%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN566-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:39:35 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN566-1 : TPTP v9.0.0. Released v2.5.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n009.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 12:38:03 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.20/0.38 % SZS status Unsatisfiable
% 0.20/0.38 % SZS output start Proof
% 0.20/0.38 tff(p3_type, type, (
% 0.20/0.38 p3: ( $i * $i ) > $o)).
% 0.20/0.38 tff(f4_type, type, (
% 0.20/0.38 f4: $i > $i)).
% 0.20/0.38 tff(f5_type, type, (
% 0.20/0.38 f5: $i > $i)).
% 0.20/0.38 tff(c15_type, type, (
% 0.20/0.38 c15: $i)).
% 0.20/0.38 tff(p2_type, type, (
% 0.20/0.38 p2: ( $i * $i ) > $o)).
% 0.20/0.38 tff(p8_type, type, (
% 0.20/0.38 p8: ( $i * $i ) > $o)).
% 0.20/0.38 tff(c12_type, type, (
% 0.20/0.38 c12: $i)).
% 0.20/0.38 tff(f6_type, type, (
% 0.20/0.38 f6: $i > $i)).
% 0.20/0.38 tff(c14_type, type, (
% 0.20/0.38 c14: $i)).
% 0.20/0.38 tff(p7_type, type, (
% 0.20/0.38 p7: ( $i * $i ) > $o)).
% 0.20/0.38 tff(c13_type, type, (
% 0.20/0.38 c13: $i)).
% 0.20/0.38 tff(p10_type, type, (
% 0.20/0.38 p10: ( $i * $i ) > $o)).
% 0.20/0.38 tff(c11_type, type, (
% 0.20/0.38 c11: $i)).
% 0.20/0.38 tff(1,assumption,(~p2(c15, c15)), introduced(assumption)).
% 0.20/0.38 tff(2,plain,
% 0.20/0.38 (^[X4: $i] : refl(p2(X4, X4) <=> p2(X4, X4))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(3,plain,
% 0.20/0.38 (![X4: $i] : p2(X4, X4) <=> ![X4: $i] : p2(X4, X4)),
% 0.20/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.38 tff(4,plain,
% 0.20/0.38 (![X4: $i] : p2(X4, X4) <=> ![X4: $i] : p2(X4, X4)),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(5,axiom,(![X4: $i] : p2(X4, X4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_2')).
% 0.20/0.38 tff(6,plain,
% 0.20/0.38 (![X4: $i] : p2(X4, X4)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.38 tff(7,plain,(
% 0.20/0.38 ![X4: $i] : p2(X4, X4)),
% 0.20/0.38 inference(skolemize,[status(sab)],[6])).
% 0.20/0.38 tff(8,plain,
% 0.20/0.38 (![X4: $i] : p2(X4, X4)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.38 tff(9,plain,
% 0.20/0.38 ((~![X4: $i] : p2(X4, X4)) | p2(c15, c15)),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(10,plain,
% 0.20/0.38 ($false),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.20/0.38 tff(11,plain,(p2(c15, c15)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.38 tff(12,plain,
% 0.20/0.38 (^[X7: $i, X8: $i] : refl(((~p2(X7, X8)) | p2(f5(X7), f5(X8))) <=> ((~p2(X7, X8)) | p2(f5(X7), f5(X8))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(13,plain,
% 0.20/0.38 (![X7: $i, X8: $i] : ((~p2(X7, X8)) | p2(f5(X7), f5(X8))) <=> ![X7: $i, X8: $i] : ((~p2(X7, X8)) | p2(f5(X7), f5(X8)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[12])).
% 0.20/0.38 tff(14,plain,
% 0.20/0.38 (![X7: $i, X8: $i] : ((~p2(X7, X8)) | p2(f5(X7), f5(X8))) <=> ![X7: $i, X8: $i] : ((~p2(X7, X8)) | p2(f5(X7), f5(X8)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(15,plain,
% 0.20/0.38 (^[X7: $i, X8: $i] : rewrite((p2(f5(X7), f5(X8)) | (~p2(X7, X8))) <=> ((~p2(X7, X8)) | p2(f5(X7), f5(X8))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(16,plain,
% 0.20/0.38 (![X7: $i, X8: $i] : (p2(f5(X7), f5(X8)) | (~p2(X7, X8))) <=> ![X7: $i, X8: $i] : ((~p2(X7, X8)) | p2(f5(X7), f5(X8)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[15])).
% 0.20/0.38 tff(17,axiom,(![X7: $i, X8: $i] : (p2(f5(X7), f5(X8)) | (~p2(X7, X8)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_10')).
% 0.20/0.38 tff(18,plain,
% 0.20/0.38 (![X7: $i, X8: $i] : ((~p2(X7, X8)) | p2(f5(X7), f5(X8)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.20/0.38 tff(19,plain,
% 0.20/0.38 (![X7: $i, X8: $i] : ((~p2(X7, X8)) | p2(f5(X7), f5(X8)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.20/0.38 tff(20,plain,(
% 0.20/0.38 ![X7: $i, X8: $i] : ((~p2(X7, X8)) | p2(f5(X7), f5(X8)))),
% 0.20/0.38 inference(skolemize,[status(sab)],[19])).
% 0.20/0.38 tff(21,plain,
% 0.20/0.38 (![X7: $i, X8: $i] : ((~p2(X7, X8)) | p2(f5(X7), f5(X8)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.20/0.38 tff(22,plain,
% 0.20/0.38 (((~![X7: $i, X8: $i] : ((~p2(X7, X8)) | p2(f5(X7), f5(X8)))) | ((~p2(c15, c15)) | p2(f5(c15), f5(c15)))) <=> ((~![X7: $i, X8: $i] : ((~p2(X7, X8)) | p2(f5(X7), f5(X8)))) | (~p2(c15, c15)) | p2(f5(c15), f5(c15)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(23,plain,
% 0.20/0.38 ((~![X7: $i, X8: $i] : ((~p2(X7, X8)) | p2(f5(X7), f5(X8)))) | ((~p2(c15, c15)) | p2(f5(c15), f5(c15)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(24,plain,
% 0.20/0.38 ((~![X7: $i, X8: $i] : ((~p2(X7, X8)) | p2(f5(X7), f5(X8)))) | (~p2(c15, c15)) | p2(f5(c15), f5(c15))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.38 tff(25,plain,
% 0.20/0.38 ((~p2(c15, c15)) | p2(f5(c15), f5(c15))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[24, 21])).
% 0.20/0.38 tff(26,plain,
% 0.20/0.38 (p2(f5(c15), f5(c15))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[25, 11])).
% 0.20/0.38 tff(27,plain,
% 0.20/0.38 (^[X14: $i, X15: $i] : refl(((~p2(X14, X15)) | p3(f4(X14), f4(X15))) <=> ((~p2(X14, X15)) | p3(f4(X14), f4(X15))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(28,plain,
% 0.20/0.38 (![X14: $i, X15: $i] : ((~p2(X14, X15)) | p3(f4(X14), f4(X15))) <=> ![X14: $i, X15: $i] : ((~p2(X14, X15)) | p3(f4(X14), f4(X15)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[27])).
% 0.20/0.38 tff(29,plain,
% 0.20/0.38 (![X14: $i, X15: $i] : ((~p2(X14, X15)) | p3(f4(X14), f4(X15))) <=> ![X14: $i, X15: $i] : ((~p2(X14, X15)) | p3(f4(X14), f4(X15)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(30,plain,
% 0.20/0.38 (^[X14: $i, X15: $i] : rewrite((p3(f4(X14), f4(X15)) | (~p2(X14, X15))) <=> ((~p2(X14, X15)) | p3(f4(X14), f4(X15))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(31,plain,
% 0.20/0.38 (![X14: $i, X15: $i] : (p3(f4(X14), f4(X15)) | (~p2(X14, X15))) <=> ![X14: $i, X15: $i] : ((~p2(X14, X15)) | p3(f4(X14), f4(X15)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[30])).
% 0.20/0.38 tff(32,axiom,(![X14: $i, X15: $i] : (p3(f4(X14), f4(X15)) | (~p2(X14, X15)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p3_9')).
% 0.20/0.38 tff(33,plain,
% 0.20/0.38 (![X14: $i, X15: $i] : ((~p2(X14, X15)) | p3(f4(X14), f4(X15)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.20/0.38 tff(34,plain,
% 0.20/0.38 (![X14: $i, X15: $i] : ((~p2(X14, X15)) | p3(f4(X14), f4(X15)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.20/0.38 tff(35,plain,(
% 0.20/0.38 ![X14: $i, X15: $i] : ((~p2(X14, X15)) | p3(f4(X14), f4(X15)))),
% 0.20/0.38 inference(skolemize,[status(sab)],[34])).
% 0.20/0.38 tff(36,plain,
% 0.20/0.38 (![X14: $i, X15: $i] : ((~p2(X14, X15)) | p3(f4(X14), f4(X15)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.20/0.38 tff(37,plain,
% 0.20/0.38 (((~![X14: $i, X15: $i] : ((~p2(X14, X15)) | p3(f4(X14), f4(X15)))) | ((~p2(f5(c15), f5(c15))) | p3(f4(f5(c15)), f4(f5(c15))))) <=> ((~![X14: $i, X15: $i] : ((~p2(X14, X15)) | p3(f4(X14), f4(X15)))) | (~p2(f5(c15), f5(c15))) | p3(f4(f5(c15)), f4(f5(c15))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(38,plain,
% 0.20/0.38 ((~![X14: $i, X15: $i] : ((~p2(X14, X15)) | p3(f4(X14), f4(X15)))) | ((~p2(f5(c15), f5(c15))) | p3(f4(f5(c15)), f4(f5(c15))))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(39,plain,
% 0.20/0.38 ((~![X14: $i, X15: $i] : ((~p2(X14, X15)) | p3(f4(X14), f4(X15)))) | (~p2(f5(c15), f5(c15))) | p3(f4(f5(c15)), f4(f5(c15)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.20/0.38 tff(40,plain,
% 0.20/0.38 (p3(f4(f5(c15)), f4(f5(c15)))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[39, 36, 26])).
% 0.20/0.38 tff(41,plain,
% 0.20/0.38 (^[X16: $i] : refl(p7(X16, X16) <=> p7(X16, X16))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(42,plain,
% 0.20/0.38 (![X16: $i] : p7(X16, X16) <=> ![X16: $i] : p7(X16, X16)),
% 0.20/0.38 inference(quant_intro,[status(thm)],[41])).
% 0.20/0.38 tff(43,plain,
% 0.20/0.38 (![X16: $i] : p7(X16, X16) <=> ![X16: $i] : p7(X16, X16)),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(44,axiom,(![X16: $i] : p7(X16, X16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p7_4')).
% 0.20/0.38 tff(45,plain,
% 0.20/0.38 (![X16: $i] : p7(X16, X16)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.20/0.38 tff(46,plain,(
% 0.20/0.38 ![X16: $i] : p7(X16, X16)),
% 0.20/0.38 inference(skolemize,[status(sab)],[45])).
% 0.20/0.38 tff(47,plain,
% 0.20/0.38 (![X16: $i] : p7(X16, X16)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.20/0.38 tff(48,plain,
% 0.20/0.38 ((~![X16: $i] : p7(X16, X16)) | p7(c12, c12)),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(49,plain,
% 0.20/0.38 (p7(c12, c12)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.20/0.38 tff(50,plain,
% 0.20/0.38 (^[X22: $i, X21: $i, X23: $i, X24: $i] : refl(((~p3(X23, X22)) | (~p8(X24, X23)) | (~p7(X24, X21)) | p8(X21, X22)) <=> ((~p3(X23, X22)) | (~p8(X24, X23)) | (~p7(X24, X21)) | p8(X21, X22)))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(51,plain,
% 0.20/0.38 (![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X23, X22)) | (~p8(X24, X23)) | (~p7(X24, X21)) | p8(X21, X22)) <=> ![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X23, X22)) | (~p8(X24, X23)) | (~p7(X24, X21)) | p8(X21, X22))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[50])).
% 0.20/0.38 tff(52,plain,
% 0.20/0.38 (![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X23, X22)) | (~p8(X24, X23)) | (~p7(X24, X21)) | p8(X21, X22)) <=> ![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X23, X22)) | (~p8(X24, X23)) | (~p7(X24, X21)) | p8(X21, X22))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(53,plain,
% 0.20/0.38 (^[X22: $i, X21: $i, X23: $i, X24: $i] : trans(monotonicity(trans(monotonicity(rewrite((p8(X21, X22) | (~p7(X24, X21))) <=> ((~p7(X24, X21)) | p8(X21, X22))), (((p8(X21, X22) | (~p7(X24, X21))) | (~p8(X24, X23))) <=> (((~p7(X24, X21)) | p8(X21, X22)) | (~p8(X24, X23))))), rewrite((((~p7(X24, X21)) | p8(X21, X22)) | (~p8(X24, X23))) <=> ((~p8(X24, X23)) | (~p7(X24, X21)) | p8(X21, X22))), (((p8(X21, X22) | (~p7(X24, X21))) | (~p8(X24, X23))) <=> ((~p8(X24, X23)) | (~p7(X24, X21)) | p8(X21, X22)))), ((((p8(X21, X22) | (~p7(X24, X21))) | (~p8(X24, X23))) | (~p3(X23, X22))) <=> (((~p8(X24, X23)) | (~p7(X24, X21)) | p8(X21, X22)) | (~p3(X23, X22))))), rewrite((((~p8(X24, X23)) | (~p7(X24, X21)) | p8(X21, X22)) | (~p3(X23, X22))) <=> ((~p3(X23, X22)) | (~p8(X24, X23)) | (~p7(X24, X21)) | p8(X21, X22))), ((((p8(X21, X22) | (~p7(X24, X21))) | (~p8(X24, X23))) | (~p3(X23, X22))) <=> ((~p3(X23, X22)) | (~p8(X24, X23)) | (~p7(X24, X21)) | p8(X21, X22))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(54,plain,
% 0.20/0.38 (![X22: $i, X21: $i, X23: $i, X24: $i] : (((p8(X21, X22) | (~p7(X24, X21))) | (~p8(X24, X23))) | (~p3(X23, X22))) <=> ![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X23, X22)) | (~p8(X24, X23)) | (~p7(X24, X21)) | p8(X21, X22))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[53])).
% 0.20/0.38 tff(55,axiom,(![X22: $i, X21: $i, X23: $i, X24: $i] : (((p8(X21, X22) | (~p7(X24, X21))) | (~p8(X24, X23))) | (~p3(X23, X22)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p8_18')).
% 0.20/0.38 tff(56,plain,
% 0.20/0.38 (![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X23, X22)) | (~p8(X24, X23)) | (~p7(X24, X21)) | p8(X21, X22))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.20/0.38 tff(57,plain,
% 0.20/0.38 (![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X23, X22)) | (~p8(X24, X23)) | (~p7(X24, X21)) | p8(X21, X22))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.20/0.38 tff(58,plain,(
% 0.20/0.38 ![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X23, X22)) | (~p8(X24, X23)) | (~p7(X24, X21)) | p8(X21, X22))),
% 0.20/0.38 inference(skolemize,[status(sab)],[57])).
% 0.20/0.38 tff(59,plain,
% 0.20/0.38 (![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X23, X22)) | (~p8(X24, X23)) | (~p7(X24, X21)) | p8(X21, X22))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.20/0.38 tff(60,plain,
% 0.20/0.38 (p3(c13, f4(c14)) <=> p3(c13, f4(c14))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(61,axiom,(p3(c13, f4(c14))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p3_8')).
% 0.20/0.38 tff(62,plain,
% 0.20/0.38 (p3(c13, f4(c14))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.20/0.38 tff(63,plain,
% 0.20/0.38 (p8(c12, c13) <=> p8(c12, c13)),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(64,axiom,(p8(c12, c13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p8_6')).
% 0.20/0.38 tff(65,plain,
% 0.20/0.38 (p8(c12, c13)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.20/0.38 tff(66,plain,
% 0.20/0.38 (((~![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X23, X22)) | (~p8(X24, X23)) | (~p7(X24, X21)) | p8(X21, X22))) | ((~p3(c13, f4(c14))) | (~p7(c12, c12)) | p8(c12, f4(c14)) | (~p8(c12, c13)))) <=> ((~![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X23, X22)) | (~p8(X24, X23)) | (~p7(X24, X21)) | p8(X21, X22))) | (~p3(c13, f4(c14))) | (~p7(c12, c12)) | p8(c12, f4(c14)) | (~p8(c12, c13)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(67,plain,
% 0.20/0.38 (((~p3(c13, f4(c14))) | (~p8(c12, c13)) | (~p7(c12, c12)) | p8(c12, f4(c14))) <=> ((~p3(c13, f4(c14))) | (~p7(c12, c12)) | p8(c12, f4(c14)) | (~p8(c12, c13)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(68,plain,
% 0.20/0.38 (((~![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X23, X22)) | (~p8(X24, X23)) | (~p7(X24, X21)) | p8(X21, X22))) | ((~p3(c13, f4(c14))) | (~p8(c12, c13)) | (~p7(c12, c12)) | p8(c12, f4(c14)))) <=> ((~![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X23, X22)) | (~p8(X24, X23)) | (~p7(X24, X21)) | p8(X21, X22))) | ((~p3(c13, f4(c14))) | (~p7(c12, c12)) | p8(c12, f4(c14)) | (~p8(c12, c13))))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[67])).
% 0.20/0.38 tff(69,plain,
% 0.20/0.38 (((~![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X23, X22)) | (~p8(X24, X23)) | (~p7(X24, X21)) | p8(X21, X22))) | ((~p3(c13, f4(c14))) | (~p8(c12, c13)) | (~p7(c12, c12)) | p8(c12, f4(c14)))) <=> ((~![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X23, X22)) | (~p8(X24, X23)) | (~p7(X24, X21)) | p8(X21, X22))) | (~p3(c13, f4(c14))) | (~p7(c12, c12)) | p8(c12, f4(c14)) | (~p8(c12, c13)))),
% 0.20/0.39 inference(transitivity,[status(thm)],[68, 66])).
% 0.20/0.39 tff(70,plain,
% 0.20/0.39 ((~![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X23, X22)) | (~p8(X24, X23)) | (~p7(X24, X21)) | p8(X21, X22))) | ((~p3(c13, f4(c14))) | (~p8(c12, c13)) | (~p7(c12, c12)) | p8(c12, f4(c14)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(71,plain,
% 0.20/0.39 ((~![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X23, X22)) | (~p8(X24, X23)) | (~p7(X24, X21)) | p8(X21, X22))) | (~p3(c13, f4(c14))) | (~p7(c12, c12)) | p8(c12, f4(c14)) | (~p8(c12, c13))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.20/0.39 tff(72,plain,
% 0.20/0.39 (p8(c12, f4(c14))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[71, 65, 62, 59, 49])).
% 0.20/0.39 tff(73,plain,
% 0.20/0.39 (p2(c14, f6(c15)) <=> p2(c14, f6(c15))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(74,axiom,(p2(c14, f6(c15))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_7')).
% 0.20/0.39 tff(75,plain,
% 0.20/0.39 (p2(c14, f6(c15))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.20/0.39 tff(76,plain,
% 0.20/0.39 (((~![X14: $i, X15: $i] : ((~p2(X14, X15)) | p3(f4(X14), f4(X15)))) | ((~p2(c14, f6(c15))) | p3(f4(c14), f4(f6(c15))))) <=> ((~![X14: $i, X15: $i] : ((~p2(X14, X15)) | p3(f4(X14), f4(X15)))) | (~p2(c14, f6(c15))) | p3(f4(c14), f4(f6(c15))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(77,plain,
% 0.20/0.39 ((~![X14: $i, X15: $i] : ((~p2(X14, X15)) | p3(f4(X14), f4(X15)))) | ((~p2(c14, f6(c15))) | p3(f4(c14), f4(f6(c15))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(78,plain,
% 0.20/0.39 ((~![X14: $i, X15: $i] : ((~p2(X14, X15)) | p3(f4(X14), f4(X15)))) | (~p2(c14, f6(c15))) | p3(f4(c14), f4(f6(c15)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.20/0.39 tff(79,plain,
% 0.20/0.39 (p3(f4(c14), f4(f6(c15)))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[78, 75, 36])).
% 0.20/0.39 tff(80,plain,
% 0.20/0.39 (((~![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X23, X22)) | (~p8(X24, X23)) | (~p7(X24, X21)) | p8(X21, X22))) | ((~p3(f4(c14), f4(f6(c15)))) | (~p7(c12, c12)) | p8(c12, f4(f6(c15))) | (~p8(c12, f4(c14))))) <=> ((~![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X23, X22)) | (~p8(X24, X23)) | (~p7(X24, X21)) | p8(X21, X22))) | (~p3(f4(c14), f4(f6(c15)))) | (~p7(c12, c12)) | p8(c12, f4(f6(c15))) | (~p8(c12, f4(c14))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(81,plain,
% 0.20/0.39 (((~p3(f4(c14), f4(f6(c15)))) | (~p8(c12, f4(c14))) | (~p7(c12, c12)) | p8(c12, f4(f6(c15)))) <=> ((~p3(f4(c14), f4(f6(c15)))) | (~p7(c12, c12)) | p8(c12, f4(f6(c15))) | (~p8(c12, f4(c14))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(82,plain,
% 0.20/0.39 (((~![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X23, X22)) | (~p8(X24, X23)) | (~p7(X24, X21)) | p8(X21, X22))) | ((~p3(f4(c14), f4(f6(c15)))) | (~p8(c12, f4(c14))) | (~p7(c12, c12)) | p8(c12, f4(f6(c15))))) <=> ((~![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X23, X22)) | (~p8(X24, X23)) | (~p7(X24, X21)) | p8(X21, X22))) | ((~p3(f4(c14), f4(f6(c15)))) | (~p7(c12, c12)) | p8(c12, f4(f6(c15))) | (~p8(c12, f4(c14)))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[81])).
% 0.20/0.39 tff(83,plain,
% 0.20/0.39 (((~![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X23, X22)) | (~p8(X24, X23)) | (~p7(X24, X21)) | p8(X21, X22))) | ((~p3(f4(c14), f4(f6(c15)))) | (~p8(c12, f4(c14))) | (~p7(c12, c12)) | p8(c12, f4(f6(c15))))) <=> ((~![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X23, X22)) | (~p8(X24, X23)) | (~p7(X24, X21)) | p8(X21, X22))) | (~p3(f4(c14), f4(f6(c15)))) | (~p7(c12, c12)) | p8(c12, f4(f6(c15))) | (~p8(c12, f4(c14))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[82, 80])).
% 0.20/0.39 tff(84,plain,
% 0.20/0.39 ((~![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X23, X22)) | (~p8(X24, X23)) | (~p7(X24, X21)) | p8(X21, X22))) | ((~p3(f4(c14), f4(f6(c15)))) | (~p8(c12, f4(c14))) | (~p7(c12, c12)) | p8(c12, f4(f6(c15))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(85,plain,
% 0.20/0.39 ((~![X22: $i, X21: $i, X23: $i, X24: $i] : ((~p3(X23, X22)) | (~p8(X24, X23)) | (~p7(X24, X21)) | p8(X21, X22))) | (~p3(f4(c14), f4(f6(c15)))) | (~p7(c12, c12)) | p8(c12, f4(f6(c15))) | (~p8(c12, f4(c14)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.20/0.39 tff(86,plain,
% 0.20/0.39 (p8(c12, f4(f6(c15)))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[85, 59, 79, 49, 72])).
% 0.20/0.39 tff(87,plain,
% 0.20/0.39 (^[X20: $i, X19: $i] : refl(((~p8(X19, f4(f6(X20)))) | p8(X19, f4(f5(X20)))) <=> ((~p8(X19, f4(f6(X20)))) | p8(X19, f4(f5(X20)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(88,plain,
% 0.20/0.39 (![X20: $i, X19: $i] : ((~p8(X19, f4(f6(X20)))) | p8(X19, f4(f5(X20)))) <=> ![X20: $i, X19: $i] : ((~p8(X19, f4(f6(X20)))) | p8(X19, f4(f5(X20))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[87])).
% 0.20/0.39 tff(89,plain,
% 0.20/0.39 (![X20: $i, X19: $i] : ((~p8(X19, f4(f6(X20)))) | p8(X19, f4(f5(X20)))) <=> ![X20: $i, X19: $i] : ((~p8(X19, f4(f6(X20)))) | p8(X19, f4(f5(X20))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(90,plain,
% 0.20/0.39 (^[X20: $i, X19: $i] : rewrite((p8(X19, f4(f5(X20))) | (~p8(X19, f4(f6(X20))))) <=> ((~p8(X19, f4(f6(X20)))) | p8(X19, f4(f5(X20)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(91,plain,
% 0.20/0.39 (![X20: $i, X19: $i] : (p8(X19, f4(f5(X20))) | (~p8(X19, f4(f6(X20))))) <=> ![X20: $i, X19: $i] : ((~p8(X19, f4(f6(X20)))) | p8(X19, f4(f5(X20))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[90])).
% 0.20/0.39 tff(92,axiom,(![X20: $i, X19: $i] : (p8(X19, f4(f5(X20))) | (~p8(X19, f4(f6(X20)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p8_16')).
% 0.20/0.39 tff(93,plain,
% 0.20/0.39 (![X20: $i, X19: $i] : ((~p8(X19, f4(f6(X20)))) | p8(X19, f4(f5(X20))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.20/0.39 tff(94,plain,
% 0.20/0.39 (![X20: $i, X19: $i] : ((~p8(X19, f4(f6(X20)))) | p8(X19, f4(f5(X20))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[93, 89])).
% 0.20/0.39 tff(95,plain,(
% 0.20/0.39 ![X20: $i, X19: $i] : ((~p8(X19, f4(f6(X20)))) | p8(X19, f4(f5(X20))))),
% 0.20/0.39 inference(skolemize,[status(sab)],[94])).
% 0.20/0.39 tff(96,plain,
% 0.20/0.39 (![X20: $i, X19: $i] : ((~p8(X19, f4(f6(X20)))) | p8(X19, f4(f5(X20))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[95, 88])).
% 0.20/0.39 tff(97,plain,
% 0.20/0.39 (((~![X20: $i, X19: $i] : ((~p8(X19, f4(f6(X20)))) | p8(X19, f4(f5(X20))))) | ((~p8(c12, f4(f6(c15)))) | p8(c12, f4(f5(c15))))) <=> ((~![X20: $i, X19: $i] : ((~p8(X19, f4(f6(X20)))) | p8(X19, f4(f5(X20))))) | (~p8(c12, f4(f6(c15)))) | p8(c12, f4(f5(c15))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(98,plain,
% 0.20/0.39 ((~![X20: $i, X19: $i] : ((~p8(X19, f4(f6(X20)))) | p8(X19, f4(f5(X20))))) | ((~p8(c12, f4(f6(c15)))) | p8(c12, f4(f5(c15))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(99,plain,
% 0.20/0.39 ((~![X20: $i, X19: $i] : ((~p8(X19, f4(f6(X20)))) | p8(X19, f4(f5(X20))))) | (~p8(c12, f4(f6(c15)))) | p8(c12, f4(f5(c15)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.20/0.39 tff(100,plain,
% 0.20/0.39 (p8(c12, f4(f5(c15)))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[99, 96, 86])).
% 0.20/0.39 tff(101,plain,
% 0.20/0.39 (^[X30: $i, X29: $i, X28: $i] : refl(((~p2(X29, f5(X28))) | (~p3(X30, f4(X29))) | (~p8(c12, X30)) | (~p10(X28, c11))) <=> ((~p2(X29, f5(X28))) | (~p3(X30, f4(X29))) | (~p8(c12, X30)) | (~p10(X28, c11))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(102,plain,
% 0.20/0.39 (![X30: $i, X29: $i, X28: $i] : ((~p2(X29, f5(X28))) | (~p3(X30, f4(X29))) | (~p8(c12, X30)) | (~p10(X28, c11))) <=> ![X30: $i, X29: $i, X28: $i] : ((~p2(X29, f5(X28))) | (~p3(X30, f4(X29))) | (~p8(c12, X30)) | (~p10(X28, c11)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[101])).
% 0.20/0.39 tff(103,plain,
% 0.20/0.39 (![X30: $i, X29: $i, X28: $i] : ((~p2(X29, f5(X28))) | (~p3(X30, f4(X29))) | (~p8(c12, X30)) | (~p10(X28, c11))) <=> ![X30: $i, X29: $i, X28: $i] : ((~p2(X29, f5(X28))) | (~p3(X30, f4(X29))) | (~p8(c12, X30)) | (~p10(X28, c11)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(104,plain,
% 0.20/0.39 (^[X30: $i, X29: $i, X28: $i] : trans(monotonicity(rewrite((((~p10(X28, c11)) | (~p8(c12, X30))) | (~p3(X30, f4(X29)))) <=> ((~p3(X30, f4(X29))) | (~p8(c12, X30)) | (~p10(X28, c11)))), (((((~p10(X28, c11)) | (~p8(c12, X30))) | (~p3(X30, f4(X29)))) | (~p2(X29, f5(X28)))) <=> (((~p3(X30, f4(X29))) | (~p8(c12, X30)) | (~p10(X28, c11))) | (~p2(X29, f5(X28)))))), rewrite((((~p3(X30, f4(X29))) | (~p8(c12, X30)) | (~p10(X28, c11))) | (~p2(X29, f5(X28)))) <=> ((~p2(X29, f5(X28))) | (~p3(X30, f4(X29))) | (~p8(c12, X30)) | (~p10(X28, c11)))), (((((~p10(X28, c11)) | (~p8(c12, X30))) | (~p3(X30, f4(X29)))) | (~p2(X29, f5(X28)))) <=> ((~p2(X29, f5(X28))) | (~p3(X30, f4(X29))) | (~p8(c12, X30)) | (~p10(X28, c11)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(105,plain,
% 0.20/0.39 (![X30: $i, X29: $i, X28: $i] : ((((~p10(X28, c11)) | (~p8(c12, X30))) | (~p3(X30, f4(X29)))) | (~p2(X29, f5(X28)))) <=> ![X30: $i, X29: $i, X28: $i] : ((~p2(X29, f5(X28))) | (~p3(X30, f4(X29))) | (~p8(c12, X30)) | (~p10(X28, c11)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[104])).
% 0.20/0.39 tff(106,axiom,(![X30: $i, X29: $i, X28: $i] : ((((~p10(X28, c11)) | (~p8(c12, X30))) | (~p3(X30, f4(X29)))) | (~p2(X29, f5(X28))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_p10_19')).
% 0.20/0.39 tff(107,plain,
% 0.20/0.39 (![X30: $i, X29: $i, X28: $i] : ((~p2(X29, f5(X28))) | (~p3(X30, f4(X29))) | (~p8(c12, X30)) | (~p10(X28, c11)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.20/0.39 tff(108,plain,
% 0.20/0.39 (![X30: $i, X29: $i, X28: $i] : ((~p2(X29, f5(X28))) | (~p3(X30, f4(X29))) | (~p8(c12, X30)) | (~p10(X28, c11)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[107, 103])).
% 0.20/0.39 tff(109,plain,(
% 0.20/0.39 ![X30: $i, X29: $i, X28: $i] : ((~p2(X29, f5(X28))) | (~p3(X30, f4(X29))) | (~p8(c12, X30)) | (~p10(X28, c11)))),
% 0.20/0.39 inference(skolemize,[status(sab)],[108])).
% 0.20/0.39 tff(110,plain,
% 0.20/0.39 (![X30: $i, X29: $i, X28: $i] : ((~p2(X29, f5(X28))) | (~p3(X30, f4(X29))) | (~p8(c12, X30)) | (~p10(X28, c11)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[109, 102])).
% 0.20/0.39 tff(111,plain,
% 0.20/0.39 (p10(c15, c11) <=> p10(c15, c11)),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(112,axiom,(p10(c15, c11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p10_5')).
% 0.20/0.39 tff(113,plain,
% 0.20/0.39 (p10(c15, c11)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.20/0.39 tff(114,plain,
% 0.20/0.39 (((~![X30: $i, X29: $i, X28: $i] : ((~p2(X29, f5(X28))) | (~p3(X30, f4(X29))) | (~p8(c12, X30)) | (~p10(X28, c11)))) | ((~p3(f4(f5(c15)), f4(f5(c15)))) | (~p8(c12, f4(f5(c15)))) | (~p10(c15, c11)) | (~p2(f5(c15), f5(c15))))) <=> ((~![X30: $i, X29: $i, X28: $i] : ((~p2(X29, f5(X28))) | (~p3(X30, f4(X29))) | (~p8(c12, X30)) | (~p10(X28, c11)))) | (~p3(f4(f5(c15)), f4(f5(c15)))) | (~p8(c12, f4(f5(c15)))) | (~p10(c15, c11)) | (~p2(f5(c15), f5(c15))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(115,plain,
% 0.20/0.39 (((~p2(f5(c15), f5(c15))) | (~p3(f4(f5(c15)), f4(f5(c15)))) | (~p8(c12, f4(f5(c15)))) | (~p10(c15, c11))) <=> ((~p3(f4(f5(c15)), f4(f5(c15)))) | (~p8(c12, f4(f5(c15)))) | (~p10(c15, c11)) | (~p2(f5(c15), f5(c15))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(116,plain,
% 0.20/0.39 (((~![X30: $i, X29: $i, X28: $i] : ((~p2(X29, f5(X28))) | (~p3(X30, f4(X29))) | (~p8(c12, X30)) | (~p10(X28, c11)))) | ((~p2(f5(c15), f5(c15))) | (~p3(f4(f5(c15)), f4(f5(c15)))) | (~p8(c12, f4(f5(c15)))) | (~p10(c15, c11)))) <=> ((~![X30: $i, X29: $i, X28: $i] : ((~p2(X29, f5(X28))) | (~p3(X30, f4(X29))) | (~p8(c12, X30)) | (~p10(X28, c11)))) | ((~p3(f4(f5(c15)), f4(f5(c15)))) | (~p8(c12, f4(f5(c15)))) | (~p10(c15, c11)) | (~p2(f5(c15), f5(c15)))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[115])).
% 0.20/0.39 tff(117,plain,
% 0.20/0.39 (((~![X30: $i, X29: $i, X28: $i] : ((~p2(X29, f5(X28))) | (~p3(X30, f4(X29))) | (~p8(c12, X30)) | (~p10(X28, c11)))) | ((~p2(f5(c15), f5(c15))) | (~p3(f4(f5(c15)), f4(f5(c15)))) | (~p8(c12, f4(f5(c15)))) | (~p10(c15, c11)))) <=> ((~![X30: $i, X29: $i, X28: $i] : ((~p2(X29, f5(X28))) | (~p3(X30, f4(X29))) | (~p8(c12, X30)) | (~p10(X28, c11)))) | (~p3(f4(f5(c15)), f4(f5(c15)))) | (~p8(c12, f4(f5(c15)))) | (~p10(c15, c11)) | (~p2(f5(c15), f5(c15))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[116, 114])).
% 0.20/0.39 tff(118,plain,
% 0.20/0.39 ((~![X30: $i, X29: $i, X28: $i] : ((~p2(X29, f5(X28))) | (~p3(X30, f4(X29))) | (~p8(c12, X30)) | (~p10(X28, c11)))) | ((~p2(f5(c15), f5(c15))) | (~p3(f4(f5(c15)), f4(f5(c15)))) | (~p8(c12, f4(f5(c15)))) | (~p10(c15, c11)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(119,plain,
% 0.20/0.39 ((~![X30: $i, X29: $i, X28: $i] : ((~p2(X29, f5(X28))) | (~p3(X30, f4(X29))) | (~p8(c12, X30)) | (~p10(X28, c11)))) | (~p3(f4(f5(c15)), f4(f5(c15)))) | (~p8(c12, f4(f5(c15)))) | (~p10(c15, c11)) | (~p2(f5(c15), f5(c15)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.20/0.40 tff(120,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[119, 113, 110, 100, 26, 40])).
% 0.20/0.40 % SZS output end Proof
% 0.20/0.40 % E exiting
%------------------------------------------------------------------------------