%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN624-1 : 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 05:39:42 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SYN624-1 : TPTP v9.0.0. Released v2.5.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 12:39:10 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.39 % SZS status Unsatisfiable
% 0.12/0.39 % SZS output start Proof
% 0.12/0.39 tff(p10_type, type, (
% 0.12/0.39 p10: ( $i * $i ) > $o)).
% 0.12/0.39 tff(f13_type, type, (
% 0.12/0.39 f13: ( $i * $i ) > $i)).
% 0.12/0.39 tff(f14_type, type, (
% 0.12/0.39 f14: $i > $i)).
% 0.12/0.39 tff(f15_type, type, (
% 0.12/0.39 f15: $i > $i)).
% 0.12/0.39 tff(f7_type, type, (
% 0.12/0.39 f7: $i > $i)).
% 0.12/0.39 tff(c25_type, type, (
% 0.12/0.39 c25: $i)).
% 0.12/0.39 tff(f6_type, type, (
% 0.12/0.39 f6: $i > $i)).
% 0.12/0.39 tff(c22_type, type, (
% 0.12/0.39 c22: $i)).
% 0.12/0.39 tff(f16_type, type, (
% 0.12/0.39 f16: ( $i * $i ) > $i)).
% 0.12/0.39 tff(c26_type, type, (
% 0.12/0.39 c26: $i)).
% 0.12/0.39 tff(c24_type, type, (
% 0.12/0.39 c24: $i)).
% 0.12/0.39 tff(p5_type, type, (
% 0.12/0.39 p5: ( $i * $i ) > $o)).
% 0.12/0.39 tff(p11_type, type, (
% 0.12/0.39 p11: ( $i * $i ) > $o)).
% 0.12/0.39 tff(p3_type, type, (
% 0.12/0.39 p3: ( $i * $i ) > $o)).
% 0.12/0.39 tff(1,assumption,(~p5(f6(c24), f6(c24))), introduced(assumption)).
% 0.12/0.39 tff(2,plain,
% 0.12/0.39 (^[X57: $i] : refl(p5(X57, X57) <=> p5(X57, X57))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(3,plain,
% 0.12/0.39 (![X57: $i] : p5(X57, X57) <=> ![X57: $i] : p5(X57, X57)),
% 0.12/0.39 inference(quant_intro,[status(thm)],[2])).
% 0.12/0.39 tff(4,plain,
% 0.12/0.39 (![X57: $i] : p5(X57, X57) <=> ![X57: $i] : p5(X57, X57)),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(5,axiom,(![X57: $i] : p5(X57, X57)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p5_2')).
% 0.12/0.39 tff(6,plain,
% 0.12/0.39 (![X57: $i] : p5(X57, X57)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.12/0.39 tff(7,plain,(
% 0.12/0.39 ![X57: $i] : p5(X57, X57)),
% 0.12/0.39 inference(skolemize,[status(sab)],[6])).
% 0.12/0.39 tff(8,plain,
% 0.12/0.39 (![X57: $i] : p5(X57, X57)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.12/0.39 tff(9,plain,
% 0.12/0.39 ((~![X57: $i] : p5(X57, X57)) | p5(f6(c24), f6(c24))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(10,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.12/0.39 tff(11,plain,(p5(f6(c24), f6(c24))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.39 tff(12,plain,
% 0.12/0.39 (^[X16: $i] : refl(p10(f16(X16, f14(f15(f7(c25)))), X16) <=> p10(f16(X16, f14(f15(f7(c25)))), X16))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(13,plain,
% 0.12/0.39 (![X16: $i] : p10(f16(X16, f14(f15(f7(c25)))), X16) <=> ![X16: $i] : p10(f16(X16, f14(f15(f7(c25)))), X16)),
% 0.12/0.39 inference(quant_intro,[status(thm)],[12])).
% 0.12/0.39 tff(14,plain,
% 0.12/0.39 (![X16: $i] : p10(f16(X16, f14(f15(f7(c25)))), X16) <=> ![X16: $i] : p10(f16(X16, f14(f15(f7(c25)))), X16)),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(15,axiom,(![X16: $i] : p10(f16(X16, f14(f15(f7(c25)))), X16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p10_11')).
% 0.12/0.39 tff(16,plain,
% 0.12/0.39 (![X16: $i] : p10(f16(X16, f14(f15(f7(c25)))), X16)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.12/0.39 tff(17,plain,(
% 0.12/0.39 ![X16: $i] : p10(f16(X16, f14(f15(f7(c25)))), X16)),
% 0.12/0.39 inference(skolemize,[status(sab)],[16])).
% 0.12/0.39 tff(18,plain,
% 0.12/0.39 (![X16: $i] : p10(f16(X16, f14(f15(f7(c25)))), X16)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.12/0.39 tff(19,plain,
% 0.12/0.39 ((~![X16: $i] : p10(f16(X16, f14(f15(f7(c25)))), X16)) | p10(f16(c26, f14(f15(f7(c25)))), c26)),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(20,plain,
% 0.12/0.39 (p10(f16(c26, f14(f15(f7(c25)))), c26)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.12/0.39 tff(21,plain,
% 0.12/0.39 (^[X6: $i, X4: $i, X3: $i, X5: $i] : refl(((~p5(X3, X5)) | (~p10(X4, X6)) | p10(f13(X3, X4), f13(X5, X6))) <=> ((~p5(X3, X5)) | (~p10(X4, X6)) | p10(f13(X3, X4), f13(X5, X6))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(22,plain,
% 0.12/0.39 (![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p5(X3, X5)) | (~p10(X4, X6)) | p10(f13(X3, X4), f13(X5, X6))) <=> ![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p5(X3, X5)) | (~p10(X4, X6)) | p10(f13(X3, X4), f13(X5, X6)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[21])).
% 0.12/0.39 tff(23,plain,
% 0.12/0.39 (![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p5(X3, X5)) | (~p10(X4, X6)) | p10(f13(X3, X4), f13(X5, X6))) <=> ![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p5(X3, X5)) | (~p10(X4, X6)) | p10(f13(X3, X4), f13(X5, X6)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(24,plain,
% 0.12/0.39 (^[X6: $i, X4: $i, X3: $i, X5: $i] : trans(monotonicity(rewrite((p10(f13(X3, X4), f13(X5, X6)) | (~p10(X4, X6))) <=> ((~p10(X4, X6)) | p10(f13(X3, X4), f13(X5, X6)))), (((p10(f13(X3, X4), f13(X5, X6)) | (~p10(X4, X6))) | (~p5(X3, X5))) <=> (((~p10(X4, X6)) | p10(f13(X3, X4), f13(X5, X6))) | (~p5(X3, X5))))), rewrite((((~p10(X4, X6)) | p10(f13(X3, X4), f13(X5, X6))) | (~p5(X3, X5))) <=> ((~p5(X3, X5)) | (~p10(X4, X6)) | p10(f13(X3, X4), f13(X5, X6)))), (((p10(f13(X3, X4), f13(X5, X6)) | (~p10(X4, X6))) | (~p5(X3, X5))) <=> ((~p5(X3, X5)) | (~p10(X4, X6)) | p10(f13(X3, X4), f13(X5, X6)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(25,plain,
% 0.12/0.39 (![X6: $i, X4: $i, X3: $i, X5: $i] : ((p10(f13(X3, X4), f13(X5, X6)) | (~p10(X4, X6))) | (~p5(X3, X5))) <=> ![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p5(X3, X5)) | (~p10(X4, X6)) | p10(f13(X3, X4), f13(X5, X6)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[24])).
% 0.12/0.39 tff(26,axiom,(![X6: $i, X4: $i, X3: $i, X5: $i] : ((p10(f13(X3, X4), f13(X5, X6)) | (~p10(X4, X6))) | (~p5(X3, X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p10_32')).
% 0.12/0.39 tff(27,plain,
% 0.12/0.39 (![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p5(X3, X5)) | (~p10(X4, X6)) | p10(f13(X3, X4), f13(X5, X6)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.12/0.39 tff(28,plain,
% 0.12/0.39 (![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p5(X3, X5)) | (~p10(X4, X6)) | p10(f13(X3, X4), f13(X5, X6)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.12/0.39 tff(29,plain,(
% 0.12/0.39 ![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p5(X3, X5)) | (~p10(X4, X6)) | p10(f13(X3, X4), f13(X5, X6)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[28])).
% 0.12/0.39 tff(30,plain,
% 0.12/0.39 (![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p5(X3, X5)) | (~p10(X4, X6)) | p10(f13(X3, X4), f13(X5, X6)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.12/0.39 tff(31,plain,
% 0.12/0.39 (((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p5(X3, X5)) | (~p10(X4, X6)) | p10(f13(X3, X4), f13(X5, X6)))) | ((~p5(f6(c24), f6(c24))) | (~p10(f16(c26, f14(f15(f7(c25)))), c26)) | p10(f13(f6(c24), f16(c26, f14(f15(f7(c25))))), f13(f6(c24), c26)))) <=> ((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p5(X3, X5)) | (~p10(X4, X6)) | p10(f13(X3, X4), f13(X5, X6)))) | (~p5(f6(c24), f6(c24))) | (~p10(f16(c26, f14(f15(f7(c25)))), c26)) | p10(f13(f6(c24), f16(c26, f14(f15(f7(c25))))), f13(f6(c24), c26)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(32,plain,
% 0.12/0.39 ((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p5(X3, X5)) | (~p10(X4, X6)) | p10(f13(X3, X4), f13(X5, X6)))) | ((~p5(f6(c24), f6(c24))) | (~p10(f16(c26, f14(f15(f7(c25)))), c26)) | p10(f13(f6(c24), f16(c26, f14(f15(f7(c25))))), f13(f6(c24), c26)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(33,plain,
% 0.12/0.39 ((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p5(X3, X5)) | (~p10(X4, X6)) | p10(f13(X3, X4), f13(X5, X6)))) | (~p5(f6(c24), f6(c24))) | (~p10(f16(c26, f14(f15(f7(c25)))), c26)) | p10(f13(f6(c24), f16(c26, f14(f15(f7(c25))))), f13(f6(c24), c26))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.12/0.39 tff(34,plain,
% 0.12/0.39 ((~p5(f6(c24), f6(c24))) | (~p10(f16(c26, f14(f15(f7(c25)))), c26)) | p10(f13(f6(c24), f16(c26, f14(f15(f7(c25))))), f13(f6(c24), c26))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[33, 30])).
% 0.12/0.39 tff(35,plain,
% 0.12/0.39 ((~p5(f6(c24), f6(c24))) | p10(f13(f6(c24), f16(c26, f14(f15(f7(c25))))), f13(f6(c24), c26))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[34, 20])).
% 0.12/0.39 tff(36,plain,
% 0.12/0.39 (p10(f13(f6(c24), f16(c26, f14(f15(f7(c25))))), f13(f6(c24), c26))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[35, 11])).
% 0.12/0.39 tff(37,assumption,(~p5(f6(c22), f6(c22))), introduced(assumption)).
% 0.12/0.39 tff(38,plain,
% 0.12/0.39 ((~![X57: $i] : p5(X57, X57)) | p5(f6(c22), f6(c22))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(39,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[38, 8, 37])).
% 0.12/0.39 tff(40,plain,(p5(f6(c22), f6(c22))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.39 tff(41,assumption,(~p3(c25, c25)), introduced(assumption)).
% 0.12/0.39 tff(42,plain,
% 0.12/0.39 (^[X46: $i] : refl(p3(X46, X46) <=> p3(X46, X46))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(43,plain,
% 0.12/0.39 (![X46: $i] : p3(X46, X46) <=> ![X46: $i] : p3(X46, X46)),
% 0.12/0.39 inference(quant_intro,[status(thm)],[42])).
% 0.12/0.39 tff(44,plain,
% 0.12/0.39 (![X46: $i] : p3(X46, X46) <=> ![X46: $i] : p3(X46, X46)),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(45,axiom,(![X46: $i] : p3(X46, X46)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p3_3')).
% 0.12/0.39 tff(46,plain,
% 0.12/0.39 (![X46: $i] : p3(X46, X46)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.12/0.39 tff(47,plain,(
% 0.12/0.39 ![X46: $i] : p3(X46, X46)),
% 0.12/0.39 inference(skolemize,[status(sab)],[46])).
% 0.12/0.39 tff(48,plain,
% 0.12/0.39 (![X46: $i] : p3(X46, X46)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.12/0.39 tff(49,plain,
% 0.12/0.39 ((~![X46: $i] : p3(X46, X46)) | p3(c25, c25)),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(50,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[49, 48, 41])).
% 0.12/0.39 tff(51,plain,(p3(c25, c25)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.39 tff(52,plain,
% 0.12/0.39 (^[X52: $i, X51: $i] : refl(((~p3(X51, X52)) | p3(f7(X51), f7(X52))) <=> ((~p3(X51, X52)) | p3(f7(X51), f7(X52))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(53,plain,
% 0.12/0.39 (![X52: $i, X51: $i] : ((~p3(X51, X52)) | p3(f7(X51), f7(X52))) <=> ![X52: $i, X51: $i] : ((~p3(X51, X52)) | p3(f7(X51), f7(X52)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[52])).
% 0.12/0.39 tff(54,plain,
% 0.12/0.39 (![X52: $i, X51: $i] : ((~p3(X51, X52)) | p3(f7(X51), f7(X52))) <=> ![X52: $i, X51: $i] : ((~p3(X51, X52)) | p3(f7(X51), f7(X52)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(55,plain,
% 0.12/0.39 (^[X52: $i, X51: $i] : rewrite((p3(f7(X51), f7(X52)) | (~p3(X51, X52))) <=> ((~p3(X51, X52)) | p3(f7(X51), f7(X52))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(56,plain,
% 0.12/0.39 (![X52: $i, X51: $i] : (p3(f7(X51), f7(X52)) | (~p3(X51, X52))) <=> ![X52: $i, X51: $i] : ((~p3(X51, X52)) | p3(f7(X51), f7(X52)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[55])).
% 0.12/0.39 tff(57,axiom,(![X52: $i, X51: $i] : (p3(f7(X51), f7(X52)) | (~p3(X51, X52)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p3_16')).
% 0.12/0.39 tff(58,plain,
% 0.12/0.39 (![X52: $i, X51: $i] : ((~p3(X51, X52)) | p3(f7(X51), f7(X52)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.12/0.39 tff(59,plain,
% 0.12/0.39 (![X52: $i, X51: $i] : ((~p3(X51, X52)) | p3(f7(X51), f7(X52)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.12/0.39 tff(60,plain,(
% 0.12/0.39 ![X52: $i, X51: $i] : ((~p3(X51, X52)) | p3(f7(X51), f7(X52)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[59])).
% 0.12/0.39 tff(61,plain,
% 0.12/0.39 (![X52: $i, X51: $i] : ((~p3(X51, X52)) | p3(f7(X51), f7(X52)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[60, 53])).
% 0.12/0.39 tff(62,plain,
% 0.12/0.39 (((~![X52: $i, X51: $i] : ((~p3(X51, X52)) | p3(f7(X51), f7(X52)))) | ((~p3(c25, c25)) | p3(f7(c25), f7(c25)))) <=> ((~![X52: $i, X51: $i] : ((~p3(X51, X52)) | p3(f7(X51), f7(X52)))) | (~p3(c25, c25)) | p3(f7(c25), f7(c25)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(63,plain,
% 0.12/0.39 ((~![X52: $i, X51: $i] : ((~p3(X51, X52)) | p3(f7(X51), f7(X52)))) | ((~p3(c25, c25)) | p3(f7(c25), f7(c25)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(64,plain,
% 0.12/0.39 ((~![X52: $i, X51: $i] : ((~p3(X51, X52)) | p3(f7(X51), f7(X52)))) | (~p3(c25, c25)) | p3(f7(c25), f7(c25))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.12/0.39 tff(65,plain,
% 0.12/0.39 ((~p3(c25, c25)) | p3(f7(c25), f7(c25))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[64, 61])).
% 0.12/0.39 tff(66,plain,
% 0.12/0.39 (p3(f7(c25), f7(c25))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[65, 51])).
% 0.12/0.39 tff(67,plain,
% 0.12/0.39 (^[X27: $i, X26: $i] : refl(((~p3(X26, X27)) | p11(f15(X26), f15(X27))) <=> ((~p3(X26, X27)) | p11(f15(X26), f15(X27))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(68,plain,
% 0.12/0.39 (![X27: $i, X26: $i] : ((~p3(X26, X27)) | p11(f15(X26), f15(X27))) <=> ![X27: $i, X26: $i] : ((~p3(X26, X27)) | p11(f15(X26), f15(X27)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[67])).
% 0.12/0.39 tff(69,plain,
% 0.12/0.39 (![X27: $i, X26: $i] : ((~p3(X26, X27)) | p11(f15(X26), f15(X27))) <=> ![X27: $i, X26: $i] : ((~p3(X26, X27)) | p11(f15(X26), f15(X27)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(70,plain,
% 0.12/0.39 (^[X27: $i, X26: $i] : rewrite((p11(f15(X26), f15(X27)) | (~p3(X26, X27))) <=> ((~p3(X26, X27)) | p11(f15(X26), f15(X27))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(71,plain,
% 0.12/0.39 (![X27: $i, X26: $i] : (p11(f15(X26), f15(X27)) | (~p3(X26, X27))) <=> ![X27: $i, X26: $i] : ((~p3(X26, X27)) | p11(f15(X26), f15(X27)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[70])).
% 0.12/0.39 tff(72,axiom,(![X27: $i, X26: $i] : (p11(f15(X26), f15(X27)) | (~p3(X26, X27)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p11_18')).
% 0.12/0.40 tff(73,plain,
% 0.12/0.40 (![X27: $i, X26: $i] : ((~p3(X26, X27)) | p11(f15(X26), f15(X27)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.12/0.40 tff(74,plain,
% 0.12/0.40 (![X27: $i, X26: $i] : ((~p3(X26, X27)) | p11(f15(X26), f15(X27)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.12/0.40 tff(75,plain,(
% 0.12/0.40 ![X27: $i, X26: $i] : ((~p3(X26, X27)) | p11(f15(X26), f15(X27)))),
% 0.12/0.40 inference(skolemize,[status(sab)],[74])).
% 0.12/0.40 tff(76,plain,
% 0.12/0.40 (![X27: $i, X26: $i] : ((~p3(X26, X27)) | p11(f15(X26), f15(X27)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[75, 68])).
% 0.12/0.40 tff(77,plain,
% 0.12/0.40 (((~![X27: $i, X26: $i] : ((~p3(X26, X27)) | p11(f15(X26), f15(X27)))) | ((~p3(f7(c25), f7(c25))) | p11(f15(f7(c25)), f15(f7(c25))))) <=> ((~![X27: $i, X26: $i] : ((~p3(X26, X27)) | p11(f15(X26), f15(X27)))) | (~p3(f7(c25), f7(c25))) | p11(f15(f7(c25)), f15(f7(c25))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(78,plain,
% 0.12/0.40 ((~![X27: $i, X26: $i] : ((~p3(X26, X27)) | p11(f15(X26), f15(X27)))) | ((~p3(f7(c25), f7(c25))) | p11(f15(f7(c25)), f15(f7(c25))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(79,plain,
% 0.12/0.40 ((~![X27: $i, X26: $i] : ((~p3(X26, X27)) | p11(f15(X26), f15(X27)))) | (~p3(f7(c25), f7(c25))) | p11(f15(f7(c25)), f15(f7(c25)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.12/0.40 tff(80,plain,
% 0.12/0.40 (p11(f15(f7(c25)), f15(f7(c25)))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[79, 76, 66])).
% 0.12/0.40 tff(81,plain,
% 0.12/0.40 (^[X11: $i, X10: $i] : refl(((~p11(X10, X11)) | p10(f14(X10), f14(X11))) <=> ((~p11(X10, X11)) | p10(f14(X10), f14(X11))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(82,plain,
% 0.12/0.40 (![X11: $i, X10: $i] : ((~p11(X10, X11)) | p10(f14(X10), f14(X11))) <=> ![X11: $i, X10: $i] : ((~p11(X10, X11)) | p10(f14(X10), f14(X11)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[81])).
% 0.12/0.40 tff(83,plain,
% 0.12/0.40 (![X11: $i, X10: $i] : ((~p11(X10, X11)) | p10(f14(X10), f14(X11))) <=> ![X11: $i, X10: $i] : ((~p11(X10, X11)) | p10(f14(X10), f14(X11)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(84,plain,
% 0.12/0.40 (^[X11: $i, X10: $i] : rewrite((p10(f14(X10), f14(X11)) | (~p11(X10, X11))) <=> ((~p11(X10, X11)) | p10(f14(X10), f14(X11))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(85,plain,
% 0.12/0.40 (![X11: $i, X10: $i] : (p10(f14(X10), f14(X11)) | (~p11(X10, X11))) <=> ![X11: $i, X10: $i] : ((~p11(X10, X11)) | p10(f14(X10), f14(X11)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[84])).
% 0.12/0.40 tff(86,axiom,(![X11: $i, X10: $i] : (p10(f14(X10), f14(X11)) | (~p11(X10, X11)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p10_12')).
% 0.12/0.40 tff(87,plain,
% 0.12/0.40 (![X11: $i, X10: $i] : ((~p11(X10, X11)) | p10(f14(X10), f14(X11)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.12/0.40 tff(88,plain,
% 0.12/0.40 (![X11: $i, X10: $i] : ((~p11(X10, X11)) | p10(f14(X10), f14(X11)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.12/0.40 tff(89,plain,(
% 0.12/0.40 ![X11: $i, X10: $i] : ((~p11(X10, X11)) | p10(f14(X10), f14(X11)))),
% 0.12/0.40 inference(skolemize,[status(sab)],[88])).
% 0.12/0.40 tff(90,plain,
% 0.12/0.40 (![X11: $i, X10: $i] : ((~p11(X10, X11)) | p10(f14(X10), f14(X11)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[89, 82])).
% 0.12/0.40 tff(91,plain,
% 0.12/0.40 (((~![X11: $i, X10: $i] : ((~p11(X10, X11)) | p10(f14(X10), f14(X11)))) | ((~p11(f15(f7(c25)), f15(f7(c25)))) | p10(f14(f15(f7(c25))), f14(f15(f7(c25)))))) <=> ((~![X11: $i, X10: $i] : ((~p11(X10, X11)) | p10(f14(X10), f14(X11)))) | (~p11(f15(f7(c25)), f15(f7(c25)))) | p10(f14(f15(f7(c25))), f14(f15(f7(c25)))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(92,plain,
% 0.12/0.40 ((~![X11: $i, X10: $i] : ((~p11(X10, X11)) | p10(f14(X10), f14(X11)))) | ((~p11(f15(f7(c25)), f15(f7(c25)))) | p10(f14(f15(f7(c25))), f14(f15(f7(c25)))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(93,plain,
% 0.12/0.40 ((~![X11: $i, X10: $i] : ((~p11(X10, X11)) | p10(f14(X10), f14(X11)))) | (~p11(f15(f7(c25)), f15(f7(c25)))) | p10(f14(f15(f7(c25))), f14(f15(f7(c25))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.12/0.40 tff(94,plain,
% 0.12/0.40 (p10(f14(f15(f7(c25))), f14(f15(f7(c25))))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[93, 90, 80])).
% 0.12/0.40 tff(95,plain,
% 0.12/0.40 (((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p5(X3, X5)) | (~p10(X4, X6)) | p10(f13(X3, X4), f13(X5, X6)))) | ((~p5(f6(c22), f6(c22))) | (~p10(f14(f15(f7(c25))), f14(f15(f7(c25))))) | p10(f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c22), f14(f15(f7(c25))))))) <=> ((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p5(X3, X5)) | (~p10(X4, X6)) | p10(f13(X3, X4), f13(X5, X6)))) | (~p5(f6(c22), f6(c22))) | (~p10(f14(f15(f7(c25))), f14(f15(f7(c25))))) | p10(f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c22), f14(f15(f7(c25))))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(96,plain,
% 0.12/0.40 ((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p5(X3, X5)) | (~p10(X4, X6)) | p10(f13(X3, X4), f13(X5, X6)))) | ((~p5(f6(c22), f6(c22))) | (~p10(f14(f15(f7(c25))), f14(f15(f7(c25))))) | p10(f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c22), f14(f15(f7(c25))))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(97,plain,
% 0.12/0.40 ((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p5(X3, X5)) | (~p10(X4, X6)) | p10(f13(X3, X4), f13(X5, X6)))) | (~p5(f6(c22), f6(c22))) | (~p10(f14(f15(f7(c25))), f14(f15(f7(c25))))) | p10(f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c22), f14(f15(f7(c25)))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.12/0.40 tff(98,plain,
% 0.12/0.40 ((~p5(f6(c22), f6(c22))) | (~p10(f14(f15(f7(c25))), f14(f15(f7(c25))))) | p10(f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c22), f14(f15(f7(c25)))))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[97, 30])).
% 0.12/0.40 tff(99,plain,
% 0.12/0.40 ((~p5(f6(c22), f6(c22))) | p10(f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c22), f14(f15(f7(c25)))))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[98, 94])).
% 0.12/0.40 tff(100,plain,
% 0.12/0.40 (p10(f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c22), f14(f15(f7(c25)))))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[99, 40])).
% 0.12/0.40 tff(101,plain,
% 0.12/0.40 ((~p10(f13(f6(c24), c26), f13(f6(c22), f14(f15(f7(c25)))))) <=> (~p10(f13(f6(c24), c26), f13(f6(c22), f14(f15(f7(c25))))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(102,axiom,(~p10(f13(f6(c24), c26), f13(f6(c22), f14(f15(f7(c25)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_p10_28')).
% 0.12/0.40 tff(103,plain,
% 0.12/0.40 (~p10(f13(f6(c24), c26), f13(f6(c22), f14(f15(f7(c25)))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.12/0.40 tff(104,plain,
% 0.12/0.40 (^[X0: $i, X2: $i, X1: $i] : refl((p10(X1, X2) | (~p10(X0, X2)) | (~p10(X0, X1))) <=> (p10(X1, X2) | (~p10(X0, X2)) | (~p10(X0, X1))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(105,plain,
% 0.12/0.40 (![X0: $i, X2: $i, X1: $i] : (p10(X1, X2) | (~p10(X0, X2)) | (~p10(X0, X1))) <=> ![X0: $i, X2: $i, X1: $i] : (p10(X1, X2) | (~p10(X0, X2)) | (~p10(X0, X1)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[104])).
% 0.12/0.40 tff(106,plain,
% 0.12/0.40 (![X0: $i, X2: $i, X1: $i] : (p10(X1, X2) | (~p10(X0, X2)) | (~p10(X0, X1))) <=> ![X0: $i, X2: $i, X1: $i] : (p10(X1, X2) | (~p10(X0, X2)) | (~p10(X0, X1)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(107,plain,
% 0.12/0.40 (^[X0: $i, X2: $i, X1: $i] : trans(monotonicity(rewrite((p10(X1, X2) | (~p10(X0, X1))) <=> (p10(X1, X2) | (~p10(X0, X1)))), (((p10(X1, X2) | (~p10(X0, X1))) | (~p10(X0, X2))) <=> ((p10(X1, X2) | (~p10(X0, X1))) | (~p10(X0, X2))))), rewrite(((p10(X1, X2) | (~p10(X0, X1))) | (~p10(X0, X2))) <=> (p10(X1, X2) | (~p10(X0, X2)) | (~p10(X0, X1)))), (((p10(X1, X2) | (~p10(X0, X1))) | (~p10(X0, X2))) <=> (p10(X1, X2) | (~p10(X0, X2)) | (~p10(X0, X1)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(108,plain,
% 0.12/0.40 (![X0: $i, X2: $i, X1: $i] : ((p10(X1, X2) | (~p10(X0, X1))) | (~p10(X0, X2))) <=> ![X0: $i, X2: $i, X1: $i] : (p10(X1, X2) | (~p10(X0, X2)) | (~p10(X0, X1)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[107])).
% 0.12/0.40 tff(109,axiom,(![X0: $i, X2: $i, X1: $i] : ((p10(X1, X2) | (~p10(X0, X1))) | (~p10(X0, X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p10_21')).
% 0.12/0.40 tff(110,plain,
% 0.12/0.40 (![X0: $i, X2: $i, X1: $i] : (p10(X1, X2) | (~p10(X0, X2)) | (~p10(X0, X1)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.12/0.40 tff(111,plain,
% 0.12/0.40 (![X0: $i, X2: $i, X1: $i] : (p10(X1, X2) | (~p10(X0, X2)) | (~p10(X0, X1)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[110, 106])).
% 0.12/0.40 tff(112,plain,(
% 0.12/0.40 ![X0: $i, X2: $i, X1: $i] : (p10(X1, X2) | (~p10(X0, X2)) | (~p10(X0, X1)))),
% 0.12/0.40 inference(skolemize,[status(sab)],[111])).
% 0.12/0.40 tff(113,plain,
% 0.12/0.40 (![X0: $i, X2: $i, X1: $i] : (p10(X1, X2) | (~p10(X0, X2)) | (~p10(X0, X1)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[112, 105])).
% 0.12/0.40 tff(114,plain,
% 0.12/0.40 (((~![X0: $i, X2: $i, X1: $i] : (p10(X1, X2) | (~p10(X0, X2)) | (~p10(X0, X1)))) | (p10(f13(f6(c24), c26), f13(f6(c22), f14(f15(f7(c25))))) | (~p10(f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c22), f14(f15(f7(c25)))))) | (~p10(f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c24), c26))))) <=> ((~![X0: $i, X2: $i, X1: $i] : (p10(X1, X2) | (~p10(X0, X2)) | (~p10(X0, X1)))) | p10(f13(f6(c24), c26), f13(f6(c22), f14(f15(f7(c25))))) | (~p10(f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c22), f14(f15(f7(c25)))))) | (~p10(f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c24), c26))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(115,plain,
% 0.12/0.40 ((~![X0: $i, X2: $i, X1: $i] : (p10(X1, X2) | (~p10(X0, X2)) | (~p10(X0, X1)))) | (p10(f13(f6(c24), c26), f13(f6(c22), f14(f15(f7(c25))))) | (~p10(f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c22), f14(f15(f7(c25)))))) | (~p10(f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c24), c26))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(116,plain,
% 0.12/0.40 ((~![X0: $i, X2: $i, X1: $i] : (p10(X1, X2) | (~p10(X0, X2)) | (~p10(X0, X1)))) | p10(f13(f6(c24), c26), f13(f6(c22), f14(f15(f7(c25))))) | (~p10(f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c22), f14(f15(f7(c25)))))) | (~p10(f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c24), c26)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.12/0.40 tff(117,plain,
% 0.12/0.40 (~p10(f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c24), c26))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[116, 113, 103, 100])).
% 0.12/0.40 tff(118,plain,
% 0.12/0.40 (((~![X0: $i, X2: $i, X1: $i] : (p10(X1, X2) | (~p10(X0, X2)) | (~p10(X0, X1)))) | (p10(f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c24), c26)) | (~p10(f13(f6(c24), f16(c26, f14(f15(f7(c25))))), f13(f6(c24), c26))) | (~p10(f13(f6(c24), f16(c26, f14(f15(f7(c25))))), f13(f6(c22), f14(f15(f7(c25)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : (p10(X1, X2) | (~p10(X0, X2)) | (~p10(X0, X1)))) | p10(f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c24), c26)) | (~p10(f13(f6(c24), f16(c26, f14(f15(f7(c25))))), f13(f6(c24), c26))) | (~p10(f13(f6(c24), f16(c26, f14(f15(f7(c25))))), f13(f6(c22), f14(f15(f7(c25)))))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(119,plain,
% 0.12/0.40 ((~![X0: $i, X2: $i, X1: $i] : (p10(X1, X2) | (~p10(X0, X2)) | (~p10(X0, X1)))) | (p10(f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c24), c26)) | (~p10(f13(f6(c24), f16(c26, f14(f15(f7(c25))))), f13(f6(c24), c26))) | (~p10(f13(f6(c24), f16(c26, f14(f15(f7(c25))))), f13(f6(c22), f14(f15(f7(c25)))))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(120,plain,
% 0.12/0.40 ((~![X0: $i, X2: $i, X1: $i] : (p10(X1, X2) | (~p10(X0, X2)) | (~p10(X0, X1)))) | p10(f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c24), c26)) | (~p10(f13(f6(c24), f16(c26, f14(f15(f7(c25))))), f13(f6(c24), c26))) | (~p10(f13(f6(c24), f16(c26, f14(f15(f7(c25))))), f13(f6(c22), f14(f15(f7(c25))))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.12/0.40 tff(121,plain,
% 0.12/0.40 (~p10(f13(f6(c24), f16(c26, f14(f15(f7(c25))))), f13(f6(c22), f14(f15(f7(c25)))))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[120, 113, 117, 36])).
% 0.12/0.40 tff(122,plain,
% 0.12/0.40 (^[X9: $i] : refl(p10(f13(f6(c22), X9), f13(f6(c24), f16(c26, X9))) <=> p10(f13(f6(c22), X9), f13(f6(c24), f16(c26, X9))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(123,plain,
% 0.12/0.40 (![X9: $i] : p10(f13(f6(c22), X9), f13(f6(c24), f16(c26, X9))) <=> ![X9: $i] : p10(f13(f6(c22), X9), f13(f6(c24), f16(c26, X9)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[122])).
% 0.12/0.40 tff(124,plain,
% 0.12/0.40 (![X9: $i] : p10(f13(f6(c22), X9), f13(f6(c24), f16(c26, X9))) <=> ![X9: $i] : p10(f13(f6(c22), X9), f13(f6(c24), f16(c26, X9)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(125,axiom,(![X9: $i] : p10(f13(f6(c22), X9), f13(f6(c24), f16(c26, X9)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p10_26')).
% 0.12/0.40 tff(126,plain,
% 0.12/0.40 (![X9: $i] : p10(f13(f6(c22), X9), f13(f6(c24), f16(c26, X9)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.12/0.41 tff(127,plain,(
% 0.12/0.41 ![X9: $i] : p10(f13(f6(c22), X9), f13(f6(c24), f16(c26, X9)))),
% 0.12/0.41 inference(skolemize,[status(sab)],[126])).
% 0.12/0.41 tff(128,plain,
% 0.12/0.41 (![X9: $i] : p10(f13(f6(c22), X9), f13(f6(c24), f16(c26, X9)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[127, 123])).
% 0.12/0.41 tff(129,plain,
% 0.12/0.41 ((~![X9: $i] : p10(f13(f6(c22), X9), f13(f6(c24), f16(c26, X9)))) | p10(f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c24), f16(c26, f14(f15(f7(c25))))))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(130,plain,
% 0.12/0.41 (p10(f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c24), f16(c26, f14(f15(f7(c25))))))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[129, 128])).
% 0.12/0.41 tff(131,plain,
% 0.12/0.41 (((~![X0: $i, X2: $i, X1: $i] : (p10(X1, X2) | (~p10(X0, X2)) | (~p10(X0, X1)))) | ((~p10(f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c24), f16(c26, f14(f15(f7(c25))))))) | p10(f13(f6(c24), f16(c26, f14(f15(f7(c25))))), f13(f6(c22), f14(f15(f7(c25))))) | (~p10(f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c22), f14(f15(f7(c25)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : (p10(X1, X2) | (~p10(X0, X2)) | (~p10(X0, X1)))) | (~p10(f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c24), f16(c26, f14(f15(f7(c25))))))) | p10(f13(f6(c24), f16(c26, f14(f15(f7(c25))))), f13(f6(c22), f14(f15(f7(c25))))) | (~p10(f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c22), f14(f15(f7(c25)))))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(132,plain,
% 0.12/0.41 ((p10(f13(f6(c24), f16(c26, f14(f15(f7(c25))))), f13(f6(c22), f14(f15(f7(c25))))) | (~p10(f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c22), f14(f15(f7(c25)))))) | (~p10(f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c24), f16(c26, f14(f15(f7(c25)))))))) <=> ((~p10(f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c24), f16(c26, f14(f15(f7(c25))))))) | p10(f13(f6(c24), f16(c26, f14(f15(f7(c25))))), f13(f6(c22), f14(f15(f7(c25))))) | (~p10(f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c22), f14(f15(f7(c25)))))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(133,plain,
% 0.12/0.41 (((~![X0: $i, X2: $i, X1: $i] : (p10(X1, X2) | (~p10(X0, X2)) | (~p10(X0, X1)))) | (p10(f13(f6(c24), f16(c26, f14(f15(f7(c25))))), f13(f6(c22), f14(f15(f7(c25))))) | (~p10(f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c22), f14(f15(f7(c25)))))) | (~p10(f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c24), f16(c26, f14(f15(f7(c25))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : (p10(X1, X2) | (~p10(X0, X2)) | (~p10(X0, X1)))) | ((~p10(f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c24), f16(c26, f14(f15(f7(c25))))))) | p10(f13(f6(c24), f16(c26, f14(f15(f7(c25))))), f13(f6(c22), f14(f15(f7(c25))))) | (~p10(f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c22), f14(f15(f7(c25))))))))),
% 0.12/0.41 inference(monotonicity,[status(thm)],[132])).
% 0.12/0.41 tff(134,plain,
% 0.12/0.41 (((~![X0: $i, X2: $i, X1: $i] : (p10(X1, X2) | (~p10(X0, X2)) | (~p10(X0, X1)))) | (p10(f13(f6(c24), f16(c26, f14(f15(f7(c25))))), f13(f6(c22), f14(f15(f7(c25))))) | (~p10(f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c22), f14(f15(f7(c25)))))) | (~p10(f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c24), f16(c26, f14(f15(f7(c25))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : (p10(X1, X2) | (~p10(X0, X2)) | (~p10(X0, X1)))) | (~p10(f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c24), f16(c26, f14(f15(f7(c25))))))) | p10(f13(f6(c24), f16(c26, f14(f15(f7(c25))))), f13(f6(c22), f14(f15(f7(c25))))) | (~p10(f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c22), f14(f15(f7(c25)))))))),
% 0.12/0.41 inference(transitivity,[status(thm)],[133, 131])).
% 0.12/0.41 tff(135,plain,
% 0.12/0.41 ((~![X0: $i, X2: $i, X1: $i] : (p10(X1, X2) | (~p10(X0, X2)) | (~p10(X0, X1)))) | (p10(f13(f6(c24), f16(c26, f14(f15(f7(c25))))), f13(f6(c22), f14(f15(f7(c25))))) | (~p10(f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c22), f14(f15(f7(c25)))))) | (~p10(f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c24), f16(c26, f14(f15(f7(c25))))))))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(136,plain,
% 0.12/0.41 ((~![X0: $i, X2: $i, X1: $i] : (p10(X1, X2) | (~p10(X0, X2)) | (~p10(X0, X1)))) | (~p10(f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c24), f16(c26, f14(f15(f7(c25))))))) | p10(f13(f6(c24), f16(c26, f14(f15(f7(c25))))), f13(f6(c22), f14(f15(f7(c25))))) | (~p10(f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c22), f14(f15(f7(c25))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.20/0.41 tff(137,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[136, 113, 100, 130, 121])).
% 0.20/0.41 % SZS output end Proof
% 0.20/0.41 % E exiting
%------------------------------------------------------------------------------