%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN673-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:39:48 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN673-1 : TPTP v9.0.0. Released v2.5.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 12:39:25 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.19/0.39 % SZS status Unsatisfiable
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(p29_type, type, (
% 0.19/0.39 p29: ( $i * $i ) > $o)).
% 0.19/0.39 tff(f14_type, type, (
% 0.19/0.39 f14: ( $i * $i ) > $i)).
% 0.19/0.39 tff(f17_type, type, (
% 0.19/0.39 f17: ( $i * $i ) > $i)).
% 0.19/0.39 tff(c40_type, type, (
% 0.19/0.39 c40: $i)).
% 0.19/0.39 tff(c36_type, type, (
% 0.19/0.39 c36: $i)).
% 0.19/0.39 tff(f19_type, type, (
% 0.19/0.39 f19: ( $i * $i ) > $i)).
% 0.19/0.39 tff(c39_type, type, (
% 0.19/0.39 c39: $i)).
% 0.19/0.39 tff(c37_type, type, (
% 0.19/0.39 c37: $i)).
% 0.19/0.39 tff(c35_type, type, (
% 0.19/0.39 c35: $i)).
% 0.19/0.39 tff(f5_type, type, (
% 0.19/0.39 f5: ( $i * $i ) > $i)).
% 0.19/0.39 tff(f8_type, type, (
% 0.19/0.39 f8: ( $i * $i ) > $i)).
% 0.19/0.39 tff(c30_type, type, (
% 0.19/0.39 c30: $i)).
% 0.19/0.39 tff(c34_type, type, (
% 0.19/0.39 c34: $i)).
% 0.19/0.39 tff(c33_type, type, (
% 0.19/0.39 c33: $i)).
% 0.19/0.39 tff(p27_type, type, (
% 0.19/0.39 p27: ( $i * $i ) > $o)).
% 0.19/0.39 tff(f12_type, type, (
% 0.19/0.39 f12: ( $i * $i ) > $i)).
% 0.19/0.39 tff(c32_type, type, (
% 0.19/0.39 c32: $i)).
% 0.19/0.39 tff(p28_type, type, (
% 0.19/0.39 p28: ( $i * $i ) > $o)).
% 0.19/0.39 tff(c31_type, type, (
% 0.19/0.39 c31: $i)).
% 0.19/0.39 tff(f21_type, type, (
% 0.19/0.39 f21: ( $i * $i ) > $i)).
% 0.19/0.39 tff(f26_type, type, (
% 0.19/0.39 f26: ( $i * $i ) > $i)).
% 0.19/0.39 tff(c43_type, type, (
% 0.19/0.39 c43: $i)).
% 0.19/0.39 tff(p10_type, type, (
% 0.19/0.39 p10: ( $i * $i ) > $o)).
% 0.19/0.39 tff(c41_type, type, (
% 0.19/0.39 c41: $i)).
% 0.19/0.39 tff(f24_type, type, (
% 0.19/0.39 f24: ( $i * $i ) > $i)).
% 0.19/0.39 tff(c42_type, type, (
% 0.19/0.39 c42: $i)).
% 0.19/0.39 tff(p16_type, type, (
% 0.19/0.39 p16: ( $i * $i ) > $o)).
% 0.19/0.39 tff(c38_type, type, (
% 0.19/0.39 c38: $i)).
% 0.19/0.39 tff(p4_type, type, (
% 0.19/0.39 p4: ( $i * $i ) > $o)).
% 0.19/0.39 tff(p3_type, type, (
% 0.19/0.39 p3: ( $i * $i ) > $o)).
% 0.19/0.39 tff(p2_type, type, (
% 0.19/0.39 p2: ( $i * $i ) > $o)).
% 0.19/0.39 tff(1,assumption,(~p29(f5(c33, f8(c34, c30)), f14(f19(c35, c37), c39))), introduced(assumption)).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 (^[X7: $i] : refl(p10(f14(f19(c35, X7), c41), X7) <=> p10(f14(f19(c35, X7), c41), X7))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 (![X7: $i] : p10(f14(f19(c35, X7), c41), X7) <=> ![X7: $i] : p10(f14(f19(c35, X7), c41), X7)),
% 0.19/0.39 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.39 tff(4,plain,
% 0.19/0.39 (![X7: $i] : p10(f14(f19(c35, X7), c41), X7) <=> ![X7: $i] : p10(f14(f19(c35, X7), c41), X7)),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(5,axiom,(![X7: $i] : p10(f14(f19(c35, X7), c41), X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p10_16')).
% 0.19/0.39 tff(6,plain,
% 0.19/0.39 (![X7: $i] : p10(f14(f19(c35, X7), c41), X7)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.19/0.39 tff(7,plain,(
% 0.19/0.39 ![X7: $i] : p10(f14(f19(c35, X7), c41), X7)),
% 0.19/0.39 inference(skolemize,[status(sab)],[6])).
% 0.19/0.39 tff(8,plain,
% 0.19/0.39 (![X7: $i] : p10(f14(f19(c35, X7), c41), X7)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.39 tff(9,plain,
% 0.19/0.39 ((~![X7: $i] : p10(f14(f19(c35, X7), c41), X7)) | p10(f14(f19(c35, f14(f19(c35, c37), c39)), c41), f14(f19(c35, c37), c39))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(10,plain,
% 0.19/0.39 (p10(f14(f19(c35, f14(f19(c35, c37), c39)), c41), f14(f19(c35, c37), c39))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.19/0.39 tff(11,plain,
% 0.19/0.39 (^[X0: $i, X2: $i, X1: $i] : refl(((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2)) <=> ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2)))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(12,plain,
% 0.19/0.39 (![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2)) <=> ![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[11])).
% 0.19/0.39 tff(13,plain,
% 0.19/0.39 (![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2)) <=> ![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(14,plain,
% 0.19/0.39 (^[X0: $i, X2: $i, X1: $i] : trans(monotonicity(rewrite((p10(X1, X2) | (~p10(X0, X1))) <=> ((~p10(X0, X1)) | p10(X1, X2))), (((p10(X1, X2) | (~p10(X0, X1))) | (~p10(X0, X2))) <=> (((~p10(X0, X1)) | p10(X1, X2)) | (~p10(X0, X2))))), rewrite((((~p10(X0, X1)) | p10(X1, X2)) | (~p10(X0, X2))) <=> ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))), (((p10(X1, X2) | (~p10(X0, X1))) | (~p10(X0, X2))) <=> ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(15,plain,
% 0.19/0.39 (![X0: $i, X2: $i, X1: $i] : ((p10(X1, X2) | (~p10(X0, X1))) | (~p10(X0, X2))) <=> ![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[14])).
% 0.19/0.39 tff(16,axiom,(![X0: $i, X2: $i, X1: $i] : ((p10(X1, X2) | (~p10(X0, X1))) | (~p10(X0, X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p10_22')).
% 0.19/0.39 tff(17,plain,
% 0.19/0.39 (![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.19/0.39 tff(18,plain,
% 0.19/0.39 (![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.19/0.39 tff(19,plain,(
% 0.19/0.39 ![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))),
% 0.19/0.39 inference(skolemize,[status(sab)],[18])).
% 0.19/0.39 tff(20,plain,
% 0.19/0.39 (![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.19/0.39 tff(21,plain,
% 0.19/0.39 (((~![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))) | (p10(f14(f19(c35, c37), c39), f14(f19(c35, c37), c39)) | (~p10(f14(f19(c35, f14(f19(c35, c37), c39)), c41), f14(f19(c35, c37), c39))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))) | p10(f14(f19(c35, c37), c39), f14(f19(c35, c37), c39)) | (~p10(f14(f19(c35, f14(f19(c35, c37), c39)), c41), f14(f19(c35, c37), c39))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(22,plain,
% 0.19/0.39 (((~p10(f14(f19(c35, f14(f19(c35, c37), c39)), c41), f14(f19(c35, c37), c39))) | (~p10(f14(f19(c35, f14(f19(c35, c37), c39)), c41), f14(f19(c35, c37), c39))) | p10(f14(f19(c35, c37), c39), f14(f19(c35, c37), c39))) <=> (p10(f14(f19(c35, c37), c39), f14(f19(c35, c37), c39)) | (~p10(f14(f19(c35, f14(f19(c35, c37), c39)), c41), f14(f19(c35, c37), c39))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(23,plain,
% 0.19/0.39 (((~![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))) | ((~p10(f14(f19(c35, f14(f19(c35, c37), c39)), c41), f14(f19(c35, c37), c39))) | (~p10(f14(f19(c35, f14(f19(c35, c37), c39)), c41), f14(f19(c35, c37), c39))) | p10(f14(f19(c35, c37), c39), f14(f19(c35, c37), c39)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))) | (p10(f14(f19(c35, c37), c39), f14(f19(c35, c37), c39)) | (~p10(f14(f19(c35, f14(f19(c35, c37), c39)), c41), f14(f19(c35, c37), c39)))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[22])).
% 0.19/0.39 tff(24,plain,
% 0.19/0.39 (((~![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))) | ((~p10(f14(f19(c35, f14(f19(c35, c37), c39)), c41), f14(f19(c35, c37), c39))) | (~p10(f14(f19(c35, f14(f19(c35, c37), c39)), c41), f14(f19(c35, c37), c39))) | p10(f14(f19(c35, c37), c39), f14(f19(c35, c37), c39)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))) | p10(f14(f19(c35, c37), c39), f14(f19(c35, c37), c39)) | (~p10(f14(f19(c35, f14(f19(c35, c37), c39)), c41), f14(f19(c35, c37), c39))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[23, 21])).
% 0.19/0.39 tff(25,plain,
% 0.19/0.39 ((~![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))) | ((~p10(f14(f19(c35, f14(f19(c35, c37), c39)), c41), f14(f19(c35, c37), c39))) | (~p10(f14(f19(c35, f14(f19(c35, c37), c39)), c41), f14(f19(c35, c37), c39))) | p10(f14(f19(c35, c37), c39), f14(f19(c35, c37), c39)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(26,plain,
% 0.19/0.39 ((~![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))) | p10(f14(f19(c35, c37), c39), f14(f19(c35, c37), c39)) | (~p10(f14(f19(c35, f14(f19(c35, c37), c39)), c41), f14(f19(c35, c37), c39)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.19/0.39 tff(27,plain,
% 0.19/0.39 (p10(f14(f19(c35, c37), c39), f14(f19(c35, c37), c39))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[26, 20, 10])).
% 0.19/0.39 tff(28,plain,
% 0.19/0.39 (^[X73: $i] : refl(((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | (~p28(f21(c30, f26(c43, X73)), c31))) <=> ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | (~p28(f21(c30, f26(c43, X73)), c31))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(29,plain,
% 0.19/0.39 (![X73: $i] : ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | (~p28(f21(c30, f26(c43, X73)), c31))) <=> ![X73: $i] : ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | (~p28(f21(c30, f26(c43, X73)), c31)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[28])).
% 0.19/0.40 tff(30,plain,
% 0.19/0.40 (![X73: $i] : ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | (~p28(f21(c30, f26(c43, X73)), c31))) <=> ![X73: $i] : ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | (~p28(f21(c30, f26(c43, X73)), c31)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(31,plain,
% 0.19/0.40 (^[X73: $i] : trans(monotonicity(rewrite((p29(f5(c33, f8(c34, c30)), X73) | (~p10(X73, f14(f19(c35, c37), c39)))) <=> ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73))), (((p29(f5(c33, f8(c34, c30)), X73) | (~p10(X73, f14(f19(c35, c37), c39)))) | (~p28(f21(c30, f26(c43, X73)), c31))) <=> (((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73)) | (~p28(f21(c30, f26(c43, X73)), c31))))), rewrite((((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73)) | (~p28(f21(c30, f26(c43, X73)), c31))) <=> ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | (~p28(f21(c30, f26(c43, X73)), c31)))), (((p29(f5(c33, f8(c34, c30)), X73) | (~p10(X73, f14(f19(c35, c37), c39)))) | (~p28(f21(c30, f26(c43, X73)), c31))) <=> ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | (~p28(f21(c30, f26(c43, X73)), c31)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(32,plain,
% 0.19/0.40 (![X73: $i] : ((p29(f5(c33, f8(c34, c30)), X73) | (~p10(X73, f14(f19(c35, c37), c39)))) | (~p28(f21(c30, f26(c43, X73)), c31))) <=> ![X73: $i] : ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | (~p28(f21(c30, f26(c43, X73)), c31)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[31])).
% 0.19/0.40 tff(33,axiom,(![X73: $i] : ((p29(f5(c33, f8(c34, c30)), X73) | (~p10(X73, f14(f19(c35, c37), c39)))) | (~p28(f21(c30, f26(c43, X73)), c31)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p29_53')).
% 0.19/0.40 tff(34,plain,
% 0.19/0.40 (![X73: $i] : ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | (~p28(f21(c30, f26(c43, X73)), c31)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.19/0.40 tff(35,plain,
% 0.19/0.40 (![X73: $i] : ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | (~p28(f21(c30, f26(c43, X73)), c31)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.19/0.40 tff(36,plain,(
% 0.19/0.40 ![X73: $i] : ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | (~p28(f21(c30, f26(c43, X73)), c31)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[35])).
% 0.19/0.40 tff(37,plain,
% 0.19/0.40 (![X73: $i] : ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | (~p28(f21(c30, f26(c43, X73)), c31)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.19/0.40 tff(38,plain,
% 0.19/0.40 (((~![X73: $i] : ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | (~p28(f21(c30, f26(c43, X73)), c31)))) | ((~p10(f14(f19(c35, c37), c39), f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), f14(f19(c35, c37), c39)) | (~p28(f21(c30, f26(c43, f14(f19(c35, c37), c39))), c31)))) <=> ((~![X73: $i] : ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | (~p28(f21(c30, f26(c43, X73)), c31)))) | (~p10(f14(f19(c35, c37), c39), f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), f14(f19(c35, c37), c39)) | (~p28(f21(c30, f26(c43, f14(f19(c35, c37), c39))), c31)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(39,plain,
% 0.19/0.40 ((~![X73: $i] : ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | (~p28(f21(c30, f26(c43, X73)), c31)))) | ((~p10(f14(f19(c35, c37), c39), f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), f14(f19(c35, c37), c39)) | (~p28(f21(c30, f26(c43, f14(f19(c35, c37), c39))), c31)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(40,plain,
% 0.19/0.40 ((~![X73: $i] : ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | (~p28(f21(c30, f26(c43, X73)), c31)))) | (~p10(f14(f19(c35, c37), c39), f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), f14(f19(c35, c37), c39)) | (~p28(f21(c30, f26(c43, f14(f19(c35, c37), c39))), c31))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.19/0.40 tff(41,plain,
% 0.19/0.40 (p29(f5(c33, f8(c34, c30)), f14(f19(c35, c37), c39)) | (~p28(f21(c30, f26(c43, f14(f19(c35, c37), c39))), c31))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[40, 37, 27])).
% 0.19/0.40 tff(42,plain,
% 0.19/0.40 (~p28(f21(c30, f26(c43, f14(f19(c35, c37), c39))), c31)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[41, 1])).
% 0.19/0.40 tff(43,plain,
% 0.19/0.40 (^[X73: $i] : refl(((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | p29(f24(c42, f26(c43, X73)), c39)) <=> ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | p29(f24(c42, f26(c43, X73)), c39)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(44,plain,
% 0.19/0.40 (![X73: $i] : ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | p29(f24(c42, f26(c43, X73)), c39)) <=> ![X73: $i] : ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | p29(f24(c42, f26(c43, X73)), c39))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[43])).
% 0.19/0.40 tff(45,plain,
% 0.19/0.40 (![X73: $i] : ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | p29(f24(c42, f26(c43, X73)), c39)) <=> ![X73: $i] : ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | p29(f24(c42, f26(c43, X73)), c39))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(46,plain,
% 0.19/0.40 (^[X73: $i] : rewrite(((p29(f24(c42, f26(c43, X73)), c39) | p29(f5(c33, f8(c34, c30)), X73)) | (~p10(X73, f14(f19(c35, c37), c39)))) <=> ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | p29(f24(c42, f26(c43, X73)), c39)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(47,plain,
% 0.19/0.40 (![X73: $i] : ((p29(f24(c42, f26(c43, X73)), c39) | p29(f5(c33, f8(c34, c30)), X73)) | (~p10(X73, f14(f19(c35, c37), c39)))) <=> ![X73: $i] : ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | p29(f24(c42, f26(c43, X73)), c39))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[46])).
% 0.19/0.40 tff(48,axiom,(![X73: $i] : ((p29(f24(c42, f26(c43, X73)), c39) | p29(f5(c33, f8(c34, c30)), X73)) | (~p10(X73, f14(f19(c35, c37), c39))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p29_52')).
% 0.19/0.40 tff(49,plain,
% 0.19/0.40 (![X73: $i] : ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | p29(f24(c42, f26(c43, X73)), c39))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.19/0.40 tff(50,plain,
% 0.19/0.40 (![X73: $i] : ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | p29(f24(c42, f26(c43, X73)), c39))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.19/0.40 tff(51,plain,(
% 0.19/0.40 ![X73: $i] : ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | p29(f24(c42, f26(c43, X73)), c39))),
% 0.19/0.40 inference(skolemize,[status(sab)],[50])).
% 0.19/0.40 tff(52,plain,
% 0.19/0.40 (![X73: $i] : ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | p29(f24(c42, f26(c43, X73)), c39))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.19/0.40 tff(53,plain,
% 0.19/0.40 (((~![X73: $i] : ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | p29(f24(c42, f26(c43, X73)), c39))) | ((~p10(f14(f19(c35, c37), c39), f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), f14(f19(c35, c37), c39)) | p29(f24(c42, f26(c43, f14(f19(c35, c37), c39))), c39))) <=> ((~![X73: $i] : ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | p29(f24(c42, f26(c43, X73)), c39))) | (~p10(f14(f19(c35, c37), c39), f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), f14(f19(c35, c37), c39)) | p29(f24(c42, f26(c43, f14(f19(c35, c37), c39))), c39))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(54,plain,
% 0.19/0.40 ((~![X73: $i] : ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | p29(f24(c42, f26(c43, X73)), c39))) | ((~p10(f14(f19(c35, c37), c39), f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), f14(f19(c35, c37), c39)) | p29(f24(c42, f26(c43, f14(f19(c35, c37), c39))), c39))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(55,plain,
% 0.19/0.40 ((~![X73: $i] : ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | p29(f24(c42, f26(c43, X73)), c39))) | (~p10(f14(f19(c35, c37), c39), f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), f14(f19(c35, c37), c39)) | p29(f24(c42, f26(c43, f14(f19(c35, c37), c39))), c39)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.19/0.41 tff(56,plain,
% 0.19/0.41 (p29(f5(c33, f8(c34, c30)), f14(f19(c35, c37), c39)) | p29(f24(c42, f26(c43, f14(f19(c35, c37), c39))), c39)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[55, 52, 27])).
% 0.19/0.41 tff(57,plain,
% 0.19/0.41 (p29(f24(c42, f26(c43, f14(f19(c35, c37), c39))), c39)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[56, 1])).
% 0.19/0.41 tff(58,plain,
% 0.19/0.41 (^[X68: $i] : refl((p28(f21(c30, X68), c31) | (~p29(f24(c42, X68), c39))) <=> (p28(f21(c30, X68), c31) | (~p29(f24(c42, X68), c39))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(59,plain,
% 0.19/0.41 (![X68: $i] : (p28(f21(c30, X68), c31) | (~p29(f24(c42, X68), c39))) <=> ![X68: $i] : (p28(f21(c30, X68), c31) | (~p29(f24(c42, X68), c39)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[58])).
% 0.19/0.41 tff(60,plain,
% 0.19/0.41 (![X68: $i] : (p28(f21(c30, X68), c31) | (~p29(f24(c42, X68), c39))) <=> ![X68: $i] : (p28(f21(c30, X68), c31) | (~p29(f24(c42, X68), c39)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(61,axiom,(![X68: $i] : (p28(f21(c30, X68), c31) | (~p29(f24(c42, X68), c39)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p28_37')).
% 0.19/0.41 tff(62,plain,
% 0.19/0.41 (![X68: $i] : (p28(f21(c30, X68), c31) | (~p29(f24(c42, X68), c39)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.19/0.41 tff(63,plain,(
% 0.19/0.41 ![X68: $i] : (p28(f21(c30, X68), c31) | (~p29(f24(c42, X68), c39)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[62])).
% 0.19/0.41 tff(64,plain,
% 0.19/0.41 (![X68: $i] : (p28(f21(c30, X68), c31) | (~p29(f24(c42, X68), c39)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.19/0.41 tff(65,plain,
% 0.19/0.41 (((~![X68: $i] : (p28(f21(c30, X68), c31) | (~p29(f24(c42, X68), c39)))) | (p28(f21(c30, f26(c43, f14(f19(c35, c37), c39))), c31) | (~p29(f24(c42, f26(c43, f14(f19(c35, c37), c39))), c39)))) <=> ((~![X68: $i] : (p28(f21(c30, X68), c31) | (~p29(f24(c42, X68), c39)))) | p28(f21(c30, f26(c43, f14(f19(c35, c37), c39))), c31) | (~p29(f24(c42, f26(c43, f14(f19(c35, c37), c39))), c39)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(66,plain,
% 0.19/0.41 ((~![X68: $i] : (p28(f21(c30, X68), c31) | (~p29(f24(c42, X68), c39)))) | (p28(f21(c30, f26(c43, f14(f19(c35, c37), c39))), c31) | (~p29(f24(c42, f26(c43, f14(f19(c35, c37), c39))), c39)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(67,plain,
% 0.19/0.41 ((~![X68: $i] : (p28(f21(c30, X68), c31) | (~p29(f24(c42, X68), c39)))) | p28(f21(c30, f26(c43, f14(f19(c35, c37), c39))), c31) | (~p29(f24(c42, f26(c43, f14(f19(c35, c37), c39))), c39))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.19/0.41 tff(68,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[67, 64, 57, 42])).
% 0.19/0.41 tff(69,plain,(p29(f5(c33, f8(c34, c30)), f14(f19(c35, c37), c39))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(70,plain,
% 0.19/0.41 (^[X59: $i, X60: $i] : refl((p27(f12(c32, X59), X60) | (~p29(X60, X59))) <=> (p27(f12(c32, X59), X60) | (~p29(X60, X59))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(71,plain,
% 0.19/0.41 (![X59: $i, X60: $i] : (p27(f12(c32, X59), X60) | (~p29(X60, X59))) <=> ![X59: $i, X60: $i] : (p27(f12(c32, X59), X60) | (~p29(X60, X59)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[70])).
% 0.19/0.41 tff(72,plain,
% 0.19/0.41 (![X59: $i, X60: $i] : (p27(f12(c32, X59), X60) | (~p29(X60, X59))) <=> ![X59: $i, X60: $i] : (p27(f12(c32, X59), X60) | (~p29(X60, X59)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(73,axiom,(![X59: $i, X60: $i] : (p27(f12(c32, X59), X60) | (~p29(X60, X59)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p27_19')).
% 0.19/0.41 tff(74,plain,
% 0.19/0.41 (![X59: $i, X60: $i] : (p27(f12(c32, X59), X60) | (~p29(X60, X59)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.19/0.41 tff(75,plain,(
% 0.19/0.41 ![X59: $i, X60: $i] : (p27(f12(c32, X59), X60) | (~p29(X60, X59)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[74])).
% 0.19/0.41 tff(76,plain,
% 0.19/0.41 (![X59: $i, X60: $i] : (p27(f12(c32, X59), X60) | (~p29(X60, X59)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[75, 71])).
% 0.19/0.41 tff(77,plain,
% 0.19/0.41 (((~![X59: $i, X60: $i] : (p27(f12(c32, X59), X60) | (~p29(X60, X59)))) | (p27(f12(c32, f14(f19(c35, c37), c39)), f5(c33, f8(c34, c30))) | (~p29(f5(c33, f8(c34, c30)), f14(f19(c35, c37), c39))))) <=> ((~![X59: $i, X60: $i] : (p27(f12(c32, X59), X60) | (~p29(X60, X59)))) | p27(f12(c32, f14(f19(c35, c37), c39)), f5(c33, f8(c34, c30))) | (~p29(f5(c33, f8(c34, c30)), f14(f19(c35, c37), c39))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(78,plain,
% 0.19/0.41 ((~![X59: $i, X60: $i] : (p27(f12(c32, X59), X60) | (~p29(X60, X59)))) | (p27(f12(c32, f14(f19(c35, c37), c39)), f5(c33, f8(c34, c30))) | (~p29(f5(c33, f8(c34, c30)), f14(f19(c35, c37), c39))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(79,plain,
% 0.19/0.41 ((~![X59: $i, X60: $i] : (p27(f12(c32, X59), X60) | (~p29(X60, X59)))) | p27(f12(c32, f14(f19(c35, c37), c39)), f5(c33, f8(c34, c30))) | (~p29(f5(c33, f8(c34, c30)), f14(f19(c35, c37), c39)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.19/0.41 tff(80,plain,
% 0.19/0.41 (p27(f12(c32, f14(f19(c35, c37), c39)), f5(c33, f8(c34, c30)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[79, 76, 69])).
% 0.19/0.41 tff(81,assumption,(~p16(c40, c40)), introduced(assumption)).
% 0.19/0.41 tff(82,plain,
% 0.19/0.41 (^[X29: $i] : refl(p16(X29, X29) <=> p16(X29, X29))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(83,plain,
% 0.19/0.41 (![X29: $i] : p16(X29, X29) <=> ![X29: $i] : p16(X29, X29)),
% 0.19/0.41 inference(quant_intro,[status(thm)],[82])).
% 0.19/0.41 tff(84,plain,
% 0.19/0.41 (![X29: $i] : p16(X29, X29) <=> ![X29: $i] : p16(X29, X29)),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(85,axiom,(![X29: $i] : p16(X29, X29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p16_12')).
% 0.19/0.41 tff(86,plain,
% 0.19/0.41 (![X29: $i] : p16(X29, X29)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.19/0.41 tff(87,plain,(
% 0.19/0.41 ![X29: $i] : p16(X29, X29)),
% 0.19/0.41 inference(skolemize,[status(sab)],[86])).
% 0.19/0.41 tff(88,plain,
% 0.19/0.41 (![X29: $i] : p16(X29, X29)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.19/0.41 tff(89,plain,
% 0.19/0.41 ((~![X29: $i] : p16(X29, X29)) | p16(c40, c40)),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(90,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[89, 88, 81])).
% 0.19/0.41 tff(91,plain,(p16(c40, c40)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(92,plain,
% 0.19/0.41 (^[X68: $i] : refl(((~p16(X68, c40)) | p28(f21(c30, X68), c31)) <=> ((~p16(X68, c40)) | p28(f21(c30, X68), c31)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(93,plain,
% 0.19/0.41 (![X68: $i] : ((~p16(X68, c40)) | p28(f21(c30, X68), c31)) <=> ![X68: $i] : ((~p16(X68, c40)) | p28(f21(c30, X68), c31))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[92])).
% 0.19/0.41 tff(94,plain,
% 0.19/0.41 (![X68: $i] : ((~p16(X68, c40)) | p28(f21(c30, X68), c31)) <=> ![X68: $i] : ((~p16(X68, c40)) | p28(f21(c30, X68), c31))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(95,plain,
% 0.19/0.41 (^[X68: $i] : rewrite((p28(f21(c30, X68), c31) | (~p16(X68, c40))) <=> ((~p16(X68, c40)) | p28(f21(c30, X68), c31)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(96,plain,
% 0.19/0.41 (![X68: $i] : (p28(f21(c30, X68), c31) | (~p16(X68, c40))) <=> ![X68: $i] : ((~p16(X68, c40)) | p28(f21(c30, X68), c31))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[95])).
% 0.19/0.41 tff(97,axiom,(![X68: $i] : (p28(f21(c30, X68), c31) | (~p16(X68, c40)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p28_20')).
% 0.19/0.41 tff(98,plain,
% 0.19/0.41 (![X68: $i] : ((~p16(X68, c40)) | p28(f21(c30, X68), c31))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.19/0.41 tff(99,plain,
% 0.19/0.41 (![X68: $i] : ((~p16(X68, c40)) | p28(f21(c30, X68), c31))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[98, 94])).
% 0.19/0.41 tff(100,plain,(
% 0.19/0.41 ![X68: $i] : ((~p16(X68, c40)) | p28(f21(c30, X68), c31))),
% 0.19/0.41 inference(skolemize,[status(sab)],[99])).
% 0.19/0.41 tff(101,plain,
% 0.19/0.41 (![X68: $i] : ((~p16(X68, c40)) | p28(f21(c30, X68), c31))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[100, 93])).
% 0.19/0.41 tff(102,plain,
% 0.19/0.41 (((~![X68: $i] : ((~p16(X68, c40)) | p28(f21(c30, X68), c31))) | ((~p16(c40, c40)) | p28(f21(c30, c40), c31))) <=> ((~![X68: $i] : ((~p16(X68, c40)) | p28(f21(c30, X68), c31))) | (~p16(c40, c40)) | p28(f21(c30, c40), c31))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(103,plain,
% 0.19/0.41 ((~![X68: $i] : ((~p16(X68, c40)) | p28(f21(c30, X68), c31))) | ((~p16(c40, c40)) | p28(f21(c30, c40), c31))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(104,plain,
% 0.19/0.42 ((~![X68: $i] : ((~p16(X68, c40)) | p28(f21(c30, X68), c31))) | (~p16(c40, c40)) | p28(f21(c30, c40), c31)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.19/0.42 tff(105,plain,
% 0.19/0.42 (p28(f21(c30, c40), c31)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[104, 101, 91])).
% 0.19/0.42 tff(106,plain,
% 0.19/0.42 (^[X62: $i, X61: $i] : refl(((~p27(f12(c32, X61), f5(c33, f8(c34, c30)))) | (~p28(f21(c30, X62), c31)) | p27(f12(c32, f14(f19(c35, X61), f17(c36, X62))), f5(c33, f8(c34, c30)))) <=> ((~p27(f12(c32, X61), f5(c33, f8(c34, c30)))) | (~p28(f21(c30, X62), c31)) | p27(f12(c32, f14(f19(c35, X61), f17(c36, X62))), f5(c33, f8(c34, c30)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(107,plain,
% 0.19/0.42 (![X62: $i, X61: $i] : ((~p27(f12(c32, X61), f5(c33, f8(c34, c30)))) | (~p28(f21(c30, X62), c31)) | p27(f12(c32, f14(f19(c35, X61), f17(c36, X62))), f5(c33, f8(c34, c30)))) <=> ![X62: $i, X61: $i] : ((~p27(f12(c32, X61), f5(c33, f8(c34, c30)))) | (~p28(f21(c30, X62), c31)) | p27(f12(c32, f14(f19(c35, X61), f17(c36, X62))), f5(c33, f8(c34, c30))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[106])).
% 0.19/0.42 tff(108,plain,
% 0.19/0.42 (![X62: $i, X61: $i] : ((~p27(f12(c32, X61), f5(c33, f8(c34, c30)))) | (~p28(f21(c30, X62), c31)) | p27(f12(c32, f14(f19(c35, X61), f17(c36, X62))), f5(c33, f8(c34, c30)))) <=> ![X62: $i, X61: $i] : ((~p27(f12(c32, X61), f5(c33, f8(c34, c30)))) | (~p28(f21(c30, X62), c31)) | p27(f12(c32, f14(f19(c35, X61), f17(c36, X62))), f5(c33, f8(c34, c30))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(109,plain,
% 0.19/0.42 (^[X62: $i, X61: $i] : trans(monotonicity(rewrite((p27(f12(c32, f14(f19(c35, X61), f17(c36, X62))), f5(c33, f8(c34, c30))) | (~p28(f21(c30, X62), c31))) <=> ((~p28(f21(c30, X62), c31)) | p27(f12(c32, f14(f19(c35, X61), f17(c36, X62))), f5(c33, f8(c34, c30))))), (((p27(f12(c32, f14(f19(c35, X61), f17(c36, X62))), f5(c33, f8(c34, c30))) | (~p28(f21(c30, X62), c31))) | (~p27(f12(c32, X61), f5(c33, f8(c34, c30))))) <=> (((~p28(f21(c30, X62), c31)) | p27(f12(c32, f14(f19(c35, X61), f17(c36, X62))), f5(c33, f8(c34, c30)))) | (~p27(f12(c32, X61), f5(c33, f8(c34, c30))))))), rewrite((((~p28(f21(c30, X62), c31)) | p27(f12(c32, f14(f19(c35, X61), f17(c36, X62))), f5(c33, f8(c34, c30)))) | (~p27(f12(c32, X61), f5(c33, f8(c34, c30))))) <=> ((~p27(f12(c32, X61), f5(c33, f8(c34, c30)))) | (~p28(f21(c30, X62), c31)) | p27(f12(c32, f14(f19(c35, X61), f17(c36, X62))), f5(c33, f8(c34, c30))))), (((p27(f12(c32, f14(f19(c35, X61), f17(c36, X62))), f5(c33, f8(c34, c30))) | (~p28(f21(c30, X62), c31))) | (~p27(f12(c32, X61), f5(c33, f8(c34, c30))))) <=> ((~p27(f12(c32, X61), f5(c33, f8(c34, c30)))) | (~p28(f21(c30, X62), c31)) | p27(f12(c32, f14(f19(c35, X61), f17(c36, X62))), f5(c33, f8(c34, c30))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(110,plain,
% 0.19/0.42 (![X62: $i, X61: $i] : ((p27(f12(c32, f14(f19(c35, X61), f17(c36, X62))), f5(c33, f8(c34, c30))) | (~p28(f21(c30, X62), c31))) | (~p27(f12(c32, X61), f5(c33, f8(c34, c30))))) <=> ![X62: $i, X61: $i] : ((~p27(f12(c32, X61), f5(c33, f8(c34, c30)))) | (~p28(f21(c30, X62), c31)) | p27(f12(c32, f14(f19(c35, X61), f17(c36, X62))), f5(c33, f8(c34, c30))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[109])).
% 0.19/0.42 tff(111,axiom,(![X62: $i, X61: $i] : ((p27(f12(c32, f14(f19(c35, X61), f17(c36, X62))), f5(c33, f8(c34, c30))) | (~p28(f21(c30, X62), c31))) | (~p27(f12(c32, X61), f5(c33, f8(c34, c30)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p27_55')).
% 0.19/0.42 tff(112,plain,
% 0.19/0.42 (![X62: $i, X61: $i] : ((~p27(f12(c32, X61), f5(c33, f8(c34, c30)))) | (~p28(f21(c30, X62), c31)) | p27(f12(c32, f14(f19(c35, X61), f17(c36, X62))), f5(c33, f8(c34, c30))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.19/0.42 tff(113,plain,
% 0.19/0.42 (![X62: $i, X61: $i] : ((~p27(f12(c32, X61), f5(c33, f8(c34, c30)))) | (~p28(f21(c30, X62), c31)) | p27(f12(c32, f14(f19(c35, X61), f17(c36, X62))), f5(c33, f8(c34, c30))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[112, 108])).
% 0.19/0.42 tff(114,plain,(
% 0.19/0.42 ![X62: $i, X61: $i] : ((~p27(f12(c32, X61), f5(c33, f8(c34, c30)))) | (~p28(f21(c30, X62), c31)) | p27(f12(c32, f14(f19(c35, X61), f17(c36, X62))), f5(c33, f8(c34, c30))))),
% 0.19/0.42 inference(skolemize,[status(sab)],[113])).
% 0.19/0.42 tff(115,plain,
% 0.19/0.42 (![X62: $i, X61: $i] : ((~p27(f12(c32, X61), f5(c33, f8(c34, c30)))) | (~p28(f21(c30, X62), c31)) | p27(f12(c32, f14(f19(c35, X61), f17(c36, X62))), f5(c33, f8(c34, c30))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[114, 107])).
% 0.19/0.42 tff(116,plain,
% 0.19/0.42 (((~![X62: $i, X61: $i] : ((~p27(f12(c32, X61), f5(c33, f8(c34, c30)))) | (~p28(f21(c30, X62), c31)) | p27(f12(c32, f14(f19(c35, X61), f17(c36, X62))), f5(c33, f8(c34, c30))))) | ((~p28(f21(c30, c40), c31)) | (~p27(f12(c32, f14(f19(c35, c37), c39)), f5(c33, f8(c34, c30)))) | p27(f12(c32, f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40))), f5(c33, f8(c34, c30))))) <=> ((~![X62: $i, X61: $i] : ((~p27(f12(c32, X61), f5(c33, f8(c34, c30)))) | (~p28(f21(c30, X62), c31)) | p27(f12(c32, f14(f19(c35, X61), f17(c36, X62))), f5(c33, f8(c34, c30))))) | (~p28(f21(c30, c40), c31)) | (~p27(f12(c32, f14(f19(c35, c37), c39)), f5(c33, f8(c34, c30)))) | p27(f12(c32, f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40))), f5(c33, f8(c34, c30))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(117,plain,
% 0.19/0.42 (((~p27(f12(c32, f14(f19(c35, c37), c39)), f5(c33, f8(c34, c30)))) | (~p28(f21(c30, c40), c31)) | p27(f12(c32, f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40))), f5(c33, f8(c34, c30)))) <=> ((~p28(f21(c30, c40), c31)) | (~p27(f12(c32, f14(f19(c35, c37), c39)), f5(c33, f8(c34, c30)))) | p27(f12(c32, f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40))), f5(c33, f8(c34, c30))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(118,plain,
% 0.19/0.42 (((~![X62: $i, X61: $i] : ((~p27(f12(c32, X61), f5(c33, f8(c34, c30)))) | (~p28(f21(c30, X62), c31)) | p27(f12(c32, f14(f19(c35, X61), f17(c36, X62))), f5(c33, f8(c34, c30))))) | ((~p27(f12(c32, f14(f19(c35, c37), c39)), f5(c33, f8(c34, c30)))) | (~p28(f21(c30, c40), c31)) | p27(f12(c32, f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40))), f5(c33, f8(c34, c30))))) <=> ((~![X62: $i, X61: $i] : ((~p27(f12(c32, X61), f5(c33, f8(c34, c30)))) | (~p28(f21(c30, X62), c31)) | p27(f12(c32, f14(f19(c35, X61), f17(c36, X62))), f5(c33, f8(c34, c30))))) | ((~p28(f21(c30, c40), c31)) | (~p27(f12(c32, f14(f19(c35, c37), c39)), f5(c33, f8(c34, c30)))) | p27(f12(c32, f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40))), f5(c33, f8(c34, c30)))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[117])).
% 0.19/0.42 tff(119,plain,
% 0.19/0.42 (((~![X62: $i, X61: $i] : ((~p27(f12(c32, X61), f5(c33, f8(c34, c30)))) | (~p28(f21(c30, X62), c31)) | p27(f12(c32, f14(f19(c35, X61), f17(c36, X62))), f5(c33, f8(c34, c30))))) | ((~p27(f12(c32, f14(f19(c35, c37), c39)), f5(c33, f8(c34, c30)))) | (~p28(f21(c30, c40), c31)) | p27(f12(c32, f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40))), f5(c33, f8(c34, c30))))) <=> ((~![X62: $i, X61: $i] : ((~p27(f12(c32, X61), f5(c33, f8(c34, c30)))) | (~p28(f21(c30, X62), c31)) | p27(f12(c32, f14(f19(c35, X61), f17(c36, X62))), f5(c33, f8(c34, c30))))) | (~p28(f21(c30, c40), c31)) | (~p27(f12(c32, f14(f19(c35, c37), c39)), f5(c33, f8(c34, c30)))) | p27(f12(c32, f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40))), f5(c33, f8(c34, c30))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[118, 116])).
% 0.19/0.42 tff(120,plain,
% 0.19/0.42 ((~![X62: $i, X61: $i] : ((~p27(f12(c32, X61), f5(c33, f8(c34, c30)))) | (~p28(f21(c30, X62), c31)) | p27(f12(c32, f14(f19(c35, X61), f17(c36, X62))), f5(c33, f8(c34, c30))))) | ((~p27(f12(c32, f14(f19(c35, c37), c39)), f5(c33, f8(c34, c30)))) | (~p28(f21(c30, c40), c31)) | p27(f12(c32, f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40))), f5(c33, f8(c34, c30))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(121,plain,
% 0.19/0.42 ((~![X62: $i, X61: $i] : ((~p27(f12(c32, X61), f5(c33, f8(c34, c30)))) | (~p28(f21(c30, X62), c31)) | p27(f12(c32, f14(f19(c35, X61), f17(c36, X62))), f5(c33, f8(c34, c30))))) | (~p28(f21(c30, c40), c31)) | (~p27(f12(c32, f14(f19(c35, c37), c39)), f5(c33, f8(c34, c30)))) | p27(f12(c32, f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40))), f5(c33, f8(c34, c30)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.19/0.43 tff(122,plain,
% 0.19/0.43 ((~p28(f21(c30, c40), c31)) | (~p27(f12(c32, f14(f19(c35, c37), c39)), f5(c33, f8(c34, c30)))) | p27(f12(c32, f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40))), f5(c33, f8(c34, c30)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[121, 115])).
% 0.19/0.43 tff(123,plain,
% 0.19/0.43 (p27(f12(c32, f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40))), f5(c33, f8(c34, c30)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[122, 105, 80])).
% 0.19/0.43 tff(124,plain,
% 0.19/0.43 (^[X59: $i, X60: $i] : refl(((~p27(f12(c32, X59), X60)) | p29(X60, X59)) <=> ((~p27(f12(c32, X59), X60)) | p29(X60, X59)))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(125,plain,
% 0.19/0.43 (![X59: $i, X60: $i] : ((~p27(f12(c32, X59), X60)) | p29(X60, X59)) <=> ![X59: $i, X60: $i] : ((~p27(f12(c32, X59), X60)) | p29(X60, X59))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[124])).
% 0.19/0.43 tff(126,plain,
% 0.19/0.43 (![X59: $i, X60: $i] : ((~p27(f12(c32, X59), X60)) | p29(X60, X59)) <=> ![X59: $i, X60: $i] : ((~p27(f12(c32, X59), X60)) | p29(X60, X59))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(127,plain,
% 0.19/0.43 (^[X59: $i, X60: $i] : rewrite((p29(X60, X59) | (~p27(f12(c32, X59), X60))) <=> ((~p27(f12(c32, X59), X60)) | p29(X60, X59)))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(128,plain,
% 0.19/0.43 (![X59: $i, X60: $i] : (p29(X60, X59) | (~p27(f12(c32, X59), X60))) <=> ![X59: $i, X60: $i] : ((~p27(f12(c32, X59), X60)) | p29(X60, X59))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[127])).
% 0.19/0.43 tff(129,axiom,(![X59: $i, X60: $i] : (p29(X60, X59) | (~p27(f12(c32, X59), X60)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p29_18')).
% 0.19/0.43 tff(130,plain,
% 0.19/0.43 (![X59: $i, X60: $i] : ((~p27(f12(c32, X59), X60)) | p29(X60, X59))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.19/0.43 tff(131,plain,
% 0.19/0.43 (![X59: $i, X60: $i] : ((~p27(f12(c32, X59), X60)) | p29(X60, X59))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[130, 126])).
% 0.19/0.43 tff(132,plain,(
% 0.19/0.43 ![X59: $i, X60: $i] : ((~p27(f12(c32, X59), X60)) | p29(X60, X59))),
% 0.19/0.43 inference(skolemize,[status(sab)],[131])).
% 0.19/0.43 tff(133,plain,
% 0.19/0.43 (![X59: $i, X60: $i] : ((~p27(f12(c32, X59), X60)) | p29(X60, X59))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[132, 125])).
% 0.19/0.43 tff(134,plain,
% 0.19/0.43 (((~![X59: $i, X60: $i] : ((~p27(f12(c32, X59), X60)) | p29(X60, X59))) | ((~p27(f12(c32, f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40))), f5(c33, f8(c34, c30)))) | p29(f5(c33, f8(c34, c30)), f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40))))) <=> ((~![X59: $i, X60: $i] : ((~p27(f12(c32, X59), X60)) | p29(X60, X59))) | (~p27(f12(c32, f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40))), f5(c33, f8(c34, c30)))) | p29(f5(c33, f8(c34, c30)), f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(135,plain,
% 0.19/0.43 ((~![X59: $i, X60: $i] : ((~p27(f12(c32, X59), X60)) | p29(X60, X59))) | ((~p27(f12(c32, f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40))), f5(c33, f8(c34, c30)))) | p29(f5(c33, f8(c34, c30)), f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(136,plain,
% 0.19/0.43 ((~![X59: $i, X60: $i] : ((~p27(f12(c32, X59), X60)) | p29(X60, X59))) | (~p27(f12(c32, f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40))), f5(c33, f8(c34, c30)))) | p29(f5(c33, f8(c34, c30)), f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.19/0.43 tff(137,plain,
% 0.19/0.43 (p29(f5(c33, f8(c34, c30)), f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[136, 133, 123])).
% 0.19/0.43 tff(138,assumption,(~p10(c38, c38)), introduced(assumption)).
% 0.19/0.43 tff(139,plain,
% 0.19/0.43 (^[X0: $i] : refl(p10(X0, X0) <=> p10(X0, X0))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(140,plain,
% 0.19/0.43 (![X0: $i] : p10(X0, X0) <=> ![X0: $i] : p10(X0, X0)),
% 0.19/0.43 inference(quant_intro,[status(thm)],[139])).
% 0.19/0.43 tff(141,plain,
% 0.19/0.43 (![X0: $i] : p10(X0, X0) <=> ![X0: $i] : p10(X0, X0)),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(142,axiom,(![X0: $i] : p10(X0, X0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p10_1')).
% 0.19/0.43 tff(143,plain,
% 0.19/0.43 (![X0: $i] : p10(X0, X0)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.19/0.43 tff(144,plain,(
% 0.19/0.43 ![X0: $i] : p10(X0, X0)),
% 0.19/0.43 inference(skolemize,[status(sab)],[143])).
% 0.19/0.43 tff(145,plain,
% 0.19/0.43 (![X0: $i] : p10(X0, X0)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[144, 140])).
% 0.19/0.43 tff(146,plain,
% 0.19/0.43 ((~![X0: $i] : p10(X0, X0)) | p10(c38, c38)),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(147,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[146, 145, 138])).
% 0.19/0.43 tff(148,plain,(p10(c38, c38)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(149,plain,
% 0.19/0.43 (p10(c38, f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40))) <=> p10(c38, f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(150,axiom,(p10(c38, f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p10_41')).
% 0.19/0.43 tff(151,plain,
% 0.19/0.43 (p10(c38, f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.19/0.43 tff(152,plain,
% 0.19/0.43 (((~![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))) | ((~p10(c38, c38)) | (~p10(c38, f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)))) | p10(f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)), c38))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))) | (~p10(c38, c38)) | (~p10(c38, f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)))) | p10(f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)), c38))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(153,plain,
% 0.19/0.43 ((~![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))) | ((~p10(c38, c38)) | (~p10(c38, f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)))) | p10(f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)), c38))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(154,plain,
% 0.19/0.43 ((~![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))) | (~p10(c38, c38)) | (~p10(c38, f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)))) | p10(f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)), c38)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.19/0.43 tff(155,plain,
% 0.19/0.43 (p10(f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)), c38)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[154, 20, 151, 148])).
% 0.19/0.43 tff(156,assumption,(~p3(f8(c34, c30), f8(c34, c30))), introduced(assumption)).
% 0.19/0.43 tff(157,plain,
% 0.19/0.43 (^[X74: $i] : refl(p3(X74, X74) <=> p3(X74, X74))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(158,plain,
% 0.19/0.43 (![X74: $i] : p3(X74, X74) <=> ![X74: $i] : p3(X74, X74)),
% 0.19/0.43 inference(quant_intro,[status(thm)],[157])).
% 0.19/0.43 tff(159,plain,
% 0.19/0.43 (![X74: $i] : p3(X74, X74) <=> ![X74: $i] : p3(X74, X74)),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(160,axiom,(![X74: $i] : p3(X74, X74)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p3_6')).
% 0.19/0.43 tff(161,plain,
% 0.19/0.43 (![X74: $i] : p3(X74, X74)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.19/0.43 tff(162,plain,(
% 0.19/0.43 ![X74: $i] : p3(X74, X74)),
% 0.19/0.43 inference(skolemize,[status(sab)],[161])).
% 0.19/0.43 tff(163,plain,
% 0.19/0.43 (![X74: $i] : p3(X74, X74)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[162, 158])).
% 0.19/0.43 tff(164,plain,
% 0.19/0.43 ((~![X74: $i] : p3(X74, X74)) | p3(f8(c34, c30), f8(c34, c30))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(165,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[164, 163, 156])).
% 0.19/0.43 tff(166,plain,(p3(f8(c34, c30), f8(c34, c30))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(167,assumption,(~p2(c33, c33)), introduced(assumption)).
% 0.19/0.43 tff(168,plain,
% 0.19/0.43 (^[X39: $i] : refl(p2(X39, X39) <=> p2(X39, X39))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(169,plain,
% 0.19/0.43 (![X39: $i] : p2(X39, X39) <=> ![X39: $i] : p2(X39, X39)),
% 0.19/0.43 inference(quant_intro,[status(thm)],[168])).
% 0.19/0.43 tff(170,plain,
% 0.19/0.43 (![X39: $i] : p2(X39, X39) <=> ![X39: $i] : p2(X39, X39)),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(171,axiom,(![X39: $i] : p2(X39, X39)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_10')).
% 0.19/0.43 tff(172,plain,
% 0.19/0.43 (![X39: $i] : p2(X39, X39)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.19/0.43 tff(173,plain,(
% 0.19/0.43 ![X39: $i] : p2(X39, X39)),
% 0.19/0.43 inference(skolemize,[status(sab)],[172])).
% 0.19/0.43 tff(174,plain,
% 0.19/0.43 (![X39: $i] : p2(X39, X39)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[173, 169])).
% 0.19/0.43 tff(175,plain,
% 0.19/0.43 ((~![X39: $i] : p2(X39, X39)) | p2(c33, c33)),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(176,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[175, 174, 167])).
% 0.19/0.43 tff(177,plain,(p2(c33, c33)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(178,plain,
% 0.19/0.43 (^[X93: $i, X95: $i, X94: $i, X92: $i] : refl(((~p3(X93, X95)) | (~p2(X92, X94)) | p4(f5(X92, X93), f5(X94, X95))) <=> ((~p3(X93, X95)) | (~p2(X92, X94)) | p4(f5(X92, X93), f5(X94, X95))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(179,plain,
% 0.19/0.43 (![X93: $i, X95: $i, X94: $i, X92: $i] : ((~p3(X93, X95)) | (~p2(X92, X94)) | p4(f5(X92, X93), f5(X94, X95))) <=> ![X93: $i, X95: $i, X94: $i, X92: $i] : ((~p3(X93, X95)) | (~p2(X92, X94)) | p4(f5(X92, X93), f5(X94, X95)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[178])).
% 0.19/0.43 tff(180,plain,
% 0.19/0.43 (![X93: $i, X95: $i, X94: $i, X92: $i] : ((~p3(X93, X95)) | (~p2(X92, X94)) | p4(f5(X92, X93), f5(X94, X95))) <=> ![X93: $i, X95: $i, X94: $i, X92: $i] : ((~p3(X93, X95)) | (~p2(X92, X94)) | p4(f5(X92, X93), f5(X94, X95)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(181,plain,
% 0.19/0.43 (^[X93: $i, X95: $i, X94: $i, X92: $i] : trans(monotonicity(rewrite((p4(f5(X92, X93), f5(X94, X95)) | (~p2(X92, X94))) <=> ((~p2(X92, X94)) | p4(f5(X92, X93), f5(X94, X95)))), (((p4(f5(X92, X93), f5(X94, X95)) | (~p2(X92, X94))) | (~p3(X93, X95))) <=> (((~p2(X92, X94)) | p4(f5(X92, X93), f5(X94, X95))) | (~p3(X93, X95))))), rewrite((((~p2(X92, X94)) | p4(f5(X92, X93), f5(X94, X95))) | (~p3(X93, X95))) <=> ((~p3(X93, X95)) | (~p2(X92, X94)) | p4(f5(X92, X93), f5(X94, X95)))), (((p4(f5(X92, X93), f5(X94, X95)) | (~p2(X92, X94))) | (~p3(X93, X95))) <=> ((~p3(X93, X95)) | (~p2(X92, X94)) | p4(f5(X92, X93), f5(X94, X95)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(182,plain,
% 0.19/0.43 (![X93: $i, X95: $i, X94: $i, X92: $i] : ((p4(f5(X92, X93), f5(X94, X95)) | (~p2(X92, X94))) | (~p3(X93, X95))) <=> ![X93: $i, X95: $i, X94: $i, X92: $i] : ((~p3(X93, X95)) | (~p2(X92, X94)) | p4(f5(X92, X93), f5(X94, X95)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[181])).
% 0.19/0.43 tff(183,axiom,(![X93: $i, X95: $i, X94: $i, X92: $i] : ((p4(f5(X92, X93), f5(X94, X95)) | (~p2(X92, X94))) | (~p3(X93, X95)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p4_42')).
% 0.19/0.43 tff(184,plain,
% 0.19/0.43 (![X93: $i, X95: $i, X94: $i, X92: $i] : ((~p3(X93, X95)) | (~p2(X92, X94)) | p4(f5(X92, X93), f5(X94, X95)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.19/0.43 tff(185,plain,
% 0.19/0.43 (![X93: $i, X95: $i, X94: $i, X92: $i] : ((~p3(X93, X95)) | (~p2(X92, X94)) | p4(f5(X92, X93), f5(X94, X95)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[184, 180])).
% 0.19/0.43 tff(186,plain,(
% 0.19/0.43 ![X93: $i, X95: $i, X94: $i, X92: $i] : ((~p3(X93, X95)) | (~p2(X92, X94)) | p4(f5(X92, X93), f5(X94, X95)))),
% 0.19/0.43 inference(skolemize,[status(sab)],[185])).
% 0.19/0.43 tff(187,plain,
% 0.19/0.43 (![X93: $i, X95: $i, X94: $i, X92: $i] : ((~p3(X93, X95)) | (~p2(X92, X94)) | p4(f5(X92, X93), f5(X94, X95)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[186, 179])).
% 0.19/0.43 tff(188,plain,
% 0.19/0.43 (((~![X93: $i, X95: $i, X94: $i, X92: $i] : ((~p3(X93, X95)) | (~p2(X92, X94)) | p4(f5(X92, X93), f5(X94, X95)))) | ((~p3(f8(c34, c30), f8(c34, c30))) | (~p2(c33, c33)) | p4(f5(c33, f8(c34, c30)), f5(c33, f8(c34, c30))))) <=> ((~![X93: $i, X95: $i, X94: $i, X92: $i] : ((~p3(X93, X95)) | (~p2(X92, X94)) | p4(f5(X92, X93), f5(X94, X95)))) | (~p3(f8(c34, c30), f8(c34, c30))) | (~p2(c33, c33)) | p4(f5(c33, f8(c34, c30)), f5(c33, f8(c34, c30))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(189,plain,
% 0.19/0.43 ((~![X93: $i, X95: $i, X94: $i, X92: $i] : ((~p3(X93, X95)) | (~p2(X92, X94)) | p4(f5(X92, X93), f5(X94, X95)))) | ((~p3(f8(c34, c30), f8(c34, c30))) | (~p2(c33, c33)) | p4(f5(c33, f8(c34, c30)), f5(c33, f8(c34, c30))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(190,plain,
% 0.19/0.43 ((~![X93: $i, X95: $i, X94: $i, X92: $i] : ((~p3(X93, X95)) | (~p2(X92, X94)) | p4(f5(X92, X93), f5(X94, X95)))) | (~p3(f8(c34, c30), f8(c34, c30))) | (~p2(c33, c33)) | p4(f5(c33, f8(c34, c30)), f5(c33, f8(c34, c30)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[189, 188])).
% 0.19/0.43 tff(191,plain,
% 0.19/0.43 ((~p3(f8(c34, c30), f8(c34, c30))) | (~p2(c33, c33)) | p4(f5(c33, f8(c34, c30)), f5(c33, f8(c34, c30)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[190, 187])).
% 0.19/0.43 tff(192,plain,
% 0.19/0.43 (p4(f5(c33, f8(c34, c30)), f5(c33, f8(c34, c30)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[191, 177, 166])).
% 0.19/0.43 tff(193,plain,
% 0.19/0.43 (^[X72: $i, X70: $i, X69: $i, X71: $i] : refl(((~p10(X71, X70)) | (~p4(X72, X69)) | (~p29(X72, X71)) | p29(X69, X70)) <=> ((~p10(X71, X70)) | (~p4(X72, X69)) | (~p29(X72, X71)) | p29(X69, X70)))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(194,plain,
% 0.19/0.43 (![X72: $i, X70: $i, X69: $i, X71: $i] : ((~p10(X71, X70)) | (~p4(X72, X69)) | (~p29(X72, X71)) | p29(X69, X70)) <=> ![X72: $i, X70: $i, X69: $i, X71: $i] : ((~p10(X71, X70)) | (~p4(X72, X69)) | (~p29(X72, X71)) | p29(X69, X70))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[193])).
% 0.19/0.43 tff(195,plain,
% 0.19/0.43 (![X72: $i, X70: $i, X69: $i, X71: $i] : ((~p10(X71, X70)) | (~p4(X72, X69)) | (~p29(X72, X71)) | p29(X69, X70)) <=> ![X72: $i, X70: $i, X69: $i, X71: $i] : ((~p10(X71, X70)) | (~p4(X72, X69)) | (~p29(X72, X71)) | p29(X69, X70))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(196,plain,
% 0.19/0.43 (^[X72: $i, X70: $i, X69: $i, X71: $i] : trans(monotonicity(trans(monotonicity(rewrite((p29(X69, X70) | (~p29(X72, X71))) <=> ((~p29(X72, X71)) | p29(X69, X70))), (((p29(X69, X70) | (~p29(X72, X71))) | (~p4(X72, X69))) <=> (((~p29(X72, X71)) | p29(X69, X70)) | (~p4(X72, X69))))), rewrite((((~p29(X72, X71)) | p29(X69, X70)) | (~p4(X72, X69))) <=> ((~p4(X72, X69)) | (~p29(X72, X71)) | p29(X69, X70))), (((p29(X69, X70) | (~p29(X72, X71))) | (~p4(X72, X69))) <=> ((~p4(X72, X69)) | (~p29(X72, X71)) | p29(X69, X70)))), ((((p29(X69, X70) | (~p29(X72, X71))) | (~p4(X72, X69))) | (~p10(X71, X70))) <=> (((~p4(X72, X69)) | (~p29(X72, X71)) | p29(X69, X70)) | (~p10(X71, X70))))), rewrite((((~p4(X72, X69)) | (~p29(X72, X71)) | p29(X69, X70)) | (~p10(X71, X70))) <=> ((~p10(X71, X70)) | (~p4(X72, X69)) | (~p29(X72, X71)) | p29(X69, X70))), ((((p29(X69, X70) | (~p29(X72, X71))) | (~p4(X72, X69))) | (~p10(X71, X70))) <=> ((~p10(X71, X70)) | (~p4(X72, X69)) | (~p29(X72, X71)) | p29(X69, X70))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(197,plain,
% 0.19/0.43 (![X72: $i, X70: $i, X69: $i, X71: $i] : (((p29(X69, X70) | (~p29(X72, X71))) | (~p4(X72, X69))) | (~p10(X71, X70))) <=> ![X72: $i, X70: $i, X69: $i, X71: $i] : ((~p10(X71, X70)) | (~p4(X72, X69)) | (~p29(X72, X71)) | p29(X69, X70))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[196])).
% 0.19/0.43 tff(198,axiom,(![X72: $i, X70: $i, X69: $i, X71: $i] : (((p29(X69, X70) | (~p29(X72, X71))) | (~p4(X72, X69))) | (~p10(X71, X70)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p29_38')).
% 0.19/0.43 tff(199,plain,
% 0.19/0.43 (![X72: $i, X70: $i, X69: $i, X71: $i] : ((~p10(X71, X70)) | (~p4(X72, X69)) | (~p29(X72, X71)) | p29(X69, X70))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.19/0.43 tff(200,plain,
% 0.19/0.43 (![X72: $i, X70: $i, X69: $i, X71: $i] : ((~p10(X71, X70)) | (~p4(X72, X69)) | (~p29(X72, X71)) | p29(X69, X70))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[199, 195])).
% 0.19/0.43 tff(201,plain,(
% 0.19/0.43 ![X72: $i, X70: $i, X69: $i, X71: $i] : ((~p10(X71, X70)) | (~p4(X72, X69)) | (~p29(X72, X71)) | p29(X69, X70))),
% 0.19/0.43 inference(skolemize,[status(sab)],[200])).
% 0.19/0.43 tff(202,plain,
% 0.19/0.43 (![X72: $i, X70: $i, X69: $i, X71: $i] : ((~p10(X71, X70)) | (~p4(X72, X69)) | (~p29(X72, X71)) | p29(X69, X70))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[201, 194])).
% 0.19/0.43 tff(203,plain,
% 0.19/0.43 ((~p29(f5(c33, f8(c34, c30)), c38)) <=> (~p29(f5(c33, f8(c34, c30)), c38))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(204,axiom,(~p29(f5(c33, f8(c34, c30)), c38)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_p29_17')).
% 0.19/0.44 tff(205,plain,
% 0.19/0.44 (~p29(f5(c33, f8(c34, c30)), c38)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.19/0.44 tff(206,plain,
% 0.19/0.44 (((~![X72: $i, X70: $i, X69: $i, X71: $i] : ((~p10(X71, X70)) | (~p4(X72, X69)) | (~p29(X72, X71)) | p29(X69, X70))) | (p29(f5(c33, f8(c34, c30)), c38) | (~p10(f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)), c38)) | (~p4(f5(c33, f8(c34, c30)), f5(c33, f8(c34, c30)))) | (~p29(f5(c33, f8(c34, c30)), f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)))))) <=> ((~![X72: $i, X70: $i, X69: $i, X71: $i] : ((~p10(X71, X70)) | (~p4(X72, X69)) | (~p29(X72, X71)) | p29(X69, X70))) | p29(f5(c33, f8(c34, c30)), c38) | (~p10(f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)), c38)) | (~p4(f5(c33, f8(c34, c30)), f5(c33, f8(c34, c30)))) | (~p29(f5(c33, f8(c34, c30)), f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(207,plain,
% 0.19/0.44 (((~p10(f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)), c38)) | (~p4(f5(c33, f8(c34, c30)), f5(c33, f8(c34, c30)))) | (~p29(f5(c33, f8(c34, c30)), f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)))) | p29(f5(c33, f8(c34, c30)), c38)) <=> (p29(f5(c33, f8(c34, c30)), c38) | (~p10(f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)), c38)) | (~p4(f5(c33, f8(c34, c30)), f5(c33, f8(c34, c30)))) | (~p29(f5(c33, f8(c34, c30)), f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(208,plain,
% 0.19/0.44 (((~![X72: $i, X70: $i, X69: $i, X71: $i] : ((~p10(X71, X70)) | (~p4(X72, X69)) | (~p29(X72, X71)) | p29(X69, X70))) | ((~p10(f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)), c38)) | (~p4(f5(c33, f8(c34, c30)), f5(c33, f8(c34, c30)))) | (~p29(f5(c33, f8(c34, c30)), f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)))) | p29(f5(c33, f8(c34, c30)), c38))) <=> ((~![X72: $i, X70: $i, X69: $i, X71: $i] : ((~p10(X71, X70)) | (~p4(X72, X69)) | (~p29(X72, X71)) | p29(X69, X70))) | (p29(f5(c33, f8(c34, c30)), c38) | (~p10(f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)), c38)) | (~p4(f5(c33, f8(c34, c30)), f5(c33, f8(c34, c30)))) | (~p29(f5(c33, f8(c34, c30)), f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40))))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[207])).
% 0.19/0.44 tff(209,plain,
% 0.19/0.44 (((~![X72: $i, X70: $i, X69: $i, X71: $i] : ((~p10(X71, X70)) | (~p4(X72, X69)) | (~p29(X72, X71)) | p29(X69, X70))) | ((~p10(f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)), c38)) | (~p4(f5(c33, f8(c34, c30)), f5(c33, f8(c34, c30)))) | (~p29(f5(c33, f8(c34, c30)), f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)))) | p29(f5(c33, f8(c34, c30)), c38))) <=> ((~![X72: $i, X70: $i, X69: $i, X71: $i] : ((~p10(X71, X70)) | (~p4(X72, X69)) | (~p29(X72, X71)) | p29(X69, X70))) | p29(f5(c33, f8(c34, c30)), c38) | (~p10(f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)), c38)) | (~p4(f5(c33, f8(c34, c30)), f5(c33, f8(c34, c30)))) | (~p29(f5(c33, f8(c34, c30)), f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[208, 206])).
% 0.19/0.44 tff(210,plain,
% 0.19/0.44 ((~![X72: $i, X70: $i, X69: $i, X71: $i] : ((~p10(X71, X70)) | (~p4(X72, X69)) | (~p29(X72, X71)) | p29(X69, X70))) | ((~p10(f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)), c38)) | (~p4(f5(c33, f8(c34, c30)), f5(c33, f8(c34, c30)))) | (~p29(f5(c33, f8(c34, c30)), f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)))) | p29(f5(c33, f8(c34, c30)), c38))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(211,plain,
% 0.19/0.44 ((~![X72: $i, X70: $i, X69: $i, X71: $i] : ((~p10(X71, X70)) | (~p4(X72, X69)) | (~p29(X72, X71)) | p29(X69, X70))) | p29(f5(c33, f8(c34, c30)), c38) | (~p10(f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)), c38)) | (~p4(f5(c33, f8(c34, c30)), f5(c33, f8(c34, c30)))) | (~p29(f5(c33, f8(c34, c30)), f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.19/0.44 tff(212,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[211, 205, 202, 192, 155, 137])).
% 0.19/0.44 % SZS output end Proof
% 0.19/0.44 % E exiting
%------------------------------------------------------------------------------