (big_r(c4, f3(c4))),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[82, 3])).
% 0.56/0.72 tff(84,plain,
% 0.56/0.72 (^[X6: $i, X4: $i, X3: $i, X5: $i] : refl(((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4))) <=> ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4))))),
% 0.56/0.72 inference(bind,[status(th)],[])).
% 0.56/0.72 tff(85,plain,
% 0.56/0.72 (![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4))) <=> ![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))),
% 0.56/0.72 inference(quant_intro,[status(thm)],[84])).
% 0.56/0.72 tff(86,plain,
% 0.56/0.72 (![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4))) <=> ![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))),
% 0.56/0.72 inference(rewrite,[status(thm)],[])).
% 0.56/0.72 tff(87,plain,
% 0.56/0.72 (^[X6: $i, X4: $i, X3: $i, X5: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~big_p(c2)) | big_r(c2, c1)) | (~big_p(X3))) <=> ((~big_p(X3)) | (~big_p(c2)) | big_r(c2, c1))), (((((~big_p(c2)) | big_r(c2, c1)) | (~big_p(X3))) | (~big_r(c4, X4))) <=> (((~big_p(X3)) | (~big_p(c2)) | big_r(c2, c1)) | (~big_r(c4, X4))))), rewrite((((~big_p(X3)) | (~big_p(c2)) | big_r(c2, c1)) | (~big_r(c4, X4))) <=> ((~big_p(X3)) | (~big_p(c2)) | big_r(c2, c1) | (~big_r(c4, X4)))), (((((~big_p(c2)) | big_r(c2, c1)) | (~big_p(X3))) | (~big_r(c4, X4))) <=> ((~big_p(X3)) | (~big_p(c2)) | big_r(c2, c1) | (~big_r(c4, X4))))), ((((((~big_p(c2)) | big_r(c2, c1)) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) <=> (((~big_p(X3)) | (~big_p(c2)) | big_r(c2, c1) | (~big_r(c4, X4))) | (~big_r(X4, X3))))), rewrite((((~big_p(X3)) | (~big_p(c2)) | big_r(c2, c1) | (~big_r(c4, X4))) | (~big_r(X4, X3))) <=> ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | big_r(c2, c1) | (~big_r(c4, X4)))), ((((((~big_p(c2)) | big_r(c2, c1)) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) <=> ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | big_r(c2, c1) | (~big_r(c4, X4))))), (((((((~big_p(c2)) | big_r(c2, c1)) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) | (~big_p(X5))) <=> (((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | big_r(c2, c1) | (~big_r(c4, X4))) | (~big_p(X5))))), rewrite((((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | big_r(c2, c1) | (~big_r(c4, X4))) | (~big_p(X5))) <=> ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(c4, X4)))), (((((((~big_p(c2)) | big_r(c2, c1)) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) | (~big_p(X5))) <=> ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(c4, X4))))), ((((((((~big_p(c2)) | big_r(c2, c1)) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) | (~big_p(X5))) | (~big_r(c4, X6))) <=> (((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(c4, X4))) | (~big_r(c4, X6))))), rewrite((((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(c4, X4))) | (~big_r(c4, X6))) <=> ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(c4, X6)) | (~big_r(c4, X4)))), ((((((((~big_p(c2)) | big_r(c2, c1)) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) | (~big_p(X5))) | (~big_r(c4, X6))) <=> ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(c4, X6)) | (~big_r(c4, X4))))), (((((((((~big_p(c2)) | big_r(c2, c1)) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) | (~big_p(X5))) | (~big_r(c4, X6))) | (~big_r(X6, X5))) <=> (((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(c4, X6)) | (~big_r(c4, X4))) | (~big_r(X6, X5))))), rewrite((((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(c4, X6)) | (~big_r(c4, X4))) | (~big_r(X6, X5))) <=> ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))), (((((((((~big_p(c2)) | big_r(c2, c1)) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) | (~big_p(X5))) | (~big_r(c4, X6))) | (~big_r(X6, X5))) <=> ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))))),
% 0.56/0.72 inference(bind,[status(th)],[])).
% 0.56/0.72 tff(88,plain,
% 0.56/0.72 (![X6: $i, X4: $i, X3: $i, X5: $i] : ((((((((~big_p(c2)) | big_r(c2, c1)) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) | (~big_p(X5))) | (~big_r(c4, X6))) | (~big_r(X6, X5))) <=> ![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))),
% 0.56/0.72 inference(quant_intro,[status(thm)],[87])).
% 0.56/0.72 tff(89,axiom,(![X6: $i, X4: $i, X3: $i, X5: $i] : ((((((((~big_p(c2)) | big_r(c2, c1)) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) | (~big_p(X5))) | (~big_r(c4, X6))) | (~big_r(X6, X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_72')).
% 0.56/0.72 tff(90,plain,
% 0.56/0.72 (![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.56/0.72 tff(91,plain,
% 0.56/0.72 (![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[90, 86])).
% 0.56/0.72 tff(92,plain,(
% 0.56/0.72 ![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))),
% 0.56/0.72 inference(skolemize,[status(sab)],[91])).
% 0.56/0.72 tff(93,plain,
% 0.56/0.72 (![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[92, 85])).
% 0.56/0.72 tff(94,assumption,(~big_p(c2)), introduced(assumption)).
% 0.56/0.72 tff(95,assumption,(~big_r(c2, f3(c2))), introduced(assumption)).
% 0.56/0.72 tff(96,plain,
% 0.56/0.72 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))) | ((~big_p(a)) | big_p(c2) | big_r(c2, f3(c2)) | big_p(f2(c2)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))) | (~big_p(a)) | big_p(c2) | big_r(c2, f3(c2)) | big_p(f2(c2)))),
% 0.56/0.72 inference(rewrite,[status(thm)],[])).
% 0.56/0.72 tff(97,plain,
% 0.56/0.72 (((~big_p(a)) | big_p(c2) | big_p(f2(c2)) | big_p(c2) | big_r(c2, f3(c2))) <=> ((~big_p(a)) | big_p(c2) | big_r(c2, f3(c2)) | big_p(f2(c2)))),
% 0.56/0.72 inference(rewrite,[status(thm)],[])).
% 0.56/0.72 tff(98,plain,
% 0.56/0.72 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))) | ((~big_p(a)) | big_p(c2) | big_p(f2(c2)) | big_p(c2) | big_r(c2, f3(c2)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))) | ((~big_p(a)) | big_p(c2) | big_r(c2, f3(c2)) | big_p(f2(c2))))),
% 0.56/0.72 inference(monotonicity,[status(thm)],[97])).
% 0.56/0.72 tff(99,plain,
% 0.56/0.72 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))) | ((~big_p(a)) | big_p(c2) | big_p(f2(c2)) | big_p(c2) | big_r(c2, f3(c2)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))) | (~big_p(a)) | big_p(c2) | big_r(c2, f3(c2)) | big_p(f2(c2)))),
% 0.56/0.72 inference(transitivity,[status(thm)],[98, 96])).
% 0.56/0.72 tff(100,plain,
% 0.56/0.72 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))) | ((~big_p(a)) | big_p(c2) | big_p(f2(c2)) | big_p(c2) | big_r(c2, f3(c2)))),
% 0.56/0.72 inference(quant_inst,[status(thm)],[])).
% 0.56/0.72 tff(101,plain,
% 0.56/0.72 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))) | (~big_p(a)) | big_p(c2) | big_r(c2, f3(c2)) | big_p(f2(c2))),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.56/0.72 tff(102,plain,
% 0.56/0.72 (big_p(f2(c2))),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[101, 57, 11, 94, 95])).
% 0.56/0.72 tff(103,plain,
% 0.56/0.72 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c2) | big_r(c2, f3(c2)) | big_r(c2, f1(c2)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))) | (~big_p(a)) | big_p(c2) | big_r(c2, f3(c2)) | big_r(c2, f1(c2)))),
% 0.56/0.72 inference(rewrite,[status(thm)],[])).
% 0.56/0.72 tff(104,plain,
% 0.56/0.72 (((~big_p(a)) | big_p(c2) | big_p(c2) | big_r(c2, f3(c2)) | big_r(c2, f1(c2))) <=> ((~big_p(a)) | big_p(c2) | big_r(c2, f3(c2)) | big_r(c2, f1(c2)))),
% 0.56/0.72 inference(rewrite,[status(thm)],[])).
% 0.56/0.72 tff(105,plain,
% 0.56/0.72 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c2) | big_p(c2) | big_r(c2, f3(c2)) | big_r(c2, f1(c2)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c2) | big_r(c2, f3(c2)) | big_r(c2, f1(c2))))),
% 0.56/0.72 inference(monotonicity,[status(thm)],[104])).
% 0.56/0.72 tff(106,plain,
% 0.56/0.72 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c2) | big_p(c2) | big_r(c2, f3(c2)) | big_r(c2, f1(c2)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))) | (~big_p(a)) | big_p(c2) | big_r(c2, f3(c2)) | big_r(c2, f1(c2)))),
% 0.56/0.72 inference(transitivity,[status(thm)],[105, 103])).
% 0.56/0.72 tff(107,plain,
% 0.56/0.72 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c2) | big_p(c2) | big_r(c2, f3(c2)) | big_r(c2, f1(c2)))),
% 0.56/0.72 inference(quant_inst,[status(thm)],[])).
% 0.56/0.72 tff(108,plain,
% 0.56/0.72 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))) | (~big_p(a)) | big_p(c2) | big_r(c2, f3(c2)) | big_r(c2, f1(c2))),
% 0.56/0.72 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.56/0.72 tff(109,plain,
% 0.56/0.72 (big_r(c2, f3(c2)) | big_r(c2, f1(c2))),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[108, 75, 11, 94])).
% 0.56/0.72 tff(110,plain,
% 0.56/0.72 (big_r(c2, f1(c2))),
% 0.56/0.72 inference(unit_resolution,[status(thm)],[109, 95])).
% 0.56/0.72 tff(111,plain,
% 0.56/0.72 (^[X7: $i, X1: $i] : refl(((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7))))),
% 0.56/0.72 inference(bind,[status(th)],[])).
% 0.56/0.72 tff(112,plain,
% 0.56/0.72 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7))) <=> ![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))),
% 0.56/0.72 inference(quant_intro,[status(thm)],[111])).
% 0.56/0.72 tff(113,plain,
% 0.56/0.72 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7))) <=> ![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))),
% 0.56/0.72 inference(rewrite,[status(thm)],[])).
% 0.56/0.72 tff(114,plain,
% 0.56/0.72 (^[X7: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~big_p(a)) | big_p(X7)) <=> ((~big_p(a)) | big_p(X7))), ((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) <=> (((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))))), rewrite((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7)))), ((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))))), (((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> (((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))) | (~big_p(a))))), rewrite((((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7)))), (((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))))), ((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) <=> (((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))) | big_p(X1)))), rewrite((((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))), ((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7))))), (((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(X1, f3(X1))) <=> (((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7))) | big_r(X1, f3(X1))))), rewrite((((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7))) | big_r(X1, f3(X1))) <=> ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))), (((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(X1, f3(X1))) <=> ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))))),
% 0.56/0.73 inference(bind,[status(th)],[])).
% 0.56/0.73 tff(115,plain,
% 0.56/0.73 (![X7: $i, X1: $i] : ((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(X1, f3(X1))) <=> ![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))),
% 0.56/0.73 inference(quant_intro,[status(thm)],[114])).
% 0.56/0.73 tff(116,axiom,(![X7: $i, X1: $i] : ((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(X1, f3(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_14')).
% 0.56/0.73 tff(117,plain,
% 0.56/0.73 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.56/0.73 tff(118,plain,
% 0.56/0.73 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[117, 113])).
% 0.56/0.73 tff(119,plain,(
% 0.56/0.73 ![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))),
% 0.56/0.73 inference(skolemize,[status(sab)],[118])).
% 0.56/0.73 tff(120,plain,
% 0.56/0.73 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[119, 112])).
% 0.56/0.73 tff(121,plain,
% 0.56/0.73 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c2) | big_r(f1(c2), f2(c2)) | big_r(c2, f3(c2)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c2) | big_r(f1(c2), f2(c2)) | big_r(c2, f3(c2)))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(122,plain,
% 0.56/0.73 (((~big_p(a)) | big_p(c2) | big_p(c2) | big_r(c2, f3(c2)) | big_r(f1(c2), f2(c2))) <=> ((~big_p(a)) | big_p(c2) | big_r(f1(c2), f2(c2)) | big_r(c2, f3(c2)))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(123,plain,
% 0.56/0.73 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c2) | big_p(c2) | big_r(c2, f3(c2)) | big_r(f1(c2), f2(c2)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c2) | big_r(f1(c2), f2(c2)) | big_r(c2, f3(c2))))),
% 0.56/0.73 inference(monotonicity,[status(thm)],[122])).
% 0.56/0.73 tff(124,plain,
% 0.56/0.73 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c2) | big_p(c2) | big_r(c2, f3(c2)) | big_r(f1(c2), f2(c2)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c2) | big_r(f1(c2), f2(c2)) | big_r(c2, f3(c2)))),
% 0.56/0.73 inference(transitivity,[status(thm)],[123, 121])).
% 0.56/0.73 tff(125,plain,
% 0.56/0.73 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c2) | big_p(c2) | big_r(c2, f3(c2)) | big_r(f1(c2), f2(c2)))),
% 0.56/0.73 inference(quant_inst,[status(thm)],[])).
% 0.56/0.73 tff(126,plain,
% 0.56/0.73 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c2) | big_r(f1(c2), f2(c2)) | big_r(c2, f3(c2))),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.56/0.73 tff(127,plain,
% 0.56/0.73 (big_r(f1(c2), f2(c2)) | big_r(c2, f3(c2))),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[126, 120, 11, 94])).
% 0.56/0.73 tff(128,plain,
% 0.56/0.73 (big_r(f1(c2), f2(c2))),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[127, 95])).
% 0.56/0.73 tff(129,plain,
% 0.56/0.73 (^[X9: $i, X10: $i] : refl(((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10))) <=> ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10))))),
% 0.56/0.73 inference(bind,[status(th)],[])).
% 0.56/0.73 tff(130,plain,
% 0.56/0.73 (![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10))) <=> ![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))),
% 0.56/0.73 inference(quant_intro,[status(thm)],[129])).
% 0.56/0.73 tff(131,plain,
% 0.56/0.73 (![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10))) <=> ![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(132,plain,
% 0.56/0.73 (^[X9: $i, X10: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) <=> ((~big_p(X9)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))), (((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) | (~big_p(c4))) <=> (((~big_p(X9)) | (~big_r(X10, X9)) | (~big_r(c2, X10))) | (~big_p(c4))))), rewrite((((~big_p(X9)) | (~big_r(X10, X9)) | (~big_r(c2, X10))) | (~big_p(c4))) <=> ((~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))), (((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) | (~big_p(c4))) <=> ((~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10))))), ((((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) | (~big_p(c4))) | big_r(c4, c3)) <=> (((~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10))) | big_r(c4, c3)))), rewrite((((~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10))) | big_r(c4, c3)) <=> ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))), ((((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) | (~big_p(c4))) | big_r(c4, c3)) <=> ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))))),
% 0.56/0.73 inference(bind,[status(th)],[])).
% 0.56/0.73 tff(133,plain,
% 0.56/0.73 (![X9: $i, X10: $i] : (((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) | (~big_p(c4))) | big_r(c4, c3)) <=> ![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))),
% 0.56/0.73 inference(quant_intro,[status(thm)],[132])).
% 0.56/0.73 tff(134,axiom,(![X9: $i, X10: $i] : (((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) | (~big_p(c4))) | big_r(c4, c3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_79')).
% 0.56/0.73 tff(135,plain,
% 0.56/0.73 (![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.56/0.73 tff(136,plain,
% 0.56/0.73 (![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[135, 131])).
% 0.56/0.73 tff(137,plain,(
% 0.56/0.73 ![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))),
% 0.56/0.73 inference(skolemize,[status(sab)],[136])).
% 0.56/0.73 tff(138,plain,
% 0.56/0.73 (![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[137, 130])).
% 0.56/0.73 tff(139,assumption,(~big_p(f4(c2))), introduced(assumption)).
% 0.56/0.73 tff(140,plain,
% 0.56/0.73 (^[X7: $i, X1: $i] : refl(((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7)) <=> ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7)))),
% 0.56/0.73 inference(bind,[status(th)],[])).
% 0.56/0.73 tff(141,plain,
% 0.56/0.73 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7)) <=> ![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))),
% 0.56/0.73 inference(quant_intro,[status(thm)],[140])).
% 0.56/0.73 tff(142,plain,
% 0.56/0.73 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7)) <=> ![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(143,plain,
% 0.56/0.73 (^[X7: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~big_p(a)) | big_p(X7)) <=> ((~big_p(a)) | big_p(X7))), ((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) <=> (((~big_p(a)) | big_p(X7)) | big_p(f2(X7))))), rewrite((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7))), ((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7)))), (((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) <=> (((~big_p(a)) | big_p(f2(X7)) | big_p(X7)) | (~big_p(a))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | big_p(X7)) | (~big_p(a))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7))), (((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7)))), ((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) <=> (((~big_p(a)) | big_p(f2(X7)) | big_p(X7)) | big_p(X1)))), rewrite((((~big_p(a)) | big_p(f2(X7)) | big_p(X7)) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))), ((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7)))), (((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) | big_p(f4(X1))) <=> (((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7)) | big_p(f4(X1))))), rewrite((((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7)) | big_p(f4(X1))) <=> ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))), (((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) | big_p(f4(X1))) <=> ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))))),
% 0.56/0.73 inference(bind,[status(th)],[])).
% 0.56/0.73 tff(144,plain,
% 0.56/0.73 (![X7: $i, X1: $i] : ((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) | big_p(f4(X1))) <=> ![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))),
% 0.56/0.73 inference(quant_intro,[status(thm)],[143])).
% 0.56/0.73 tff(145,axiom,(![X7: $i, X1: $i] : ((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) | big_p(f4(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_1')).
% 0.56/0.73 tff(146,plain,
% 0.56/0.73 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.56/0.73 tff(147,plain,
% 0.56/0.73 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[146, 142])).
% 0.56/0.73 tff(148,plain,(
% 0.56/0.73 ![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))),
% 0.56/0.73 inference(skolemize,[status(sab)],[147])).
% 0.56/0.73 tff(149,plain,
% 0.56/0.73 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[148, 141])).
% 0.56/0.73 tff(150,plain,
% 0.56/0.73 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))) | ((~big_p(a)) | big_p(c2) | big_p(c4) | big_p(f4(c2)) | big_p(f2(c4)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))) | (~big_p(a)) | big_p(c2) | big_p(c4) | big_p(f4(c2)) | big_p(f2(c4)))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(151,plain,
% 0.56/0.73 (((~big_p(a)) | big_p(f4(c2)) | big_p(c2) | big_p(f2(c4)) | big_p(c4)) <=> ((~big_p(a)) | big_p(c2) | big_p(c4) | big_p(f4(c2)) | big_p(f2(c4)))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(152,plain,
% 0.56/0.73 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))) | ((~big_p(a)) | big_p(f4(c2)) | big_p(c2) | big_p(f2(c4)) | big_p(c4))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))) | ((~big_p(a)) | big_p(c2) | big_p(c4) | big_p(f4(c2)) | big_p(f2(c4))))),
% 0.56/0.73 inference(monotonicity,[status(thm)],[151])).
% 0.56/0.73 tff(153,plain,
% 0.56/0.73 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))) | ((~big_p(a)) | big_p(f4(c2)) | big_p(c2) | big_p(f2(c4)) | big_p(c4))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))) | (~big_p(a)) | big_p(c2) | big_p(c4) | big_p(f4(c2)) | big_p(f2(c4)))),
% 0.56/0.73 inference(transitivity,[status(thm)],[152, 150])).
% 0.56/0.73 tff(154,plain,
% 0.56/0.73 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))) | ((~big_p(a)) | big_p(f4(c2)) | big_p(c2) | big_p(f2(c4)) | big_p(c4))),
% 0.56/0.73 inference(quant_inst,[status(thm)],[])).
% 0.56/0.73 tff(155,plain,
% 0.56/0.73 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))) | (~big_p(a)) | big_p(c2) | big_p(c4) | big_p(f4(c2)) | big_p(f2(c4))),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.56/0.73 tff(156,plain,
% 0.56/0.73 (big_p(f4(c2)) | big_p(f2(c4))),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[155, 149, 11, 4, 94])).
% 0.56/0.73 tff(157,plain,
% 0.56/0.73 (big_p(f2(c4))),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[156, 139])).
% 0.56/0.73 tff(158,plain,
% 0.56/0.73 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c2) | big_p(c4) | big_p(f4(c2)) | big_r(c4, f1(c4)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | (~big_p(a)) | big_p(c2) | big_p(c4) | big_p(f4(c2)) | big_r(c4, f1(c4)))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(159,plain,
% 0.56/0.73 (((~big_p(a)) | big_p(f4(c2)) | big_p(c2) | big_p(c4) | big_r(c4, f1(c4))) <=> ((~big_p(a)) | big_p(c2) | big_p(c4) | big_p(f4(c2)) | big_r(c4, f1(c4)))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(160,plain,
% 0.56/0.73 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(f4(c2)) | big_p(c2) | big_p(c4) | big_r(c4, f1(c4)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c2) | big_p(c4) | big_p(f4(c2)) | big_r(c4, f1(c4))))),
% 0.56/0.73 inference(monotonicity,[status(thm)],[159])).
% 0.56/0.73 tff(161,plain,
% 0.56/0.73 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(f4(c2)) | big_p(c2) | big_p(c4) | big_r(c4, f1(c4)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | (~big_p(a)) | big_p(c2) | big_p(c4) | big_p(f4(c2)) | big_r(c4, f1(c4)))),
% 0.56/0.73 inference(transitivity,[status(thm)],[160, 158])).
% 0.56/0.73 tff(162,plain,
% 0.56/0.73 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(f4(c2)) | big_p(c2) | big_p(c4) | big_r(c4, f1(c4)))),
% 0.56/0.73 inference(quant_inst,[status(thm)],[])).
% 0.56/0.73 tff(163,plain,
% 0.56/0.73 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | (~big_p(a)) | big_p(c2) | big_p(c4) | big_p(f4(c2)) | big_r(c4, f1(c4))),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.56/0.73 tff(164,plain,
% 0.56/0.73 (big_p(f4(c2)) | big_r(c4, f1(c4))),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[163, 21, 11, 4, 94])).
% 0.56/0.73 tff(165,plain,
% 0.56/0.73 (big_p(f4(c2))),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[164, 3])).
% 0.56/0.73 tff(166,plain,
% 0.56/0.73 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))) | ((~big_p(a)) | big_p(c2) | big_p(c4) | big_r(c2, f3(c2)) | big_p(f2(c4)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))) | (~big_p(a)) | big_p(c2) | big_p(c4) | big_r(c2, f3(c2)) | big_p(f2(c4)))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(167,plain,
% 0.56/0.73 (((~big_p(a)) | big_p(c2) | big_p(f2(c4)) | big_p(c4) | big_r(c2, f3(c2))) <=> ((~big_p(a)) | big_p(c2) | big_p(c4) | big_r(c2, f3(c2)) | big_p(f2(c4)))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(168,plain,
% 0.56/0.73 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))) | ((~big_p(a)) | big_p(c2) | big_p(f2(c4)) | big_p(c4) | big_r(c2, f3(c2)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))) | ((~big_p(a)) | big_p(c2) | big_p(c4) | big_r(c2, f3(c2)) | big_p(f2(c4))))),
% 0.56/0.73 inference(monotonicity,[status(thm)],[167])).
% 0.56/0.73 tff(169,plain,
% 0.56/0.73 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))) | ((~big_p(a)) | big_p(c2) | big_p(f2(c4)) | big_p(c4) | big_r(c2, f3(c2)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))) | (~big_p(a)) | big_p(c2) | big_p(c4) | big_r(c2, f3(c2)) | big_p(f2(c4)))),
% 0.56/0.73 inference(transitivity,[status(thm)],[168, 166])).
% 0.56/0.73 tff(170,plain,
% 0.56/0.73 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))) | ((~big_p(a)) | big_p(c2) | big_p(f2(c4)) | big_p(c4) | big_r(c2, f3(c2)))),
% 0.56/0.73 inference(quant_inst,[status(thm)],[])).
% 0.56/0.73 tff(171,plain,
% 0.56/0.73 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(X1, f3(X1)))) | (~big_p(a)) | big_p(c2) | big_p(c4) | big_r(c2, f3(c2)) | big_p(f2(c4))),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.56/0.73 tff(172,plain,
% 0.56/0.73 (big_r(c2, f3(c2)) | big_p(f2(c4))),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[171, 57, 11, 4, 94])).
% 0.56/0.73 tff(173,plain,
% 0.56/0.73 (big_p(f2(c4))),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[172, 95])).
% 0.56/0.73 tff(174,plain,
% 0.56/0.73 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c2) | big_p(c4) | big_r(c2, f3(c2)) | big_r(c4, f1(c4)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))) | (~big_p(a)) | big_p(c2) | big_p(c4) | big_r(c2, f3(c2)) | big_r(c4, f1(c4)))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(175,plain,
% 0.56/0.73 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c2) | big_p(c4) | big_r(c2, f3(c2)) | big_r(c4, f1(c4)))),
% 0.56/0.73 inference(quant_inst,[status(thm)],[])).
% 0.56/0.73 tff(176,plain,
% 0.56/0.73 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))) | (~big_p(a)) | big_p(c2) | big_p(c4) | big_r(c2, f3(c2)) | big_r(c4, f1(c4))),
% 0.56/0.73 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.56/0.73 tff(177,plain,
% 0.56/0.73 (big_r(c2, f3(c2)) | big_r(c4, f1(c4))),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[176, 75, 11, 4, 94])).
% 0.56/0.73 tff(178,plain,
% 0.56/0.73 (big_r(c4, f1(c4))),
% 0.56/0.73 inference(unit_resolution,[status(thm)],[177, 95])).
% 0.56/0.73 tff(179,assumption,(~big_r(f1(c4), f2(c4))), introduced(assumption)).
% 0.56/0.73 tff(180,plain,
% 0.56/0.73 (^[X7: $i, X1: $i] : refl(((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7))))),
% 0.56/0.73 inference(bind,[status(th)],[])).
% 0.56/0.73 tff(181,plain,
% 0.56/0.73 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7))) <=> ![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))),
% 0.56/0.73 inference(quant_intro,[status(thm)],[180])).
% 0.56/0.73 tff(182,plain,
% 0.56/0.73 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7))) <=> ![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))),
% 0.56/0.73 inference(rewrite,[status(thm)],[])).
% 0.56/0.73 tff(183,plain,
% 0.56/0.73 (^[X7: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~big_p(a)) | big_p(X7)) <=> ((~big_p(a)) | big_p(X7))), ((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) <=> (((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))))), rewrite((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7)))), ((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))))), (((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> (((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))) | (~big_p(a))))), rewrite((((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7)))), (((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))))), ((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) <=> (((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))) | big_p(X1)))), rewrite((((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))), ((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7))))), (((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) | big_p(f4(X1))) <=> (((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7))) | big_p(f4(X1))))), rewrite((((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7))) | big_p(f4(X1))) <=> ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))), (((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) | big_p(f4(X1))) <=> ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))))),
% 0.56/0.74 inference(bind,[status(th)],[])).
% 0.56/0.74 tff(184,plain,
% 0.56/0.74 (![X7: $i, X1: $i] : ((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) | big_p(f4(X1))) <=> ![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))),
% 0.56/0.74 inference(quant_intro,[status(thm)],[183])).
% 0.56/0.74 tff(185,axiom,(![X7: $i, X1: $i] : ((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) | big_p(f4(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_13')).
% 0.56/0.74 tff(186,plain,
% 0.56/0.74 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.56/0.74 tff(187,plain,
% 0.56/0.74 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[186, 182])).
% 0.56/0.74 tff(188,plain,(
% 0.56/0.74 ![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))),
% 0.56/0.74 inference(skolemize,[status(sab)],[187])).
% 0.56/0.74 tff(189,plain,
% 0.56/0.74 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[188, 181])).
% 0.56/0.74 tff(190,plain,
% 0.56/0.74 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c2) | big_p(c4) | big_p(f4(c2)) | big_r(f1(c4), f2(c4)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c2) | big_p(c4) | big_p(f4(c2)) | big_r(f1(c4), f2(c4)))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(191,plain,
% 0.56/0.74 (((~big_p(a)) | big_p(f4(c2)) | big_p(c2) | big_p(c4) | big_r(f1(c4), f2(c4))) <=> ((~big_p(a)) | big_p(c2) | big_p(c4) | big_p(f4(c2)) | big_r(f1(c4), f2(c4)))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(192,plain,
% 0.56/0.74 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(f4(c2)) | big_p(c2) | big_p(c4) | big_r(f1(c4), f2(c4)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c2) | big_p(c4) | big_p(f4(c2)) | big_r(f1(c4), f2(c4))))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[191])).
% 0.56/0.74 tff(193,plain,
% 0.56/0.74 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(f4(c2)) | big_p(c2) | big_p(c4) | big_r(f1(c4), f2(c4)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c2) | big_p(c4) | big_p(f4(c2)) | big_r(f1(c4), f2(c4)))),
% 0.56/0.74 inference(transitivity,[status(thm)],[192, 190])).
% 0.56/0.74 tff(194,plain,
% 0.56/0.74 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(f4(c2)) | big_p(c2) | big_p(c4) | big_r(f1(c4), f2(c4)))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(195,plain,
% 0.56/0.74 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c2) | big_p(c4) | big_p(f4(c2)) | big_r(f1(c4), f2(c4))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[194, 193])).
% 0.56/0.74 tff(196,plain,
% 0.56/0.74 (big_p(f4(c2)) | big_r(f1(c4), f2(c4))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[195, 189, 11, 4, 94])).
% 0.56/0.74 tff(197,plain,
% 0.56/0.74 (big_p(f4(c2))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[196, 179])).
% 0.56/0.74 tff(198,plain,
% 0.56/0.74 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c4) | big_r(c4, f3(c4)) | big_r(f1(c4), f2(c4)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c4) | big_r(c4, f3(c4)) | big_r(f1(c4), f2(c4)))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(199,plain,
% 0.56/0.74 (((~big_p(a)) | big_p(c4) | big_p(c4) | big_r(c4, f3(c4)) | big_r(f1(c4), f2(c4))) <=> ((~big_p(a)) | big_p(c4) | big_r(c4, f3(c4)) | big_r(f1(c4), f2(c4)))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(200,plain,
% 0.56/0.74 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c4) | big_p(c4) | big_r(c4, f3(c4)) | big_r(f1(c4), f2(c4)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c4) | big_r(c4, f3(c4)) | big_r(f1(c4), f2(c4))))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[199])).
% 0.56/0.74 tff(201,plain,
% 0.56/0.74 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c4) | big_p(c4) | big_r(c4, f3(c4)) | big_r(f1(c4), f2(c4)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c4) | big_r(c4, f3(c4)) | big_r(f1(c4), f2(c4)))),
% 0.56/0.74 inference(transitivity,[status(thm)],[200, 198])).
% 0.56/0.74 tff(202,plain,
% 0.56/0.74 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c4) | big_p(c4) | big_r(c4, f3(c4)) | big_r(f1(c4), f2(c4)))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(203,plain,
% 0.56/0.74 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c4) | big_r(c4, f3(c4)) | big_r(f1(c4), f2(c4))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.56/0.74 tff(204,plain,
% 0.56/0.74 (big_r(c4, f3(c4)) | big_r(f1(c4), f2(c4))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[203, 120, 11, 4])).
% 0.56/0.74 tff(205,plain,
% 0.56/0.74 (big_r(c4, f3(c4))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[204, 179])).
% 0.56/0.74 tff(206,plain,
% 0.56/0.74 (^[X7: $i, X1: $i] : refl(((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7))))),
% 0.56/0.74 inference(bind,[status(th)],[])).
% 0.56/0.74 tff(207,plain,
% 0.56/0.74 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7))) <=> ![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))),
% 0.56/0.74 inference(quant_intro,[status(thm)],[206])).
% 0.56/0.74 tff(208,plain,
% 0.56/0.74 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7))) <=> ![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(209,plain,
% 0.56/0.74 (^[X7: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~big_p(a)) | big_p(X7)) <=> ((~big_p(a)) | big_p(X7))), ((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) <=> (((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))))), rewrite((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7)))), ((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))))), (((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> (((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))) | (~big_p(a))))), rewrite((((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7)))), (((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))))), ((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) <=> (((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))) | big_p(X1)))), rewrite((((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))), ((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7))))), (((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(f3(X1), f4(X1))) <=> (((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7))) | big_r(f3(X1), f4(X1))))), rewrite((((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7))) | big_r(f3(X1), f4(X1))) <=> ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))), (((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(f3(X1), f4(X1))) <=> ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))))),
% 0.56/0.74 inference(bind,[status(th)],[])).
% 0.56/0.74 tff(210,plain,
% 0.56/0.74 (![X7: $i, X1: $i] : ((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(f3(X1), f4(X1))) <=> ![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))),
% 0.56/0.74 inference(quant_intro,[status(thm)],[209])).
% 0.56/0.74 tff(211,axiom,(![X7: $i, X1: $i] : ((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(f3(X1), f4(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_15')).
% 0.56/0.74 tff(212,plain,
% 0.56/0.74 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[211, 210])).
% 0.56/0.74 tff(213,plain,
% 0.56/0.74 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[212, 208])).
% 0.56/0.74 tff(214,plain,(
% 0.56/0.74 ![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))),
% 0.56/0.74 inference(skolemize,[status(sab)],[213])).
% 0.56/0.74 tff(215,plain,
% 0.56/0.74 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[214, 207])).
% 0.56/0.74 tff(216,plain,
% 0.56/0.74 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c4) | big_r(f3(c4), f4(c4)) | big_r(f1(c4), f2(c4)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c4) | big_r(f3(c4), f4(c4)) | big_r(f1(c4), f2(c4)))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(217,plain,
% 0.56/0.74 (((~big_p(a)) | big_p(c4) | big_p(c4) | big_r(f3(c4), f4(c4)) | big_r(f1(c4), f2(c4))) <=> ((~big_p(a)) | big_p(c4) | big_r(f3(c4), f4(c4)) | big_r(f1(c4), f2(c4)))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(218,plain,
% 0.56/0.74 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c4) | big_p(c4) | big_r(f3(c4), f4(c4)) | big_r(f1(c4), f2(c4)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c4) | big_r(f3(c4), f4(c4)) | big_r(f1(c4), f2(c4))))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[217])).
% 0.56/0.74 tff(219,plain,
% 0.56/0.74 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c4) | big_p(c4) | big_r(f3(c4), f4(c4)) | big_r(f1(c4), f2(c4)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c4) | big_r(f3(c4), f4(c4)) | big_r(f1(c4), f2(c4)))),
% 0.56/0.74 inference(transitivity,[status(thm)],[218, 216])).
% 0.56/0.74 tff(220,plain,
% 0.56/0.74 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c4) | big_p(c4) | big_r(f3(c4), f4(c4)) | big_r(f1(c4), f2(c4)))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(221,plain,
% 0.56/0.74 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c4) | big_r(f3(c4), f4(c4)) | big_r(f1(c4), f2(c4))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[220, 219])).
% 0.56/0.74 tff(222,plain,
% 0.56/0.74 (big_r(f3(c4), f4(c4)) | big_r(f1(c4), f2(c4))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[221, 215, 11, 4])).
% 0.56/0.74 tff(223,plain,
% 0.56/0.74 (big_r(f3(c4), f4(c4))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[222, 179])).
% 0.56/0.74 tff(224,plain,
% 0.56/0.74 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c2) | big_p(c4) | big_r(c2, f3(c2)) | big_r(f1(c4), f2(c4)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c2) | big_p(c4) | big_r(c2, f3(c2)) | big_r(f1(c4), f2(c4)))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(225,plain,
% 0.56/0.74 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c2) | big_p(c4) | big_r(c2, f3(c2)) | big_r(f1(c4), f2(c4)))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(226,plain,
% 0.56/0.74 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c2) | big_p(c4) | big_r(c2, f3(c2)) | big_r(f1(c4), f2(c4))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.56/0.74 tff(227,plain,
% 0.56/0.74 (big_r(c2, f3(c2)) | big_r(f1(c4), f2(c4))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[226, 120, 11, 4, 94])).
% 0.56/0.74 tff(228,plain,
% 0.56/0.74 (big_r(c2, f3(c2))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[227, 179])).
% 0.56/0.74 tff(229,assumption,(~big_r(f3(c2), f4(c2))), introduced(assumption)).
% 0.56/0.74 tff(230,plain,
% 0.56/0.74 (^[X7: $i, X1: $i] : refl(((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1))) <=> ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1))))),
% 0.56/0.74 inference(bind,[status(th)],[])).
% 0.56/0.74 tff(231,plain,
% 0.56/0.74 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1))) <=> ![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))),
% 0.56/0.74 inference(quant_intro,[status(thm)],[230])).
% 0.56/0.74 tff(232,plain,
% 0.56/0.74 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1))) <=> ![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(233,plain,
% 0.56/0.74 (^[X7: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~big_p(a)) | big_p(X7)) <=> ((~big_p(a)) | big_p(X7))), ((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) <=> (((~big_p(a)) | big_p(X7)) | big_p(f2(X7))))), rewrite((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7))), ((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7)))), (((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) <=> (((~big_p(a)) | big_p(f2(X7)) | big_p(X7)) | (~big_p(a))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | big_p(X7)) | (~big_p(a))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7))), (((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7)))), ((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) <=> (((~big_p(a)) | big_p(f2(X7)) | big_p(X7)) | big_p(X1)))), rewrite((((~big_p(a)) | big_p(f2(X7)) | big_p(X7)) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))), ((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7)))), (((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(f3(X1), f4(X1))) <=> (((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7)) | big_r(f3(X1), f4(X1))))), rewrite((((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7)) | big_r(f3(X1), f4(X1))) <=> ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))), (((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(f3(X1), f4(X1))) <=> ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))))),
% 0.56/0.74 inference(bind,[status(th)],[])).
% 0.56/0.74 tff(234,plain,
% 0.56/0.74 (![X7: $i, X1: $i] : ((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(f3(X1), f4(X1))) <=> ![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))),
% 0.56/0.74 inference(quant_intro,[status(thm)],[233])).
% 0.56/0.74 tff(235,axiom,(![X7: $i, X1: $i] : ((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(f3(X1), f4(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_3')).
% 0.56/0.74 tff(236,plain,
% 0.56/0.74 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[235, 234])).
% 0.56/0.74 tff(237,plain,
% 0.56/0.74 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[236, 232])).
% 0.56/0.74 tff(238,plain,(
% 0.56/0.74 ![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))),
% 0.56/0.74 inference(skolemize,[status(sab)],[237])).
% 0.56/0.74 tff(239,plain,
% 0.56/0.74 (![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[238, 231])).
% 0.56/0.74 tff(240,plain,
% 0.56/0.74 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))) | ((~big_p(a)) | big_p(c2) | big_r(f3(c2), f4(c2)) | big_p(f2(c2)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))) | (~big_p(a)) | big_p(c2) | big_r(f3(c2), f4(c2)) | big_p(f2(c2)))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(241,plain,
% 0.56/0.74 (((~big_p(a)) | big_p(c2) | big_p(f2(c2)) | big_p(c2) | big_r(f3(c2), f4(c2))) <=> ((~big_p(a)) | big_p(c2) | big_r(f3(c2), f4(c2)) | big_p(f2(c2)))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(242,plain,
% 0.56/0.74 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))) | ((~big_p(a)) | big_p(c2) | big_p(f2(c2)) | big_p(c2) | big_r(f3(c2), f4(c2)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))) | ((~big_p(a)) | big_p(c2) | big_r(f3(c2), f4(c2)) | big_p(f2(c2))))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[241])).
% 0.56/0.74 tff(243,plain,
% 0.56/0.74 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))) | ((~big_p(a)) | big_p(c2) | big_p(f2(c2)) | big_p(c2) | big_r(f3(c2), f4(c2)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))) | (~big_p(a)) | big_p(c2) | big_r(f3(c2), f4(c2)) | big_p(f2(c2)))),
% 0.56/0.74 inference(transitivity,[status(thm)],[242, 240])).
% 0.56/0.74 tff(244,plain,
% 0.56/0.74 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))) | ((~big_p(a)) | big_p(c2) | big_p(f2(c2)) | big_p(c2) | big_r(f3(c2), f4(c2)))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(245,plain,
% 0.56/0.74 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))) | (~big_p(a)) | big_p(c2) | big_r(f3(c2), f4(c2)) | big_p(f2(c2))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[244, 243])).
% 0.56/0.74 tff(246,plain,
% 0.56/0.74 (big_p(f2(c2))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[245, 239, 11, 94, 229])).
% 0.56/0.74 tff(247,plain,
% 0.56/0.74 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))) | ((~big_p(a)) | big_p(c2) | big_p(c4) | big_r(f3(c2), f4(c2)) | big_p(f2(c4)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))) | (~big_p(a)) | big_p(c2) | big_p(c4) | big_r(f3(c2), f4(c2)) | big_p(f2(c4)))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(248,plain,
% 0.56/0.74 (((~big_p(a)) | big_p(c2) | big_p(f2(c4)) | big_p(c4) | big_r(f3(c2), f4(c2))) <=> ((~big_p(a)) | big_p(c2) | big_p(c4) | big_r(f3(c2), f4(c2)) | big_p(f2(c4)))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(249,plain,
% 0.56/0.74 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))) | ((~big_p(a)) | big_p(c2) | big_p(f2(c4)) | big_p(c4) | big_r(f3(c2), f4(c2)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))) | ((~big_p(a)) | big_p(c2) | big_p(c4) | big_r(f3(c2), f4(c2)) | big_p(f2(c4))))),
% 0.56/0.74 inference(monotonicity,[status(thm)],[248])).
% 0.56/0.74 tff(250,plain,
% 0.56/0.74 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))) | ((~big_p(a)) | big_p(c2) | big_p(f2(c4)) | big_p(c4) | big_r(f3(c2), f4(c2)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))) | (~big_p(a)) | big_p(c2) | big_p(c4) | big_r(f3(c2), f4(c2)) | big_p(f2(c4)))),
% 0.56/0.74 inference(transitivity,[status(thm)],[249, 247])).
% 0.56/0.74 tff(251,plain,
% 0.56/0.74 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))) | ((~big_p(a)) | big_p(c2) | big_p(f2(c4)) | big_p(c4) | big_r(f3(c2), f4(c2)))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.74 tff(252,plain,
% 0.56/0.74 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))) | (~big_p(a)) | big_p(c2) | big_p(c4) | big_r(f3(c2), f4(c2)) | big_p(f2(c4))),
% 0.56/0.74 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.56/0.74 tff(253,plain,
% 0.56/0.74 (big_p(f2(c4))),
% 0.56/0.74 inference(unit_resolution,[status(thm)],[252, 239, 11, 4, 94, 229])).
% 0.56/0.74 tff(254,plain,
% 0.56/0.74 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c2) | big_p(c4) | big_r(f3(c2), f4(c2)) | big_r(c4, f1(c4)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))) | (~big_p(a)) | big_p(c2) | big_p(c4) | big_r(f3(c2), f4(c2)) | big_r(c4, f1(c4)))),
% 0.56/0.74 inference(rewrite,[status(thm)],[])).
% 0.56/0.74 tff(255,plain,
% 0.56/0.74 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c2) | big_p(c4) | big_r(f3(c2), f4(c2)) | big_r(c4, f1(c4)))),
% 0.56/0.74 inference(quant_inst,[status(thm)],[])).
% 0.56/0.75 tff(256,plain,
% 0.56/0.75 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))) | (~big_p(a)) | big_p(c2) | big_p(c4) | big_r(f3(c2), f4(c2)) | big_r(c4, f1(c4))),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[255, 254])).
% 0.56/0.75 tff(257,plain,
% 0.56/0.75 (big_r(f3(c2), f4(c2)) | big_r(c4, f1(c4))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[256, 38, 11, 4, 94])).
% 0.56/0.75 tff(258,plain,
% 0.56/0.75 (big_r(c4, f1(c4))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[257, 229])).
% 0.56/0.75 tff(259,plain,
% 0.56/0.75 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c2) | big_p(c4) | big_r(f3(c2), f4(c2)) | big_r(f1(c4), f2(c4)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c2) | big_p(c4) | big_r(f3(c2), f4(c2)) | big_r(f1(c4), f2(c4)))),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(260,plain,
% 0.56/0.75 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c2) | big_p(c4) | big_r(f3(c2), f4(c2)) | big_r(f1(c4), f2(c4)))),
% 0.56/0.75 inference(quant_inst,[status(thm)],[])).
% 0.56/0.75 tff(261,plain,
% 0.56/0.75 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c2) | big_p(c4) | big_r(f3(c2), f4(c2)) | big_r(f1(c4), f2(c4))),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[260, 259])).
% 0.56/0.75 tff(262,plain,
% 0.56/0.75 (big_r(f3(c2), f4(c2)) | big_r(f1(c4), f2(c4))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[261, 215, 11, 4, 94])).
% 0.56/0.75 tff(263,plain,
% 0.56/0.75 (big_r(f1(c4), f2(c4))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[262, 229])).
% 0.56/0.75 tff(264,assumption,(~big_r(c2, f1(c2))), introduced(assumption)).
% 0.56/0.75 tff(265,plain,
% 0.56/0.75 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c2) | big_p(c4) | big_r(c2, f1(c2)) | big_r(c4, f3(c4)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))) | (~big_p(a)) | big_p(c2) | big_p(c4) | big_r(c2, f1(c2)) | big_r(c4, f3(c4)))),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(266,plain,
% 0.56/0.75 (((~big_p(a)) | big_p(c4) | big_p(c2) | big_r(c4, f3(c4)) | big_r(c2, f1(c2))) <=> ((~big_p(a)) | big_p(c2) | big_p(c4) | big_r(c2, f1(c2)) | big_r(c4, f3(c4)))),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(267,plain,
% 0.56/0.75 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c4) | big_p(c2) | big_r(c4, f3(c4)) | big_r(c2, f1(c2)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c2) | big_p(c4) | big_r(c2, f1(c2)) | big_r(c4, f3(c4))))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[266])).
% 0.56/0.75 tff(268,plain,
% 0.56/0.75 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c4) | big_p(c2) | big_r(c4, f3(c4)) | big_r(c2, f1(c2)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))) | (~big_p(a)) | big_p(c2) | big_p(c4) | big_r(c2, f1(c2)) | big_r(c4, f3(c4)))),
% 0.56/0.75 inference(transitivity,[status(thm)],[267, 265])).
% 0.56/0.75 tff(269,plain,
% 0.56/0.75 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c4) | big_p(c2) | big_r(c4, f3(c4)) | big_r(c2, f1(c2)))),
% 0.56/0.75 inference(quant_inst,[status(thm)],[])).
% 0.56/0.75 tff(270,plain,
% 0.56/0.75 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(X7, f1(X7)))) | (~big_p(a)) | big_p(c2) | big_p(c4) | big_r(c2, f1(c2)) | big_r(c4, f3(c4))),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[269, 268])).
% 0.56/0.75 tff(271,plain,
% 0.56/0.75 (big_r(c4, f3(c4))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[270, 75, 11, 4, 94, 264])).
% 0.56/0.75 tff(272,plain,
% 0.56/0.75 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c2) | big_p(c4) | big_r(c2, f1(c2)) | big_r(f3(c4), f4(c4)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))) | (~big_p(a)) | big_p(c2) | big_p(c4) | big_r(c2, f1(c2)) | big_r(f3(c4), f4(c4)))),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(273,plain,
% 0.56/0.75 (((~big_p(a)) | big_p(c4) | big_p(c2) | big_r(f3(c4), f4(c4)) | big_r(c2, f1(c2))) <=> ((~big_p(a)) | big_p(c2) | big_p(c4) | big_r(c2, f1(c2)) | big_r(f3(c4), f4(c4)))),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(274,plain,
% 0.56/0.75 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c4) | big_p(c2) | big_r(f3(c4), f4(c4)) | big_r(c2, f1(c2)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c2) | big_p(c4) | big_r(c2, f1(c2)) | big_r(f3(c4), f4(c4))))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[273])).
% 0.56/0.75 tff(275,plain,
% 0.56/0.75 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c4) | big_p(c2) | big_r(f3(c4), f4(c4)) | big_r(c2, f1(c2)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))) | (~big_p(a)) | big_p(c2) | big_p(c4) | big_r(c2, f1(c2)) | big_r(f3(c4), f4(c4)))),
% 0.56/0.75 inference(transitivity,[status(thm)],[274, 272])).
% 0.56/0.75 tff(276,plain,
% 0.56/0.75 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c4) | big_p(c2) | big_r(f3(c4), f4(c4)) | big_r(c2, f1(c2)))),
% 0.56/0.75 inference(quant_inst,[status(thm)],[])).
% 0.56/0.75 tff(277,plain,
% 0.56/0.75 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))) | (~big_p(a)) | big_p(c2) | big_p(c4) | big_r(c2, f1(c2)) | big_r(f3(c4), f4(c4))),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[276, 275])).
% 0.56/0.75 tff(278,plain,
% 0.56/0.75 (big_r(f3(c4), f4(c4))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[277, 38, 11, 4, 94, 264])).
% 0.56/0.75 tff(279,plain,
% 0.56/0.75 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c2) | big_r(c2, f1(c2)) | big_p(f4(c2)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | (~big_p(a)) | big_p(c2) | big_r(c2, f1(c2)) | big_p(f4(c2)))),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(280,plain,
% 0.56/0.75 (((~big_p(a)) | big_p(f4(c2)) | big_p(c2) | big_p(c2) | big_r(c2, f1(c2))) <=> ((~big_p(a)) | big_p(c2) | big_r(c2, f1(c2)) | big_p(f4(c2)))),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(281,plain,
% 0.56/0.75 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(f4(c2)) | big_p(c2) | big_p(c2) | big_r(c2, f1(c2)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c2) | big_r(c2, f1(c2)) | big_p(f4(c2))))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[280])).
% 0.56/0.75 tff(282,plain,
% 0.56/0.75 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(f4(c2)) | big_p(c2) | big_p(c2) | big_r(c2, f1(c2)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | (~big_p(a)) | big_p(c2) | big_r(c2, f1(c2)) | big_p(f4(c2)))),
% 0.56/0.75 inference(transitivity,[status(thm)],[281, 279])).
% 0.56/0.75 tff(283,plain,
% 0.56/0.75 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(f4(c2)) | big_p(c2) | big_p(c2) | big_r(c2, f1(c2)))),
% 0.56/0.75 inference(quant_inst,[status(thm)],[])).
% 0.56/0.75 tff(284,plain,
% 0.56/0.75 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | (~big_p(a)) | big_p(c2) | big_r(c2, f1(c2)) | big_p(f4(c2))),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[283, 282])).
% 0.56/0.75 tff(285,plain,
% 0.56/0.75 (big_p(f4(c2))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[284, 21, 11, 94, 264])).
% 0.56/0.75 tff(286,plain,
% 0.56/0.75 (big_r(c2, f3(c2))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[109, 264])).
% 0.56/0.75 tff(287,plain,
% 0.56/0.75 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c2) | big_r(f3(c2), f4(c2)) | big_r(c2, f1(c2)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))) | (~big_p(a)) | big_p(c2) | big_r(f3(c2), f4(c2)) | big_r(c2, f1(c2)))),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(288,plain,
% 0.56/0.75 (((~big_p(a)) | big_p(c2) | big_p(c2) | big_r(f3(c2), f4(c2)) | big_r(c2, f1(c2))) <=> ((~big_p(a)) | big_p(c2) | big_r(f3(c2), f4(c2)) | big_r(c2, f1(c2)))),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(289,plain,
% 0.56/0.75 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c2) | big_p(c2) | big_r(f3(c2), f4(c2)) | big_r(c2, f1(c2)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c2) | big_r(f3(c2), f4(c2)) | big_r(c2, f1(c2))))),
% 0.56/0.75 inference(monotonicity,[status(thm)],[288])).
% 0.56/0.75 tff(290,plain,
% 0.56/0.75 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c2) | big_p(c2) | big_r(f3(c2), f4(c2)) | big_r(c2, f1(c2)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))) | (~big_p(a)) | big_p(c2) | big_r(f3(c2), f4(c2)) | big_r(c2, f1(c2)))),
% 0.56/0.75 inference(transitivity,[status(thm)],[289, 287])).
% 0.56/0.75 tff(291,plain,
% 0.56/0.75 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c2) | big_p(c2) | big_r(f3(c2), f4(c2)) | big_r(c2, f1(c2)))),
% 0.56/0.75 inference(quant_inst,[status(thm)],[])).
% 0.56/0.75 tff(292,plain,
% 0.56/0.75 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(X7, f1(X7)))) | (~big_p(a)) | big_p(c2) | big_r(f3(c2), f4(c2)) | big_r(c2, f1(c2))),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[291, 290])).
% 0.56/0.75 tff(293,plain,
% 0.56/0.75 (big_r(f3(c2), f4(c2)) | big_r(c2, f1(c2))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[292, 38, 11, 94])).
% 0.56/0.75 tff(294,plain,
% 0.56/0.75 (big_r(f3(c2), f4(c2))),
% 0.56/0.75 inference(unit_resolution,[status(thm)],[293, 264])).
% 0.56/0.75 tff(295,plain,
% 0.56/0.75 (^[X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : refl(((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9))) <=> ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9))))),
% 0.56/0.75 inference(bind,[status(th)],[])).
% 0.56/0.75 tff(296,plain,
% 0.56/0.75 (![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9))) <=> ![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))),
% 0.56/0.75 inference(quant_intro,[status(thm)],[295])).
% 0.56/0.75 tff(297,plain,
% 0.56/0.75 (![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9))) <=> ![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(298,plain,
% 0.56/0.75 (^[X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) <=> ((~big_r(c2, X10)) | (~big_r(X10, X9)) | (~big_p(X9)))), (((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) | (~big_p(X3))) <=> (((~big_r(c2, X10)) | (~big_r(X10, X9)) | (~big_p(X9))) | (~big_p(X3))))), rewrite((((~big_r(c2, X10)) | (~big_r(X10, X9)) | (~big_p(X9))) | (~big_p(X3))) <=> ((~big_p(X3)) | (~big_r(c2, X10)) | (~big_r(X10, X9)) | (~big_p(X9)))), (((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) | (~big_p(X3))) <=> ((~big_p(X3)) | (~big_r(c2, X10)) | (~big_r(X10, X9)) | (~big_p(X9))))), ((((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) | (~big_p(X3))) | (~big_r(c4, X4))) <=> (((~big_p(X3)) | (~big_r(c2, X10)) | (~big_r(X10, X9)) | (~big_p(X9))) | (~big_r(c4, X4))))), rewrite((((~big_p(X3)) | (~big_r(c2, X10)) | (~big_r(X10, X9)) | (~big_p(X9))) | (~big_r(c4, X4))) <=> ((~big_p(X3)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X10, X9)) | (~big_p(X9)))), ((((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) | (~big_p(X3))) | (~big_r(c4, X4))) <=> ((~big_p(X3)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X10, X9)) | (~big_p(X9))))), (((((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) <=> (((~big_p(X3)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X10, X9)) | (~big_p(X9))) | (~big_r(X4, X3))))), rewrite((((~big_p(X3)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X10, X9)) | (~big_p(X9))) | (~big_r(X4, X3))) <=> ((~big_p(X3)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))), (((((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) <=> ((~big_p(X3)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9))))), ((((((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) | (~big_p(X5))) <=> (((~big_p(X3)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9))) | (~big_p(X5))))), rewrite((((~big_p(X3)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9))) | (~big_p(X5))) <=> ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))), ((((((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) | (~big_p(X5))) <=> ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9))))), (((((((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) | (~big_p(X5))) | (~big_r(c4, X6))) <=> (((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9))) | (~big_r(c4, X6))))), rewrite((((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9))) | (~big_r(c4, X6))) <=> ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))), (((((((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) | (~big_p(X5))) | (~big_r(c4, X6))) <=> ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9))))), ((((((((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) | (~big_p(X5))) | (~big_r(c4, X6))) | (~big_r(X6, X5))) <=> (((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9))) | (~big_r(X6, X5))))), rewrite((((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9))) | (~big_r(X6, X5))) <=> ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))), ((((((((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) | (~big_p(X5))) | (~big_r(c4, X6))) | (~big_r(X6, X5))) <=> ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))))),
% 0.56/0.75 inference(bind,[status(th)],[])).
% 0.56/0.75 tff(299,plain,
% 0.56/0.75 (![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : (((((((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) | (~big_p(X5))) | (~big_r(c4, X6))) | (~big_r(X6, X5))) <=> ![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))),
% 0.56/0.75 inference(quant_intro,[status(thm)],[298])).
% 0.56/0.75 tff(300,axiom,(![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : (((((((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) | (~big_p(X5))) | (~big_r(c4, X6))) | (~big_r(X6, X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_84')).
% 0.56/0.75 tff(301,plain,
% 0.56/0.75 (![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[300, 299])).
% 0.56/0.75 tff(302,plain,
% 0.56/0.75 (![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[301, 297])).
% 0.56/0.75 tff(303,plain,(
% 0.56/0.75 ![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))),
% 0.56/0.75 inference(skolemize,[status(sab)],[302])).
% 0.56/0.75 tff(304,plain,
% 0.56/0.75 (![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))),
% 0.56/0.75 inference(modus_ponens,[status(thm)],[303, 296])).
% 0.56/0.75 tff(305,plain,
% 0.56/0.75 (((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2))) | (~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4))))) <=> ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | (~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2))) | (~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4))))),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(306,plain,
% 0.56/0.75 (((~big_p(f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c4), f4(c4))) | (~big_r(c4, f3(c4))) | (~big_r(f3(c4), f4(c4))) | (~big_r(f3(c2), f4(c2))) | (~big_p(f4(c2)))) <=> ((~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2))) | (~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4))))),
% 0.56/0.75 inference(rewrite,[status(thm)],[])).
% 0.56/0.75 tff(307,plain,
% 0.56/0.75 (((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c4), f4(c4))) | (~big_r(c4, f3(c4))) | (~big_r(f3(c4), f4(c4))) | (~big_r(f3(c2), f4(c2))) | (~big_p(f4(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2))) | (~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4)))))),
% 0.56/0.76 inference(monotonicity,[status(thm)],[306])).
% 0.56/0.76 tff(308,plain,
% 0.56/0.76 (((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c4), f4(c4))) | (~big_r(c4, f3(c4))) | (~big_r(f3(c4), f4(c4))) | (~big_r(f3(c2), f4(c2))) | (~big_p(f4(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | (~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2))) | (~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4))))),
% 0.56/0.76 inference(transitivity,[status(thm)],[307, 305])).
% 0.56/0.76 tff(309,plain,
% 0.56/0.76 ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c4), f4(c4))) | (~big_r(c4, f3(c4))) | (~big_r(f3(c4), f4(c4))) | (~big_r(f3(c2), f4(c2))) | (~big_p(f4(c2))))),
% 0.56/0.76 inference(quant_inst,[status(thm)],[])).
% 0.56/0.76 tff(310,plain,
% 0.56/0.76 ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | (~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2))) | (~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4)))),
% 0.56/0.76 inference(modus_ponens,[status(thm)],[309, 308])).
% 0.56/0.76 tff(311,plain,
% 0.56/0.76 (~big_p(f4(c4))),
% 0.56/0.76 inference(unit_resolution,[status(thm)],[310, 304, 294, 286, 285, 278, 271])).
% 0.56/0.76 tff(312,plain,
% 0.56/0.76 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c2) | big_p(c4) | big_r(c2, f1(c2)) | big_p(f4(c4)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | (~big_p(a)) | big_p(c2) | big_p(c4) | big_r(c2, f1(c2)) | big_p(f4(c4)))),
% 0.56/0.76 inference(rewrite,[status(thm)],[])).
% 0.56/0.76 tff(313,plain,
% 0.56/0.76 (((~big_p(a)) | big_p(f4(c4)) | big_p(c4) | big_p(c2) | big_r(c2, f1(c2))) <=> ((~big_p(a)) | big_p(c2) | big_p(c4) | big_r(c2, f1(c2)) | big_p(f4(c4)))),
% 0.56/0.76 inference(rewrite,[status(thm)],[])).
% 0.56/0.76 tff(314,plain,
% 0.56/0.76 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(f4(c4)) | big_p(c4) | big_p(c2) | big_r(c2, f1(c2)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c2) | big_p(c4) | big_r(c2, f1(c2)) | big_p(f4(c4))))),
% 0.56/0.76 inference(monotonicity,[status(thm)],[313])).
% 0.56/0.76 tff(315,plain,
% 0.56/0.76 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(f4(c4)) | big_p(c4) | big_p(c2) | big_r(c2, f1(c2)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | (~big_p(a)) | big_p(c2) | big_p(c4) | big_r(c2, f1(c2)) | big_p(f4(c4)))),
% 0.56/0.76 inference(transitivity,[status(thm)],[314, 312])).
% 0.56/0.76 tff(316,plain,
% 0.56/0.76 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(f4(c4)) | big_p(c4) | big_p(c2) | big_r(c2, f1(c2)))),
% 0.56/0.76 inference(quant_inst,[status(thm)],[])).
% 0.56/0.76 tff(317,plain,
% 0.56/0.76 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(X7, f1(X7)))) | (~big_p(a)) | big_p(c2) | big_p(c4) | big_r(c2, f1(c2)) | big_p(f4(c4))),
% 0.56/0.76 inference(modus_ponens,[status(thm)],[316, 315])).
% 0.56/0.76 tff(318,plain,
% 0.56/0.76 ($false),
% 0.56/0.76 inference(unit_resolution,[status(thm)],[317, 21, 11, 4, 94, 264, 311])).
% 0.56/0.76 tff(319,plain,(big_r(c2, f1(c2)) | big_p(c4) | big_p(c2)), inference(lemma,lemma(discharge,[]))).
% 0.56/0.76 tff(320,plain,
% 0.56/0.76 (big_r(c2, f1(c2))),
% 0.56/0.76 inference(unit_resolution,[status(thm)],[319, 4, 94])).
% 0.56/0.76 tff(321,plain,
% 0.56/0.76 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c2) | big_r(f3(c2), f4(c2)) | big_r(f1(c2), f2(c2)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c2) | big_r(f3(c2), f4(c2)) | big_r(f1(c2), f2(c2)))),
% 0.56/0.76 inference(rewrite,[status(thm)],[])).
% 0.56/0.76 tff(322,plain,
% 0.56/0.76 (((~big_p(a)) | big_p(c2) | big_p(c2) | big_r(f3(c2), f4(c2)) | big_r(f1(c2), f2(c2))) <=> ((~big_p(a)) | big_p(c2) | big_r(f3(c2), f4(c2)) | big_r(f1(c2), f2(c2)))),
% 0.56/0.76 inference(rewrite,[status(thm)],[])).
% 0.56/0.76 tff(323,plain,
% 0.56/0.76 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c2) | big_p(c2) | big_r(f3(c2), f4(c2)) | big_r(f1(c2), f2(c2)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c2) | big_r(f3(c2), f4(c2)) | big_r(f1(c2), f2(c2))))),
% 0.56/0.76 inference(monotonicity,[status(thm)],[322])).
% 0.56/0.76 tff(324,plain,
% 0.56/0.76 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c2) | big_p(c2) | big_r(f3(c2), f4(c2)) | big_r(f1(c2), f2(c2)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c2) | big_r(f3(c2), f4(c2)) | big_r(f1(c2), f2(c2)))),
% 0.56/0.76 inference(transitivity,[status(thm)],[323, 321])).
% 0.56/0.76 tff(325,plain,
% 0.56/0.76 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c2) | big_p(c2) | big_r(f3(c2), f4(c2)) | big_r(f1(c2), f2(c2)))),
% 0.56/0.76 inference(quant_inst,[status(thm)],[])).
% 0.56/0.76 tff(326,plain,
% 0.56/0.76 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(f3(X1), f4(X1)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c2) | big_r(f3(c2), f4(c2)) | big_r(f1(c2), f2(c2))),
% 0.56/0.76 inference(modus_ponens,[status(thm)],[325, 324])).
% 0.56/0.76 tff(327,plain,
% 0.56/0.76 (big_r(f3(c2), f4(c2)) | big_r(f1(c2), f2(c2))),
% 0.56/0.76 inference(unit_resolution,[status(thm)],[326, 215, 11, 94])).
% 0.56/0.76 tff(328,plain,
% 0.56/0.76 (big_r(f1(c2), f2(c2))),
% 0.56/0.76 inference(unit_resolution,[status(thm)],[327, 229])).
% 0.56/0.76 tff(329,plain,
% 0.56/0.76 (((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f2(c2))) | (~big_r(f1(c2), f2(c2))) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))) | (~big_r(c2, f1(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | (~big_p(f2(c2))) | (~big_r(f1(c2), f2(c2))) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))) | (~big_r(c2, f1(c2))))),
% 0.56/0.76 inference(rewrite,[status(thm)],[])).
% 0.56/0.76 tff(330,plain,
% 0.56/0.76 (((~big_p(f2(c4))) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(c2, f1(c2))) | (~big_r(f1(c4), f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))) | (~big_r(f1(c2), f2(c2))) | (~big_p(f2(c2)))) <=> ((~big_p(f2(c2))) | (~big_r(f1(c2), f2(c2))) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))) | (~big_r(c2, f1(c2))))),
% 0.56/0.76 inference(rewrite,[status(thm)],[])).
% 0.56/0.76 tff(331,plain,
% 0.56/0.76 (((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f2(c4))) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(c2, f1(c2))) | (~big_r(f1(c4), f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))) | (~big_r(f1(c2), f2(c2))) | (~big_p(f2(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f2(c2))) | (~big_r(f1(c2), f2(c2))) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))) | (~big_r(c2, f1(c2)))))),
% 0.56/0.76 inference(monotonicity,[status(thm)],[330])).
% 0.56/0.76 tff(332,plain,
% 0.56/0.76 (((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f2(c4))) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(c2, f1(c2))) | (~big_r(f1(c4), f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))) | (~big_r(f1(c2), f2(c2))) | (~big_p(f2(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | (~big_p(f2(c2))) | (~big_r(f1(c2), f2(c2))) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))) | (~big_r(c2, f1(c2))))),
% 0.56/0.76 inference(transitivity,[status(thm)],[331, 329])).
% 0.56/0.76 tff(333,plain,
% 0.56/0.76 ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f2(c4))) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(c2, f1(c2))) | (~big_r(f1(c4), f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))) | (~big_r(f1(c2), f2(c2))) | (~big_p(f2(c2))))),
% 0.56/0.76 inference(quant_inst,[status(thm)],[])).
% 0.56/0.76 tff(334,plain,
% 0.56/0.76 ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | (~big_p(f2(c2))) | (~big_r(f1(c2), f2(c2))) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))) | (~big_r(c2, f1(c2)))),
% 0.56/0.76 inference(modus_ponens,[status(thm)],[333, 332])).
% 0.56/0.76 tff(335,plain,
% 0.56/0.76 ((~big_p(f2(c2))) | (~big_p(f2(c4)))),
% 0.56/0.76 inference(unit_resolution,[status(thm)],[334, 304, 328, 320, 263, 258])).
% 0.56/0.76 tff(336,plain,
% 0.56/0.76 ($false),
% 0.56/0.76 inference(unit_resolution,[status(thm)],[335, 253, 246])).
% 0.56/0.76 tff(337,plain,(big_r(f3(c2), f4(c2)) | big_p(c4) | big_p(c2)), inference(lemma,lemma(discharge,[]))).
% 0.56/0.76 tff(338,plain,
% 0.56/0.76 (big_r(f3(c2), f4(c2))),
% 0.56/0.76 inference(unit_resolution,[status(thm)],[337, 4, 94])).
% 0.56/0.76 tff(339,plain,
% 0.56/0.76 (~big_p(f4(c4))),
% 0.56/0.76 inference(unit_resolution,[status(thm)],[310, 304, 338, 228, 223, 205, 197])).
% 0.56/0.76 tff(340,plain,
% 0.56/0.76 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c4) | big_r(f1(c4), f2(c4)) | big_p(f4(c4)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c4) | big_r(f1(c4), f2(c4)) | big_p(f4(c4)))),
% 0.56/0.76 inference(rewrite,[status(thm)],[])).
% 0.56/0.76 tff(341,plain,
% 0.56/0.76 (((~big_p(a)) | big_p(f4(c4)) | big_p(c4) | big_p(c4) | big_r(f1(c4), f2(c4))) <=> ((~big_p(a)) | big_p(c4) | big_r(f1(c4), f2(c4)) | big_p(f4(c4)))),
% 0.56/0.76 inference(rewrite,[status(thm)],[])).
% 0.56/0.76 tff(342,plain,
% 0.56/0.76 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(f4(c4)) | big_p(c4) | big_p(c4) | big_r(f1(c4), f2(c4)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c4) | big_r(f1(c4), f2(c4)) | big_p(f4(c4))))),
% 0.60/0.76 inference(monotonicity,[status(thm)],[341])).
% 0.60/0.76 tff(343,plain,
% 0.60/0.76 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(f4(c4)) | big_p(c4) | big_p(c4) | big_r(f1(c4), f2(c4)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c4) | big_r(f1(c4), f2(c4)) | big_p(f4(c4)))),
% 0.60/0.76 inference(transitivity,[status(thm)],[342, 340])).
% 0.60/0.76 tff(344,plain,
% 0.60/0.76 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(f4(c4)) | big_p(c4) | big_p(c4) | big_r(f1(c4), f2(c4)))),
% 0.60/0.76 inference(quant_inst,[status(thm)],[])).
% 0.60/0.76 tff(345,plain,
% 0.60/0.76 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c4) | big_r(f1(c4), f2(c4)) | big_p(f4(c4))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[344, 343])).
% 0.60/0.76 tff(346,plain,
% 0.60/0.76 ($false),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[345, 189, 11, 4, 179, 339])).
% 0.60/0.76 tff(347,plain,(big_r(f1(c4), f2(c4)) | big_p(c4) | big_p(c2)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.76 tff(348,plain,
% 0.60/0.76 (big_r(f1(c4), f2(c4))),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[347, 4, 94])).
% 0.60/0.76 tff(349,plain,
% 0.60/0.76 (~big_p(f2(c2))),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[334, 304, 128, 320, 348, 178, 173])).
% 0.60/0.76 tff(350,plain,
% 0.60/0.76 ($false),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[101, 57, 11, 94, 95, 349])).
% 0.60/0.76 tff(351,plain,(big_r(c2, f3(c2)) | big_p(c2) | big_p(c4)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.76 tff(352,plain,
% 0.60/0.76 (big_r(c2, f3(c2))),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[351, 4, 94])).
% 0.60/0.76 tff(353,plain,
% 0.60/0.76 (~big_p(f4(c4))),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[310, 304, 338, 352, 46, 83, 165])).
% 0.60/0.76 tff(354,plain,
% 0.60/0.76 ($false),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[27, 21, 11, 4, 3, 353])).
% 0.60/0.76 tff(355,plain,(big_r(c4, f1(c4)) | big_p(c4) | big_p(c2)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.76 tff(356,plain,
% 0.60/0.76 (big_r(c4, f1(c4))),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[355, 4, 94])).
% 0.60/0.76 tff(357,assumption,(~big_p(f2(c2))), introduced(assumption)).
% 0.60/0.76 tff(358,plain,
% 0.60/0.76 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))) | ((~big_p(a)) | big_p(c2) | big_p(c4) | big_p(f2(c2)) | big_p(f4(c4)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))) | (~big_p(a)) | big_p(c2) | big_p(c4) | big_p(f2(c2)) | big_p(f4(c4)))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(359,plain,
% 0.60/0.76 (((~big_p(a)) | big_p(f4(c4)) | big_p(c4) | big_p(f2(c2)) | big_p(c2)) <=> ((~big_p(a)) | big_p(c2) | big_p(c4) | big_p(f2(c2)) | big_p(f4(c4)))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(360,plain,
% 0.60/0.76 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))) | ((~big_p(a)) | big_p(f4(c4)) | big_p(c4) | big_p(f2(c2)) | big_p(c2))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))) | ((~big_p(a)) | big_p(c2) | big_p(c4) | big_p(f2(c2)) | big_p(f4(c4))))),
% 0.60/0.76 inference(monotonicity,[status(thm)],[359])).
% 0.60/0.76 tff(361,plain,
% 0.60/0.76 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))) | ((~big_p(a)) | big_p(f4(c4)) | big_p(c4) | big_p(f2(c2)) | big_p(c2))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))) | (~big_p(a)) | big_p(c2) | big_p(c4) | big_p(f2(c2)) | big_p(f4(c4)))),
% 0.60/0.76 inference(transitivity,[status(thm)],[360, 358])).
% 0.60/0.76 tff(362,plain,
% 0.60/0.76 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))) | ((~big_p(a)) | big_p(f4(c4)) | big_p(c4) | big_p(f2(c2)) | big_p(c2))),
% 0.60/0.76 inference(quant_inst,[status(thm)],[])).
% 0.60/0.76 tff(363,plain,
% 0.60/0.76 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))) | (~big_p(a)) | big_p(c2) | big_p(c4) | big_p(f2(c2)) | big_p(f4(c4))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[362, 361])).
% 0.60/0.76 tff(364,plain,
% 0.60/0.76 (big_p(f4(c4))),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[363, 149, 11, 4, 94, 357])).
% 0.60/0.76 tff(365,plain,
% 0.60/0.76 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))) | ((~big_p(a)) | big_p(c2) | big_p(f4(c2)) | big_p(f2(c2)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))) | (~big_p(a)) | big_p(c2) | big_p(f4(c2)) | big_p(f2(c2)))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(366,plain,
% 0.60/0.76 (((~big_p(a)) | big_p(f4(c2)) | big_p(c2) | big_p(f2(c2)) | big_p(c2)) <=> ((~big_p(a)) | big_p(c2) | big_p(f4(c2)) | big_p(f2(c2)))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(367,plain,
% 0.60/0.76 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))) | ((~big_p(a)) | big_p(f4(c2)) | big_p(c2) | big_p(f2(c2)) | big_p(c2))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))) | ((~big_p(a)) | big_p(c2) | big_p(f4(c2)) | big_p(f2(c2))))),
% 0.60/0.76 inference(monotonicity,[status(thm)],[366])).
% 0.60/0.76 tff(368,plain,
% 0.60/0.76 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))) | ((~big_p(a)) | big_p(f4(c2)) | big_p(c2) | big_p(f2(c2)) | big_p(c2))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))) | (~big_p(a)) | big_p(c2) | big_p(f4(c2)) | big_p(f2(c2)))),
% 0.60/0.76 inference(transitivity,[status(thm)],[367, 365])).
% 0.60/0.76 tff(369,plain,
% 0.60/0.76 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))) | ((~big_p(a)) | big_p(f4(c2)) | big_p(c2) | big_p(f2(c2)) | big_p(c2))),
% 0.60/0.76 inference(quant_inst,[status(thm)],[])).
% 0.60/0.76 tff(370,plain,
% 0.60/0.76 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))) | (~big_p(a)) | big_p(c2) | big_p(f4(c2)) | big_p(f2(c2))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[369, 368])).
% 0.60/0.76 tff(371,plain,
% 0.60/0.76 ($false),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[370, 149, 11, 94, 357, 139])).
% 0.60/0.76 tff(372,plain,(big_p(f4(c2)) | big_p(c2) | big_p(f2(c2))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.76 tff(373,plain,
% 0.60/0.76 (big_p(f4(c2))),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[372, 357, 94])).
% 0.60/0.76 tff(374,plain,
% 0.60/0.76 (big_r(c4, f3(c4)) | big_p(f2(c4))),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[63, 57, 11, 4])).
% 0.60/0.76 tff(375,plain,
% 0.60/0.76 (big_p(f2(c4))),
% 0.60/0.76 inference(unit_resolution,[status(thm)],[374, 47])).
% 0.60/0.76 tff(376,plain,
% 0.60/0.76 (((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2))) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))))) <=> ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | (~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2))) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(377,plain,
% 0.60/0.76 (((~big_p(f2(c4))) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(c2, f3(c2))) | (~big_r(f1(c4), f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))) | (~big_r(f3(c2), f4(c2))) | (~big_p(f4(c2)))) <=> ((~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2))) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))))),
% 0.60/0.76 inference(rewrite,[status(thm)],[])).
% 0.60/0.76 tff(378,plain,
% 0.60/0.76 (((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f2(c4))) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(c2, f3(c2))) | (~big_r(f1(c4), f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))) | (~big_r(f3(c2), f4(c2))) | (~big_p(f4(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2))) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4)))))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[377])).
% 0.60/0.77 tff(379,plain,
% 0.60/0.77 (((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f2(c4))) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(c2, f3(c2))) | (~big_r(f1(c4), f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))) | (~big_r(f3(c2), f4(c2))) | (~big_p(f4(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | (~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2))) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))))),
% 0.60/0.77 inference(transitivity,[status(thm)],[378, 376])).
% 0.60/0.77 tff(380,plain,
% 0.60/0.77 ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f2(c4))) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(c2, f3(c2))) | (~big_r(f1(c4), f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))) | (~big_r(f3(c2), f4(c2))) | (~big_p(f4(c2))))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(381,plain,
% 0.60/0.77 ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | (~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2))) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4)))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[380, 379])).
% 0.60/0.77 tff(382,plain,
% 0.60/0.77 ((~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4)))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[381, 304, 338, 348])).
% 0.60/0.77 tff(383,plain,
% 0.60/0.77 (~big_p(f4(c2))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[382, 375, 352, 356])).
% 0.60/0.77 tff(384,plain,
% 0.60/0.77 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c2) | big_p(c4) | big_r(f1(c2), f2(c2)) | big_r(c4, f3(c4)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c2) | big_p(c4) | big_r(f1(c2), f2(c2)) | big_r(c4, f3(c4)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(385,plain,
% 0.60/0.77 (((~big_p(a)) | big_p(c4) | big_p(c2) | big_r(c4, f3(c4)) | big_r(f1(c2), f2(c2))) <=> ((~big_p(a)) | big_p(c2) | big_p(c4) | big_r(f1(c2), f2(c2)) | big_r(c4, f3(c4)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(386,plain,
% 0.60/0.77 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c4) | big_p(c2) | big_r(c4, f3(c4)) | big_r(f1(c2), f2(c2)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c2) | big_p(c4) | big_r(f1(c2), f2(c2)) | big_r(c4, f3(c4))))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[385])).
% 0.60/0.77 tff(387,plain,
% 0.60/0.77 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c4) | big_p(c2) | big_r(c4, f3(c4)) | big_r(f1(c2), f2(c2)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c2) | big_p(c4) | big_r(f1(c2), f2(c2)) | big_r(c4, f3(c4)))),
% 0.60/0.77 inference(transitivity,[status(thm)],[386, 384])).
% 0.60/0.77 tff(388,plain,
% 0.60/0.77 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c4) | big_p(c2) | big_r(c4, f3(c4)) | big_r(f1(c2), f2(c2)))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(389,plain,
% 0.60/0.77 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(X7) | big_r(X1, f3(X1)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c2) | big_p(c4) | big_r(f1(c2), f2(c2)) | big_r(c4, f3(c4))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[388, 387])).
% 0.60/0.77 tff(390,plain,
% 0.60/0.77 (big_r(f1(c2), f2(c2)) | big_r(c4, f3(c4))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[389, 120, 11, 4, 94])).
% 0.60/0.77 tff(391,plain,
% 0.60/0.77 (big_r(f1(c2), f2(c2))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[390, 47])).
% 0.60/0.77 tff(392,plain,
% 0.60/0.77 (~big_p(f2(c2))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[334, 304, 391, 320, 348, 356, 375])).
% 0.60/0.77 tff(393,plain,
% 0.60/0.77 ($false),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[370, 149, 11, 94, 392, 383])).
% 0.60/0.77 tff(394,plain,(big_r(c4, f3(c4)) | big_p(c2) | big_p(c4)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.77 tff(395,plain,
% 0.60/0.77 (big_r(c4, f3(c4))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[394, 4, 94])).
% 0.60/0.77 tff(396,plain,
% 0.60/0.77 (~big_p(f2(c4))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[382, 373, 352, 356])).
% 0.60/0.77 tff(397,plain,
% 0.60/0.77 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))) | ((~big_p(a)) | big_p(c4) | big_r(f3(c4), f4(c4)) | big_p(f2(c4)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))) | (~big_p(a)) | big_p(c4) | big_r(f3(c4), f4(c4)) | big_p(f2(c4)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(398,plain,
% 0.60/0.77 (((~big_p(a)) | big_p(c4) | big_p(f2(c4)) | big_p(c4) | big_r(f3(c4), f4(c4))) <=> ((~big_p(a)) | big_p(c4) | big_r(f3(c4), f4(c4)) | big_p(f2(c4)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(399,plain,
% 0.60/0.77 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))) | ((~big_p(a)) | big_p(c4) | big_p(f2(c4)) | big_p(c4) | big_r(f3(c4), f4(c4)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))) | ((~big_p(a)) | big_p(c4) | big_r(f3(c4), f4(c4)) | big_p(f2(c4))))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[398])).
% 0.60/0.77 tff(400,plain,
% 0.60/0.77 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))) | ((~big_p(a)) | big_p(c4) | big_p(f2(c4)) | big_p(c4) | big_r(f3(c4), f4(c4)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))) | (~big_p(a)) | big_p(c4) | big_r(f3(c4), f4(c4)) | big_p(f2(c4)))),
% 0.60/0.77 inference(transitivity,[status(thm)],[399, 397])).
% 0.60/0.77 tff(401,plain,
% 0.60/0.77 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))) | ((~big_p(a)) | big_p(c4) | big_p(f2(c4)) | big_p(c4) | big_r(f3(c4), f4(c4)))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(402,plain,
% 0.60/0.77 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | big_p(X7) | big_r(f3(X1), f4(X1)))) | (~big_p(a)) | big_p(c4) | big_r(f3(c4), f4(c4)) | big_p(f2(c4))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[401, 400])).
% 0.60/0.77 tff(403,plain,
% 0.60/0.77 (big_r(f3(c4), f4(c4)) | big_p(f2(c4))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[402, 239, 11, 4])).
% 0.60/0.77 tff(404,plain,
% 0.60/0.77 (big_r(f3(c4), f4(c4))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[403, 396])).
% 0.60/0.77 tff(405,plain,
% 0.60/0.77 ($false),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[310, 304, 338, 352, 404, 395, 373, 364])).
% 0.60/0.77 tff(406,plain,(big_p(f2(c2)) | big_p(c4) | big_p(c2)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.77 tff(407,plain,
% 0.60/0.77 (big_p(f2(c2))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[406, 4, 94])).
% 0.60/0.77 tff(408,plain,
% 0.60/0.77 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c2) | big_r(f1(c2), f2(c2)) | big_p(f4(c2)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c2) | big_r(f1(c2), f2(c2)) | big_p(f4(c2)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(409,plain,
% 0.60/0.77 (((~big_p(a)) | big_p(f4(c2)) | big_p(c2) | big_p(c2) | big_r(f1(c2), f2(c2))) <=> ((~big_p(a)) | big_p(c2) | big_r(f1(c2), f2(c2)) | big_p(f4(c2)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(410,plain,
% 0.60/0.77 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(f4(c2)) | big_p(c2) | big_p(c2) | big_r(f1(c2), f2(c2)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c2) | big_r(f1(c2), f2(c2)) | big_p(f4(c2))))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[409])).
% 0.60/0.77 tff(411,plain,
% 0.60/0.77 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(f4(c2)) | big_p(c2) | big_p(c2) | big_r(f1(c2), f2(c2)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c2) | big_r(f1(c2), f2(c2)) | big_p(f4(c2)))),
% 0.60/0.77 inference(transitivity,[status(thm)],[410, 408])).
% 0.60/0.77 tff(412,plain,
% 0.60/0.77 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(f4(c2)) | big_p(c2) | big_p(c2) | big_r(f1(c2), f2(c2)))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(413,plain,
% 0.60/0.77 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(X7) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c2) | big_r(f1(c2), f2(c2)) | big_p(f4(c2))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[412, 411])).
% 0.60/0.77 tff(414,plain,
% 0.60/0.77 (big_r(f1(c2), f2(c2)) | big_p(f4(c2))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[413, 189, 11, 94])).
% 0.60/0.77 tff(415,plain,
% 0.60/0.77 (big_r(f1(c2), f2(c2))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[414, 139])).
% 0.60/0.77 tff(416,plain,
% 0.60/0.77 ($false),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[334, 304, 415, 320, 407, 348, 356, 157])).
% 0.60/0.77 tff(417,plain,(big_p(f4(c2)) | big_p(c4) | big_p(c2)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.77 tff(418,plain,
% 0.60/0.77 (big_p(f4(c2))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[417, 4, 94])).
% 0.60/0.77 tff(419,plain,
% 0.60/0.77 (~big_p(f2(c4))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[382, 418, 352, 356])).
% 0.60/0.77 tff(420,plain,
% 0.60/0.77 (big_r(f3(c4), f4(c4))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[403, 419])).
% 0.60/0.77 tff(421,plain,
% 0.60/0.77 (~big_p(f4(c4))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[310, 304, 338, 352, 420, 395, 418])).
% 0.60/0.77 tff(422,plain,
% 0.60/0.77 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))) | ((~big_p(a)) | big_p(c4) | big_p(f4(c4)) | big_p(f2(c4)))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))) | (~big_p(a)) | big_p(c4) | big_p(f4(c4)) | big_p(f2(c4)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(423,plain,
% 0.60/0.77 (((~big_p(a)) | big_p(f4(c4)) | big_p(c4) | big_p(f2(c4)) | big_p(c4)) <=> ((~big_p(a)) | big_p(c4) | big_p(f4(c4)) | big_p(f2(c4)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(424,plain,
% 0.60/0.77 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))) | ((~big_p(a)) | big_p(f4(c4)) | big_p(c4) | big_p(f2(c4)) | big_p(c4))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))) | ((~big_p(a)) | big_p(c4) | big_p(f4(c4)) | big_p(f2(c4))))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[423])).
% 0.60/0.77 tff(425,plain,
% 0.60/0.77 (((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))) | ((~big_p(a)) | big_p(f4(c4)) | big_p(c4) | big_p(f2(c4)) | big_p(c4))) <=> ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))) | (~big_p(a)) | big_p(c4) | big_p(f4(c4)) | big_p(f2(c4)))),
% 0.60/0.77 inference(transitivity,[status(thm)],[424, 422])).
% 0.60/0.77 tff(426,plain,
% 0.60/0.77 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))) | ((~big_p(a)) | big_p(f4(c4)) | big_p(c4) | big_p(f2(c4)) | big_p(c4))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(427,plain,
% 0.60/0.77 ((~![X7: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | big_p(X7))) | (~big_p(a)) | big_p(c4) | big_p(f4(c4)) | big_p(f2(c4))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[426, 425])).
% 0.60/0.77 tff(428,plain,
% 0.60/0.77 ($false),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[427, 149, 11, 4, 419, 421])).
% 0.60/0.77 tff(429,plain,(big_p(c4) | big_p(c2)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.77 tff(430,plain,
% 0.60/0.77 (big_p(c4)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[429, 94])).
% 0.60/0.77 tff(431,plain,
% 0.60/0.77 (((~![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | ((~big_p(c4)) | big_r(c4, c3) | (~big_p(f2(c2))) | (~big_r(f1(c2), f2(c2))) | (~big_r(c2, f1(c2))))) <=> ((~![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | (~big_p(c4)) | big_r(c4, c3) | (~big_p(f2(c2))) | (~big_r(f1(c2), f2(c2))) | (~big_r(c2, f1(c2))))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(432,plain,
% 0.60/0.77 (((~big_p(f2(c2))) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(f1(c2), f2(c2))) | (~big_r(c2, f1(c2)))) <=> ((~big_p(c4)) | big_r(c4, c3) | (~big_p(f2(c2))) | (~big_r(f1(c2), f2(c2))) | (~big_r(c2, f1(c2))))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(433,plain,
% 0.60/0.77 (((~![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | ((~big_p(f2(c2))) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(f1(c2), f2(c2))) | (~big_r(c2, f1(c2))))) <=> ((~![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | ((~big_p(c4)) | big_r(c4, c3) | (~big_p(f2(c2))) | (~big_r(f1(c2), f2(c2))) | (~big_r(c2, f1(c2)))))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[432])).
% 0.60/0.77 tff(434,plain,
% 0.60/0.77 (((~![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | ((~big_p(f2(c2))) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(f1(c2), f2(c2))) | (~big_r(c2, f1(c2))))) <=> ((~![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | (~big_p(c4)) | big_r(c4, c3) | (~big_p(f2(c2))) | (~big_r(f1(c2), f2(c2))) | (~big_r(c2, f1(c2))))),
% 0.60/0.77 inference(transitivity,[status(thm)],[433, 431])).
% 0.60/0.77 tff(435,plain,
% 0.60/0.77 ((~![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | ((~big_p(f2(c2))) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(f1(c2), f2(c2))) | (~big_r(c2, f1(c2))))),
% 0.60/0.77 inference(quant_inst,[status(thm)],[])).
% 0.60/0.77 tff(436,plain,
% 0.60/0.77 ((~![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | (~big_p(c4)) | big_r(c4, c3) | (~big_p(f2(c2))) | (~big_r(f1(c2), f2(c2))) | (~big_r(c2, f1(c2)))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[435, 434])).
% 0.60/0.77 tff(437,plain,
% 0.60/0.77 (big_r(c4, c3) | (~big_p(f2(c2)))),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[436, 430, 138, 128, 110])).
% 0.60/0.77 tff(438,plain,
% 0.60/0.77 (big_r(c4, c3)),
% 0.60/0.77 inference(unit_resolution,[status(thm)],[437, 102])).
% 0.60/0.77 tff(439,plain,
% 0.60/0.77 (^[X9: $i, X10: $i] : refl((big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10))) <=> (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10))))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(440,plain,
% 0.60/0.77 (![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10))) <=> ![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[439])).
% 0.60/0.77 tff(441,plain,
% 0.60/0.77 (![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10))) <=> ![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(442,plain,
% 0.60/0.77 (^[X9: $i, X10: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) <=> ((~big_p(X9)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))), (((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) | (~big_p(c4))) <=> (((~big_p(X9)) | (~big_r(X10, X9)) | (~big_r(c2, X10))) | (~big_p(c4))))), rewrite((((~big_p(X9)) | (~big_r(X10, X9)) | (~big_r(c2, X10))) | (~big_p(c4))) <=> ((~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))), (((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) | (~big_p(c4))) <=> ((~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10))))), ((((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) | (~big_p(c4))) | big_p(c3)) <=> (((~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10))) | big_p(c3)))), rewrite((((~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10))) | big_p(c3)) <=> (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))), ((((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) | (~big_p(c4))) | big_p(c3)) <=> (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(443,plain,
% 0.60/0.77 (![X9: $i, X10: $i] : (((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) | (~big_p(c4))) | big_p(c3)) <=> ![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[442])).
% 0.60/0.77 tff(444,axiom,(![X9: $i, X10: $i] : (((((~big_p(X9)) | (~big_r(c2, X10))) | (~big_r(X10, X9))) | (~big_p(c4))) | big_p(c3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_78')).
% 0.60/0.77 tff(445,plain,
% 0.60/0.77 (![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[444, 443])).
% 0.60/0.77 tff(446,plain,
% 0.60/0.77 (![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[445, 441])).
% 0.60/0.77 tff(447,plain,(
% 0.60/0.77 ![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))),
% 0.60/0.77 inference(skolemize,[status(sab)],[446])).
% 0.60/0.77 tff(448,plain,
% 0.60/0.77 (![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))),
% 0.60/0.77 inference(modus_ponens,[status(thm)],[447, 440])).
% 0.60/0.77 tff(449,plain,
% 0.60/0.77 (((~![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | (big_p(c3) | (~big_p(c4)) | (~big_p(f2(c2))) | (~big_r(f1(c2), f2(c2))) | (~big_r(c2, f1(c2))))) <=> ((~![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | big_p(c3) | (~big_p(c4)) | (~big_p(f2(c2))) | (~big_r(f1(c2), f2(c2))) | (~big_r(c2, f1(c2))))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(450,plain,
% 0.60/0.77 ((big_p(c3) | (~big_p(f2(c2))) | (~big_p(c4)) | (~big_r(f1(c2), f2(c2))) | (~big_r(c2, f1(c2)))) <=> (big_p(c3) | (~big_p(c4)) | (~big_p(f2(c2))) | (~big_r(f1(c2), f2(c2))) | (~big_r(c2, f1(c2))))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(451,plain,
% 0.60/0.77 (((~![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | (big_p(c3) | (~big_p(f2(c2))) | (~big_p(c4)) | (~big_r(f1(c2), f2(c2))) | (~big_r(c2, f1(c2))))) <=> ((~![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | (big_p(c3) | (~big_p(c4)) | (~big_p(f2(c2))) | (~big_r(f1(c2), f2(c2))) | (~big_r(c2, f1(c2)))))),
% 0.60/0.77 inference(monotonicity,[status(thm)],[450])).
% 0.60/0.77 tff(452,plain,
% 0.60/0.77 (((~![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | (big_p(c3) | (~big_p(f2(c2))) | (~big_p(c4)) | (~big_r(f1(c2), f2(c2))) | (~big_r(c2, f1(c2))))) <=> ((~![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | big_p(c3) | (~big_p(c4)) | (~big_p(f2(c2))) | (~big_r(f1(c2), f2(c2))) | (~big_r(c2, f1(c2))))),
% 0.60/0.77 inference(transitivity,[status(thm)],[451, 449])).
% 0.60/0.77 tff(453,plain,
% 0.60/0.77 ((~![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | (big_p(c3) | (~big_p(f2(c2))) | (~big_p(c4)) | (~big_r(f1(c2), f2(c2))) | (~big_r(c2, f1(c2))))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(454,plain,
% 0.60/0.78 ((~![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | big_p(c3) | (~big_p(c4)) | (~big_p(f2(c2))) | (~big_r(f1(c2), f2(c2))) | (~big_r(c2, f1(c2)))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[453, 452])).
% 0.60/0.78 tff(455,plain,
% 0.60/0.78 (big_p(c3) | (~big_p(f2(c2)))),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[454, 430, 448, 128, 110])).
% 0.60/0.78 tff(456,plain,
% 0.60/0.78 (big_p(c3)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[455, 102])).
% 0.60/0.78 tff(457,plain,
% 0.60/0.78 (^[X7: $i, X8: $i, X1: $i] : refl(((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) <=> ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))))),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.78 tff(458,plain,
% 0.60/0.78 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) <=> ![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))),
% 0.60/0.78 inference(quant_intro,[status(thm)],[457])).
% 0.60/0.78 tff(459,plain,
% 0.60/0.78 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) <=> ![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(460,plain,
% 0.60/0.78 (^[X7: $i, X8: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_p(f2(X7))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_p(f2(X7))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) <=> (((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | (~big_p(a))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) <=> (((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_p(X1)))), rewrite((((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(X1, f3(X1))) <=> (((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_r(X1, f3(X1))))), rewrite((((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_r(X1, f3(X1))) <=> ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(X1, f3(X1))) <=> ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))))),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.78 tff(461,plain,
% 0.60/0.78 (![X7: $i, X8: $i, X1: $i] : (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(X1, f3(X1))) <=> ![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))),
% 0.60/0.78 inference(quant_intro,[status(thm)],[460])).
% 0.60/0.78 tff(462,axiom,(![X7: $i, X8: $i, X1: $i] : (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(X1, f3(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_20')).
% 0.60/0.78 tff(463,plain,
% 0.60/0.78 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[462, 461])).
% 0.60/0.78 tff(464,plain,
% 0.60/0.78 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[463, 459])).
% 0.60/0.78 tff(465,plain,(
% 0.60/0.78 ![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))),
% 0.60/0.78 inference(skolemize,[status(sab)],[464])).
% 0.60/0.78 tff(466,plain,
% 0.60/0.78 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[465, 458])).
% 0.60/0.78 tff(467,plain,
% 0.60/0.78 (((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | ((~big_p(a)) | big_p(c2) | big_r(c2, f3(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f2(c4)))) <=> ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | (~big_p(a)) | big_p(c2) | big_r(c2, f3(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f2(c4)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(468,plain,
% 0.60/0.78 (((~big_p(a)) | big_p(c2) | big_r(c2, f3(c2)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3))) <=> ((~big_p(a)) | big_p(c2) | big_r(c2, f3(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f2(c4)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(469,plain,
% 0.60/0.78 (((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | ((~big_p(a)) | big_p(c2) | big_r(c2, f3(c2)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)))) <=> ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | ((~big_p(a)) | big_p(c2) | big_r(c2, f3(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f2(c4))))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[468])).
% 0.60/0.78 tff(470,plain,
% 0.60/0.78 (((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | ((~big_p(a)) | big_p(c2) | big_r(c2, f3(c2)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)))) <=> ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | (~big_p(a)) | big_p(c2) | big_r(c2, f3(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f2(c4)))),
% 0.60/0.78 inference(transitivity,[status(thm)],[469, 467])).
% 0.60/0.78 tff(471,plain,
% 0.60/0.78 ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | ((~big_p(a)) | big_p(c2) | big_r(c2, f3(c2)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(472,plain,
% 0.60/0.78 ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | (~big_p(a)) | big_p(c2) | big_r(c2, f3(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f2(c4))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[471, 470])).
% 0.60/0.78 tff(473,plain,
% 0.60/0.78 (big_p(f2(c4))),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[472, 466, 11, 456, 438, 94, 95])).
% 0.60/0.78 tff(474,plain,
% 0.60/0.78 (^[X7: $i, X8: $i, X1: $i] : refl(((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) <=> ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))))),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.78 tff(475,plain,
% 0.60/0.78 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) <=> ![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))),
% 0.60/0.78 inference(quant_intro,[status(thm)],[474])).
% 0.60/0.78 tff(476,plain,
% 0.60/0.78 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) <=> ![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(477,plain,
% 0.60/0.78 (^[X7: $i, X8: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_r(X7, f1(X7))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_r(X7, f1(X7))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | (~big_p(a))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | big_p(X1)))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) | big_r(X1, f3(X1))) <=> (((~big_p(a)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | big_r(X1, f3(X1))))), rewrite((((~big_p(a)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | big_r(X1, f3(X1))) <=> ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) | big_r(X1, f3(X1))) <=> ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))))),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.78 tff(478,plain,
% 0.60/0.78 (![X7: $i, X8: $i, X1: $i] : (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) | big_r(X1, f3(X1))) <=> ![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))),
% 0.60/0.78 inference(quant_intro,[status(thm)],[477])).
% 0.60/0.78 tff(479,axiom,(![X7: $i, X8: $i, X1: $i] : (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) | big_r(X1, f3(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_26')).
% 0.60/0.78 tff(480,plain,
% 0.60/0.78 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[479, 478])).
% 0.60/0.78 tff(481,plain,
% 0.60/0.78 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[480, 476])).
% 0.60/0.78 tff(482,plain,(
% 0.60/0.78 ![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))),
% 0.60/0.78 inference(skolemize,[status(sab)],[481])).
% 0.60/0.78 tff(483,plain,
% 0.60/0.78 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[482, 475])).
% 0.60/0.78 tff(484,plain,
% 0.60/0.78 (((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c2) | big_r(c2, f3(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)))) <=> ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | (~big_p(a)) | big_p(c2) | big_r(c2, f3(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(485,plain,
% 0.60/0.78 (((~big_p(a)) | big_p(c2) | big_r(c2, f3(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4))) <=> ((~big_p(a)) | big_p(c2) | big_r(c2, f3(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(486,plain,
% 0.60/0.78 (((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c2) | big_r(c2, f3(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)))) <=> ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c2) | big_r(c2, f3(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4))))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[485])).
% 0.60/0.78 tff(487,plain,
% 0.60/0.78 (((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c2) | big_r(c2, f3(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)))) <=> ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | (~big_p(a)) | big_p(c2) | big_r(c2, f3(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)))),
% 0.60/0.78 inference(transitivity,[status(thm)],[486, 484])).
% 0.60/0.78 tff(488,plain,
% 0.60/0.78 ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c2) | big_r(c2, f3(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(489,plain,
% 0.60/0.78 ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | (~big_p(a)) | big_p(c2) | big_r(c2, f3(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[488, 487])).
% 0.60/0.78 tff(490,plain,
% 0.60/0.78 (big_r(c4, f1(c4))),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[489, 483, 11, 456, 438, 94, 95])).
% 0.60/0.78 tff(491,plain,
% 0.60/0.78 (^[X7: $i, X8: $i, X1: $i] : refl(((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))))),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.78 tff(492,plain,
% 0.60/0.78 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) <=> ![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))),
% 0.60/0.78 inference(quant_intro,[status(thm)],[491])).
% 0.60/0.78 tff(493,plain,
% 0.60/0.78 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) <=> ![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(494,plain,
% 0.60/0.78 (^[X7: $i, X8: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_r(f1(X7), f2(X7))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | (~big_p(a))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | big_p(X1)))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(X1, f3(X1))) <=> (((~big_p(a)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | big_r(X1, f3(X1))))), rewrite((((~big_p(a)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | big_r(X1, f3(X1))) <=> ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(X1, f3(X1))) <=> ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))))),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.78 tff(495,plain,
% 0.60/0.78 (![X7: $i, X8: $i, X1: $i] : (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(X1, f3(X1))) <=> ![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))),
% 0.60/0.78 inference(quant_intro,[status(thm)],[494])).
% 0.60/0.78 tff(496,axiom,(![X7: $i, X8: $i, X1: $i] : (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(X1, f3(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_32')).
% 0.60/0.78 tff(497,plain,
% 0.60/0.78 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[496, 495])).
% 0.60/0.78 tff(498,plain,
% 0.60/0.78 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[497, 493])).
% 0.60/0.78 tff(499,plain,(
% 0.60/0.78 ![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))),
% 0.60/0.78 inference(skolemize,[status(sab)],[498])).
% 0.60/0.78 tff(500,plain,
% 0.60/0.78 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[499, 492])).
% 0.60/0.78 tff(501,plain,
% 0.60/0.78 (((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c2) | big_r(c2, f3(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)))) <=> ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c2) | big_r(c2, f3(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(502,plain,
% 0.60/0.78 (((~big_p(a)) | big_p(c2) | big_r(c2, f3(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f1(c4), f2(c4))) <=> ((~big_p(a)) | big_p(c2) | big_r(c2, f3(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(503,plain,
% 0.60/0.78 (((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c2) | big_r(c2, f3(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f1(c4), f2(c4)))) <=> ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c2) | big_r(c2, f3(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4))))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[502])).
% 0.60/0.78 tff(504,plain,
% 0.60/0.78 (((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c2) | big_r(c2, f3(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f1(c4), f2(c4)))) <=> ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c2) | big_r(c2, f3(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)))),
% 0.60/0.78 inference(transitivity,[status(thm)],[503, 501])).
% 0.60/0.78 tff(505,plain,
% 0.60/0.78 ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c2) | big_r(c2, f3(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f1(c4), f2(c4)))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(506,plain,
% 0.60/0.78 ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c2) | big_r(c2, f3(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[505, 504])).
% 0.60/0.78 tff(507,plain,
% 0.60/0.78 (big_r(f1(c4), f2(c4))),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[506, 500, 11, 456, 438, 94, 95])).
% 0.60/0.78 tff(508,plain,
% 0.60/0.78 ($false),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[334, 304, 128, 110, 507, 490, 102, 473])).
% 0.60/0.78 tff(509,plain,(big_r(c2, f3(c2)) | big_p(c2)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.78 tff(510,plain,
% 0.60/0.78 (big_r(c2, f3(c2))),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[509, 94])).
% 0.60/0.78 tff(511,assumption,(~big_r(c4, c3)), introduced(assumption)).
% 0.60/0.78 tff(512,plain,
% 0.60/0.78 (big_r(c2, f1(c2))),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[293, 229])).
% 0.60/0.78 tff(513,plain,
% 0.60/0.78 (big_r(c4, c3) | (~big_p(f2(c2)))),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[436, 430, 138, 328, 512])).
% 0.60/0.78 tff(514,plain,
% 0.60/0.78 (big_r(c4, c3)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[513, 246])).
% 0.60/0.78 tff(515,plain,
% 0.60/0.78 (big_p(c3) | (~big_p(f2(c2)))),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[454, 430, 448, 328, 512])).
% 0.60/0.78 tff(516,plain,
% 0.60/0.78 (big_p(c3)),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[515, 246])).
% 0.60/0.78 tff(517,plain,
% 0.60/0.78 (^[X7: $i, X8: $i, X1: $i] : refl(((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) <=> ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))))),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.78 tff(518,plain,
% 0.60/0.78 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) <=> ![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))),
% 0.60/0.78 inference(quant_intro,[status(thm)],[517])).
% 0.60/0.79 tff(519,plain,
% 0.60/0.79 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) <=> ![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(520,plain,
% 0.60/0.79 (^[X7: $i, X8: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_p(f2(X7))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_p(f2(X7))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) <=> (((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | (~big_p(a))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) <=> (((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_p(X1)))), rewrite((((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(f3(X1), f4(X1))) <=> (((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_r(f3(X1), f4(X1))))), rewrite((((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_r(f3(X1), f4(X1))) <=> ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(f3(X1), f4(X1))) <=> ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))))),
% 0.60/0.79 inference(bind,[status(th)],[])).
% 0.60/0.79 tff(521,plain,
% 0.60/0.79 (![X7: $i, X8: $i, X1: $i] : (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(f3(X1), f4(X1))) <=> ![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))),
% 0.60/0.79 inference(quant_intro,[status(thm)],[520])).
% 0.60/0.79 tff(522,axiom,(![X7: $i, X8: $i, X1: $i] : (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(f3(X1), f4(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_21')).
% 0.60/0.79 tff(523,plain,
% 0.60/0.79 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[522, 521])).
% 0.60/0.79 tff(524,plain,
% 0.60/0.79 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[523, 519])).
% 0.60/0.79 tff(525,plain,(
% 0.60/0.79 ![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))),
% 0.60/0.79 inference(skolemize,[status(sab)],[524])).
% 0.60/0.79 tff(526,plain,
% 0.60/0.79 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[525, 518])).
% 0.60/0.79 tff(527,plain,
% 0.60/0.79 (((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | ((~big_p(a)) | big_p(c2) | big_r(f3(c2), f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f2(c4)))) <=> ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | (~big_p(a)) | big_p(c2) | big_r(f3(c2), f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f2(c4)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(528,plain,
% 0.60/0.79 (((~big_p(a)) | big_p(c2) | big_r(f3(c2), f4(c2)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3))) <=> ((~big_p(a)) | big_p(c2) | big_r(f3(c2), f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f2(c4)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(529,plain,
% 0.60/0.79 (((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | ((~big_p(a)) | big_p(c2) | big_r(f3(c2), f4(c2)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)))) <=> ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | ((~big_p(a)) | big_p(c2) | big_r(f3(c2), f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f2(c4))))),
% 0.60/0.79 inference(monotonicity,[status(thm)],[528])).
% 0.60/0.79 tff(530,plain,
% 0.60/0.79 (((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | ((~big_p(a)) | big_p(c2) | big_r(f3(c2), f4(c2)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)))) <=> ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | (~big_p(a)) | big_p(c2) | big_r(f3(c2), f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f2(c4)))),
% 0.60/0.79 inference(transitivity,[status(thm)],[529, 527])).
% 0.60/0.79 tff(531,plain,
% 0.60/0.79 ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | ((~big_p(a)) | big_p(c2) | big_r(f3(c2), f4(c2)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)))),
% 0.60/0.79 inference(quant_inst,[status(thm)],[])).
% 0.60/0.79 tff(532,plain,
% 0.60/0.79 ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | (~big_p(a)) | big_p(c2) | big_r(f3(c2), f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f2(c4))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[531, 530])).
% 0.60/0.79 tff(533,plain,
% 0.60/0.79 (big_p(f2(c4))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[532, 526, 11, 516, 514, 94, 229])).
% 0.60/0.79 tff(534,plain,
% 0.60/0.79 (^[X7: $i, X8: $i, X1: $i] : refl(((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) <=> ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))))),
% 0.60/0.79 inference(bind,[status(th)],[])).
% 0.60/0.79 tff(535,plain,
% 0.60/0.79 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) <=> ![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))),
% 0.60/0.79 inference(quant_intro,[status(thm)],[534])).
% 0.60/0.79 tff(536,plain,
% 0.60/0.79 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) <=> ![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(537,plain,
% 0.60/0.79 (^[X7: $i, X8: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_r(X7, f1(X7))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_r(X7, f1(X7))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | (~big_p(a))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | big_p(X1)))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) | big_r(f3(X1), f4(X1))) <=> (((~big_p(a)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | big_r(f3(X1), f4(X1))))), rewrite((((~big_p(a)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | big_r(f3(X1), f4(X1))) <=> ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) | big_r(f3(X1), f4(X1))) <=> ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))))),
% 0.60/0.79 inference(bind,[status(th)],[])).
% 0.60/0.79 tff(538,plain,
% 0.60/0.79 (![X7: $i, X8: $i, X1: $i] : (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) | big_r(f3(X1), f4(X1))) <=> ![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))),
% 0.60/0.79 inference(quant_intro,[status(thm)],[537])).
% 0.60/0.79 tff(539,axiom,(![X7: $i, X8: $i, X1: $i] : (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) | big_r(f3(X1), f4(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_27')).
% 0.60/0.79 tff(540,plain,
% 0.60/0.79 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[539, 538])).
% 0.60/0.79 tff(541,plain,
% 0.60/0.79 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[540, 536])).
% 0.60/0.79 tff(542,plain,(
% 0.60/0.79 ![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))),
% 0.60/0.79 inference(skolemize,[status(sab)],[541])).
% 0.60/0.79 tff(543,plain,
% 0.60/0.79 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[542, 535])).
% 0.60/0.79 tff(544,plain,
% 0.60/0.79 (((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c2) | big_r(f3(c2), f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)))) <=> ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | (~big_p(a)) | big_p(c2) | big_r(f3(c2), f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(545,plain,
% 0.60/0.79 (((~big_p(a)) | big_p(c2) | big_r(f3(c2), f4(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4))) <=> ((~big_p(a)) | big_p(c2) | big_r(f3(c2), f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(546,plain,
% 0.60/0.79 (((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c2) | big_r(f3(c2), f4(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)))) <=> ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c2) | big_r(f3(c2), f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4))))),
% 0.60/0.79 inference(monotonicity,[status(thm)],[545])).
% 0.60/0.79 tff(547,plain,
% 0.60/0.79 (((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c2) | big_r(f3(c2), f4(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)))) <=> ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | (~big_p(a)) | big_p(c2) | big_r(f3(c2), f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)))),
% 0.60/0.79 inference(transitivity,[status(thm)],[546, 544])).
% 0.60/0.79 tff(548,plain,
% 0.60/0.79 ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c2) | big_r(f3(c2), f4(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)))),
% 0.60/0.79 inference(quant_inst,[status(thm)],[])).
% 0.60/0.79 tff(549,plain,
% 0.60/0.79 ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | (~big_p(a)) | big_p(c2) | big_r(f3(c2), f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[548, 547])).
% 0.60/0.79 tff(550,plain,
% 0.60/0.79 (big_r(c4, f1(c4))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[549, 543, 11, 516, 514, 94, 229])).
% 0.60/0.79 tff(551,plain,
% 0.60/0.79 (^[X7: $i, X8: $i, X1: $i] : refl(((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))))),
% 0.60/0.79 inference(bind,[status(th)],[])).
% 0.60/0.79 tff(552,plain,
% 0.60/0.79 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) <=> ![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))),
% 0.60/0.79 inference(quant_intro,[status(thm)],[551])).
% 0.60/0.79 tff(553,plain,
% 0.60/0.79 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) <=> ![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(554,plain,
% 0.60/0.79 (^[X7: $i, X8: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_r(f1(X7), f2(X7))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | (~big_p(a))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | big_p(X1)))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(f3(X1), f4(X1))) <=> (((~big_p(a)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | big_r(f3(X1), f4(X1))))), rewrite((((~big_p(a)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | big_r(f3(X1), f4(X1))) <=> ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(f3(X1), f4(X1))) <=> ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))))),
% 0.60/0.79 inference(bind,[status(th)],[])).
% 0.60/0.79 tff(555,plain,
% 0.60/0.79 (![X7: $i, X8: $i, X1: $i] : (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(f3(X1), f4(X1))) <=> ![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))),
% 0.60/0.79 inference(quant_intro,[status(thm)],[554])).
% 0.60/0.79 tff(556,axiom,(![X7: $i, X8: $i, X1: $i] : (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) | big_r(f3(X1), f4(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_33')).
% 0.60/0.79 tff(557,plain,
% 0.60/0.79 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[556, 555])).
% 0.60/0.79 tff(558,plain,
% 0.60/0.79 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[557, 553])).
% 0.60/0.79 tff(559,plain,(
% 0.60/0.79 ![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))),
% 0.60/0.79 inference(skolemize,[status(sab)],[558])).
% 0.60/0.79 tff(560,plain,
% 0.60/0.79 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[559, 552])).
% 0.60/0.79 tff(561,plain,
% 0.60/0.79 (((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c2) | big_r(f3(c2), f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)))) <=> ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c2) | big_r(f3(c2), f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(562,plain,
% 0.60/0.79 (((~big_p(a)) | big_p(c2) | big_r(f3(c2), f4(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f1(c4), f2(c4))) <=> ((~big_p(a)) | big_p(c2) | big_r(f3(c2), f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(563,plain,
% 0.60/0.79 (((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c2) | big_r(f3(c2), f4(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f1(c4), f2(c4)))) <=> ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c2) | big_r(f3(c2), f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4))))),
% 0.60/0.79 inference(monotonicity,[status(thm)],[562])).
% 0.60/0.79 tff(564,plain,
% 0.60/0.79 (((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c2) | big_r(f3(c2), f4(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f1(c4), f2(c4)))) <=> ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c2) | big_r(f3(c2), f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)))),
% 0.60/0.79 inference(transitivity,[status(thm)],[563, 561])).
% 0.60/0.79 tff(565,plain,
% 0.60/0.79 ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c2) | big_r(f3(c2), f4(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f1(c4), f2(c4)))),
% 0.60/0.79 inference(quant_inst,[status(thm)],[])).
% 0.60/0.79 tff(566,plain,
% 0.60/0.79 ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c2) | big_r(f3(c2), f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[565, 564])).
% 0.60/0.79 tff(567,plain,
% 0.60/0.79 (big_r(f1(c4), f2(c4))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[566, 560, 11, 516, 514, 94, 229])).
% 0.60/0.79 tff(568,plain,
% 0.60/0.79 ($false),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[334, 304, 328, 512, 567, 550, 246, 533])).
% 0.60/0.79 tff(569,plain,(big_r(f3(c2), f4(c2)) | big_p(c2)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.79 tff(570,plain,
% 0.60/0.79 (big_r(f3(c2), f4(c2))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[569, 94])).
% 0.60/0.79 tff(571,plain,
% 0.60/0.79 (((~![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | ((~big_p(c4)) | big_r(c4, c3) | (~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2))))) <=> ((~![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | (~big_p(c4)) | big_r(c4, c3) | (~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2))))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(572,plain,
% 0.60/0.79 (((~big_p(f4(c2))) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(f3(c2), f4(c2))) | (~big_r(c2, f3(c2)))) <=> ((~big_p(c4)) | big_r(c4, c3) | (~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2))))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(573,plain,
% 0.60/0.79 (((~![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | ((~big_p(f4(c2))) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(f3(c2), f4(c2))) | (~big_r(c2, f3(c2))))) <=> ((~![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | ((~big_p(c4)) | big_r(c4, c3) | (~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2)))))),
% 0.60/0.79 inference(monotonicity,[status(thm)],[572])).
% 0.60/0.79 tff(574,plain,
% 0.60/0.79 (((~![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | ((~big_p(f4(c2))) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(f3(c2), f4(c2))) | (~big_r(c2, f3(c2))))) <=> ((~![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | (~big_p(c4)) | big_r(c4, c3) | (~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2))))),
% 0.60/0.79 inference(transitivity,[status(thm)],[573, 571])).
% 0.60/0.79 tff(575,plain,
% 0.60/0.79 ((~![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | ((~big_p(f4(c2))) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(f3(c2), f4(c2))) | (~big_r(c2, f3(c2))))),
% 0.60/0.79 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(576,plain,
% 0.60/0.80 ((~![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | (~big_p(c4)) | big_r(c4, c3) | (~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2)))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[575, 574])).
% 0.60/0.80 tff(577,plain,
% 0.60/0.80 (big_r(c4, c3) | (~big_p(f4(c2))) | (~big_r(c2, f3(c2)))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[576, 430, 138, 570])).
% 0.60/0.80 tff(578,plain,
% 0.60/0.80 (~big_p(f4(c2))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[577, 511, 510])).
% 0.60/0.80 tff(579,plain,
% 0.60/0.80 (big_r(c2, f1(c2)) | big_p(f4(c2))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[284, 21, 11, 94])).
% 0.60/0.80 tff(580,plain,
% 0.60/0.80 (big_p(f4(c2))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[579, 264])).
% 0.60/0.80 tff(581,plain,
% 0.60/0.80 (big_r(c4, c3)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[577, 580, 510])).
% 0.60/0.80 tff(582,plain,
% 0.60/0.80 (((~![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | (big_p(c3) | (~big_p(c4)) | (~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2))))) <=> ((~![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | big_p(c3) | (~big_p(c4)) | (~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2))))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(583,plain,
% 0.60/0.80 ((big_p(c3) | (~big_p(f4(c2))) | (~big_p(c4)) | (~big_r(f3(c2), f4(c2))) | (~big_r(c2, f3(c2)))) <=> (big_p(c3) | (~big_p(c4)) | (~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2))))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(584,plain,
% 0.60/0.80 (((~![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | (big_p(c3) | (~big_p(f4(c2))) | (~big_p(c4)) | (~big_r(f3(c2), f4(c2))) | (~big_r(c2, f3(c2))))) <=> ((~![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | (big_p(c3) | (~big_p(c4)) | (~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2)))))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[583])).
% 0.60/0.80 tff(585,plain,
% 0.60/0.80 (((~![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | (big_p(c3) | (~big_p(f4(c2))) | (~big_p(c4)) | (~big_r(f3(c2), f4(c2))) | (~big_r(c2, f3(c2))))) <=> ((~![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | big_p(c3) | (~big_p(c4)) | (~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2))))),
% 0.60/0.80 inference(transitivity,[status(thm)],[584, 582])).
% 0.60/0.80 tff(586,plain,
% 0.60/0.80 ((~![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | (big_p(c3) | (~big_p(f4(c2))) | (~big_p(c4)) | (~big_r(f3(c2), f4(c2))) | (~big_r(c2, f3(c2))))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(587,plain,
% 0.60/0.80 ((~![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | big_p(c3) | (~big_p(c4)) | (~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2)))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[586, 585])).
% 0.60/0.80 tff(588,plain,
% 0.60/0.80 (big_p(c3) | (~big_p(f4(c2))) | (~big_r(c2, f3(c2)))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[587, 430, 448, 570])).
% 0.60/0.80 tff(589,plain,
% 0.60/0.80 (big_p(c3)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[588, 580, 510])).
% 0.60/0.80 tff(590,plain,
% 0.60/0.80 (^[X2: $i, X7: $i, X1: $i] : refl(((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2))))),
% 0.60/0.80 inference(bind,[status(th)],[])).
% 0.60/0.80 tff(591,plain,
% 0.60/0.80 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> ![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.60/0.80 inference(quant_intro,[status(thm)],[590])).
% 0.60/0.80 tff(592,plain,
% 0.60/0.80 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> ![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(593,plain,
% 0.60/0.80 (^[X2: $i, X7: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~big_p(a)) | big_p(X7)) <=> ((~big_p(a)) | big_p(X7))), ((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) <=> (((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))))), rewrite((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)))), ((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))))), (((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) <=> (((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))) | (~big_p(a))))), rewrite((((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)))), (((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))))), ((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) <=> (((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))) | (~big_p(X2))))), rewrite((((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))) | (~big_p(X2))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_p(X2)))), ((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_p(X2))))), (((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> (((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_p(X2))) | (~big_r(X1, X2))))), rewrite((((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))), (((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))))), ((((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_p(f6(X1))) <=> (((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))) | big_p(f6(X1))))), rewrite((((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))) | big_p(f6(X1))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))), ((((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_p(f6(X1))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))))),
% 0.60/0.80 inference(bind,[status(th)],[])).
% 0.60/0.80 tff(594,plain,
% 0.60/0.80 (![X2: $i, X7: $i, X1: $i] : (((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_p(f6(X1))) <=> ![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.60/0.80 inference(quant_intro,[status(thm)],[593])).
% 0.60/0.80 tff(595,axiom,(![X2: $i, X7: $i, X1: $i] : (((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_p(f6(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_10')).
% 0.60/0.80 tff(596,plain,
% 0.60/0.80 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[595, 594])).
% 0.60/0.80 tff(597,plain,
% 0.60/0.80 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[596, 592])).
% 0.60/0.80 tff(598,plain,(
% 0.60/0.80 ![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.60/0.80 inference(skolemize,[status(sab)],[597])).
% 0.60/0.80 tff(599,plain,
% 0.60/0.80 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[598, 591])).
% 0.60/0.80 tff(600,plain,
% 0.60/0.80 (((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_p(c2) | big_r(c2, f1(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f6(c4)))) <=> ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | big_p(c2) | big_r(c2, f1(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f6(c4)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(601,plain,
% 0.60/0.80 (((~big_p(a)) | big_p(c2) | big_r(c2, f1(c2)) | big_p(f6(c4)) | (~big_r(c4, c3)) | (~big_p(c3))) <=> ((~big_p(a)) | big_p(c2) | big_r(c2, f1(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f6(c4)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(602,plain,
% 0.60/0.80 (((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_p(c2) | big_r(c2, f1(c2)) | big_p(f6(c4)) | (~big_r(c4, c3)) | (~big_p(c3)))) <=> ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_p(c2) | big_r(c2, f1(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f6(c4))))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[601])).
% 0.60/0.80 tff(603,plain,
% 0.60/0.80 (((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_p(c2) | big_r(c2, f1(c2)) | big_p(f6(c4)) | (~big_r(c4, c3)) | (~big_p(c3)))) <=> ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | big_p(c2) | big_r(c2, f1(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f6(c4)))),
% 0.60/0.80 inference(transitivity,[status(thm)],[602, 600])).
% 0.60/0.80 tff(604,plain,
% 0.60/0.80 ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_p(c2) | big_r(c2, f1(c2)) | big_p(f6(c4)) | (~big_r(c4, c3)) | (~big_p(c3)))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(605,plain,
% 0.60/0.80 ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | big_p(c2) | big_r(c2, f1(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f6(c4))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[604, 603])).
% 0.60/0.80 tff(606,plain,
% 0.60/0.80 (big_p(f6(c4))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[605, 599, 11, 589, 581, 94, 264])).
% 0.60/0.80 tff(607,plain,
% 0.60/0.80 (^[X2: $i, X7: $i, X1: $i] : refl(((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1))))),
% 0.60/0.80 inference(bind,[status(th)],[])).
% 0.60/0.80 tff(608,plain,
% 0.60/0.80 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1))) <=> ![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))),
% 0.60/0.80 inference(quant_intro,[status(thm)],[607])).
% 0.60/0.80 tff(609,plain,
% 0.60/0.80 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1))) <=> ![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(610,plain,
% 0.60/0.80 (^[X2: $i, X7: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~big_p(a)) | big_p(X7)) <=> ((~big_p(a)) | big_p(X7))), ((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) <=> (((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))))), rewrite((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)))), ((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))))), (((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) <=> (((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))) | (~big_p(a))))), rewrite((((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)))), (((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))))), ((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) <=> (((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))) | (~big_p(X2))))), rewrite((((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))) | (~big_p(X2))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_p(X2)))), ((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_p(X2))))), (((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> (((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_p(X2))) | (~big_r(X1, X2))))), rewrite((((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))), (((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))))), ((((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(X1, f5(X1))) <=> (((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))) | big_r(X1, f5(X1))))), rewrite((((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))) | big_r(X1, f5(X1))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))), ((((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(X1, f5(X1))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))))),
% 0.60/0.80 inference(bind,[status(th)],[])).
% 0.60/0.80 tff(611,plain,
% 0.60/0.80 (![X2: $i, X7: $i, X1: $i] : (((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(X1, f5(X1))) <=> ![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))),
% 0.60/0.80 inference(quant_intro,[status(thm)],[610])).
% 0.60/0.80 tff(612,axiom,(![X2: $i, X7: $i, X1: $i] : (((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(X1, f5(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_11')).
% 0.60/0.80 tff(613,plain,
% 0.60/0.80 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[612, 611])).
% 0.60/0.80 tff(614,plain,
% 0.60/0.80 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[613, 609])).
% 0.60/0.80 tff(615,plain,(
% 0.60/0.80 ![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))),
% 0.60/0.80 inference(skolemize,[status(sab)],[614])).
% 0.60/0.80 tff(616,plain,
% 0.60/0.80 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[615, 608])).
% 0.60/0.80 tff(617,plain,
% 0.60/0.80 (((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))) | ((~big_p(a)) | big_p(c2) | big_r(c2, f1(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f5(c4)))) <=> ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))) | (~big_p(a)) | big_p(c2) | big_r(c2, f1(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f5(c4)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(618,plain,
% 0.60/0.80 (((~big_p(a)) | big_p(c2) | big_r(c2, f1(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f5(c4))) <=> ((~big_p(a)) | big_p(c2) | big_r(c2, f1(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f5(c4)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(619,plain,
% 0.60/0.80 (((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))) | ((~big_p(a)) | big_p(c2) | big_r(c2, f1(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f5(c4)))) <=> ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))) | ((~big_p(a)) | big_p(c2) | big_r(c2, f1(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f5(c4))))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[618])).
% 0.60/0.80 tff(620,plain,
% 0.60/0.80 (((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))) | ((~big_p(a)) | big_p(c2) | big_r(c2, f1(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f5(c4)))) <=> ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))) | (~big_p(a)) | big_p(c2) | big_r(c2, f1(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f5(c4)))),
% 0.60/0.80 inference(transitivity,[status(thm)],[619, 617])).
% 0.60/0.80 tff(621,plain,
% 0.60/0.80 ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))) | ((~big_p(a)) | big_p(c2) | big_r(c2, f1(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f5(c4)))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(622,plain,
% 0.60/0.80 ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))) | (~big_p(a)) | big_p(c2) | big_r(c2, f1(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f5(c4))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[621, 620])).
% 0.60/0.80 tff(623,plain,
% 0.60/0.80 (big_r(c4, f5(c4))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[622, 616, 11, 589, 581, 94, 264])).
% 0.60/0.80 tff(624,plain,
% 0.60/0.80 (^[X2: $i, X7: $i, X1: $i] : refl(((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1))))),
% 0.60/0.80 inference(bind,[status(th)],[])).
% 0.60/0.80 tff(625,plain,
% 0.60/0.80 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1))) <=> ![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))),
% 0.60/0.80 inference(quant_intro,[status(thm)],[624])).
% 0.60/0.80 tff(626,plain,
% 0.60/0.80 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1))) <=> ![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(627,plain,
% 0.60/0.80 (^[X2: $i, X7: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~big_p(a)) | big_p(X7)) <=> ((~big_p(a)) | big_p(X7))), ((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) <=> (((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))))), rewrite((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)))), ((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))))), (((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) <=> (((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))) | (~big_p(a))))), rewrite((((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)))), (((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))))), ((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) <=> (((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))) | (~big_p(X2))))), rewrite((((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7))) | (~big_p(X2))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_p(X2)))), ((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_p(X2))))), (((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> (((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_p(X2))) | (~big_r(X1, X2))))), rewrite((((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))), (((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))))), ((((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(f5(X1), f6(X1))) <=> (((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))) | big_r(f5(X1), f6(X1))))), rewrite((((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))) | big_r(f5(X1), f6(X1))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))), ((((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(f5(X1), f6(X1))) <=> ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))))),
% 0.60/0.80 inference(bind,[status(th)],[])).
% 0.60/0.80 tff(628,plain,
% 0.60/0.80 (![X2: $i, X7: $i, X1: $i] : (((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(f5(X1), f6(X1))) <=> ![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))),
% 0.60/0.80 inference(quant_intro,[status(thm)],[627])).
% 0.60/0.80 tff(629,axiom,(![X2: $i, X7: $i, X1: $i] : (((((((~big_p(a)) | big_p(X7)) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(f5(X1), f6(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_12')).
% 0.60/0.80 tff(630,plain,
% 0.60/0.80 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[629, 628])).
% 0.60/0.80 tff(631,plain,
% 0.60/0.80 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[630, 626])).
% 0.60/0.80 tff(632,plain,(
% 0.60/0.80 ![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))),
% 0.60/0.80 inference(skolemize,[status(sab)],[631])).
% 0.60/0.80 tff(633,plain,
% 0.60/0.80 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[632, 625])).
% 0.60/0.80 tff(634,plain,
% 0.60/0.80 (((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))) | ((~big_p(a)) | big_p(c2) | big_r(c2, f1(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f5(c4), f6(c4)))) <=> ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))) | (~big_p(a)) | big_p(c2) | big_r(c2, f1(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f5(c4), f6(c4)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(635,plain,
% 0.60/0.80 (((~big_p(a)) | big_p(c2) | big_r(c2, f1(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f5(c4), f6(c4))) <=> ((~big_p(a)) | big_p(c2) | big_r(c2, f1(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f5(c4), f6(c4)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(636,plain,
% 0.60/0.80 (((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))) | ((~big_p(a)) | big_p(c2) | big_r(c2, f1(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f5(c4), f6(c4)))) <=> ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))) | ((~big_p(a)) | big_p(c2) | big_r(c2, f1(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f5(c4), f6(c4))))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[635])).
% 0.60/0.81 tff(637,plain,
% 0.60/0.81 (((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))) | ((~big_p(a)) | big_p(c2) | big_r(c2, f1(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f5(c4), f6(c4)))) <=> ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))) | (~big_p(a)) | big_p(c2) | big_r(c2, f1(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f5(c4), f6(c4)))),
% 0.60/0.81 inference(transitivity,[status(thm)],[636, 634])).
% 0.60/0.81 tff(638,plain,
% 0.60/0.81 ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))) | ((~big_p(a)) | big_p(c2) | big_r(c2, f1(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f5(c4), f6(c4)))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(639,plain,
% 0.60/0.81 ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))) | (~big_p(a)) | big_p(c2) | big_r(c2, f1(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f5(c4), f6(c4))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[638, 637])).
% 0.60/0.81 tff(640,plain,
% 0.60/0.81 (big_r(f5(c4), f6(c4))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[639, 633, 11, 589, 581, 94, 264])).
% 0.60/0.81 tff(641,plain,
% 0.60/0.81 (((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2))) | (~big_r(f5(c4), f6(c4))) | (~big_p(f6(c4))) | (~big_r(c4, f5(c4))))) <=> ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | (~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2))) | (~big_r(f5(c4), f6(c4))) | (~big_p(f6(c4))) | (~big_r(c4, f5(c4))))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(642,plain,
% 0.60/0.81 (((~big_p(f6(c4))) | (~big_p(f6(c4))) | (~big_r(c4, f5(c4))) | (~big_r(c2, f3(c2))) | (~big_r(f5(c4), f6(c4))) | (~big_r(c4, f5(c4))) | (~big_r(f5(c4), f6(c4))) | (~big_r(f3(c2), f4(c2))) | (~big_p(f4(c2)))) <=> ((~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2))) | (~big_r(f5(c4), f6(c4))) | (~big_p(f6(c4))) | (~big_r(c4, f5(c4))))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(643,plain,
% 0.60/0.81 (((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f6(c4))) | (~big_p(f6(c4))) | (~big_r(c4, f5(c4))) | (~big_r(c2, f3(c2))) | (~big_r(f5(c4), f6(c4))) | (~big_r(c4, f5(c4))) | (~big_r(f5(c4), f6(c4))) | (~big_r(f3(c2), f4(c2))) | (~big_p(f4(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2))) | (~big_r(f5(c4), f6(c4))) | (~big_p(f6(c4))) | (~big_r(c4, f5(c4)))))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[642])).
% 0.60/0.81 tff(644,plain,
% 0.60/0.81 (((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f6(c4))) | (~big_p(f6(c4))) | (~big_r(c4, f5(c4))) | (~big_r(c2, f3(c2))) | (~big_r(f5(c4), f6(c4))) | (~big_r(c4, f5(c4))) | (~big_r(f5(c4), f6(c4))) | (~big_r(f3(c2), f4(c2))) | (~big_p(f4(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | (~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2))) | (~big_r(f5(c4), f6(c4))) | (~big_p(f6(c4))) | (~big_r(c4, f5(c4))))),
% 0.60/0.81 inference(transitivity,[status(thm)],[643, 641])).
% 0.60/0.81 tff(645,plain,
% 0.60/0.81 ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f6(c4))) | (~big_p(f6(c4))) | (~big_r(c4, f5(c4))) | (~big_r(c2, f3(c2))) | (~big_r(f5(c4), f6(c4))) | (~big_r(c4, f5(c4))) | (~big_r(f5(c4), f6(c4))) | (~big_r(f3(c2), f4(c2))) | (~big_p(f4(c2))))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(646,plain,
% 0.60/0.81 ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | (~big_p(f4(c2))) | (~big_r(c2, f3(c2))) | (~big_r(f3(c2), f4(c2))) | (~big_r(f5(c4), f6(c4))) | (~big_p(f6(c4))) | (~big_r(c4, f5(c4)))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[645, 644])).
% 0.60/0.81 tff(647,plain,
% 0.60/0.81 ($false),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[646, 304, 570, 510, 580, 640, 623, 606])).
% 0.60/0.81 tff(648,plain,(big_r(c2, f1(c2)) | big_p(c2)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.81 tff(649,plain,
% 0.60/0.81 (big_r(c2, f1(c2))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[648, 94])).
% 0.60/0.81 tff(650,assumption,(~big_r(f1(c2), f2(c2))), introduced(assumption)).
% 0.60/0.81 tff(651,plain,
% 0.60/0.81 (big_p(f4(c2))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[414, 650])).
% 0.60/0.81 tff(652,plain,
% 0.60/0.81 (big_r(c4, c3)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[577, 651, 510])).
% 0.60/0.81 tff(653,plain,
% 0.60/0.81 (big_p(c3)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[588, 651, 510])).
% 0.60/0.81 tff(654,plain,
% 0.60/0.81 (^[X2: $i, X7: $i, X1: $i] : refl(((~big_p(a)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))))),
% 0.60/0.81 inference(bind,[status(th)],[])).
% 0.60/0.81 tff(655,plain,
% 0.60/0.81 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) <=> ![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.60/0.81 inference(quant_intro,[status(thm)],[654])).
% 0.60/0.81 tff(656,plain,
% 0.60/0.81 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) <=> ![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(657,plain,
% 0.60/0.81 (^[X2: $i, X7: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~big_p(a)) | big_p(X7)) <=> ((~big_p(a)) | big_p(X7))), ((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) <=> (((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))))), rewrite((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7)))), ((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))))), (((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> (((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))) | (~big_p(a))))), rewrite((((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7)))), (((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))))), ((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) <=> (((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))) | (~big_p(X2))))), rewrite((((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))) | (~big_p(X2))) <=> ((~big_p(a)) | big_p(X7) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))), ((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) <=> ((~big_p(a)) | big_p(X7) | (~big_p(X2)) | big_r(f1(X7), f2(X7))))), (((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> (((~big_p(a)) | big_p(X7) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) | (~big_r(X1, X2))))), rewrite((((~big_p(a)) | big_p(X7) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))), (((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))))), ((((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_p(f6(X1))) <=> (((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) | big_p(f6(X1))))), rewrite((((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) | big_p(f6(X1))) <=> ((~big_p(a)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))), ((((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_p(f6(X1))) <=> ((~big_p(a)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))))),
% 0.60/0.81 inference(bind,[status(th)],[])).
% 0.60/0.81 tff(658,plain,
% 0.60/0.81 (![X2: $i, X7: $i, X1: $i] : (((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_p(f6(X1))) <=> ![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.60/0.81 inference(quant_intro,[status(thm)],[657])).
% 0.60/0.81 tff(659,axiom,(![X2: $i, X7: $i, X1: $i] : (((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_p(f6(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_16')).
% 0.60/0.81 tff(660,plain,
% 0.60/0.81 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[659, 658])).
% 0.60/0.81 tff(661,plain,
% 0.60/0.81 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[660, 656])).
% 0.60/0.81 tff(662,plain,(
% 0.60/0.81 ![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.60/0.81 inference(skolemize,[status(sab)],[661])).
% 0.60/0.81 tff(663,plain,
% 0.60/0.81 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[662, 655])).
% 0.60/0.81 tff(664,plain,
% 0.60/0.81 (((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c2) | big_r(f1(c2), f2(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f6(c4)))) <=> ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c2) | big_r(f1(c2), f2(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f6(c4)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(665,plain,
% 0.60/0.81 (((~big_p(a)) | big_p(c2) | big_p(f6(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f1(c2), f2(c2))) <=> ((~big_p(a)) | big_p(c2) | big_r(f1(c2), f2(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f6(c4)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(666,plain,
% 0.60/0.81 (((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c2) | big_p(f6(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f1(c2), f2(c2)))) <=> ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c2) | big_r(f1(c2), f2(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f6(c4))))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[665])).
% 0.60/0.81 tff(667,plain,
% 0.60/0.81 (((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c2) | big_p(f6(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f1(c2), f2(c2)))) <=> ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c2) | big_r(f1(c2), f2(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f6(c4)))),
% 0.60/0.81 inference(transitivity,[status(thm)],[666, 664])).
% 0.60/0.81 tff(668,plain,
% 0.60/0.81 ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c2) | big_p(f6(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f1(c2), f2(c2)))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(669,plain,
% 0.60/0.81 ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c2) | big_r(f1(c2), f2(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f6(c4))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[668, 667])).
% 0.60/0.81 tff(670,plain,
% 0.60/0.81 (big_p(f6(c4))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[669, 663, 11, 653, 652, 94, 650])).
% 0.60/0.81 tff(671,plain,
% 0.60/0.81 (^[X2: $i, X7: $i, X1: $i] : refl(((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7))))),
% 0.60/0.81 inference(bind,[status(th)],[])).
% 0.60/0.81 tff(672,plain,
% 0.60/0.81 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7))) <=> ![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7)))),
% 0.60/0.81 inference(quant_intro,[status(thm)],[671])).
% 0.60/0.81 tff(673,plain,
% 0.60/0.81 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7))) <=> ![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(674,plain,
% 0.60/0.81 (^[X2: $i, X7: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~big_p(a)) | big_p(X7)) <=> ((~big_p(a)) | big_p(X7))), ((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) <=> (((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))))), rewrite((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7)))), ((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))))), (((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> (((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))) | (~big_p(a))))), rewrite((((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7)))), (((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))))), ((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) <=> (((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))) | (~big_p(X2))))), rewrite((((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))) | (~big_p(X2))) <=> ((~big_p(a)) | big_p(X7) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))), ((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) <=> ((~big_p(a)) | big_p(X7) | (~big_p(X2)) | big_r(f1(X7), f2(X7))))), (((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> (((~big_p(a)) | big_p(X7) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) | (~big_r(X1, X2))))), rewrite((((~big_p(a)) | big_p(X7) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))), (((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))))), ((((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(X1, f5(X1))) <=> (((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) | big_r(X1, f5(X1))))), rewrite((((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) | big_r(X1, f5(X1))) <=> ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7)))), ((((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(X1, f5(X1))) <=> ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7)))))),
% 0.60/0.81 inference(bind,[status(th)],[])).
% 0.60/0.81 tff(675,plain,
% 0.60/0.81 (![X2: $i, X7: $i, X1: $i] : (((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(X1, f5(X1))) <=> ![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7)))),
% 0.60/0.81 inference(quant_intro,[status(thm)],[674])).
% 0.60/0.81 tff(676,axiom,(![X2: $i, X7: $i, X1: $i] : (((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(X1, f5(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_17')).
% 0.60/0.81 tff(677,plain,
% 0.60/0.81 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7)))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[676, 675])).
% 0.60/0.81 tff(678,plain,
% 0.60/0.81 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7)))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[677, 673])).
% 0.60/0.81 tff(679,plain,(
% 0.60/0.81 ![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7)))),
% 0.60/0.81 inference(skolemize,[status(sab)],[678])).
% 0.60/0.81 tff(680,plain,
% 0.60/0.81 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7)))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[679, 672])).
% 0.60/0.81 tff(681,plain,
% 0.60/0.81 (((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c2) | big_r(f1(c2), f2(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f5(c4)))) <=> ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c2) | big_r(f1(c2), f2(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f5(c4)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(682,plain,
% 0.60/0.81 (((~big_p(a)) | big_p(c2) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f5(c4)) | big_r(f1(c2), f2(c2))) <=> ((~big_p(a)) | big_p(c2) | big_r(f1(c2), f2(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f5(c4)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(683,plain,
% 0.60/0.81 (((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c2) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f5(c4)) | big_r(f1(c2), f2(c2)))) <=> ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c2) | big_r(f1(c2), f2(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f5(c4))))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[682])).
% 0.60/0.81 tff(684,plain,
% 0.60/0.81 (((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c2) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f5(c4)) | big_r(f1(c2), f2(c2)))) <=> ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c2) | big_r(f1(c2), f2(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f5(c4)))),
% 0.60/0.82 inference(transitivity,[status(thm)],[683, 681])).
% 0.60/0.82 tff(685,plain,
% 0.60/0.82 ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c2) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f5(c4)) | big_r(f1(c2), f2(c2)))),
% 0.60/0.82 inference(quant_inst,[status(thm)],[])).
% 0.60/0.82 tff(686,plain,
% 0.60/0.82 ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c2) | big_r(f1(c2), f2(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f5(c4))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[685, 684])).
% 0.60/0.82 tff(687,plain,
% 0.60/0.82 (big_r(c4, f5(c4))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[686, 680, 11, 653, 652, 94, 650])).
% 0.60/0.82 tff(688,plain,
% 0.60/0.82 (^[X2: $i, X7: $i, X1: $i] : refl(((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7))))),
% 0.60/0.82 inference(bind,[status(th)],[])).
% 0.60/0.82 tff(689,plain,
% 0.60/0.82 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7))) <=> ![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7)))),
% 0.60/0.82 inference(quant_intro,[status(thm)],[688])).
% 0.60/0.82 tff(690,plain,
% 0.60/0.82 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7))) <=> ![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(691,plain,
% 0.60/0.82 (^[X2: $i, X7: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~big_p(a)) | big_p(X7)) <=> ((~big_p(a)) | big_p(X7))), ((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) <=> (((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))))), rewrite((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7)))), ((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))))), (((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> (((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))) | (~big_p(a))))), rewrite((((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7)))), (((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))))), ((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) <=> (((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))) | (~big_p(X2))))), rewrite((((~big_p(a)) | big_p(X7) | big_r(f1(X7), f2(X7))) | (~big_p(X2))) <=> ((~big_p(a)) | big_p(X7) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))), ((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) <=> ((~big_p(a)) | big_p(X7) | (~big_p(X2)) | big_r(f1(X7), f2(X7))))), (((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> (((~big_p(a)) | big_p(X7) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) | (~big_r(X1, X2))))), rewrite((((~big_p(a)) | big_p(X7) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))), (((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))))), ((((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(f5(X1), f6(X1))) <=> (((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) | big_r(f5(X1), f6(X1))))), rewrite((((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) | big_r(f5(X1), f6(X1))) <=> ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7)))), ((((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(f5(X1), f6(X1))) <=> ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7)))))),
% 0.60/0.82 inference(bind,[status(th)],[])).
% 0.60/0.82 tff(692,plain,
% 0.60/0.82 (![X2: $i, X7: $i, X1: $i] : (((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(f5(X1), f6(X1))) <=> ![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7)))),
% 0.60/0.82 inference(quant_intro,[status(thm)],[691])).
% 0.60/0.82 tff(693,axiom,(![X2: $i, X7: $i, X1: $i] : (((((((~big_p(a)) | big_p(X7)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(f5(X1), f6(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_18')).
% 0.60/0.82 tff(694,plain,
% 0.60/0.82 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7)))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[693, 692])).
% 0.60/0.82 tff(695,plain,
% 0.60/0.82 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7)))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[694, 690])).
% 0.60/0.82 tff(696,plain,(
% 0.60/0.82 ![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7)))),
% 0.60/0.82 inference(skolemize,[status(sab)],[695])).
% 0.60/0.82 tff(697,plain,
% 0.60/0.82 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7)))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[696, 689])).
% 0.60/0.82 tff(698,plain,
% 0.60/0.82 (((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c2) | big_r(f1(c2), f2(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f5(c4), f6(c4)))) <=> ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c2) | big_r(f1(c2), f2(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f5(c4), f6(c4)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(699,plain,
% 0.60/0.82 (((~big_p(a)) | big_p(c2) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f5(c4), f6(c4)) | big_r(f1(c2), f2(c2))) <=> ((~big_p(a)) | big_p(c2) | big_r(f1(c2), f2(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f5(c4), f6(c4)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(700,plain,
% 0.60/0.82 (((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c2) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f5(c4), f6(c4)) | big_r(f1(c2), f2(c2)))) <=> ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c2) | big_r(f1(c2), f2(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f5(c4), f6(c4))))),
% 0.60/0.82 inference(monotonicity,[status(thm)],[699])).
% 0.60/0.82 tff(701,plain,
% 0.60/0.82 (((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c2) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f5(c4), f6(c4)) | big_r(f1(c2), f2(c2)))) <=> ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c2) | big_r(f1(c2), f2(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f5(c4), f6(c4)))),
% 0.60/0.82 inference(transitivity,[status(thm)],[700, 698])).
% 0.60/0.82 tff(702,plain,
% 0.60/0.82 ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c2) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f5(c4), f6(c4)) | big_r(f1(c2), f2(c2)))),
% 0.60/0.82 inference(quant_inst,[status(thm)],[])).
% 0.60/0.82 tff(703,plain,
% 0.60/0.82 ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c2) | big_r(f1(c2), f2(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f5(c4), f6(c4))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[702, 701])).
% 0.60/0.82 tff(704,plain,
% 0.60/0.82 (big_r(f5(c4), f6(c4))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[703, 697, 11, 653, 652, 94, 650])).
% 0.60/0.82 tff(705,plain,
% 0.60/0.82 ($false),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[646, 304, 570, 510, 651, 704, 687, 670])).
% 0.60/0.82 tff(706,plain,(big_r(f1(c2), f2(c2)) | big_p(c2)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.82 tff(707,plain,
% 0.60/0.82 (big_r(f1(c2), f2(c2))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[706, 94])).
% 0.60/0.82 tff(708,plain,
% 0.60/0.82 (big_r(c4, c3) | (~big_p(f2(c2)))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[436, 430, 138, 707, 649])).
% 0.60/0.82 tff(709,plain,
% 0.60/0.82 (~big_p(f2(c2))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[708, 511])).
% 0.60/0.82 tff(710,plain,
% 0.60/0.82 ($false),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[372, 709, 578, 94])).
% 0.60/0.82 tff(711,plain,(big_r(c4, c3) | big_p(c2)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.82 tff(712,plain,
% 0.60/0.82 (big_r(c4, c3)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[711, 94])).
% 0.60/0.82 tff(713,assumption,(~big_p(c3)), introduced(assumption)).
% 0.60/0.82 tff(714,plain,
% 0.60/0.82 (~big_p(f4(c2))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[588, 713, 510])).
% 0.60/0.82 tff(715,plain,
% 0.60/0.82 (big_p(c3) | (~big_p(f2(c2)))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[454, 430, 448, 707, 649])).
% 0.60/0.82 tff(716,plain,
% 0.60/0.82 (~big_p(f2(c2))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[715, 713])).
% 0.60/0.82 tff(717,plain,
% 0.60/0.82 ($false),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[372, 716, 714, 94])).
% 0.60/0.82 tff(718,plain,(big_p(c3) | big_p(c2)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.82 tff(719,plain,
% 0.60/0.82 (big_p(c3)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[718, 94])).
% 0.60/0.82 tff(720,plain,
% 0.60/0.82 (^[X7: $i, X8: $i, X1: $i] : refl(((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) <=> ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))))),
% 0.60/0.82 inference(bind,[status(th)],[])).
% 0.60/0.82 tff(721,plain,
% 0.60/0.82 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) <=> ![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))),
% 0.60/0.82 inference(quant_intro,[status(thm)],[720])).
% 0.60/0.82 tff(722,plain,
% 0.60/0.82 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) <=> ![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(723,plain,
% 0.60/0.82 (^[X7: $i, X8: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_p(f2(X7))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_p(f2(X7))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) <=> (((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | (~big_p(a))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) <=> (((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_p(X1)))), rewrite((((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) | big_p(f4(X1))) <=> (((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_p(f4(X1))))), rewrite((((~big_p(a)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_p(f4(X1))) <=> ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) | big_p(f4(X1))) <=> ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))))),
% 0.60/0.82 inference(bind,[status(th)],[])).
% 0.60/0.82 tff(724,plain,
% 0.60/0.82 (![X7: $i, X8: $i, X1: $i] : (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) | big_p(f4(X1))) <=> ![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))),
% 0.60/0.82 inference(quant_intro,[status(thm)],[723])).
% 0.60/0.82 tff(725,axiom,(![X7: $i, X8: $i, X1: $i] : (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | big_p(X1)) | big_p(f4(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_19')).
% 0.60/0.82 tff(726,plain,
% 0.60/0.82 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[725, 724])).
% 0.60/0.82 tff(727,plain,
% 0.60/0.82 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[726, 722])).
% 0.60/0.82 tff(728,plain,(
% 0.60/0.82 ![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))),
% 0.60/0.82 inference(skolemize,[status(sab)],[727])).
% 0.60/0.82 tff(729,plain,
% 0.60/0.82 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[728, 721])).
% 0.60/0.82 tff(730,plain,
% 0.60/0.82 (((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | ((~big_p(a)) | big_p(c2) | big_p(f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f2(c4)))) <=> ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | (~big_p(a)) | big_p(c2) | big_p(f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f2(c4)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(731,plain,
% 0.60/0.82 (((~big_p(a)) | big_p(f4(c2)) | big_p(c2) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3))) <=> ((~big_p(a)) | big_p(c2) | big_p(f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f2(c4)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(732,plain,
% 0.60/0.82 (((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | ((~big_p(a)) | big_p(f4(c2)) | big_p(c2) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)))) <=> ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | ((~big_p(a)) | big_p(c2) | big_p(f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f2(c4))))),
% 0.60/0.82 inference(monotonicity,[status(thm)],[731])).
% 0.60/0.82 tff(733,plain,
% 0.60/0.82 (((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | ((~big_p(a)) | big_p(f4(c2)) | big_p(c2) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)))) <=> ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | (~big_p(a)) | big_p(c2) | big_p(f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f2(c4)))),
% 0.60/0.82 inference(transitivity,[status(thm)],[732, 730])).
% 0.60/0.82 tff(734,plain,
% 0.60/0.82 ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | ((~big_p(a)) | big_p(f4(c2)) | big_p(c2) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)))),
% 0.60/0.82 inference(quant_inst,[status(thm)],[])).
% 0.60/0.82 tff(735,plain,
% 0.60/0.82 ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | (~big_p(a)) | big_p(c2) | big_p(f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f2(c4))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[734, 733])).
% 0.60/0.82 tff(736,plain,
% 0.60/0.82 (big_p(f4(c2)) | big_p(f2(c4))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[735, 729, 11, 719, 712, 94])).
% 0.60/0.82 tff(737,plain,
% 0.60/0.82 (big_p(f2(c4))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[736, 139])).
% 0.60/0.82 tff(738,plain,
% 0.60/0.82 (big_p(f2(c2))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[372, 139, 94])).
% 0.60/0.82 tff(739,plain,
% 0.60/0.82 (^[X7: $i, X8: $i, X1: $i] : refl(((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) <=> ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))))),
% 0.60/0.82 inference(bind,[status(th)],[])).
% 0.60/0.82 tff(740,plain,
% 0.60/0.82 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) <=> ![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))),
% 0.60/0.82 inference(quant_intro,[status(thm)],[739])).
% 0.60/0.82 tff(741,plain,
% 0.60/0.82 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) <=> ![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(742,plain,
% 0.60/0.82 (^[X7: $i, X8: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_r(X7, f1(X7))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_r(X7, f1(X7))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | (~big_p(a))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | big_p(X1)))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) | big_p(f4(X1))) <=> (((~big_p(a)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | big_p(f4(X1))))), rewrite((((~big_p(a)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | big_p(f4(X1))) <=> ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) | big_p(f4(X1))) <=> ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))))),
% 0.60/0.82 inference(bind,[status(th)],[])).
% 0.60/0.82 tff(743,plain,
% 0.60/0.82 (![X7: $i, X8: $i, X1: $i] : (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) | big_p(f4(X1))) <=> ![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))),
% 0.60/0.82 inference(quant_intro,[status(thm)],[742])).
% 0.60/0.82 tff(744,axiom,(![X7: $i, X8: $i, X1: $i] : (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | big_p(X1)) | big_p(f4(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_25')).
% 0.60/0.82 tff(745,plain,
% 0.60/0.82 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[744, 743])).
% 0.60/0.82 tff(746,plain,
% 0.60/0.82 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[745, 741])).
% 0.60/0.82 tff(747,plain,(
% 0.60/0.82 ![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))),
% 0.60/0.82 inference(skolemize,[status(sab)],[746])).
% 0.60/0.82 tff(748,plain,
% 0.60/0.82 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[747, 740])).
% 0.60/0.82 tff(749,plain,
% 0.60/0.82 (((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c2) | big_p(f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)))) <=> ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | (~big_p(a)) | big_p(c2) | big_p(f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(750,plain,
% 0.60/0.82 (((~big_p(a)) | big_p(f4(c2)) | big_p(c2) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4))) <=> ((~big_p(a)) | big_p(c2) | big_p(f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(751,plain,
% 0.60/0.82 (((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(f4(c2)) | big_p(c2) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)))) <=> ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c2) | big_p(f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4))))),
% 0.60/0.82 inference(monotonicity,[status(thm)],[750])).
% 0.60/0.82 tff(752,plain,
% 0.60/0.82 (((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(f4(c2)) | big_p(c2) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)))) <=> ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | (~big_p(a)) | big_p(c2) | big_p(f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)))),
% 0.60/0.82 inference(transitivity,[status(thm)],[751, 749])).
% 0.60/0.82 tff(753,plain,
% 0.60/0.82 ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(f4(c2)) | big_p(c2) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)))),
% 0.60/0.82 inference(quant_inst,[status(thm)],[])).
% 0.60/0.82 tff(754,plain,
% 0.60/0.82 ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | (~big_p(a)) | big_p(c2) | big_p(f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[753, 752])).
% 0.60/0.82 tff(755,plain,
% 0.60/0.82 (big_p(f4(c2)) | big_r(c4, f1(c4))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[754, 748, 11, 719, 712, 94])).
% 0.60/0.82 tff(756,plain,
% 0.60/0.82 (big_r(c4, f1(c4))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[755, 139])).
% 0.60/0.82 tff(757,plain,
% 0.60/0.82 (^[X7: $i, X8: $i, X1: $i] : refl(((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))))),
% 0.60/0.82 inference(bind,[status(th)],[])).
% 0.60/0.82 tff(758,plain,
% 0.60/0.82 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) <=> ![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))),
% 0.60/0.82 inference(quant_intro,[status(thm)],[757])).
% 0.60/0.82 tff(759,plain,
% 0.60/0.82 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) <=> ![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(760,plain,
% 0.60/0.82 (^[X7: $i, X8: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_r(f1(X7), f2(X7))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | (~big_p(a))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | big_p(X1)))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) <=> ((~big_p(a)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) | big_p(f4(X1))) <=> (((~big_p(a)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | big_p(f4(X1))))), rewrite((((~big_p(a)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | big_p(f4(X1))) <=> ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) | big_p(f4(X1))) <=> ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))))),
% 0.60/0.82 inference(bind,[status(th)],[])).
% 0.60/0.82 tff(761,plain,
% 0.60/0.82 (![X7: $i, X8: $i, X1: $i] : (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) | big_p(f4(X1))) <=> ![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))),
% 0.60/0.82 inference(quant_intro,[status(thm)],[760])).
% 0.60/0.82 tff(762,axiom,(![X7: $i, X8: $i, X1: $i] : (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | big_p(X1)) | big_p(f4(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_31')).
% 0.60/0.82 tff(763,plain,
% 0.60/0.82 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[762, 761])).
% 0.60/0.82 tff(764,plain,
% 0.60/0.82 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[763, 759])).
% 0.60/0.82 tff(765,plain,(
% 0.60/0.82 ![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))),
% 0.60/0.82 inference(skolemize,[status(sab)],[764])).
% 0.60/0.82 tff(766,plain,
% 0.60/0.82 (![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[765, 758])).
% 0.60/0.82 tff(767,plain,
% 0.60/0.82 (((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c2) | big_p(f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)))) <=> ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c2) | big_p(f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(768,plain,
% 0.60/0.82 (((~big_p(a)) | big_p(f4(c2)) | big_p(c2) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f1(c4), f2(c4))) <=> ((~big_p(a)) | big_p(c2) | big_p(f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(769,plain,
% 0.60/0.82 (((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(f4(c2)) | big_p(c2) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f1(c4), f2(c4)))) <=> ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c2) | big_p(f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4))))),
% 0.60/0.82 inference(monotonicity,[status(thm)],[768])).
% 0.60/0.82 tff(770,plain,
% 0.60/0.82 (((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(f4(c2)) | big_p(c2) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f1(c4), f2(c4)))) <=> ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c2) | big_p(f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)))),
% 0.60/0.82 inference(transitivity,[status(thm)],[769, 767])).
% 0.60/0.82 tff(771,plain,
% 0.60/0.82 ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(f4(c2)) | big_p(c2) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f1(c4), f2(c4)))),
% 0.60/0.82 inference(quant_inst,[status(thm)],[])).
% 0.60/0.82 tff(772,plain,
% 0.60/0.82 ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f4(X1)) | big_p(X1) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c2) | big_p(f4(c2)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[771, 770])).
% 0.60/0.83 tff(773,plain,
% 0.60/0.83 (big_p(f4(c2)) | big_r(f1(c4), f2(c4))),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[772, 766, 11, 719, 712, 94])).
% 0.60/0.83 tff(774,plain,
% 0.60/0.83 (big_r(f1(c4), f2(c4))),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[773, 139])).
% 0.60/0.83 tff(775,plain,
% 0.60/0.83 ($false),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[334, 304, 707, 649, 774, 756, 738, 737])).
% 0.60/0.83 tff(776,plain,(big_p(f4(c2)) | big_p(c2)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.83 tff(777,plain,
% 0.60/0.83 (big_p(f4(c2))),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[776, 94])).
% 0.60/0.83 tff(778,assumption,(big_r(c4, c3)), introduced(assumption)).
% 0.60/0.83 tff(779,assumption,(big_p(c3)), introduced(assumption)).
% 0.60/0.83 tff(780,plain,
% 0.60/0.83 (^[X2: $i, X7: $i, X8: $i, X1: $i] : refl(((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))))),
% 0.60/0.83 inference(bind,[status(th)],[])).
% 0.60/0.83 tff(781,plain,
% 0.60/0.83 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.60/0.83 inference(quant_intro,[status(thm)],[780])).
% 0.60/0.83 tff(782,plain,
% 0.60/0.83 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(783,plain,
% 0.60/0.83 (^[X2: $i, X7: $i, X8: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_r(X7, f1(X7))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_r(X7, f1(X7))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | (~big_p(a))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | (~big_p(X2))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | (~big_p(X2))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_p(X2)))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_p(X2))))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_p(X2))) | (~big_r(X1, X2))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))))), (((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_p(f6(X1))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))) | big_p(f6(X1))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))) | big_p(f6(X1))) <=> ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))), (((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_p(f6(X1))) <=> ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))))),
% 0.60/0.83 inference(bind,[status(th)],[])).
% 0.60/0.83 tff(784,plain,
% 0.60/0.83 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_p(f6(X1))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.60/0.83 inference(quant_intro,[status(thm)],[783])).
% 0.60/0.83 tff(785,axiom,(![X2: $i, X7: $i, X8: $i, X1: $i] : ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_p(f6(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_28')).
% 0.60/0.83 tff(786,plain,
% 0.60/0.83 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[785, 784])).
% 0.60/0.83 tff(787,plain,
% 0.60/0.83 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[786, 782])).
% 0.60/0.83 tff(788,plain,(
% 0.60/0.83 ![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.60/0.83 inference(skolemize,[status(sab)],[787])).
% 0.60/0.83 tff(789,plain,
% 0.60/0.83 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[788, 781])).
% 0.60/0.83 tff(790,plain,
% 0.60/0.83 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)) | big_p(f6(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)) | big_p(f6(c4)))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(791,plain,
% 0.60/0.83 (((~big_p(a)) | big_p(f6(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)) | (~big_r(c4, c3)) | (~big_p(c3))) <=> ((~big_p(a)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)) | big_p(f6(c4)))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(792,plain,
% 0.60/0.83 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_p(f6(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)) | (~big_r(c4, c3)) | (~big_p(c3)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)) | big_p(f6(c4))))),
% 0.60/0.83 inference(monotonicity,[status(thm)],[791])).
% 0.60/0.83 tff(793,plain,
% 0.60/0.83 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_p(f6(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)) | (~big_r(c4, c3)) | (~big_p(c3)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)) | big_p(f6(c4)))),
% 0.60/0.83 inference(transitivity,[status(thm)],[792, 790])).
% 0.60/0.83 tff(794,plain,
% 0.60/0.83 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_p(f6(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)) | (~big_r(c4, c3)) | (~big_p(c3)))),
% 0.60/0.83 inference(quant_inst,[status(thm)],[])).
% 0.60/0.83 tff(795,plain,
% 0.60/0.83 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)) | big_p(f6(c4))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[794, 793])).
% 0.60/0.83 tff(796,plain,
% 0.60/0.83 (big_r(c4, f1(c4)) | big_p(f6(c4))),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[795, 789, 11, 779, 778])).
% 0.60/0.83 tff(797,plain,
% 0.60/0.83 (big_p(f6(c4))),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[796, 3])).
% 0.60/0.83 tff(798,plain,
% 0.60/0.83 (^[X2: $i, X7: $i, X8: $i, X1: $i] : refl(((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))))),
% 0.60/0.83 inference(bind,[status(th)],[])).
% 0.60/0.83 tff(799,plain,
% 0.60/0.83 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.60/0.83 inference(quant_intro,[status(thm)],[798])).
% 0.60/0.83 tff(800,plain,
% 0.60/0.83 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(801,plain,
% 0.60/0.83 (^[X2: $i, X7: $i, X8: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_r(X7, f1(X7))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_r(X7, f1(X7))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | (~big_p(a))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | (~big_p(X2))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | (~big_p(X2))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_p(X2)))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_p(X2))))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_p(X2))) | (~big_r(X1, X2))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))))), (((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(X1, f5(X1))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))) | big_r(X1, f5(X1))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))) | big_r(X1, f5(X1))) <=> ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))), (((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(X1, f5(X1))) <=> ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))))),
% 0.60/0.83 inference(bind,[status(th)],[])).
% 0.60/0.83 tff(802,plain,
% 0.60/0.83 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(X1, f5(X1))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.60/0.83 inference(quant_intro,[status(thm)],[801])).
% 0.60/0.83 tff(803,axiom,(![X2: $i, X7: $i, X8: $i, X1: $i] : ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(X1, f5(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_29')).
% 0.60/0.83 tff(804,plain,
% 0.60/0.83 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[803, 802])).
% 0.60/0.83 tff(805,plain,
% 0.60/0.83 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[804, 800])).
% 0.60/0.83 tff(806,plain,(
% 0.60/0.83 ![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.60/0.83 inference(skolemize,[status(sab)],[805])).
% 0.60/0.83 tff(807,plain,
% 0.60/0.83 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[806, 799])).
% 0.60/0.83 tff(808,plain,
% 0.60/0.83 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)) | big_r(c4, f5(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)) | big_r(c4, f5(c4)))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(809,plain,
% 0.60/0.83 (((~big_p(a)) | big_r(c4, f5(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)) | (~big_r(c4, c3)) | (~big_p(c3))) <=> ((~big_p(a)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)) | big_r(c4, f5(c4)))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(810,plain,
% 0.60/0.83 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_r(c4, f5(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)) | (~big_r(c4, c3)) | (~big_p(c3)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)) | big_r(c4, f5(c4))))),
% 0.60/0.83 inference(monotonicity,[status(thm)],[809])).
% 0.60/0.83 tff(811,plain,
% 0.60/0.83 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_r(c4, f5(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)) | (~big_r(c4, c3)) | (~big_p(c3)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)) | big_r(c4, f5(c4)))),
% 0.60/0.83 inference(transitivity,[status(thm)],[810, 808])).
% 0.60/0.83 tff(812,plain,
% 0.60/0.83 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_r(c4, f5(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)) | (~big_r(c4, c3)) | (~big_p(c3)))),
% 0.60/0.83 inference(quant_inst,[status(thm)],[])).
% 0.60/0.83 tff(813,plain,
% 0.60/0.83 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)) | big_r(c4, f5(c4))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[812, 811])).
% 0.60/0.83 tff(814,plain,
% 0.60/0.83 (big_r(c4, f1(c4)) | big_r(c4, f5(c4))),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[813, 807, 11, 779, 778])).
% 0.60/0.83 tff(815,plain,
% 0.60/0.83 (big_r(c4, f5(c4))),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[814, 3])).
% 0.60/0.83 tff(816,plain,
% 0.60/0.83 (^[X2: $i, X7: $i, X8: $i, X1: $i] : refl(((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))))),
% 0.60/0.83 inference(bind,[status(th)],[])).
% 0.60/0.83 tff(817,plain,
% 0.60/0.83 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.60/0.83 inference(quant_intro,[status(thm)],[816])).
% 0.60/0.83 tff(818,plain,
% 0.60/0.83 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(819,plain,
% 0.60/0.83 (^[X2: $i, X7: $i, X8: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_r(X7, f1(X7))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_r(X7, f1(X7))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | (~big_p(a))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | (~big_p(X2))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7))) | (~big_p(X2))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_p(X2)))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_p(X2))))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_p(X2))) | (~big_r(X1, X2))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))))), (((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(f5(X1), f6(X1))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))) | big_r(f5(X1), f6(X1))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2))) | big_r(f5(X1), f6(X1))) <=> ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))), (((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(f5(X1), f6(X1))) <=> ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))))),
% 0.60/0.83 inference(bind,[status(th)],[])).
% 0.60/0.83 tff(820,plain,
% 0.60/0.83 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(f5(X1), f6(X1))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.60/0.83 inference(quant_intro,[status(thm)],[819])).
% 0.60/0.83 tff(821,axiom,(![X2: $i, X7: $i, X8: $i, X1: $i] : ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(X7, f1(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(f5(X1), f6(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_30')).
% 0.60/0.83 tff(822,plain,
% 0.60/0.83 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[821, 820])).
% 0.60/0.83 tff(823,plain,
% 0.60/0.83 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[822, 818])).
% 0.60/0.83 tff(824,plain,(
% 0.60/0.83 ![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.60/0.83 inference(skolemize,[status(sab)],[823])).
% 0.60/0.83 tff(825,plain,
% 0.60/0.83 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[824, 817])).
% 0.60/0.83 tff(826,plain,
% 0.60/0.83 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)) | big_r(f5(c4), f6(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)) | big_r(f5(c4), f6(c4)))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(827,plain,
% 0.60/0.83 (((~big_p(a)) | big_r(f5(c4), f6(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)) | (~big_r(c4, c3)) | (~big_p(c3))) <=> ((~big_p(a)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)) | big_r(f5(c4), f6(c4)))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(828,plain,
% 0.60/0.83 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_r(f5(c4), f6(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)) | (~big_r(c4, c3)) | (~big_p(c3)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)) | big_r(f5(c4), f6(c4))))),
% 0.60/0.83 inference(monotonicity,[status(thm)],[827])).
% 0.60/0.83 tff(829,plain,
% 0.60/0.83 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_r(f5(c4), f6(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)) | (~big_r(c4, c3)) | (~big_p(c3)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)) | big_r(f5(c4), f6(c4)))),
% 0.60/0.83 inference(transitivity,[status(thm)],[828, 826])).
% 0.60/0.83 tff(830,plain,
% 0.60/0.83 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_r(f5(c4), f6(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)) | (~big_r(c4, c3)) | (~big_p(c3)))),
% 0.60/0.83 inference(quant_inst,[status(thm)],[])).
% 0.60/0.83 tff(831,plain,
% 0.60/0.83 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f1(c4)) | big_r(f5(c4), f6(c4))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[830, 829])).
% 0.60/0.83 tff(832,plain,
% 0.60/0.83 (big_r(c4, f1(c4)) | big_r(f5(c4), f6(c4))),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[831, 825, 11, 779, 778])).
% 0.60/0.83 tff(833,plain,
% 0.60/0.83 (big_r(f5(c4), f6(c4))),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[832, 3])).
% 0.60/0.83 tff(834,assumption,(big_p(f4(c2))), introduced(assumption)).
% 0.60/0.83 tff(835,assumption,(big_r(c2, f3(c2))), introduced(assumption)).
% 0.60/0.83 tff(836,assumption,(big_r(f3(c2), f4(c2))), introduced(assumption)).
% 0.60/0.83 tff(837,plain,
% 0.60/0.83 ($false),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[646, 304, 836, 835, 834, 833, 815, 797])).
% 0.60/0.83 tff(838,plain,(big_r(c4, f1(c4)) | (~big_r(f3(c2), f4(c2))) | (~big_r(c2, f3(c2))) | (~big_p(f4(c2))) | (~big_p(c3)) | (~big_r(c4, c3))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.83 tff(839,plain,
% 0.60/0.83 (big_r(c4, f1(c4))),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[838, 570, 510, 777, 719, 712])).
% 0.60/0.83 tff(840,plain,
% 0.60/0.83 (^[X2: $i, X7: $i, X8: $i, X1: $i] : refl(((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))))),
% 0.60/0.83 inference(bind,[status(th)],[])).
% 0.60/0.83 tff(841,plain,
% 0.60/0.83 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.60/0.83 inference(quant_intro,[status(thm)],[840])).
% 0.60/0.83 tff(842,plain,
% 0.60/0.83 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(843,plain,
% 0.60/0.83 (^[X2: $i, X7: $i, X8: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_r(f1(X7), f2(X7))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | (~big_p(a))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | (~big_p(X2))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | (~big_p(X2))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) | (~big_r(X1, X2))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))))), (((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_p(f6(X1))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) | big_p(f6(X1))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) | big_p(f6(X1))) <=> ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))), (((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_p(f6(X1))) <=> ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))))),
% 0.60/0.84 inference(bind,[status(th)],[])).
% 0.60/0.84 tff(844,plain,
% 0.60/0.84 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_p(f6(X1))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.60/0.84 inference(quant_intro,[status(thm)],[843])).
% 0.60/0.84 tff(845,axiom,(![X2: $i, X7: $i, X8: $i, X1: $i] : ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_p(f6(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_34')).
% 0.60/0.84 tff(846,plain,
% 0.60/0.84 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.60/0.84 inference(modus_ponens,[status(thm)],[845, 844])).
% 0.60/0.84 tff(847,plain,
% 0.60/0.84 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.60/0.84 inference(modus_ponens,[status(thm)],[846, 842])).
% 0.60/0.84 tff(848,plain,(
% 0.60/0.84 ![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.60/0.84 inference(skolemize,[status(sab)],[847])).
% 0.60/0.84 tff(849,plain,
% 0.60/0.84 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.60/0.84 inference(modus_ponens,[status(thm)],[848, 841])).
% 0.60/0.84 tff(850,plain,
% 0.60/0.84 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)) | big_p(f6(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)) | big_p(f6(c4)))),
% 0.60/0.84 inference(rewrite,[status(thm)],[])).
% 0.60/0.84 tff(851,plain,
% 0.60/0.84 (((~big_p(a)) | big_p(f6(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f1(c4), f2(c4))) <=> ((~big_p(a)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)) | big_p(f6(c4)))),
% 0.60/0.84 inference(rewrite,[status(thm)],[])).
% 0.60/0.84 tff(852,plain,
% 0.60/0.84 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(f6(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f1(c4), f2(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)) | big_p(f6(c4))))),
% 0.60/0.84 inference(monotonicity,[status(thm)],[851])).
% 0.60/0.84 tff(853,plain,
% 0.60/0.84 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(f6(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f1(c4), f2(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)) | big_p(f6(c4)))),
% 0.60/0.84 inference(transitivity,[status(thm)],[852, 850])).
% 0.60/0.84 tff(854,plain,
% 0.60/0.84 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(f6(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f1(c4), f2(c4)))),
% 0.60/0.84 inference(quant_inst,[status(thm)],[])).
% 0.60/0.84 tff(855,plain,
% 0.60/0.84 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)) | big_p(f6(c4))),
% 0.60/0.84 inference(modus_ponens,[status(thm)],[854, 853])).
% 0.60/0.84 tff(856,plain,
% 0.60/0.84 (big_r(f1(c4), f2(c4)) | big_p(f6(c4))),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[855, 849, 11, 779, 778])).
% 0.60/0.84 tff(857,plain,
% 0.60/0.84 (big_p(f6(c4))),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[856, 179])).
% 0.60/0.84 tff(858,plain,
% 0.60/0.84 (^[X2: $i, X7: $i, X8: $i, X1: $i] : refl(((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))))),
% 0.60/0.84 inference(bind,[status(th)],[])).
% 0.60/0.84 tff(859,plain,
% 0.60/0.84 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.60/0.84 inference(quant_intro,[status(thm)],[858])).
% 0.60/0.84 tff(860,plain,
% 0.60/0.84 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.60/0.84 inference(rewrite,[status(thm)],[])).
% 0.60/0.84 tff(861,plain,
% 0.60/0.84 (^[X2: $i, X7: $i, X8: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_r(f1(X7), f2(X7))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | (~big_p(a))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | (~big_p(X2))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | (~big_p(X2))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) | (~big_r(X1, X2))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))))), (((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(X1, f5(X1))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) | big_r(X1, f5(X1))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) | big_r(X1, f5(X1))) <=> ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))), (((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(X1, f5(X1))) <=> ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))))),
% 0.60/0.84 inference(bind,[status(th)],[])).
% 0.60/0.84 tff(862,plain,
% 0.60/0.84 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(X1, f5(X1))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.60/0.84 inference(quant_intro,[status(thm)],[861])).
% 0.60/0.84 tff(863,axiom,(![X2: $i, X7: $i, X8: $i, X1: $i] : ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(X1, f5(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_35')).
% 0.60/0.84 tff(864,plain,
% 0.60/0.84 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.60/0.84 inference(modus_ponens,[status(thm)],[863, 862])).
% 0.60/0.84 tff(865,plain,
% 0.60/0.84 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.60/0.84 inference(modus_ponens,[status(thm)],[864, 860])).
% 0.60/0.84 tff(866,plain,(
% 0.60/0.84 ![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.60/0.84 inference(skolemize,[status(sab)],[865])).
% 0.60/0.84 tff(867,plain,
% 0.60/0.84 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.60/0.84 inference(modus_ponens,[status(thm)],[866, 859])).
% 0.60/0.84 tff(868,plain,
% 0.60/0.84 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)) | big_r(c4, f5(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)) | big_r(c4, f5(c4)))),
% 0.60/0.84 inference(rewrite,[status(thm)],[])).
% 0.60/0.84 tff(869,plain,
% 0.60/0.84 (((~big_p(a)) | big_r(c4, f5(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f1(c4), f2(c4))) <=> ((~big_p(a)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)) | big_r(c4, f5(c4)))),
% 0.60/0.84 inference(rewrite,[status(thm)],[])).
% 0.60/0.84 tff(870,plain,
% 0.60/0.84 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_r(c4, f5(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f1(c4), f2(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)) | big_r(c4, f5(c4))))),
% 0.67/0.84 inference(monotonicity,[status(thm)],[869])).
% 0.67/0.84 tff(871,plain,
% 0.67/0.84 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_r(c4, f5(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f1(c4), f2(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)) | big_r(c4, f5(c4)))),
% 0.67/0.84 inference(transitivity,[status(thm)],[870, 868])).
% 0.67/0.84 tff(872,plain,
% 0.67/0.84 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_r(c4, f5(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f1(c4), f2(c4)))),
% 0.67/0.84 inference(quant_inst,[status(thm)],[])).
% 0.67/0.84 tff(873,plain,
% 0.67/0.84 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)) | big_r(c4, f5(c4))),
% 0.67/0.84 inference(modus_ponens,[status(thm)],[872, 871])).
% 0.67/0.84 tff(874,plain,
% 0.67/0.84 (big_r(f1(c4), f2(c4)) | big_r(c4, f5(c4))),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[873, 867, 11, 779, 778])).
% 0.67/0.84 tff(875,plain,
% 0.67/0.84 (big_r(c4, f5(c4))),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[874, 179])).
% 0.67/0.84 tff(876,plain,
% 0.67/0.84 (^[X2: $i, X7: $i, X8: $i, X1: $i] : refl(((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))))),
% 0.67/0.84 inference(bind,[status(th)],[])).
% 0.67/0.84 tff(877,plain,
% 0.67/0.84 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.67/0.84 inference(quant_intro,[status(thm)],[876])).
% 0.67/0.84 tff(878,plain,
% 0.67/0.84 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.67/0.84 inference(rewrite,[status(thm)],[])).
% 0.67/0.84 tff(879,plain,
% 0.67/0.84 (^[X2: $i, X7: $i, X8: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_r(f1(X7), f2(X7))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | (~big_p(a))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | (~big_p(X2))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7))) | (~big_p(X2))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) | (~big_r(X1, X2))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))))), (((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(f5(X1), f6(X1))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) | big_r(f5(X1), f6(X1))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7))) | big_r(f5(X1), f6(X1))) <=> ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))), (((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(f5(X1), f6(X1))) <=> ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))))),
% 0.67/0.84 inference(bind,[status(th)],[])).
% 0.67/0.84 tff(880,plain,
% 0.67/0.84 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(f5(X1), f6(X1))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.67/0.84 inference(quant_intro,[status(thm)],[879])).
% 0.67/0.84 tff(881,axiom,(![X2: $i, X7: $i, X8: $i, X1: $i] : ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_r(f1(X7), f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(f5(X1), f6(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_36')).
% 0.67/0.84 tff(882,plain,
% 0.67/0.84 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.67/0.84 inference(modus_ponens,[status(thm)],[881, 880])).
% 0.67/0.84 tff(883,plain,
% 0.67/0.84 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.67/0.84 inference(modus_ponens,[status(thm)],[882, 878])).
% 0.67/0.84 tff(884,plain,(
% 0.67/0.84 ![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.67/0.84 inference(skolemize,[status(sab)],[883])).
% 0.67/0.84 tff(885,plain,
% 0.67/0.84 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))),
% 0.67/0.84 inference(modus_ponens,[status(thm)],[884, 877])).
% 0.67/0.84 tff(886,plain,
% 0.67/0.84 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)) | big_r(f5(c4), f6(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)) | big_r(f5(c4), f6(c4)))),
% 0.67/0.84 inference(rewrite,[status(thm)],[])).
% 0.67/0.84 tff(887,plain,
% 0.67/0.84 (((~big_p(a)) | big_r(f5(c4), f6(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f1(c4), f2(c4))) <=> ((~big_p(a)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)) | big_r(f5(c4), f6(c4)))),
% 0.67/0.84 inference(rewrite,[status(thm)],[])).
% 0.67/0.84 tff(888,plain,
% 0.67/0.84 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_r(f5(c4), f6(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f1(c4), f2(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)) | big_r(f5(c4), f6(c4))))),
% 0.67/0.84 inference(monotonicity,[status(thm)],[887])).
% 0.67/0.84 tff(889,plain,
% 0.67/0.84 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_r(f5(c4), f6(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f1(c4), f2(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)) | big_r(f5(c4), f6(c4)))),
% 0.67/0.84 inference(transitivity,[status(thm)],[888, 886])).
% 0.67/0.84 tff(890,plain,
% 0.67/0.84 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_r(f5(c4), f6(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(f1(c4), f2(c4)))),
% 0.67/0.84 inference(quant_inst,[status(thm)],[])).
% 0.67/0.84 tff(891,plain,
% 0.67/0.84 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f1(c4), f2(c4)) | big_r(f5(c4), f6(c4))),
% 0.67/0.84 inference(modus_ponens,[status(thm)],[890, 889])).
% 0.67/0.84 tff(892,plain,
% 0.67/0.84 (big_r(f1(c4), f2(c4)) | big_r(f5(c4), f6(c4))),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[891, 885, 11, 779, 778])).
% 0.67/0.84 tff(893,plain,
% 0.67/0.84 (big_r(f5(c4), f6(c4))),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[892, 179])).
% 0.67/0.84 tff(894,plain,
% 0.67/0.84 ($false),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[646, 304, 836, 835, 834, 893, 875, 857])).
% 0.67/0.84 tff(895,plain,(big_r(f1(c4), f2(c4)) | (~big_r(f3(c2), f4(c2))) | (~big_r(c2, f3(c2))) | (~big_p(f4(c2))) | (~big_p(c3)) | (~big_r(c4, c3))), inference(lemma,lemma(discharge,[]))).
% 0.67/0.84 tff(896,plain,
% 0.67/0.84 (big_r(f1(c4), f2(c4))),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[895, 570, 510, 777, 719, 712])).
% 0.67/0.84 tff(897,plain,
% 0.67/0.84 ((~big_p(f2(c4))) | (~big_r(c4, f1(c4)))),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[381, 304, 570, 510, 896, 777])).
% 0.67/0.84 tff(898,plain,
% 0.67/0.84 (~big_p(f2(c4))),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[897, 839])).
% 0.67/0.84 tff(899,plain,
% 0.67/0.84 (^[X2: $i, X7: $i, X8: $i, X1: $i] : refl(((~big_p(a)) | big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> ((~big_p(a)) | big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2))))),
% 0.67/0.84 inference(bind,[status(th)],[])).
% 0.67/0.84 tff(900,plain,
% 0.67/0.84 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.67/0.84 inference(quant_intro,[status(thm)],[899])).
% 0.67/0.84 tff(901,plain,
% 0.67/0.84 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.67/0.84 inference(rewrite,[status(thm)],[])).
% 0.67/0.84 tff(902,plain,
% 0.67/0.84 (^[X2: $i, X7: $i, X8: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_p(f2(X7))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_p(f2(X7))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) <=> (((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | (~big_p(a))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) <=> (((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | (~big_p(X2))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | (~big_p(X2))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_p(X2)))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_p(X2))))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> (((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_p(X2))) | (~big_r(X1, X2))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2))))), (((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_p(f6(X1))) <=> (((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2))) | big_p(f6(X1))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2))) | big_p(f6(X1))) <=> ((~big_p(a)) | big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))), (((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_p(f6(X1))) <=> ((~big_p(a)) | big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))))),
% 0.67/0.84 inference(bind,[status(th)],[])).
% 0.67/0.84 tff(903,plain,
% 0.67/0.84 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_p(f6(X1))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.67/0.84 inference(quant_intro,[status(thm)],[902])).
% 0.67/0.84 tff(904,axiom,(![X2: $i, X7: $i, X8: $i, X1: $i] : ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_p(f6(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_22')).
% 0.67/0.84 tff(905,plain,
% 0.67/0.84 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.67/0.84 inference(modus_ponens,[status(thm)],[904, 903])).
% 0.67/0.84 tff(906,plain,
% 0.67/0.84 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.67/0.84 inference(modus_ponens,[status(thm)],[905, 901])).
% 0.67/0.84 tff(907,plain,(
% 0.67/0.84 ![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.67/0.84 inference(skolemize,[status(sab)],[906])).
% 0.67/0.84 tff(908,plain,
% 0.67/0.84 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.67/0.84 inference(modus_ponens,[status(thm)],[907, 900])).
% 0.67/0.84 tff(909,plain,
% 0.67/0.84 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f6(c4)) | big_p(f2(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f6(c4)) | big_p(f2(c4)))),
% 0.67/0.84 inference(rewrite,[status(thm)],[])).
% 0.67/0.84 tff(910,plain,
% 0.67/0.84 (((~big_p(a)) | big_p(f6(c4)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c3))) <=> ((~big_p(a)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f6(c4)) | big_p(f2(c4)))),
% 0.67/0.84 inference(rewrite,[status(thm)],[])).
% 0.67/0.84 tff(911,plain,
% 0.67/0.84 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_p(f6(c4)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c3)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f6(c4)) | big_p(f2(c4))))),
% 0.67/0.84 inference(monotonicity,[status(thm)],[910])).
% 0.67/0.84 tff(912,plain,
% 0.67/0.84 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_p(f6(c4)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c3)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f6(c4)) | big_p(f2(c4)))),
% 0.67/0.84 inference(transitivity,[status(thm)],[911, 909])).
% 0.67/0.84 tff(913,plain,
% 0.67/0.84 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_p(f6(c4)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c3)))),
% 0.67/0.84 inference(quant_inst,[status(thm)],[])).
% 0.67/0.84 tff(914,plain,
% 0.67/0.84 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_p(f6(c4)) | big_p(f2(c4))),
% 0.67/0.84 inference(modus_ponens,[status(thm)],[913, 912])).
% 0.67/0.84 tff(915,plain,
% 0.67/0.84 (big_p(f6(c4)) | big_p(f2(c4))),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[914, 908, 11, 719, 712])).
% 0.67/0.84 tff(916,plain,
% 0.67/0.84 (big_p(f6(c4))),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[915, 898])).
% 0.67/0.84 tff(917,plain,
% 0.67/0.84 (^[X2: $i, X7: $i, X8: $i, X1: $i] : refl(((~big_p(a)) | big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> ((~big_p(a)) | big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2))))),
% 0.67/0.84 inference(bind,[status(th)],[])).
% 0.67/0.84 tff(918,plain,
% 0.67/0.84 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.67/0.84 inference(quant_intro,[status(thm)],[917])).
% 0.67/0.84 tff(919,plain,
% 0.67/0.84 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.67/0.84 inference(rewrite,[status(thm)],[])).
% 0.67/0.84 tff(920,plain,
% 0.67/0.84 (^[X2: $i, X7: $i, X8: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_p(f2(X7))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_p(f2(X7))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) <=> (((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | (~big_p(a))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) <=> (((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | (~big_p(X2))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | (~big_p(X2))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_p(X2)))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_p(X2))))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> (((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_p(X2))) | (~big_r(X1, X2))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2))))), (((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(X1, f5(X1))) <=> (((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2))) | big_r(X1, f5(X1))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2))) | big_r(X1, f5(X1))) <=> ((~big_p(a)) | big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))), (((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(X1, f5(X1))) <=> ((~big_p(a)) | big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))))),
% 0.67/0.85 inference(bind,[status(th)],[])).
% 0.67/0.85 tff(921,plain,
% 0.67/0.85 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(X1, f5(X1))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.67/0.85 inference(quant_intro,[status(thm)],[920])).
% 0.67/0.85 tff(922,axiom,(![X2: $i, X7: $i, X8: $i, X1: $i] : ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(X1, f5(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_23')).
% 0.67/0.85 tff(923,plain,
% 0.67/0.85 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[922, 921])).
% 0.67/0.85 tff(924,plain,
% 0.67/0.85 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[923, 919])).
% 0.67/0.85 tff(925,plain,(
% 0.67/0.85 ![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.67/0.85 inference(skolemize,[status(sab)],[924])).
% 0.67/0.85 tff(926,plain,
% 0.67/0.85 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[925, 918])).
% 0.67/0.85 tff(927,plain,
% 0.67/0.85 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f5(c4)) | big_p(f2(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f5(c4)) | big_p(f2(c4)))),
% 0.67/0.85 inference(rewrite,[status(thm)],[])).
% 0.67/0.85 tff(928,plain,
% 0.67/0.85 (((~big_p(a)) | big_r(c4, f5(c4)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c3))) <=> ((~big_p(a)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f5(c4)) | big_p(f2(c4)))),
% 0.67/0.85 inference(rewrite,[status(thm)],[])).
% 0.67/0.85 tff(929,plain,
% 0.67/0.85 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_r(c4, f5(c4)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c3)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f5(c4)) | big_p(f2(c4))))),
% 0.67/0.85 inference(monotonicity,[status(thm)],[928])).
% 0.67/0.85 tff(930,plain,
% 0.67/0.85 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_r(c4, f5(c4)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c3)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f5(c4)) | big_p(f2(c4)))),
% 0.67/0.85 inference(transitivity,[status(thm)],[929, 927])).
% 0.67/0.85 tff(931,plain,
% 0.67/0.85 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_r(c4, f5(c4)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c3)))),
% 0.67/0.85 inference(quant_inst,[status(thm)],[])).
% 0.67/0.85 tff(932,plain,
% 0.67/0.85 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(c4, f5(c4)) | big_p(f2(c4))),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[931, 930])).
% 0.67/0.85 tff(933,plain,
% 0.67/0.85 (big_r(c4, f5(c4)) | big_p(f2(c4))),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[932, 926, 11, 719, 712])).
% 0.67/0.85 tff(934,plain,
% 0.67/0.85 (big_r(c4, f5(c4))),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[933, 898])).
% 0.67/0.85 tff(935,plain,
% 0.67/0.85 (^[X2: $i, X7: $i, X8: $i, X1: $i] : refl(((~big_p(a)) | big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> ((~big_p(a)) | big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2))))),
% 0.67/0.85 inference(bind,[status(th)],[])).
% 0.67/0.85 tff(936,plain,
% 0.67/0.85 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.67/0.85 inference(quant_intro,[status(thm)],[935])).
% 0.67/0.85 tff(937,plain,
% 0.67/0.85 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.67/0.85 inference(rewrite,[status(thm)],[])).
% 0.67/0.85 tff(938,plain,
% 0.67/0.85 (^[X2: $i, X7: $i, X8: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) <=> ((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) <=> (((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_p(f2(X7))))), rewrite((((~big_p(a)) | (~big_r(X7, X8)) | (~big_p(X8))) | big_p(f2(X7))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))), (((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) <=> (((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | (~big_p(a))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))), ((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) <=> (((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | (~big_p(X2))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8))) | (~big_p(X2))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_p(X2)))), (((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_p(X2))))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> (((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_p(X2))) | (~big_r(X1, X2))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))), ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2))))), (((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(f5(X1), f6(X1))) <=> (((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2))) | big_r(f5(X1), f6(X1))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2))) | big_r(f5(X1), f6(X1))) <=> ((~big_p(a)) | big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))), (((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(f5(X1), f6(X1))) <=> ((~big_p(a)) | big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))))),
% 0.67/0.85 inference(bind,[status(th)],[])).
% 0.67/0.85 tff(939,plain,
% 0.67/0.85 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(f5(X1), f6(X1))) <=> ![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.67/0.85 inference(quant_intro,[status(thm)],[938])).
% 0.67/0.85 tff(940,axiom,(![X2: $i, X7: $i, X8: $i, X1: $i] : ((((((((~big_p(a)) | (~big_p(X8))) | (~big_r(X7, X8))) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(f5(X1), f6(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_24')).
% 0.67/0.85 tff(941,plain,
% 0.67/0.85 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[940, 939])).
% 0.67/0.85 tff(942,plain,
% 0.67/0.85 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[941, 937])).
% 0.67/0.85 tff(943,plain,(
% 0.67/0.85 ![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.67/0.85 inference(skolemize,[status(sab)],[942])).
% 0.67/0.85 tff(944,plain,
% 0.67/0.85 (![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[943, 936])).
% 0.67/0.85 tff(945,plain,
% 0.67/0.85 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f5(c4), f6(c4)) | big_p(f2(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f5(c4), f6(c4)) | big_p(f2(c4)))),
% 0.67/0.85 inference(rewrite,[status(thm)],[])).
% 0.67/0.85 tff(946,plain,
% 0.67/0.85 (((~big_p(a)) | big_r(f5(c4), f6(c4)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c3))) <=> ((~big_p(a)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f5(c4), f6(c4)) | big_p(f2(c4)))),
% 0.67/0.85 inference(rewrite,[status(thm)],[])).
% 0.67/0.85 tff(947,plain,
% 0.67/0.85 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_r(f5(c4), f6(c4)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c3)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f5(c4), f6(c4)) | big_p(f2(c4))))),
% 0.67/0.85 inference(monotonicity,[status(thm)],[946])).
% 0.67/0.85 tff(948,plain,
% 0.67/0.85 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_r(f5(c4), f6(c4)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c3)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f5(c4), f6(c4)) | big_p(f2(c4)))),
% 0.67/0.85 inference(transitivity,[status(thm)],[947, 945])).
% 0.67/0.85 tff(949,plain,
% 0.67/0.85 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_r(f5(c4), f6(c4)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c3)))),
% 0.67/0.85 inference(quant_inst,[status(thm)],[])).
% 0.67/0.85 tff(950,plain,
% 0.67/0.85 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | (~big_p(c3)) | (~big_r(c4, c3)) | big_r(f5(c4), f6(c4)) | big_p(f2(c4))),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[949, 948])).
% 0.67/0.85 tff(951,plain,
% 0.67/0.85 (big_r(f5(c4), f6(c4)) | big_p(f2(c4))),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[950, 944, 11, 719, 712])).
% 0.67/0.85 tff(952,plain,
% 0.67/0.85 (big_r(f5(c4), f6(c4))),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[951, 898])).
% 0.67/0.85 tff(953,plain,
% 0.67/0.85 ($false),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[646, 304, 570, 510, 777, 952, 934, 916])).
% 0.67/0.85 tff(954,plain,(big_p(c2)), inference(lemma,lemma(discharge,[]))).
% 0.67/0.85 tff(955,plain,
% 0.67/0.85 (((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | ((~big_p(c2)) | big_r(c2, c1) | (~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4))))) <=> ((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | (~big_p(c2)) | big_r(c2, c1) | (~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4))))),
% 0.67/0.85 inference(rewrite,[status(thm)],[])).
% 0.67/0.85 tff(956,plain,
% 0.67/0.85 (((~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_p(c2)) | (~big_p(f4(c4))) | big_r(c2, c1) | (~big_r(f3(c4), f4(c4))) | (~big_r(c4, f3(c4))) | (~big_r(c4, f3(c4)))) <=> ((~big_p(c2)) | big_r(c2, c1) | (~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4))))),
% 0.67/0.85 inference(rewrite,[status(thm)],[])).
% 0.67/0.85 tff(957,plain,
% 0.67/0.85 (((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | ((~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_p(c2)) | (~big_p(f4(c4))) | big_r(c2, c1) | (~big_r(f3(c4), f4(c4))) | (~big_r(c4, f3(c4))) | (~big_r(c4, f3(c4))))) <=> ((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | ((~big_p(c2)) | big_r(c2, c1) | (~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4)))))),
% 0.67/0.85 inference(monotonicity,[status(thm)],[956])).
% 0.67/0.85 tff(958,plain,
% 0.67/0.85 (((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | ((~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_p(c2)) | (~big_p(f4(c4))) | big_r(c2, c1) | (~big_r(f3(c4), f4(c4))) | (~big_r(c4, f3(c4))) | (~big_r(c4, f3(c4))))) <=> ((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | (~big_p(c2)) | big_r(c2, c1) | (~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4))))),
% 0.67/0.85 inference(transitivity,[status(thm)],[957, 955])).
% 0.67/0.85 tff(959,plain,
% 0.67/0.85 ((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | ((~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_p(c2)) | (~big_p(f4(c4))) | big_r(c2, c1) | (~big_r(f3(c4), f4(c4))) | (~big_r(c4, f3(c4))) | (~big_r(c4, f3(c4))))),
% 0.67/0.85 inference(quant_inst,[status(thm)],[])).
% 0.67/0.85 tff(960,plain,
% 0.67/0.85 ((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | (~big_p(c2)) | big_r(c2, c1) | (~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4)))),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[959, 958])).
% 0.67/0.85 tff(961,plain,
% 0.67/0.85 (~big_p(f4(c4))),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[960, 954, 65, 93, 83, 46])).
% 0.67/0.85 tff(962,plain,
% 0.67/0.85 ($false),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[27, 21, 11, 4, 3, 961])).
% 0.67/0.85 tff(963,plain,(big_r(c4, f1(c4)) | big_p(c4) | big_r(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 0.67/0.85 tff(964,plain,
% 0.67/0.85 (big_r(c4, f1(c4))),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[963, 65, 4])).
% 0.67/0.85 tff(965,plain,
% 0.67/0.85 (big_r(f1(c4), f2(c4))),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[204, 47])).
% 0.67/0.85 tff(966,plain,
% 0.67/0.85 (((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | ((~big_p(c2)) | big_r(c2, c1) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))))) <=> ((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | (~big_p(c2)) | big_r(c2, c1) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))))),
% 0.67/0.85 inference(rewrite,[status(thm)],[])).
% 0.67/0.85 tff(967,plain,
% 0.67/0.85 (((~big_r(f1(c4), f2(c4))) | (~big_p(f2(c4))) | (~big_p(c2)) | (~big_p(f2(c4))) | big_r(c2, c1) | (~big_r(f1(c4), f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(c4, f1(c4)))) <=> ((~big_p(c2)) | big_r(c2, c1) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))))),
% 0.67/0.85 inference(rewrite,[status(thm)],[])).
% 0.67/0.85 tff(968,plain,
% 0.67/0.85 (((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | ((~big_r(f1(c4), f2(c4))) | (~big_p(f2(c4))) | (~big_p(c2)) | (~big_p(f2(c4))) | big_r(c2, c1) | (~big_r(f1(c4), f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(c4, f1(c4))))) <=> ((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | ((~big_p(c2)) | big_r(c2, c1) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4)))))),
% 0.67/0.85 inference(monotonicity,[status(thm)],[967])).
% 0.67/0.85 tff(969,plain,
% 0.67/0.85 (((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | ((~big_r(f1(c4), f2(c4))) | (~big_p(f2(c4))) | (~big_p(c2)) | (~big_p(f2(c4))) | big_r(c2, c1) | (~big_r(f1(c4), f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(c4, f1(c4))))) <=> ((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | (~big_p(c2)) | big_r(c2, c1) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))))),
% 0.67/0.85 inference(transitivity,[status(thm)],[968, 966])).
% 0.67/0.85 tff(970,plain,
% 0.67/0.85 ((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | ((~big_r(f1(c4), f2(c4))) | (~big_p(f2(c4))) | (~big_p(c2)) | (~big_p(f2(c4))) | big_r(c2, c1) | (~big_r(f1(c4), f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(c4, f1(c4))))),
% 0.67/0.85 inference(quant_inst,[status(thm)],[])).
% 0.67/0.85 tff(971,plain,
% 0.67/0.85 ((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | (~big_p(c2)) | big_r(c2, c1) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4)))),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[970, 969])).
% 0.67/0.85 tff(972,plain,
% 0.67/0.85 (~big_p(f2(c4))),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[971, 954, 65, 93, 965, 964])).
% 0.67/0.85 tff(973,plain,
% 0.67/0.85 ($false),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[63, 57, 11, 4, 47, 972])).
% 0.67/0.85 tff(974,plain,(big_r(c4, f3(c4)) | big_p(c4) | big_r(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 0.67/0.85 tff(975,plain,
% 0.67/0.85 (big_r(c4, f3(c4))),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[974, 65, 4])).
% 0.67/0.85 tff(976,plain,
% 0.67/0.85 (~big_p(f4(c4))),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[960, 954, 65, 93, 975, 223])).
% 0.67/0.85 tff(977,plain,
% 0.67/0.85 ($false),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[345, 189, 11, 4, 179, 976])).
% 0.67/0.85 tff(978,plain,(big_r(f1(c4), f2(c4)) | big_p(c4) | big_r(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 0.67/0.85 tff(979,plain,
% 0.67/0.85 (big_r(f1(c4), f2(c4))),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[978, 65, 4])).
% 0.67/0.85 tff(980,plain,
% 0.67/0.85 (~big_p(f2(c4))),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[971, 954, 65, 93, 979, 964])).
% 0.67/0.85 tff(981,plain,
% 0.67/0.85 (big_r(f3(c4), f4(c4))),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[402, 239, 11, 4, 980])).
% 0.67/0.85 tff(982,plain,
% 0.67/0.85 (~big_p(f4(c4))),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[960, 954, 65, 93, 975, 981])).
% 0.67/0.85 tff(983,plain,
% 0.67/0.85 ($false),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[427, 149, 11, 4, 980, 982])).
% 0.67/0.85 tff(984,plain,(big_r(c2, c1) | big_p(c4)), inference(lemma,lemma(discharge,[]))).
% 0.67/0.85 tff(985,plain,
% 0.67/0.85 (big_r(c2, c1)),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[984, 4])).
% 0.67/0.85 tff(986,plain,
% 0.67/0.85 (big_r(c4, f1(c4))),
% 0.67/0.85 inference(unit_resolution,[status(thm)],[82, 47])).
% 0.67/0.85 tff(987,plain,
% 0.67/0.85 (^[X6: $i, X4: $i, X3: $i, X5: $i] : refl((big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4))) <=> (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4))))),
% 0.67/0.85 inference(bind,[status(th)],[])).
% 0.67/0.85 tff(988,plain,
% 0.67/0.85 (![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4))) <=> ![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))),
% 0.67/0.85 inference(quant_intro,[status(thm)],[987])).
% 0.67/0.85 tff(989,plain,
% 0.67/0.85 (![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4))) <=> ![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))),
% 0.67/0.85 inference(rewrite,[status(thm)],[])).
% 0.67/0.85 tff(990,plain,
% 0.67/0.85 (^[X6: $i, X4: $i, X3: $i, X5: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~big_p(c2)) | big_p(c1)) <=> (big_p(c1) | (~big_p(c2)))), ((((~big_p(c2)) | big_p(c1)) | (~big_p(X3))) <=> ((big_p(c1) | (~big_p(c2))) | (~big_p(X3))))), rewrite(((big_p(c1) | (~big_p(c2))) | (~big_p(X3))) <=> (big_p(c1) | (~big_p(X3)) | (~big_p(c2)))), ((((~big_p(c2)) | big_p(c1)) | (~big_p(X3))) <=> (big_p(c1) | (~big_p(X3)) | (~big_p(c2))))), (((((~big_p(c2)) | big_p(c1)) | (~big_p(X3))) | (~big_r(c4, X4))) <=> ((big_p(c1) | (~big_p(X3)) | (~big_p(c2))) | (~big_r(c4, X4))))), rewrite(((big_p(c1) | (~big_p(X3)) | (~big_p(c2))) | (~big_r(c4, X4))) <=> (big_p(c1) | (~big_p(X3)) | (~big_p(c2)) | (~big_r(c4, X4)))), (((((~big_p(c2)) | big_p(c1)) | (~big_p(X3))) | (~big_r(c4, X4))) <=> (big_p(c1) | (~big_p(X3)) | (~big_p(c2)) | (~big_r(c4, X4))))), ((((((~big_p(c2)) | big_p(c1)) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) <=> ((big_p(c1) | (~big_p(X3)) | (~big_p(c2)) | (~big_r(c4, X4))) | (~big_r(X4, X3))))), rewrite(((big_p(c1) | (~big_p(X3)) | (~big_p(c2)) | (~big_r(c4, X4))) | (~big_r(X4, X3))) <=> (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_r(c4, X4)))), ((((((~big_p(c2)) | big_p(c1)) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) <=> (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_r(c4, X4))))), (((((((~big_p(c2)) | big_p(c1)) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) | (~big_p(X5))) <=> ((big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_r(c4, X4))) | (~big_p(X5))))), rewrite(((big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_r(c4, X4))) | (~big_p(X5))) <=> (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(c4, X4)))), (((((((~big_p(c2)) | big_p(c1)) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) | (~big_p(X5))) <=> (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(c4, X4))))), ((((((((~big_p(c2)) | big_p(c1)) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) | (~big_p(X5))) | (~big_r(c4, X6))) <=> ((big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(c4, X4))) | (~big_r(c4, X6))))), rewrite(((big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(c4, X4))) | (~big_r(c4, X6))) <=> (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))), ((((((((~big_p(c2)) | big_p(c1)) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) | (~big_p(X5))) | (~big_r(c4, X6))) <=> (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4))))), (((((((((~big_p(c2)) | big_p(c1)) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) | (~big_p(X5))) | (~big_r(c4, X6))) | (~big_r(X6, X5))) <=> ((big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4))) | (~big_r(X6, X5))))), rewrite(((big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4))) | (~big_r(X6, X5))) <=> (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))), (((((((((~big_p(c2)) | big_p(c1)) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) | (~big_p(X5))) | (~big_r(c4, X6))) | (~big_r(X6, X5))) <=> (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))))),
% 0.67/0.85 inference(bind,[status(th)],[])).
% 0.67/0.85 tff(991,plain,
% 0.67/0.85 (![X6: $i, X4: $i, X3: $i, X5: $i] : ((((((((~big_p(c2)) | big_p(c1)) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) | (~big_p(X5))) | (~big_r(c4, X6))) | (~big_r(X6, X5))) <=> ![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))),
% 0.67/0.85 inference(quant_intro,[status(thm)],[990])).
% 0.67/0.85 tff(992,axiom,(![X6: $i, X4: $i, X3: $i, X5: $i] : ((((((((~big_p(c2)) | big_p(c1)) | (~big_p(X3))) | (~big_r(c4, X4))) | (~big_r(X4, X3))) | (~big_p(X5))) | (~big_r(c4, X6))) | (~big_r(X6, X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_60')).
% 0.67/0.85 tff(993,plain,
% 0.67/0.85 (![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[992, 991])).
% 0.67/0.85 tff(994,plain,
% 0.67/0.85 (![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))),
% 0.67/0.85 inference(modus_ponens,[status(thm)],[993, 989])).
% 0.67/0.86 tff(995,plain,(
% 0.67/0.86 ![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))),
% 0.67/0.86 inference(skolemize,[status(sab)],[994])).
% 0.67/0.86 tff(996,plain,
% 0.67/0.86 (![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[995, 988])).
% 0.67/0.86 tff(997,plain,
% 0.67/0.86 (((~![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | (big_p(c1) | (~big_p(c2)) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))))) <=> ((~![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | big_p(c1) | (~big_p(c2)) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(998,plain,
% 0.67/0.86 ((big_p(c1) | (~big_r(f1(c4), f2(c4))) | (~big_p(f2(c4))) | (~big_p(c2)) | (~big_p(f2(c4))) | (~big_r(f1(c4), f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(c4, f1(c4)))) <=> (big_p(c1) | (~big_p(c2)) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(999,plain,
% 0.67/0.86 (((~![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | (big_p(c1) | (~big_r(f1(c4), f2(c4))) | (~big_p(f2(c4))) | (~big_p(c2)) | (~big_p(f2(c4))) | (~big_r(f1(c4), f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(c4, f1(c4))))) <=> ((~![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | (big_p(c1) | (~big_p(c2)) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4)))))),
% 0.67/0.86 inference(monotonicity,[status(thm)],[998])).
% 0.67/0.86 tff(1000,plain,
% 0.67/0.86 (((~![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | (big_p(c1) | (~big_r(f1(c4), f2(c4))) | (~big_p(f2(c4))) | (~big_p(c2)) | (~big_p(f2(c4))) | (~big_r(f1(c4), f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(c4, f1(c4))))) <=> ((~![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | big_p(c1) | (~big_p(c2)) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))))),
% 0.67/0.86 inference(transitivity,[status(thm)],[999, 997])).
% 0.67/0.86 tff(1001,plain,
% 0.67/0.86 ((~![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | (big_p(c1) | (~big_r(f1(c4), f2(c4))) | (~big_p(f2(c4))) | (~big_p(c2)) | (~big_p(f2(c4))) | (~big_r(f1(c4), f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(c4, f1(c4))))),
% 0.67/0.86 inference(quant_inst,[status(thm)],[])).
% 0.67/0.86 tff(1002,plain,
% 0.67/0.86 ((~![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | big_p(c1) | (~big_p(c2)) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4)))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1001, 1000])).
% 0.67/0.86 tff(1003,plain,
% 0.67/0.86 (big_p(c1) | (~big_p(f2(c4)))),
% 0.67/0.86 inference(unit_resolution,[status(thm)],[1002, 954, 996, 965, 986])).
% 0.67/0.86 tff(1004,plain,
% 0.67/0.86 (big_p(c1)),
% 0.67/0.86 inference(unit_resolution,[status(thm)],[1003, 64])).
% 0.67/0.86 tff(1005,plain,
% 0.67/0.86 (((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c4) | big_r(f1(c2), f2(c2)) | (~big_r(c2, c1)) | big_r(c4, f3(c4)) | (~big_p(c1)))) <=> ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c4) | big_r(f1(c2), f2(c2)) | (~big_r(c2, c1)) | big_r(c4, f3(c4)) | (~big_p(c1)))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(1006,plain,
% 0.67/0.86 (((~big_p(a)) | big_p(c4) | big_r(c4, f3(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c2), f2(c2))) <=> ((~big_p(a)) | big_p(c4) | big_r(f1(c2), f2(c2)) | (~big_r(c2, c1)) | big_r(c4, f3(c4)) | (~big_p(c1)))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(1007,plain,
% 0.67/0.86 (((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c4) | big_r(c4, f3(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c2), f2(c2)))) <=> ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c4) | big_r(f1(c2), f2(c2)) | (~big_r(c2, c1)) | big_r(c4, f3(c4)) | (~big_p(c1))))),
% 0.67/0.86 inference(monotonicity,[status(thm)],[1006])).
% 0.67/0.86 tff(1008,plain,
% 0.67/0.86 (((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c4) | big_r(c4, f3(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c2), f2(c2)))) <=> ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c4) | big_r(f1(c2), f2(c2)) | (~big_r(c2, c1)) | big_r(c4, f3(c4)) | (~big_p(c1)))),
% 0.67/0.86 inference(transitivity,[status(thm)],[1007, 1005])).
% 0.67/0.86 tff(1009,plain,
% 0.67/0.86 ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c4) | big_r(c4, f3(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c2), f2(c2)))),
% 0.67/0.86 inference(quant_inst,[status(thm)],[])).
% 0.67/0.86 tff(1010,plain,
% 0.67/0.86 ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c4) | big_r(f1(c2), f2(c2)) | (~big_r(c2, c1)) | big_r(c4, f3(c4)) | (~big_p(c1))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1009, 1008])).
% 0.67/0.86 tff(1011,plain,
% 0.67/0.86 (big_r(f1(c2), f2(c2))),
% 0.67/0.86 inference(unit_resolution,[status(thm)],[1010, 500, 11, 4, 1004, 985, 47])).
% 0.67/0.86 tff(1012,plain,
% 0.67/0.86 (((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | ((~big_p(a)) | big_p(c4) | big_p(f2(c2)) | (~big_r(c2, c1)) | big_r(c4, f3(c4)) | (~big_p(c1)))) <=> ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | (~big_p(a)) | big_p(c4) | big_p(f2(c2)) | (~big_r(c2, c1)) | big_r(c4, f3(c4)) | (~big_p(c1)))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(1013,plain,
% 0.67/0.86 (((~big_p(a)) | big_p(c4) | big_r(c4, f3(c4)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1))) <=> ((~big_p(a)) | big_p(c4) | big_p(f2(c2)) | (~big_r(c2, c1)) | big_r(c4, f3(c4)) | (~big_p(c1)))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(1014,plain,
% 0.67/0.86 (((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | ((~big_p(a)) | big_p(c4) | big_r(c4, f3(c4)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | ((~big_p(a)) | big_p(c4) | big_p(f2(c2)) | (~big_r(c2, c1)) | big_r(c4, f3(c4)) | (~big_p(c1))))),
% 0.67/0.86 inference(monotonicity,[status(thm)],[1013])).
% 0.67/0.86 tff(1015,plain,
% 0.67/0.86 (((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | ((~big_p(a)) | big_p(c4) | big_r(c4, f3(c4)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | (~big_p(a)) | big_p(c4) | big_p(f2(c2)) | (~big_r(c2, c1)) | big_r(c4, f3(c4)) | (~big_p(c1)))),
% 0.67/0.86 inference(transitivity,[status(thm)],[1014, 1012])).
% 0.67/0.86 tff(1016,plain,
% 0.67/0.86 ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | ((~big_p(a)) | big_p(c4) | big_r(c4, f3(c4)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 0.67/0.86 inference(quant_inst,[status(thm)],[])).
% 0.67/0.86 tff(1017,plain,
% 0.67/0.86 ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | (~big_p(a)) | big_p(c4) | big_p(f2(c2)) | (~big_r(c2, c1)) | big_r(c4, f3(c4)) | (~big_p(c1))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1016, 1015])).
% 0.67/0.86 tff(1018,plain,
% 0.67/0.86 (big_p(f2(c2))),
% 0.67/0.86 inference(unit_resolution,[status(thm)],[1017, 466, 11, 4, 1004, 985, 47])).
% 0.67/0.86 tff(1019,plain,
% 0.67/0.86 (((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c4) | big_r(c2, f1(c2)) | (~big_r(c2, c1)) | big_r(c4, f3(c4)) | (~big_p(c1)))) <=> ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | (~big_p(a)) | big_p(c4) | big_r(c2, f1(c2)) | (~big_r(c2, c1)) | big_r(c4, f3(c4)) | (~big_p(c1)))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(1020,plain,
% 0.67/0.86 (((~big_p(a)) | big_p(c4) | big_r(c4, f3(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f1(c2))) <=> ((~big_p(a)) | big_p(c4) | big_r(c2, f1(c2)) | (~big_r(c2, c1)) | big_r(c4, f3(c4)) | (~big_p(c1)))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(1021,plain,
% 0.67/0.86 (((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c4) | big_r(c4, f3(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f1(c2)))) <=> ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c4) | big_r(c2, f1(c2)) | (~big_r(c2, c1)) | big_r(c4, f3(c4)) | (~big_p(c1))))),
% 0.67/0.86 inference(monotonicity,[status(thm)],[1020])).
% 0.67/0.86 tff(1022,plain,
% 0.67/0.86 (((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c4) | big_r(c4, f3(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f1(c2)))) <=> ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | (~big_p(a)) | big_p(c4) | big_r(c2, f1(c2)) | (~big_r(c2, c1)) | big_r(c4, f3(c4)) | (~big_p(c1)))),
% 0.67/0.86 inference(transitivity,[status(thm)],[1021, 1019])).
% 0.67/0.86 tff(1023,plain,
% 0.67/0.86 ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c4) | big_r(c4, f3(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f1(c2)))),
% 0.67/0.86 inference(quant_inst,[status(thm)],[])).
% 0.67/0.86 tff(1024,plain,
% 0.67/0.86 ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(X1, f3(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | (~big_p(a)) | big_p(c4) | big_r(c2, f1(c2)) | (~big_r(c2, c1)) | big_r(c4, f3(c4)) | (~big_p(c1))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1023, 1022])).
% 0.67/0.86 tff(1025,plain,
% 0.67/0.86 (big_r(c2, f1(c2))),
% 0.67/0.86 inference(unit_resolution,[status(thm)],[1024, 483, 11, 4, 1004, 985, 47])).
% 0.67/0.86 tff(1026,plain,
% 0.67/0.86 ($false),
% 0.67/0.86 inference(unit_resolution,[status(thm)],[334, 304, 1025, 965, 986, 1018, 1011, 64])).
% 0.67/0.86 tff(1027,plain,(big_r(c4, f3(c4)) | big_p(c4)), inference(lemma,lemma(discharge,[]))).
% 0.67/0.86 tff(1028,plain,
% 0.67/0.86 (big_r(c4, f3(c4))),
% 0.67/0.86 inference(unit_resolution,[status(thm)],[1027, 4])).
% 0.67/0.86 tff(1029,plain,
% 0.67/0.86 (((~![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | (big_p(c1) | (~big_p(c2)) | (~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4))))) <=> ((~![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | big_p(c1) | (~big_p(c2)) | (~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4))))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(1030,plain,
% 0.67/0.86 ((big_p(c1) | (~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_p(c2)) | (~big_p(f4(c4))) | (~big_r(f3(c4), f4(c4))) | (~big_r(c4, f3(c4))) | (~big_r(c4, f3(c4)))) <=> (big_p(c1) | (~big_p(c2)) | (~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4))))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(1031,plain,
% 0.67/0.86 (((~![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | (big_p(c1) | (~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_p(c2)) | (~big_p(f4(c4))) | (~big_r(f3(c4), f4(c4))) | (~big_r(c4, f3(c4))) | (~big_r(c4, f3(c4))))) <=> ((~![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | (big_p(c1) | (~big_p(c2)) | (~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4)))))),
% 0.67/0.86 inference(monotonicity,[status(thm)],[1030])).
% 0.67/0.86 tff(1032,plain,
% 0.67/0.86 (((~![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | (big_p(c1) | (~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_p(c2)) | (~big_p(f4(c4))) | (~big_r(f3(c4), f4(c4))) | (~big_r(c4, f3(c4))) | (~big_r(c4, f3(c4))))) <=> ((~![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | big_p(c1) | (~big_p(c2)) | (~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4))))),
% 0.67/0.86 inference(transitivity,[status(thm)],[1031, 1029])).
% 0.67/0.86 tff(1033,plain,
% 0.67/0.86 ((~![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | (big_p(c1) | (~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_p(c2)) | (~big_p(f4(c4))) | (~big_r(f3(c4), f4(c4))) | (~big_r(c4, f3(c4))) | (~big_r(c4, f3(c4))))),
% 0.67/0.86 inference(quant_inst,[status(thm)],[])).
% 0.67/0.86 tff(1034,plain,
% 0.67/0.86 ((~![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | big_p(c1) | (~big_p(c2)) | (~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4)))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1033, 1032])).
% 0.67/0.86 tff(1035,plain,
% 0.67/0.86 (big_p(c1) | (~big_p(f4(c4)))),
% 0.67/0.86 inference(unit_resolution,[status(thm)],[1034, 954, 996, 1028, 46])).
% 0.67/0.86 tff(1036,plain,
% 0.67/0.86 (big_p(c1)),
% 0.67/0.86 inference(unit_resolution,[status(thm)],[1035, 28])).
% 0.67/0.86 tff(1037,plain,
% 0.67/0.86 (((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_p(c4) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c4, f1(c4)))) <=> ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | big_p(c4) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c4, f1(c4)))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(1038,plain,
% 0.67/0.86 (((~big_p(a)) | big_p(c4) | big_r(c4, f1(c4)) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1))) <=> ((~big_p(a)) | big_p(c4) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c4, f1(c4)))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(1039,plain,
% 0.67/0.86 (((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_p(c4) | big_r(c4, f1(c4)) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_p(c4) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c4, f1(c4))))),
% 0.67/0.86 inference(monotonicity,[status(thm)],[1038])).
% 0.67/0.86 tff(1040,plain,
% 0.67/0.86 (((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_p(c4) | big_r(c4, f1(c4)) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | big_p(c4) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c4, f1(c4)))),
% 0.67/0.86 inference(transitivity,[status(thm)],[1039, 1037])).
% 0.67/0.86 tff(1041,plain,
% 0.67/0.86 ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_p(c4) | big_r(c4, f1(c4)) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 0.67/0.86 inference(quant_inst,[status(thm)],[])).
% 0.67/0.86 tff(1042,plain,
% 0.67/0.86 ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | big_p(c4) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c4, f1(c4))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1041, 1040])).
% 0.67/0.86 tff(1043,plain,
% 0.67/0.86 (big_p(f6(c2)) | (~big_p(c1)) | big_r(c4, f1(c4))),
% 0.67/0.86 inference(unit_resolution,[status(thm)],[1042, 599, 11, 4, 985])).
% 0.67/0.86 tff(1044,plain,
% 0.67/0.86 (big_p(f6(c2))),
% 0.67/0.86 inference(unit_resolution,[status(thm)],[1043, 1036, 3])).
% 0.67/0.86 tff(1045,plain,
% 0.67/0.86 (((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))) | ((~big_p(a)) | big_p(c4) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c4, f1(c4)))) <=> ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))) | (~big_p(a)) | big_p(c4) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c4, f1(c4)))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(1046,plain,
% 0.67/0.86 (((~big_p(a)) | big_p(c4) | big_r(c4, f1(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f5(c2))) <=> ((~big_p(a)) | big_p(c4) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c4, f1(c4)))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(1047,plain,
% 0.67/0.86 (((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))) | ((~big_p(a)) | big_p(c4) | big_r(c4, f1(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f5(c2)))) <=> ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))) | ((~big_p(a)) | big_p(c4) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c4, f1(c4))))),
% 0.67/0.86 inference(monotonicity,[status(thm)],[1046])).
% 0.67/0.86 tff(1048,plain,
% 0.67/0.86 (((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))) | ((~big_p(a)) | big_p(c4) | big_r(c4, f1(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f5(c2)))) <=> ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))) | (~big_p(a)) | big_p(c4) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c4, f1(c4)))),
% 0.67/0.86 inference(transitivity,[status(thm)],[1047, 1045])).
% 0.67/0.86 tff(1049,plain,
% 0.67/0.86 ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))) | ((~big_p(a)) | big_p(c4) | big_r(c4, f1(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f5(c2)))),
% 0.67/0.86 inference(quant_inst,[status(thm)],[])).
% 0.67/0.86 tff(1050,plain,
% 0.67/0.86 ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))) | (~big_p(a)) | big_p(c4) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c4, f1(c4))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1049, 1048])).
% 0.67/0.86 tff(1051,plain,
% 0.67/0.86 (big_r(c2, f5(c2)) | (~big_p(c1)) | big_r(c4, f1(c4))),
% 0.67/0.86 inference(unit_resolution,[status(thm)],[1050, 616, 11, 4, 985])).
% 0.67/0.86 tff(1052,plain,
% 0.67/0.86 (big_r(c2, f5(c2))),
% 0.67/0.86 inference(unit_resolution,[status(thm)],[1051, 1036, 3])).
% 0.67/0.86 tff(1053,plain,
% 0.67/0.86 (((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))) | ((~big_p(a)) | big_p(c4) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c4, f1(c4)))) <=> ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))) | (~big_p(a)) | big_p(c4) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c4, f1(c4)))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(1054,plain,
% 0.67/0.86 (((~big_p(a)) | big_p(c4) | big_r(c4, f1(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f5(c2), f6(c2))) <=> ((~big_p(a)) | big_p(c4) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c4, f1(c4)))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(1055,plain,
% 0.67/0.86 (((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))) | ((~big_p(a)) | big_p(c4) | big_r(c4, f1(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f5(c2), f6(c2)))) <=> ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))) | ((~big_p(a)) | big_p(c4) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c4, f1(c4))))),
% 0.67/0.86 inference(monotonicity,[status(thm)],[1054])).
% 0.67/0.86 tff(1056,plain,
% 0.67/0.86 (((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))) | ((~big_p(a)) | big_p(c4) | big_r(c4, f1(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f5(c2), f6(c2)))) <=> ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))) | (~big_p(a)) | big_p(c4) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c4, f1(c4)))),
% 0.67/0.86 inference(transitivity,[status(thm)],[1055, 1053])).
% 0.67/0.86 tff(1057,plain,
% 0.67/0.86 ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))) | ((~big_p(a)) | big_p(c4) | big_r(c4, f1(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f5(c2), f6(c2)))),
% 0.67/0.86 inference(quant_inst,[status(thm)],[])).
% 0.67/0.86 tff(1058,plain,
% 0.67/0.86 ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))) | (~big_p(a)) | big_p(c4) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c4, f1(c4))),
% 0.67/0.86 inference(modus_ponens,[status(thm)],[1057, 1056])).
% 0.67/0.86 tff(1059,plain,
% 0.67/0.86 (big_r(f5(c2), f6(c2)) | (~big_p(c1)) | big_r(c4, f1(c4))),
% 0.67/0.86 inference(unit_resolution,[status(thm)],[1058, 633, 11, 4, 985])).
% 0.67/0.86 tff(1060,plain,
% 0.67/0.86 (big_r(f5(c2), f6(c2))),
% 0.67/0.86 inference(unit_resolution,[status(thm)],[1059, 1036, 3])).
% 0.67/0.86 tff(1061,plain,
% 0.67/0.86 (((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4))) | (~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2))) | (~big_r(c2, f5(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | (~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4))) | (~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2))) | (~big_r(c2, f5(c2))))),
% 0.67/0.86 inference(rewrite,[status(thm)],[])).
% 0.67/0.86 tff(1062,plain,
% 0.67/0.86 (((~big_p(f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4))) | (~big_r(c2, f5(c2))) | (~big_r(f3(c4), f4(c4))) | (~big_r(c4, f3(c4))) | (~big_r(f3(c4), f4(c4))) | (~big_r(f5(c2), f6(c2))) | (~big_p(f6(c2)))) <=> ((~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4))) | (~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2))) | (~big_r(c2, f5(c2))))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(1063,plain,
% 0.67/0.87 (((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4))) | (~big_r(c2, f5(c2))) | (~big_r(f3(c4), f4(c4))) | (~big_r(c4, f3(c4))) | (~big_r(f3(c4), f4(c4))) | (~big_r(f5(c2), f6(c2))) | (~big_p(f6(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4))) | (~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2))) | (~big_r(c2, f5(c2)))))),
% 0.67/0.87 inference(monotonicity,[status(thm)],[1062])).
% 0.67/0.87 tff(1064,plain,
% 0.67/0.87 (((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4))) | (~big_r(c2, f5(c2))) | (~big_r(f3(c4), f4(c4))) | (~big_r(c4, f3(c4))) | (~big_r(f3(c4), f4(c4))) | (~big_r(f5(c2), f6(c2))) | (~big_p(f6(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | (~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4))) | (~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2))) | (~big_r(c2, f5(c2))))),
% 0.67/0.87 inference(transitivity,[status(thm)],[1063, 1061])).
% 0.67/0.87 tff(1065,plain,
% 0.67/0.87 ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4))) | (~big_r(c2, f5(c2))) | (~big_r(f3(c4), f4(c4))) | (~big_r(c4, f3(c4))) | (~big_r(f3(c4), f4(c4))) | (~big_r(f5(c2), f6(c2))) | (~big_p(f6(c2))))),
% 0.67/0.87 inference(quant_inst,[status(thm)],[])).
% 0.67/0.87 tff(1066,plain,
% 0.67/0.87 ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | (~big_r(f3(c4), f4(c4))) | (~big_p(f4(c4))) | (~big_r(c4, f3(c4))) | (~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2))) | (~big_r(c2, f5(c2)))),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[1065, 1064])).
% 0.67/0.87 tff(1067,plain,
% 0.67/0.87 ($false),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[1066, 304, 1028, 46, 1060, 1052, 1044, 28])).
% 0.67/0.87 tff(1068,plain,(big_r(c4, f1(c4)) | big_p(c4)), inference(lemma,lemma(discharge,[]))).
% 0.67/0.87 tff(1069,plain,
% 0.67/0.87 (big_r(c4, f1(c4))),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[1068, 4])).
% 0.67/0.87 tff(1070,plain,
% 0.67/0.87 (big_p(f4(c4))),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[345, 189, 11, 4, 179])).
% 0.67/0.87 tff(1071,plain,
% 0.67/0.87 (big_p(c1) | (~big_p(f4(c4)))),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[1034, 954, 996, 1028, 223])).
% 0.67/0.87 tff(1072,plain,
% 0.67/0.87 (big_p(c1)),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[1071, 1070])).
% 0.67/0.87 tff(1073,plain,
% 0.67/0.87 (((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c4) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c4), f2(c4)))) <=> ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c4) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c4), f2(c4)))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(1074,plain,
% 0.67/0.87 ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c4) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c4), f2(c4)))),
% 0.67/0.87 inference(quant_inst,[status(thm)],[])).
% 0.67/0.87 tff(1075,plain,
% 0.67/0.87 ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c4) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c4), f2(c4))),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[1074, 1073])).
% 0.67/0.87 tff(1076,plain,
% 0.67/0.87 (big_p(f6(c2)) | (~big_p(c1)) | big_r(f1(c4), f2(c4))),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[1075, 663, 11, 4, 985])).
% 0.67/0.87 tff(1077,plain,
% 0.67/0.87 (big_p(f6(c2))),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[1076, 1072, 179])).
% 0.67/0.87 tff(1078,plain,
% 0.67/0.87 (((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c4) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c4), f2(c4)))) <=> ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c4) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c4), f2(c4)))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(1079,plain,
% 0.67/0.87 (((~big_p(a)) | big_p(c4) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f5(c2)) | big_r(f1(c4), f2(c4))) <=> ((~big_p(a)) | big_p(c4) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c4), f2(c4)))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(1080,plain,
% 0.67/0.87 (((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c4) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f5(c2)) | big_r(f1(c4), f2(c4)))) <=> ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c4) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c4), f2(c4))))),
% 0.67/0.87 inference(monotonicity,[status(thm)],[1079])).
% 0.67/0.87 tff(1081,plain,
% 0.67/0.87 (((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c4) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f5(c2)) | big_r(f1(c4), f2(c4)))) <=> ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c4) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c4), f2(c4)))),
% 0.67/0.87 inference(transitivity,[status(thm)],[1080, 1078])).
% 0.67/0.87 tff(1082,plain,
% 0.67/0.87 ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c4) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f5(c2)) | big_r(f1(c4), f2(c4)))),
% 0.67/0.87 inference(quant_inst,[status(thm)],[])).
% 0.67/0.87 tff(1083,plain,
% 0.67/0.87 ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c4) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c4), f2(c4))),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[1082, 1081])).
% 0.67/0.87 tff(1084,plain,
% 0.67/0.87 (big_r(c2, f5(c2)) | (~big_p(c1)) | big_r(f1(c4), f2(c4))),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[1083, 680, 11, 4, 985])).
% 0.67/0.87 tff(1085,plain,
% 0.67/0.87 (big_r(c2, f5(c2))),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[1084, 1072, 179])).
% 0.67/0.87 tff(1086,plain,
% 0.67/0.87 (((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c4) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c4), f2(c4)))) <=> ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c4) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c4), f2(c4)))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(1087,plain,
% 0.67/0.87 (((~big_p(a)) | big_p(c4) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | big_r(f1(c4), f2(c4))) <=> ((~big_p(a)) | big_p(c4) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c4), f2(c4)))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(1088,plain,
% 0.67/0.87 (((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c4) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | big_r(f1(c4), f2(c4)))) <=> ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c4) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c4), f2(c4))))),
% 0.67/0.87 inference(monotonicity,[status(thm)],[1087])).
% 0.67/0.87 tff(1089,plain,
% 0.67/0.87 (((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c4) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | big_r(f1(c4), f2(c4)))) <=> ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c4) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c4), f2(c4)))),
% 0.67/0.87 inference(transitivity,[status(thm)],[1088, 1086])).
% 0.67/0.87 tff(1090,plain,
% 0.67/0.87 ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c4) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f5(c2), f6(c2)) | big_r(f1(c4), f2(c4)))),
% 0.67/0.87 inference(quant_inst,[status(thm)],[])).
% 0.67/0.87 tff(1091,plain,
% 0.67/0.87 ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c4) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c4), f2(c4))),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[1090, 1089])).
% 0.67/0.87 tff(1092,plain,
% 0.67/0.87 (big_r(f5(c2), f6(c2)) | (~big_p(c1)) | big_r(f1(c4), f2(c4))),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[1091, 697, 11, 4, 985])).
% 0.67/0.87 tff(1093,plain,
% 0.67/0.87 (big_r(f5(c2), f6(c2))),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[1092, 1072, 179])).
% 0.67/0.87 tff(1094,plain,
% 0.67/0.87 ($false),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[1066, 304, 1028, 223, 1093, 1085, 1077, 1070])).
% 0.67/0.87 tff(1095,plain,(big_r(f1(c4), f2(c4)) | big_p(c4)), inference(lemma,lemma(discharge,[]))).
% 0.67/0.87 tff(1096,plain,
% 0.67/0.87 (big_r(f1(c4), f2(c4))),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[1095, 4])).
% 0.67/0.87 tff(1097,plain,
% 0.67/0.87 (big_p(c1) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4)))),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[1002, 954, 996, 1096])).
% 0.67/0.87 tff(1098,plain,
% 0.67/0.87 (~big_p(f2(c4))),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[1097, 2, 1069])).
% 0.67/0.87 tff(1099,assumption,(~big_r(f3(c4), f4(c4))), introduced(assumption)).
% 0.67/0.87 tff(1100,plain,
% 0.67/0.87 (big_p(f2(c4))),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[403, 1099])).
% 0.67/0.87 tff(1101,plain,
% 0.67/0.87 (big_p(c1)),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[1097, 1100, 1069])).
% 0.67/0.87 tff(1102,plain,
% 0.67/0.87 (((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c4) | big_r(f1(c2), f2(c2)) | (~big_r(c2, c1)) | big_r(f3(c4), f4(c4)) | (~big_p(c1)))) <=> ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c4) | big_r(f1(c2), f2(c2)) | (~big_r(c2, c1)) | big_r(f3(c4), f4(c4)) | (~big_p(c1)))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(1103,plain,
% 0.67/0.87 (((~big_p(a)) | big_p(c4) | big_r(f3(c4), f4(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c2), f2(c2))) <=> ((~big_p(a)) | big_p(c4) | big_r(f1(c2), f2(c2)) | (~big_r(c2, c1)) | big_r(f3(c4), f4(c4)) | (~big_p(c1)))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(1104,plain,
% 0.67/0.87 (((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c4) | big_r(f3(c4), f4(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c2), f2(c2)))) <=> ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c4) | big_r(f1(c2), f2(c2)) | (~big_r(c2, c1)) | big_r(f3(c4), f4(c4)) | (~big_p(c1))))),
% 0.67/0.87 inference(monotonicity,[status(thm)],[1103])).
% 0.67/0.87 tff(1105,plain,
% 0.67/0.87 (((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c4) | big_r(f3(c4), f4(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c2), f2(c2)))) <=> ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c4) | big_r(f1(c2), f2(c2)) | (~big_r(c2, c1)) | big_r(f3(c4), f4(c4)) | (~big_p(c1)))),
% 0.67/0.87 inference(transitivity,[status(thm)],[1104, 1102])).
% 0.67/0.87 tff(1106,plain,
% 0.67/0.87 ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(c4) | big_r(f3(c4), f4(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c2), f2(c2)))),
% 0.67/0.87 inference(quant_inst,[status(thm)],[])).
% 0.67/0.87 tff(1107,plain,
% 0.67/0.87 ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(c4) | big_r(f1(c2), f2(c2)) | (~big_r(c2, c1)) | big_r(f3(c4), f4(c4)) | (~big_p(c1))),
% 0.67/0.87 inference(modus_ponens,[status(thm)],[1106, 1105])).
% 0.67/0.87 tff(1108,plain,
% 0.67/0.87 (big_r(f1(c2), f2(c2)) | big_r(f3(c4), f4(c4)) | (~big_p(c1))),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[1107, 560, 11, 4, 985])).
% 0.67/0.87 tff(1109,plain,
% 0.67/0.87 (big_r(f1(c2), f2(c2))),
% 0.67/0.87 inference(unit_resolution,[status(thm)],[1108, 1101, 1099])).
% 0.67/0.87 tff(1110,plain,
% 0.67/0.87 (((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | ((~big_p(a)) | big_p(c4) | big_p(f2(c2)) | (~big_r(c2, c1)) | big_r(f3(c4), f4(c4)) | (~big_p(c1)))) <=> ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | (~big_p(a)) | big_p(c4) | big_p(f2(c2)) | (~big_r(c2, c1)) | big_r(f3(c4), f4(c4)) | (~big_p(c1)))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(1111,plain,
% 0.67/0.87 (((~big_p(a)) | big_p(c4) | big_r(f3(c4), f4(c4)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1))) <=> ((~big_p(a)) | big_p(c4) | big_p(f2(c2)) | (~big_r(c2, c1)) | big_r(f3(c4), f4(c4)) | (~big_p(c1)))),
% 0.67/0.87 inference(rewrite,[status(thm)],[])).
% 0.67/0.87 tff(1112,plain,
% 0.67/0.87 (((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | ((~big_p(a)) | big_p(c4) | big_r(f3(c4), f4(c4)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | ((~big_p(a)) | big_p(c4) | big_p(f2(c2)) | (~big_r(c2, c1)) | big_r(f3(c4), f4(c4)) | (~big_p(c1))))),
% 0.67/0.87 inference(monotonicity,[status(thm)],[1111])).
% 0.67/0.87 tff(1113,plain,
% 0.67/0.87 (((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | ((~big_p(a)) | big_p(c4) | big_r(f3(c4), f4(c4)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | (~big_p(a)) | big_p(c4) | big_p(f2(c2)) | (~big_r(c2, c1)) | big_r(f3(c4), f4(c4)) | (~big_p(c1)))),
% 0.67/0.87 inference(transitivity,[status(thm)],[1112, 1110])).
% 0.71/0.87 tff(1114,plain,
% 0.71/0.87 ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | ((~big_p(a)) | big_p(c4) | big_r(f3(c4), f4(c4)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(1115,plain,
% 0.71/0.87 ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)))) | (~big_p(a)) | big_p(c4) | big_p(f2(c2)) | (~big_r(c2, c1)) | big_r(f3(c4), f4(c4)) | (~big_p(c1))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1114, 1113])).
% 0.71/0.87 tff(1116,plain,
% 0.71/0.87 (big_p(f2(c2)) | big_r(f3(c4), f4(c4)) | (~big_p(c1))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1115, 526, 11, 4, 985])).
% 0.71/0.87 tff(1117,plain,
% 0.71/0.87 (big_p(f2(c2))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1116, 1101, 1099])).
% 0.71/0.87 tff(1118,plain,
% 0.71/0.87 (((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c4) | big_r(c2, f1(c2)) | (~big_r(c2, c1)) | big_r(f3(c4), f4(c4)) | (~big_p(c1)))) <=> ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | (~big_p(a)) | big_p(c4) | big_r(c2, f1(c2)) | (~big_r(c2, c1)) | big_r(f3(c4), f4(c4)) | (~big_p(c1)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(1119,plain,
% 0.71/0.87 (((~big_p(a)) | big_p(c4) | big_r(f3(c4), f4(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f1(c2))) <=> ((~big_p(a)) | big_p(c4) | big_r(c2, f1(c2)) | (~big_r(c2, c1)) | big_r(f3(c4), f4(c4)) | (~big_p(c1)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(1120,plain,
% 0.71/0.87 (((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c4) | big_r(f3(c4), f4(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f1(c2)))) <=> ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c4) | big_r(c2, f1(c2)) | (~big_r(c2, c1)) | big_r(f3(c4), f4(c4)) | (~big_p(c1))))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[1119])).
% 0.71/0.87 tff(1121,plain,
% 0.71/0.87 (((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c4) | big_r(f3(c4), f4(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f1(c2)))) <=> ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | (~big_p(a)) | big_p(c4) | big_r(c2, f1(c2)) | (~big_r(c2, c1)) | big_r(f3(c4), f4(c4)) | (~big_p(c1)))),
% 0.71/0.87 inference(transitivity,[status(thm)],[1120, 1118])).
% 0.71/0.87 tff(1122,plain,
% 0.71/0.87 ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | ((~big_p(a)) | big_p(c4) | big_r(f3(c4), f4(c4)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f1(c2)))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(1123,plain,
% 0.71/0.87 ((~![X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(X1) | big_r(f3(X1), f4(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)))) | (~big_p(a)) | big_p(c4) | big_r(c2, f1(c2)) | (~big_r(c2, c1)) | big_r(f3(c4), f4(c4)) | (~big_p(c1))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1122, 1121])).
% 0.71/0.87 tff(1124,plain,
% 0.71/0.87 (big_r(c2, f1(c2)) | big_r(f3(c4), f4(c4)) | (~big_p(c1))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1123, 543, 11, 4, 985])).
% 0.71/0.87 tff(1125,plain,
% 0.71/0.87 (big_r(c2, f1(c2))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1124, 1101, 1099])).
% 0.71/0.87 tff(1126,plain,
% 0.71/0.87 ($false),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[334, 304, 1125, 1096, 1069, 1117, 1109, 1100])).
% 0.71/0.87 tff(1127,plain,(big_r(f3(c4), f4(c4)) | big_p(c4)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.87 tff(1128,plain,
% 0.71/0.87 (big_r(f3(c4), f4(c4))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1127, 4])).
% 0.71/0.87 tff(1129,plain,
% 0.71/0.87 (big_p(c1) | (~big_p(f4(c4)))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1034, 954, 996, 1028, 1128])).
% 0.71/0.87 tff(1130,plain,
% 0.71/0.87 (~big_p(f4(c4))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1129, 2])).
% 0.71/0.87 tff(1131,plain,
% 0.71/0.87 (big_p(f4(c4)) | big_p(f2(c4))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[427, 149, 11, 4])).
% 0.71/0.87 tff(1132,plain,
% 0.71/0.87 ($false),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1131, 1130, 1098])).
% 0.71/0.87 tff(1133,plain,(big_p(c1) | big_p(c4)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.87 tff(1134,plain,
% 0.71/0.87 (big_p(c1)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1133, 4])).
% 0.71/0.87 tff(1135,assumption,(~big_p(f2(c4))), introduced(assumption)).
% 0.71/0.87 tff(1136,plain,
% 0.71/0.87 (big_p(f4(c4))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1131, 1135])).
% 0.71/0.87 tff(1137,plain,
% 0.71/0.87 (^[X2: $i, X7: $i, X1: $i] : refl(((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2))))),
% 0.71/0.87 inference(bind,[status(th)],[])).
% 0.71/0.87 tff(1138,plain,
% 0.71/0.87 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> ![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.71/0.87 inference(quant_intro,[status(thm)],[1137])).
% 0.71/0.87 tff(1139,plain,
% 0.71/0.87 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2))) <=> ![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(1140,plain,
% 0.71/0.87 (^[X2: $i, X7: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~big_p(a)) | big_p(X7)) <=> ((~big_p(a)) | big_p(X7))), ((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) <=> (((~big_p(a)) | big_p(X7)) | big_p(f2(X7))))), rewrite((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7))), ((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7)))), (((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) <=> (((~big_p(a)) | big_p(f2(X7)) | big_p(X7)) | (~big_p(a))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | big_p(X7)) | (~big_p(a))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7))), (((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7)))), ((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) <=> (((~big_p(a)) | big_p(f2(X7)) | big_p(X7)) | (~big_p(X2))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | big_p(X7)) | (~big_p(X2))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_p(X2)))), ((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_p(X2))))), (((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> (((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_p(X2))) | (~big_r(X1, X2))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)))), (((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2))))), ((((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_p(f6(X1))) <=> (((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2))) | big_p(f6(X1))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2))) | big_p(f6(X1))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))), ((((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_p(f6(X1))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))))),
% 0.71/0.87 inference(bind,[status(th)],[])).
% 0.71/0.88 tff(1141,plain,
% 0.71/0.88 (![X2: $i, X7: $i, X1: $i] : (((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_p(f6(X1))) <=> ![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.71/0.88 inference(quant_intro,[status(thm)],[1140])).
% 0.71/0.88 tff(1142,axiom,(![X2: $i, X7: $i, X1: $i] : (((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_p(f6(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_4')).
% 0.71/0.88 tff(1143,plain,
% 0.71/0.88 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1142, 1141])).
% 0.71/0.88 tff(1144,plain,
% 0.71/0.88 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1143, 1139])).
% 0.71/0.88 tff(1145,plain,(
% 0.71/0.88 ![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.71/0.88 inference(skolemize,[status(sab)],[1144])).
% 0.71/0.88 tff(1146,plain,
% 0.71/0.88 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1145, 1138])).
% 0.71/0.88 tff(1147,plain,
% 0.71/0.88 (((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_p(c4) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_p(f2(c4)))) <=> ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | big_p(c4) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_p(f2(c4)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(1148,plain,
% 0.71/0.88 (((~big_p(a)) | big_p(f2(c4)) | big_p(c4) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1))) <=> ((~big_p(a)) | big_p(c4) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_p(f2(c4)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(1149,plain,
% 0.71/0.88 (((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_p(f2(c4)) | big_p(c4) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_p(c4) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_p(f2(c4))))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[1148])).
% 0.71/0.88 tff(1150,plain,
% 0.71/0.88 (((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_p(f2(c4)) | big_p(c4) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | big_p(c4) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_p(f2(c4)))),
% 0.71/0.88 inference(transitivity,[status(thm)],[1149, 1147])).
% 0.71/0.88 tff(1151,plain,
% 0.71/0.88 ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_p(f2(c4)) | big_p(c4) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 0.71/0.88 inference(quant_inst,[status(thm)],[])).
% 0.71/0.88 tff(1152,plain,
% 0.71/0.88 ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | big_p(f6(X1)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | big_p(c4) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_p(f2(c4))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1151, 1150])).
% 0.71/0.88 tff(1153,plain,
% 0.71/0.88 (big_p(f6(c2)) | (~big_p(c1)) | big_p(f2(c4))),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1152, 1146, 11, 4, 985])).
% 0.71/0.88 tff(1154,plain,
% 0.71/0.88 (big_p(f6(c2))),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1153, 1135, 1134])).
% 0.71/0.88 tff(1155,plain,
% 0.71/0.88 (^[X2: $i, X7: $i, X1: $i] : refl(((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1))))),
% 0.71/0.88 inference(bind,[status(th)],[])).
% 0.71/0.88 tff(1156,plain,
% 0.71/0.88 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1))) <=> ![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))),
% 0.71/0.88 inference(quant_intro,[status(thm)],[1155])).
% 0.71/0.88 tff(1157,plain,
% 0.71/0.88 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1))) <=> ![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(1158,plain,
% 0.71/0.88 (^[X2: $i, X7: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~big_p(a)) | big_p(X7)) <=> ((~big_p(a)) | big_p(X7))), ((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) <=> (((~big_p(a)) | big_p(X7)) | big_p(f2(X7))))), rewrite((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7))), ((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7)))), (((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) <=> (((~big_p(a)) | big_p(f2(X7)) | big_p(X7)) | (~big_p(a))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | big_p(X7)) | (~big_p(a))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7))), (((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7)))), ((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) <=> (((~big_p(a)) | big_p(f2(X7)) | big_p(X7)) | (~big_p(X2))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | big_p(X7)) | (~big_p(X2))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_p(X2)))), ((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_p(X2))))), (((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> (((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_p(X2))) | (~big_r(X1, X2))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)))), (((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2))))), ((((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(X1, f5(X1))) <=> (((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2))) | big_r(X1, f5(X1))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2))) | big_r(X1, f5(X1))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))), ((((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(X1, f5(X1))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))))),
% 0.71/0.88 inference(bind,[status(th)],[])).
% 0.71/0.88 tff(1159,plain,
% 0.71/0.88 (![X2: $i, X7: $i, X1: $i] : (((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(X1, f5(X1))) <=> ![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))),
% 0.71/0.88 inference(quant_intro,[status(thm)],[1158])).
% 0.71/0.88 tff(1160,axiom,(![X2: $i, X7: $i, X1: $i] : (((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(X1, f5(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_5')).
% 0.71/0.88 tff(1161,plain,
% 0.71/0.88 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1160, 1159])).
% 0.71/0.88 tff(1162,plain,
% 0.71/0.88 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1161, 1157])).
% 0.71/0.88 tff(1163,plain,(
% 0.71/0.88 ![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))),
% 0.71/0.88 inference(skolemize,[status(sab)],[1162])).
% 0.71/0.88 tff(1164,plain,
% 0.71/0.88 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1163, 1156])).
% 0.71/0.88 tff(1165,plain,
% 0.71/0.88 (((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))) | ((~big_p(a)) | big_p(c4) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_p(f2(c4)))) <=> ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))) | (~big_p(a)) | big_p(c4) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_p(f2(c4)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(1166,plain,
% 0.71/0.88 (((~big_p(a)) | big_p(f2(c4)) | big_p(c4) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f5(c2))) <=> ((~big_p(a)) | big_p(c4) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_p(f2(c4)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(1167,plain,
% 0.71/0.88 (((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))) | ((~big_p(a)) | big_p(f2(c4)) | big_p(c4) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f5(c2)))) <=> ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))) | ((~big_p(a)) | big_p(c4) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_p(f2(c4))))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[1166])).
% 0.71/0.88 tff(1168,plain,
% 0.71/0.88 (((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))) | ((~big_p(a)) | big_p(f2(c4)) | big_p(c4) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f5(c2)))) <=> ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))) | (~big_p(a)) | big_p(c4) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_p(f2(c4)))),
% 0.71/0.88 inference(transitivity,[status(thm)],[1167, 1165])).
% 0.71/0.88 tff(1169,plain,
% 0.71/0.88 ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))) | ((~big_p(a)) | big_p(f2(c4)) | big_p(c4) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f5(c2)))),
% 0.71/0.88 inference(quant_inst,[status(thm)],[])).
% 0.71/0.88 tff(1170,plain,
% 0.71/0.88 ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(X1, f5(X1)))) | (~big_p(a)) | big_p(c4) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_p(f2(c4))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1169, 1168])).
% 0.71/0.88 tff(1171,plain,
% 0.71/0.88 (big_r(c2, f5(c2)) | (~big_p(c1)) | big_p(f2(c4))),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1170, 1164, 11, 4, 985])).
% 0.71/0.88 tff(1172,plain,
% 0.71/0.88 (big_r(c2, f5(c2))),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1171, 1135, 1134])).
% 0.71/0.88 tff(1173,plain,
% 0.71/0.88 (^[X2: $i, X7: $i, X1: $i] : refl(((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1))))),
% 0.71/0.88 inference(bind,[status(th)],[])).
% 0.71/0.88 tff(1174,plain,
% 0.71/0.88 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1))) <=> ![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))),
% 0.71/0.88 inference(quant_intro,[status(thm)],[1173])).
% 0.71/0.88 tff(1175,plain,
% 0.71/0.88 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1))) <=> ![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(1176,plain,
% 0.71/0.88 (^[X2: $i, X7: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~big_p(a)) | big_p(X7)) <=> ((~big_p(a)) | big_p(X7))), ((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) <=> (((~big_p(a)) | big_p(X7)) | big_p(f2(X7))))), rewrite((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7))), ((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7)))), (((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) <=> (((~big_p(a)) | big_p(f2(X7)) | big_p(X7)) | (~big_p(a))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | big_p(X7)) | (~big_p(a))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7))), (((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7)))), ((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) <=> (((~big_p(a)) | big_p(f2(X7)) | big_p(X7)) | (~big_p(X2))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | big_p(X7)) | (~big_p(X2))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_p(X2)))), ((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_p(X2))))), (((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> (((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_p(X2))) | (~big_r(X1, X2))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)))), (((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2))))), ((((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(f5(X1), f6(X1))) <=> (((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2))) | big_r(f5(X1), f6(X1))))), rewrite((((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2))) | big_r(f5(X1), f6(X1))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))), ((((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(f5(X1), f6(X1))) <=> ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))))),
% 0.71/0.88 inference(bind,[status(th)],[])).
% 0.71/0.88 tff(1177,plain,
% 0.71/0.88 (![X2: $i, X7: $i, X1: $i] : (((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(f5(X1), f6(X1))) <=> ![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))),
% 0.71/0.88 inference(quant_intro,[status(thm)],[1176])).
% 0.71/0.88 tff(1178,axiom,(![X2: $i, X7: $i, X1: $i] : (((((((~big_p(a)) | big_p(X7)) | big_p(f2(X7))) | (~big_p(a))) | (~big_p(X2))) | (~big_r(X1, X2))) | big_r(f5(X1), f6(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_6')).
% 0.71/0.88 tff(1179,plain,
% 0.71/0.88 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1178, 1177])).
% 0.71/0.88 tff(1180,plain,
% 0.71/0.88 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1179, 1175])).
% 0.71/0.88 tff(1181,plain,(
% 0.71/0.88 ![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))),
% 0.71/0.88 inference(skolemize,[status(sab)],[1180])).
% 0.71/0.88 tff(1182,plain,
% 0.71/0.88 (![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1181, 1174])).
% 0.71/0.88 tff(1183,plain,
% 0.71/0.88 (((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))) | ((~big_p(a)) | big_p(c4) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_p(f2(c4)))) <=> ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))) | (~big_p(a)) | big_p(c4) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_p(f2(c4)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(1184,plain,
% 0.71/0.88 (((~big_p(a)) | big_p(f2(c4)) | big_p(c4) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f5(c2), f6(c2))) <=> ((~big_p(a)) | big_p(c4) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_p(f2(c4)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(1185,plain,
% 0.71/0.88 (((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))) | ((~big_p(a)) | big_p(f2(c4)) | big_p(c4) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f5(c2), f6(c2)))) <=> ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))) | ((~big_p(a)) | big_p(c4) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_p(f2(c4))))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[1184])).
% 0.71/0.88 tff(1186,plain,
% 0.71/0.88 (((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))) | ((~big_p(a)) | big_p(f2(c4)) | big_p(c4) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f5(c2), f6(c2)))) <=> ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))) | (~big_p(a)) | big_p(c4) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_p(f2(c4)))),
% 0.71/0.88 inference(transitivity,[status(thm)],[1185, 1183])).
% 0.71/0.88 tff(1187,plain,
% 0.71/0.88 ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))) | ((~big_p(a)) | big_p(f2(c4)) | big_p(c4) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f5(c2), f6(c2)))),
% 0.71/0.88 inference(quant_inst,[status(thm)],[])).
% 0.71/0.88 tff(1188,plain,
% 0.71/0.88 ((~![X2: $i, X7: $i, X1: $i] : ((~big_p(a)) | big_p(f2(X7)) | big_p(X7) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f5(X1), f6(X1)))) | (~big_p(a)) | big_p(c4) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_p(f2(c4))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1187, 1186])).
% 0.71/0.88 tff(1189,plain,
% 0.71/0.88 (big_r(f5(c2), f6(c2)) | (~big_p(c1)) | big_p(f2(c4))),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1188, 1182, 11, 4, 985])).
% 0.71/0.88 tff(1190,plain,
% 0.71/0.88 (big_r(f5(c2), f6(c2))),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1189, 1135, 1134])).
% 0.71/0.88 tff(1191,plain,
% 0.71/0.88 ($false),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1066, 304, 1028, 1128, 1190, 1172, 1154, 1136])).
% 0.71/0.88 tff(1192,plain,(big_p(f2(c4)) | big_p(c4)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.88 tff(1193,plain,
% 0.71/0.88 (big_p(f2(c4))),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1192, 4])).
% 0.71/0.88 tff(1194,assumption,(big_p(c1)), introduced(assumption)).
% 0.71/0.88 tff(1195,assumption,(big_r(c2, c1)), introduced(assumption)).
% 0.71/0.88 tff(1196,plain,
% 0.71/0.88 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_r(c2, f1(c2)) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | big_r(c2, f1(c2)) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(1197,plain,
% 0.71/0.88 (((~big_p(a)) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f1(c2)) | (~big_r(c2, c1)) | (~big_p(c1))) <=> ((~big_p(a)) | big_r(c2, f1(c2)) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(1198,plain,
% 0.71/0.88 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f1(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_r(c2, f1(c2)) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1))))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[1197])).
% 0.71/0.88 tff(1199,plain,
% 0.71/0.88 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f1(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | big_r(c2, f1(c2)) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 0.71/0.88 inference(transitivity,[status(thm)],[1198, 1196])).
% 0.71/0.88 tff(1200,plain,
% 0.71/0.88 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f1(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 0.71/0.88 inference(quant_inst,[status(thm)],[])).
% 0.71/0.88 tff(1201,plain,
% 0.71/0.88 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | big_r(c2, f1(c2)) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1200, 1199])).
% 0.71/0.88 tff(1202,plain,
% 0.71/0.88 (big_r(c2, f1(c2)) | big_p(f6(c2)) | (~big_p(c1))),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1201, 789, 11, 1195])).
% 0.71/0.88 tff(1203,plain,
% 0.71/0.88 (big_r(c2, f1(c2))),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1202, 1, 1194])).
% 0.71/0.88 tff(1204,plain,
% 0.71/0.88 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_p(f6(c2)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | big_p(f6(c2)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(1205,plain,
% 0.71/0.88 (((~big_p(a)) | big_p(f6(c2)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | (~big_r(c2, c1)) | (~big_p(c1))) <=> ((~big_p(a)) | big_p(f6(c2)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(1206,plain,
% 0.71/0.88 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_p(f6(c2)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_p(f6(c2)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1))))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[1205])).
% 0.71/0.88 tff(1207,plain,
% 0.71/0.88 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_p(f6(c2)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | big_p(f6(c2)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 0.71/0.88 inference(transitivity,[status(thm)],[1206, 1204])).
% 0.71/0.88 tff(1208,plain,
% 0.71/0.88 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_p(f6(c2)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 0.71/0.88 inference(quant_inst,[status(thm)],[])).
% 0.71/0.88 tff(1209,plain,
% 0.71/0.88 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | big_p(f6(c2)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1208, 1207])).
% 0.71/0.88 tff(1210,plain,
% 0.71/0.88 (big_p(f6(c2)) | big_p(f2(c2)) | (~big_p(c1))),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1209, 908, 11, 1195])).
% 0.71/0.88 tff(1211,plain,
% 0.71/0.88 (big_p(f2(c2))),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1210, 1, 1194])).
% 0.71/0.88 tff(1212,assumption,(big_p(f2(c4))), introduced(assumption)).
% 0.71/0.88 tff(1213,assumption,(big_r(c4, f1(c4))), introduced(assumption)).
% 0.71/0.88 tff(1214,assumption,(big_r(f1(c4), f2(c4))), introduced(assumption)).
% 0.71/0.88 tff(1215,plain,
% 0.71/0.88 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_r(f1(c2), f2(c2)) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_r(f1(c2), f2(c2)) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(1216,plain,
% 0.71/0.88 (((~big_p(a)) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c2), f2(c2))) <=> ((~big_p(a)) | big_r(f1(c2), f2(c2)) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(1217,plain,
% 0.71/0.88 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c2), f2(c2)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_r(f1(c2), f2(c2)) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1))))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[1216])).
% 0.71/0.88 tff(1218,plain,
% 0.71/0.88 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c2), f2(c2)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_r(f1(c2), f2(c2)) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 0.71/0.88 inference(transitivity,[status(thm)],[1217, 1215])).
% 0.71/0.88 tff(1219,plain,
% 0.71/0.88 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c2), f2(c2)))),
% 0.71/0.88 inference(quant_inst,[status(thm)],[])).
% 0.71/0.88 tff(1220,plain,
% 0.71/0.88 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_r(f1(c2), f2(c2)) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1219, 1218])).
% 0.71/0.88 tff(1221,plain,
% 0.71/0.88 (big_r(f1(c2), f2(c2)) | big_p(f6(c2)) | (~big_p(c1))),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1220, 849, 11, 1195])).
% 0.71/0.88 tff(1222,plain,
% 0.71/0.88 (big_p(f6(c2))),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1221, 650, 1194])).
% 0.71/0.88 tff(1223,assumption,(~big_r(c2, f5(c2))), introduced(assumption)).
% 0.71/0.89 tff(1224,plain,
% 0.71/0.89 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_r(f1(c2), f2(c2)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_r(f1(c2), f2(c2)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1225,plain,
% 0.71/0.89 (((~big_p(a)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c2), f2(c2))) <=> ((~big_p(a)) | big_r(f1(c2), f2(c2)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1226,plain,
% 0.71/0.89 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c2), f2(c2)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_r(f1(c2), f2(c2)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c1))))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[1225])).
% 0.71/0.89 tff(1227,plain,
% 0.71/0.89 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c2), f2(c2)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_r(f1(c2), f2(c2)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 0.71/0.89 inference(transitivity,[status(thm)],[1226, 1224])).
% 0.71/0.89 tff(1228,plain,
% 0.71/0.89 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c2), f2(c2)))),
% 0.71/0.89 inference(quant_inst,[status(thm)],[])).
% 0.71/0.89 tff(1229,plain,
% 0.71/0.89 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_r(f1(c2), f2(c2)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c1))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1228, 1227])).
% 0.71/0.89 tff(1230,plain,
% 0.71/0.89 (big_r(f1(c2), f2(c2)) | big_r(c2, f5(c2)) | (~big_p(c1))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1229, 867, 11, 1195])).
% 0.71/0.89 tff(1231,plain,
% 0.71/0.89 (big_r(f1(c2), f2(c2))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1230, 1223, 1194])).
% 0.71/0.89 tff(1232,plain,
% 0.71/0.89 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_r(c2, f5(c2)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | big_r(c2, f5(c2)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1233,plain,
% 0.71/0.89 (((~big_p(a)) | big_r(c2, f5(c2)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | (~big_r(c2, c1)) | (~big_p(c1))) <=> ((~big_p(a)) | big_r(c2, f5(c2)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1234,plain,
% 0.71/0.89 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_r(c2, f5(c2)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_r(c2, f5(c2)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1))))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[1233])).
% 0.71/0.89 tff(1235,plain,
% 0.71/0.89 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_r(c2, f5(c2)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | big_r(c2, f5(c2)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 0.71/0.89 inference(transitivity,[status(thm)],[1234, 1232])).
% 0.71/0.89 tff(1236,plain,
% 0.71/0.89 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_r(c2, f5(c2)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 0.71/0.89 inference(quant_inst,[status(thm)],[])).
% 0.71/0.89 tff(1237,plain,
% 0.71/0.89 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | big_r(c2, f5(c2)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1236, 1235])).
% 0.71/0.89 tff(1238,plain,
% 0.71/0.89 (big_r(c2, f5(c2)) | big_p(f2(c2)) | (~big_p(c1))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1237, 926, 11, 1195])).
% 0.71/0.89 tff(1239,plain,
% 0.71/0.89 (big_p(f2(c2))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1238, 1223, 1194])).
% 0.71/0.89 tff(1240,plain,
% 0.71/0.89 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_r(c2, f1(c2)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | big_r(c2, f1(c2)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1241,plain,
% 0.71/0.89 (((~big_p(a)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f1(c2)) | (~big_r(c2, c1)) | (~big_p(c1))) <=> ((~big_p(a)) | big_r(c2, f1(c2)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1242,plain,
% 0.71/0.89 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f1(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_r(c2, f1(c2)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c1))))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[1241])).
% 0.71/0.89 tff(1243,plain,
% 0.71/0.89 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f1(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | big_r(c2, f1(c2)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 0.71/0.89 inference(transitivity,[status(thm)],[1242, 1240])).
% 0.71/0.89 tff(1244,plain,
% 0.71/0.89 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f1(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 0.71/0.89 inference(quant_inst,[status(thm)],[])).
% 0.71/0.89 tff(1245,plain,
% 0.71/0.89 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | big_r(c2, f1(c2)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c1))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1244, 1243])).
% 0.71/0.89 tff(1246,plain,
% 0.71/0.89 (big_r(c2, f1(c2)) | big_r(c2, f5(c2)) | (~big_p(c1))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1245, 807, 11, 1195])).
% 0.71/0.89 tff(1247,plain,
% 0.71/0.89 (big_r(c2, f1(c2))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1246, 1223, 1194])).
% 0.71/0.89 tff(1248,plain,
% 0.71/0.89 ($false),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[334, 304, 1247, 1214, 1213, 1239, 1231, 1212])).
% 0.71/0.89 tff(1249,plain,(big_r(c2, f5(c2)) | (~big_r(f1(c4), f2(c4))) | (~big_r(c4, f1(c4))) | (~big_p(f2(c4))) | (~big_p(c1)) | (~big_r(c2, c1))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.89 tff(1250,plain,
% 0.71/0.89 (big_r(c2, f5(c2))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1249, 1214, 1213, 1212, 1194, 1195])).
% 0.71/0.89 tff(1251,plain,
% 0.71/0.89 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_r(f1(c2), f2(c2)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_r(f1(c2), f2(c2)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1252,plain,
% 0.71/0.89 (((~big_p(a)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c2), f2(c2))) <=> ((~big_p(a)) | big_r(f1(c2), f2(c2)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1253,plain,
% 0.71/0.89 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c2), f2(c2)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_r(f1(c2), f2(c2)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1))))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[1252])).
% 0.71/0.89 tff(1254,plain,
% 0.71/0.89 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c2), f2(c2)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_r(f1(c2), f2(c2)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 0.71/0.89 inference(transitivity,[status(thm)],[1253, 1251])).
% 0.71/0.89 tff(1255,plain,
% 0.71/0.89 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c2), f2(c2)))),
% 0.71/0.89 inference(quant_inst,[status(thm)],[])).
% 0.71/0.89 tff(1256,plain,
% 0.71/0.89 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_r(f1(c2), f2(c2)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1255, 1254])).
% 0.71/0.89 tff(1257,plain,
% 0.71/0.89 (big_r(f1(c2), f2(c2)) | big_r(f5(c2), f6(c2)) | (~big_p(c1))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1256, 885, 11, 1195])).
% 0.71/0.89 tff(1258,plain,
% 0.71/0.89 (big_r(f5(c2), f6(c2))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1257, 650, 1194])).
% 0.71/0.89 tff(1259,plain,
% 0.71/0.89 (((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))) | (~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2))) | (~big_r(c2, f5(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))) | (~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2))) | (~big_r(c2, f5(c2))))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1260,plain,
% 0.71/0.89 (((~big_p(f2(c4))) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(c2, f5(c2))) | (~big_r(f1(c4), f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))) | (~big_r(f5(c2), f6(c2))) | (~big_p(f6(c2)))) <=> ((~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))) | (~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2))) | (~big_r(c2, f5(c2))))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1261,plain,
% 0.71/0.89 (((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f2(c4))) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(c2, f5(c2))) | (~big_r(f1(c4), f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))) | (~big_r(f5(c2), f6(c2))) | (~big_p(f6(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))) | (~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2))) | (~big_r(c2, f5(c2)))))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[1260])).
% 0.71/0.89 tff(1262,plain,
% 0.71/0.89 (((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f2(c4))) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(c2, f5(c2))) | (~big_r(f1(c4), f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))) | (~big_r(f5(c2), f6(c2))) | (~big_p(f6(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))) | (~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2))) | (~big_r(c2, f5(c2))))),
% 0.71/0.89 inference(transitivity,[status(thm)],[1261, 1259])).
% 0.71/0.89 tff(1263,plain,
% 0.71/0.89 ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f2(c4))) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(c2, f5(c2))) | (~big_r(f1(c4), f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))) | (~big_r(f5(c2), f6(c2))) | (~big_p(f6(c2))))),
% 0.71/0.89 inference(quant_inst,[status(thm)],[])).
% 0.71/0.89 tff(1264,plain,
% 0.71/0.89 ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | (~big_p(f2(c4))) | (~big_r(c4, f1(c4))) | (~big_r(f1(c4), f2(c4))) | (~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2))) | (~big_r(c2, f5(c2)))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1263, 1262])).
% 0.71/0.89 tff(1265,plain,
% 0.71/0.89 ($false),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1264, 304, 1214, 1213, 1212, 1258, 1250, 1222])).
% 0.71/0.89 tff(1266,plain,(big_r(f1(c2), f2(c2)) | (~big_r(f1(c4), f2(c4))) | (~big_r(c4, f1(c4))) | (~big_p(f2(c4))) | (~big_p(c1)) | (~big_r(c2, c1))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.89 tff(1267,plain,
% 0.71/0.89 (big_r(f1(c2), f2(c2))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1266, 1214, 1213, 1212, 1194, 1195])).
% 0.71/0.89 tff(1268,plain,
% 0.71/0.89 ((~big_p(f2(c2))) | (~big_r(c2, f1(c2)))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[334, 304, 1214, 1213, 1267, 1212])).
% 0.71/0.89 tff(1269,plain,
% 0.71/0.89 ($false),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1268, 1211, 1203])).
% 0.71/0.89 tff(1270,plain,(big_p(f6(c2)) | (~big_r(f1(c4), f2(c4))) | (~big_r(c4, f1(c4))) | (~big_p(f2(c4))) | (~big_p(c1)) | (~big_r(c2, c1))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.89 tff(1271,plain,
% 0.71/0.89 (big_p(f6(c2))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1270, 1096, 1069, 1193, 1134, 985])).
% 0.71/0.89 tff(1272,plain,
% 0.71/0.89 (big_r(c2, f5(c2))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1249, 1096, 1069, 1193, 1134, 985])).
% 0.71/0.89 tff(1273,assumption,(big_p(f6(c2))), introduced(assumption)).
% 0.71/0.89 tff(1274,assumption,(big_r(c2, f5(c2))), introduced(assumption)).
% 0.71/0.89 tff(1275,assumption,(big_r(f5(c2), f6(c2))), introduced(assumption)).
% 0.71/0.89 tff(1276,plain,
% 0.71/0.89 ($false),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1264, 304, 1214, 1213, 1212, 1275, 1274, 1273])).
% 0.71/0.89 tff(1277,plain,((~big_r(f5(c2), f6(c2))) | (~big_r(f1(c4), f2(c4))) | (~big_r(c4, f1(c4))) | (~big_p(f2(c4))) | (~big_r(c2, f5(c2))) | (~big_p(f6(c2)))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.89 tff(1278,plain,
% 0.71/0.89 (~big_r(f5(c2), f6(c2))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1277, 1096, 1069, 1193, 1272, 1271])).
% 0.71/0.89 tff(1279,plain,
% 0.71/0.89 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_r(c2, f1(c2)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | big_r(c2, f1(c2)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1280,plain,
% 0.71/0.89 (((~big_p(a)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f1(c2)) | (~big_r(c2, c1)) | (~big_p(c1))) <=> ((~big_p(a)) | big_r(c2, f1(c2)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1281,plain,
% 0.71/0.89 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f1(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_r(c2, f1(c2)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1))))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[1280])).
% 0.71/0.89 tff(1282,plain,
% 0.71/0.89 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f1(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | big_r(c2, f1(c2)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 0.71/0.89 inference(transitivity,[status(thm)],[1281, 1279])).
% 0.71/0.89 tff(1283,plain,
% 0.71/0.89 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(c2, f1(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 0.71/0.89 inference(quant_inst,[status(thm)],[])).
% 0.71/0.89 tff(1284,plain,
% 0.71/0.89 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | big_r(c2, f1(c2)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c1))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1283, 1282])).
% 0.71/0.89 tff(1285,plain,
% 0.71/0.89 (big_r(c2, f1(c2)) | big_r(f5(c2), f6(c2)) | (~big_p(c1))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1284, 825, 11, 985])).
% 0.71/0.89 tff(1286,plain,
% 0.71/0.89 (big_r(c2, f1(c2))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1285, 1278, 1134])).
% 0.71/0.89 tff(1287,plain,
% 0.71/0.89 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_r(f5(c2), f6(c2)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | big_r(f5(c2), f6(c2)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1288,plain,
% 0.71/0.89 (((~big_p(a)) | big_r(f5(c2), f6(c2)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | (~big_r(c2, c1)) | (~big_p(c1))) <=> ((~big_p(a)) | big_r(f5(c2), f6(c2)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1289,plain,
% 0.71/0.89 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_r(f5(c2), f6(c2)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_r(f5(c2), f6(c2)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1))))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[1288])).
% 0.71/0.89 tff(1290,plain,
% 0.71/0.89 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_r(f5(c2), f6(c2)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | big_r(f5(c2), f6(c2)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 0.71/0.89 inference(transitivity,[status(thm)],[1289, 1287])).
% 0.71/0.89 tff(1291,plain,
% 0.71/0.89 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_r(f5(c2), f6(c2)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 0.71/0.89 inference(quant_inst,[status(thm)],[])).
% 0.71/0.89 tff(1292,plain,
% 0.71/0.89 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | big_r(f5(c2), f6(c2)) | big_p(f2(c2)) | (~big_r(c2, c1)) | (~big_p(c1))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1291, 1290])).
% 0.71/0.89 tff(1293,plain,
% 0.71/0.89 (big_r(f5(c2), f6(c2)) | big_p(f2(c2)) | (~big_p(c1))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1292, 944, 11, 985])).
% 0.71/0.89 tff(1294,plain,
% 0.71/0.89 (big_p(f2(c2))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1293, 1278, 1134])).
% 0.71/0.89 tff(1295,plain,
% 0.71/0.89 (big_r(f1(c2), f2(c2))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1266, 1096, 1069, 1193, 1134, 985])).
% 0.71/0.89 tff(1296,plain,
% 0.71/0.89 ((~big_p(f2(c2))) | (~big_r(c2, f1(c2)))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[334, 304, 1096, 1069, 1295, 1193])).
% 0.71/0.89 tff(1297,plain,
% 0.71/0.89 ($false),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1296, 1294, 1286])).
% 0.71/0.89 tff(1298,plain,(big_p(c4)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.89 tff(1299,plain,
% 0.71/0.89 ((big_p(c1) | (~big_p(c4)) | (~big_p(c2)) | big_r(c4, c3)) <=> (big_p(c1) | (~big_p(c4)) | (~big_p(c2)) | big_r(c4, c3))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1300,plain,
% 0.71/0.89 (((big_p(c1) | (~big_p(c4)) | (~big_p(c2))) | big_r(c4, c3)) <=> (big_p(c1) | (~big_p(c4)) | (~big_p(c2)) | big_r(c4, c3))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1301,plain,
% 0.71/0.89 (((big_p(c1) | (~big_p(c2))) | (~big_p(c4))) <=> (big_p(c1) | (~big_p(c4)) | (~big_p(c2)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1302,plain,
% 0.71/0.89 (((~big_p(c2)) | big_p(c1)) <=> (big_p(c1) | (~big_p(c2)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1303,plain,
% 0.71/0.89 ((((~big_p(c2)) | big_p(c1)) | (~big_p(c4))) <=> ((big_p(c1) | (~big_p(c2))) | (~big_p(c4)))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[1302])).
% 0.71/0.89 tff(1304,plain,
% 0.71/0.89 ((((~big_p(c2)) | big_p(c1)) | (~big_p(c4))) <=> (big_p(c1) | (~big_p(c4)) | (~big_p(c2)))),
% 0.71/0.89 inference(transitivity,[status(thm)],[1303, 1301])).
% 0.71/0.89 tff(1305,plain,
% 0.71/0.89 (((((~big_p(c2)) | big_p(c1)) | (~big_p(c4))) | big_r(c4, c3)) <=> ((big_p(c1) | (~big_p(c4)) | (~big_p(c2))) | big_r(c4, c3))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[1304])).
% 0.71/0.89 tff(1306,plain,
% 0.71/0.89 (((((~big_p(c2)) | big_p(c1)) | (~big_p(c4))) | big_r(c4, c3)) <=> (big_p(c1) | (~big_p(c4)) | (~big_p(c2)) | big_r(c4, c3))),
% 0.71/0.89 inference(transitivity,[status(thm)],[1305, 1300])).
% 0.71/0.89 tff(1307,axiom,((((~big_p(c2)) | big_p(c1)) | (~big_p(c4))) | big_r(c4, c3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_55')).
% 0.71/0.89 tff(1308,plain,
% 0.71/0.89 (big_p(c1) | (~big_p(c4)) | (~big_p(c2)) | big_r(c4, c3)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1307, 1306])).
% 0.71/0.89 tff(1309,plain,
% 0.71/0.89 (big_p(c1) | (~big_p(c4)) | (~big_p(c2)) | big_r(c4, c3)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1308, 1299])).
% 0.71/0.89 tff(1310,plain,
% 0.71/0.89 (big_p(c1) | (~big_p(c4)) | (~big_p(c2)) | big_r(c4, c3)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1309, 1299])).
% 0.71/0.89 tff(1311,plain,
% 0.71/0.89 (big_p(c1) | (~big_p(c4)) | (~big_p(c2)) | big_r(c4, c3)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1310, 1299])).
% 0.71/0.89 tff(1312,plain,
% 0.71/0.89 (big_p(c1) | (~big_p(c4)) | (~big_p(c2)) | big_r(c4, c3)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1311, 1299])).
% 0.71/0.89 tff(1313,plain,
% 0.71/0.89 (big_p(c1) | (~big_p(c4)) | big_r(c4, c3)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1312, 954])).
% 0.71/0.89 tff(1314,plain,
% 0.71/0.89 (big_p(c1) | big_r(c4, c3)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1313, 1298])).
% 0.71/0.89 tff(1315,plain,
% 0.71/0.89 (big_r(c4, c3)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1314, 2])).
% 0.71/0.89 tff(1316,plain,
% 0.71/0.89 ((big_p(c3) | big_p(c1) | (~big_p(c4)) | (~big_p(c2))) <=> (big_p(c3) | big_p(c1) | (~big_p(c4)) | (~big_p(c2)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1317,plain,
% 0.71/0.89 (((big_p(c1) | (~big_p(c4)) | (~big_p(c2))) | big_p(c3)) <=> (big_p(c3) | big_p(c1) | (~big_p(c4)) | (~big_p(c2)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1318,plain,
% 0.71/0.89 (((((~big_p(c2)) | big_p(c1)) | (~big_p(c4))) | big_p(c3)) <=> ((big_p(c1) | (~big_p(c4)) | (~big_p(c2))) | big_p(c3))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[1304])).
% 0.71/0.89 tff(1319,plain,
% 0.71/0.89 (((((~big_p(c2)) | big_p(c1)) | (~big_p(c4))) | big_p(c3)) <=> (big_p(c3) | big_p(c1) | (~big_p(c4)) | (~big_p(c2)))),
% 0.71/0.89 inference(transitivity,[status(thm)],[1318, 1317])).
% 0.71/0.89 tff(1320,axiom,((((~big_p(c2)) | big_p(c1)) | (~big_p(c4))) | big_p(c3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_54')).
% 0.71/0.89 tff(1321,plain,
% 0.71/0.89 (big_p(c3) | big_p(c1) | (~big_p(c4)) | (~big_p(c2))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1320, 1319])).
% 0.71/0.89 tff(1322,plain,
% 0.71/0.89 (big_p(c3) | big_p(c1) | (~big_p(c4)) | (~big_p(c2))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1321, 1316])).
% 0.71/0.89 tff(1323,plain,
% 0.71/0.89 (big_p(c3) | big_p(c1) | (~big_p(c4)) | (~big_p(c2))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1322, 1316])).
% 0.71/0.90 tff(1324,plain,
% 0.71/0.90 (big_p(c3) | big_p(c1) | (~big_p(c4)) | (~big_p(c2))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1323, 1316])).
% 0.71/0.90 tff(1325,plain,
% 0.71/0.90 (big_p(c3) | big_p(c1) | (~big_p(c4)) | (~big_p(c2))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1324, 1316])).
% 0.71/0.90 tff(1326,plain,
% 0.71/0.90 (big_p(c3) | big_p(c1) | (~big_p(c4))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1325, 954])).
% 0.71/0.90 tff(1327,plain,
% 0.71/0.90 (big_p(c3) | big_p(c1)),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1326, 1298])).
% 0.71/0.90 tff(1328,plain,
% 0.71/0.90 (big_p(c3)),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1327, 2])).
% 0.71/0.90 tff(1329,plain,
% 0.71/0.90 (big_r(c4, f1(c4)) | big_p(f6(c4))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[795, 789, 11, 1328, 1315])).
% 0.71/0.90 tff(1330,plain,
% 0.71/0.90 (big_p(f6(c4))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1329, 3])).
% 0.71/0.90 tff(1331,plain,
% 0.71/0.90 (big_r(c4, f1(c4)) | big_r(c4, f5(c4))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[813, 807, 11, 1328, 1315])).
% 0.71/0.90 tff(1332,plain,
% 0.71/0.90 (big_r(c4, f5(c4))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1331, 3])).
% 0.71/0.90 tff(1333,plain,
% 0.71/0.90 (big_r(c4, f1(c4)) | big_r(f5(c4), f6(c4))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[831, 825, 11, 1328, 1315])).
% 0.71/0.90 tff(1334,plain,
% 0.71/0.90 (big_r(f5(c4), f6(c4))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1333, 3])).
% 0.71/0.90 tff(1335,plain,
% 0.71/0.90 (((~![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | (big_p(c1) | (~big_p(c2)) | (~big_r(f5(c4), f6(c4))) | (~big_p(f6(c4))) | (~big_r(c4, f5(c4))))) <=> ((~![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | big_p(c1) | (~big_p(c2)) | (~big_r(f5(c4), f6(c4))) | (~big_p(f6(c4))) | (~big_r(c4, f5(c4))))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(1336,plain,
% 0.71/0.90 ((big_p(c1) | (~big_r(f5(c4), f6(c4))) | (~big_p(f6(c4))) | (~big_p(c2)) | (~big_p(f6(c4))) | (~big_r(f5(c4), f6(c4))) | (~big_r(c4, f5(c4))) | (~big_r(c4, f5(c4)))) <=> (big_p(c1) | (~big_p(c2)) | (~big_r(f5(c4), f6(c4))) | (~big_p(f6(c4))) | (~big_r(c4, f5(c4))))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(1337,plain,
% 0.71/0.90 (((~![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | (big_p(c1) | (~big_r(f5(c4), f6(c4))) | (~big_p(f6(c4))) | (~big_p(c2)) | (~big_p(f6(c4))) | (~big_r(f5(c4), f6(c4))) | (~big_r(c4, f5(c4))) | (~big_r(c4, f5(c4))))) <=> ((~![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | (big_p(c1) | (~big_p(c2)) | (~big_r(f5(c4), f6(c4))) | (~big_p(f6(c4))) | (~big_r(c4, f5(c4)))))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[1336])).
% 0.71/0.90 tff(1338,plain,
% 0.71/0.90 (((~![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | (big_p(c1) | (~big_r(f5(c4), f6(c4))) | (~big_p(f6(c4))) | (~big_p(c2)) | (~big_p(f6(c4))) | (~big_r(f5(c4), f6(c4))) | (~big_r(c4, f5(c4))) | (~big_r(c4, f5(c4))))) <=> ((~![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | big_p(c1) | (~big_p(c2)) | (~big_r(f5(c4), f6(c4))) | (~big_p(f6(c4))) | (~big_r(c4, f5(c4))))),
% 0.71/0.90 inference(transitivity,[status(thm)],[1337, 1335])).
% 0.71/0.90 tff(1339,plain,
% 0.71/0.90 ((~![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | (big_p(c1) | (~big_r(f5(c4), f6(c4))) | (~big_p(f6(c4))) | (~big_p(c2)) | (~big_p(f6(c4))) | (~big_r(f5(c4), f6(c4))) | (~big_r(c4, f5(c4))) | (~big_r(c4, f5(c4))))),
% 0.71/0.90 inference(quant_inst,[status(thm)],[])).
% 0.71/0.90 tff(1340,plain,
% 0.71/0.90 ((~![X6: $i, X4: $i, X3: $i, X5: $i] : (big_p(c1) | (~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | big_p(c1) | (~big_p(c2)) | (~big_r(f5(c4), f6(c4))) | (~big_p(f6(c4))) | (~big_r(c4, f5(c4)))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1339, 1338])).
% 0.71/0.90 tff(1341,plain,
% 0.71/0.90 ($false),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1340, 2, 954, 996, 1334, 1332, 1330])).
% 0.71/0.90 tff(1342,plain,(big_r(c4, f1(c4)) | big_p(c1)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.90 tff(1343,plain,
% 0.71/0.90 (big_r(c4, f1(c4))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1342, 2])).
% 0.71/0.90 tff(1344,plain,
% 0.71/0.90 (big_p(f6(c4))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[855, 849, 11, 1328, 1315, 179])).
% 0.71/0.90 tff(1345,plain,
% 0.71/0.90 (big_r(c4, f5(c4))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[873, 867, 11, 1328, 1315, 179])).
% 0.71/0.90 tff(1346,plain,
% 0.71/0.90 (big_r(f5(c4), f6(c4))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[891, 885, 11, 1328, 1315, 179])).
% 0.71/0.90 tff(1347,plain,
% 0.71/0.90 ($false),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1340, 2, 954, 996, 1346, 1345, 1344])).
% 0.71/0.90 tff(1348,plain,(big_p(c1) | big_r(f1(c4), f2(c4))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.90 tff(1349,plain,
% 0.71/0.90 (big_p(c1)),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1348, 179])).
% 0.71/0.90 tff(1350,plain,
% 0.71/0.90 (((~big_p(c4)) | (~big_p(c2)) | big_r(c4, c3) | big_r(c2, c1)) <=> ((~big_p(c4)) | (~big_p(c2)) | big_r(c4, c3) | big_r(c2, c1))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(1351,plain,
% 0.71/0.90 ((((~big_p(c4)) | (~big_p(c2)) | big_r(c2, c1)) | big_r(c4, c3)) <=> ((~big_p(c4)) | (~big_p(c2)) | big_r(c4, c3) | big_r(c2, c1))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(1352,plain,
% 0.71/0.90 ((((~big_p(c2)) | big_r(c2, c1)) | (~big_p(c4))) <=> ((~big_p(c4)) | (~big_p(c2)) | big_r(c2, c1))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(1353,plain,
% 0.71/0.90 (((((~big_p(c2)) | big_r(c2, c1)) | (~big_p(c4))) | big_r(c4, c3)) <=> (((~big_p(c4)) | (~big_p(c2)) | big_r(c2, c1)) | big_r(c4, c3))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[1352])).
% 0.71/0.90 tff(1354,plain,
% 0.71/0.90 (((((~big_p(c2)) | big_r(c2, c1)) | (~big_p(c4))) | big_r(c4, c3)) <=> ((~big_p(c4)) | (~big_p(c2)) | big_r(c4, c3) | big_r(c2, c1))),
% 0.71/0.90 inference(transitivity,[status(thm)],[1353, 1351])).
% 0.71/0.90 tff(1355,axiom,((((~big_p(c2)) | big_r(c2, c1)) | (~big_p(c4))) | big_r(c4, c3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_67')).
% 0.71/0.90 tff(1356,plain,
% 0.71/0.90 ((~big_p(c4)) | (~big_p(c2)) | big_r(c4, c3) | big_r(c2, c1)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1355, 1354])).
% 0.71/0.90 tff(1357,plain,
% 0.71/0.90 ((~big_p(c4)) | (~big_p(c2)) | big_r(c4, c3) | big_r(c2, c1)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1356, 1350])).
% 0.71/0.90 tff(1358,plain,
% 0.71/0.90 ((~big_p(c4)) | (~big_p(c2)) | big_r(c4, c3) | big_r(c2, c1)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1357, 1350])).
% 0.71/0.90 tff(1359,plain,
% 0.71/0.90 ((~big_p(c4)) | (~big_p(c2)) | big_r(c4, c3) | big_r(c2, c1)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1358, 1350])).
% 0.71/0.90 tff(1360,plain,
% 0.71/0.90 ((~big_p(c4)) | (~big_p(c2)) | big_r(c4, c3) | big_r(c2, c1)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1359, 1350])).
% 0.71/0.90 tff(1361,plain,
% 0.71/0.90 ((~big_p(c4)) | big_r(c4, c3) | big_r(c2, c1)),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1360, 954])).
% 0.71/0.90 tff(1362,plain,
% 0.71/0.90 (big_r(c4, c3) | big_r(c2, c1)),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1361, 1298])).
% 0.71/0.90 tff(1363,plain,
% 0.71/0.90 (big_r(c4, c3)),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1362, 65])).
% 0.71/0.90 tff(1364,plain,
% 0.71/0.90 ((big_p(c3) | (~big_p(c4)) | (~big_p(c2)) | big_r(c2, c1)) <=> (big_p(c3) | (~big_p(c4)) | (~big_p(c2)) | big_r(c2, c1))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(1365,plain,
% 0.71/0.90 ((((~big_p(c4)) | (~big_p(c2)) | big_r(c2, c1)) | big_p(c3)) <=> (big_p(c3) | (~big_p(c4)) | (~big_p(c2)) | big_r(c2, c1))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(1366,plain,
% 0.71/0.90 (((((~big_p(c2)) | big_r(c2, c1)) | (~big_p(c4))) | big_p(c3)) <=> (((~big_p(c4)) | (~big_p(c2)) | big_r(c2, c1)) | big_p(c3))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[1352])).
% 0.71/0.90 tff(1367,plain,
% 0.71/0.90 (((((~big_p(c2)) | big_r(c2, c1)) | (~big_p(c4))) | big_p(c3)) <=> (big_p(c3) | (~big_p(c4)) | (~big_p(c2)) | big_r(c2, c1))),
% 0.71/0.90 inference(transitivity,[status(thm)],[1366, 1365])).
% 0.71/0.90 tff(1368,axiom,((((~big_p(c2)) | big_r(c2, c1)) | (~big_p(c4))) | big_p(c3)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_66')).
% 0.71/0.90 tff(1369,plain,
% 0.71/0.90 (big_p(c3) | (~big_p(c4)) | (~big_p(c2)) | big_r(c2, c1)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1368, 1367])).
% 0.71/0.90 tff(1370,plain,
% 0.71/0.90 (big_p(c3) | (~big_p(c4)) | (~big_p(c2)) | big_r(c2, c1)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1369, 1364])).
% 0.71/0.90 tff(1371,plain,
% 0.71/0.90 (big_p(c3) | (~big_p(c4)) | (~big_p(c2)) | big_r(c2, c1)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1370, 1364])).
% 0.71/0.90 tff(1372,plain,
% 0.71/0.90 (big_p(c3) | (~big_p(c4)) | (~big_p(c2)) | big_r(c2, c1)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1371, 1364])).
% 0.71/0.90 tff(1373,plain,
% 0.71/0.90 (big_p(c3) | (~big_p(c4)) | (~big_p(c2)) | big_r(c2, c1)),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1372, 1364])).
% 0.71/0.90 tff(1374,plain,
% 0.71/0.90 (big_p(c3) | (~big_p(c4)) | big_r(c2, c1)),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1373, 954])).
% 0.71/0.90 tff(1375,plain,
% 0.71/0.90 (big_p(c3) | big_r(c2, c1)),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1374, 1298])).
% 0.71/0.90 tff(1376,plain,
% 0.71/0.90 (big_p(c3)),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1375, 65])).
% 0.71/0.90 tff(1377,plain,
% 0.71/0.90 (big_r(c4, f1(c4)) | big_p(f6(c4))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[795, 789, 11, 1376, 1363])).
% 0.71/0.90 tff(1378,plain,
% 0.71/0.90 (big_p(f6(c4))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1377, 3])).
% 0.71/0.90 tff(1379,plain,
% 0.71/0.90 (big_r(c4, f1(c4)) | big_r(c4, f5(c4))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[813, 807, 11, 1376, 1363])).
% 0.71/0.90 tff(1380,plain,
% 0.71/0.90 (big_r(c4, f5(c4))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1379, 3])).
% 0.71/0.90 tff(1381,plain,
% 0.71/0.90 (big_r(c4, f1(c4)) | big_r(f5(c4), f6(c4))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[831, 825, 11, 1376, 1363])).
% 0.71/0.90 tff(1382,plain,
% 0.71/0.90 (big_r(f5(c4), f6(c4))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1381, 3])).
% 0.71/0.90 tff(1383,plain,
% 0.71/0.90 (((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | ((~big_p(c2)) | big_r(c2, c1) | (~big_r(f5(c4), f6(c4))) | (~big_p(f6(c4))) | (~big_r(c4, f5(c4))))) <=> ((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | (~big_p(c2)) | big_r(c2, c1) | (~big_r(f5(c4), f6(c4))) | (~big_p(f6(c4))) | (~big_r(c4, f5(c4))))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(1384,plain,
% 0.71/0.90 (((~big_r(f5(c4), f6(c4))) | (~big_p(f6(c4))) | (~big_p(c2)) | (~big_p(f6(c4))) | big_r(c2, c1) | (~big_r(f5(c4), f6(c4))) | (~big_r(c4, f5(c4))) | (~big_r(c4, f5(c4)))) <=> ((~big_p(c2)) | big_r(c2, c1) | (~big_r(f5(c4), f6(c4))) | (~big_p(f6(c4))) | (~big_r(c4, f5(c4))))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(1385,plain,
% 0.71/0.90 (((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | ((~big_r(f5(c4), f6(c4))) | (~big_p(f6(c4))) | (~big_p(c2)) | (~big_p(f6(c4))) | big_r(c2, c1) | (~big_r(f5(c4), f6(c4))) | (~big_r(c4, f5(c4))) | (~big_r(c4, f5(c4))))) <=> ((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | ((~big_p(c2)) | big_r(c2, c1) | (~big_r(f5(c4), f6(c4))) | (~big_p(f6(c4))) | (~big_r(c4, f5(c4)))))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[1384])).
% 0.71/0.90 tff(1386,plain,
% 0.71/0.90 (((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | ((~big_r(f5(c4), f6(c4))) | (~big_p(f6(c4))) | (~big_p(c2)) | (~big_p(f6(c4))) | big_r(c2, c1) | (~big_r(f5(c4), f6(c4))) | (~big_r(c4, f5(c4))) | (~big_r(c4, f5(c4))))) <=> ((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | (~big_p(c2)) | big_r(c2, c1) | (~big_r(f5(c4), f6(c4))) | (~big_p(f6(c4))) | (~big_r(c4, f5(c4))))),
% 0.71/0.90 inference(transitivity,[status(thm)],[1385, 1383])).
% 0.71/0.90 tff(1387,plain,
% 0.71/0.90 ((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | ((~big_r(f5(c4), f6(c4))) | (~big_p(f6(c4))) | (~big_p(c2)) | (~big_p(f6(c4))) | big_r(c2, c1) | (~big_r(f5(c4), f6(c4))) | (~big_r(c4, f5(c4))) | (~big_r(c4, f5(c4))))),
% 0.71/0.90 inference(quant_inst,[status(thm)],[])).
% 0.71/0.90 tff(1388,plain,
% 0.71/0.90 ((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~big_r(X4, X3)) | (~big_p(X3)) | (~big_p(c2)) | (~big_p(X5)) | big_r(c2, c1) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(c4, X4)))) | (~big_p(c2)) | big_r(c2, c1) | (~big_r(f5(c4), f6(c4))) | (~big_p(f6(c4))) | (~big_r(c4, f5(c4)))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1387, 1386])).
% 0.71/0.90 tff(1389,plain,
% 0.71/0.90 ($false),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1388, 954, 65, 93, 1382, 1380, 1378])).
% 0.71/0.90 tff(1390,plain,(big_r(c4, f1(c4)) | big_r(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.90 tff(1391,plain,
% 0.71/0.90 (big_r(c4, f1(c4))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1390, 65])).
% 0.71/0.90 tff(1392,plain,
% 0.71/0.90 (big_r(f1(c4), f2(c4)) | big_p(f6(c4))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[855, 849, 11, 1376, 1363])).
% 0.71/0.90 tff(1393,plain,
% 0.71/0.90 (big_p(f6(c4))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1392, 179])).
% 0.71/0.90 tff(1394,plain,
% 0.71/0.90 (big_r(f1(c4), f2(c4)) | big_r(c4, f5(c4))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[873, 867, 11, 1376, 1363])).
% 0.71/0.90 tff(1395,plain,
% 0.71/0.90 (big_r(c4, f5(c4))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1394, 179])).
% 0.71/0.90 tff(1396,plain,
% 0.71/0.90 (big_r(f1(c4), f2(c4)) | big_r(f5(c4), f6(c4))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[891, 885, 11, 1376, 1363])).
% 0.71/0.90 tff(1397,plain,
% 0.71/0.90 (big_r(f5(c4), f6(c4))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1396, 179])).
% 0.71/0.90 tff(1398,plain,
% 0.71/0.90 ($false),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1388, 954, 65, 93, 1397, 1395, 1393])).
% 0.71/0.90 tff(1399,plain,(big_r(f1(c4), f2(c4)) | big_r(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.90 tff(1400,plain,
% 0.71/0.90 (big_r(f1(c4), f2(c4))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1399, 65])).
% 0.71/0.90 tff(1401,plain,
% 0.71/0.90 (~big_p(f2(c4))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[971, 954, 65, 93, 1400, 1391])).
% 0.71/0.90 tff(1402,plain,
% 0.71/0.90 (big_p(f6(c4)) | big_p(f2(c4))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[914, 908, 11, 1376, 1363])).
% 0.71/0.90 tff(1403,plain,
% 0.71/0.90 (big_p(f6(c4))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1402, 1401])).
% 0.71/0.90 tff(1404,plain,
% 0.71/0.90 (big_r(c4, f5(c4)) | big_p(f2(c4))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[932, 926, 11, 1376, 1363])).
% 0.71/0.90 tff(1405,plain,
% 0.71/0.90 (big_r(c4, f5(c4))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1404, 1401])).
% 0.71/0.90 tff(1406,plain,
% 0.71/0.90 (big_r(f5(c4), f6(c4)) | big_p(f2(c4))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[950, 944, 11, 1376, 1363])).
% 0.71/0.90 tff(1407,plain,
% 0.71/0.90 (big_r(f5(c4), f6(c4))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1406, 1401])).
% 0.71/0.90 tff(1408,plain,
% 0.71/0.90 ($false),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1388, 954, 65, 93, 1407, 1405, 1403])).
% 0.71/0.90 tff(1409,plain,(big_r(c2, c1)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.90 tff(1410,plain,
% 0.71/0.90 (big_r(c2, f1(c2)) | big_r(f5(c2), f6(c2)) | (~big_p(c1))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1284, 825, 11, 1409])).
% 0.71/0.90 tff(1411,plain,
% 0.71/0.90 (big_r(f5(c2), f6(c2))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1410, 264, 1194])).
% 0.71/0.90 tff(1412,plain,
% 0.71/0.90 (big_r(c2, f1(c2)) | big_p(f6(c2)) | (~big_p(c1))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1201, 789, 11, 1409])).
% 0.71/0.90 tff(1413,plain,
% 0.71/0.90 (big_p(f6(c2))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1412, 264, 1194])).
% 0.71/0.90 tff(1414,plain,
% 0.71/0.90 (big_r(c2, f1(c2)) | big_r(c2, f5(c2)) | (~big_p(c1))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1245, 807, 11, 1409])).
% 0.71/0.90 tff(1415,plain,
% 0.71/0.90 (big_r(c2, f5(c2))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1414, 264, 1194])).
% 0.71/0.90 tff(1416,plain,
% 0.71/0.90 (((~![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | (big_p(c3) | (~big_p(c4)) | (~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2))) | (~big_r(c2, f5(c2))))) <=> ((~![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | big_p(c3) | (~big_p(c4)) | (~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2))) | (~big_r(c2, f5(c2))))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(1417,plain,
% 0.71/0.90 ((big_p(c3) | (~big_p(f6(c2))) | (~big_p(c4)) | (~big_r(f5(c2), f6(c2))) | (~big_r(c2, f5(c2)))) <=> (big_p(c3) | (~big_p(c4)) | (~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2))) | (~big_r(c2, f5(c2))))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(1418,plain,
% 0.71/0.90 (((~![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | (big_p(c3) | (~big_p(f6(c2))) | (~big_p(c4)) | (~big_r(f5(c2), f6(c2))) | (~big_r(c2, f5(c2))))) <=> ((~![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | (big_p(c3) | (~big_p(c4)) | (~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2))) | (~big_r(c2, f5(c2)))))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[1417])).
% 0.71/0.90 tff(1419,plain,
% 0.71/0.90 (((~![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | (big_p(c3) | (~big_p(f6(c2))) | (~big_p(c4)) | (~big_r(f5(c2), f6(c2))) | (~big_r(c2, f5(c2))))) <=> ((~![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | big_p(c3) | (~big_p(c4)) | (~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2))) | (~big_r(c2, f5(c2))))),
% 0.71/0.90 inference(transitivity,[status(thm)],[1418, 1416])).
% 0.71/0.90 tff(1420,plain,
% 0.71/0.90 ((~![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | (big_p(c3) | (~big_p(f6(c2))) | (~big_p(c4)) | (~big_r(f5(c2), f6(c2))) | (~big_r(c2, f5(c2))))),
% 0.71/0.90 inference(quant_inst,[status(thm)],[])).
% 0.71/0.90 tff(1421,plain,
% 0.71/0.90 ((~![X9: $i, X10: $i] : (big_p(c3) | (~big_p(X9)) | (~big_p(c4)) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | big_p(c3) | (~big_p(c4)) | (~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2))) | (~big_r(c2, f5(c2)))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1420, 1419])).
% 0.71/0.90 tff(1422,plain,
% 0.71/0.90 ($false),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1421, 713, 1298, 448, 1415, 1413, 1411])).
% 0.71/0.90 tff(1423,plain,(big_r(c2, f1(c2)) | big_p(c3) | (~big_p(c1))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.90 tff(1424,plain,
% 0.71/0.90 (big_r(c2, f1(c2))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1423, 713, 1194])).
% 0.71/0.90 tff(1425,plain,
% 0.71/0.90 (big_r(f1(c2), f2(c2)) | big_r(f5(c2), f6(c2)) | (~big_p(c1))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1256, 885, 11, 1409])).
% 0.71/0.90 tff(1426,plain,
% 0.71/0.90 (big_r(f5(c2), f6(c2))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1425, 650, 1194])).
% 0.71/0.90 tff(1427,plain,
% 0.71/0.90 (big_r(f1(c2), f2(c2)) | big_p(f6(c2)) | (~big_p(c1))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1220, 849, 11, 1409])).
% 0.71/0.90 tff(1428,plain,
% 0.71/0.90 (big_p(f6(c2))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1427, 650, 1194])).
% 0.71/0.90 tff(1429,plain,
% 0.71/0.90 (big_r(f1(c2), f2(c2)) | big_r(c2, f5(c2)) | (~big_p(c1))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1229, 867, 11, 1409])).
% 0.71/0.90 tff(1430,plain,
% 0.71/0.90 (big_r(c2, f5(c2))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1429, 650, 1194])).
% 0.71/0.90 tff(1431,plain,
% 0.71/0.90 ($false),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1421, 713, 1298, 448, 1430, 1428, 1426])).
% 0.71/0.90 tff(1432,plain,(big_r(f1(c2), f2(c2)) | big_p(c3) | (~big_p(c1))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.90 tff(1433,plain,
% 0.71/0.90 (big_r(f1(c2), f2(c2))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1432, 713, 1194])).
% 0.71/0.90 tff(1434,plain,
% 0.71/0.90 ((~big_p(f2(c2))) | (~big_r(c2, f1(c2)))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[454, 713, 1298, 448, 1433])).
% 0.71/0.90 tff(1435,plain,
% 0.71/0.90 (~big_p(f2(c2))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1434, 1424])).
% 0.71/0.90 tff(1436,plain,
% 0.71/0.90 (big_r(f5(c2), f6(c2)) | big_p(f2(c2)) | (~big_p(c1))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1292, 944, 11, 1409])).
% 0.71/0.90 tff(1437,plain,
% 0.71/0.90 (big_r(f5(c2), f6(c2))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1436, 1435, 1194])).
% 0.71/0.90 tff(1438,plain,
% 0.71/0.90 (big_p(f6(c2)) | big_p(f2(c2)) | (~big_p(c1))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1209, 908, 11, 1409])).
% 0.71/0.90 tff(1439,plain,
% 0.71/0.90 (big_p(f6(c2))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1438, 1435, 1194])).
% 0.71/0.90 tff(1440,plain,
% 0.71/0.90 (big_r(c2, f5(c2)) | big_p(f2(c2)) | (~big_p(c1))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1237, 926, 11, 1409])).
% 0.71/0.90 tff(1441,plain,
% 0.71/0.90 (big_r(c2, f5(c2))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1440, 1435, 1194])).
% 0.71/0.90 tff(1442,plain,
% 0.71/0.90 ($false),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1421, 713, 1298, 448, 1441, 1439, 1437])).
% 0.71/0.90 tff(1443,plain,(big_p(c3) | (~big_p(c1))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.90 tff(1444,plain,
% 0.71/0.90 (big_p(c3)),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1443, 1349])).
% 0.71/0.90 tff(1445,plain,
% 0.71/0.90 (((~![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | ((~big_p(c4)) | big_r(c4, c3) | (~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2))) | (~big_r(c2, f5(c2))))) <=> ((~![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | (~big_p(c4)) | big_r(c4, c3) | (~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2))) | (~big_r(c2, f5(c2))))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(1446,plain,
% 0.71/0.90 (((~big_p(f6(c2))) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(f5(c2), f6(c2))) | (~big_r(c2, f5(c2)))) <=> ((~big_p(c4)) | big_r(c4, c3) | (~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2))) | (~big_r(c2, f5(c2))))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(1447,plain,
% 0.71/0.90 (((~![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | ((~big_p(f6(c2))) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(f5(c2), f6(c2))) | (~big_r(c2, f5(c2))))) <=> ((~![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | ((~big_p(c4)) | big_r(c4, c3) | (~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2))) | (~big_r(c2, f5(c2)))))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[1446])).
% 0.71/0.90 tff(1448,plain,
% 0.71/0.90 (((~![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | ((~big_p(f6(c2))) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(f5(c2), f6(c2))) | (~big_r(c2, f5(c2))))) <=> ((~![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | (~big_p(c4)) | big_r(c4, c3) | (~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2))) | (~big_r(c2, f5(c2))))),
% 0.71/0.90 inference(transitivity,[status(thm)],[1447, 1445])).
% 0.71/0.90 tff(1449,plain,
% 0.71/0.90 ((~![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | ((~big_p(f6(c2))) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(f5(c2), f6(c2))) | (~big_r(c2, f5(c2))))),
% 0.71/0.90 inference(quant_inst,[status(thm)],[])).
% 0.71/0.90 tff(1450,plain,
% 0.71/0.90 ((~![X9: $i, X10: $i] : ((~big_p(X9)) | (~big_p(c4)) | big_r(c4, c3) | (~big_r(X10, X9)) | (~big_r(c2, X10)))) | (~big_p(c4)) | big_r(c4, c3) | (~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2))) | (~big_r(c2, f5(c2)))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[1449, 1448])).
% 0.71/0.90 tff(1451,plain,
% 0.71/0.90 ($false),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1450, 511, 1298, 138, 1415, 1413, 1411])).
% 0.71/0.90 tff(1452,plain,(big_r(c2, f1(c2)) | big_r(c4, c3) | (~big_p(c1))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.90 tff(1453,plain,
% 0.71/0.90 (big_r(c2, f1(c2))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1452, 511, 1194])).
% 0.71/0.90 tff(1454,plain,
% 0.71/0.90 ($false),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1450, 511, 1298, 138, 1430, 1428, 1426])).
% 0.71/0.90 tff(1455,plain,(big_r(f1(c2), f2(c2)) | big_r(c4, c3) | (~big_p(c1))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.90 tff(1456,plain,
% 0.71/0.90 (big_r(f1(c2), f2(c2))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1455, 511, 1194])).
% 0.71/0.90 tff(1457,plain,
% 0.71/0.90 ((~big_p(f2(c2))) | (~big_r(c2, f1(c2)))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[436, 511, 1298, 138, 1456])).
% 0.71/0.90 tff(1458,plain,
% 0.71/0.90 (~big_p(f2(c2))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1457, 1453])).
% 0.71/0.90 tff(1459,plain,
% 0.71/0.90 (big_r(f5(c2), f6(c2))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1436, 1458, 1194])).
% 0.71/0.90 tff(1460,plain,
% 0.71/0.90 (big_p(f6(c2))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1438, 1458, 1194])).
% 0.71/0.90 tff(1461,plain,
% 0.71/0.90 (big_r(c2, f5(c2))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1440, 1458, 1194])).
% 0.71/0.90 tff(1462,plain,
% 0.71/0.90 ($false),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1450, 511, 1298, 138, 1461, 1460, 1459])).
% 0.71/0.90 tff(1463,plain,(big_r(c4, c3) | (~big_p(c1))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.90 tff(1464,plain,
% 0.71/0.90 (big_r(c4, c3)),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1463, 1349])).
% 0.71/0.90 tff(1465,plain,
% 0.71/0.90 ((~big_p(c3)) | big_p(f6(c4))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[855, 849, 11, 1464, 179])).
% 0.71/0.90 tff(1466,plain,
% 0.71/0.90 (big_p(f6(c4))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1465, 1444])).
% 0.71/0.90 tff(1467,plain,
% 0.71/0.90 ((~big_p(c3)) | big_r(c4, f5(c4))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[873, 867, 11, 1464, 179])).
% 0.71/0.90 tff(1468,plain,
% 0.71/0.90 (big_r(c4, f5(c4))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1467, 1444])).
% 0.71/0.90 tff(1469,plain,
% 0.71/0.90 ((~big_p(c3)) | big_r(f5(c4), f6(c4))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[891, 885, 11, 1464, 179])).
% 0.71/0.90 tff(1470,plain,
% 0.71/0.90 (big_r(f5(c4), f6(c4))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[1469, 1444])).
% 0.71/0.90 tff(1471,plain,
% 0.71/0.90 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c1)) | big_r(f1(c4), f2(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c1)) | big_r(f1(c4), f2(c4)))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(1472,plain,
% 0.71/0.90 (((~big_p(a)) | big_r(f5(c2), f6(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c4), f2(c4))) <=> ((~big_p(a)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c1)) | big_r(f1(c4), f2(c4)))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(1473,plain,
% 0.71/0.90 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_r(f5(c2), f6(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c4), f2(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c1)) | big_r(f1(c4), f2(c4))))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[1472])).
% 0.71/0.90 tff(1474,plain,
% 0.71/0.90 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_r(f5(c2), f6(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c4), f2(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c1)) | big_r(f1(c4), f2(c4)))),
% 0.71/0.90 inference(transitivity,[status(thm)],[1473, 1471])).
% 0.71/0.90 tff(1475,plain,
% 0.71/0.90 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_r(f5(c2), f6(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c4), f2(c4)))),
% 0.71/0.90 inference(quant_inst,[status(thm)],[])).
% 0.71/0.91 tff(1476,plain,
% 0.71/0.91 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c1)) | big_r(f1(c4), f2(c4))),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[1475, 1474])).
% 0.71/0.91 tff(1477,plain,
% 0.71/0.91 (big_r(f5(c2), f6(c2)) | (~big_p(c3))),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[1476, 885, 11, 1464, 1349, 1409, 179])).
% 0.71/0.91 tff(1478,plain,
% 0.71/0.91 (big_r(f5(c2), f6(c2))),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[1477, 1444])).
% 0.71/0.91 tff(1479,plain,
% 0.71/0.91 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c1)) | big_r(f1(c4), f2(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c1)) | big_r(f1(c4), f2(c4)))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(1480,plain,
% 0.71/0.91 (((~big_p(a)) | big_p(f6(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c4), f2(c4))) <=> ((~big_p(a)) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c1)) | big_r(f1(c4), f2(c4)))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(1481,plain,
% 0.71/0.91 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(f6(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c4), f2(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c1)) | big_r(f1(c4), f2(c4))))),
% 0.71/0.91 inference(monotonicity,[status(thm)],[1480])).
% 0.71/0.91 tff(1482,plain,
% 0.71/0.91 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(f6(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c4), f2(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c1)) | big_r(f1(c4), f2(c4)))),
% 0.71/0.91 inference(transitivity,[status(thm)],[1481, 1479])).
% 0.71/0.91 tff(1483,plain,
% 0.71/0.91 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_p(f6(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c4), f2(c4)))),
% 0.71/0.91 inference(quant_inst,[status(thm)],[])).
% 0.71/0.91 tff(1484,plain,
% 0.71/0.91 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c1)) | big_r(f1(c4), f2(c4))),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[1483, 1482])).
% 0.71/0.91 tff(1485,plain,
% 0.71/0.91 (big_p(f6(c2)) | (~big_p(c3))),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[1484, 849, 11, 1464, 1349, 1409, 179])).
% 0.71/0.91 tff(1486,plain,
% 0.71/0.91 (big_p(f6(c2))),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[1485, 1444])).
% 0.71/0.91 tff(1487,plain,
% 0.71/0.91 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c1)) | big_r(f1(c4), f2(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c1)) | big_r(f1(c4), f2(c4)))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(1488,plain,
% 0.71/0.91 (((~big_p(a)) | big_r(c2, f5(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c4), f2(c4))) <=> ((~big_p(a)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c1)) | big_r(f1(c4), f2(c4)))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(1489,plain,
% 0.71/0.91 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_r(c2, f5(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c4), f2(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c1)) | big_r(f1(c4), f2(c4))))),
% 0.71/0.91 inference(monotonicity,[status(thm)],[1488])).
% 0.71/0.91 tff(1490,plain,
% 0.71/0.91 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_r(c2, f5(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c4), f2(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c1)) | big_r(f1(c4), f2(c4)))),
% 0.71/0.91 inference(transitivity,[status(thm)],[1489, 1487])).
% 0.71/0.91 tff(1491,plain,
% 0.71/0.91 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | ((~big_p(a)) | big_r(c2, f5(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c2, c1)) | (~big_p(c1)) | big_r(f1(c4), f2(c4)))),
% 0.71/0.91 inference(quant_inst,[status(thm)],[])).
% 0.71/0.91 tff(1492,plain,
% 0.71/0.91 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)) | big_r(f1(X7), f2(X7)))) | (~big_p(a)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c1)) | big_r(f1(c4), f2(c4))),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[1491, 1490])).
% 0.71/0.91 tff(1493,plain,
% 0.71/0.91 (big_r(c2, f5(c2)) | (~big_p(c3))),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[1492, 867, 11, 1464, 1349, 1409, 179])).
% 0.71/0.91 tff(1494,plain,
% 0.71/0.91 (big_r(c2, f5(c2))),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[1493, 1444])).
% 0.71/0.91 tff(1495,plain,
% 0.71/0.91 (((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2))) | (~big_r(c2, f5(c2))) | (~big_r(f5(c4), f6(c4))) | (~big_p(f6(c4))) | (~big_r(c4, f5(c4))))) <=> ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | (~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2))) | (~big_r(c2, f5(c2))) | (~big_r(f5(c4), f6(c4))) | (~big_p(f6(c4))) | (~big_r(c4, f5(c4))))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(1496,plain,
% 0.71/0.91 (((~big_p(f6(c4))) | (~big_p(f6(c4))) | (~big_r(c4, f5(c4))) | (~big_r(c2, f5(c2))) | (~big_r(f5(c4), f6(c4))) | (~big_r(c4, f5(c4))) | (~big_r(f5(c4), f6(c4))) | (~big_r(f5(c2), f6(c2))) | (~big_p(f6(c2)))) <=> ((~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2))) | (~big_r(c2, f5(c2))) | (~big_r(f5(c4), f6(c4))) | (~big_p(f6(c4))) | (~big_r(c4, f5(c4))))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(1497,plain,
% 0.71/0.91 (((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f6(c4))) | (~big_p(f6(c4))) | (~big_r(c4, f5(c4))) | (~big_r(c2, f5(c2))) | (~big_r(f5(c4), f6(c4))) | (~big_r(c4, f5(c4))) | (~big_r(f5(c4), f6(c4))) | (~big_r(f5(c2), f6(c2))) | (~big_p(f6(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2))) | (~big_r(c2, f5(c2))) | (~big_r(f5(c4), f6(c4))) | (~big_p(f6(c4))) | (~big_r(c4, f5(c4)))))),
% 0.71/0.91 inference(monotonicity,[status(thm)],[1496])).
% 0.71/0.91 tff(1498,plain,
% 0.71/0.91 (((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f6(c4))) | (~big_p(f6(c4))) | (~big_r(c4, f5(c4))) | (~big_r(c2, f5(c2))) | (~big_r(f5(c4), f6(c4))) | (~big_r(c4, f5(c4))) | (~big_r(f5(c4), f6(c4))) | (~big_r(f5(c2), f6(c2))) | (~big_p(f6(c2))))) <=> ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | (~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2))) | (~big_r(c2, f5(c2))) | (~big_r(f5(c4), f6(c4))) | (~big_p(f6(c4))) | (~big_r(c4, f5(c4))))),
% 0.71/0.91 inference(transitivity,[status(thm)],[1497, 1495])).
% 0.71/0.91 tff(1499,plain,
% 0.71/0.91 ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | ((~big_p(f6(c4))) | (~big_p(f6(c4))) | (~big_r(c4, f5(c4))) | (~big_r(c2, f5(c2))) | (~big_r(f5(c4), f6(c4))) | (~big_r(c4, f5(c4))) | (~big_r(f5(c4), f6(c4))) | (~big_r(f5(c2), f6(c2))) | (~big_p(f6(c2))))),
% 0.71/0.91 inference(quant_inst,[status(thm)],[])).
% 0.71/0.91 tff(1500,plain,
% 0.71/0.91 ((~![X9: $i, X6: $i, X4: $i, X3: $i, X10: $i, X5: $i] : ((~big_p(X3)) | (~big_p(X5)) | (~big_r(c4, X4)) | (~big_r(c2, X10)) | (~big_r(X6, X5)) | (~big_r(c4, X6)) | (~big_r(X4, X3)) | (~big_r(X10, X9)) | (~big_p(X9)))) | (~big_p(f6(c2))) | (~big_r(f5(c2), f6(c2))) | (~big_r(c2, f5(c2))) | (~big_r(f5(c4), f6(c4))) | (~big_p(f6(c4))) | (~big_r(c4, f5(c4)))),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[1499, 1498])).
% 0.71/0.91 tff(1501,plain,
% 0.71/0.91 ($false),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[1500, 304, 1494, 1486, 1478, 1470, 1468, 1466])).
% 0.71/0.91 tff(1502,plain,(big_r(f1(c4), f2(c4))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.91 tff(1503,plain,
% 0.71/0.91 ((~big_p(f2(c4))) | (~big_r(c4, f1(c4)))),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[1002, 2, 954, 996, 1502])).
% 0.71/0.91 tff(1504,plain,
% 0.71/0.91 (~big_p(f2(c4))),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[1503, 1343])).
% 0.71/0.91 tff(1505,plain,
% 0.71/0.91 (big_p(f6(c4)) | big_p(f2(c4))),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[914, 908, 11, 1328, 1315])).
% 0.71/0.91 tff(1506,plain,
% 0.71/0.91 (big_p(f6(c4))),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[1505, 1504])).
% 0.71/0.91 tff(1507,plain,
% 0.71/0.91 (big_r(c4, f5(c4)) | big_p(f2(c4))),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[932, 926, 11, 1328, 1315])).
% 0.71/0.91 tff(1508,plain,
% 0.71/0.91 (big_r(c4, f5(c4))),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[1507, 1504])).
% 0.71/0.91 tff(1509,plain,
% 0.71/0.91 (big_r(f5(c4), f6(c4)) | big_p(f2(c4))),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[950, 944, 11, 1328, 1315])).
% 0.71/0.91 tff(1510,plain,
% 0.71/0.91 (big_r(f5(c4), f6(c4))),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[1509, 1504])).
% 0.71/0.91 tff(1511,plain,
% 0.71/0.91 ($false),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[1340, 2, 954, 996, 1510, 1508, 1506])).
% 0.71/0.91 tff(1512,plain,(big_p(c1)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.91 tff(1513,plain,
% 0.71/0.91 (big_r(c4, c3)),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[1463, 1512])).
% 0.71/0.91 tff(1514,plain,
% 0.71/0.91 (big_p(c3)),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[1443, 1512])).
% 0.71/0.91 tff(1515,plain,
% 0.71/0.91 (big_r(c4, f1(c4)) | big_p(f6(c4))),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[795, 789, 11, 1514, 1513])).
% 0.71/0.91 tff(1516,plain,
% 0.71/0.91 (big_p(f6(c4))),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[1515, 3])).
% 0.71/0.91 tff(1517,plain,
% 0.71/0.91 (big_r(c4, f1(c4)) | big_r(c4, f5(c4))),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[813, 807, 11, 1514, 1513])).
% 0.71/0.91 tff(1518,plain,
% 0.71/0.91 (big_r(c4, f5(c4))),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[1517, 3])).
% 0.71/0.91 tff(1519,plain,
% 0.71/0.91 (big_r(c4, f1(c4)) | big_r(f5(c4), f6(c4))),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[831, 825, 11, 1514, 1513])).
% 0.71/0.91 tff(1520,plain,
% 0.71/0.91 (big_r(f5(c4), f6(c4))),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[1519, 3])).
% 0.71/0.91 tff(1521,plain,
% 0.71/0.91 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c1)) | big_r(c4, f1(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c1)) | big_r(c4, f1(c4)))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(1522,plain,
% 0.71/0.91 (((~big_p(a)) | big_r(f5(c2), f6(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)) | (~big_r(c2, c1)) | (~big_p(c1))) <=> ((~big_p(a)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c1)) | big_r(c4, f1(c4)))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(1523,plain,
% 0.71/0.91 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_r(f5(c2), f6(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c1)) | big_r(c4, f1(c4))))),
% 0.71/0.91 inference(monotonicity,[status(thm)],[1522])).
% 0.71/0.91 tff(1524,plain,
% 0.71/0.91 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_r(f5(c2), f6(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c1)) | big_r(c4, f1(c4)))),
% 0.71/0.91 inference(transitivity,[status(thm)],[1523, 1521])).
% 0.71/0.91 tff(1525,plain,
% 0.71/0.91 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_r(f5(c2), f6(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 0.71/0.91 inference(quant_inst,[status(thm)],[])).
% 0.71/0.91 tff(1526,plain,
% 0.71/0.91 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c1)) | big_r(c4, f1(c4))),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[1525, 1524])).
% 0.71/0.91 tff(1527,plain,
% 0.71/0.91 (big_r(f5(c2), f6(c2)) | big_r(c4, f1(c4))),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[1526, 825, 11, 1514, 1513, 1512, 1409])).
% 0.71/0.91 tff(1528,plain,
% 0.71/0.91 (big_r(f5(c2), f6(c2))),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[1527, 3])).
% 0.71/0.91 tff(1529,plain,
% 0.71/0.91 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c1)) | big_r(c4, f1(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c1)) | big_r(c4, f1(c4)))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(1530,plain,
% 0.71/0.91 (((~big_p(a)) | big_p(f6(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)) | (~big_r(c2, c1)) | (~big_p(c1))) <=> ((~big_p(a)) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c1)) | big_r(c4, f1(c4)))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(1531,plain,
% 0.71/0.91 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_p(f6(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c1)) | big_r(c4, f1(c4))))),
% 0.71/0.91 inference(monotonicity,[status(thm)],[1530])).
% 0.71/0.91 tff(1532,plain,
% 0.71/0.91 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_p(f6(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c1)) | big_r(c4, f1(c4)))),
% 0.71/0.91 inference(transitivity,[status(thm)],[1531, 1529])).
% 0.71/0.91 tff(1533,plain,
% 0.71/0.91 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_p(f6(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 0.71/0.91 inference(quant_inst,[status(thm)],[])).
% 0.71/0.91 tff(1534,plain,
% 0.71/0.91 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c1)) | big_r(c4, f1(c4))),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[1533, 1532])).
% 0.71/0.91 tff(1535,plain,
% 0.71/0.91 (big_p(f6(c2)) | big_r(c4, f1(c4))),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[1534, 789, 11, 1514, 1513, 1512, 1409])).
% 0.71/0.91 tff(1536,plain,
% 0.71/0.91 (big_p(f6(c2))),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[1535, 3])).
% 0.71/0.91 tff(1537,plain,
% 0.71/0.91 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c1)) | big_r(c4, f1(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c1)) | big_r(c4, f1(c4)))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(1538,plain,
% 0.71/0.91 (((~big_p(a)) | big_r(c2, f5(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)) | (~big_r(c2, c1)) | (~big_p(c1))) <=> ((~big_p(a)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c1)) | big_r(c4, f1(c4)))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(1539,plain,
% 0.71/0.91 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_r(c2, f5(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c1)) | big_r(c4, f1(c4))))),
% 0.71/0.91 inference(monotonicity,[status(thm)],[1538])).
% 0.71/0.91 tff(1540,plain,
% 0.71/0.91 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_r(c2, f5(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c1)) | big_r(c4, f1(c4)))),
% 0.71/0.91 inference(transitivity,[status(thm)],[1539, 1537])).
% 0.71/0.91 tff(1541,plain,
% 0.71/0.91 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_r(c2, f5(c2)) | (~big_r(c4, c3)) | (~big_p(c3)) | big_r(c4, f1(c4)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 0.71/0.91 inference(quant_inst,[status(thm)],[])).
% 0.71/0.91 tff(1542,plain,
% 0.71/0.91 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | (~big_r(X7, X8)) | (~big_p(X8)) | big_r(X7, f1(X7)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c1)) | big_r(c4, f1(c4))),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[1541, 1540])).
% 0.71/0.91 tff(1543,plain,
% 0.71/0.91 (big_r(c2, f5(c2)) | big_r(c4, f1(c4))),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[1542, 807, 11, 1514, 1513, 1512, 1409])).
% 0.71/0.91 tff(1544,plain,
% 0.71/0.91 (big_r(c2, f5(c2))),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[1543, 3])).
% 0.71/0.91 tff(1545,plain,
% 0.71/0.91 ($false),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[1500, 304, 1544, 1536, 1528, 1520, 1518, 1516])).
% 0.71/0.91 tff(1546,plain,(big_r(c4, f1(c4))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.91 tff(1547,plain,
% 0.71/0.91 (big_p(f6(c2)) | (~big_r(c4, f1(c4))) | (~big_p(f2(c4))) | (~big_p(c1))),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[1270, 1409, 1502])).
% 0.71/0.91 tff(1548,plain,
% 0.71/0.91 (~big_p(f2(c4))),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[1547, 1, 1546, 1512])).
% 0.71/0.91 tff(1549,plain,
% 0.71/0.91 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c1)) | big_p(f2(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c1)) | big_p(f2(c4)))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(1550,plain,
% 0.71/0.91 (((~big_p(a)) | big_p(f6(c2)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c2, c1)) | (~big_p(c1))) <=> ((~big_p(a)) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c1)) | big_p(f2(c4)))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(1551,plain,
% 0.71/0.91 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_p(f6(c2)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c1)) | big_p(f2(c4))))),
% 0.71/0.92 inference(monotonicity,[status(thm)],[1550])).
% 0.71/0.92 tff(1552,plain,
% 0.71/0.92 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_p(f6(c2)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c1)) | big_p(f2(c4)))),
% 0.71/0.92 inference(transitivity,[status(thm)],[1551, 1549])).
% 0.71/0.92 tff(1553,plain,
% 0.71/0.92 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_p(f6(c2)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 0.71/0.92 inference(quant_inst,[status(thm)],[])).
% 0.71/0.92 tff(1554,plain,
% 0.71/0.92 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_p(f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | big_p(f6(c2)) | (~big_r(c2, c1)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c1)) | big_p(f2(c4))),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[1553, 1552])).
% 0.71/0.92 tff(1555,plain,
% 0.71/0.92 (big_p(f6(c2)) | big_p(f2(c4))),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[1554, 908, 11, 1514, 1513, 1512, 1409])).
% 0.71/0.92 tff(1556,plain,
% 0.71/0.92 ($false),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[1555, 1548, 1])).
% 0.71/0.92 tff(1557,plain,(big_p(f6(c2))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.92 tff(1558,plain,
% 0.71/0.92 (big_r(c2, f5(c2)) | (~big_r(c4, f1(c4))) | (~big_p(f2(c4))) | (~big_p(c1))),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[1249, 1409, 1502])).
% 0.71/0.92 tff(1559,plain,
% 0.71/0.92 (~big_p(f2(c4))),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[1558, 1223, 1546, 1512])).
% 0.71/0.92 tff(1560,plain,
% 0.71/0.92 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c1)) | big_p(f2(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c1)) | big_p(f2(c4)))),
% 0.71/0.92 inference(rewrite,[status(thm)],[])).
% 0.71/0.92 tff(1561,plain,
% 0.71/0.92 (((~big_p(a)) | big_r(c2, f5(c2)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c2, c1)) | (~big_p(c1))) <=> ((~big_p(a)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c1)) | big_p(f2(c4)))),
% 0.71/0.92 inference(rewrite,[status(thm)],[])).
% 0.71/0.92 tff(1562,plain,
% 0.71/0.92 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_r(c2, f5(c2)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c1)) | big_p(f2(c4))))),
% 0.71/0.92 inference(monotonicity,[status(thm)],[1561])).
% 0.71/0.92 tff(1563,plain,
% 0.71/0.92 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_r(c2, f5(c2)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c1)) | big_p(f2(c4)))),
% 0.71/0.92 inference(transitivity,[status(thm)],[1562, 1560])).
% 0.71/0.92 tff(1564,plain,
% 0.71/0.92 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_r(c2, f5(c2)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 0.71/0.92 inference(quant_inst,[status(thm)],[])).
% 0.71/0.92 tff(1565,plain,
% 0.71/0.92 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(X1, f5(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | big_r(c2, f5(c2)) | (~big_r(c2, c1)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c1)) | big_p(f2(c4))),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[1564, 1563])).
% 0.71/0.92 tff(1566,plain,
% 0.71/0.92 (big_r(c2, f5(c2)) | big_p(f2(c4))),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[1565, 926, 11, 1514, 1513, 1512, 1409])).
% 0.71/0.92 tff(1567,plain,
% 0.71/0.92 ($false),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[1566, 1559, 1223])).
% 0.71/0.92 tff(1568,plain,(big_r(c2, f5(c2))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.92 tff(1569,assumption,(~big_r(f5(c2), f6(c2))), introduced(assumption)).
% 0.71/0.92 tff(1570,plain,
% 0.71/0.92 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c1)) | big_p(f2(c4)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c1)) | big_p(f2(c4)))),
% 0.71/0.92 inference(rewrite,[status(thm)],[])).
% 0.71/0.92 tff(1571,plain,
% 0.71/0.92 (((~big_p(a)) | big_r(f5(c2), f6(c2)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c2, c1)) | (~big_p(c1))) <=> ((~big_p(a)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c1)) | big_p(f2(c4)))),
% 0.71/0.92 inference(rewrite,[status(thm)],[])).
% 0.71/0.92 tff(1572,plain,
% 0.71/0.92 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_r(f5(c2), f6(c2)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c1)) | big_p(f2(c4))))),
% 0.71/0.92 inference(monotonicity,[status(thm)],[1571])).
% 0.71/0.92 tff(1573,plain,
% 0.71/0.92 (((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_r(f5(c2), f6(c2)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c2, c1)) | (~big_p(c1)))) <=> ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c1)) | big_p(f2(c4)))),
% 0.71/0.92 inference(transitivity,[status(thm)],[1572, 1570])).
% 0.71/0.92 tff(1574,plain,
% 0.71/0.92 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | ((~big_p(a)) | big_r(f5(c2), f6(c2)) | big_p(f2(c4)) | (~big_r(c4, c3)) | (~big_p(c3)) | (~big_r(c2, c1)) | (~big_p(c1)))),
% 0.71/0.92 inference(quant_inst,[status(thm)],[])).
% 0.71/0.92 tff(1575,plain,
% 0.71/0.92 ((~![X2: $i, X7: $i, X8: $i, X1: $i] : ((~big_p(a)) | big_r(f5(X1), f6(X1)) | big_p(f2(X7)) | (~big_r(X7, X8)) | (~big_p(X8)) | (~big_r(X1, X2)) | (~big_p(X2)))) | (~big_p(a)) | big_r(f5(c2), f6(c2)) | (~big_r(c2, c1)) | (~big_p(c3)) | (~big_r(c4, c3)) | (~big_p(c1)) | big_p(f2(c4))),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[1574, 1573])).
% 0.71/0.92 tff(1576,plain,
% 0.71/0.92 (big_r(f5(c2), f6(c2)) | big_p(f2(c4))),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[1575, 944, 11, 1514, 1513, 1512, 1409])).
% 0.71/0.92 tff(1577,plain,
% 0.71/0.92 (big_p(f2(c4))),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[1576, 1569])).
% 0.71/0.92 tff(1578,plain,
% 0.71/0.92 (big_r(f1(c2), f2(c2))),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[1425, 1569, 1512])).
% 0.71/0.92 tff(1579,plain,
% 0.71/0.92 (big_p(f2(c2))),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[1436, 1569, 1512])).
% 0.71/0.92 tff(1580,plain,
% 0.71/0.92 (big_r(c2, f1(c2))),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[1410, 1569, 1512])).
% 0.71/0.92 tff(1581,plain,
% 0.71/0.92 ($false),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[334, 304, 1580, 1502, 1546, 1579, 1578, 1577])).
% 0.71/0.92 tff(1582,plain,(big_r(f5(c2), f6(c2))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.92 tff(1583,plain,
% 0.71/0.92 ((~big_p(f2(c4))) | (~big_p(f6(c2))) | (~big_r(c2, f5(c2)))),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[1264, 304, 1502, 1546, 1582])).
% 0.71/0.92 tff(1584,plain,
% 0.71/0.92 (~big_p(f2(c4))),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[1583, 1568, 1557])).
% 0.71/0.92 tff(1585,plain,
% 0.71/0.92 (big_p(f6(c4)) | big_p(f2(c4))),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[914, 908, 11, 1514, 1513])).
% 0.71/0.92 tff(1586,plain,
% 0.71/0.92 (big_p(f6(c4))),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[1585, 1584])).
% 0.71/0.92 tff(1587,plain,
% 0.71/0.92 (big_r(c4, f5(c4)) | big_p(f2(c4))),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[932, 926, 11, 1514, 1513])).
% 0.71/0.92 tff(1588,plain,
% 0.71/0.92 (big_r(c4, f5(c4))),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[1587, 1584])).
% 0.71/0.92 tff(1589,plain,
% 0.71/0.92 (big_r(f5(c4), f6(c4)) | big_p(f2(c4))),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[950, 944, 11, 1514, 1513])).
% 0.71/0.92 tff(1590,plain,
% 0.71/0.92 (big_r(f5(c4), f6(c4))),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[1589, 1584])).
% 0.71/0.92 tff(1591,plain,
% 0.71/0.92 ($false),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[1500, 304, 1568, 1557, 1582, 1590, 1588, 1586])).
% 0.71/0.92 % SZS output end Proof
% 0.71/0.92 % E exiting
%------------------------------------------------------------------------------