%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN715-1 : 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 05:39:53 AM UTC 2025
% Result : Unsatisfiable 1.16s 1.35s
% Output : Proof 1.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN715-1 : TPTP v9.0.0. Released v2.5.0.
% 0.07/0.12 % 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 12:40:10 EDT 2025
% 0.12/0.33 % CPUTime :
% 1.16/1.35 % SZS status Unsatisfiable
% 1.16/1.35 % SZS output start Proof
% 1.16/1.35 tff(p62_type, type, (
% 1.16/1.35 p62: ( $i * $i ) > $o)).
% 1.16/1.35 tff(c72_type, type, (
% 1.16/1.35 c72: $i)).
% 1.16/1.35 tff(f33_type, type, (
% 1.16/1.35 f33: ( $i * $i ) > $i)).
% 1.16/1.35 tff(c71_type, type, (
% 1.16/1.35 c71: $i)).
% 1.16/1.35 tff(f35_type, type, (
% 1.16/1.35 f35: ( $i * $i ) > $i)).
% 1.16/1.35 tff(c70_type, type, (
% 1.16/1.35 c70: $i)).
% 1.16/1.35 tff(f37_type, type, (
% 1.16/1.35 f37: ( $i * $i ) > $i)).
% 1.16/1.35 tff(c69_type, type, (
% 1.16/1.35 c69: $i)).
% 1.16/1.35 tff(f39_type, type, (
% 1.16/1.35 f39: ( $i * $i ) > $i)).
% 1.16/1.35 tff(c68_type, type, (
% 1.16/1.35 c68: $i)).
% 1.16/1.35 tff(f41_type, type, (
% 1.16/1.35 f41: ( $i * $i ) > $i)).
% 1.16/1.35 tff(c67_type, type, (
% 1.16/1.35 c67: $i)).
% 1.16/1.35 tff(c74_type, type, (
% 1.16/1.35 c74: $i)).
% 1.16/1.35 tff(f5_type, type, (
% 1.16/1.35 f5: ( $i * $i ) > $i)).
% 1.16/1.35 tff(f16_type, type, (
% 1.16/1.35 f16: ( $i * $i ) > $i)).
% 1.16/1.35 tff(f53_type, type, (
% 1.16/1.35 f53: ( $i * $i ) > $i)).
% 1.16/1.35 tff(f55_type, type, (
% 1.16/1.35 f55: ( $i * $i ) > $i)).
% 1.16/1.35 tff(f57_type, type, (
% 1.16/1.35 f57: ( $i * $i ) > $i)).
% 1.16/1.35 tff(f59_type, type, (
% 1.16/1.35 f59: ( $i * $i ) > $i)).
% 1.16/1.35 tff(f61_type, type, (
% 1.16/1.35 f61: ( $i * $i ) > $i)).
% 1.16/1.35 tff(c76_type, type, (
% 1.16/1.35 c76: $i)).
% 1.16/1.35 tff(f19_type, type, (
% 1.16/1.35 f19: ( $i * $i ) > $i)).
% 1.16/1.35 tff(f43_type, type, (
% 1.16/1.35 f43: ( $i * $i ) > $i)).
% 1.16/1.35 tff(f45_type, type, (
% 1.16/1.35 f45: ( $i * $i ) > $i)).
% 1.16/1.35 tff(f47_type, type, (
% 1.16/1.35 f47: ( $i * $i ) > $i)).
% 1.16/1.35 tff(f49_type, type, (
% 1.16/1.35 f49: ( $i * $i ) > $i)).
% 1.16/1.35 tff(f51_type, type, (
% 1.16/1.35 f51: ( $i * $i ) > $i)).
% 1.16/1.35 tff(c75_type, type, (
% 1.16/1.35 c75: $i)).
% 1.16/1.35 tff(f21_type, type, (
% 1.16/1.35 f21: ( $i * $i ) > $i)).
% 1.16/1.35 tff(c66_type, type, (
% 1.16/1.35 c66: $i)).
% 1.16/1.35 tff(c64_type, type, (
% 1.16/1.35 c64: $i)).
% 1.16/1.35 tff(p4_type, type, (
% 1.16/1.35 p4: ( $i * $i ) > $o)).
% 1.16/1.35 tff(f8_type, type, (
% 1.16/1.35 f8: ( $i * $i ) > $i)).
% 1.16/1.35 tff(f11_type, type, (
% 1.16/1.35 f11: ( $i * $i ) > $i)).
% 1.16/1.35 tff(f13_type, type, (
% 1.16/1.35 f13: ( $i * $i ) > $i)).
% 1.16/1.35 tff(c65_type, type, (
% 1.16/1.35 c65: $i)).
% 1.16/1.35 tff(p2_type, type, (
% 1.16/1.35 p2: ( $i * $i ) > $o)).
% 1.16/1.35 tff(p3_type, type, (
% 1.16/1.35 p3: ( $i * $i ) > $o)).
% 1.16/1.35 tff(p27_type, type, (
% 1.16/1.35 p27: ( $i * $i ) > $o)).
% 1.16/1.35 tff(p63_type, type, (
% 1.16/1.35 p63: ( $i * $i ) > $o)).
% 1.16/1.35 tff(f28_type, type, (
% 1.16/1.35 f28: ( $i * $i ) > $i)).
% 1.16/1.35 tff(f24_type, type, (
% 1.16/1.35 f24: ( $i * $i ) > $i)).
% 1.16/1.35 tff(f31_type, type, (
% 1.16/1.35 f31: ( $i * $i ) > $i)).
% 1.16/1.35 tff(f26_type, type, (
% 1.16/1.35 f26: ( $i * $i ) > $i)).
% 1.16/1.35 tff(f30_type, type, (
% 1.16/1.35 f30: ( $i * $i ) > $i)).
% 1.16/1.35 tff(c73_type, type, (
% 1.16/1.35 c73: $i)).
% 1.16/1.35 tff(1,assumption,(~p2(c64, c64)), introduced(assumption)).
% 1.16/1.35 tff(2,plain,
% 1.16/1.35 (^[X44: $i] : refl(p2(X44, X44) <=> p2(X44, X44))),
% 1.16/1.35 inference(bind,[status(th)],[])).
% 1.16/1.35 tff(3,plain,
% 1.16/1.35 (![X44: $i] : p2(X44, X44) <=> ![X44: $i] : p2(X44, X44)),
% 1.16/1.35 inference(quant_intro,[status(thm)],[2])).
% 1.16/1.35 tff(4,plain,
% 1.16/1.35 (![X44: $i] : p2(X44, X44) <=> ![X44: $i] : p2(X44, X44)),
% 1.16/1.35 inference(rewrite,[status(thm)],[])).
% 1.16/1.35 tff(5,axiom,(![X44: $i] : p2(X44, X44)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_28')).
% 1.16/1.35 tff(6,plain,
% 1.16/1.35 (![X44: $i] : p2(X44, X44)),
% 1.16/1.35 inference(modus_ponens,[status(thm)],[5, 4])).
% 1.16/1.35 tff(7,plain,(
% 1.16/1.35 ![X44: $i] : p2(X44, X44)),
% 1.16/1.35 inference(skolemize,[status(sab)],[6])).
% 1.16/1.35 tff(8,plain,
% 1.16/1.35 (![X44: $i] : p2(X44, X44)),
% 1.16/1.35 inference(modus_ponens,[status(thm)],[7, 3])).
% 1.16/1.35 tff(9,plain,
% 1.16/1.35 ((~![X44: $i] : p2(X44, X44)) | p2(c64, c64)),
% 1.16/1.35 inference(quant_inst,[status(thm)],[])).
% 1.16/1.35 tff(10,plain,
% 1.16/1.35 ($false),
% 1.16/1.35 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 1.16/1.35 tff(11,plain,(p2(c64, c64)), inference(lemma,lemma(discharge,[]))).
% 1.16/1.35 tff(12,plain,
% 1.16/1.35 (^[X9: $i, X11: $i, X10: $i, X7: $i, X8: $i] : refl(p3(f8(f11(f13(c65, f16(f19(f21(c66, X7), X8), X9)), X10), X11), f16(f19(f21(c66, f33(f35(f37(f39(f41(c74, X7), X8), X9), X10), X11)), f43(f45(f47(f49(f51(c75, X7), X8), X9), X10), X11)), f53(f55(f57(f59(f61(c76, X7), X8), X9), X10), X11))) <=> p3(f8(f11(f13(c65, f16(f19(f21(c66, X7), X8), X9)), X10), X11), f16(f19(f21(c66, f33(f35(f37(f39(f41(c74, X7), X8), X9), X10), X11)), f43(f45(f47(f49(f51(c75, X7), X8), X9), X10), X11)), f53(f55(f57(f59(f61(c76, X7), X8), X9), X10), X11))))),
% 1.16/1.35 inference(bind,[status(th)],[])).
% 1.16/1.35 tff(13,plain,
% 1.16/1.35 (![X9: $i, X11: $i, X10: $i, X7: $i, X8: $i] : p3(f8(f11(f13(c65, f16(f19(f21(c66, X7), X8), X9)), X10), X11), f16(f19(f21(c66, f33(f35(f37(f39(f41(c74, X7), X8), X9), X10), X11)), f43(f45(f47(f49(f51(c75, X7), X8), X9), X10), X11)), f53(f55(f57(f59(f61(c76, X7), X8), X9), X10), X11))) <=> ![X9: $i, X11: $i, X10: $i, X7: $i, X8: $i] : p3(f8(f11(f13(c65, f16(f19(f21(c66, X7), X8), X9)), X10), X11), f16(f19(f21(c66, f33(f35(f37(f39(f41(c74, X7), X8), X9), X10), X11)), f43(f45(f47(f49(f51(c75, X7), X8), X9), X10), X11)), f53(f55(f57(f59(f61(c76, X7), X8), X9), X10), X11)))),
% 1.16/1.35 inference(quant_intro,[status(thm)],[12])).
% 1.16/1.35 tff(14,plain,
% 1.16/1.35 (![X9: $i, X11: $i, X10: $i, X7: $i, X8: $i] : p3(f8(f11(f13(c65, f16(f19(f21(c66, X7), X8), X9)), X10), X11), f16(f19(f21(c66, f33(f35(f37(f39(f41(c74, X7), X8), X9), X10), X11)), f43(f45(f47(f49(f51(c75, X7), X8), X9), X10), X11)), f53(f55(f57(f59(f61(c76, X7), X8), X9), X10), X11))) <=> ![X9: $i, X11: $i, X10: $i, X7: $i, X8: $i] : p3(f8(f11(f13(c65, f16(f19(f21(c66, X7), X8), X9)), X10), X11), f16(f19(f21(c66, f33(f35(f37(f39(f41(c74, X7), X8), X9), X10), X11)), f43(f45(f47(f49(f51(c75, X7), X8), X9), X10), X11)), f53(f55(f57(f59(f61(c76, X7), X8), X9), X10), X11)))),
% 1.16/1.35 inference(rewrite,[status(thm)],[])).
% 1.16/1.35 tff(15,axiom,(![X9: $i, X11: $i, X10: $i, X7: $i, X8: $i] : p3(f8(f11(f13(c65, f16(f19(f21(c66, X7), X8), X9)), X10), X11), f16(f19(f21(c66, f33(f35(f37(f39(f41(c74, X7), X8), X9), X10), X11)), f43(f45(f47(f49(f51(c75, X7), X8), X9), X10), X11)), f53(f55(f57(f59(f61(c76, X7), X8), X9), X10), X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p3_106')).
% 1.16/1.35 tff(16,plain,
% 1.16/1.35 (![X9: $i, X11: $i, X10: $i, X7: $i, X8: $i] : p3(f8(f11(f13(c65, f16(f19(f21(c66, X7), X8), X9)), X10), X11), f16(f19(f21(c66, f33(f35(f37(f39(f41(c74, X7), X8), X9), X10), X11)), f43(f45(f47(f49(f51(c75, X7), X8), X9), X10), X11)), f53(f55(f57(f59(f61(c76, X7), X8), X9), X10), X11)))),
% 1.16/1.35 inference(modus_ponens,[status(thm)],[15, 14])).
% 1.16/1.35 tff(17,plain,(
% 1.16/1.35 ![X9: $i, X11: $i, X10: $i, X7: $i, X8: $i] : p3(f8(f11(f13(c65, f16(f19(f21(c66, X7), X8), X9)), X10), X11), f16(f19(f21(c66, f33(f35(f37(f39(f41(c74, X7), X8), X9), X10), X11)), f43(f45(f47(f49(f51(c75, X7), X8), X9), X10), X11)), f53(f55(f57(f59(f61(c76, X7), X8), X9), X10), X11)))),
% 1.16/1.35 inference(skolemize,[status(sab)],[16])).
% 1.16/1.35 tff(18,plain,
% 1.16/1.35 (![X9: $i, X11: $i, X10: $i, X7: $i, X8: $i] : p3(f8(f11(f13(c65, f16(f19(f21(c66, X7), X8), X9)), X10), X11), f16(f19(f21(c66, f33(f35(f37(f39(f41(c74, X7), X8), X9), X10), X11)), f43(f45(f47(f49(f51(c75, X7), X8), X9), X10), X11)), f53(f55(f57(f59(f61(c76, X7), X8), X9), X10), X11)))),
% 1.16/1.35 inference(modus_ponens,[status(thm)],[17, 13])).
% 1.16/1.35 tff(19,plain,
% 1.16/1.35 ((~![X9: $i, X11: $i, X10: $i, X7: $i, X8: $i] : p3(f8(f11(f13(c65, f16(f19(f21(c66, X7), X8), X9)), X10), X11), f16(f19(f21(c66, f33(f35(f37(f39(f41(c74, X7), X8), X9), X10), X11)), f43(f45(f47(f49(f51(c75, X7), X8), X9), X10), X11)), f53(f55(f57(f59(f61(c76, X7), X8), X9), X10), X11)))) | p3(f8(f11(f13(c65, f16(f19(f21(c66, c67), c68), c69)), c70), c71), f16(f19(f21(c66, f33(f35(f37(f39(f41(c74, c67), c68), c69), c70), c71)), f43(f45(f47(f49(f51(c75, c67), c68), c69), c70), c71)), f53(f55(f57(f59(f61(c76, c67), c68), c69), c70), c71)))),
% 1.16/1.35 inference(quant_inst,[status(thm)],[])).
% 1.16/1.35 tff(20,plain,
% 1.16/1.35 (p3(f8(f11(f13(c65, f16(f19(f21(c66, c67), c68), c69)), c70), c71), f16(f19(f21(c66, f33(f35(f37(f39(f41(c74, c67), c68), c69), c70), c71)), f43(f45(f47(f49(f51(c75, c67), c68), c69), c70), c71)), f53(f55(f57(f59(f61(c76, c67), c68), c69), c70), c71)))),
% 1.16/1.35 inference(unit_resolution,[status(thm)],[19, 18])).
% 1.16/1.35 tff(21,plain,
% 1.16/1.35 (^[X124: $i, X123: $i, X125: $i, X126: $i] : refl(((~p3(X124, X126)) | (~p2(X123, X125)) | p4(f5(X123, X124), f5(X125, X126))) <=> ((~p3(X124, X126)) | (~p2(X123, X125)) | p4(f5(X123, X124), f5(X125, X126))))),
% 1.16/1.35 inference(bind,[status(th)],[])).
% 1.16/1.35 tff(22,plain,
% 1.16/1.35 (![X124: $i, X123: $i, X125: $i, X126: $i] : ((~p3(X124, X126)) | (~p2(X123, X125)) | p4(f5(X123, X124), f5(X125, X126))) <=> ![X124: $i, X123: $i, X125: $i, X126: $i] : ((~p3(X124, X126)) | (~p2(X123, X125)) | p4(f5(X123, X124), f5(X125, X126)))),
% 1.16/1.35 inference(quant_intro,[status(thm)],[21])).
% 1.16/1.35 tff(23,plain,
% 1.16/1.35 (![X124: $i, X123: $i, X125: $i, X126: $i] : ((~p3(X124, X126)) | (~p2(X123, X125)) | p4(f5(X123, X124), f5(X125, X126))) <=> ![X124: $i, X123: $i, X125: $i, X126: $i] : ((~p3(X124, X126)) | (~p2(X123, X125)) | p4(f5(X123, X124), f5(X125, X126)))),
% 1.16/1.35 inference(rewrite,[status(thm)],[])).
% 1.16/1.35 tff(24,plain,
% 1.16/1.35 (^[X124: $i, X123: $i, X125: $i, X126: $i] : trans(monotonicity(rewrite((p4(f5(X123, X124), f5(X125, X126)) | (~p2(X123, X125))) <=> ((~p2(X123, X125)) | p4(f5(X123, X124), f5(X125, X126)))), (((p4(f5(X123, X124), f5(X125, X126)) | (~p2(X123, X125))) | (~p3(X124, X126))) <=> (((~p2(X123, X125)) | p4(f5(X123, X124), f5(X125, X126))) | (~p3(X124, X126))))), rewrite((((~p2(X123, X125)) | p4(f5(X123, X124), f5(X125, X126))) | (~p3(X124, X126))) <=> ((~p3(X124, X126)) | (~p2(X123, X125)) | p4(f5(X123, X124), f5(X125, X126)))), (((p4(f5(X123, X124), f5(X125, X126)) | (~p2(X123, X125))) | (~p3(X124, X126))) <=> ((~p3(X124, X126)) | (~p2(X123, X125)) | p4(f5(X123, X124), f5(X125, X126)))))),
% 1.16/1.35 inference(bind,[status(th)],[])).
% 1.16/1.35 tff(25,plain,
% 1.16/1.35 (![X124: $i, X123: $i, X125: $i, X126: $i] : ((p4(f5(X123, X124), f5(X125, X126)) | (~p2(X123, X125))) | (~p3(X124, X126))) <=> ![X124: $i, X123: $i, X125: $i, X126: $i] : ((~p3(X124, X126)) | (~p2(X123, X125)) | p4(f5(X123, X124), f5(X125, X126)))),
% 1.16/1.35 inference(quant_intro,[status(thm)],[24])).
% 1.16/1.35 tff(26,axiom,(![X124: $i, X123: $i, X125: $i, X126: $i] : ((p4(f5(X123, X124), f5(X125, X126)) | (~p2(X123, X125))) | (~p3(X124, X126)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p4_86')).
% 1.16/1.35 tff(27,plain,
% 1.16/1.35 (![X124: $i, X123: $i, X125: $i, X126: $i] : ((~p3(X124, X126)) | (~p2(X123, X125)) | p4(f5(X123, X124), f5(X125, X126)))),
% 1.16/1.35 inference(modus_ponens,[status(thm)],[26, 25])).
% 1.16/1.35 tff(28,plain,
% 1.16/1.35 (![X124: $i, X123: $i, X125: $i, X126: $i] : ((~p3(X124, X126)) | (~p2(X123, X125)) | p4(f5(X123, X124), f5(X125, X126)))),
% 1.16/1.35 inference(modus_ponens,[status(thm)],[27, 23])).
% 1.16/1.35 tff(29,plain,(
% 1.16/1.35 ![X124: $i, X123: $i, X125: $i, X126: $i] : ((~p3(X124, X126)) | (~p2(X123, X125)) | p4(f5(X123, X124), f5(X125, X126)))),
% 1.16/1.35 inference(skolemize,[status(sab)],[28])).
% 1.16/1.35 tff(30,plain,
% 1.16/1.35 (![X124: $i, X123: $i, X125: $i, X126: $i] : ((~p3(X124, X126)) | (~p2(X123, X125)) | p4(f5(X123, X124), f5(X125, X126)))),
% 1.16/1.35 inference(modus_ponens,[status(thm)],[29, 22])).
% 1.16/1.35 tff(31,plain,
% 1.16/1.35 (((~![X124: $i, X123: $i, X125: $i, X126: $i] : ((~p3(X124, X126)) | (~p2(X123, X125)) | p4(f5(X123, X124), f5(X125, X126)))) | ((~p2(c64, c64)) | (~p3(f8(f11(f13(c65, f16(f19(f21(c66, c67), c68), c69)), c70), c71), f16(f19(f21(c66, f33(f35(f37(f39(f41(c74, c67), c68), c69), c70), c71)), f43(f45(f47(f49(f51(c75, c67), c68), c69), c70), c71)), f53(f55(f57(f59(f61(c76, c67), c68), c69), c70), c71)))) | p4(f5(c64, f8(f11(f13(c65, f16(f19(f21(c66, c67), c68), c69)), c70), c71)), f5(c64, f16(f19(f21(c66, f33(f35(f37(f39(f41(c74, c67), c68), c69), c70), c71)), f43(f45(f47(f49(f51(c75, c67), c68), c69), c70), c71)), f53(f55(f57(f59(f61(c76, c67), c68), c69), c70), c71)))))) <=> ((~![X124: $i, X123: $i, X125: $i, X126: $i] : ((~p3(X124, X126)) | (~p2(X123, X125)) | p4(f5(X123, X124), f5(X125, X126)))) | (~p2(c64, c64)) | (~p3(f8(f11(f13(c65, f16(f19(f21(c66, c67), c68), c69)), c70), c71), f16(f19(f21(c66, f33(f35(f37(f39(f41(c74, c67), c68), c69), c70), c71)), f43(f45(f47(f49(f51(c75, c67), c68), c69), c70), c71)), f53(f55(f57(f59(f61(c76, c67), c68), c69), c70), c71)))) | p4(f5(c64, f8(f11(f13(c65, f16(f19(f21(c66, c67), c68), c69)), c70), c71)), f5(c64, f16(f19(f21(c66, f33(f35(f37(f39(f41(c74, c67), c68), c69), c70), c71)), f43(f45(f47(f49(f51(c75, c67), c68), c69), c70), c71)), f53(f55(f57(f59(f61(c76, c67), c68), c69), c70), c71)))))),
% 1.16/1.35 inference(rewrite,[status(thm)],[])).
% 1.16/1.35 tff(32,plain,
% 1.16/1.35 (((~p3(f8(f11(f13(c65, f16(f19(f21(c66, c67), c68), c69)), c70), c71), f16(f19(f21(c66, f33(f35(f37(f39(f41(c74, c67), c68), c69), c70), c71)), f43(f45(f47(f49(f51(c75, c67), c68), c69), c70), c71)), f53(f55(f57(f59(f61(c76, c67), c68), c69), c70), c71)))) | (~p2(c64, c64)) | p4(f5(c64, f8(f11(f13(c65, f16(f19(f21(c66, c67), c68), c69)), c70), c71)), f5(c64, f16(f19(f21(c66, f33(f35(f37(f39(f41(c74, c67), c68), c69), c70), c71)), f43(f45(f47(f49(f51(c75, c67), c68), c69), c70), c71)), f53(f55(f57(f59(f61(c76, c67), c68), c69), c70), c71))))) <=> ((~p2(c64, c64)) | (~p3(f8(f11(f13(c65, f16(f19(f21(c66, c67), c68), c69)), c70), c71), f16(f19(f21(c66, f33(f35(f37(f39(f41(c74, c67), c68), c69), c70), c71)), f43(f45(f47(f49(f51(c75, c67), c68), c69), c70), c71)), f53(f55(f57(f59(f61(c76, c67), c68), c69), c70), c71)))) | p4(f5(c64, f8(f11(f13(c65, f16(f19(f21(c66, c67), c68), c69)), c70), c71)), f5(c64, f16(f19(f21(c66, f33(f35(f37(f39(f41(c74, c67), c68), c69), c70), c71)), f43(f45(f47(f49(f51(c75, c67), c68), c69), c70), c71)), f53(f55(f57(f59(f61(c76, c67), c68), c69), c70), c71)))))),
% 1.16/1.35 inference(rewrite,[status(thm)],[])).
% 1.16/1.35 tff(33,plain,
% 1.16/1.35 (((~![X124: $i, X123: $i, X125: $i, X126: $i] : ((~p3(X124, X126)) | (~p2(X123, X125)) | p4(f5(X123, X124), f5(X125, X126)))) | ((~p3(f8(f11(f13(c65, f16(f19(f21(c66, c67), c68), c69)), c70), c71), f16(f19(f21(c66, f33(f35(f37(f39(f41(c74, c67), c68), c69), c70), c71)), f43(f45(f47(f49(f51(c75, c67), c68), c69), c70), c71)), f53(f55(f57(f59(f61(c76, c67), c68), c69), c70), c71)))) | (~p2(c64, c64)) | p4(f5(c64, f8(f11(f13(c65, f16(f19(f21(c66, c67), c68), c69)), c70), c71)), f5(c64, f16(f19(f21(c66, f33(f35(f37(f39(f41(c74, c67), c68), c69), c70), c71)), f43(f45(f47(f49(f51(c75, c67), c68), c69), c70), c71)), f53(f55(f57(f59(f61(c76, c67), c68), c69), c70), c71)))))) <=> ((~![X124: $i, X123: $i, X125: $i, X126: $i] : ((~p3(X124, X126)) | (~p2(X123, X125)) | p4(f5(X123, X124), f5(X125, X126)))) | ((~p2(c64, c64)) | (~p3(f8(f11(f13(c65, f16(f19(f21(c66, c67), c68), c69)), c70), c71), f16(f19(f21(c66, f33(f35(f37(f39(f41(c74, c67), c68), c69), c70), c71)), f43(f45(f47(f49(f51(c75, c67), c68), c69), c70), c71)), f53(f55(f57(f59(f61(c76, c67), c68), c69), c70), c71)))) | p4(f5(c64, f8(f11(f13(c65, f16(f19(f21(c66, c67), c68), c69)), c70), c71)), f5(c64, f16(f19(f21(c66, f33(f35(f37(f39(f41(c74, c67), c68), c69), c70), c71)), f43(f45(f47(f49(f51(c75, c67), c68), c69), c70), c71)), f53(f55(f57(f59(f61(c76, c67), c68), c69), c70), c71))))))),
% 1.16/1.35 inference(monotonicity,[status(thm)],[32])).
% 1.16/1.35 tff(34,plain,
% 1.16/1.35 (((~![X124: $i, X123: $i, X125: $i, X126: $i] : ((~p3(X124, X126)) | (~p2(X123, X125)) | p4(f5(X123, X124), f5(X125, X126)))) | ((~p3(f8(f11(f13(c65, f16(f19(f21(c66, c67), c68), c69)), c70), c71), f16(f19(f21(c66, f33(f35(f37(f39(f41(c74, c67), c68), c69), c70), c71)), f43(f45(f47(f49(f51(c75, c67), c68), c69), c70), c71)), f53(f55(f57(f59(f61(c76, c67), c68), c69), c70), c71)))) | (~p2(c64, c64)) | p4(f5(c64, f8(f11(f13(c65, f16(f19(f21(c66, c67), c68), c69)), c70), c71)), f5(c64, f16(f19(f21(c66, f33(f35(f37(f39(f41(c74, c67), c68), c69), c70), c71)), f43(f45(f47(f49(f51(c75, c67), c68), c69), c70), c71)), f53(f55(f57(f59(f61(c76, c67), c68), c69), c70), c71)))))) <=> ((~![X124: $i, X123: $i, X125: $i, X126: $i] : ((~p3(X124, X126)) | (~p2(X123, X125)) | p4(f5(X123, X124), f5(X125, X126)))) | (~p2(c64, c64)) | (~p3(f8(f11(f13(c65, f16(f19(f21(c66, c67), c68), c69)), c70), c71), f16(f19(f21(c66, f33(f35(f37(f39(f41(c74, c67), c68), c69), c70), c71)), f43(f45(f47(f49(f51(c75, c67), c68), c69), c70), c71)), f53(f55(f57(f59(f61(c76, c67), c68), c69), c70), c71)))) | p4(f5(c64, f8(f11(f13(c65, f16(f19(f21(c66, c67), c68), c69)), c70), c71)), f5(c64, f16(f19(f21(c66, f33(f35(f37(f39(f41(c74, c67), c68), c69), c70), c71)), f43(f45(f47(f49(f51(c75, c67), c68), c69), c70), c71)), f53(f55(f57(f59(f61(c76, c67), c68), c69), c70), c71)))))),
% 1.16/1.35 inference(transitivity,[status(thm)],[33, 31])).
% 1.16/1.35 tff(35,plain,
% 1.16/1.35 ((~![X124: $i, X123: $i, X125: $i, X126: $i] : ((~p3(X124, X126)) | (~p2(X123, X125)) | p4(f5(X123, X124), f5(X125, X126)))) | ((~p3(f8(f11(f13(c65, f16(f19(f21(c66, c67), c68), c69)), c70), c71), f16(f19(f21(c66, f33(f35(f37(f39(f41(c74, c67), c68), c69), c70), c71)), f43(f45(f47(f49(f51(c75, c67), c68), c69), c70), c71)), f53(f55(f57(f59(f61(c76, c67), c68), c69), c70), c71)))) | (~p2(c64, c64)) | p4(f5(c64, f8(f11(f13(c65, f16(f19(f21(c66, c67), c68), c69)), c70), c71)), f5(c64, f16(f19(f21(c66, f33(f35(f37(f39(f41(c74, c67), c68), c69), c70), c71)), f43(f45(f47(f49(f51(c75, c67), c68), c69), c70), c71)), f53(f55(f57(f59(f61(c76, c67), c68), c69), c70), c71)))))),
% 1.16/1.36 inference(quant_inst,[status(thm)],[])).
% 1.16/1.36 tff(36,plain,
% 1.16/1.36 ((~![X124: $i, X123: $i, X125: $i, X126: $i] : ((~p3(X124, X126)) | (~p2(X123, X125)) | p4(f5(X123, X124), f5(X125, X126)))) | (~p2(c64, c64)) | (~p3(f8(f11(f13(c65, f16(f19(f21(c66, c67), c68), c69)), c70), c71), f16(f19(f21(c66, f33(f35(f37(f39(f41(c74, c67), c68), c69), c70), c71)), f43(f45(f47(f49(f51(c75, c67), c68), c69), c70), c71)), f53(f55(f57(f59(f61(c76, c67), c68), c69), c70), c71)))) | p4(f5(c64, f8(f11(f13(c65, f16(f19(f21(c66, c67), c68), c69)), c70), c71)), f5(c64, f16(f19(f21(c66, f33(f35(f37(f39(f41(c74, c67), c68), c69), c70), c71)), f43(f45(f47(f49(f51(c75, c67), c68), c69), c70), c71)), f53(f55(f57(f59(f61(c76, c67), c68), c69), c70), c71))))),
% 1.16/1.36 inference(modus_ponens,[status(thm)],[35, 34])).
% 1.16/1.36 tff(37,plain,
% 1.16/1.36 (p4(f5(c64, f8(f11(f13(c65, f16(f19(f21(c66, c67), c68), c69)), c70), c71)), f5(c64, f16(f19(f21(c66, f33(f35(f37(f39(f41(c74, c67), c68), c69), c70), c71)), f43(f45(f47(f49(f51(c75, c67), c68), c69), c70), c71)), f53(f55(f57(f59(f61(c76, c67), c68), c69), c70), c71))))),
% 1.16/1.36 inference(unit_resolution,[status(thm)],[36, 30, 20, 11])).
% 1.16/1.36 tff(38,assumption,(~p62(f5(c64, f16(f19(f21(c66, f33(f35(f37(f39(f41(c74, c67), c68), c69), c70), c71)), f43(f45(f47(f49(f51(c75, c67), c68), c69), c70), c71)), f53(f55(f57(f59(f61(c76, c67), c68), c69), c70), c71))), c72)), introduced(assumption)).
% 1.16/1.36 tff(39,plain,
% 1.16/1.36 (^[X71: $i] : refl(p27(X71, X71) <=> p27(X71, X71))),
% 1.16/1.36 inference(bind,[status(th)],[])).
% 1.16/1.36 tff(40,plain,
% 1.16/1.36 (![X71: $i] : p27(X71, X71) <=> ![X71: $i] : p27(X71, X71)),
% 1.16/1.36 inference(quant_intro,[status(thm)],[39])).
% 1.16/1.36 tff(41,plain,
% 1.16/1.36 (![X71: $i] : p27(X71, X71) <=> ![X71: $i] : p27(X71, X71)),
% 1.16/1.36 inference(rewrite,[status(thm)],[])).
% 1.16/1.36 tff(42,axiom,(![X71: $i] : p27(X71, X71)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p27_23')).
% 1.16/1.36 tff(43,plain,
% 1.16/1.36 (![X71: $i] : p27(X71, X71)),
% 1.16/1.36 inference(modus_ponens,[status(thm)],[42, 41])).
% 1.16/1.36 tff(44,plain,(
% 1.16/1.36 ![X71: $i] : p27(X71, X71)),
% 1.16/1.36 inference(skolemize,[status(sab)],[43])).
% 1.16/1.36 tff(45,plain,
% 1.16/1.36 (![X71: $i] : p27(X71, X71)),
% 1.16/1.36 inference(modus_ponens,[status(thm)],[44, 40])).
% 1.16/1.36 tff(46,plain,
% 1.16/1.36 ((~![X71: $i] : p27(X71, X71)) | p27(c72, c72)),
% 1.16/1.36 inference(quant_inst,[status(thm)],[])).
% 1.16/1.36 tff(47,plain,
% 1.16/1.36 (p27(c72, c72)),
% 1.16/1.36 inference(unit_resolution,[status(thm)],[46, 45])).
% 1.16/1.36 tff(48,plain,
% 1.16/1.36 (p62(f5(c64, f8(f11(f13(c65, f16(f19(f21(c66, c67), c68), c69)), c70), c71)), c72) <=> p62(f5(c64, f8(f11(f13(c65, f16(f19(f21(c66, c67), c68), c69)), c70), c71)), c72)),
% 1.16/1.36 inference(rewrite,[status(thm)],[])).
% 1.16/1.36 tff(49,axiom,(p62(f5(c64, f8(f11(f13(c65, f16(f19(f21(c66, c67), c68), c69)), c70), c71)), c72)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p62_100')).
% 1.16/1.36 tff(50,plain,
% 1.16/1.36 (p62(f5(c64, f8(f11(f13(c65, f16(f19(f21(c66, c67), c68), c69)), c70), c71)), c72)),
% 1.16/1.36 inference(modus_ponens,[status(thm)],[49, 48])).
% 1.16/1.36 tff(51,plain,
% 1.16/1.36 (^[X202: $i, X201: $i, X200: $i, X199: $i] : refl(((~p27(X201, X200)) | (~p62(X202, X201)) | (~p4(X202, X199)) | p62(X199, X200)) <=> ((~p27(X201, X200)) | (~p62(X202, X201)) | (~p4(X202, X199)) | p62(X199, X200)))),
% 1.16/1.36 inference(bind,[status(th)],[])).
% 1.16/1.36 tff(52,plain,
% 1.16/1.36 (![X202: $i, X201: $i, X200: $i, X199: $i] : ((~p27(X201, X200)) | (~p62(X202, X201)) | (~p4(X202, X199)) | p62(X199, X200)) <=> ![X202: $i, X201: $i, X200: $i, X199: $i] : ((~p27(X201, X200)) | (~p62(X202, X201)) | (~p4(X202, X199)) | p62(X199, X200))),
% 1.16/1.36 inference(quant_intro,[status(thm)],[51])).
% 1.16/1.36 tff(53,plain,
% 1.16/1.36 (![X202: $i, X201: $i, X200: $i, X199: $i] : ((~p27(X201, X200)) | (~p62(X202, X201)) | (~p4(X202, X199)) | p62(X199, X200)) <=> ![X202: $i, X201: $i, X200: $i, X199: $i] : ((~p27(X201, X200)) | (~p62(X202, X201)) | (~p4(X202, X199)) | p62(X199, X200))),
% 1.16/1.36 inference(rewrite,[status(thm)],[])).
% 1.16/1.36 tff(54,plain,
% 1.16/1.36 (^[X202: $i, X201: $i, X200: $i, X199: $i] : trans(monotonicity(trans(monotonicity(rewrite((p62(X199, X200) | (~p4(X202, X199))) <=> ((~p4(X202, X199)) | p62(X199, X200))), (((p62(X199, X200) | (~p4(X202, X199))) | (~p62(X202, X201))) <=> (((~p4(X202, X199)) | p62(X199, X200)) | (~p62(X202, X201))))), rewrite((((~p4(X202, X199)) | p62(X199, X200)) | (~p62(X202, X201))) <=> ((~p62(X202, X201)) | (~p4(X202, X199)) | p62(X199, X200))), (((p62(X199, X200) | (~p4(X202, X199))) | (~p62(X202, X201))) <=> ((~p62(X202, X201)) | (~p4(X202, X199)) | p62(X199, X200)))), ((((p62(X199, X200) | (~p4(X202, X199))) | (~p62(X202, X201))) | (~p27(X201, X200))) <=> (((~p62(X202, X201)) | (~p4(X202, X199)) | p62(X199, X200)) | (~p27(X201, X200))))), rewrite((((~p62(X202, X201)) | (~p4(X202, X199)) | p62(X199, X200)) | (~p27(X201, X200))) <=> ((~p27(X201, X200)) | (~p62(X202, X201)) | (~p4(X202, X199)) | p62(X199, X200))), ((((p62(X199, X200) | (~p4(X202, X199))) | (~p62(X202, X201))) | (~p27(X201, X200))) <=> ((~p27(X201, X200)) | (~p62(X202, X201)) | (~p4(X202, X199)) | p62(X199, X200))))),
% 1.16/1.36 inference(bind,[status(th)],[])).
% 1.16/1.36 tff(55,plain,
% 1.16/1.36 (![X202: $i, X201: $i, X200: $i, X199: $i] : (((p62(X199, X200) | (~p4(X202, X199))) | (~p62(X202, X201))) | (~p27(X201, X200))) <=> ![X202: $i, X201: $i, X200: $i, X199: $i] : ((~p27(X201, X200)) | (~p62(X202, X201)) | (~p4(X202, X199)) | p62(X199, X200))),
% 1.16/1.36 inference(quant_intro,[status(thm)],[54])).
% 1.16/1.36 tff(56,axiom,(![X202: $i, X201: $i, X200: $i, X199: $i] : (((p62(X199, X200) | (~p4(X202, X199))) | (~p62(X202, X201))) | (~p27(X201, X200)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p62_67')).
% 1.16/1.36 tff(57,plain,
% 1.16/1.36 (![X202: $i, X201: $i, X200: $i, X199: $i] : ((~p27(X201, X200)) | (~p62(X202, X201)) | (~p4(X202, X199)) | p62(X199, X200))),
% 1.16/1.36 inference(modus_ponens,[status(thm)],[56, 55])).
% 1.16/1.36 tff(58,plain,
% 1.16/1.36 (![X202: $i, X201: $i, X200: $i, X199: $i] : ((~p27(X201, X200)) | (~p62(X202, X201)) | (~p4(X202, X199)) | p62(X199, X200))),
% 1.16/1.36 inference(modus_ponens,[status(thm)],[57, 53])).
% 1.16/1.36 tff(59,plain,(
% 1.16/1.36 ![X202: $i, X201: $i, X200: $i, X199: $i] : ((~p27(X201, X200)) | (~p62(X202, X201)) | (~p4(X202, X199)) | p62(X199, X200))),
% 1.16/1.36 inference(skolemize,[status(sab)],[58])).
% 1.16/1.36 tff(60,plain,
% 1.16/1.36 (![X202: $i, X201: $i, X200: $i, X199: $i] : ((~p27(X201, X200)) | (~p62(X202, X201)) | (~p4(X202, X199)) | p62(X199, X200))),
% 1.16/1.36 inference(modus_ponens,[status(thm)],[59, 52])).
% 1.16/1.36 tff(61,plain,
% 1.16/1.36 (((~![X202: $i, X201: $i, X200: $i, X199: $i] : ((~p27(X201, X200)) | (~p62(X202, X201)) | (~p4(X202, X199)) | p62(X199, X200))) | ((~p27(c72, c72)) | (~p62(f5(c64, f8(f11(f13(c65, f16(f19(f21(c66, c67), c68), c69)), c70), c71)), c72)) | (~p4(f5(c64, f8(f11(f13(c65, f16(f19(f21(c66, c67), c68), c69)), c70), c71)), f5(c64, f16(f19(f21(c66, f33(f35(f37(f39(f41(c74, c67), c68), c69), c70), c71)), f43(f45(f47(f49(f51(c75, c67), c68), c69), c70), c71)), f53(f55(f57(f59(f61(c76, c67), c68), c69), c70), c71))))) | p62(f5(c64, f16(f19(f21(c66, f33(f35(f37(f39(f41(c74, c67), c68), c69), c70), c71)), f43(f45(f47(f49(f51(c75, c67), c68), c69), c70), c71)), f53(f55(f57(f59(f61(c76, c67), c68), c69), c70), c71))), c72))) <=> ((~![X202: $i, X201: $i, X200: $i, X199: $i] : ((~p27(X201, X200)) | (~p62(X202, X201)) | (~p4(X202, X199)) | p62(X199, X200))) | (~p27(c72, c72)) | (~p62(f5(c64, f8(f11(f13(c65, f16(f19(f21(c66, c67), c68), c69)), c70), c71)), c72)) | (~p4(f5(c64, f8(f11(f13(c65, f16(f19(f21(c66, c67), c68), c69)), c70), c71)), f5(c64, f16(f19(f21(c66, f33(f35(f37(f39(f41(c74, c67), c68), c69), c70), c71)), f43(f45(f47(f49(f51(c75, c67), c68), c69), c70), c71)), f53(f55(f57(f59(f61(c76, c67), c68), c69), c70), c71))))) | p62(f5(c64, f16(f19(f21(c66, f33(f35(f37(f39(f41(c74, c67), c68), c69), c70), c71)), f43(f45(f47(f49(f51(c75, c67), c68), c69), c70), c71)), f53(f55(f57(f59(f61(c76, c67), c68), c69), c70), c71))), c72))),
% 1.16/1.36 inference(rewrite,[status(thm)],[])).
% 1.16/1.36 tff(62,plain,
% 1.16/1.36 ((~![X202: $i, X201: $i, X200: $i, X199: $i] : ((~p27(X201, X200)) | (~p62(X202, X201)) | (~p4(X202, X199)) | p62(X199, X200))) | ((~p27(c72, c72)) | (~p62(f5(c64, f8(f11(f13(c65, f16(f19(f21(c66, c67), c68), c69)), c70), c71)), c72)) | (~p4(f5(c64, f8(f11(f13(c65, f16(f19(f21(c66, c67), c68), c69)), c70), c71)), f5(c64, f16(f19(f21(c66, f33(f35(f37(f39(f41(c74, c67), c68), c69), c70), c71)), f43(f45(f47(f49(f51(c75, c67), c68), c69), c70), c71)), f53(f55(f57(f59(f61(c76, c67), c68), c69), c70), c71))))) | p62(f5(c64, f16(f19(f21(c66, f33(f35(f37(f39(f41(c74, c67), c68), c69), c70), c71)), f43(f45(f47(f49(f51(c75, c67), c68), c69), c70), c71)), f53(f55(f57(f59(f61(c76, c67), c68), c69), c70), c71))), c72))),
% 1.16/1.36 inference(quant_inst,[status(thm)],[])).
% 1.16/1.36 tff(63,plain,
% 1.16/1.36 ((~![X202: $i, X201: $i, X200: $i, X199: $i] : ((~p27(X201, X200)) | (~p62(X202, X201)) | (~p4(X202, X199)) | p62(X199, X200))) | (~p27(c72, c72)) | (~p62(f5(c64, f8(f11(f13(c65, f16(f19(f21(c66, c67), c68), c69)), c70), c71)), c72)) | (~p4(f5(c64, f8(f11(f13(c65, f16(f19(f21(c66, c67), c68), c69)), c70), c71)), f5(c64, f16(f19(f21(c66, f33(f35(f37(f39(f41(c74, c67), c68), c69), c70), c71)), f43(f45(f47(f49(f51(c75, c67), c68), c69), c70), c71)), f53(f55(f57(f59(f61(c76, c67), c68), c69), c70), c71))))) | p62(f5(c64, f16(f19(f21(c66, f33(f35(f37(f39(f41(c74, c67), c68), c69), c70), c71)), f43(f45(f47(f49(f51(c75, c67), c68), c69), c70), c71)), f53(f55(f57(f59(f61(c76, c67), c68), c69), c70), c71))), c72)),
% 1.16/1.36 inference(modus_ponens,[status(thm)],[62, 61])).
% 1.16/1.36 tff(64,plain,
% 1.16/1.36 ($false),
% 1.16/1.36 inference(unit_resolution,[status(thm)],[63, 60, 50, 47, 38, 37])).
% 1.16/1.36 tff(65,plain,(p62(f5(c64, f16(f19(f21(c66, f33(f35(f37(f39(f41(c74, c67), c68), c69), c70), c71)), f43(f45(f47(f49(f51(c75, c67), c68), c69), c70), c71)), f53(f55(f57(f59(f61(c76, c67), c68), c69), c70), c71))), c72)), inference(lemma,lemma(discharge,[]))).
% 1.16/1.36 tff(66,plain,
% 1.16/1.36 (^[X204: $i, X206: $i, X205: $i, X203: $i] : refl(((~p62(f5(c64, f16(f19(f21(c66, X203), X205), X206)), X204)) | p62(X203, X204)) <=> ((~p62(f5(c64, f16(f19(f21(c66, X203), X205), X206)), X204)) | p62(X203, X204)))),
% 1.16/1.36 inference(bind,[status(th)],[])).
% 1.16/1.36 tff(67,plain,
% 1.16/1.36 (![X204: $i, X206: $i, X205: $i, X203: $i] : ((~p62(f5(c64, f16(f19(f21(c66, X203), X205), X206)), X204)) | p62(X203, X204)) <=> ![X204: $i, X206: $i, X205: $i, X203: $i] : ((~p62(f5(c64, f16(f19(f21(c66, X203), X205), X206)), X204)) | p62(X203, X204))),
% 1.16/1.36 inference(quant_intro,[status(thm)],[66])).
% 1.16/1.36 tff(68,plain,
% 1.16/1.36 (![X204: $i, X206: $i, X205: $i, X203: $i] : ((~p62(f5(c64, f16(f19(f21(c66, X203), X205), X206)), X204)) | p62(X203, X204)) <=> ![X204: $i, X206: $i, X205: $i, X203: $i] : ((~p62(f5(c64, f16(f19(f21(c66, X203), X205), X206)), X204)) | p62(X203, X204))),
% 1.16/1.36 inference(rewrite,[status(thm)],[])).
% 1.16/1.36 tff(69,plain,
% 1.16/1.36 (^[X204: $i, X206: $i, X205: $i, X203: $i] : rewrite((p62(X203, X204) | (~p62(f5(c64, f16(f19(f21(c66, X203), X205), X206)), X204))) <=> ((~p62(f5(c64, f16(f19(f21(c66, X203), X205), X206)), X204)) | p62(X203, X204)))),
% 1.16/1.36 inference(bind,[status(th)],[])).
% 1.16/1.36 tff(70,plain,
% 1.16/1.36 (![X204: $i, X206: $i, X205: $i, X203: $i] : (p62(X203, X204) | (~p62(f5(c64, f16(f19(f21(c66, X203), X205), X206)), X204))) <=> ![X204: $i, X206: $i, X205: $i, X203: $i] : ((~p62(f5(c64, f16(f19(f21(c66, X203), X205), X206)), X204)) | p62(X203, X204))),
% 1.16/1.36 inference(quant_intro,[status(thm)],[69])).
% 1.16/1.36 tff(71,axiom,(![X204: $i, X206: $i, X205: $i, X203: $i] : (p62(X203, X204) | (~p62(f5(c64, f16(f19(f21(c66, X203), X205), X206)), X204)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p62_97')).
% 1.16/1.36 tff(72,plain,
% 1.16/1.36 (![X204: $i, X206: $i, X205: $i, X203: $i] : ((~p62(f5(c64, f16(f19(f21(c66, X203), X205), X206)), X204)) | p62(X203, X204))),
% 1.16/1.36 inference(modus_ponens,[status(thm)],[71, 70])).
% 1.16/1.36 tff(73,plain,
% 1.16/1.36 (![X204: $i, X206: $i, X205: $i, X203: $i] : ((~p62(f5(c64, f16(f19(f21(c66, X203), X205), X206)), X204)) | p62(X203, X204))),
% 1.16/1.36 inference(modus_ponens,[status(thm)],[72, 68])).
% 1.16/1.36 tff(74,plain,(
% 1.16/1.36 ![X204: $i, X206: $i, X205: $i, X203: $i] : ((~p62(f5(c64, f16(f19(f21(c66, X203), X205), X206)), X204)) | p62(X203, X204))),
% 1.16/1.36 inference(skolemize,[status(sab)],[73])).
% 1.16/1.36 tff(75,plain,
% 1.16/1.36 (![X204: $i, X206: $i, X205: $i, X203: $i] : ((~p62(f5(c64, f16(f19(f21(c66, X203), X205), X206)), X204)) | p62(X203, X204))),
% 1.16/1.36 inference(modus_ponens,[status(thm)],[74, 67])).
% 1.16/1.36 tff(76,plain,
% 1.16/1.36 (((~![X204: $i, X206: $i, X205: $i, X203: $i] : ((~p62(f5(c64, f16(f19(f21(c66, X203), X205), X206)), X204)) | p62(X203, X204))) | ((~p62(f5(c64, f16(f19(f21(c66, f33(f35(f37(f39(f41(c74, c67), c68), c69), c70), c71)), f43(f45(f47(f49(f51(c75, c67), c68), c69), c70), c71)), f53(f55(f57(f59(f61(c76, c67), c68), c69), c70), c71))), c72)) | p62(f33(f35(f37(f39(f41(c74, c67), c68), c69), c70), c71), c72))) <=> ((~![X204: $i, X206: $i, X205: $i, X203: $i] : ((~p62(f5(c64, f16(f19(f21(c66, X203), X205), X206)), X204)) | p62(X203, X204))) | (~p62(f5(c64, f16(f19(f21(c66, f33(f35(f37(f39(f41(c74, c67), c68), c69), c70), c71)), f43(f45(f47(f49(f51(c75, c67), c68), c69), c70), c71)), f53(f55(f57(f59(f61(c76, c67), c68), c69), c70), c71))), c72)) | p62(f33(f35(f37(f39(f41(c74, c67), c68), c69), c70), c71), c72))),
% 1.16/1.36 inference(rewrite,[status(thm)],[])).
% 1.16/1.36 tff(77,plain,
% 1.16/1.36 ((~![X204: $i, X206: $i, X205: $i, X203: $i] : ((~p62(f5(c64, f16(f19(f21(c66, X203), X205), X206)), X204)) | p62(X203, X204))) | ((~p62(f5(c64, f16(f19(f21(c66, f33(f35(f37(f39(f41(c74, c67), c68), c69), c70), c71)), f43(f45(f47(f49(f51(c75, c67), c68), c69), c70), c71)), f53(f55(f57(f59(f61(c76, c67), c68), c69), c70), c71))), c72)) | p62(f33(f35(f37(f39(f41(c74, c67), c68), c69), c70), c71), c72))),
% 1.16/1.36 inference(quant_inst,[status(thm)],[])).
% 1.16/1.36 tff(78,plain,
% 1.16/1.36 ((~![X204: $i, X206: $i, X205: $i, X203: $i] : ((~p62(f5(c64, f16(f19(f21(c66, X203), X205), X206)), X204)) | p62(X203, X204))) | (~p62(f5(c64, f16(f19(f21(c66, f33(f35(f37(f39(f41(c74, c67), c68), c69), c70), c71)), f43(f45(f47(f49(f51(c75, c67), c68), c69), c70), c71)), f53(f55(f57(f59(f61(c76, c67), c68), c69), c70), c71))), c72)) | p62(f33(f35(f37(f39(f41(c74, c67), c68), c69), c70), c71), c72)),
% 1.16/1.36 inference(modus_ponens,[status(thm)],[77, 76])).
% 1.16/1.36 tff(79,plain,
% 1.16/1.36 ((~p62(f5(c64, f16(f19(f21(c66, f33(f35(f37(f39(f41(c74, c67), c68), c69), c70), c71)), f43(f45(f47(f49(f51(c75, c67), c68), c69), c70), c71)), f53(f55(f57(f59(f61(c76, c67), c68), c69), c70), c71))), c72)) | p62(f33(f35(f37(f39(f41(c74, c67), c68), c69), c70), c71), c72)),
% 1.16/1.36 inference(unit_resolution,[status(thm)],[78, 75])).
% 1.16/1.36 tff(80,plain,
% 1.16/1.36 (p62(f33(f35(f37(f39(f41(c74, c67), c68), c69), c70), c71), c72)),
% 1.16/1.36 inference(unit_resolution,[status(thm)],[79, 65])).
% 1.16/1.36 tff(81,plain,
% 1.16/1.36 (^[X212: $i, X214: $i, X211: $i, X213: $i] : refl((p63(f24(f26(f30(c73, X211), X212), X213), X214) | (~p63(f24(f26(f30(c73, X213), X214), X211), X212))) <=> (p63(f24(f26(f30(c73, X211), X212), X213), X214) | (~p63(f24(f26(f30(c73, X213), X214), X211), X212))))),
% 1.16/1.36 inference(bind,[status(th)],[])).
% 1.16/1.36 tff(82,plain,
% 1.16/1.36 (![X212: $i, X214: $i, X211: $i, X213: $i] : (p63(f24(f26(f30(c73, X211), X212), X213), X214) | (~p63(f24(f26(f30(c73, X213), X214), X211), X212))) <=> ![X212: $i, X214: $i, X211: $i, X213: $i] : (p63(f24(f26(f30(c73, X211), X212), X213), X214) | (~p63(f24(f26(f30(c73, X213), X214), X211), X212)))),
% 1.16/1.36 inference(quant_intro,[status(thm)],[81])).
% 1.16/1.36 tff(83,plain,
% 1.16/1.36 (![X212: $i, X214: $i, X211: $i, X213: $i] : (p63(f24(f26(f30(c73, X211), X212), X213), X214) | (~p63(f24(f26(f30(c73, X213), X214), X211), X212))) <=> ![X212: $i, X214: $i, X211: $i, X213: $i] : (p63(f24(f26(f30(c73, X211), X212), X213), X214) | (~p63(f24(f26(f30(c73, X213), X214), X211), X212)))),
% 1.16/1.36 inference(rewrite,[status(thm)],[])).
% 1.16/1.36 tff(84,axiom,(![X212: $i, X214: $i, X211: $i, X213: $i] : (p63(f24(f26(f30(c73, X211), X212), X213), X214) | (~p63(f24(f26(f30(c73, X213), X214), X211), X212)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p63_102')).
% 1.16/1.36 tff(85,plain,
% 1.16/1.36 (![X212: $i, X214: $i, X211: $i, X213: $i] : (p63(f24(f26(f30(c73, X211), X212), X213), X214) | (~p63(f24(f26(f30(c73, X213), X214), X211), X212)))),
% 1.16/1.36 inference(modus_ponens,[status(thm)],[84, 83])).
% 1.16/1.36 tff(86,plain,(
% 1.16/1.36 ![X212: $i, X214: $i, X211: $i, X213: $i] : (p63(f24(f26(f30(c73, X211), X212), X213), X214) | (~p63(f24(f26(f30(c73, X213), X214), X211), X212)))),
% 1.16/1.36 inference(skolemize,[status(sab)],[85])).
% 1.16/1.36 tff(87,plain,
% 1.16/1.36 (![X212: $i, X214: $i, X211: $i, X213: $i] : (p63(f24(f26(f30(c73, X211), X212), X213), X214) | (~p63(f24(f26(f30(c73, X213), X214), X211), X212)))),
% 1.16/1.36 inference(modus_ponens,[status(thm)],[86, 82])).
% 1.16/1.36 tff(88,plain,
% 1.16/1.36 (p63(f24(f26(f30(c73, f31(c68, c72)), f28(c69, c72)), c70), c71) <=> p63(f24(f26(f30(c73, f31(c68, c72)), f28(c69, c72)), c70), c71)),
% 1.16/1.36 inference(rewrite,[status(thm)],[])).
% 1.16/1.36 tff(89,axiom,(p63(f24(f26(f30(c73, f31(c68, c72)), f28(c69, c72)), c70), c71)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p63_69')).
% 1.16/1.36 tff(90,plain,
% 1.16/1.36 (p63(f24(f26(f30(c73, f31(c68, c72)), f28(c69, c72)), c70), c71)),
% 1.16/1.36 inference(modus_ponens,[status(thm)],[89, 88])).
% 1.16/1.36 tff(91,plain,
% 1.16/1.36 (((~![X212: $i, X214: $i, X211: $i, X213: $i] : (p63(f24(f26(f30(c73, X211), X212), X213), X214) | (~p63(f24(f26(f30(c73, X213), X214), X211), X212)))) | (p63(f24(f26(f30(c73, c70), c71), f31(c68, c72)), f28(c69, c72)) | (~p63(f24(f26(f30(c73, f31(c68, c72)), f28(c69, c72)), c70), c71)))) <=> ((~![X212: $i, X214: $i, X211: $i, X213: $i] : (p63(f24(f26(f30(c73, X211), X212), X213), X214) | (~p63(f24(f26(f30(c73, X213), X214), X211), X212)))) | p63(f24(f26(f30(c73, c70), c71), f31(c68, c72)), f28(c69, c72)) | (~p63(f24(f26(f30(c73, f31(c68, c72)), f28(c69, c72)), c70), c71)))),
% 1.16/1.36 inference(rewrite,[status(thm)],[])).
% 1.16/1.36 tff(92,plain,
% 1.16/1.36 ((~![X212: $i, X214: $i, X211: $i, X213: $i] : (p63(f24(f26(f30(c73, X211), X212), X213), X214) | (~p63(f24(f26(f30(c73, X213), X214), X211), X212)))) | (p63(f24(f26(f30(c73, c70), c71), f31(c68, c72)), f28(c69, c72)) | (~p63(f24(f26(f30(c73, f31(c68, c72)), f28(c69, c72)), c70), c71)))),
% 1.16/1.36 inference(quant_inst,[status(thm)],[])).
% 1.16/1.36 tff(93,plain,
% 1.16/1.36 ((~![X212: $i, X214: $i, X211: $i, X213: $i] : (p63(f24(f26(f30(c73, X211), X212), X213), X214) | (~p63(f24(f26(f30(c73, X213), X214), X211), X212)))) | p63(f24(f26(f30(c73, c70), c71), f31(c68, c72)), f28(c69, c72)) | (~p63(f24(f26(f30(c73, f31(c68, c72)), f28(c69, c72)), c70), c71))),
% 1.16/1.36 inference(modus_ponens,[status(thm)],[92, 91])).
% 1.16/1.36 tff(94,plain,
% 1.16/1.36 (p63(f24(f26(f30(c73, c70), c71), f31(c68, c72)), f28(c69, c72))),
% 1.16/1.36 inference(unit_resolution,[status(thm)],[93, 90, 87])).
% 1.16/1.36 tff(95,plain,
% 1.16/1.36 (^[X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : refl(((~p63(f24(f26(f30(c73, X10), X11), f31(X8, X12)), f28(X9, X12))) | (~p62(f33(f35(f37(f39(f41(c74, X7), X8), X9), X10), X11), X12))) <=> ((~p63(f24(f26(f30(c73, X10), X11), f31(X8, X12)), f28(X9, X12))) | (~p62(f33(f35(f37(f39(f41(c74, X7), X8), X9), X10), X11), X12))))),
% 1.16/1.36 inference(bind,[status(th)],[])).
% 1.16/1.36 tff(96,plain,
% 1.16/1.36 (![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p63(f24(f26(f30(c73, X10), X11), f31(X8, X12)), f28(X9, X12))) | (~p62(f33(f35(f37(f39(f41(c74, X7), X8), X9), X10), X11), X12))) <=> ![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p63(f24(f26(f30(c73, X10), X11), f31(X8, X12)), f28(X9, X12))) | (~p62(f33(f35(f37(f39(f41(c74, X7), X8), X9), X10), X11), X12)))),
% 1.16/1.36 inference(quant_intro,[status(thm)],[95])).
% 1.16/1.36 tff(97,plain,
% 1.16/1.36 (![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p63(f24(f26(f30(c73, X10), X11), f31(X8, X12)), f28(X9, X12))) | (~p62(f33(f35(f37(f39(f41(c74, X7), X8), X9), X10), X11), X12))) <=> ![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p63(f24(f26(f30(c73, X10), X11), f31(X8, X12)), f28(X9, X12))) | (~p62(f33(f35(f37(f39(f41(c74, X7), X8), X9), X10), X11), X12)))),
% 1.16/1.36 inference(rewrite,[status(thm)],[])).
% 1.16/1.36 tff(98,axiom,(![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p63(f24(f26(f30(c73, X10), X11), f31(X8, X12)), f28(X9, X12))) | (~p62(f33(f35(f37(f39(f41(c74, X7), X8), X9), X10), X11), X12)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_p63_103')).
% 1.16/1.36 tff(99,plain,
% 1.16/1.36 (![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p63(f24(f26(f30(c73, X10), X11), f31(X8, X12)), f28(X9, X12))) | (~p62(f33(f35(f37(f39(f41(c74, X7), X8), X9), X10), X11), X12)))),
% 1.16/1.36 inference(modus_ponens,[status(thm)],[98, 97])).
% 1.16/1.36 tff(100,plain,(
% 1.16/1.36 ![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p63(f24(f26(f30(c73, X10), X11), f31(X8, X12)), f28(X9, X12))) | (~p62(f33(f35(f37(f39(f41(c74, X7), X8), X9), X10), X11), X12)))),
% 1.18/1.37 inference(skolemize,[status(sab)],[99])).
% 1.18/1.37 tff(101,plain,
% 1.18/1.37 (![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p63(f24(f26(f30(c73, X10), X11), f31(X8, X12)), f28(X9, X12))) | (~p62(f33(f35(f37(f39(f41(c74, X7), X8), X9), X10), X11), X12)))),
% 1.18/1.37 inference(modus_ponens,[status(thm)],[100, 96])).
% 1.18/1.37 tff(102,plain,
% 1.18/1.37 (((~![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p63(f24(f26(f30(c73, X10), X11), f31(X8, X12)), f28(X9, X12))) | (~p62(f33(f35(f37(f39(f41(c74, X7), X8), X9), X10), X11), X12)))) | ((~p63(f24(f26(f30(c73, c70), c71), f31(c68, c72)), f28(c69, c72))) | (~p62(f33(f35(f37(f39(f41(c74, c67), c68), c69), c70), c71), c72)))) <=> ((~![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p63(f24(f26(f30(c73, X10), X11), f31(X8, X12)), f28(X9, X12))) | (~p62(f33(f35(f37(f39(f41(c74, X7), X8), X9), X10), X11), X12)))) | (~p63(f24(f26(f30(c73, c70), c71), f31(c68, c72)), f28(c69, c72))) | (~p62(f33(f35(f37(f39(f41(c74, c67), c68), c69), c70), c71), c72)))),
% 1.18/1.37 inference(rewrite,[status(thm)],[])).
% 1.18/1.37 tff(103,plain,
% 1.18/1.37 ((~![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p63(f24(f26(f30(c73, X10), X11), f31(X8, X12)), f28(X9, X12))) | (~p62(f33(f35(f37(f39(f41(c74, X7), X8), X9), X10), X11), X12)))) | ((~p63(f24(f26(f30(c73, c70), c71), f31(c68, c72)), f28(c69, c72))) | (~p62(f33(f35(f37(f39(f41(c74, c67), c68), c69), c70), c71), c72)))),
% 1.18/1.37 inference(quant_inst,[status(thm)],[])).
% 1.18/1.37 tff(104,plain,
% 1.18/1.37 ((~![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p63(f24(f26(f30(c73, X10), X11), f31(X8, X12)), f28(X9, X12))) | (~p62(f33(f35(f37(f39(f41(c74, X7), X8), X9), X10), X11), X12)))) | (~p63(f24(f26(f30(c73, c70), c71), f31(c68, c72)), f28(c69, c72))) | (~p62(f33(f35(f37(f39(f41(c74, c67), c68), c69), c70), c71), c72))),
% 1.18/1.37 inference(modus_ponens,[status(thm)],[103, 102])).
% 1.18/1.37 tff(105,plain,
% 1.18/1.37 ($false),
% 1.18/1.37 inference(unit_resolution,[status(thm)],[104, 101, 94, 80])).
% 1.18/1.37 % SZS output end Proof
% 1.18/1.37 % E exiting
%------------------------------------------------------------------------------