%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN716-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:39:54 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.50s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN716-1 : TPTP v9.0.0. Released v2.5.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n007.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 12:42:20 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.50 % SZS status Unsatisfiable
% 0.19/0.50 % SZS output start Proof
% 0.19/0.50 tff(p62_type, type, (
% 0.19/0.50 p62: ( $i * $i ) > $o)).
% 0.19/0.50 tff(c72_type, type, (
% 0.19/0.50 c72: $i)).
% 0.19/0.50 tff(f23_type, type, (
% 0.19/0.50 f23: ( $i * $i ) > $i)).
% 0.19/0.50 tff(c71_type, type, (
% 0.19/0.50 c71: $i)).
% 0.19/0.50 tff(f25_type, type, (
% 0.19/0.50 f25: ( $i * $i ) > $i)).
% 0.19/0.50 tff(c70_type, type, (
% 0.19/0.50 c70: $i)).
% 0.19/0.50 tff(f27_type, type, (
% 0.19/0.50 f27: ( $i * $i ) > $i)).
% 0.19/0.50 tff(c69_type, type, (
% 0.19/0.50 c69: $i)).
% 0.19/0.50 tff(f29_type, type, (
% 0.19/0.50 f29: ( $i * $i ) > $i)).
% 0.19/0.50 tff(c68_type, type, (
% 0.19/0.50 c68: $i)).
% 0.19/0.50 tff(f31_type, type, (
% 0.19/0.50 f31: ( $i * $i ) > $i)).
% 0.19/0.50 tff(c67_type, type, (
% 0.19/0.50 c67: $i)).
% 0.19/0.50 tff(c74_type, type, (
% 0.19/0.50 c74: $i)).
% 0.19/0.50 tff(f5_type, type, (
% 0.19/0.50 f5: ( $i * $i ) > $i)).
% 0.19/0.50 tff(f16_type, type, (
% 0.19/0.50 f16: ( $i * $i ) > $i)).
% 0.19/0.50 tff(f53_type, type, (
% 0.19/0.50 f53: ( $i * $i ) > $i)).
% 0.19/0.50 tff(f55_type, type, (
% 0.19/0.50 f55: ( $i * $i ) > $i)).
% 0.19/0.50 tff(f57_type, type, (
% 0.19/0.50 f57: ( $i * $i ) > $i)).
% 0.19/0.50 tff(f59_type, type, (
% 0.19/0.50 f59: ( $i * $i ) > $i)).
% 0.19/0.50 tff(f61_type, type, (
% 0.19/0.50 f61: ( $i * $i ) > $i)).
% 0.19/0.50 tff(c76_type, type, (
% 0.19/0.50 c76: $i)).
% 0.19/0.50 tff(f19_type, type, (
% 0.19/0.50 f19: ( $i * $i ) > $i)).
% 0.19/0.50 tff(f43_type, type, (
% 0.19/0.50 f43: ( $i * $i ) > $i)).
% 0.19/0.50 tff(f45_type, type, (
% 0.19/0.50 f45: ( $i * $i ) > $i)).
% 0.19/0.50 tff(f47_type, type, (
% 0.19/0.50 f47: ( $i * $i ) > $i)).
% 0.19/0.50 tff(f49_type, type, (
% 0.19/0.50 f49: ( $i * $i ) > $i)).
% 0.19/0.50 tff(f51_type, type, (
% 0.19/0.50 f51: ( $i * $i ) > $i)).
% 0.19/0.50 tff(c75_type, type, (
% 0.19/0.50 c75: $i)).
% 0.19/0.50 tff(f21_type, type, (
% 0.19/0.50 f21: ( $i * $i ) > $i)).
% 0.19/0.50 tff(c66_type, type, (
% 0.19/0.50 c66: $i)).
% 0.19/0.50 tff(c64_type, type, (
% 0.19/0.50 c64: $i)).
% 0.19/0.50 tff(p4_type, type, (
% 0.19/0.50 p4: ( $i * $i ) > $o)).
% 0.19/0.50 tff(f8_type, type, (
% 0.19/0.50 f8: ( $i * $i ) > $i)).
% 0.19/0.50 tff(f11_type, type, (
% 0.19/0.50 f11: ( $i * $i ) > $i)).
% 0.19/0.50 tff(f13_type, type, (
% 0.19/0.50 f13: ( $i * $i ) > $i)).
% 0.19/0.50 tff(c65_type, type, (
% 0.19/0.50 c65: $i)).
% 0.19/0.50 tff(p2_type, type, (
% 0.19/0.50 p2: ( $i * $i ) > $o)).
% 0.19/0.50 tff(p3_type, type, (
% 0.19/0.50 p3: ( $i * $i ) > $o)).
% 0.19/0.50 tff(p32_type, type, (
% 0.19/0.50 p32: ( $i * $i ) > $o)).
% 0.19/0.50 tff(1,assumption,(~p2(c64, c64)), introduced(assumption)).
% 0.19/0.50 tff(2,plain,
% 0.19/0.50 (^[X44: $i] : refl(p2(X44, X44) <=> p2(X44, X44))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(3,plain,
% 0.19/0.50 (![X44: $i] : p2(X44, X44) <=> ![X44: $i] : p2(X44, X44)),
% 0.19/0.50 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.50 tff(4,plain,
% 0.19/0.50 (![X44: $i] : p2(X44, X44) <=> ![X44: $i] : p2(X44, X44)),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(5,axiom,(![X44: $i] : p2(X44, X44)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_28')).
% 0.19/0.50 tff(6,plain,
% 0.19/0.50 (![X44: $i] : p2(X44, X44)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.19/0.50 tff(7,plain,(
% 0.19/0.50 ![X44: $i] : p2(X44, X44)),
% 0.19/0.50 inference(skolemize,[status(sab)],[6])).
% 0.19/0.50 tff(8,plain,
% 0.19/0.50 (![X44: $i] : p2(X44, X44)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.50 tff(9,plain,
% 0.19/0.50 ((~![X44: $i] : p2(X44, X44)) | p2(c64, c64)),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(10,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.19/0.50 tff(11,plain,(p2(c64, c64)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.50 tff(12,plain,
% 0.19/0.50 (^[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, f23(f25(f27(f29(f31(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, f23(f25(f27(f29(f31(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))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(13,plain,
% 0.19/0.50 (![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, f23(f25(f27(f29(f31(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, f23(f25(f27(f29(f31(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)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[12])).
% 0.19/0.50 tff(14,plain,
% 0.19/0.50 (![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, f23(f25(f27(f29(f31(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, f23(f25(f27(f29(f31(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)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 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, f23(f25(f27(f29(f31(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/sandbox/benchmark/theBenchmark.p','p3_106')).
% 0.19/0.50 tff(16,plain,
% 0.19/0.50 (![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, f23(f25(f27(f29(f31(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)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.19/0.50 tff(17,plain,(
% 0.19/0.50 ![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, f23(f25(f27(f29(f31(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)))),
% 0.19/0.50 inference(skolemize,[status(sab)],[16])).
% 0.19/0.50 tff(18,plain,
% 0.19/0.50 (![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, f23(f25(f27(f29(f31(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)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.19/0.50 tff(19,plain,
% 0.19/0.50 ((~![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, f23(f25(f27(f29(f31(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, f23(f25(f27(f29(f31(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)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(20,plain,
% 0.19/0.50 (p3(f8(f11(f13(c65, f16(f19(f21(c66, c67), c68), c69)), c70), c71), f16(f19(f21(c66, f23(f25(f27(f29(f31(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)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.19/0.50 tff(21,plain,
% 0.19/0.50 (^[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))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(22,plain,
% 0.19/0.50 (![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)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[21])).
% 0.19/0.50 tff(23,plain,
% 0.19/0.50 (![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)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(24,plain,
% 0.19/0.50 (^[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)))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(25,plain,
% 0.19/0.50 (![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)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[24])).
% 0.19/0.50 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/sandbox/benchmark/theBenchmark.p','p4_86')).
% 0.19/0.50 tff(27,plain,
% 0.19/0.50 (![X124: $i, X123: $i, X125: $i, X126: $i] : ((~p3(X124, X126)) | (~p2(X123, X125)) | p4(f5(X123, X124), f5(X125, X126)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.19/0.50 tff(28,plain,
% 0.19/0.50 (![X124: $i, X123: $i, X125: $i, X126: $i] : ((~p3(X124, X126)) | (~p2(X123, X125)) | p4(f5(X123, X124), f5(X125, X126)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.19/0.50 tff(29,plain,(
% 0.19/0.50 ![X124: $i, X123: $i, X125: $i, X126: $i] : ((~p3(X124, X126)) | (~p2(X123, X125)) | p4(f5(X123, X124), f5(X125, X126)))),
% 0.19/0.50 inference(skolemize,[status(sab)],[28])).
% 0.19/0.50 tff(30,plain,
% 0.19/0.50 (![X124: $i, X123: $i, X125: $i, X126: $i] : ((~p3(X124, X126)) | (~p2(X123, X125)) | p4(f5(X123, X124), f5(X125, X126)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.19/0.50 tff(31,plain,
% 0.19/0.50 (((~![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, f23(f25(f27(f29(f31(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, f23(f25(f27(f29(f31(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, f23(f25(f27(f29(f31(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, f23(f25(f27(f29(f31(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)))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(32,plain,
% 0.19/0.50 (((~p3(f8(f11(f13(c65, f16(f19(f21(c66, c67), c68), c69)), c70), c71), f16(f19(f21(c66, f23(f25(f27(f29(f31(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, f23(f25(f27(f29(f31(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, f23(f25(f27(f29(f31(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, f23(f25(f27(f29(f31(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)))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(33,plain,
% 0.19/0.50 (((~![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, f23(f25(f27(f29(f31(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, f23(f25(f27(f29(f31(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, f23(f25(f27(f29(f31(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, f23(f25(f27(f29(f31(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))))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[32])).
% 0.19/0.50 tff(34,plain,
% 0.19/0.50 (((~![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, f23(f25(f27(f29(f31(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, f23(f25(f27(f29(f31(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, f23(f25(f27(f29(f31(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, f23(f25(f27(f29(f31(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)))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[33, 31])).
% 0.19/0.50 tff(35,plain,
% 0.19/0.50 ((~![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, f23(f25(f27(f29(f31(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, f23(f25(f27(f29(f31(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)))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(36,plain,
% 0.19/0.50 ((~![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, f23(f25(f27(f29(f31(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, f23(f25(f27(f29(f31(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))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.19/0.51 tff(37,plain,
% 0.19/0.51 (p4(f5(c64, f8(f11(f13(c65, f16(f19(f21(c66, c67), c68), c69)), c70), c71)), f5(c64, f16(f19(f21(c66, f23(f25(f27(f29(f31(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))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[36, 30, 20, 11])).
% 0.19/0.51 tff(38,assumption,(~p62(f5(c64, f16(f19(f21(c66, f23(f25(f27(f29(f31(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)).
% 0.19/0.51 tff(39,assumption,(~p32(c72, c72)), introduced(assumption)).
% 0.19/0.51 tff(40,plain,
% 0.19/0.51 (^[X92: $i] : refl(p32(X92, X92) <=> p32(X92, X92))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(41,plain,
% 0.19/0.51 (![X92: $i] : p32(X92, X92) <=> ![X92: $i] : p32(X92, X92)),
% 0.19/0.51 inference(quant_intro,[status(thm)],[40])).
% 0.19/0.51 tff(42,plain,
% 0.19/0.51 (![X92: $i] : p32(X92, X92) <=> ![X92: $i] : p32(X92, X92)),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(43,axiom,(![X92: $i] : p32(X92, X92)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p32_20')).
% 0.19/0.51 tff(44,plain,
% 0.19/0.51 (![X92: $i] : p32(X92, X92)),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.19/0.51 tff(45,plain,(
% 0.19/0.51 ![X92: $i] : p32(X92, X92)),
% 0.19/0.51 inference(skolemize,[status(sab)],[44])).
% 0.19/0.51 tff(46,plain,
% 0.19/0.51 (![X92: $i] : p32(X92, X92)),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.19/0.51 tff(47,plain,
% 0.19/0.51 ((~![X92: $i] : p32(X92, X92)) | p32(c72, c72)),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(48,plain,
% 0.19/0.51 ($false),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[47, 46, 39])).
% 0.19/0.51 tff(49,plain,(p32(c72, c72)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.51 tff(50,plain,
% 0.19/0.51 (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)),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(51,axiom,(p62(f5(c64, f8(f11(f13(c65, f16(f19(f21(c66, c67), c68), c69)), c70), c71)), c72)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p62_100')).
% 0.19/0.51 tff(52,plain,
% 0.19/0.51 (p62(f5(c64, f8(f11(f13(c65, f16(f19(f21(c66, c67), c68), c69)), c70), c71)), c72)),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.19/0.51 tff(53,plain,
% 0.19/0.51 (^[X202: $i, X201: $i, X200: $i, X199: $i] : refl(((~p32(X201, X200)) | (~p62(X202, X201)) | (~p4(X202, X199)) | p62(X199, X200)) <=> ((~p32(X201, X200)) | (~p62(X202, X201)) | (~p4(X202, X199)) | p62(X199, X200)))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(54,plain,
% 0.19/0.51 (![X202: $i, X201: $i, X200: $i, X199: $i] : ((~p32(X201, X200)) | (~p62(X202, X201)) | (~p4(X202, X199)) | p62(X199, X200)) <=> ![X202: $i, X201: $i, X200: $i, X199: $i] : ((~p32(X201, X200)) | (~p62(X202, X201)) | (~p4(X202, X199)) | p62(X199, X200))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[53])).
% 0.19/0.51 tff(55,plain,
% 0.19/0.51 (![X202: $i, X201: $i, X200: $i, X199: $i] : ((~p32(X201, X200)) | (~p62(X202, X201)) | (~p4(X202, X199)) | p62(X199, X200)) <=> ![X202: $i, X201: $i, X200: $i, X199: $i] : ((~p32(X201, X200)) | (~p62(X202, X201)) | (~p4(X202, X199)) | p62(X199, X200))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(56,plain,
% 0.19/0.51 (^[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))) | (~p32(X201, X200))) <=> (((~p62(X202, X201)) | (~p4(X202, X199)) | p62(X199, X200)) | (~p32(X201, X200))))), rewrite((((~p62(X202, X201)) | (~p4(X202, X199)) | p62(X199, X200)) | (~p32(X201, X200))) <=> ((~p32(X201, X200)) | (~p62(X202, X201)) | (~p4(X202, X199)) | p62(X199, X200))), ((((p62(X199, X200) | (~p4(X202, X199))) | (~p62(X202, X201))) | (~p32(X201, X200))) <=> ((~p32(X201, X200)) | (~p62(X202, X201)) | (~p4(X202, X199)) | p62(X199, X200))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(57,plain,
% 0.19/0.51 (![X202: $i, X201: $i, X200: $i, X199: $i] : (((p62(X199, X200) | (~p4(X202, X199))) | (~p62(X202, X201))) | (~p32(X201, X200))) <=> ![X202: $i, X201: $i, X200: $i, X199: $i] : ((~p32(X201, X200)) | (~p62(X202, X201)) | (~p4(X202, X199)) | p62(X199, X200))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[56])).
% 0.19/0.51 tff(58,axiom,(![X202: $i, X201: $i, X200: $i, X199: $i] : (((p62(X199, X200) | (~p4(X202, X199))) | (~p62(X202, X201))) | (~p32(X201, X200)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p62_68')).
% 0.19/0.51 tff(59,plain,
% 0.19/0.51 (![X202: $i, X201: $i, X200: $i, X199: $i] : ((~p32(X201, X200)) | (~p62(X202, X201)) | (~p4(X202, X199)) | p62(X199, X200))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.19/0.51 tff(60,plain,
% 0.19/0.51 (![X202: $i, X201: $i, X200: $i, X199: $i] : ((~p32(X201, X200)) | (~p62(X202, X201)) | (~p4(X202, X199)) | p62(X199, X200))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.19/0.51 tff(61,plain,(
% 0.19/0.51 ![X202: $i, X201: $i, X200: $i, X199: $i] : ((~p32(X201, X200)) | (~p62(X202, X201)) | (~p4(X202, X199)) | p62(X199, X200))),
% 0.19/0.51 inference(skolemize,[status(sab)],[60])).
% 0.19/0.51 tff(62,plain,
% 0.19/0.51 (![X202: $i, X201: $i, X200: $i, X199: $i] : ((~p32(X201, X200)) | (~p62(X202, X201)) | (~p4(X202, X199)) | p62(X199, X200))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[61, 54])).
% 0.19/0.51 tff(63,plain,
% 0.19/0.51 (((~![X202: $i, X201: $i, X200: $i, X199: $i] : ((~p32(X201, X200)) | (~p62(X202, X201)) | (~p4(X202, X199)) | p62(X199, X200))) | ((~p32(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, f23(f25(f27(f29(f31(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, f23(f25(f27(f29(f31(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] : ((~p32(X201, X200)) | (~p62(X202, X201)) | (~p4(X202, X199)) | p62(X199, X200))) | (~p32(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, f23(f25(f27(f29(f31(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, f23(f25(f27(f29(f31(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))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(64,plain,
% 0.19/0.51 ((~![X202: $i, X201: $i, X200: $i, X199: $i] : ((~p32(X201, X200)) | (~p62(X202, X201)) | (~p4(X202, X199)) | p62(X199, X200))) | ((~p32(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, f23(f25(f27(f29(f31(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, f23(f25(f27(f29(f31(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))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(65,plain,
% 0.19/0.51 ((~![X202: $i, X201: $i, X200: $i, X199: $i] : ((~p32(X201, X200)) | (~p62(X202, X201)) | (~p4(X202, X199)) | p62(X199, X200))) | (~p32(c72, c72)) | (~p62(f5(c64, f8(f11(f13(c65, f16(f19(f21(c66, c67), c68), c69)), c70), c71)), c72)) | (~p4(f5(c64, f8(f11(f13(c65, f16(f19(f21(c66, c67), c68), c69)), c70), c71)), f5(c64, f16(f19(f21(c66, f23(f25(f27(f29(f31(c74, c67), c68), c69), c70), c71)), f43(f45(f47(f49(f51(c75, c67), c68), c69), c70), c71)), f53(f55(f57(f59(f61(c76, c67), c68), c69), c70), c71))))) | p62(f5(c64, f16(f19(f21(c66, f23(f25(f27(f29(f31(c74, c67), c68), c69), c70), c71)), f43(f45(f47(f49(f51(c75, c67), c68), c69), c70), c71)), f53(f55(f57(f59(f61(c76, c67), c68), c69), c70), c71))), c72)),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.19/0.51 tff(66,plain,
% 0.19/0.51 ($false),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[65, 62, 52, 49, 38, 37])).
% 0.19/0.51 tff(67,plain,(p62(f5(c64, f16(f19(f21(c66, f23(f25(f27(f29(f31(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,[]))).
% 0.19/0.51 tff(68,plain,
% 0.19/0.51 (^[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)))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(69,plain,
% 0.19/0.51 (![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))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[68])).
% 0.19/0.51 tff(70,plain,
% 0.19/0.51 (![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))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(71,plain,
% 0.19/0.51 (^[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)))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(72,plain,
% 0.19/0.51 (![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))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[71])).
% 0.19/0.51 tff(73,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/sandbox/benchmark/theBenchmark.p','p62_97')).
% 0.19/0.51 tff(74,plain,
% 0.19/0.51 (![X204: $i, X206: $i, X205: $i, X203: $i] : ((~p62(f5(c64, f16(f19(f21(c66, X203), X205), X206)), X204)) | p62(X203, X204))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.19/0.51 tff(75,plain,
% 0.19/0.51 (![X204: $i, X206: $i, X205: $i, X203: $i] : ((~p62(f5(c64, f16(f19(f21(c66, X203), X205), X206)), X204)) | p62(X203, X204))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.19/0.51 tff(76,plain,(
% 0.19/0.51 ![X204: $i, X206: $i, X205: $i, X203: $i] : ((~p62(f5(c64, f16(f19(f21(c66, X203), X205), X206)), X204)) | p62(X203, X204))),
% 0.19/0.51 inference(skolemize,[status(sab)],[75])).
% 0.19/0.51 tff(77,plain,
% 0.19/0.51 (![X204: $i, X206: $i, X205: $i, X203: $i] : ((~p62(f5(c64, f16(f19(f21(c66, X203), X205), X206)), X204)) | p62(X203, X204))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[76, 69])).
% 0.19/0.51 tff(78,plain,
% 0.19/0.51 (((~![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, f23(f25(f27(f29(f31(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(f23(f25(f27(f29(f31(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, f23(f25(f27(f29(f31(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(f23(f25(f27(f29(f31(c74, c67), c68), c69), c70), c71), c72))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(79,plain,
% 0.19/0.51 ((~![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, f23(f25(f27(f29(f31(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(f23(f25(f27(f29(f31(c74, c67), c68), c69), c70), c71), c72))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(80,plain,
% 0.19/0.51 ((~![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, f23(f25(f27(f29(f31(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(f23(f25(f27(f29(f31(c74, c67), c68), c69), c70), c71), c72)),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.19/0.51 tff(81,plain,
% 0.19/0.51 ((~p62(f5(c64, f16(f19(f21(c66, f23(f25(f27(f29(f31(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(f23(f25(f27(f29(f31(c74, c67), c68), c69), c70), c71), c72)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[80, 77])).
% 0.19/0.51 tff(82,plain,
% 0.19/0.51 (p62(f23(f25(f27(f29(f31(c74, c67), c68), c69), c70), c71), c72)),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[81, 67])).
% 0.19/0.51 tff(83,plain,
% 0.19/0.51 (^[X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : refl(((~p62(f23(f25(f27(f29(f31(c74, X7), X8), X9), X10), X11), X12)) | p62(X7, X12)) <=> ((~p62(f23(f25(f27(f29(f31(c74, X7), X8), X9), X10), X11), X12)) | p62(X7, X12)))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(84,plain,
% 0.19/0.51 (![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p62(f23(f25(f27(f29(f31(c74, X7), X8), X9), X10), X11), X12)) | p62(X7, X12)) <=> ![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p62(f23(f25(f27(f29(f31(c74, X7), X8), X9), X10), X11), X12)) | p62(X7, X12))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[83])).
% 0.19/0.51 tff(85,plain,
% 0.19/0.51 (![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p62(f23(f25(f27(f29(f31(c74, X7), X8), X9), X10), X11), X12)) | p62(X7, X12)) <=> ![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p62(f23(f25(f27(f29(f31(c74, X7), X8), X9), X10), X11), X12)) | p62(X7, X12))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(86,plain,
% 0.19/0.51 (^[X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : rewrite((p62(X7, X12) | (~p62(f23(f25(f27(f29(f31(c74, X7), X8), X9), X10), X11), X12))) <=> ((~p62(f23(f25(f27(f29(f31(c74, X7), X8), X9), X10), X11), X12)) | p62(X7, X12)))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(87,plain,
% 0.19/0.51 (![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : (p62(X7, X12) | (~p62(f23(f25(f27(f29(f31(c74, X7), X8), X9), X10), X11), X12))) <=> ![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p62(f23(f25(f27(f29(f31(c74, X7), X8), X9), X10), X11), X12)) | p62(X7, X12))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[86])).
% 0.19/0.51 tff(88,axiom,(![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : (p62(X7, X12) | (~p62(f23(f25(f27(f29(f31(c74, X7), X8), X9), X10), X11), X12)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p62_99')).
% 0.19/0.51 tff(89,plain,
% 0.19/0.51 (![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p62(f23(f25(f27(f29(f31(c74, X7), X8), X9), X10), X11), X12)) | p62(X7, X12))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.19/0.52 tff(90,plain,
% 0.19/0.52 (![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p62(f23(f25(f27(f29(f31(c74, X7), X8), X9), X10), X11), X12)) | p62(X7, X12))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.19/0.52 tff(91,plain,(
% 0.19/0.52 ![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p62(f23(f25(f27(f29(f31(c74, X7), X8), X9), X10), X11), X12)) | p62(X7, X12))),
% 0.19/0.52 inference(skolemize,[status(sab)],[90])).
% 0.19/0.52 tff(92,plain,
% 0.19/0.52 (![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p62(f23(f25(f27(f29(f31(c74, X7), X8), X9), X10), X11), X12)) | p62(X7, X12))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[91, 84])).
% 0.19/0.52 tff(93,plain,
% 0.19/0.52 ((~p62(c67, c72)) <=> (~p62(c67, c72))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(94,axiom,(~p62(c67, c72)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_p62_34')).
% 0.19/0.52 tff(95,plain,
% 0.19/0.52 (~p62(c67, c72)),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.19/0.52 tff(96,plain,
% 0.19/0.52 (((~![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p62(f23(f25(f27(f29(f31(c74, X7), X8), X9), X10), X11), X12)) | p62(X7, X12))) | ((~p62(f23(f25(f27(f29(f31(c74, c67), c68), c69), c70), c71), c72)) | p62(c67, c72))) <=> ((~![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p62(f23(f25(f27(f29(f31(c74, X7), X8), X9), X10), X11), X12)) | p62(X7, X12))) | (~p62(f23(f25(f27(f29(f31(c74, c67), c68), c69), c70), c71), c72)) | p62(c67, c72))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(97,plain,
% 0.19/0.52 ((~![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p62(f23(f25(f27(f29(f31(c74, X7), X8), X9), X10), X11), X12)) | p62(X7, X12))) | ((~p62(f23(f25(f27(f29(f31(c74, c67), c68), c69), c70), c71), c72)) | p62(c67, c72))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(98,plain,
% 0.19/0.52 ((~![X9: $i, X12: $i, X11: $i, X10: $i, X7: $i, X8: $i] : ((~p62(f23(f25(f27(f29(f31(c74, X7), X8), X9), X10), X11), X12)) | p62(X7, X12))) | (~p62(f23(f25(f27(f29(f31(c74, c67), c68), c69), c70), c71), c72)) | p62(c67, c72)),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.19/0.52 tff(99,plain,
% 0.19/0.52 ($false),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[98, 95, 92, 82])).
% 0.19/0.52 % SZS output end Proof
% 0.19/0.52 % E exiting
%------------------------------------------------------------------------------