%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN585-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:39:37 AM UTC 2025
% Result : Unsatisfiable 0.11s 0.37s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN585-1 : TPTP v9.0.0. Released v2.5.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n008.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 12:38:48 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.37 % SZS status Unsatisfiable
% 0.11/0.37 % SZS output start Proof
% 0.11/0.37 tff(p11_type, type, (
% 0.11/0.37 p11: ( $i * $i ) > $o)).
% 0.11/0.37 tff(f9_type, type, (
% 0.11/0.37 f9: ( $i * $i ) > $i)).
% 0.11/0.37 tff(f8_type, type, (
% 0.11/0.37 f8: ( $i * $i ) > $i)).
% 0.11/0.37 tff(c14_type, type, (
% 0.11/0.37 c14: $i)).
% 0.11/0.37 tff(c16_type, type, (
% 0.11/0.37 c16: $i)).
% 0.11/0.37 tff(c12_type, type, (
% 0.11/0.37 c12: $i)).
% 0.11/0.37 tff(p2_type, type, (
% 0.11/0.37 p2: ( $i * $i ) > $o)).
% 0.11/0.37 tff(f3_type, type, (
% 0.11/0.37 f3: $i > $i)).
% 0.11/0.37 tff(c13_type, type, (
% 0.11/0.37 c13: $i)).
% 0.11/0.37 tff(c18_type, type, (
% 0.11/0.37 c18: $i)).
% 0.11/0.37 tff(1,assumption,(~p11(c14, f8(c16, c14))), introduced(assumption)).
% 0.11/0.37 tff(2,assumption,(~p11(c14, c14)), introduced(assumption)).
% 0.11/0.37 tff(3,plain,
% 0.11/0.37 (^[X8: $i] : refl(p11(X8, X8) <=> p11(X8, X8))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(4,plain,
% 0.11/0.37 (![X8: $i] : p11(X8, X8) <=> ![X8: $i] : p11(X8, X8)),
% 0.11/0.37 inference(quant_intro,[status(thm)],[3])).
% 0.11/0.37 tff(5,plain,
% 0.11/0.37 (![X8: $i] : p11(X8, X8) <=> ![X8: $i] : p11(X8, X8)),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(6,axiom,(![X8: $i] : p11(X8, X8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p11_2')).
% 0.11/0.37 tff(7,plain,
% 0.11/0.37 (![X8: $i] : p11(X8, X8)),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.11/0.37 tff(8,plain,(
% 0.11/0.37 ![X8: $i] : p11(X8, X8)),
% 0.11/0.37 inference(skolemize,[status(sab)],[7])).
% 0.11/0.37 tff(9,plain,
% 0.11/0.37 (![X8: $i] : p11(X8, X8)),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.11/0.37 tff(10,plain,
% 0.11/0.37 ((~![X8: $i] : p11(X8, X8)) | p11(c14, c14)),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(11,plain,
% 0.11/0.37 ($false),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[10, 9, 2])).
% 0.11/0.37 tff(12,plain,(p11(c14, c14)), inference(lemma,lemma(discharge,[]))).
% 0.11/0.37 tff(13,plain,
% 0.11/0.37 (^[X9: $i, X11: $i, X10: $i] : refl(((~p11(X9, X11)) | p11(X9, f8(X10, X11))) <=> ((~p11(X9, X11)) | p11(X9, f8(X10, X11))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(14,plain,
% 0.11/0.37 (![X9: $i, X11: $i, X10: $i] : ((~p11(X9, X11)) | p11(X9, f8(X10, X11))) <=> ![X9: $i, X11: $i, X10: $i] : ((~p11(X9, X11)) | p11(X9, f8(X10, X11)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[13])).
% 0.11/0.37 tff(15,plain,
% 0.11/0.37 (![X9: $i, X11: $i, X10: $i] : ((~p11(X9, X11)) | p11(X9, f8(X10, X11))) <=> ![X9: $i, X11: $i, X10: $i] : ((~p11(X9, X11)) | p11(X9, f8(X10, X11)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(16,plain,
% 0.11/0.37 (^[X9: $i, X11: $i, X10: $i] : rewrite((p11(X9, f8(X10, X11)) | (~p11(X9, X11))) <=> ((~p11(X9, X11)) | p11(X9, f8(X10, X11))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(17,plain,
% 0.11/0.37 (![X9: $i, X11: $i, X10: $i] : (p11(X9, f8(X10, X11)) | (~p11(X9, X11))) <=> ![X9: $i, X11: $i, X10: $i] : ((~p11(X9, X11)) | p11(X9, f8(X10, X11)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[16])).
% 0.11/0.37 tff(18,axiom,(![X9: $i, X11: $i, X10: $i] : (p11(X9, f8(X10, X11)) | (~p11(X9, X11)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p11_13')).
% 0.11/0.37 tff(19,plain,
% 0.11/0.37 (![X9: $i, X11: $i, X10: $i] : ((~p11(X9, X11)) | p11(X9, f8(X10, X11)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.11/0.37 tff(20,plain,
% 0.11/0.37 (![X9: $i, X11: $i, X10: $i] : ((~p11(X9, X11)) | p11(X9, f8(X10, X11)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.11/0.37 tff(21,plain,(
% 0.11/0.37 ![X9: $i, X11: $i, X10: $i] : ((~p11(X9, X11)) | p11(X9, f8(X10, X11)))),
% 0.11/0.37 inference(skolemize,[status(sab)],[20])).
% 0.11/0.37 tff(22,plain,
% 0.11/0.37 (![X9: $i, X11: $i, X10: $i] : ((~p11(X9, X11)) | p11(X9, f8(X10, X11)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.11/0.37 tff(23,plain,
% 0.11/0.37 (((~![X9: $i, X11: $i, X10: $i] : ((~p11(X9, X11)) | p11(X9, f8(X10, X11)))) | ((~p11(c14, c14)) | p11(c14, f8(c16, c14)))) <=> ((~![X9: $i, X11: $i, X10: $i] : ((~p11(X9, X11)) | p11(X9, f8(X10, X11)))) | (~p11(c14, c14)) | p11(c14, f8(c16, c14)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(24,plain,
% 0.11/0.37 ((~![X9: $i, X11: $i, X10: $i] : ((~p11(X9, X11)) | p11(X9, f8(X10, X11)))) | ((~p11(c14, c14)) | p11(c14, f8(c16, c14)))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(25,plain,
% 0.11/0.37 ((~![X9: $i, X11: $i, X10: $i] : ((~p11(X9, X11)) | p11(X9, f8(X10, X11)))) | (~p11(c14, c14)) | p11(c14, f8(c16, c14))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.11/0.37 tff(26,plain,
% 0.11/0.37 ($false),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[25, 22, 12, 1])).
% 0.11/0.37 tff(27,plain,(p11(c14, f8(c16, c14))), inference(lemma,lemma(discharge,[]))).
% 0.11/0.37 tff(28,plain,
% 0.11/0.37 (^[X17: $i, X16: $i, X15: $i] : refl((p11(f9(X17, X15), f9(X17, X16)) | p2(X17, f3(c13)) | (~p11(X15, X16))) <=> (p11(f9(X17, X15), f9(X17, X16)) | p2(X17, f3(c13)) | (~p11(X15, X16))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(29,plain,
% 0.11/0.37 (![X17: $i, X16: $i, X15: $i] : (p11(f9(X17, X15), f9(X17, X16)) | p2(X17, f3(c13)) | (~p11(X15, X16))) <=> ![X17: $i, X16: $i, X15: $i] : (p11(f9(X17, X15), f9(X17, X16)) | p2(X17, f3(c13)) | (~p11(X15, X16)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[28])).
% 0.11/0.37 tff(30,plain,
% 0.11/0.37 (![X17: $i, X16: $i, X15: $i] : (p11(f9(X17, X15), f9(X17, X16)) | p2(X17, f3(c13)) | (~p11(X15, X16))) <=> ![X17: $i, X16: $i, X15: $i] : (p11(f9(X17, X15), f9(X17, X16)) | p2(X17, f3(c13)) | (~p11(X15, X16)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(31,plain,
% 0.11/0.37 (^[X17: $i, X16: $i, X15: $i] : trans(monotonicity(rewrite((p2(X17, f3(c13)) | p11(f9(X17, X15), f9(X17, X16))) <=> (p11(f9(X17, X15), f9(X17, X16)) | p2(X17, f3(c13)))), (((p2(X17, f3(c13)) | p11(f9(X17, X15), f9(X17, X16))) | (~p11(X15, X16))) <=> ((p11(f9(X17, X15), f9(X17, X16)) | p2(X17, f3(c13))) | (~p11(X15, X16))))), rewrite(((p11(f9(X17, X15), f9(X17, X16)) | p2(X17, f3(c13))) | (~p11(X15, X16))) <=> (p11(f9(X17, X15), f9(X17, X16)) | p2(X17, f3(c13)) | (~p11(X15, X16)))), (((p2(X17, f3(c13)) | p11(f9(X17, X15), f9(X17, X16))) | (~p11(X15, X16))) <=> (p11(f9(X17, X15), f9(X17, X16)) | p2(X17, f3(c13)) | (~p11(X15, X16)))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(32,plain,
% 0.11/0.37 (![X17: $i, X16: $i, X15: $i] : ((p2(X17, f3(c13)) | p11(f9(X17, X15), f9(X17, X16))) | (~p11(X15, X16))) <=> ![X17: $i, X16: $i, X15: $i] : (p11(f9(X17, X15), f9(X17, X16)) | p2(X17, f3(c13)) | (~p11(X15, X16)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[31])).
% 0.11/0.37 tff(33,axiom,(![X17: $i, X16: $i, X15: $i] : ((p2(X17, f3(c13)) | p11(f9(X17, X15), f9(X17, X16))) | (~p11(X15, X16)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_26')).
% 0.11/0.37 tff(34,plain,
% 0.11/0.37 (![X17: $i, X16: $i, X15: $i] : (p11(f9(X17, X15), f9(X17, X16)) | p2(X17, f3(c13)) | (~p11(X15, X16)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.11/0.37 tff(35,plain,
% 0.11/0.37 (![X17: $i, X16: $i, X15: $i] : (p11(f9(X17, X15), f9(X17, X16)) | p2(X17, f3(c13)) | (~p11(X15, X16)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.11/0.37 tff(36,plain,(
% 0.11/0.37 ![X17: $i, X16: $i, X15: $i] : (p11(f9(X17, X15), f9(X17, X16)) | p2(X17, f3(c13)) | (~p11(X15, X16)))),
% 0.11/0.37 inference(skolemize,[status(sab)],[35])).
% 0.11/0.37 tff(37,plain,
% 0.11/0.37 (![X17: $i, X16: $i, X15: $i] : (p11(f9(X17, X15), f9(X17, X16)) | p2(X17, f3(c13)) | (~p11(X15, X16)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.11/0.37 tff(38,plain,
% 0.11/0.37 ((~p2(c12, f3(c13))) <=> (~p2(c12, f3(c13)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(39,axiom,(~p2(c12, f3(c13))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_p2_6')).
% 0.11/0.37 tff(40,plain,
% 0.11/0.37 (~p2(c12, f3(c13))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.11/0.37 tff(41,plain,
% 0.11/0.37 (((~![X17: $i, X16: $i, X15: $i] : (p11(f9(X17, X15), f9(X17, X16)) | p2(X17, f3(c13)) | (~p11(X15, X16)))) | (p2(c12, f3(c13)) | p11(f9(c12, c14), f9(c12, f8(c16, c14))) | (~p11(c14, f8(c16, c14))))) <=> ((~![X17: $i, X16: $i, X15: $i] : (p11(f9(X17, X15), f9(X17, X16)) | p2(X17, f3(c13)) | (~p11(X15, X16)))) | p2(c12, f3(c13)) | p11(f9(c12, c14), f9(c12, f8(c16, c14))) | (~p11(c14, f8(c16, c14))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(42,plain,
% 0.11/0.37 ((p11(f9(c12, c14), f9(c12, f8(c16, c14))) | p2(c12, f3(c13)) | (~p11(c14, f8(c16, c14)))) <=> (p2(c12, f3(c13)) | p11(f9(c12, c14), f9(c12, f8(c16, c14))) | (~p11(c14, f8(c16, c14))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(43,plain,
% 0.11/0.37 (((~![X17: $i, X16: $i, X15: $i] : (p11(f9(X17, X15), f9(X17, X16)) | p2(X17, f3(c13)) | (~p11(X15, X16)))) | (p11(f9(c12, c14), f9(c12, f8(c16, c14))) | p2(c12, f3(c13)) | (~p11(c14, f8(c16, c14))))) <=> ((~![X17: $i, X16: $i, X15: $i] : (p11(f9(X17, X15), f9(X17, X16)) | p2(X17, f3(c13)) | (~p11(X15, X16)))) | (p2(c12, f3(c13)) | p11(f9(c12, c14), f9(c12, f8(c16, c14))) | (~p11(c14, f8(c16, c14)))))),
% 0.11/0.38 inference(monotonicity,[status(thm)],[42])).
% 0.11/0.38 tff(44,plain,
% 0.11/0.38 (((~![X17: $i, X16: $i, X15: $i] : (p11(f9(X17, X15), f9(X17, X16)) | p2(X17, f3(c13)) | (~p11(X15, X16)))) | (p11(f9(c12, c14), f9(c12, f8(c16, c14))) | p2(c12, f3(c13)) | (~p11(c14, f8(c16, c14))))) <=> ((~![X17: $i, X16: $i, X15: $i] : (p11(f9(X17, X15), f9(X17, X16)) | p2(X17, f3(c13)) | (~p11(X15, X16)))) | p2(c12, f3(c13)) | p11(f9(c12, c14), f9(c12, f8(c16, c14))) | (~p11(c14, f8(c16, c14))))),
% 0.11/0.38 inference(transitivity,[status(thm)],[43, 41])).
% 0.11/0.38 tff(45,plain,
% 0.11/0.38 ((~![X17: $i, X16: $i, X15: $i] : (p11(f9(X17, X15), f9(X17, X16)) | p2(X17, f3(c13)) | (~p11(X15, X16)))) | (p11(f9(c12, c14), f9(c12, f8(c16, c14))) | p2(c12, f3(c13)) | (~p11(c14, f8(c16, c14))))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(46,plain,
% 0.11/0.38 ((~![X17: $i, X16: $i, X15: $i] : (p11(f9(X17, X15), f9(X17, X16)) | p2(X17, f3(c13)) | (~p11(X15, X16)))) | p2(c12, f3(c13)) | p11(f9(c12, c14), f9(c12, f8(c16, c14))) | (~p11(c14, f8(c16, c14)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.11/0.38 tff(47,plain,
% 0.11/0.38 (p11(f9(c12, c14), f9(c12, f8(c16, c14))) | (~p11(c14, f8(c16, c14)))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[46, 40, 37])).
% 0.11/0.38 tff(48,plain,
% 0.11/0.38 (p11(f9(c12, c14), f9(c12, f8(c16, c14)))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[47, 27])).
% 0.11/0.38 tff(49,plain,
% 0.11/0.38 (![X14: $i, X12: $i, X13: $i] : ((~p11(X14, X13)) | (~p11(X12, X14)) | p11(X12, X13)) <=> ![X14: $i, X12: $i, X13: $i] : ((~p11(X14, X13)) | (~p11(X12, X14)) | p11(X12, X13))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(50,plain,
% 0.11/0.38 (![X14: $i, X12: $i, X13: $i] : ((~p11(X14, X13)) | (~p11(X12, X14)) | p11(X12, X13)) <=> ![X14: $i, X12: $i, X13: $i] : ((~p11(X14, X13)) | (~p11(X12, X14)) | p11(X12, X13))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(51,plain,
% 0.11/0.38 (^[X14: $i, X12: $i, X13: $i] : trans(monotonicity(rewrite((p11(X12, X13) | (~p11(X12, X14))) <=> ((~p11(X12, X14)) | p11(X12, X13))), (((p11(X12, X13) | (~p11(X12, X14))) | (~p11(X14, X13))) <=> (((~p11(X12, X14)) | p11(X12, X13)) | (~p11(X14, X13))))), rewrite((((~p11(X12, X14)) | p11(X12, X13)) | (~p11(X14, X13))) <=> ((~p11(X14, X13)) | (~p11(X12, X14)) | p11(X12, X13))), (((p11(X12, X13) | (~p11(X12, X14))) | (~p11(X14, X13))) <=> ((~p11(X14, X13)) | (~p11(X12, X14)) | p11(X12, X13))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(52,plain,
% 0.11/0.38 (![X14: $i, X12: $i, X13: $i] : ((p11(X12, X13) | (~p11(X12, X14))) | (~p11(X14, X13))) <=> ![X14: $i, X12: $i, X13: $i] : ((~p11(X14, X13)) | (~p11(X12, X14)) | p11(X12, X13))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[51])).
% 0.11/0.38 tff(53,axiom,(![X14: $i, X12: $i, X13: $i] : ((p11(X12, X13) | (~p11(X12, X14))) | (~p11(X14, X13)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p11_16')).
% 0.11/0.38 tff(54,plain,
% 0.11/0.38 (![X14: $i, X12: $i, X13: $i] : ((~p11(X14, X13)) | (~p11(X12, X14)) | p11(X12, X13))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.11/0.38 tff(55,plain,
% 0.11/0.38 (![X14: $i, X12: $i, X13: $i] : ((~p11(X14, X13)) | (~p11(X12, X14)) | p11(X12, X13))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.11/0.38 tff(56,plain,(
% 0.11/0.38 ![X14: $i, X12: $i, X13: $i] : ((~p11(X14, X13)) | (~p11(X12, X14)) | p11(X12, X13))),
% 0.11/0.38 inference(skolemize,[status(sab)],[55])).
% 0.11/0.38 tff(57,plain,
% 0.11/0.38 (![X14: $i, X12: $i, X13: $i] : ((~p11(X14, X13)) | (~p11(X12, X14)) | p11(X12, X13))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[56, 49])).
% 0.11/0.38 tff(58,plain,
% 0.11/0.38 ((~p11(c18, f9(c12, f8(c16, c14)))) <=> (~p11(c18, f9(c12, f8(c16, c14))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(59,axiom,(~p11(c18, f9(c12, f8(c16, c14)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_p11_12')).
% 0.11/0.38 tff(60,plain,
% 0.11/0.38 (~p11(c18, f9(c12, f8(c16, c14)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.11/0.38 tff(61,plain,
% 0.11/0.38 (p11(c18, f9(c12, c14)) <=> p11(c18, f9(c12, c14))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(62,axiom,(p11(c18, f9(c12, c14))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p11_7')).
% 0.11/0.38 tff(63,plain,
% 0.11/0.38 (p11(c18, f9(c12, c14))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.11/0.38 tff(64,plain,
% 0.11/0.38 (((~![X14: $i, X12: $i, X13: $i] : ((~p11(X14, X13)) | (~p11(X12, X14)) | p11(X12, X13))) | (p11(c18, f9(c12, f8(c16, c14))) | (~p11(f9(c12, c14), f9(c12, f8(c16, c14)))) | (~p11(c18, f9(c12, c14))))) <=> ((~![X14: $i, X12: $i, X13: $i] : ((~p11(X14, X13)) | (~p11(X12, X14)) | p11(X12, X13))) | p11(c18, f9(c12, f8(c16, c14))) | (~p11(f9(c12, c14), f9(c12, f8(c16, c14)))) | (~p11(c18, f9(c12, c14))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(65,plain,
% 0.11/0.38 (((~p11(f9(c12, c14), f9(c12, f8(c16, c14)))) | (~p11(c18, f9(c12, c14))) | p11(c18, f9(c12, f8(c16, c14)))) <=> (p11(c18, f9(c12, f8(c16, c14))) | (~p11(f9(c12, c14), f9(c12, f8(c16, c14)))) | (~p11(c18, f9(c12, c14))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(66,plain,
% 0.11/0.38 (((~![X14: $i, X12: $i, X13: $i] : ((~p11(X14, X13)) | (~p11(X12, X14)) | p11(X12, X13))) | ((~p11(f9(c12, c14), f9(c12, f8(c16, c14)))) | (~p11(c18, f9(c12, c14))) | p11(c18, f9(c12, f8(c16, c14))))) <=> ((~![X14: $i, X12: $i, X13: $i] : ((~p11(X14, X13)) | (~p11(X12, X14)) | p11(X12, X13))) | (p11(c18, f9(c12, f8(c16, c14))) | (~p11(f9(c12, c14), f9(c12, f8(c16, c14)))) | (~p11(c18, f9(c12, c14)))))),
% 0.11/0.38 inference(monotonicity,[status(thm)],[65])).
% 0.11/0.38 tff(67,plain,
% 0.11/0.38 (((~![X14: $i, X12: $i, X13: $i] : ((~p11(X14, X13)) | (~p11(X12, X14)) | p11(X12, X13))) | ((~p11(f9(c12, c14), f9(c12, f8(c16, c14)))) | (~p11(c18, f9(c12, c14))) | p11(c18, f9(c12, f8(c16, c14))))) <=> ((~![X14: $i, X12: $i, X13: $i] : ((~p11(X14, X13)) | (~p11(X12, X14)) | p11(X12, X13))) | p11(c18, f9(c12, f8(c16, c14))) | (~p11(f9(c12, c14), f9(c12, f8(c16, c14)))) | (~p11(c18, f9(c12, c14))))),
% 0.11/0.38 inference(transitivity,[status(thm)],[66, 64])).
% 0.11/0.38 tff(68,plain,
% 0.11/0.38 ((~![X14: $i, X12: $i, X13: $i] : ((~p11(X14, X13)) | (~p11(X12, X14)) | p11(X12, X13))) | ((~p11(f9(c12, c14), f9(c12, f8(c16, c14)))) | (~p11(c18, f9(c12, c14))) | p11(c18, f9(c12, f8(c16, c14))))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(69,plain,
% 0.11/0.38 ((~![X14: $i, X12: $i, X13: $i] : ((~p11(X14, X13)) | (~p11(X12, X14)) | p11(X12, X13))) | p11(c18, f9(c12, f8(c16, c14))) | (~p11(f9(c12, c14), f9(c12, f8(c16, c14)))) | (~p11(c18, f9(c12, c14)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.11/0.38 tff(70,plain,
% 0.11/0.38 ($false),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[69, 63, 60, 57, 48])).
% 0.11/0.38 % SZS output end Proof
% 0.11/0.38 % E exiting
%------------------------------------------------------------------------------