%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN632-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:39:43 AM UTC 2025
% Result : Unsatisfiable 0.18s 0.44s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYN632-1 : TPTP v9.0.0. Released v2.5.0.
% 0.03/0.11 % Command : run_E %s %d THM
% 0.10/0.32 % Computer : n015.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Fri Jun 20 12:39:41 EDT 2025
% 0.10/0.32 % CPUTime :
% 0.18/0.44 % SZS status Unsatisfiable
% 0.18/0.44 % SZS output start Proof
% 0.18/0.44 tff(p4_type, type, (
% 0.18/0.44 p4: ( $i * $i ) > $o)).
% 0.18/0.44 tff(f5_type, type, (
% 0.18/0.44 f5: ( $i * $i ) > $i)).
% 0.18/0.44 tff(c23_type, type, (
% 0.18/0.44 c23: $i)).
% 0.18/0.44 tff(c22_type, type, (
% 0.18/0.44 c22: $i)).
% 0.18/0.44 tff(f14_type, type, (
% 0.18/0.44 f14: ( $i * $i ) > $i)).
% 0.18/0.44 tff(c27_type, type, (
% 0.18/0.44 c27: $i)).
% 0.18/0.44 tff(f16_type, type, (
% 0.18/0.44 f16: ( $i * $i ) > $i)).
% 0.18/0.44 tff(f18_type, type, (
% 0.18/0.44 f18: ( $i * $i ) > $i)).
% 0.18/0.44 tff(f20_type, type, (
% 0.18/0.44 f20: ( $i * $i ) > $i)).
% 0.18/0.44 tff(f12_type, type, (
% 0.18/0.44 f12: ( $i * $i ) > $i)).
% 0.18/0.44 tff(c26_type, type, (
% 0.18/0.44 c26: $i)).
% 0.18/0.44 tff(c25_type, type, (
% 0.18/0.44 c25: $i)).
% 0.18/0.44 tff(c29_type, type, (
% 0.18/0.44 c29: $i)).
% 0.18/0.44 tff(p3_type, type, (
% 0.18/0.44 p3: ( $i * $i ) > $o)).
% 0.18/0.44 tff(p21_type, type, (
% 0.18/0.44 p21: ( $i * $i ) > $o)).
% 0.18/0.44 tff(f7_type, type, (
% 0.18/0.44 f7: ( $i * $i ) > $i)).
% 0.18/0.44 tff(f10_type, type, (
% 0.18/0.44 f10: ( $i * $i ) > $i)).
% 0.18/0.44 tff(c24_type, type, (
% 0.18/0.44 c24: $i)).
% 0.18/0.44 tff(c28_type, type, (
% 0.18/0.44 c28: $i)).
% 0.18/0.44 tff(p2_type, type, (
% 0.18/0.44 p2: ( $i * $i ) > $o)).
% 0.18/0.44 tff(1,plain,
% 0.18/0.44 (^[X39: $i, X38: $i, X41: $i, X40: $i] : refl(((~p21(f5(f7(f10(c24, f12(c28, X39)), X38), X40), X41)) | p21(f5(f7(f10(c24, X39), X38), X40), f14(f16(f18(f20(c29, X39), X40), X38), X41))) <=> ((~p21(f5(f7(f10(c24, f12(c28, X39)), X38), X40), X41)) | p21(f5(f7(f10(c24, X39), X38), X40), f14(f16(f18(f20(c29, X39), X40), X38), X41))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(2,plain,
% 0.18/0.44 (![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p21(f5(f7(f10(c24, f12(c28, X39)), X38), X40), X41)) | p21(f5(f7(f10(c24, X39), X38), X40), f14(f16(f18(f20(c29, X39), X40), X38), X41))) <=> ![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p21(f5(f7(f10(c24, f12(c28, X39)), X38), X40), X41)) | p21(f5(f7(f10(c24, X39), X38), X40), f14(f16(f18(f20(c29, X39), X40), X38), X41)))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[1])).
% 0.18/0.44 tff(3,plain,
% 0.18/0.44 (![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p21(f5(f7(f10(c24, f12(c28, X39)), X38), X40), X41)) | p21(f5(f7(f10(c24, X39), X38), X40), f14(f16(f18(f20(c29, X39), X40), X38), X41))) <=> ![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p21(f5(f7(f10(c24, f12(c28, X39)), X38), X40), X41)) | p21(f5(f7(f10(c24, X39), X38), X40), f14(f16(f18(f20(c29, X39), X40), X38), X41)))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(4,plain,
% 0.18/0.44 (^[X39: $i, X38: $i, X41: $i, X40: $i] : rewrite((p21(f5(f7(f10(c24, X39), X38), X40), f14(f16(f18(f20(c29, X39), X40), X38), X41)) | (~p21(f5(f7(f10(c24, f12(c28, X39)), X38), X40), X41))) <=> ((~p21(f5(f7(f10(c24, f12(c28, X39)), X38), X40), X41)) | p21(f5(f7(f10(c24, X39), X38), X40), f14(f16(f18(f20(c29, X39), X40), X38), X41))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(5,plain,
% 0.18/0.44 (![X39: $i, X38: $i, X41: $i, X40: $i] : (p21(f5(f7(f10(c24, X39), X38), X40), f14(f16(f18(f20(c29, X39), X40), X38), X41)) | (~p21(f5(f7(f10(c24, f12(c28, X39)), X38), X40), X41))) <=> ![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p21(f5(f7(f10(c24, f12(c28, X39)), X38), X40), X41)) | p21(f5(f7(f10(c24, X39), X38), X40), f14(f16(f18(f20(c29, X39), X40), X38), X41)))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[4])).
% 0.18/0.44 tff(6,axiom,(![X39: $i, X38: $i, X41: $i, X40: $i] : (p21(f5(f7(f10(c24, X39), X38), X40), f14(f16(f18(f20(c29, X39), X40), X38), X41)) | (~p21(f5(f7(f10(c24, f12(c28, X39)), X38), X40), X41)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p21_38')).
% 0.18/0.44 tff(7,plain,
% 0.18/0.44 (![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p21(f5(f7(f10(c24, f12(c28, X39)), X38), X40), X41)) | p21(f5(f7(f10(c24, X39), X38), X40), f14(f16(f18(f20(c29, X39), X40), X38), X41)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.18/0.44 tff(8,plain,
% 0.18/0.44 (![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p21(f5(f7(f10(c24, f12(c28, X39)), X38), X40), X41)) | p21(f5(f7(f10(c24, X39), X38), X40), f14(f16(f18(f20(c29, X39), X40), X38), X41)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.18/0.44 tff(9,plain,(
% 0.18/0.44 ![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p21(f5(f7(f10(c24, f12(c28, X39)), X38), X40), X41)) | p21(f5(f7(f10(c24, X39), X38), X40), f14(f16(f18(f20(c29, X39), X40), X38), X41)))),
% 0.18/0.44 inference(skolemize,[status(sab)],[8])).
% 0.18/0.44 tff(10,plain,
% 0.18/0.44 (![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p21(f5(f7(f10(c24, f12(c28, X39)), X38), X40), X41)) | p21(f5(f7(f10(c24, X39), X38), X40), f14(f16(f18(f20(c29, X39), X40), X38), X41)))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.18/0.45 tff(11,plain,
% 0.18/0.45 (p21(f5(f7(f10(c24, f12(c28, f12(c25, c26))), c22), c23), c27) <=> p21(f5(f7(f10(c24, f12(c28, f12(c25, c26))), c22), c23), c27)),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(12,axiom,(p21(f5(f7(f10(c24, f12(c28, f12(c25, c26))), c22), c23), c27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p21_24')).
% 0.18/0.45 tff(13,plain,
% 0.18/0.45 (p21(f5(f7(f10(c24, f12(c28, f12(c25, c26))), c22), c23), c27)),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.18/0.45 tff(14,plain,
% 0.18/0.45 (((~![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p21(f5(f7(f10(c24, f12(c28, X39)), X38), X40), X41)) | p21(f5(f7(f10(c24, X39), X38), X40), f14(f16(f18(f20(c29, X39), X40), X38), X41)))) | ((~p21(f5(f7(f10(c24, f12(c28, f12(c25, c26))), c22), c23), c27)) | p21(f5(f7(f10(c24, f12(c25, c26)), c22), c23), f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27)))) <=> ((~![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p21(f5(f7(f10(c24, f12(c28, X39)), X38), X40), X41)) | p21(f5(f7(f10(c24, X39), X38), X40), f14(f16(f18(f20(c29, X39), X40), X38), X41)))) | (~p21(f5(f7(f10(c24, f12(c28, f12(c25, c26))), c22), c23), c27)) | p21(f5(f7(f10(c24, f12(c25, c26)), c22), c23), f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27)))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(15,plain,
% 0.18/0.45 ((~![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p21(f5(f7(f10(c24, f12(c28, X39)), X38), X40), X41)) | p21(f5(f7(f10(c24, X39), X38), X40), f14(f16(f18(f20(c29, X39), X40), X38), X41)))) | ((~p21(f5(f7(f10(c24, f12(c28, f12(c25, c26))), c22), c23), c27)) | p21(f5(f7(f10(c24, f12(c25, c26)), c22), c23), f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27)))),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(16,plain,
% 0.18/0.45 ((~![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p21(f5(f7(f10(c24, f12(c28, X39)), X38), X40), X41)) | p21(f5(f7(f10(c24, X39), X38), X40), f14(f16(f18(f20(c29, X39), X40), X38), X41)))) | (~p21(f5(f7(f10(c24, f12(c28, f12(c25, c26))), c22), c23), c27)) | p21(f5(f7(f10(c24, f12(c25, c26)), c22), c23), f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.18/0.45 tff(17,plain,
% 0.18/0.45 (p21(f5(f7(f10(c24, f12(c25, c26)), c22), c23), f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[16, 13, 10])).
% 0.18/0.45 tff(18,plain,
% 0.18/0.45 (^[X43: $i, X42: $i, X44: $i] : refl((p3(X43, X44) | (~p21(f5(f7(f10(c24, f12(c25, c26)), X42), X43), X44))) <=> (p3(X43, X44) | (~p21(f5(f7(f10(c24, f12(c25, c26)), X42), X43), X44))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(19,plain,
% 0.18/0.45 (![X43: $i, X42: $i, X44: $i] : (p3(X43, X44) | (~p21(f5(f7(f10(c24, f12(c25, c26)), X42), X43), X44))) <=> ![X43: $i, X42: $i, X44: $i] : (p3(X43, X44) | (~p21(f5(f7(f10(c24, f12(c25, c26)), X42), X43), X44)))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[18])).
% 0.18/0.45 tff(20,plain,
% 0.18/0.45 (![X43: $i, X42: $i, X44: $i] : (p3(X43, X44) | (~p21(f5(f7(f10(c24, f12(c25, c26)), X42), X43), X44))) <=> ![X43: $i, X42: $i, X44: $i] : (p3(X43, X44) | (~p21(f5(f7(f10(c24, f12(c25, c26)), X42), X43), X44)))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(21,axiom,(![X43: $i, X42: $i, X44: $i] : (p3(X43, X44) | (~p21(f5(f7(f10(c24, f12(c25, c26)), X42), X43), X44)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p3_33')).
% 0.18/0.45 tff(22,plain,
% 0.18/0.45 (![X43: $i, X42: $i, X44: $i] : (p3(X43, X44) | (~p21(f5(f7(f10(c24, f12(c25, c26)), X42), X43), X44)))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.18/0.45 tff(23,plain,(
% 0.18/0.45 ![X43: $i, X42: $i, X44: $i] : (p3(X43, X44) | (~p21(f5(f7(f10(c24, f12(c25, c26)), X42), X43), X44)))),
% 0.18/0.45 inference(skolemize,[status(sab)],[22])).
% 0.18/0.45 tff(24,plain,
% 0.18/0.45 (![X43: $i, X42: $i, X44: $i] : (p3(X43, X44) | (~p21(f5(f7(f10(c24, f12(c25, c26)), X42), X43), X44)))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.18/0.45 tff(25,plain,
% 0.18/0.45 (((~![X43: $i, X42: $i, X44: $i] : (p3(X43, X44) | (~p21(f5(f7(f10(c24, f12(c25, c26)), X42), X43), X44)))) | (p3(c23, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27)) | (~p21(f5(f7(f10(c24, f12(c25, c26)), c22), c23), f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27))))) <=> ((~![X43: $i, X42: $i, X44: $i] : (p3(X43, X44) | (~p21(f5(f7(f10(c24, f12(c25, c26)), X42), X43), X44)))) | p3(c23, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27)) | (~p21(f5(f7(f10(c24, f12(c25, c26)), c22), c23), f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27))))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(26,plain,
% 0.18/0.45 ((~![X43: $i, X42: $i, X44: $i] : (p3(X43, X44) | (~p21(f5(f7(f10(c24, f12(c25, c26)), X42), X43), X44)))) | (p3(c23, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27)) | (~p21(f5(f7(f10(c24, f12(c25, c26)), c22), c23), f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27))))),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(27,plain,
% 0.18/0.45 ((~![X43: $i, X42: $i, X44: $i] : (p3(X43, X44) | (~p21(f5(f7(f10(c24, f12(c25, c26)), X42), X43), X44)))) | p3(c23, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27)) | (~p21(f5(f7(f10(c24, f12(c25, c26)), c22), c23), f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27)))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.18/0.45 tff(28,plain,
% 0.18/0.45 (p3(c23, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[27, 24, 17])).
% 0.18/0.45 tff(29,assumption,(~p3(c23, c23)), introduced(assumption)).
% 0.18/0.45 tff(30,plain,
% 0.18/0.45 (^[X46: $i] : refl(p3(X46, X46) <=> p3(X46, X46))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(31,plain,
% 0.18/0.45 (![X46: $i] : p3(X46, X46) <=> ![X46: $i] : p3(X46, X46)),
% 0.18/0.45 inference(quant_intro,[status(thm)],[30])).
% 0.18/0.45 tff(32,plain,
% 0.18/0.45 (![X46: $i] : p3(X46, X46) <=> ![X46: $i] : p3(X46, X46)),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(33,axiom,(![X46: $i] : p3(X46, X46)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p3_6')).
% 0.18/0.45 tff(34,plain,
% 0.18/0.45 (![X46: $i] : p3(X46, X46)),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.18/0.45 tff(35,plain,(
% 0.18/0.45 ![X46: $i] : p3(X46, X46)),
% 0.18/0.45 inference(skolemize,[status(sab)],[34])).
% 0.18/0.45 tff(36,plain,
% 0.18/0.45 (![X46: $i] : p3(X46, X46)),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.18/0.45 tff(37,plain,
% 0.18/0.45 ((~![X46: $i] : p3(X46, X46)) | p3(c23, c23)),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(38,plain,
% 0.18/0.45 ($false),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[37, 36, 29])).
% 0.18/0.45 tff(39,plain,(p3(c23, c23)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.45 tff(40,plain,
% 0.18/0.45 (^[X47: $i, X46: $i, X48: $i] : refl(((~p3(X46, X48)) | (~p3(X46, X47)) | p3(X47, X48)) <=> ((~p3(X46, X48)) | (~p3(X46, X47)) | p3(X47, X48)))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(41,plain,
% 0.18/0.45 (![X47: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p3(X46, X47)) | p3(X47, X48)) <=> ![X47: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p3(X46, X47)) | p3(X47, X48))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[40])).
% 0.18/0.45 tff(42,plain,
% 0.18/0.45 (![X47: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p3(X46, X47)) | p3(X47, X48)) <=> ![X47: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p3(X46, X47)) | p3(X47, X48))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(43,plain,
% 0.18/0.45 (^[X47: $i, X46: $i, X48: $i] : trans(monotonicity(rewrite((p3(X47, X48) | (~p3(X46, X47))) <=> ((~p3(X46, X47)) | p3(X47, X48))), (((p3(X47, X48) | (~p3(X46, X47))) | (~p3(X46, X48))) <=> (((~p3(X46, X47)) | p3(X47, X48)) | (~p3(X46, X48))))), rewrite((((~p3(X46, X47)) | p3(X47, X48)) | (~p3(X46, X48))) <=> ((~p3(X46, X48)) | (~p3(X46, X47)) | p3(X47, X48))), (((p3(X47, X48) | (~p3(X46, X47))) | (~p3(X46, X48))) <=> ((~p3(X46, X48)) | (~p3(X46, X47)) | p3(X47, X48))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(44,plain,
% 0.18/0.45 (![X47: $i, X46: $i, X48: $i] : ((p3(X47, X48) | (~p3(X46, X47))) | (~p3(X46, X48))) <=> ![X47: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p3(X46, X47)) | p3(X47, X48))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[43])).
% 0.18/0.45 tff(45,axiom,(![X47: $i, X46: $i, X48: $i] : ((p3(X47, X48) | (~p3(X46, X47))) | (~p3(X46, X48)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p3_17')).
% 0.18/0.45 tff(46,plain,
% 0.18/0.45 (![X47: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p3(X46, X47)) | p3(X47, X48))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.18/0.45 tff(47,plain,
% 0.18/0.45 (![X47: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p3(X46, X47)) | p3(X47, X48))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.18/0.45 tff(48,plain,(
% 0.18/0.45 ![X47: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p3(X46, X47)) | p3(X47, X48))),
% 0.18/0.45 inference(skolemize,[status(sab)],[47])).
% 0.18/0.45 tff(49,plain,
% 0.18/0.45 (![X47: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p3(X46, X47)) | p3(X47, X48))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[48, 41])).
% 0.18/0.45 tff(50,plain,
% 0.18/0.45 (((~![X47: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p3(X46, X47)) | p3(X47, X48))) | ((~p3(c23, c23)) | (~p3(c23, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27))) | p3(f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27), c23))) <=> ((~![X47: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p3(X46, X47)) | p3(X47, X48))) | (~p3(c23, c23)) | (~p3(c23, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27))) | p3(f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27), c23))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(51,plain,
% 0.18/0.45 ((~![X47: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p3(X46, X47)) | p3(X47, X48))) | ((~p3(c23, c23)) | (~p3(c23, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27))) | p3(f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27), c23))),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(52,plain,
% 0.18/0.45 ((~![X47: $i, X46: $i, X48: $i] : ((~p3(X46, X48)) | (~p3(X46, X47)) | p3(X47, X48))) | (~p3(c23, c23)) | (~p3(c23, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27))) | p3(f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27), c23)),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.18/0.45 tff(53,plain,
% 0.18/0.45 (p3(f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27), c23)),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[52, 49, 39, 28])).
% 0.18/0.45 tff(54,assumption,(~p2(c22, c22)), introduced(assumption)).
% 0.18/0.45 tff(55,plain,
% 0.18/0.45 (^[X27: $i] : refl(p2(X27, X27) <=> p2(X27, X27))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(56,plain,
% 0.18/0.45 (![X27: $i] : p2(X27, X27) <=> ![X27: $i] : p2(X27, X27)),
% 0.18/0.45 inference(quant_intro,[status(thm)],[55])).
% 0.18/0.45 tff(57,plain,
% 0.18/0.45 (![X27: $i] : p2(X27, X27) <=> ![X27: $i] : p2(X27, X27)),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(58,axiom,(![X27: $i] : p2(X27, X27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_7')).
% 0.18/0.45 tff(59,plain,
% 0.18/0.45 (![X27: $i] : p2(X27, X27)),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.18/0.45 tff(60,plain,(
% 0.18/0.45 ![X27: $i] : p2(X27, X27)),
% 0.18/0.45 inference(skolemize,[status(sab)],[59])).
% 0.18/0.45 tff(61,plain,
% 0.18/0.45 (![X27: $i] : p2(X27, X27)),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.18/0.45 tff(62,plain,
% 0.18/0.45 ((~![X27: $i] : p2(X27, X27)) | p2(c22, c22)),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(63,plain,
% 0.18/0.45 ($false),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[62, 61, 54])).
% 0.18/0.45 tff(64,plain,(p2(c22, c22)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.45 tff(65,plain,
% 0.18/0.45 (^[X57: $i, X56: $i, X59: $i, X58: $i] : refl(((~p2(X56, X58)) | (~p3(X57, X59)) | p4(f5(X56, X57), f5(X58, X59))) <=> ((~p2(X56, X58)) | (~p3(X57, X59)) | p4(f5(X56, X57), f5(X58, X59))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(66,plain,
% 0.18/0.45 (![X57: $i, X56: $i, X59: $i, X58: $i] : ((~p2(X56, X58)) | (~p3(X57, X59)) | p4(f5(X56, X57), f5(X58, X59))) <=> ![X57: $i, X56: $i, X59: $i, X58: $i] : ((~p2(X56, X58)) | (~p3(X57, X59)) | p4(f5(X56, X57), f5(X58, X59)))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[65])).
% 0.18/0.45 tff(67,plain,
% 0.18/0.45 (![X57: $i, X56: $i, X59: $i, X58: $i] : ((~p2(X56, X58)) | (~p3(X57, X59)) | p4(f5(X56, X57), f5(X58, X59))) <=> ![X57: $i, X56: $i, X59: $i, X58: $i] : ((~p2(X56, X58)) | (~p3(X57, X59)) | p4(f5(X56, X57), f5(X58, X59)))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(68,plain,
% 0.18/0.45 (^[X57: $i, X56: $i, X59: $i, X58: $i] : trans(monotonicity(rewrite((p4(f5(X56, X57), f5(X58, X59)) | (~p2(X56, X58))) <=> ((~p2(X56, X58)) | p4(f5(X56, X57), f5(X58, X59)))), (((p4(f5(X56, X57), f5(X58, X59)) | (~p2(X56, X58))) | (~p3(X57, X59))) <=> (((~p2(X56, X58)) | p4(f5(X56, X57), f5(X58, X59))) | (~p3(X57, X59))))), rewrite((((~p2(X56, X58)) | p4(f5(X56, X57), f5(X58, X59))) | (~p3(X57, X59))) <=> ((~p2(X56, X58)) | (~p3(X57, X59)) | p4(f5(X56, X57), f5(X58, X59)))), (((p4(f5(X56, X57), f5(X58, X59)) | (~p2(X56, X58))) | (~p3(X57, X59))) <=> ((~p2(X56, X58)) | (~p3(X57, X59)) | p4(f5(X56, X57), f5(X58, X59)))))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(69,plain,
% 0.18/0.46 (![X57: $i, X56: $i, X59: $i, X58: $i] : ((p4(f5(X56, X57), f5(X58, X59)) | (~p2(X56, X58))) | (~p3(X57, X59))) <=> ![X57: $i, X56: $i, X59: $i, X58: $i] : ((~p2(X56, X58)) | (~p3(X57, X59)) | p4(f5(X56, X57), f5(X58, X59)))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[68])).
% 0.18/0.46 tff(70,axiom,(![X57: $i, X56: $i, X59: $i, X58: $i] : ((p4(f5(X56, X57), f5(X58, X59)) | (~p2(X56, X58))) | (~p3(X57, X59)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p4_31')).
% 0.18/0.46 tff(71,plain,
% 0.18/0.46 (![X57: $i, X56: $i, X59: $i, X58: $i] : ((~p2(X56, X58)) | (~p3(X57, X59)) | p4(f5(X56, X57), f5(X58, X59)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.18/0.46 tff(72,plain,
% 0.18/0.46 (![X57: $i, X56: $i, X59: $i, X58: $i] : ((~p2(X56, X58)) | (~p3(X57, X59)) | p4(f5(X56, X57), f5(X58, X59)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.18/0.46 tff(73,plain,(
% 0.18/0.46 ![X57: $i, X56: $i, X59: $i, X58: $i] : ((~p2(X56, X58)) | (~p3(X57, X59)) | p4(f5(X56, X57), f5(X58, X59)))),
% 0.18/0.46 inference(skolemize,[status(sab)],[72])).
% 0.18/0.46 tff(74,plain,
% 0.18/0.46 (![X57: $i, X56: $i, X59: $i, X58: $i] : ((~p2(X56, X58)) | (~p3(X57, X59)) | p4(f5(X56, X57), f5(X58, X59)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.18/0.46 tff(75,plain,
% 0.18/0.46 (((~![X57: $i, X56: $i, X59: $i, X58: $i] : ((~p2(X56, X58)) | (~p3(X57, X59)) | p4(f5(X56, X57), f5(X58, X59)))) | ((~p2(c22, c22)) | (~p3(f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27), c23)) | p4(f5(c22, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27)), f5(c22, c23)))) <=> ((~![X57: $i, X56: $i, X59: $i, X58: $i] : ((~p2(X56, X58)) | (~p3(X57, X59)) | p4(f5(X56, X57), f5(X58, X59)))) | (~p2(c22, c22)) | (~p3(f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27), c23)) | p4(f5(c22, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27)), f5(c22, c23)))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(76,plain,
% 0.18/0.46 ((~![X57: $i, X56: $i, X59: $i, X58: $i] : ((~p2(X56, X58)) | (~p3(X57, X59)) | p4(f5(X56, X57), f5(X58, X59)))) | ((~p2(c22, c22)) | (~p3(f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27), c23)) | p4(f5(c22, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27)), f5(c22, c23)))),
% 0.18/0.46 inference(quant_inst,[status(thm)],[])).
% 0.18/0.46 tff(77,plain,
% 0.18/0.46 ((~![X57: $i, X56: $i, X59: $i, X58: $i] : ((~p2(X56, X58)) | (~p3(X57, X59)) | p4(f5(X56, X57), f5(X58, X59)))) | (~p2(c22, c22)) | (~p3(f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27), c23)) | p4(f5(c22, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27)), f5(c22, c23))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.18/0.46 tff(78,plain,
% 0.18/0.46 (p4(f5(c22, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27)), f5(c22, c23))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[77, 74, 64, 53])).
% 0.18/0.46 tff(79,assumption,(~p21(f5(f7(f10(c24, f12(c25, c26)), c22), c27), c27)), introduced(assumption)).
% 0.18/0.46 tff(80,assumption,(~p3(c27, c27)), introduced(assumption)).
% 0.18/0.46 tff(81,plain,
% 0.18/0.46 ((~![X46: $i] : p3(X46, X46)) | p3(c27, c27)),
% 0.18/0.46 inference(quant_inst,[status(thm)],[])).
% 0.18/0.46 tff(82,plain,
% 0.18/0.46 ($false),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[81, 36, 80])).
% 0.18/0.46 tff(83,plain,(p3(c27, c27)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.46 tff(84,plain,
% 0.18/0.46 (^[X43: $i, X42: $i, X44: $i] : refl((p21(f5(f7(f10(c24, f12(c25, c26)), X42), X43), X44) | (~p3(X43, X44))) <=> (p21(f5(f7(f10(c24, f12(c25, c26)), X42), X43), X44) | (~p3(X43, X44))))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(85,plain,
% 0.18/0.46 (![X43: $i, X42: $i, X44: $i] : (p21(f5(f7(f10(c24, f12(c25, c26)), X42), X43), X44) | (~p3(X43, X44))) <=> ![X43: $i, X42: $i, X44: $i] : (p21(f5(f7(f10(c24, f12(c25, c26)), X42), X43), X44) | (~p3(X43, X44)))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[84])).
% 0.18/0.46 tff(86,plain,
% 0.18/0.46 (![X43: $i, X42: $i, X44: $i] : (p21(f5(f7(f10(c24, f12(c25, c26)), X42), X43), X44) | (~p3(X43, X44))) <=> ![X43: $i, X42: $i, X44: $i] : (p21(f5(f7(f10(c24, f12(c25, c26)), X42), X43), X44) | (~p3(X43, X44)))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(87,axiom,(![X43: $i, X42: $i, X44: $i] : (p21(f5(f7(f10(c24, f12(c25, c26)), X42), X43), X44) | (~p3(X43, X44)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p21_34')).
% 0.18/0.46 tff(88,plain,
% 0.18/0.46 (![X43: $i, X42: $i, X44: $i] : (p21(f5(f7(f10(c24, f12(c25, c26)), X42), X43), X44) | (~p3(X43, X44)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.18/0.46 tff(89,plain,(
% 0.18/0.46 ![X43: $i, X42: $i, X44: $i] : (p21(f5(f7(f10(c24, f12(c25, c26)), X42), X43), X44) | (~p3(X43, X44)))),
% 0.18/0.46 inference(skolemize,[status(sab)],[88])).
% 0.18/0.46 tff(90,plain,
% 0.18/0.46 (![X43: $i, X42: $i, X44: $i] : (p21(f5(f7(f10(c24, f12(c25, c26)), X42), X43), X44) | (~p3(X43, X44)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.18/0.46 tff(91,plain,
% 0.18/0.46 (((~![X43: $i, X42: $i, X44: $i] : (p21(f5(f7(f10(c24, f12(c25, c26)), X42), X43), X44) | (~p3(X43, X44)))) | ((~p3(c27, c27)) | p21(f5(f7(f10(c24, f12(c25, c26)), c22), c27), c27))) <=> ((~![X43: $i, X42: $i, X44: $i] : (p21(f5(f7(f10(c24, f12(c25, c26)), X42), X43), X44) | (~p3(X43, X44)))) | (~p3(c27, c27)) | p21(f5(f7(f10(c24, f12(c25, c26)), c22), c27), c27))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(92,plain,
% 0.18/0.46 ((p21(f5(f7(f10(c24, f12(c25, c26)), c22), c27), c27) | (~p3(c27, c27))) <=> ((~p3(c27, c27)) | p21(f5(f7(f10(c24, f12(c25, c26)), c22), c27), c27))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(93,plain,
% 0.18/0.46 (((~![X43: $i, X42: $i, X44: $i] : (p21(f5(f7(f10(c24, f12(c25, c26)), X42), X43), X44) | (~p3(X43, X44)))) | (p21(f5(f7(f10(c24, f12(c25, c26)), c22), c27), c27) | (~p3(c27, c27)))) <=> ((~![X43: $i, X42: $i, X44: $i] : (p21(f5(f7(f10(c24, f12(c25, c26)), X42), X43), X44) | (~p3(X43, X44)))) | ((~p3(c27, c27)) | p21(f5(f7(f10(c24, f12(c25, c26)), c22), c27), c27)))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[92])).
% 0.18/0.46 tff(94,plain,
% 0.18/0.46 (((~![X43: $i, X42: $i, X44: $i] : (p21(f5(f7(f10(c24, f12(c25, c26)), X42), X43), X44) | (~p3(X43, X44)))) | (p21(f5(f7(f10(c24, f12(c25, c26)), c22), c27), c27) | (~p3(c27, c27)))) <=> ((~![X43: $i, X42: $i, X44: $i] : (p21(f5(f7(f10(c24, f12(c25, c26)), X42), X43), X44) | (~p3(X43, X44)))) | (~p3(c27, c27)) | p21(f5(f7(f10(c24, f12(c25, c26)), c22), c27), c27))),
% 0.18/0.46 inference(transitivity,[status(thm)],[93, 91])).
% 0.18/0.46 tff(95,plain,
% 0.18/0.46 ((~![X43: $i, X42: $i, X44: $i] : (p21(f5(f7(f10(c24, f12(c25, c26)), X42), X43), X44) | (~p3(X43, X44)))) | (p21(f5(f7(f10(c24, f12(c25, c26)), c22), c27), c27) | (~p3(c27, c27)))),
% 0.18/0.46 inference(quant_inst,[status(thm)],[])).
% 0.18/0.46 tff(96,plain,
% 0.18/0.46 ((~![X43: $i, X42: $i, X44: $i] : (p21(f5(f7(f10(c24, f12(c25, c26)), X42), X43), X44) | (~p3(X43, X44)))) | (~p3(c27, c27)) | p21(f5(f7(f10(c24, f12(c25, c26)), c22), c27), c27)),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.18/0.46 tff(97,plain,
% 0.18/0.46 ($false),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[96, 90, 83, 79])).
% 0.18/0.46 tff(98,plain,(p21(f5(f7(f10(c24, f12(c25, c26)), c22), c27), c27)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.46 tff(99,plain,
% 0.18/0.46 (^[X77: $i] : refl(((~p21(f5(c22, c23), X77)) | (~p21(f5(f7(f10(c24, f12(c25, c26)), c22), X77), c27))) <=> ((~p21(f5(c22, c23), X77)) | (~p21(f5(f7(f10(c24, f12(c25, c26)), c22), X77), c27))))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(100,plain,
% 0.18/0.46 (![X77: $i] : ((~p21(f5(c22, c23), X77)) | (~p21(f5(f7(f10(c24, f12(c25, c26)), c22), X77), c27))) <=> ![X77: $i] : ((~p21(f5(c22, c23), X77)) | (~p21(f5(f7(f10(c24, f12(c25, c26)), c22), X77), c27)))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[99])).
% 0.18/0.46 tff(101,plain,
% 0.18/0.46 (![X77: $i] : ((~p21(f5(c22, c23), X77)) | (~p21(f5(f7(f10(c24, f12(c25, c26)), c22), X77), c27))) <=> ![X77: $i] : ((~p21(f5(c22, c23), X77)) | (~p21(f5(f7(f10(c24, f12(c25, c26)), c22), X77), c27)))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(102,axiom,(![X77: $i] : ((~p21(f5(c22, c23), X77)) | (~p21(f5(f7(f10(c24, f12(c25, c26)), c22), X77), c27)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_p21_35')).
% 0.18/0.46 tff(103,plain,
% 0.18/0.46 (![X77: $i] : ((~p21(f5(c22, c23), X77)) | (~p21(f5(f7(f10(c24, f12(c25, c26)), c22), X77), c27)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.18/0.46 tff(104,plain,(
% 0.18/0.46 ![X77: $i] : ((~p21(f5(c22, c23), X77)) | (~p21(f5(f7(f10(c24, f12(c25, c26)), c22), X77), c27)))),
% 0.18/0.46 inference(skolemize,[status(sab)],[103])).
% 0.18/0.46 tff(105,plain,
% 0.18/0.46 (![X77: $i] : ((~p21(f5(c22, c23), X77)) | (~p21(f5(f7(f10(c24, f12(c25, c26)), c22), X77), c27)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[104, 100])).
% 0.18/0.46 tff(106,plain,
% 0.18/0.46 (((~![X77: $i] : ((~p21(f5(c22, c23), X77)) | (~p21(f5(f7(f10(c24, f12(c25, c26)), c22), X77), c27)))) | ((~p21(f5(c22, c23), c27)) | (~p21(f5(f7(f10(c24, f12(c25, c26)), c22), c27), c27)))) <=> ((~![X77: $i] : ((~p21(f5(c22, c23), X77)) | (~p21(f5(f7(f10(c24, f12(c25, c26)), c22), X77), c27)))) | (~p21(f5(c22, c23), c27)) | (~p21(f5(f7(f10(c24, f12(c25, c26)), c22), c27), c27)))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(107,plain,
% 0.18/0.46 ((~![X77: $i] : ((~p21(f5(c22, c23), X77)) | (~p21(f5(f7(f10(c24, f12(c25, c26)), c22), X77), c27)))) | ((~p21(f5(c22, c23), c27)) | (~p21(f5(f7(f10(c24, f12(c25, c26)), c22), c27), c27)))),
% 0.18/0.46 inference(quant_inst,[status(thm)],[])).
% 0.18/0.46 tff(108,plain,
% 0.18/0.46 ((~![X77: $i] : ((~p21(f5(c22, c23), X77)) | (~p21(f5(f7(f10(c24, f12(c25, c26)), c22), X77), c27)))) | (~p21(f5(c22, c23), c27)) | (~p21(f5(f7(f10(c24, f12(c25, c26)), c22), c27), c27))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.18/0.46 tff(109,plain,
% 0.18/0.46 ((~p21(f5(c22, c23), c27)) | (~p21(f5(f7(f10(c24, f12(c25, c26)), c22), c27), c27))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[108, 105])).
% 0.18/0.46 tff(110,plain,
% 0.18/0.46 (~p21(f5(c22, c23), c27)),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[109, 98])).
% 0.18/0.46 tff(111,plain,
% 0.18/0.46 (^[X39: $i, X38: $i, X41: $i, X40: $i] : refl(((~p21(f5(f7(f10(c24, f12(c28, X39)), X38), X40), X41)) | p21(f5(X38, f14(f16(f18(f20(c29, X39), X40), X38), X41)), X41)) <=> ((~p21(f5(f7(f10(c24, f12(c28, X39)), X38), X40), X41)) | p21(f5(X38, f14(f16(f18(f20(c29, X39), X40), X38), X41)), X41)))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(112,plain,
% 0.18/0.46 (![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p21(f5(f7(f10(c24, f12(c28, X39)), X38), X40), X41)) | p21(f5(X38, f14(f16(f18(f20(c29, X39), X40), X38), X41)), X41)) <=> ![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p21(f5(f7(f10(c24, f12(c28, X39)), X38), X40), X41)) | p21(f5(X38, f14(f16(f18(f20(c29, X39), X40), X38), X41)), X41))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[111])).
% 0.18/0.46 tff(113,plain,
% 0.18/0.46 (![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p21(f5(f7(f10(c24, f12(c28, X39)), X38), X40), X41)) | p21(f5(X38, f14(f16(f18(f20(c29, X39), X40), X38), X41)), X41)) <=> ![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p21(f5(f7(f10(c24, f12(c28, X39)), X38), X40), X41)) | p21(f5(X38, f14(f16(f18(f20(c29, X39), X40), X38), X41)), X41))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(114,plain,
% 0.18/0.46 (^[X39: $i, X38: $i, X41: $i, X40: $i] : rewrite((p21(f5(X38, f14(f16(f18(f20(c29, X39), X40), X38), X41)), X41) | (~p21(f5(f7(f10(c24, f12(c28, X39)), X38), X40), X41))) <=> ((~p21(f5(f7(f10(c24, f12(c28, X39)), X38), X40), X41)) | p21(f5(X38, f14(f16(f18(f20(c29, X39), X40), X38), X41)), X41)))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(115,plain,
% 0.18/0.46 (![X39: $i, X38: $i, X41: $i, X40: $i] : (p21(f5(X38, f14(f16(f18(f20(c29, X39), X40), X38), X41)), X41) | (~p21(f5(f7(f10(c24, f12(c28, X39)), X38), X40), X41))) <=> ![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p21(f5(f7(f10(c24, f12(c28, X39)), X38), X40), X41)) | p21(f5(X38, f14(f16(f18(f20(c29, X39), X40), X38), X41)), X41))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[114])).
% 0.18/0.46 tff(116,axiom,(![X39: $i, X38: $i, X41: $i, X40: $i] : (p21(f5(X38, f14(f16(f18(f20(c29, X39), X40), X38), X41)), X41) | (~p21(f5(f7(f10(c24, f12(c28, X39)), X38), X40), X41)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p21_36')).
% 0.18/0.46 tff(117,plain,
% 0.18/0.46 (![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p21(f5(f7(f10(c24, f12(c28, X39)), X38), X40), X41)) | p21(f5(X38, f14(f16(f18(f20(c29, X39), X40), X38), X41)), X41))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.18/0.47 tff(118,plain,
% 0.18/0.47 (![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p21(f5(f7(f10(c24, f12(c28, X39)), X38), X40), X41)) | p21(f5(X38, f14(f16(f18(f20(c29, X39), X40), X38), X41)), X41))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[117, 113])).
% 0.18/0.47 tff(119,plain,(
% 0.18/0.47 ![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p21(f5(f7(f10(c24, f12(c28, X39)), X38), X40), X41)) | p21(f5(X38, f14(f16(f18(f20(c29, X39), X40), X38), X41)), X41))),
% 0.18/0.47 inference(skolemize,[status(sab)],[118])).
% 0.18/0.47 tff(120,plain,
% 0.18/0.47 (![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p21(f5(f7(f10(c24, f12(c28, X39)), X38), X40), X41)) | p21(f5(X38, f14(f16(f18(f20(c29, X39), X40), X38), X41)), X41))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[119, 112])).
% 0.18/0.47 tff(121,plain,
% 0.18/0.47 (((~![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p21(f5(f7(f10(c24, f12(c28, X39)), X38), X40), X41)) | p21(f5(X38, f14(f16(f18(f20(c29, X39), X40), X38), X41)), X41))) | ((~p21(f5(f7(f10(c24, f12(c28, f12(c25, c26))), c22), c23), c27)) | p21(f5(c22, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27)), c27))) <=> ((~![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p21(f5(f7(f10(c24, f12(c28, X39)), X38), X40), X41)) | p21(f5(X38, f14(f16(f18(f20(c29, X39), X40), X38), X41)), X41))) | (~p21(f5(f7(f10(c24, f12(c28, f12(c25, c26))), c22), c23), c27)) | p21(f5(c22, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27)), c27))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(122,plain,
% 0.18/0.47 ((~![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p21(f5(f7(f10(c24, f12(c28, X39)), X38), X40), X41)) | p21(f5(X38, f14(f16(f18(f20(c29, X39), X40), X38), X41)), X41))) | ((~p21(f5(f7(f10(c24, f12(c28, f12(c25, c26))), c22), c23), c27)) | p21(f5(c22, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27)), c27))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(123,plain,
% 0.18/0.47 ((~![X39: $i, X38: $i, X41: $i, X40: $i] : ((~p21(f5(f7(f10(c24, f12(c28, X39)), X38), X40), X41)) | p21(f5(X38, f14(f16(f18(f20(c29, X39), X40), X38), X41)), X41))) | (~p21(f5(f7(f10(c24, f12(c28, f12(c25, c26))), c22), c23), c27)) | p21(f5(c22, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27)), c27)),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.18/0.47 tff(124,plain,
% 0.18/0.47 (p21(f5(c22, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27)), c27)),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[123, 13, 120])).
% 0.18/0.47 tff(125,plain,
% 0.18/0.47 (^[X37: $i, X35: $i, X34: $i, X36: $i] : refl(((~p21(X36, X37)) | (~p4(X36, X34)) | (~p3(X37, X35)) | p21(X34, X35)) <=> ((~p21(X36, X37)) | (~p4(X36, X34)) | (~p3(X37, X35)) | p21(X34, X35)))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(126,plain,
% 0.18/0.47 (![X37: $i, X35: $i, X34: $i, X36: $i] : ((~p21(X36, X37)) | (~p4(X36, X34)) | (~p3(X37, X35)) | p21(X34, X35)) <=> ![X37: $i, X35: $i, X34: $i, X36: $i] : ((~p21(X36, X37)) | (~p4(X36, X34)) | (~p3(X37, X35)) | p21(X34, X35))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[125])).
% 0.18/0.47 tff(127,plain,
% 0.18/0.47 (![X37: $i, X35: $i, X34: $i, X36: $i] : ((~p21(X36, X37)) | (~p4(X36, X34)) | (~p3(X37, X35)) | p21(X34, X35)) <=> ![X37: $i, X35: $i, X34: $i, X36: $i] : ((~p21(X36, X37)) | (~p4(X36, X34)) | (~p3(X37, X35)) | p21(X34, X35))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(128,plain,
% 0.18/0.47 (^[X37: $i, X35: $i, X34: $i, X36: $i] : trans(monotonicity(trans(monotonicity(rewrite((p21(X34, X35) | (~p3(X37, X35))) <=> ((~p3(X37, X35)) | p21(X34, X35))), (((p21(X34, X35) | (~p3(X37, X35))) | (~p4(X36, X34))) <=> (((~p3(X37, X35)) | p21(X34, X35)) | (~p4(X36, X34))))), rewrite((((~p3(X37, X35)) | p21(X34, X35)) | (~p4(X36, X34))) <=> ((~p4(X36, X34)) | (~p3(X37, X35)) | p21(X34, X35))), (((p21(X34, X35) | (~p3(X37, X35))) | (~p4(X36, X34))) <=> ((~p4(X36, X34)) | (~p3(X37, X35)) | p21(X34, X35)))), ((((p21(X34, X35) | (~p3(X37, X35))) | (~p4(X36, X34))) | (~p21(X36, X37))) <=> (((~p4(X36, X34)) | (~p3(X37, X35)) | p21(X34, X35)) | (~p21(X36, X37))))), rewrite((((~p4(X36, X34)) | (~p3(X37, X35)) | p21(X34, X35)) | (~p21(X36, X37))) <=> ((~p21(X36, X37)) | (~p4(X36, X34)) | (~p3(X37, X35)) | p21(X34, X35))), ((((p21(X34, X35) | (~p3(X37, X35))) | (~p4(X36, X34))) | (~p21(X36, X37))) <=> ((~p21(X36, X37)) | (~p4(X36, X34)) | (~p3(X37, X35)) | p21(X34, X35))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(129,plain,
% 0.18/0.47 (![X37: $i, X35: $i, X34: $i, X36: $i] : (((p21(X34, X35) | (~p3(X37, X35))) | (~p4(X36, X34))) | (~p21(X36, X37))) <=> ![X37: $i, X35: $i, X34: $i, X36: $i] : ((~p21(X36, X37)) | (~p4(X36, X34)) | (~p3(X37, X35)) | p21(X34, X35))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[128])).
% 0.18/0.47 tff(130,axiom,(![X37: $i, X35: $i, X34: $i, X36: $i] : (((p21(X34, X35) | (~p3(X37, X35))) | (~p4(X36, X34))) | (~p21(X36, X37)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p21_23')).
% 0.18/0.47 tff(131,plain,
% 0.18/0.47 (![X37: $i, X35: $i, X34: $i, X36: $i] : ((~p21(X36, X37)) | (~p4(X36, X34)) | (~p3(X37, X35)) | p21(X34, X35))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.18/0.47 tff(132,plain,
% 0.18/0.47 (![X37: $i, X35: $i, X34: $i, X36: $i] : ((~p21(X36, X37)) | (~p4(X36, X34)) | (~p3(X37, X35)) | p21(X34, X35))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[131, 127])).
% 0.18/0.47 tff(133,plain,(
% 0.18/0.47 ![X37: $i, X35: $i, X34: $i, X36: $i] : ((~p21(X36, X37)) | (~p4(X36, X34)) | (~p3(X37, X35)) | p21(X34, X35))),
% 0.18/0.47 inference(skolemize,[status(sab)],[132])).
% 0.18/0.47 tff(134,plain,
% 0.18/0.47 (![X37: $i, X35: $i, X34: $i, X36: $i] : ((~p21(X36, X37)) | (~p4(X36, X34)) | (~p3(X37, X35)) | p21(X34, X35))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[133, 126])).
% 0.18/0.47 tff(135,plain,
% 0.18/0.47 (((~![X37: $i, X35: $i, X34: $i, X36: $i] : ((~p21(X36, X37)) | (~p4(X36, X34)) | (~p3(X37, X35)) | p21(X34, X35))) | ((~p3(c27, c27)) | p21(f5(c22, c23), c27) | (~p21(f5(c22, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27)), c27)) | (~p4(f5(c22, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27)), f5(c22, c23))))) <=> ((~![X37: $i, X35: $i, X34: $i, X36: $i] : ((~p21(X36, X37)) | (~p4(X36, X34)) | (~p3(X37, X35)) | p21(X34, X35))) | (~p3(c27, c27)) | p21(f5(c22, c23), c27) | (~p21(f5(c22, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27)), c27)) | (~p4(f5(c22, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27)), f5(c22, c23))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(136,plain,
% 0.18/0.47 (((~p21(f5(c22, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27)), c27)) | (~p4(f5(c22, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27)), f5(c22, c23))) | (~p3(c27, c27)) | p21(f5(c22, c23), c27)) <=> ((~p3(c27, c27)) | p21(f5(c22, c23), c27) | (~p21(f5(c22, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27)), c27)) | (~p4(f5(c22, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27)), f5(c22, c23))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(137,plain,
% 0.18/0.47 (((~![X37: $i, X35: $i, X34: $i, X36: $i] : ((~p21(X36, X37)) | (~p4(X36, X34)) | (~p3(X37, X35)) | p21(X34, X35))) | ((~p21(f5(c22, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27)), c27)) | (~p4(f5(c22, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27)), f5(c22, c23))) | (~p3(c27, c27)) | p21(f5(c22, c23), c27))) <=> ((~![X37: $i, X35: $i, X34: $i, X36: $i] : ((~p21(X36, X37)) | (~p4(X36, X34)) | (~p3(X37, X35)) | p21(X34, X35))) | ((~p3(c27, c27)) | p21(f5(c22, c23), c27) | (~p21(f5(c22, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27)), c27)) | (~p4(f5(c22, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27)), f5(c22, c23)))))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[136])).
% 0.18/0.47 tff(138,plain,
% 0.18/0.47 (((~![X37: $i, X35: $i, X34: $i, X36: $i] : ((~p21(X36, X37)) | (~p4(X36, X34)) | (~p3(X37, X35)) | p21(X34, X35))) | ((~p21(f5(c22, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27)), c27)) | (~p4(f5(c22, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27)), f5(c22, c23))) | (~p3(c27, c27)) | p21(f5(c22, c23), c27))) <=> ((~![X37: $i, X35: $i, X34: $i, X36: $i] : ((~p21(X36, X37)) | (~p4(X36, X34)) | (~p3(X37, X35)) | p21(X34, X35))) | (~p3(c27, c27)) | p21(f5(c22, c23), c27) | (~p21(f5(c22, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27)), c27)) | (~p4(f5(c22, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27)), f5(c22, c23))))),
% 0.18/0.47 inference(transitivity,[status(thm)],[137, 135])).
% 0.18/0.47 tff(139,plain,
% 0.18/0.47 ((~![X37: $i, X35: $i, X34: $i, X36: $i] : ((~p21(X36, X37)) | (~p4(X36, X34)) | (~p3(X37, X35)) | p21(X34, X35))) | ((~p21(f5(c22, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27)), c27)) | (~p4(f5(c22, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27)), f5(c22, c23))) | (~p3(c27, c27)) | p21(f5(c22, c23), c27))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(140,plain,
% 0.18/0.47 ((~![X37: $i, X35: $i, X34: $i, X36: $i] : ((~p21(X36, X37)) | (~p4(X36, X34)) | (~p3(X37, X35)) | p21(X34, X35))) | (~p3(c27, c27)) | p21(f5(c22, c23), c27) | (~p21(f5(c22, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27)), c27)) | (~p4(f5(c22, f14(f16(f18(f20(c29, f12(c25, c26)), c23), c22), c27)), f5(c22, c23)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.18/0.47 tff(141,plain,
% 0.18/0.47 ($false),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[140, 134, 124, 83, 110, 78])).
% 0.18/0.47 % SZS output end Proof
% 0.18/0.47 % E exiting
%------------------------------------------------------------------------------