%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN601-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:39:40 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYN601-1 : TPTP v9.0.0. Released v2.5.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 12:38:26 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.20/0.39 % SZS status Unsatisfiable
% 0.20/0.39 % SZS output start Proof
% 0.20/0.39 tff(p2_type, type, (
% 0.20/0.39 p2: ( $i * $i ) > $o)).
% 0.20/0.39 tff(c21_type, type, (
% 0.20/0.39 c21: $i)).
% 0.20/0.39 tff(p10_type, type, (
% 0.20/0.39 p10: ( $i * $i ) > $o)).
% 0.20/0.39 tff(f11_type, type, (
% 0.20/0.39 f11: ( $i * $i * $i ) > $i)).
% 0.20/0.39 tff(c25_type, type, (
% 0.20/0.39 c25: $i)).
% 0.20/0.39 tff(c24_type, type, (
% 0.20/0.39 c24: $i)).
% 0.20/0.39 tff(f13_type, type, (
% 0.20/0.39 f13: ( $i * $i ) > $i)).
% 0.20/0.39 tff(f14_type, type, (
% 0.20/0.39 f14: ( $i * $i ) > $i)).
% 0.20/0.39 tff(c23_type, type, (
% 0.20/0.39 c23: $i)).
% 0.20/0.39 tff(f4_type, type, (
% 0.20/0.39 f4: $i > $i)).
% 0.20/0.39 tff(f15_type, type, (
% 0.20/0.39 f15: $i > $i)).
% 0.20/0.39 tff(c22_type, type, (
% 0.20/0.39 c22: $i)).
% 0.20/0.39 tff(p3_type, type, (
% 0.20/0.39 p3: ( $i * $i ) > $o)).
% 0.20/0.39 tff(p12_type, type, (
% 0.20/0.39 p12: ( $i * $i ) > $o)).
% 0.20/0.39 tff(p9_type, type, (
% 0.20/0.39 p9: ( $i * $i ) > $o)).
% 0.20/0.39 tff(p19_type, type, (
% 0.20/0.39 p19: ( $i * $i ) > $o)).
% 0.20/0.39 tff(1,assumption,(~p2(c21, c21)), introduced(assumption)).
% 0.20/0.39 tff(2,plain,
% 0.20/0.39 (^[X30: $i] : refl(p2(X30, X30) <=> p2(X30, X30))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(3,plain,
% 0.20/0.39 (![X30: $i] : p2(X30, X30) <=> ![X30: $i] : p2(X30, X30)),
% 0.20/0.39 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.39 tff(4,plain,
% 0.20/0.39 (![X30: $i] : p2(X30, X30) <=> ![X30: $i] : p2(X30, X30)),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(5,axiom,(![X30: $i] : p2(X30, X30)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_4')).
% 0.20/0.39 tff(6,plain,
% 0.20/0.39 (![X30: $i] : p2(X30, X30)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.39 tff(7,plain,(
% 0.20/0.39 ![X30: $i] : p2(X30, X30)),
% 0.20/0.39 inference(skolemize,[status(sab)],[6])).
% 0.20/0.39 tff(8,plain,
% 0.20/0.39 (![X30: $i] : p2(X30, X30)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.39 tff(9,plain,
% 0.20/0.39 ((~![X30: $i] : p2(X30, X30)) | p2(c21, c21)),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(10,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.20/0.39 tff(11,plain,(p2(c21, c21)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(12,assumption,(~p10(c25, c25)), introduced(assumption)).
% 0.20/0.39 tff(13,plain,
% 0.20/0.39 (^[X0: $i] : refl(p10(X0, X0) <=> p10(X0, X0))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(14,plain,
% 0.20/0.39 (![X0: $i] : p10(X0, X0) <=> ![X0: $i] : p10(X0, X0)),
% 0.20/0.39 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.39 tff(15,plain,
% 0.20/0.39 (![X0: $i] : p10(X0, X0) <=> ![X0: $i] : p10(X0, X0)),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(16,axiom,(![X0: $i] : p10(X0, X0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p10_1')).
% 0.20/0.39 tff(17,plain,
% 0.20/0.39 (![X0: $i] : p10(X0, X0)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.20/0.39 tff(18,plain,(
% 0.20/0.39 ![X0: $i] : p10(X0, X0)),
% 0.20/0.39 inference(skolemize,[status(sab)],[17])).
% 0.20/0.39 tff(19,plain,
% 0.20/0.39 (![X0: $i] : p10(X0, X0)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.20/0.39 tff(20,plain,
% 0.20/0.39 ((~![X0: $i] : p10(X0, X0)) | p10(c25, c25)),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(21,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[20, 19, 12])).
% 0.20/0.39 tff(22,plain,(p10(c25, c25)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(23,assumption,(~p3(f15(c21), f15(c21))), introduced(assumption)).
% 0.20/0.39 tff(24,plain,
% 0.20/0.39 (^[X37: $i] : refl(p3(X37, X37) <=> p3(X37, X37))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(25,plain,
% 0.20/0.39 (![X37: $i] : p3(X37, X37) <=> ![X37: $i] : p3(X37, X37)),
% 0.20/0.39 inference(quant_intro,[status(thm)],[24])).
% 0.20/0.39 tff(26,plain,
% 0.20/0.39 (![X37: $i] : p3(X37, X37) <=> ![X37: $i] : p3(X37, X37)),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(27,axiom,(![X37: $i] : p3(X37, X37)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p3_3')).
% 0.20/0.39 tff(28,plain,
% 0.20/0.39 (![X37: $i] : p3(X37, X37)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.20/0.39 tff(29,plain,(
% 0.20/0.39 ![X37: $i] : p3(X37, X37)),
% 0.20/0.39 inference(skolemize,[status(sab)],[28])).
% 0.20/0.39 tff(30,plain,
% 0.20/0.39 (![X37: $i] : p3(X37, X37)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.20/0.39 tff(31,plain,
% 0.20/0.39 ((~![X37: $i] : p3(X37, X37)) | p3(f15(c21), f15(c21))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(32,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[31, 30, 23])).
% 0.20/0.39 tff(33,plain,(p3(f15(c21), f15(c21))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(34,assumption,(~p3(f4(c21), f4(c21))), introduced(assumption)).
% 0.20/0.39 tff(35,plain,
% 0.20/0.39 ((~![X37: $i] : p3(X37, X37)) | p3(f4(c21), f4(c21))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(36,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[35, 30, 34])).
% 0.20/0.39 tff(37,plain,(p3(f4(c21), f4(c21))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(38,plain,
% 0.20/0.39 (^[X14: $i, X17: $i, X16: $i, X15: $i] : refl(((~p3(X15, X17)) | (~p3(X14, X16)) | p12(f14(X14, X15), f14(X16, X17))) <=> ((~p3(X15, X17)) | (~p3(X14, X16)) | p12(f14(X14, X15), f14(X16, X17))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(39,plain,
% 0.20/0.39 (![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p3(X15, X17)) | (~p3(X14, X16)) | p12(f14(X14, X15), f14(X16, X17))) <=> ![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p3(X15, X17)) | (~p3(X14, X16)) | p12(f14(X14, X15), f14(X16, X17)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[38])).
% 0.20/0.39 tff(40,plain,
% 0.20/0.39 (![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p3(X15, X17)) | (~p3(X14, X16)) | p12(f14(X14, X15), f14(X16, X17))) <=> ![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p3(X15, X17)) | (~p3(X14, X16)) | p12(f14(X14, X15), f14(X16, X17)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(41,plain,
% 0.20/0.39 (^[X14: $i, X17: $i, X16: $i, X15: $i] : trans(monotonicity(rewrite((p12(f14(X14, X15), f14(X16, X17)) | (~p3(X14, X16))) <=> ((~p3(X14, X16)) | p12(f14(X14, X15), f14(X16, X17)))), (((p12(f14(X14, X15), f14(X16, X17)) | (~p3(X14, X16))) | (~p3(X15, X17))) <=> (((~p3(X14, X16)) | p12(f14(X14, X15), f14(X16, X17))) | (~p3(X15, X17))))), rewrite((((~p3(X14, X16)) | p12(f14(X14, X15), f14(X16, X17))) | (~p3(X15, X17))) <=> ((~p3(X15, X17)) | (~p3(X14, X16)) | p12(f14(X14, X15), f14(X16, X17)))), (((p12(f14(X14, X15), f14(X16, X17)) | (~p3(X14, X16))) | (~p3(X15, X17))) <=> ((~p3(X15, X17)) | (~p3(X14, X16)) | p12(f14(X14, X15), f14(X16, X17)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(42,plain,
% 0.20/0.39 (![X14: $i, X17: $i, X16: $i, X15: $i] : ((p12(f14(X14, X15), f14(X16, X17)) | (~p3(X14, X16))) | (~p3(X15, X17))) <=> ![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p3(X15, X17)) | (~p3(X14, X16)) | p12(f14(X14, X15), f14(X16, X17)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[41])).
% 0.20/0.39 tff(43,axiom,(![X14: $i, X17: $i, X16: $i, X15: $i] : ((p12(f14(X14, X15), f14(X16, X17)) | (~p3(X14, X16))) | (~p3(X15, X17)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p12_27')).
% 0.20/0.39 tff(44,plain,
% 0.20/0.39 (![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p3(X15, X17)) | (~p3(X14, X16)) | p12(f14(X14, X15), f14(X16, X17)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.20/0.39 tff(45,plain,
% 0.20/0.39 (![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p3(X15, X17)) | (~p3(X14, X16)) | p12(f14(X14, X15), f14(X16, X17)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.20/0.39 tff(46,plain,(
% 0.20/0.39 ![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p3(X15, X17)) | (~p3(X14, X16)) | p12(f14(X14, X15), f14(X16, X17)))),
% 0.20/0.39 inference(skolemize,[status(sab)],[45])).
% 0.20/0.39 tff(47,plain,
% 0.20/0.39 (![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p3(X15, X17)) | (~p3(X14, X16)) | p12(f14(X14, X15), f14(X16, X17)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[46, 39])).
% 0.20/0.39 tff(48,plain,
% 0.20/0.39 (p3(c22, c23) <=> p3(c22, c23)),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(49,axiom,(p3(c22, c23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p3_7')).
% 0.20/0.39 tff(50,plain,
% 0.20/0.39 (p3(c22, c23)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.20/0.39 tff(51,plain,
% 0.20/0.39 (((~![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p3(X15, X17)) | (~p3(X14, X16)) | p12(f14(X14, X15), f14(X16, X17)))) | ((~p3(c22, c23)) | (~p3(f4(c21), f4(c21))) | p12(f14(f4(c21), c22), f14(f4(c21), c23)))) <=> ((~![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p3(X15, X17)) | (~p3(X14, X16)) | p12(f14(X14, X15), f14(X16, X17)))) | (~p3(c22, c23)) | (~p3(f4(c21), f4(c21))) | p12(f14(f4(c21), c22), f14(f4(c21), c23)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(52,plain,
% 0.20/0.39 ((~![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p3(X15, X17)) | (~p3(X14, X16)) | p12(f14(X14, X15), f14(X16, X17)))) | ((~p3(c22, c23)) | (~p3(f4(c21), f4(c21))) | p12(f14(f4(c21), c22), f14(f4(c21), c23)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(53,plain,
% 0.20/0.39 ((~![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p3(X15, X17)) | (~p3(X14, X16)) | p12(f14(X14, X15), f14(X16, X17)))) | (~p3(c22, c23)) | (~p3(f4(c21), f4(c21))) | p12(f14(f4(c21), c22), f14(f4(c21), c23))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.20/0.39 tff(54,plain,
% 0.20/0.39 ((~p3(f4(c21), f4(c21))) | p12(f14(f4(c21), c22), f14(f4(c21), c23))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[53, 50, 47])).
% 0.20/0.39 tff(55,plain,
% 0.20/0.39 (p12(f14(f4(c21), c22), f14(f4(c21), c23))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[54, 37])).
% 0.20/0.39 tff(56,plain,
% 0.20/0.39 (^[X35: $i, X34: $i, X36: $i, X33: $i] : refl(((~p3(X33, X35)) | (~p12(X34, X36)) | p2(f13(X33, X34), f13(X35, X36))) <=> ((~p3(X33, X35)) | (~p12(X34, X36)) | p2(f13(X33, X34), f13(X35, X36))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(57,plain,
% 0.20/0.39 (![X35: $i, X34: $i, X36: $i, X33: $i] : ((~p3(X33, X35)) | (~p12(X34, X36)) | p2(f13(X33, X34), f13(X35, X36))) <=> ![X35: $i, X34: $i, X36: $i, X33: $i] : ((~p3(X33, X35)) | (~p12(X34, X36)) | p2(f13(X33, X34), f13(X35, X36)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[56])).
% 0.20/0.40 tff(58,plain,
% 0.20/0.40 (![X35: $i, X34: $i, X36: $i, X33: $i] : ((~p3(X33, X35)) | (~p12(X34, X36)) | p2(f13(X33, X34), f13(X35, X36))) <=> ![X35: $i, X34: $i, X36: $i, X33: $i] : ((~p3(X33, X35)) | (~p12(X34, X36)) | p2(f13(X33, X34), f13(X35, X36)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(59,plain,
% 0.20/0.40 (^[X35: $i, X34: $i, X36: $i, X33: $i] : trans(monotonicity(rewrite((p2(f13(X33, X34), f13(X35, X36)) | (~p12(X34, X36))) <=> ((~p12(X34, X36)) | p2(f13(X33, X34), f13(X35, X36)))), (((p2(f13(X33, X34), f13(X35, X36)) | (~p12(X34, X36))) | (~p3(X33, X35))) <=> (((~p12(X34, X36)) | p2(f13(X33, X34), f13(X35, X36))) | (~p3(X33, X35))))), rewrite((((~p12(X34, X36)) | p2(f13(X33, X34), f13(X35, X36))) | (~p3(X33, X35))) <=> ((~p3(X33, X35)) | (~p12(X34, X36)) | p2(f13(X33, X34), f13(X35, X36)))), (((p2(f13(X33, X34), f13(X35, X36)) | (~p12(X34, X36))) | (~p3(X33, X35))) <=> ((~p3(X33, X35)) | (~p12(X34, X36)) | p2(f13(X33, X34), f13(X35, X36)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(60,plain,
% 0.20/0.40 (![X35: $i, X34: $i, X36: $i, X33: $i] : ((p2(f13(X33, X34), f13(X35, X36)) | (~p12(X34, X36))) | (~p3(X33, X35))) <=> ![X35: $i, X34: $i, X36: $i, X33: $i] : ((~p3(X33, X35)) | (~p12(X34, X36)) | p2(f13(X33, X34), f13(X35, X36)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[59])).
% 0.20/0.40 tff(61,axiom,(![X35: $i, X34: $i, X36: $i, X33: $i] : ((p2(f13(X33, X34), f13(X35, X36)) | (~p12(X34, X36))) | (~p3(X33, X35)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_28')).
% 0.20/0.40 tff(62,plain,
% 0.20/0.40 (![X35: $i, X34: $i, X36: $i, X33: $i] : ((~p3(X33, X35)) | (~p12(X34, X36)) | p2(f13(X33, X34), f13(X35, X36)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.20/0.40 tff(63,plain,
% 0.20/0.40 (![X35: $i, X34: $i, X36: $i, X33: $i] : ((~p3(X33, X35)) | (~p12(X34, X36)) | p2(f13(X33, X34), f13(X35, X36)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.20/0.40 tff(64,plain,(
% 0.20/0.40 ![X35: $i, X34: $i, X36: $i, X33: $i] : ((~p3(X33, X35)) | (~p12(X34, X36)) | p2(f13(X33, X34), f13(X35, X36)))),
% 0.20/0.40 inference(skolemize,[status(sab)],[63])).
% 0.20/0.40 tff(65,plain,
% 0.20/0.40 (![X35: $i, X34: $i, X36: $i, X33: $i] : ((~p3(X33, X35)) | (~p12(X34, X36)) | p2(f13(X33, X34), f13(X35, X36)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[64, 57])).
% 0.20/0.40 tff(66,plain,
% 0.20/0.40 (((~![X35: $i, X34: $i, X36: $i, X33: $i] : ((~p3(X33, X35)) | (~p12(X34, X36)) | p2(f13(X33, X34), f13(X35, X36)))) | ((~p3(f15(c21), f15(c21))) | (~p12(f14(f4(c21), c22), f14(f4(c21), c23))) | p2(f13(f15(c21), f14(f4(c21), c22)), f13(f15(c21), f14(f4(c21), c23))))) <=> ((~![X35: $i, X34: $i, X36: $i, X33: $i] : ((~p3(X33, X35)) | (~p12(X34, X36)) | p2(f13(X33, X34), f13(X35, X36)))) | (~p3(f15(c21), f15(c21))) | (~p12(f14(f4(c21), c22), f14(f4(c21), c23))) | p2(f13(f15(c21), f14(f4(c21), c22)), f13(f15(c21), f14(f4(c21), c23))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(67,plain,
% 0.20/0.40 ((~![X35: $i, X34: $i, X36: $i, X33: $i] : ((~p3(X33, X35)) | (~p12(X34, X36)) | p2(f13(X33, X34), f13(X35, X36)))) | ((~p3(f15(c21), f15(c21))) | (~p12(f14(f4(c21), c22), f14(f4(c21), c23))) | p2(f13(f15(c21), f14(f4(c21), c22)), f13(f15(c21), f14(f4(c21), c23))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(68,plain,
% 0.20/0.40 ((~![X35: $i, X34: $i, X36: $i, X33: $i] : ((~p3(X33, X35)) | (~p12(X34, X36)) | p2(f13(X33, X34), f13(X35, X36)))) | (~p3(f15(c21), f15(c21))) | (~p12(f14(f4(c21), c22), f14(f4(c21), c23))) | p2(f13(f15(c21), f14(f4(c21), c22)), f13(f15(c21), f14(f4(c21), c23)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.20/0.40 tff(69,plain,
% 0.20/0.40 ((~p3(f15(c21), f15(c21))) | (~p12(f14(f4(c21), c22), f14(f4(c21), c23))) | p2(f13(f15(c21), f14(f4(c21), c22)), f13(f15(c21), f14(f4(c21), c23)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[68, 65])).
% 0.20/0.40 tff(70,plain,
% 0.20/0.40 ((~p3(f15(c21), f15(c21))) | p2(f13(f15(c21), f14(f4(c21), c22)), f13(f15(c21), f14(f4(c21), c23)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[69, 55])).
% 0.20/0.40 tff(71,plain,
% 0.20/0.40 (p2(f13(f15(c21), f14(f4(c21), c22)), f13(f15(c21), f14(f4(c21), c23)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[70, 33])).
% 0.20/0.40 tff(72,assumption,(~p9(c24, c24)), introduced(assumption)).
% 0.20/0.40 tff(73,plain,
% 0.20/0.40 (^[X52: $i] : refl(p9(X52, X52) <=> p9(X52, X52))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(74,plain,
% 0.20/0.40 (![X52: $i] : p9(X52, X52) <=> ![X52: $i] : p9(X52, X52)),
% 0.20/0.40 inference(quant_intro,[status(thm)],[73])).
% 0.20/0.40 tff(75,plain,
% 0.20/0.40 (![X52: $i] : p9(X52, X52) <=> ![X52: $i] : p9(X52, X52)),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(76,axiom,(![X52: $i] : p9(X52, X52)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p9_2')).
% 0.20/0.40 tff(77,plain,
% 0.20/0.40 (![X52: $i] : p9(X52, X52)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.20/0.40 tff(78,plain,(
% 0.20/0.40 ![X52: $i] : p9(X52, X52)),
% 0.20/0.40 inference(skolemize,[status(sab)],[77])).
% 0.20/0.40 tff(79,plain,
% 0.20/0.40 (![X52: $i] : p9(X52, X52)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.20/0.40 tff(80,plain,
% 0.20/0.40 ((~![X52: $i] : p9(X52, X52)) | p9(c24, c24)),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(81,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[80, 79, 72])).
% 0.20/0.40 tff(82,plain,(p9(c24, c24)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(83,plain,
% 0.20/0.40 (^[X6: $i, X4: $i, X3: $i, X7: $i, X5: $i, X8: $i] : refl(((~p10(X5, X8)) | (~p9(X4, X7)) | (~p2(X3, X6)) | p10(f11(X3, X4, X5), f11(X6, X7, X8))) <=> ((~p10(X5, X8)) | (~p9(X4, X7)) | (~p2(X3, X6)) | p10(f11(X3, X4, X5), f11(X6, X7, X8))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(84,plain,
% 0.20/0.40 (![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i, X8: $i] : ((~p10(X5, X8)) | (~p9(X4, X7)) | (~p2(X3, X6)) | p10(f11(X3, X4, X5), f11(X6, X7, X8))) <=> ![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i, X8: $i] : ((~p10(X5, X8)) | (~p9(X4, X7)) | (~p2(X3, X6)) | p10(f11(X3, X4, X5), f11(X6, X7, X8)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[83])).
% 0.20/0.40 tff(85,plain,
% 0.20/0.40 (![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i, X8: $i] : ((~p10(X5, X8)) | (~p9(X4, X7)) | (~p2(X3, X6)) | p10(f11(X3, X4, X5), f11(X6, X7, X8))) <=> ![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i, X8: $i] : ((~p10(X5, X8)) | (~p9(X4, X7)) | (~p2(X3, X6)) | p10(f11(X3, X4, X5), f11(X6, X7, X8)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(86,plain,
% 0.20/0.40 (^[X6: $i, X4: $i, X3: $i, X7: $i, X5: $i, X8: $i] : trans(monotonicity(trans(monotonicity(rewrite((p10(f11(X3, X4, X5), f11(X6, X7, X8)) | (~p2(X3, X6))) <=> ((~p2(X3, X6)) | p10(f11(X3, X4, X5), f11(X6, X7, X8)))), (((p10(f11(X3, X4, X5), f11(X6, X7, X8)) | (~p2(X3, X6))) | (~p9(X4, X7))) <=> (((~p2(X3, X6)) | p10(f11(X3, X4, X5), f11(X6, X7, X8))) | (~p9(X4, X7))))), rewrite((((~p2(X3, X6)) | p10(f11(X3, X4, X5), f11(X6, X7, X8))) | (~p9(X4, X7))) <=> ((~p9(X4, X7)) | (~p2(X3, X6)) | p10(f11(X3, X4, X5), f11(X6, X7, X8)))), (((p10(f11(X3, X4, X5), f11(X6, X7, X8)) | (~p2(X3, X6))) | (~p9(X4, X7))) <=> ((~p9(X4, X7)) | (~p2(X3, X6)) | p10(f11(X3, X4, X5), f11(X6, X7, X8))))), ((((p10(f11(X3, X4, X5), f11(X6, X7, X8)) | (~p2(X3, X6))) | (~p9(X4, X7))) | (~p10(X5, X8))) <=> (((~p9(X4, X7)) | (~p2(X3, X6)) | p10(f11(X3, X4, X5), f11(X6, X7, X8))) | (~p10(X5, X8))))), rewrite((((~p9(X4, X7)) | (~p2(X3, X6)) | p10(f11(X3, X4, X5), f11(X6, X7, X8))) | (~p10(X5, X8))) <=> ((~p10(X5, X8)) | (~p9(X4, X7)) | (~p2(X3, X6)) | p10(f11(X3, X4, X5), f11(X6, X7, X8)))), ((((p10(f11(X3, X4, X5), f11(X6, X7, X8)) | (~p2(X3, X6))) | (~p9(X4, X7))) | (~p10(X5, X8))) <=> ((~p10(X5, X8)) | (~p9(X4, X7)) | (~p2(X3, X6)) | p10(f11(X3, X4, X5), f11(X6, X7, X8)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(87,plain,
% 0.20/0.40 (![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i, X8: $i] : (((p10(f11(X3, X4, X5), f11(X6, X7, X8)) | (~p2(X3, X6))) | (~p9(X4, X7))) | (~p10(X5, X8))) <=> ![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i, X8: $i] : ((~p10(X5, X8)) | (~p9(X4, X7)) | (~p2(X3, X6)) | p10(f11(X3, X4, X5), f11(X6, X7, X8)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[86])).
% 0.20/0.40 tff(88,axiom,(![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i, X8: $i] : (((p10(f11(X3, X4, X5), f11(X6, X7, X8)) | (~p2(X3, X6))) | (~p9(X4, X7))) | (~p10(X5, X8)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p10_30')).
% 0.20/0.40 tff(89,plain,
% 0.20/0.40 (![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i, X8: $i] : ((~p10(X5, X8)) | (~p9(X4, X7)) | (~p2(X3, X6)) | p10(f11(X3, X4, X5), f11(X6, X7, X8)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.20/0.40 tff(90,plain,
% 0.20/0.40 (![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i, X8: $i] : ((~p10(X5, X8)) | (~p9(X4, X7)) | (~p2(X3, X6)) | p10(f11(X3, X4, X5), f11(X6, X7, X8)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.20/0.40 tff(91,plain,(
% 0.20/0.40 ![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i, X8: $i] : ((~p10(X5, X8)) | (~p9(X4, X7)) | (~p2(X3, X6)) | p10(f11(X3, X4, X5), f11(X6, X7, X8)))),
% 0.20/0.40 inference(skolemize,[status(sab)],[90])).
% 0.20/0.40 tff(92,plain,
% 0.20/0.40 (![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i, X8: $i] : ((~p10(X5, X8)) | (~p9(X4, X7)) | (~p2(X3, X6)) | p10(f11(X3, X4, X5), f11(X6, X7, X8)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[91, 84])).
% 0.20/0.40 tff(93,plain,
% 0.20/0.40 (((~![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i, X8: $i] : ((~p10(X5, X8)) | (~p9(X4, X7)) | (~p2(X3, X6)) | p10(f11(X3, X4, X5), f11(X6, X7, X8)))) | ((~p10(c25, c25)) | (~p9(c24, c24)) | (~p2(f13(f15(c21), f14(f4(c21), c22)), f13(f15(c21), f14(f4(c21), c23)))) | p10(f11(f13(f15(c21), f14(f4(c21), c22)), c24, c25), f11(f13(f15(c21), f14(f4(c21), c23)), c24, c25)))) <=> ((~![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i, X8: $i] : ((~p10(X5, X8)) | (~p9(X4, X7)) | (~p2(X3, X6)) | p10(f11(X3, X4, X5), f11(X6, X7, X8)))) | (~p10(c25, c25)) | (~p9(c24, c24)) | (~p2(f13(f15(c21), f14(f4(c21), c22)), f13(f15(c21), f14(f4(c21), c23)))) | p10(f11(f13(f15(c21), f14(f4(c21), c22)), c24, c25), f11(f13(f15(c21), f14(f4(c21), c23)), c24, c25)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(94,plain,
% 0.20/0.40 ((~![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i, X8: $i] : ((~p10(X5, X8)) | (~p9(X4, X7)) | (~p2(X3, X6)) | p10(f11(X3, X4, X5), f11(X6, X7, X8)))) | ((~p10(c25, c25)) | (~p9(c24, c24)) | (~p2(f13(f15(c21), f14(f4(c21), c22)), f13(f15(c21), f14(f4(c21), c23)))) | p10(f11(f13(f15(c21), f14(f4(c21), c22)), c24, c25), f11(f13(f15(c21), f14(f4(c21), c23)), c24, c25)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(95,plain,
% 0.20/0.40 ((~![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i, X8: $i] : ((~p10(X5, X8)) | (~p9(X4, X7)) | (~p2(X3, X6)) | p10(f11(X3, X4, X5), f11(X6, X7, X8)))) | (~p10(c25, c25)) | (~p9(c24, c24)) | (~p2(f13(f15(c21), f14(f4(c21), c22)), f13(f15(c21), f14(f4(c21), c23)))) | p10(f11(f13(f15(c21), f14(f4(c21), c22)), c24, c25), f11(f13(f15(c21), f14(f4(c21), c23)), c24, c25))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.20/0.40 tff(96,plain,
% 0.20/0.40 ((~p10(c25, c25)) | (~p9(c24, c24)) | (~p2(f13(f15(c21), f14(f4(c21), c22)), f13(f15(c21), f14(f4(c21), c23)))) | p10(f11(f13(f15(c21), f14(f4(c21), c22)), c24, c25), f11(f13(f15(c21), f14(f4(c21), c23)), c24, c25))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[95, 92])).
% 0.20/0.40 tff(97,plain,
% 0.20/0.40 ((~p10(c25, c25)) | (~p2(f13(f15(c21), f14(f4(c21), c22)), f13(f15(c21), f14(f4(c21), c23)))) | p10(f11(f13(f15(c21), f14(f4(c21), c22)), c24, c25), f11(f13(f15(c21), f14(f4(c21), c23)), c24, c25))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[96, 82])).
% 0.20/0.40 tff(98,plain,
% 0.20/0.40 (p10(f11(f13(f15(c21), f14(f4(c21), c22)), c24, c25), f11(f13(f15(c21), f14(f4(c21), c23)), c24, c25))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[97, 71, 22])).
% 0.20/0.40 tff(99,plain,
% 0.20/0.40 (^[X27: $i, X29: $i, X28: $i, X26: $i] : refl(((~p10(X28, X27)) | (~p2(X29, X26)) | (~p19(X29, X28)) | p19(X26, X27)) <=> ((~p10(X28, X27)) | (~p2(X29, X26)) | (~p19(X29, X28)) | p19(X26, X27)))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(100,plain,
% 0.20/0.40 (![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p10(X28, X27)) | (~p2(X29, X26)) | (~p19(X29, X28)) | p19(X26, X27)) <=> ![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p10(X28, X27)) | (~p2(X29, X26)) | (~p19(X29, X28)) | p19(X26, X27))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[99])).
% 0.20/0.40 tff(101,plain,
% 0.20/0.40 (![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p10(X28, X27)) | (~p2(X29, X26)) | (~p19(X29, X28)) | p19(X26, X27)) <=> ![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p10(X28, X27)) | (~p2(X29, X26)) | (~p19(X29, X28)) | p19(X26, X27))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(102,plain,
% 0.20/0.40 (^[X27: $i, X29: $i, X28: $i, X26: $i] : trans(monotonicity(trans(monotonicity(rewrite((p19(X26, X27) | (~p19(X29, X28))) <=> ((~p19(X29, X28)) | p19(X26, X27))), (((p19(X26, X27) | (~p19(X29, X28))) | (~p2(X29, X26))) <=> (((~p19(X29, X28)) | p19(X26, X27)) | (~p2(X29, X26))))), rewrite((((~p19(X29, X28)) | p19(X26, X27)) | (~p2(X29, X26))) <=> ((~p2(X29, X26)) | (~p19(X29, X28)) | p19(X26, X27))), (((p19(X26, X27) | (~p19(X29, X28))) | (~p2(X29, X26))) <=> ((~p2(X29, X26)) | (~p19(X29, X28)) | p19(X26, X27)))), ((((p19(X26, X27) | (~p19(X29, X28))) | (~p2(X29, X26))) | (~p10(X28, X27))) <=> (((~p2(X29, X26)) | (~p19(X29, X28)) | p19(X26, X27)) | (~p10(X28, X27))))), rewrite((((~p2(X29, X26)) | (~p19(X29, X28)) | p19(X26, X27)) | (~p10(X28, X27))) <=> ((~p10(X28, X27)) | (~p2(X29, X26)) | (~p19(X29, X28)) | p19(X26, X27))), ((((p19(X26, X27) | (~p19(X29, X28))) | (~p2(X29, X26))) | (~p10(X28, X27))) <=> ((~p10(X28, X27)) | (~p2(X29, X26)) | (~p19(X29, X28)) | p19(X26, X27))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(103,plain,
% 0.20/0.40 (![X27: $i, X29: $i, X28: $i, X26: $i] : (((p19(X26, X27) | (~p19(X29, X28))) | (~p2(X29, X26))) | (~p10(X28, X27))) <=> ![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p10(X28, X27)) | (~p2(X29, X26)) | (~p19(X29, X28)) | p19(X26, X27))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[102])).
% 0.20/0.40 tff(104,axiom,(![X27: $i, X29: $i, X28: $i, X26: $i] : (((p19(X26, X27) | (~p19(X29, X28))) | (~p2(X29, X26))) | (~p10(X28, X27)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p19_24')).
% 0.20/0.40 tff(105,plain,
% 0.20/0.40 (![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p10(X28, X27)) | (~p2(X29, X26)) | (~p19(X29, X28)) | p19(X26, X27))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.20/0.40 tff(106,plain,
% 0.20/0.40 (![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p10(X28, X27)) | (~p2(X29, X26)) | (~p19(X29, X28)) | p19(X26, X27))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[105, 101])).
% 0.20/0.40 tff(107,plain,(
% 0.20/0.40 ![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p10(X28, X27)) | (~p2(X29, X26)) | (~p19(X29, X28)) | p19(X26, X27))),
% 0.20/0.40 inference(skolemize,[status(sab)],[106])).
% 0.20/0.40 tff(108,plain,
% 0.20/0.40 (![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p10(X28, X27)) | (~p2(X29, X26)) | (~p19(X29, X28)) | p19(X26, X27))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[107, 100])).
% 0.20/0.40 tff(109,plain,
% 0.20/0.40 ((~p19(c21, f11(f13(f15(c21), f14(f4(c21), c23)), c24, c25))) <=> (~p19(c21, f11(f13(f15(c21), f14(f4(c21), c23)), c24, c25)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(110,axiom,(~p19(c21, f11(f13(f15(c21), f14(f4(c21), c23)), c24, c25))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_p19_23')).
% 0.20/0.40 tff(111,plain,
% 0.20/0.40 (~p19(c21, f11(f13(f15(c21), f14(f4(c21), c23)), c24, c25))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.20/0.40 tff(112,plain,
% 0.20/0.40 (p19(c21, f11(f13(f15(c21), f14(f4(c21), c22)), c24, c25)) <=> p19(c21, f11(f13(f15(c21), f14(f4(c21), c22)), c24, c25))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(113,axiom,(p19(c21, f11(f13(f15(c21), f14(f4(c21), c22)), c24, c25))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p19_22')).
% 0.20/0.40 tff(114,plain,
% 0.20/0.40 (p19(c21, f11(f13(f15(c21), f14(f4(c21), c22)), c24, c25))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.20/0.41 tff(115,plain,
% 0.20/0.41 (((~![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p10(X28, X27)) | (~p2(X29, X26)) | (~p19(X29, X28)) | p19(X26, X27))) | (p19(c21, f11(f13(f15(c21), f14(f4(c21), c23)), c24, c25)) | (~p10(f11(f13(f15(c21), f14(f4(c21), c22)), c24, c25), f11(f13(f15(c21), f14(f4(c21), c23)), c24, c25))) | (~p2(c21, c21)) | (~p19(c21, f11(f13(f15(c21), f14(f4(c21), c22)), c24, c25))))) <=> ((~![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p10(X28, X27)) | (~p2(X29, X26)) | (~p19(X29, X28)) | p19(X26, X27))) | p19(c21, f11(f13(f15(c21), f14(f4(c21), c23)), c24, c25)) | (~p10(f11(f13(f15(c21), f14(f4(c21), c22)), c24, c25), f11(f13(f15(c21), f14(f4(c21), c23)), c24, c25))) | (~p2(c21, c21)) | (~p19(c21, f11(f13(f15(c21), f14(f4(c21), c22)), c24, c25))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(116,plain,
% 0.20/0.41 (((~p10(f11(f13(f15(c21), f14(f4(c21), c22)), c24, c25), f11(f13(f15(c21), f14(f4(c21), c23)), c24, c25))) | (~p2(c21, c21)) | (~p19(c21, f11(f13(f15(c21), f14(f4(c21), c22)), c24, c25))) | p19(c21, f11(f13(f15(c21), f14(f4(c21), c23)), c24, c25))) <=> (p19(c21, f11(f13(f15(c21), f14(f4(c21), c23)), c24, c25)) | (~p10(f11(f13(f15(c21), f14(f4(c21), c22)), c24, c25), f11(f13(f15(c21), f14(f4(c21), c23)), c24, c25))) | (~p2(c21, c21)) | (~p19(c21, f11(f13(f15(c21), f14(f4(c21), c22)), c24, c25))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(117,plain,
% 0.20/0.41 (((~![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p10(X28, X27)) | (~p2(X29, X26)) | (~p19(X29, X28)) | p19(X26, X27))) | ((~p10(f11(f13(f15(c21), f14(f4(c21), c22)), c24, c25), f11(f13(f15(c21), f14(f4(c21), c23)), c24, c25))) | (~p2(c21, c21)) | (~p19(c21, f11(f13(f15(c21), f14(f4(c21), c22)), c24, c25))) | p19(c21, f11(f13(f15(c21), f14(f4(c21), c23)), c24, c25)))) <=> ((~![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p10(X28, X27)) | (~p2(X29, X26)) | (~p19(X29, X28)) | p19(X26, X27))) | (p19(c21, f11(f13(f15(c21), f14(f4(c21), c23)), c24, c25)) | (~p10(f11(f13(f15(c21), f14(f4(c21), c22)), c24, c25), f11(f13(f15(c21), f14(f4(c21), c23)), c24, c25))) | (~p2(c21, c21)) | (~p19(c21, f11(f13(f15(c21), f14(f4(c21), c22)), c24, c25)))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[116])).
% 0.20/0.41 tff(118,plain,
% 0.20/0.41 (((~![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p10(X28, X27)) | (~p2(X29, X26)) | (~p19(X29, X28)) | p19(X26, X27))) | ((~p10(f11(f13(f15(c21), f14(f4(c21), c22)), c24, c25), f11(f13(f15(c21), f14(f4(c21), c23)), c24, c25))) | (~p2(c21, c21)) | (~p19(c21, f11(f13(f15(c21), f14(f4(c21), c22)), c24, c25))) | p19(c21, f11(f13(f15(c21), f14(f4(c21), c23)), c24, c25)))) <=> ((~![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p10(X28, X27)) | (~p2(X29, X26)) | (~p19(X29, X28)) | p19(X26, X27))) | p19(c21, f11(f13(f15(c21), f14(f4(c21), c23)), c24, c25)) | (~p10(f11(f13(f15(c21), f14(f4(c21), c22)), c24, c25), f11(f13(f15(c21), f14(f4(c21), c23)), c24, c25))) | (~p2(c21, c21)) | (~p19(c21, f11(f13(f15(c21), f14(f4(c21), c22)), c24, c25))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[117, 115])).
% 0.20/0.41 tff(119,plain,
% 0.20/0.41 ((~![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p10(X28, X27)) | (~p2(X29, X26)) | (~p19(X29, X28)) | p19(X26, X27))) | ((~p10(f11(f13(f15(c21), f14(f4(c21), c22)), c24, c25), f11(f13(f15(c21), f14(f4(c21), c23)), c24, c25))) | (~p2(c21, c21)) | (~p19(c21, f11(f13(f15(c21), f14(f4(c21), c22)), c24, c25))) | p19(c21, f11(f13(f15(c21), f14(f4(c21), c23)), c24, c25)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(120,plain,
% 0.20/0.41 ((~![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p10(X28, X27)) | (~p2(X29, X26)) | (~p19(X29, X28)) | p19(X26, X27))) | p19(c21, f11(f13(f15(c21), f14(f4(c21), c23)), c24, c25)) | (~p10(f11(f13(f15(c21), f14(f4(c21), c22)), c24, c25), f11(f13(f15(c21), f14(f4(c21), c23)), c24, c25))) | (~p2(c21, c21)) | (~p19(c21, f11(f13(f15(c21), f14(f4(c21), c22)), c24, c25)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.20/0.41 tff(121,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[120, 114, 111, 108, 98, 11])).
% 0.20/0.41 % SZS output end Proof
% 0.20/0.41 % E exiting
%------------------------------------------------------------------------------