%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN657-1 : 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 05:39:46 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.12 % Problem : SYN657-1 : TPTP v9.0.0. Released v2.5.0.
% 0.13/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 12:39:10 EDT 2025
% 0.19/0.34 % CPUTime :
% 0.19/0.40 % SZS status Unsatisfiable
% 0.19/0.40 % SZS output start Proof
% 0.19/0.40 tff(p24_type, type, (
% 0.19/0.40 p24: ( $i * $i ) > $o)).
% 0.19/0.40 tff(f19_type, type, (
% 0.19/0.40 f19: $i > $i)).
% 0.19/0.40 tff(f20_type, type, (
% 0.19/0.40 f20: ( $i * $i ) > $i)).
% 0.19/0.40 tff(f22_type, type, (
% 0.19/0.40 f22: ( $i * $i * $i ) > $i)).
% 0.19/0.40 tff(c34_type, type, (
% 0.19/0.40 c34: $i)).
% 0.19/0.40 tff(c31_type, type, (
% 0.19/0.40 c31: $i)).
% 0.19/0.40 tff(f8_type, type, (
% 0.19/0.40 f8: ( $i * $i ) > $i)).
% 0.19/0.40 tff(f9_type, type, (
% 0.19/0.40 f9: ( $i * $i ) > $i)).
% 0.19/0.40 tff(c29_type, type, (
% 0.19/0.40 c29: $i)).
% 0.19/0.40 tff(c28_type, type, (
% 0.19/0.40 c28: $i)).
% 0.19/0.40 tff(c27_type, type, (
% 0.19/0.40 c27: $i)).
% 0.19/0.40 tff(p25_type, type, (
% 0.19/0.40 p25: ( $i * $i ) > $o)).
% 0.19/0.40 tff(f18_type, type, (
% 0.19/0.40 f18: $i > $i)).
% 0.19/0.40 tff(p6_type, type, (
% 0.19/0.40 p6: ( $i * $i ) > $o)).
% 0.19/0.40 tff(f10_type, type, (
% 0.19/0.40 f10: $i > $i)).
% 0.19/0.40 tff(c33_type, type, (
% 0.19/0.40 c33: $i)).
% 0.19/0.40 tff(f21_type, type, (
% 0.19/0.40 f21: $i > $i)).
% 0.19/0.40 tff(p4_type, type, (
% 0.19/0.40 p4: ( $i * $i ) > $o)).
% 0.19/0.40 tff(f5_type, type, (
% 0.19/0.40 f5: ( $i * $i * $i ) > $i)).
% 0.19/0.40 tff(c36_type, type, (
% 0.19/0.40 c36: $i)).
% 0.19/0.40 tff(1,assumption,(p6(f21(f8(c27, f9(c28, c29))), f10(c33))), introduced(assumption)).
% 0.19/0.40 tff(2,plain,
% 0.19/0.40 (^[X82: $i, X83: $i, X84: $i] : refl(p6(f21(f8(X82, f9(X83, X84))), X83) <=> p6(f21(f8(X82, f9(X83, X84))), X83))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(3,plain,
% 0.19/0.40 (![X82: $i, X83: $i, X84: $i] : p6(f21(f8(X82, f9(X83, X84))), X83) <=> ![X82: $i, X83: $i, X84: $i] : p6(f21(f8(X82, f9(X83, X84))), X83)),
% 0.19/0.40 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.40 tff(4,plain,
% 0.19/0.40 (![X82: $i, X83: $i, X84: $i] : p6(f21(f8(X82, f9(X83, X84))), X83) <=> ![X82: $i, X83: $i, X84: $i] : p6(f21(f8(X82, f9(X83, X84))), X83)),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(5,axiom,(![X82: $i, X83: $i, X84: $i] : p6(f21(f8(X82, f9(X83, X84))), X83)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p6_15')).
% 0.19/0.40 tff(6,plain,
% 0.19/0.40 (![X82: $i, X83: $i, X84: $i] : p6(f21(f8(X82, f9(X83, X84))), X83)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.19/0.40 tff(7,plain,(
% 0.19/0.40 ![X82: $i, X83: $i, X84: $i] : p6(f21(f8(X82, f9(X83, X84))), X83)),
% 0.19/0.40 inference(skolemize,[status(sab)],[6])).
% 0.19/0.40 tff(8,plain,
% 0.19/0.40 (![X82: $i, X83: $i, X84: $i] : p6(f21(f8(X82, f9(X83, X84))), X83)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.40 tff(9,plain,
% 0.19/0.40 ((~![X82: $i, X83: $i, X84: $i] : p6(f21(f8(X82, f9(X83, X84))), X83)) | p6(f21(f8(c27, f9(c28, c29))), c28)),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(10,plain,
% 0.19/0.40 (p6(f21(f8(c27, f9(c28, c29))), c28)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.19/0.40 tff(11,plain,
% 0.19/0.40 (^[X73: $i, X72: $i, X71: $i] : refl(((~p6(X71, X72)) | (~p6(X71, X73)) | p6(X72, X73)) <=> ((~p6(X71, X72)) | (~p6(X71, X73)) | p6(X72, X73)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(12,plain,
% 0.19/0.40 (![X73: $i, X72: $i, X71: $i] : ((~p6(X71, X72)) | (~p6(X71, X73)) | p6(X72, X73)) <=> ![X73: $i, X72: $i, X71: $i] : ((~p6(X71, X72)) | (~p6(X71, X73)) | p6(X72, X73))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[11])).
% 0.19/0.40 tff(13,plain,
% 0.19/0.40 (![X73: $i, X72: $i, X71: $i] : ((~p6(X71, X72)) | (~p6(X71, X73)) | p6(X72, X73)) <=> ![X73: $i, X72: $i, X71: $i] : ((~p6(X71, X72)) | (~p6(X71, X73)) | p6(X72, X73))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(14,plain,
% 0.19/0.40 (^[X73: $i, X72: $i, X71: $i] : trans(monotonicity(rewrite((p6(X72, X73) | (~p6(X71, X72))) <=> ((~p6(X71, X72)) | p6(X72, X73))), (((p6(X72, X73) | (~p6(X71, X72))) | (~p6(X71, X73))) <=> (((~p6(X71, X72)) | p6(X72, X73)) | (~p6(X71, X73))))), rewrite((((~p6(X71, X72)) | p6(X72, X73)) | (~p6(X71, X73))) <=> ((~p6(X71, X72)) | (~p6(X71, X73)) | p6(X72, X73))), (((p6(X72, X73) | (~p6(X71, X72))) | (~p6(X71, X73))) <=> ((~p6(X71, X72)) | (~p6(X71, X73)) | p6(X72, X73))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(15,plain,
% 0.19/0.40 (![X73: $i, X72: $i, X71: $i] : ((p6(X72, X73) | (~p6(X71, X72))) | (~p6(X71, X73))) <=> ![X73: $i, X72: $i, X71: $i] : ((~p6(X71, X72)) | (~p6(X71, X73)) | p6(X72, X73))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[14])).
% 0.19/0.40 tff(16,axiom,(![X73: $i, X72: $i, X71: $i] : ((p6(X72, X73) | (~p6(X71, X72))) | (~p6(X71, X73)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p6_25')).
% 0.19/0.40 tff(17,plain,
% 0.19/0.40 (![X73: $i, X72: $i, X71: $i] : ((~p6(X71, X72)) | (~p6(X71, X73)) | p6(X72, X73))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.19/0.40 tff(18,plain,
% 0.19/0.40 (![X73: $i, X72: $i, X71: $i] : ((~p6(X71, X72)) | (~p6(X71, X73)) | p6(X72, X73))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.19/0.40 tff(19,plain,(
% 0.19/0.40 ![X73: $i, X72: $i, X71: $i] : ((~p6(X71, X72)) | (~p6(X71, X73)) | p6(X72, X73))),
% 0.19/0.40 inference(skolemize,[status(sab)],[18])).
% 0.19/0.40 tff(20,plain,
% 0.19/0.40 (![X73: $i, X72: $i, X71: $i] : ((~p6(X71, X72)) | (~p6(X71, X73)) | p6(X72, X73))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.19/0.40 tff(21,plain,
% 0.19/0.40 ((~p6(c28, f10(c33))) <=> (~p6(c28, f10(c33)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(22,axiom,(~p6(c28, f10(c33))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_p6_11')).
% 0.19/0.40 tff(23,plain,
% 0.19/0.40 (~p6(c28, f10(c33))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.19/0.40 tff(24,plain,
% 0.19/0.40 (((~![X73: $i, X72: $i, X71: $i] : ((~p6(X71, X72)) | (~p6(X71, X73)) | p6(X72, X73))) | ((~p6(f21(f8(c27, f9(c28, c29))), c28)) | (~p6(f21(f8(c27, f9(c28, c29))), f10(c33))) | p6(c28, f10(c33)))) <=> ((~![X73: $i, X72: $i, X71: $i] : ((~p6(X71, X72)) | (~p6(X71, X73)) | p6(X72, X73))) | (~p6(f21(f8(c27, f9(c28, c29))), c28)) | (~p6(f21(f8(c27, f9(c28, c29))), f10(c33))) | p6(c28, f10(c33)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(25,plain,
% 0.19/0.40 ((~![X73: $i, X72: $i, X71: $i] : ((~p6(X71, X72)) | (~p6(X71, X73)) | p6(X72, X73))) | ((~p6(f21(f8(c27, f9(c28, c29))), c28)) | (~p6(f21(f8(c27, f9(c28, c29))), f10(c33))) | p6(c28, f10(c33)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(26,plain,
% 0.19/0.40 ((~![X73: $i, X72: $i, X71: $i] : ((~p6(X71, X72)) | (~p6(X71, X73)) | p6(X72, X73))) | (~p6(f21(f8(c27, f9(c28, c29))), c28)) | (~p6(f21(f8(c27, f9(c28, c29))), f10(c33))) | p6(c28, f10(c33))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.19/0.40 tff(27,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[26, 23, 20, 10, 1])).
% 0.19/0.40 tff(28,plain,(~p6(f21(f8(c27, f9(c28, c29))), f10(c33))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(29,plain,
% 0.19/0.40 (^[X25: $i, X27: $i, X26: $i] : refl((p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33))) <=> (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(30,plain,
% 0.19/0.40 (![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33))) <=> ![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[29])).
% 0.19/0.40 tff(31,plain,
% 0.19/0.40 (![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33))) <=> ![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(32,plain,
% 0.19/0.40 (^[X25: $i, X27: $i, X26: $i] : trans(monotonicity(rewrite((p6(f21(X25), f10(c33)) | p25(f22(X25, X26, X27), f18(X25))) <=> (p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33)))), (((p6(f21(X25), f10(c33)) | p25(f22(X25, X26, X27), f18(X25))) | p4(f5(X25, c36, X26), f5(X25, c36, X27))) <=> ((p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33))) | p4(f5(X25, c36, X26), f5(X25, c36, X27))))), rewrite(((p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33))) | p4(f5(X25, c36, X26), f5(X25, c36, X27))) <=> (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33)))), (((p6(f21(X25), f10(c33)) | p25(f22(X25, X26, X27), f18(X25))) | p4(f5(X25, c36, X26), f5(X25, c36, X27))) <=> (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(33,plain,
% 0.19/0.40 (![X25: $i, X27: $i, X26: $i] : ((p6(f21(X25), f10(c33)) | p25(f22(X25, X26, X27), f18(X25))) | p4(f5(X25, c36, X26), f5(X25, c36, X27))) <=> ![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[32])).
% 0.19/0.41 tff(34,axiom,(![X25: $i, X27: $i, X26: $i] : ((p6(f21(X25), f10(c33)) | p25(f22(X25, X26, X27), f18(X25))) | p4(f5(X25, c36, X26), f5(X25, c36, X27)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p6_48')).
% 0.19/0.41 tff(35,plain,
% 0.19/0.41 (![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.19/0.41 tff(36,plain,
% 0.19/0.41 (![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.19/0.41 tff(37,plain,(
% 0.19/0.41 ![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[36])).
% 0.19/0.41 tff(38,plain,
% 0.19/0.41 (![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.19/0.41 tff(39,plain,
% 0.19/0.41 ((~p4(f5(f8(c27, f9(c28, c29)), c36, c31), f5(f8(c27, f9(c28, c29)), c36, c34))) <=> (~p4(f5(f8(c27, f9(c28, c29)), c36, c31), f5(f8(c27, f9(c28, c29)), c36, c34)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(40,axiom,(~p4(f5(f8(c27, f9(c28, c29)), c36, c31), f5(f8(c27, f9(c28, c29)), c36, c34))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_p4_44')).
% 0.19/0.41 tff(41,plain,
% 0.19/0.41 (~p4(f5(f8(c27, f9(c28, c29)), c36, c31), f5(f8(c27, f9(c28, c29)), c36, c34))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.19/0.41 tff(42,plain,
% 0.19/0.41 (((~![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33)))) | (p4(f5(f8(c27, f9(c28, c29)), c36, c31), f5(f8(c27, f9(c28, c29)), c36, c34)) | p6(f21(f8(c27, f9(c28, c29))), f10(c33)) | p25(f22(f8(c27, f9(c28, c29)), c31, c34), f18(f8(c27, f9(c28, c29)))))) <=> ((~![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33)))) | p4(f5(f8(c27, f9(c28, c29)), c36, c31), f5(f8(c27, f9(c28, c29)), c36, c34)) | p6(f21(f8(c27, f9(c28, c29))), f10(c33)) | p25(f22(f8(c27, f9(c28, c29)), c31, c34), f18(f8(c27, f9(c28, c29)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(43,plain,
% 0.19/0.41 ((p4(f5(f8(c27, f9(c28, c29)), c36, c31), f5(f8(c27, f9(c28, c29)), c36, c34)) | p25(f22(f8(c27, f9(c28, c29)), c31, c34), f18(f8(c27, f9(c28, c29)))) | p6(f21(f8(c27, f9(c28, c29))), f10(c33))) <=> (p4(f5(f8(c27, f9(c28, c29)), c36, c31), f5(f8(c27, f9(c28, c29)), c36, c34)) | p6(f21(f8(c27, f9(c28, c29))), f10(c33)) | p25(f22(f8(c27, f9(c28, c29)), c31, c34), f18(f8(c27, f9(c28, c29)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(44,plain,
% 0.19/0.41 (((~![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33)))) | (p4(f5(f8(c27, f9(c28, c29)), c36, c31), f5(f8(c27, f9(c28, c29)), c36, c34)) | p25(f22(f8(c27, f9(c28, c29)), c31, c34), f18(f8(c27, f9(c28, c29)))) | p6(f21(f8(c27, f9(c28, c29))), f10(c33)))) <=> ((~![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33)))) | (p4(f5(f8(c27, f9(c28, c29)), c36, c31), f5(f8(c27, f9(c28, c29)), c36, c34)) | p6(f21(f8(c27, f9(c28, c29))), f10(c33)) | p25(f22(f8(c27, f9(c28, c29)), c31, c34), f18(f8(c27, f9(c28, c29))))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[43])).
% 0.19/0.41 tff(45,plain,
% 0.19/0.41 (((~![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33)))) | (p4(f5(f8(c27, f9(c28, c29)), c36, c31), f5(f8(c27, f9(c28, c29)), c36, c34)) | p25(f22(f8(c27, f9(c28, c29)), c31, c34), f18(f8(c27, f9(c28, c29)))) | p6(f21(f8(c27, f9(c28, c29))), f10(c33)))) <=> ((~![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33)))) | p4(f5(f8(c27, f9(c28, c29)), c36, c31), f5(f8(c27, f9(c28, c29)), c36, c34)) | p6(f21(f8(c27, f9(c28, c29))), f10(c33)) | p25(f22(f8(c27, f9(c28, c29)), c31, c34), f18(f8(c27, f9(c28, c29)))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[44, 42])).
% 0.19/0.41 tff(46,plain,
% 0.19/0.41 ((~![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33)))) | (p4(f5(f8(c27, f9(c28, c29)), c36, c31), f5(f8(c27, f9(c28, c29)), c36, c34)) | p25(f22(f8(c27, f9(c28, c29)), c31, c34), f18(f8(c27, f9(c28, c29)))) | p6(f21(f8(c27, f9(c28, c29))), f10(c33)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(47,plain,
% 0.19/0.41 ((~![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p25(f22(X25, X26, X27), f18(X25)) | p6(f21(X25), f10(c33)))) | p4(f5(f8(c27, f9(c28, c29)), c36, c31), f5(f8(c27, f9(c28, c29)), c36, c34)) | p6(f21(f8(c27, f9(c28, c29))), f10(c33)) | p25(f22(f8(c27, f9(c28, c29)), c31, c34), f18(f8(c27, f9(c28, c29))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.19/0.41 tff(48,plain,
% 0.19/0.41 (p25(f22(f8(c27, f9(c28, c29)), c31, c34), f18(f8(c27, f9(c28, c29))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[47, 41, 38, 28])).
% 0.19/0.41 tff(49,assumption,(~p24(f19(f20(c31, c34)), f19(f20(c31, f22(f8(c27, f9(c28, c29)), c31, c34))))), introduced(assumption)).
% 0.19/0.41 tff(50,plain,
% 0.19/0.41 (^[X20: $i] : refl(((~p25(X20, f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c31, c34)), f19(f20(c31, X20)))) <=> ((~p25(X20, f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c31, c34)), f19(f20(c31, X20)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(51,plain,
% 0.19/0.41 (![X20: $i] : ((~p25(X20, f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c31, c34)), f19(f20(c31, X20)))) <=> ![X20: $i] : ((~p25(X20, f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c31, c34)), f19(f20(c31, X20))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[50])).
% 0.19/0.41 tff(52,plain,
% 0.19/0.41 (![X20: $i] : ((~p25(X20, f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c31, c34)), f19(f20(c31, X20)))) <=> ![X20: $i] : ((~p25(X20, f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c31, c34)), f19(f20(c31, X20))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(53,plain,
% 0.19/0.41 (^[X20: $i] : rewrite((p24(f19(f20(c31, c34)), f19(f20(c31, X20))) | (~p25(X20, f18(f8(c27, f9(c28, c29)))))) <=> ((~p25(X20, f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c31, c34)), f19(f20(c31, X20)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(54,plain,
% 0.19/0.41 (![X20: $i] : (p24(f19(f20(c31, c34)), f19(f20(c31, X20))) | (~p25(X20, f18(f8(c27, f9(c28, c29)))))) <=> ![X20: $i] : ((~p25(X20, f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c31, c34)), f19(f20(c31, X20))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[53])).
% 0.19/0.41 tff(55,axiom,(![X20: $i] : (p24(f19(f20(c31, c34)), f19(f20(c31, X20))) | (~p25(X20, f18(f8(c27, f9(c28, c29))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p24_45')).
% 0.19/0.41 tff(56,plain,
% 0.19/0.41 (![X20: $i] : ((~p25(X20, f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c31, c34)), f19(f20(c31, X20))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.19/0.41 tff(57,plain,
% 0.19/0.41 (![X20: $i] : ((~p25(X20, f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c31, c34)), f19(f20(c31, X20))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.19/0.41 tff(58,plain,(
% 0.19/0.41 ![X20: $i] : ((~p25(X20, f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c31, c34)), f19(f20(c31, X20))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[57])).
% 0.19/0.41 tff(59,plain,
% 0.19/0.41 (![X20: $i] : ((~p25(X20, f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c31, c34)), f19(f20(c31, X20))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.19/0.41 tff(60,plain,
% 0.19/0.41 (((~![X20: $i] : ((~p25(X20, f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c31, c34)), f19(f20(c31, X20))))) | ((~p25(f22(f8(c27, f9(c28, c29)), c31, c34), f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c31, c34)), f19(f20(c31, f22(f8(c27, f9(c28, c29)), c31, c34)))))) <=> ((~![X20: $i] : ((~p25(X20, f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c31, c34)), f19(f20(c31, X20))))) | (~p25(f22(f8(c27, f9(c28, c29)), c31, c34), f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c31, c34)), f19(f20(c31, f22(f8(c27, f9(c28, c29)), c31, c34)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(61,plain,
% 0.19/0.41 ((~![X20: $i] : ((~p25(X20, f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c31, c34)), f19(f20(c31, X20))))) | ((~p25(f22(f8(c27, f9(c28, c29)), c31, c34), f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c31, c34)), f19(f20(c31, f22(f8(c27, f9(c28, c29)), c31, c34)))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(62,plain,
% 0.19/0.41 ((~![X20: $i] : ((~p25(X20, f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c31, c34)), f19(f20(c31, X20))))) | (~p25(f22(f8(c27, f9(c28, c29)), c31, c34), f18(f8(c27, f9(c28, c29))))) | p24(f19(f20(c31, c34)), f19(f20(c31, f22(f8(c27, f9(c28, c29)), c31, c34))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.19/0.41 tff(63,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[62, 59, 49, 48])).
% 0.19/0.41 tff(64,plain,(p24(f19(f20(c31, c34)), f19(f20(c31, f22(f8(c27, f9(c28, c29)), c31, c34))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(65,plain,
% 0.19/0.41 (^[X25: $i, X27: $i, X26: $i] : refl((p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33)) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27)))))) <=> (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33)) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27)))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(66,plain,
% 0.19/0.41 (![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33)) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27)))))) <=> ![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33)) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[65])).
% 0.19/0.41 tff(67,plain,
% 0.19/0.41 (![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33)) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27)))))) <=> ![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33)) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(68,plain,
% 0.19/0.41 (^[X25: $i, X27: $i, X26: $i] : trans(monotonicity(rewrite((p6(f21(X25), f10(c33)) | p4(f5(X25, c36, X26), f5(X25, c36, X27))) <=> (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33)))), (((p6(f21(X25), f10(c33)) | p4(f5(X25, c36, X26), f5(X25, c36, X27))) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27)))))) <=> ((p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33))) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27)))))))), rewrite(((p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33))) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27)))))) <=> (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33)) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27))))))), (((p6(f21(X25), f10(c33)) | p4(f5(X25, c36, X26), f5(X25, c36, X27))) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27)))))) <=> (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33)) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(69,plain,
% 0.19/0.41 (![X25: $i, X27: $i, X26: $i] : ((p6(f21(X25), f10(c33)) | p4(f5(X25, c36, X26), f5(X25, c36, X27))) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27)))))) <=> ![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33)) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[68])).
% 0.19/0.41 tff(70,axiom,(![X25: $i, X27: $i, X26: $i] : ((p6(f21(X25), f10(c33)) | p4(f5(X25, c36, X26), f5(X25, c36, X27))) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p6_49')).
% 0.19/0.41 tff(71,plain,
% 0.19/0.41 (![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33)) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.19/0.42 tff(72,plain,
% 0.19/0.42 (![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33)) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.19/0.42 tff(73,plain,(
% 0.19/0.42 ![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33)) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27))))))),
% 0.19/0.42 inference(skolemize,[status(sab)],[72])).
% 0.19/0.42 tff(74,plain,
% 0.19/0.42 (![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33)) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.19/0.42 tff(75,plain,
% 0.19/0.42 (((~![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33)) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27))))))) | (p4(f5(f8(c27, f9(c28, c29)), c36, c31), f5(f8(c27, f9(c28, c29)), c36, c34)) | p6(f21(f8(c27, f9(c28, c29))), f10(c33)) | (~p24(f19(f20(c31, c34)), f19(f20(c31, f22(f8(c27, f9(c28, c29)), c31, c34))))))) <=> ((~![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33)) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27))))))) | p4(f5(f8(c27, f9(c28, c29)), c36, c31), f5(f8(c27, f9(c28, c29)), c36, c34)) | p6(f21(f8(c27, f9(c28, c29))), f10(c33)) | (~p24(f19(f20(c31, c34)), f19(f20(c31, f22(f8(c27, f9(c28, c29)), c31, c34))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(76,plain,
% 0.19/0.42 ((~![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33)) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27))))))) | (p4(f5(f8(c27, f9(c28, c29)), c36, c31), f5(f8(c27, f9(c28, c29)), c36, c34)) | p6(f21(f8(c27, f9(c28, c29))), f10(c33)) | (~p24(f19(f20(c31, c34)), f19(f20(c31, f22(f8(c27, f9(c28, c29)), c31, c34))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(77,plain,
% 0.19/0.42 ((~![X25: $i, X27: $i, X26: $i] : (p4(f5(X25, c36, X26), f5(X25, c36, X27)) | p6(f21(X25), f10(c33)) | (~p24(f19(f20(X26, X27)), f19(f20(X26, f22(X25, X26, X27))))))) | p4(f5(f8(c27, f9(c28, c29)), c36, c31), f5(f8(c27, f9(c28, c29)), c36, c34)) | p6(f21(f8(c27, f9(c28, c29))), f10(c33)) | (~p24(f19(f20(c31, c34)), f19(f20(c31, f22(f8(c27, f9(c28, c29)), c31, c34)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.19/0.42 tff(78,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[77, 41, 74, 28, 64])).
% 0.19/0.42 % SZS output end Proof
% 0.21/0.42 % E exiting
%------------------------------------------------------------------------------