%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN620-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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
% 0.11/0.13 % Problem : SYN620-1 : TPTP v9.0.0. Released v2.5.0.
% 0.11/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n011.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 12:39:26 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(p11_type, type, (
% 0.12/0.39 p11: ( $i * $i ) > $o)).
% 0.12/0.39 tff(f12_type, type, (
% 0.12/0.39 f12: $i > $i)).
% 0.12/0.39 tff(f13_type, type, (
% 0.12/0.39 f13: ( $i * $i ) > $i)).
% 0.12/0.39 tff(c27_type, type, (
% 0.12/0.39 c27: $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(p10_type, type, (
% 0.12/0.39 p10: ( $i * $i ) > $o)).
% 0.12/0.39 tff(p5_type, type, (
% 0.12/0.39 p5: ( $i * $i ) > $o)).
% 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(p3_type, type, (
% 0.12/0.39 p3: ( $i * $i ) > $o)).
% 0.12/0.39 tff(p20_type, type, (
% 0.12/0.39 p20: ( $i * $i ) > $o)).
% 0.12/0.39 tff(1,assumption,(~p10(c27, c27)), introduced(assumption)).
% 0.12/0.39 tff(2,plain,
% 0.12/0.39 (^[X0: $i] : refl(p10(X0, X0) <=> p10(X0, X0))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(3,plain,
% 0.12/0.39 (![X0: $i] : p10(X0, X0) <=> ![X0: $i] : p10(X0, X0)),
% 0.12/0.39 inference(quant_intro,[status(thm)],[2])).
% 0.12/0.39 tff(4,plain,
% 0.12/0.39 (![X0: $i] : p10(X0, X0) <=> ![X0: $i] : p10(X0, X0)),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(5,axiom,(![X0: $i] : p10(X0, X0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p10_1')).
% 0.12/0.39 tff(6,plain,
% 0.12/0.39 (![X0: $i] : p10(X0, X0)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.12/0.39 tff(7,plain,(
% 0.12/0.39 ![X0: $i] : p10(X0, X0)),
% 0.12/0.39 inference(skolemize,[status(sab)],[6])).
% 0.12/0.39 tff(8,plain,
% 0.12/0.39 (![X0: $i] : p10(X0, X0)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.12/0.39 tff(9,plain,
% 0.12/0.39 ((~![X0: $i] : p10(X0, X0)) | p10(c27, c27)),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(10,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.12/0.39 tff(11,plain,(p10(c27, c27)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.39 tff(12,assumption,(~p5(f6(c22), f6(c22))), introduced(assumption)).
% 0.12/0.39 tff(13,plain,
% 0.12/0.39 (^[X56: $i] : refl(p5(X56, X56) <=> p5(X56, X56))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(14,plain,
% 0.12/0.39 (![X56: $i] : p5(X56, X56) <=> ![X56: $i] : p5(X56, X56)),
% 0.12/0.39 inference(quant_intro,[status(thm)],[13])).
% 0.12/0.39 tff(15,plain,
% 0.12/0.39 (![X56: $i] : p5(X56, X56) <=> ![X56: $i] : p5(X56, X56)),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(16,axiom,(![X56: $i] : p5(X56, X56)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p5_2')).
% 0.12/0.39 tff(17,plain,
% 0.12/0.39 (![X56: $i] : p5(X56, X56)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.12/0.39 tff(18,plain,(
% 0.12/0.39 ![X56: $i] : p5(X56, X56)),
% 0.12/0.39 inference(skolemize,[status(sab)],[17])).
% 0.12/0.39 tff(19,plain,
% 0.12/0.39 (![X56: $i] : p5(X56, X56)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.12/0.39 tff(20,plain,
% 0.12/0.39 ((~![X56: $i] : p5(X56, X56)) | p5(f6(c22), f6(c22))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(21,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[20, 19, 12])).
% 0.12/0.39 tff(22,plain,(p5(f6(c22), f6(c22))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.39 tff(23,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(24,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)],[23])).
% 0.12/0.39 tff(25,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(26,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(27,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)],[26])).
% 0.12/0.39 tff(28,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_29')).
% 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(modus_ponens,[status(thm)],[28, 27])).
% 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, 25])).
% 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)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[30])).
% 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)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[31, 24])).
% 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(c22), f6(c22))) | (~p10(c27, c27)) | p10(f13(f6(c22), c27), f13(f6(c22), c27)))) <=> ((~![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(c27, c27)) | p10(f13(f6(c22), c27), f13(f6(c22), c27)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(34,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(c22), f6(c22))) | (~p10(c27, c27)) | p10(f13(f6(c22), c27), f13(f6(c22), c27)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(35,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(c22), f6(c22))) | (~p10(c27, c27)) | p10(f13(f6(c22), c27), f13(f6(c22), c27))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.12/0.39 tff(36,plain,
% 0.12/0.39 ((~p5(f6(c22), f6(c22))) | (~p10(c27, c27)) | p10(f13(f6(c22), c27), f13(f6(c22), c27))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[35, 32])).
% 0.12/0.39 tff(37,plain,
% 0.12/0.39 (p10(f13(f6(c22), c27), f13(f6(c22), c27))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[36, 22, 11])).
% 0.12/0.39 tff(38,plain,
% 0.12/0.39 (^[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))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(39,plain,
% 0.12/0.39 (![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)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[38])).
% 0.12/0.40 tff(40,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(41,axiom,(![X9: $i] : p10(f13(f6(c22), X9), f13(f6(c24), f16(c26, X9)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p10_24')).
% 0.12/0.40 tff(42,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)],[41, 40])).
% 0.12/0.40 tff(43,plain,(
% 0.12/0.40 ![X9: $i] : p10(f13(f6(c22), X9), f13(f6(c24), f16(c26, X9)))),
% 0.12/0.40 inference(skolemize,[status(sab)],[42])).
% 0.12/0.40 tff(44,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)],[43, 39])).
% 0.12/0.40 tff(45,plain,
% 0.12/0.40 ((~![X9: $i] : p10(f13(f6(c22), X9), f13(f6(c24), f16(c26, X9)))) | p10(f13(f6(c22), c27), f13(f6(c24), f16(c26, c27)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(46,plain,
% 0.12/0.40 (p10(f13(f6(c22), c27), f13(f6(c24), f16(c26, c27)))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.12/0.40 tff(47,plain,
% 0.12/0.40 (^[X0: $i, X2: $i, X1: $i] : refl(((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2)) <=> ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2)))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(48,plain,
% 0.12/0.40 (![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2)) <=> ![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[47])).
% 0.12/0.40 tff(49,plain,
% 0.12/0.40 (![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2)) <=> ![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(50,plain,
% 0.12/0.40 (^[X0: $i, X2: $i, X1: $i] : trans(monotonicity(rewrite((p10(X1, X2) | (~p10(X0, X1))) <=> ((~p10(X0, X1)) | p10(X1, X2))), (((p10(X1, X2) | (~p10(X0, X1))) | (~p10(X0, X2))) <=> (((~p10(X0, X1)) | p10(X1, X2)) | (~p10(X0, X2))))), rewrite((((~p10(X0, X1)) | p10(X1, X2)) | (~p10(X0, X2))) <=> ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))), (((p10(X1, X2) | (~p10(X0, X1))) | (~p10(X0, X2))) <=> ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(51,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(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[50])).
% 0.12/0.40 tff(52,axiom,(![X0: $i, X2: $i, X1: $i] : ((p10(X1, X2) | (~p10(X0, X1))) | (~p10(X0, X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p10_19')).
% 0.12/0.40 tff(53,plain,
% 0.12/0.40 (![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.12/0.40 tff(54,plain,
% 0.12/0.40 (![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.12/0.40 tff(55,plain,(
% 0.12/0.40 ![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))),
% 0.12/0.40 inference(skolemize,[status(sab)],[54])).
% 0.12/0.40 tff(56,plain,
% 0.12/0.40 (![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[55, 48])).
% 0.12/0.40 tff(57,plain,
% 0.12/0.40 (((~![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))) | ((~p10(f13(f6(c22), c27), f13(f6(c22), c27))) | (~p10(f13(f6(c22), c27), f13(f6(c24), f16(c26, c27)))) | p10(f13(f6(c24), f16(c26, c27)), f13(f6(c22), c27)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))) | (~p10(f13(f6(c22), c27), f13(f6(c22), c27))) | (~p10(f13(f6(c22), c27), f13(f6(c24), f16(c26, c27)))) | p10(f13(f6(c24), f16(c26, c27)), f13(f6(c22), c27)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(58,plain,
% 0.12/0.40 ((~![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))) | ((~p10(f13(f6(c22), c27), f13(f6(c22), c27))) | (~p10(f13(f6(c22), c27), f13(f6(c24), f16(c26, c27)))) | p10(f13(f6(c24), f16(c26, c27)), f13(f6(c22), c27)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(59,plain,
% 0.12/0.40 ((~![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))) | (~p10(f13(f6(c22), c27), f13(f6(c22), c27))) | (~p10(f13(f6(c22), c27), f13(f6(c24), f16(c26, c27)))) | p10(f13(f6(c24), f16(c26, c27)), f13(f6(c22), c27))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.12/0.40 tff(60,plain,
% 0.12/0.40 (p10(f13(f6(c24), f16(c26, c27)), f13(f6(c22), c27))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[59, 56, 46, 37])).
% 0.12/0.40 tff(61,plain,
% 0.12/0.40 (^[X23: $i, X24: $i] : refl(((~p10(X23, X24)) | p11(f12(X23), f12(X24))) <=> ((~p10(X23, X24)) | p11(f12(X23), f12(X24))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(62,plain,
% 0.12/0.40 (![X23: $i, X24: $i] : ((~p10(X23, X24)) | p11(f12(X23), f12(X24))) <=> ![X23: $i, X24: $i] : ((~p10(X23, X24)) | p11(f12(X23), f12(X24)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[61])).
% 0.12/0.40 tff(63,plain,
% 0.12/0.40 (![X23: $i, X24: $i] : ((~p10(X23, X24)) | p11(f12(X23), f12(X24))) <=> ![X23: $i, X24: $i] : ((~p10(X23, X24)) | p11(f12(X23), f12(X24)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(64,plain,
% 0.12/0.40 (^[X23: $i, X24: $i] : rewrite((p11(f12(X23), f12(X24)) | (~p10(X23, X24))) <=> ((~p10(X23, X24)) | p11(f12(X23), f12(X24))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(65,plain,
% 0.12/0.40 (![X23: $i, X24: $i] : (p11(f12(X23), f12(X24)) | (~p10(X23, X24))) <=> ![X23: $i, X24: $i] : ((~p10(X23, X24)) | p11(f12(X23), f12(X24)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[64])).
% 0.12/0.40 tff(66,axiom,(![X23: $i, X24: $i] : (p11(f12(X23), f12(X24)) | (~p10(X23, X24)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p11_18')).
% 0.12/0.40 tff(67,plain,
% 0.12/0.40 (![X23: $i, X24: $i] : ((~p10(X23, X24)) | p11(f12(X23), f12(X24)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.12/0.40 tff(68,plain,
% 0.12/0.40 (![X23: $i, X24: $i] : ((~p10(X23, X24)) | p11(f12(X23), f12(X24)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.12/0.40 tff(69,plain,(
% 0.12/0.40 ![X23: $i, X24: $i] : ((~p10(X23, X24)) | p11(f12(X23), f12(X24)))),
% 0.12/0.40 inference(skolemize,[status(sab)],[68])).
% 0.12/0.40 tff(70,plain,
% 0.12/0.40 (![X23: $i, X24: $i] : ((~p10(X23, X24)) | p11(f12(X23), f12(X24)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[69, 62])).
% 0.12/0.40 tff(71,plain,
% 0.12/0.40 (((~![X23: $i, X24: $i] : ((~p10(X23, X24)) | p11(f12(X23), f12(X24)))) | ((~p10(f13(f6(c24), f16(c26, c27)), f13(f6(c22), c27))) | p11(f12(f13(f6(c24), f16(c26, c27))), f12(f13(f6(c22), c27))))) <=> ((~![X23: $i, X24: $i] : ((~p10(X23, X24)) | p11(f12(X23), f12(X24)))) | (~p10(f13(f6(c24), f16(c26, c27)), f13(f6(c22), c27))) | p11(f12(f13(f6(c24), f16(c26, c27))), f12(f13(f6(c22), c27))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(72,plain,
% 0.12/0.40 ((~![X23: $i, X24: $i] : ((~p10(X23, X24)) | p11(f12(X23), f12(X24)))) | ((~p10(f13(f6(c24), f16(c26, c27)), f13(f6(c22), c27))) | p11(f12(f13(f6(c24), f16(c26, c27))), f12(f13(f6(c22), c27))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(73,plain,
% 0.12/0.40 ((~![X23: $i, X24: $i] : ((~p10(X23, X24)) | p11(f12(X23), f12(X24)))) | (~p10(f13(f6(c24), f16(c26, c27)), f13(f6(c22), c27))) | p11(f12(f13(f6(c24), f16(c26, c27))), f12(f13(f6(c22), c27)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.12/0.40 tff(74,plain,
% 0.12/0.40 (p11(f12(f13(f6(c24), f16(c26, c27))), f12(f13(f6(c22), c27)))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[73, 70, 60])).
% 0.12/0.40 tff(75,assumption,(~p3(c25, c25)), introduced(assumption)).
% 0.12/0.40 tff(76,plain,
% 0.12/0.40 (^[X45: $i] : refl(p3(X45, X45) <=> p3(X45, X45))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(77,plain,
% 0.12/0.40 (![X45: $i] : p3(X45, X45) <=> ![X45: $i] : p3(X45, X45)),
% 0.12/0.40 inference(quant_intro,[status(thm)],[76])).
% 0.12/0.40 tff(78,plain,
% 0.12/0.40 (![X45: $i] : p3(X45, X45) <=> ![X45: $i] : p3(X45, X45)),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(79,axiom,(![X45: $i] : p3(X45, X45)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p3_3')).
% 0.12/0.40 tff(80,plain,
% 0.12/0.40 (![X45: $i] : p3(X45, X45)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.12/0.40 tff(81,plain,(
% 0.12/0.40 ![X45: $i] : p3(X45, X45)),
% 0.12/0.40 inference(skolemize,[status(sab)],[80])).
% 0.12/0.40 tff(82,plain,
% 0.12/0.40 (![X45: $i] : p3(X45, X45)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.12/0.40 tff(83,plain,
% 0.12/0.40 ((~![X45: $i] : p3(X45, X45)) | p3(c25, c25)),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(84,plain,
% 0.12/0.40 ($false),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[83, 82, 75])).
% 0.12/0.40 tff(85,plain,(p3(c25, c25)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.40 tff(86,plain,
% 0.12/0.40 (^[X51: $i, X50: $i] : refl(((~p3(X50, X51)) | p3(f7(X50), f7(X51))) <=> ((~p3(X50, X51)) | p3(f7(X50), f7(X51))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(87,plain,
% 0.12/0.40 (![X51: $i, X50: $i] : ((~p3(X50, X51)) | p3(f7(X50), f7(X51))) <=> ![X51: $i, X50: $i] : ((~p3(X50, X51)) | p3(f7(X50), f7(X51)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[86])).
% 0.12/0.40 tff(88,plain,
% 0.12/0.40 (![X51: $i, X50: $i] : ((~p3(X50, X51)) | p3(f7(X50), f7(X51))) <=> ![X51: $i, X50: $i] : ((~p3(X50, X51)) | p3(f7(X50), f7(X51)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(89,plain,
% 0.12/0.40 (^[X51: $i, X50: $i] : rewrite((p3(f7(X50), f7(X51)) | (~p3(X50, X51))) <=> ((~p3(X50, X51)) | p3(f7(X50), f7(X51))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(90,plain,
% 0.12/0.40 (![X51: $i, X50: $i] : (p3(f7(X50), f7(X51)) | (~p3(X50, X51))) <=> ![X51: $i, X50: $i] : ((~p3(X50, X51)) | p3(f7(X50), f7(X51)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[89])).
% 0.12/0.40 tff(91,axiom,(![X51: $i, X50: $i] : (p3(f7(X50), f7(X51)) | (~p3(X50, X51)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p3_15')).
% 0.12/0.40 tff(92,plain,
% 0.12/0.40 (![X51: $i, X50: $i] : ((~p3(X50, X51)) | p3(f7(X50), f7(X51)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.12/0.40 tff(93,plain,
% 0.12/0.40 (![X51: $i, X50: $i] : ((~p3(X50, X51)) | p3(f7(X50), f7(X51)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[92, 88])).
% 0.12/0.40 tff(94,plain,(
% 0.12/0.40 ![X51: $i, X50: $i] : ((~p3(X50, X51)) | p3(f7(X50), f7(X51)))),
% 0.12/0.40 inference(skolemize,[status(sab)],[93])).
% 0.12/0.40 tff(95,plain,
% 0.12/0.40 (![X51: $i, X50: $i] : ((~p3(X50, X51)) | p3(f7(X50), f7(X51)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[94, 87])).
% 0.12/0.40 tff(96,plain,
% 0.12/0.40 (((~![X51: $i, X50: $i] : ((~p3(X50, X51)) | p3(f7(X50), f7(X51)))) | ((~p3(c25, c25)) | p3(f7(c25), f7(c25)))) <=> ((~![X51: $i, X50: $i] : ((~p3(X50, X51)) | p3(f7(X50), f7(X51)))) | (~p3(c25, c25)) | p3(f7(c25), f7(c25)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(97,plain,
% 0.12/0.40 ((~![X51: $i, X50: $i] : ((~p3(X50, X51)) | p3(f7(X50), f7(X51)))) | ((~p3(c25, c25)) | p3(f7(c25), f7(c25)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(98,plain,
% 0.12/0.40 ((~![X51: $i, X50: $i] : ((~p3(X50, X51)) | p3(f7(X50), f7(X51)))) | (~p3(c25, c25)) | p3(f7(c25), f7(c25))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.12/0.40 tff(99,plain,
% 0.12/0.40 ((~p3(c25, c25)) | p3(f7(c25), f7(c25))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[98, 95])).
% 0.12/0.40 tff(100,plain,
% 0.12/0.40 (p3(f7(c25), f7(c25))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[99, 85])).
% 0.12/0.40 tff(101,plain,
% 0.12/0.40 (^[X25: $i, X26: $i] : refl(((~p3(X25, X26)) | p11(f15(X25), f15(X26))) <=> ((~p3(X25, X26)) | p11(f15(X25), f15(X26))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(102,plain,
% 0.12/0.40 (![X25: $i, X26: $i] : ((~p3(X25, X26)) | p11(f15(X25), f15(X26))) <=> ![X25: $i, X26: $i] : ((~p3(X25, X26)) | p11(f15(X25), f15(X26)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[101])).
% 0.12/0.40 tff(103,plain,
% 0.12/0.40 (![X25: $i, X26: $i] : ((~p3(X25, X26)) | p11(f15(X25), f15(X26))) <=> ![X25: $i, X26: $i] : ((~p3(X25, X26)) | p11(f15(X25), f15(X26)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(104,plain,
% 0.12/0.40 (^[X25: $i, X26: $i] : rewrite((p11(f15(X25), f15(X26)) | (~p3(X25, X26))) <=> ((~p3(X25, X26)) | p11(f15(X25), f15(X26))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(105,plain,
% 0.12/0.40 (![X25: $i, X26: $i] : (p11(f15(X25), f15(X26)) | (~p3(X25, X26))) <=> ![X25: $i, X26: $i] : ((~p3(X25, X26)) | p11(f15(X25), f15(X26)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[104])).
% 0.12/0.40 tff(106,axiom,(![X25: $i, X26: $i] : (p11(f15(X25), f15(X26)) | (~p3(X25, X26)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p11_17')).
% 0.12/0.40 tff(107,plain,
% 0.12/0.40 (![X25: $i, X26: $i] : ((~p3(X25, X26)) | p11(f15(X25), f15(X26)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.12/0.40 tff(108,plain,
% 0.12/0.40 (![X25: $i, X26: $i] : ((~p3(X25, X26)) | p11(f15(X25), f15(X26)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[107, 103])).
% 0.12/0.40 tff(109,plain,(
% 0.12/0.40 ![X25: $i, X26: $i] : ((~p3(X25, X26)) | p11(f15(X25), f15(X26)))),
% 0.12/0.40 inference(skolemize,[status(sab)],[108])).
% 0.12/0.40 tff(110,plain,
% 0.12/0.40 (![X25: $i, X26: $i] : ((~p3(X25, X26)) | p11(f15(X25), f15(X26)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[109, 102])).
% 0.12/0.40 tff(111,plain,
% 0.12/0.40 (((~![X25: $i, X26: $i] : ((~p3(X25, X26)) | p11(f15(X25), f15(X26)))) | ((~p3(f7(c25), f7(c25))) | p11(f15(f7(c25)), f15(f7(c25))))) <=> ((~![X25: $i, X26: $i] : ((~p3(X25, X26)) | p11(f15(X25), f15(X26)))) | (~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(112,plain,
% 0.12/0.40 ((~![X25: $i, X26: $i] : ((~p3(X25, X26)) | p11(f15(X25), f15(X26)))) | ((~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(113,plain,
% 0.12/0.40 ((~![X25: $i, X26: $i] : ((~p3(X25, X26)) | p11(f15(X25), f15(X26)))) | (~p3(f7(c25), f7(c25))) | p11(f15(f7(c25)), f15(f7(c25)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.12/0.40 tff(114,plain,
% 0.12/0.40 (p11(f15(f7(c25)), f15(f7(c25)))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[113, 110, 100])).
% 0.12/0.41 tff(115,plain,
% 0.12/0.41 (^[X11: $i, X10: $i] : refl(((~p11(X10, X11)) | p10(f14(X10), f14(X11))) <=> ((~p11(X10, X11)) | p10(f14(X10), f14(X11))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(116,plain,
% 0.12/0.41 (![X11: $i, X10: $i] : ((~p11(X10, X11)) | p10(f14(X10), f14(X11))) <=> ![X11: $i, X10: $i] : ((~p11(X10, X11)) | p10(f14(X10), f14(X11)))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[115])).
% 0.12/0.41 tff(117,plain,
% 0.12/0.41 (![X11: $i, X10: $i] : ((~p11(X10, X11)) | p10(f14(X10), f14(X11))) <=> ![X11: $i, X10: $i] : ((~p11(X10, X11)) | p10(f14(X10), f14(X11)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(118,plain,
% 0.12/0.41 (^[X11: $i, X10: $i] : rewrite((p10(f14(X10), f14(X11)) | (~p11(X10, X11))) <=> ((~p11(X10, X11)) | p10(f14(X10), f14(X11))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(119,plain,
% 0.12/0.41 (![X11: $i, X10: $i] : (p10(f14(X10), f14(X11)) | (~p11(X10, X11))) <=> ![X11: $i, X10: $i] : ((~p11(X10, X11)) | p10(f14(X10), f14(X11)))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[118])).
% 0.12/0.41 tff(120,axiom,(![X11: $i, X10: $i] : (p10(f14(X10), f14(X11)) | (~p11(X10, X11)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p10_11')).
% 0.12/0.41 tff(121,plain,
% 0.12/0.41 (![X11: $i, X10: $i] : ((~p11(X10, X11)) | p10(f14(X10), f14(X11)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.12/0.41 tff(122,plain,
% 0.12/0.41 (![X11: $i, X10: $i] : ((~p11(X10, X11)) | p10(f14(X10), f14(X11)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[121, 117])).
% 0.12/0.41 tff(123,plain,(
% 0.12/0.41 ![X11: $i, X10: $i] : ((~p11(X10, X11)) | p10(f14(X10), f14(X11)))),
% 0.12/0.41 inference(skolemize,[status(sab)],[122])).
% 0.12/0.41 tff(124,plain,
% 0.12/0.41 (![X11: $i, X10: $i] : ((~p11(X10, X11)) | p10(f14(X10), f14(X11)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[123, 116])).
% 0.12/0.41 tff(125,plain,
% 0.12/0.41 (((~![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)))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(126,plain,
% 0.12/0.41 ((~![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)))))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(127,plain,
% 0.12/0.41 ((~![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))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.12/0.41 tff(128,plain,
% 0.12/0.41 (p10(f14(f15(f7(c25))), f14(f15(f7(c25))))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[127, 124, 114])).
% 0.12/0.41 tff(129,plain,
% 0.12/0.41 (((~![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))))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(130,plain,
% 0.12/0.41 ((~![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))))))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(131,plain,
% 0.12/0.41 ((~![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)))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.12/0.41 tff(132,plain,
% 0.12/0.41 ((~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)))))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[131, 32])).
% 0.12/0.41 tff(133,plain,
% 0.12/0.41 ((~p5(f6(c22), f6(c22))) | p10(f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c22), f14(f15(f7(c25)))))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[132, 128])).
% 0.12/0.41 tff(134,plain,
% 0.12/0.41 (p10(f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c22), f14(f15(f7(c25)))))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[133, 22])).
% 0.12/0.41 tff(135,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(136,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)],[135, 44])).
% 0.12/0.41 tff(137,plain,
% 0.12/0.41 (((~![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))) | ((~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(c24), f16(c26, f14(f15(f7(c25))))), f13(f6(c22), f14(f15(f7(c25))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))) | (~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(c24), f16(c26, f14(f15(f7(c25))))), f13(f6(c22), f14(f15(f7(c25))))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(138,plain,
% 0.12/0.41 ((~![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))) | ((~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(c24), f16(c26, f14(f15(f7(c25))))), f13(f6(c22), f14(f15(f7(c25))))))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(139,plain,
% 0.12/0.41 ((~![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))) | (~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(c24), f16(c26, f14(f15(f7(c25))))), f13(f6(c22), f14(f15(f7(c25)))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.12/0.41 tff(140,plain,
% 0.12/0.41 (p10(f13(f6(c24), f16(c26, f14(f15(f7(c25))))), f13(f6(c22), f14(f15(f7(c25)))))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[139, 56, 136, 134])).
% 0.12/0.41 tff(141,plain,
% 0.12/0.41 (((~![X23: $i, X24: $i] : ((~p10(X23, X24)) | p11(f12(X23), f12(X24)))) | ((~p10(f13(f6(c24), f16(c26, f14(f15(f7(c25))))), f13(f6(c22), f14(f15(f7(c25)))))) | p11(f12(f13(f6(c24), f16(c26, f14(f15(f7(c25)))))), f12(f13(f6(c22), f14(f15(f7(c25)))))))) <=> ((~![X23: $i, X24: $i] : ((~p10(X23, X24)) | p11(f12(X23), f12(X24)))) | (~p10(f13(f6(c24), f16(c26, f14(f15(f7(c25))))), f13(f6(c22), f14(f15(f7(c25)))))) | p11(f12(f13(f6(c24), f16(c26, f14(f15(f7(c25)))))), f12(f13(f6(c22), f14(f15(f7(c25)))))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(142,plain,
% 0.12/0.41 ((~![X23: $i, X24: $i] : ((~p10(X23, X24)) | p11(f12(X23), f12(X24)))) | ((~p10(f13(f6(c24), f16(c26, f14(f15(f7(c25))))), f13(f6(c22), f14(f15(f7(c25)))))) | p11(f12(f13(f6(c24), f16(c26, f14(f15(f7(c25)))))), f12(f13(f6(c22), f14(f15(f7(c25)))))))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(143,plain,
% 0.12/0.41 ((~![X23: $i, X24: $i] : ((~p10(X23, X24)) | p11(f12(X23), f12(X24)))) | (~p10(f13(f6(c24), f16(c26, f14(f15(f7(c25))))), f13(f6(c22), f14(f15(f7(c25)))))) | p11(f12(f13(f6(c24), f16(c26, f14(f15(f7(c25)))))), f12(f13(f6(c22), f14(f15(f7(c25))))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.12/0.41 tff(144,plain,
% 0.12/0.41 (p11(f12(f13(f6(c24), f16(c26, f14(f15(f7(c25)))))), f12(f13(f6(c22), f14(f15(f7(c25))))))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[143, 70, 140])).
% 0.12/0.41 tff(145,plain,
% 0.12/0.41 (((~![X23: $i, X24: $i] : ((~p10(X23, X24)) | p11(f12(X23), f12(X24)))) | ((~p10(f13(f6(c22), c27), f13(f6(c24), f16(c26, c27)))) | p11(f12(f13(f6(c22), c27)), f12(f13(f6(c24), f16(c26, c27)))))) <=> ((~![X23: $i, X24: $i] : ((~p10(X23, X24)) | p11(f12(X23), f12(X24)))) | (~p10(f13(f6(c22), c27), f13(f6(c24), f16(c26, c27)))) | p11(f12(f13(f6(c22), c27)), f12(f13(f6(c24), f16(c26, c27)))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(146,plain,
% 0.12/0.41 ((~![X23: $i, X24: $i] : ((~p10(X23, X24)) | p11(f12(X23), f12(X24)))) | ((~p10(f13(f6(c22), c27), f13(f6(c24), f16(c26, c27)))) | p11(f12(f13(f6(c22), c27)), f12(f13(f6(c24), f16(c26, c27)))))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(147,plain,
% 0.12/0.41 ((~![X23: $i, X24: $i] : ((~p10(X23, X24)) | p11(f12(X23), f12(X24)))) | (~p10(f13(f6(c22), c27), f13(f6(c24), f16(c26, c27)))) | p11(f12(f13(f6(c22), c27)), f12(f13(f6(c24), f16(c26, c27))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.12/0.41 tff(148,plain,
% 0.12/0.41 (p11(f12(f13(f6(c22), c27)), f12(f13(f6(c24), f16(c26, c27))))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[147, 70, 46])).
% 0.12/0.41 tff(149,plain,
% 0.12/0.41 (^[X22: $i, X21: $i, X20: $i] : refl(((~p11(X20, X21)) | (~p11(X20, X22)) | p11(X21, X22)) <=> ((~p11(X20, X21)) | (~p11(X20, X22)) | p11(X21, X22)))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(150,plain,
% 0.12/0.41 (![X22: $i, X21: $i, X20: $i] : ((~p11(X20, X21)) | (~p11(X20, X22)) | p11(X21, X22)) <=> ![X22: $i, X21: $i, X20: $i] : ((~p11(X20, X21)) | (~p11(X20, X22)) | p11(X21, X22))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[149])).
% 0.12/0.41 tff(151,plain,
% 0.12/0.41 (![X22: $i, X21: $i, X20: $i] : ((~p11(X20, X21)) | (~p11(X20, X22)) | p11(X21, X22)) <=> ![X22: $i, X21: $i, X20: $i] : ((~p11(X20, X21)) | (~p11(X20, X22)) | p11(X21, X22))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(152,plain,
% 0.12/0.41 (^[X22: $i, X21: $i, X20: $i] : trans(monotonicity(rewrite((p11(X21, X22) | (~p11(X20, X21))) <=> ((~p11(X20, X21)) | p11(X21, X22))), (((p11(X21, X22) | (~p11(X20, X21))) | (~p11(X20, X22))) <=> (((~p11(X20, X21)) | p11(X21, X22)) | (~p11(X20, X22))))), rewrite((((~p11(X20, X21)) | p11(X21, X22)) | (~p11(X20, X22))) <=> ((~p11(X20, X21)) | (~p11(X20, X22)) | p11(X21, X22))), (((p11(X21, X22) | (~p11(X20, X21))) | (~p11(X20, X22))) <=> ((~p11(X20, X21)) | (~p11(X20, X22)) | p11(X21, X22))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(153,plain,
% 0.12/0.41 (![X22: $i, X21: $i, X20: $i] : ((p11(X21, X22) | (~p11(X20, X21))) | (~p11(X20, X22))) <=> ![X22: $i, X21: $i, X20: $i] : ((~p11(X20, X21)) | (~p11(X20, X22)) | p11(X21, X22))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[152])).
% 0.12/0.41 tff(154,axiom,(![X22: $i, X21: $i, X20: $i] : ((p11(X21, X22) | (~p11(X20, X21))) | (~p11(X20, X22)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p11_23')).
% 0.12/0.41 tff(155,plain,
% 0.12/0.41 (![X22: $i, X21: $i, X20: $i] : ((~p11(X20, X21)) | (~p11(X20, X22)) | p11(X21, X22))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.12/0.41 tff(156,plain,
% 0.12/0.41 (![X22: $i, X21: $i, X20: $i] : ((~p11(X20, X21)) | (~p11(X20, X22)) | p11(X21, X22))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[155, 151])).
% 0.12/0.41 tff(157,plain,(
% 0.12/0.41 ![X22: $i, X21: $i, X20: $i] : ((~p11(X20, X21)) | (~p11(X20, X22)) | p11(X21, X22))),
% 0.12/0.41 inference(skolemize,[status(sab)],[156])).
% 0.12/0.41 tff(158,plain,
% 0.12/0.41 (![X22: $i, X21: $i, X20: $i] : ((~p11(X20, X21)) | (~p11(X20, X22)) | p11(X21, X22))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[157, 150])).
% 0.12/0.41 tff(159,plain,
% 0.12/0.41 (((~![X22: $i, X21: $i, X20: $i] : ((~p11(X20, X21)) | (~p11(X20, X22)) | p11(X21, X22))) | ((~p11(f12(f13(f6(c22), c27)), f12(f13(f6(c24), f16(c26, c27))))) | p11(f12(f13(f6(c24), f16(c26, c27))), f12(f13(f6(c24), f16(c26, c27)))))) <=> ((~![X22: $i, X21: $i, X20: $i] : ((~p11(X20, X21)) | (~p11(X20, X22)) | p11(X21, X22))) | (~p11(f12(f13(f6(c22), c27)), f12(f13(f6(c24), f16(c26, c27))))) | p11(f12(f13(f6(c24), f16(c26, c27))), f12(f13(f6(c24), f16(c26, c27)))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(160,plain,
% 0.12/0.41 (((~p11(f12(f13(f6(c22), c27)), f12(f13(f6(c24), f16(c26, c27))))) | (~p11(f12(f13(f6(c22), c27)), f12(f13(f6(c24), f16(c26, c27))))) | p11(f12(f13(f6(c24), f16(c26, c27))), f12(f13(f6(c24), f16(c26, c27))))) <=> ((~p11(f12(f13(f6(c22), c27)), f12(f13(f6(c24), f16(c26, c27))))) | p11(f12(f13(f6(c24), f16(c26, c27))), f12(f13(f6(c24), f16(c26, c27)))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(161,plain,
% 0.20/0.42 (((~![X22: $i, X21: $i, X20: $i] : ((~p11(X20, X21)) | (~p11(X20, X22)) | p11(X21, X22))) | ((~p11(f12(f13(f6(c22), c27)), f12(f13(f6(c24), f16(c26, c27))))) | (~p11(f12(f13(f6(c22), c27)), f12(f13(f6(c24), f16(c26, c27))))) | p11(f12(f13(f6(c24), f16(c26, c27))), f12(f13(f6(c24), f16(c26, c27)))))) <=> ((~![X22: $i, X21: $i, X20: $i] : ((~p11(X20, X21)) | (~p11(X20, X22)) | p11(X21, X22))) | ((~p11(f12(f13(f6(c22), c27)), f12(f13(f6(c24), f16(c26, c27))))) | p11(f12(f13(f6(c24), f16(c26, c27))), f12(f13(f6(c24), f16(c26, c27))))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[160])).
% 0.20/0.42 tff(162,plain,
% 0.20/0.42 (((~![X22: $i, X21: $i, X20: $i] : ((~p11(X20, X21)) | (~p11(X20, X22)) | p11(X21, X22))) | ((~p11(f12(f13(f6(c22), c27)), f12(f13(f6(c24), f16(c26, c27))))) | (~p11(f12(f13(f6(c22), c27)), f12(f13(f6(c24), f16(c26, c27))))) | p11(f12(f13(f6(c24), f16(c26, c27))), f12(f13(f6(c24), f16(c26, c27)))))) <=> ((~![X22: $i, X21: $i, X20: $i] : ((~p11(X20, X21)) | (~p11(X20, X22)) | p11(X21, X22))) | (~p11(f12(f13(f6(c22), c27)), f12(f13(f6(c24), f16(c26, c27))))) | p11(f12(f13(f6(c24), f16(c26, c27))), f12(f13(f6(c24), f16(c26, c27)))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[161, 159])).
% 0.20/0.42 tff(163,plain,
% 0.20/0.42 ((~![X22: $i, X21: $i, X20: $i] : ((~p11(X20, X21)) | (~p11(X20, X22)) | p11(X21, X22))) | ((~p11(f12(f13(f6(c22), c27)), f12(f13(f6(c24), f16(c26, c27))))) | (~p11(f12(f13(f6(c22), c27)), f12(f13(f6(c24), f16(c26, c27))))) | p11(f12(f13(f6(c24), f16(c26, c27))), f12(f13(f6(c24), f16(c26, c27)))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(164,plain,
% 0.20/0.42 ((~![X22: $i, X21: $i, X20: $i] : ((~p11(X20, X21)) | (~p11(X20, X22)) | p11(X21, X22))) | (~p11(f12(f13(f6(c22), c27)), f12(f13(f6(c24), f16(c26, c27))))) | p11(f12(f13(f6(c24), f16(c26, c27))), f12(f13(f6(c24), f16(c26, c27))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.20/0.42 tff(165,plain,
% 0.20/0.42 (p11(f12(f13(f6(c24), f16(c26, c27))), f12(f13(f6(c24), f16(c26, c27))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[164, 158, 148])).
% 0.20/0.42 tff(166,plain,
% 0.20/0.42 (^[X40: $i] : refl(p20(f12(f13(f6(c22), f14(f15(f7(c25))))), f12(f13(f6(c24), X40))) <=> p20(f12(f13(f6(c22), f14(f15(f7(c25))))), f12(f13(f6(c24), X40))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(167,plain,
% 0.20/0.42 (![X40: $i] : p20(f12(f13(f6(c22), f14(f15(f7(c25))))), f12(f13(f6(c24), X40))) <=> ![X40: $i] : p20(f12(f13(f6(c22), f14(f15(f7(c25))))), f12(f13(f6(c24), X40)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[166])).
% 0.20/0.42 tff(168,plain,
% 0.20/0.42 (![X40: $i] : p20(f12(f13(f6(c22), f14(f15(f7(c25))))), f12(f13(f6(c24), X40))) <=> ![X40: $i] : p20(f12(f13(f6(c22), f14(f15(f7(c25))))), f12(f13(f6(c24), X40)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(169,axiom,(![X40: $i] : p20(f12(f13(f6(c22), f14(f15(f7(c25))))), f12(f13(f6(c24), X40)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p20_32')).
% 0.20/0.42 tff(170,plain,
% 0.20/0.42 (![X40: $i] : p20(f12(f13(f6(c22), f14(f15(f7(c25))))), f12(f13(f6(c24), X40)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.20/0.42 tff(171,plain,(
% 0.20/0.42 ![X40: $i] : p20(f12(f13(f6(c22), f14(f15(f7(c25))))), f12(f13(f6(c24), X40)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[170])).
% 0.20/0.42 tff(172,plain,
% 0.20/0.42 (![X40: $i] : p20(f12(f13(f6(c22), f14(f15(f7(c25))))), f12(f13(f6(c24), X40)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[171, 167])).
% 0.20/0.42 tff(173,plain,
% 0.20/0.42 ((~![X40: $i] : p20(f12(f13(f6(c22), f14(f15(f7(c25))))), f12(f13(f6(c24), X40)))) | p20(f12(f13(f6(c22), f14(f15(f7(c25))))), f12(f13(f6(c24), f16(c26, c27))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(174,plain,
% 0.20/0.42 (p20(f12(f13(f6(c22), f14(f15(f7(c25))))), f12(f13(f6(c24), f16(c26, c27))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[173, 172])).
% 0.20/0.42 tff(175,plain,
% 0.20/0.42 (((~![X23: $i, X24: $i] : ((~p10(X23, X24)) | p11(f12(X23), f12(X24)))) | ((~p10(f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c24), f16(c26, f14(f15(f7(c25))))))) | p11(f12(f13(f6(c22), f14(f15(f7(c25))))), f12(f13(f6(c24), f16(c26, f14(f15(f7(c25))))))))) <=> ((~![X23: $i, X24: $i] : ((~p10(X23, X24)) | p11(f12(X23), f12(X24)))) | (~p10(f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c24), f16(c26, f14(f15(f7(c25))))))) | p11(f12(f13(f6(c22), f14(f15(f7(c25))))), f12(f13(f6(c24), f16(c26, f14(f15(f7(c25))))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(176,plain,
% 0.20/0.42 ((~![X23: $i, X24: $i] : ((~p10(X23, X24)) | p11(f12(X23), f12(X24)))) | ((~p10(f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c24), f16(c26, f14(f15(f7(c25))))))) | p11(f12(f13(f6(c22), f14(f15(f7(c25))))), f12(f13(f6(c24), f16(c26, f14(f15(f7(c25))))))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(177,plain,
% 0.20/0.42 ((~![X23: $i, X24: $i] : ((~p10(X23, X24)) | p11(f12(X23), f12(X24)))) | (~p10(f13(f6(c22), f14(f15(f7(c25)))), f13(f6(c24), f16(c26, f14(f15(f7(c25))))))) | p11(f12(f13(f6(c22), f14(f15(f7(c25))))), f12(f13(f6(c24), f16(c26, f14(f15(f7(c25)))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.20/0.42 tff(178,plain,
% 0.20/0.42 (p11(f12(f13(f6(c22), f14(f15(f7(c25))))), f12(f13(f6(c24), f16(c26, f14(f15(f7(c25)))))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[177, 70, 136])).
% 0.20/0.42 tff(179,plain,
% 0.20/0.42 (^[X39: $i, X38: $i, X37: $i, X36: $i] : refl(((~p11(X38, X36)) | (~p20(X38, X39)) | (~p11(X39, X37)) | p20(X36, X37)) <=> ((~p11(X38, X36)) | (~p20(X38, X39)) | (~p11(X39, X37)) | p20(X36, X37)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(180,plain,
% 0.20/0.42 (![X39: $i, X38: $i, X37: $i, X36: $i] : ((~p11(X38, X36)) | (~p20(X38, X39)) | (~p11(X39, X37)) | p20(X36, X37)) <=> ![X39: $i, X38: $i, X37: $i, X36: $i] : ((~p11(X38, X36)) | (~p20(X38, X39)) | (~p11(X39, X37)) | p20(X36, X37))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[179])).
% 0.20/0.42 tff(181,plain,
% 0.20/0.42 (![X39: $i, X38: $i, X37: $i, X36: $i] : ((~p11(X38, X36)) | (~p20(X38, X39)) | (~p11(X39, X37)) | p20(X36, X37)) <=> ![X39: $i, X38: $i, X37: $i, X36: $i] : ((~p11(X38, X36)) | (~p20(X38, X39)) | (~p11(X39, X37)) | p20(X36, X37))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(182,plain,
% 0.20/0.42 (^[X39: $i, X38: $i, X37: $i, X36: $i] : trans(monotonicity(trans(monotonicity(rewrite((p20(X36, X37) | (~p11(X39, X37))) <=> ((~p11(X39, X37)) | p20(X36, X37))), (((p20(X36, X37) | (~p11(X39, X37))) | (~p20(X38, X39))) <=> (((~p11(X39, X37)) | p20(X36, X37)) | (~p20(X38, X39))))), rewrite((((~p11(X39, X37)) | p20(X36, X37)) | (~p20(X38, X39))) <=> ((~p20(X38, X39)) | (~p11(X39, X37)) | p20(X36, X37))), (((p20(X36, X37) | (~p11(X39, X37))) | (~p20(X38, X39))) <=> ((~p20(X38, X39)) | (~p11(X39, X37)) | p20(X36, X37)))), ((((p20(X36, X37) | (~p11(X39, X37))) | (~p20(X38, X39))) | (~p11(X38, X36))) <=> (((~p20(X38, X39)) | (~p11(X39, X37)) | p20(X36, X37)) | (~p11(X38, X36))))), rewrite((((~p20(X38, X39)) | (~p11(X39, X37)) | p20(X36, X37)) | (~p11(X38, X36))) <=> ((~p11(X38, X36)) | (~p20(X38, X39)) | (~p11(X39, X37)) | p20(X36, X37))), ((((p20(X36, X37) | (~p11(X39, X37))) | (~p20(X38, X39))) | (~p11(X38, X36))) <=> ((~p11(X38, X36)) | (~p20(X38, X39)) | (~p11(X39, X37)) | p20(X36, X37))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(183,plain,
% 0.20/0.42 (![X39: $i, X38: $i, X37: $i, X36: $i] : (((p20(X36, X37) | (~p11(X39, X37))) | (~p20(X38, X39))) | (~p11(X38, X36))) <=> ![X39: $i, X38: $i, X37: $i, X36: $i] : ((~p11(X38, X36)) | (~p20(X38, X39)) | (~p11(X39, X37)) | p20(X36, X37))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[182])).
% 0.20/0.42 tff(184,axiom,(![X39: $i, X38: $i, X37: $i, X36: $i] : (((p20(X36, X37) | (~p11(X39, X37))) | (~p20(X38, X39))) | (~p11(X38, X36)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p20_28')).
% 0.20/0.42 tff(185,plain,
% 0.20/0.42 (![X39: $i, X38: $i, X37: $i, X36: $i] : ((~p11(X38, X36)) | (~p20(X38, X39)) | (~p11(X39, X37)) | p20(X36, X37))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.20/0.42 tff(186,plain,
% 0.20/0.42 (![X39: $i, X38: $i, X37: $i, X36: $i] : ((~p11(X38, X36)) | (~p20(X38, X39)) | (~p11(X39, X37)) | p20(X36, X37))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[185, 181])).
% 0.20/0.42 tff(187,plain,(
% 0.20/0.42 ![X39: $i, X38: $i, X37: $i, X36: $i] : ((~p11(X38, X36)) | (~p20(X38, X39)) | (~p11(X39, X37)) | p20(X36, X37))),
% 0.20/0.42 inference(skolemize,[status(sab)],[186])).
% 0.20/0.42 tff(188,plain,
% 0.20/0.42 (![X39: $i, X38: $i, X37: $i, X36: $i] : ((~p11(X38, X36)) | (~p20(X38, X39)) | (~p11(X39, X37)) | p20(X36, X37))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[187, 180])).
% 0.20/0.42 tff(189,plain,
% 0.20/0.42 (((~![X39: $i, X38: $i, X37: $i, X36: $i] : ((~p11(X38, X36)) | (~p20(X38, X39)) | (~p11(X39, X37)) | p20(X36, X37))) | ((~p11(f12(f13(f6(c22), f14(f15(f7(c25))))), f12(f13(f6(c24), f16(c26, f14(f15(f7(c25)))))))) | (~p20(f12(f13(f6(c22), f14(f15(f7(c25))))), f12(f13(f6(c24), f16(c26, c27))))) | (~p11(f12(f13(f6(c24), f16(c26, c27))), f12(f13(f6(c24), f16(c26, c27))))) | p20(f12(f13(f6(c24), f16(c26, f14(f15(f7(c25)))))), f12(f13(f6(c24), f16(c26, c27)))))) <=> ((~![X39: $i, X38: $i, X37: $i, X36: $i] : ((~p11(X38, X36)) | (~p20(X38, X39)) | (~p11(X39, X37)) | p20(X36, X37))) | (~p11(f12(f13(f6(c22), f14(f15(f7(c25))))), f12(f13(f6(c24), f16(c26, f14(f15(f7(c25)))))))) | (~p20(f12(f13(f6(c22), f14(f15(f7(c25))))), f12(f13(f6(c24), f16(c26, c27))))) | (~p11(f12(f13(f6(c24), f16(c26, c27))), f12(f13(f6(c24), f16(c26, c27))))) | p20(f12(f13(f6(c24), f16(c26, f14(f15(f7(c25)))))), f12(f13(f6(c24), f16(c26, c27)))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(190,plain,
% 0.20/0.42 ((~![X39: $i, X38: $i, X37: $i, X36: $i] : ((~p11(X38, X36)) | (~p20(X38, X39)) | (~p11(X39, X37)) | p20(X36, X37))) | ((~p11(f12(f13(f6(c22), f14(f15(f7(c25))))), f12(f13(f6(c24), f16(c26, f14(f15(f7(c25)))))))) | (~p20(f12(f13(f6(c22), f14(f15(f7(c25))))), f12(f13(f6(c24), f16(c26, c27))))) | (~p11(f12(f13(f6(c24), f16(c26, c27))), f12(f13(f6(c24), f16(c26, c27))))) | p20(f12(f13(f6(c24), f16(c26, f14(f15(f7(c25)))))), f12(f13(f6(c24), f16(c26, c27)))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(191,plain,
% 0.20/0.42 ((~![X39: $i, X38: $i, X37: $i, X36: $i] : ((~p11(X38, X36)) | (~p20(X38, X39)) | (~p11(X39, X37)) | p20(X36, X37))) | (~p11(f12(f13(f6(c22), f14(f15(f7(c25))))), f12(f13(f6(c24), f16(c26, f14(f15(f7(c25)))))))) | (~p20(f12(f13(f6(c22), f14(f15(f7(c25))))), f12(f13(f6(c24), f16(c26, c27))))) | (~p11(f12(f13(f6(c24), f16(c26, c27))), f12(f13(f6(c24), f16(c26, c27))))) | p20(f12(f13(f6(c24), f16(c26, f14(f15(f7(c25)))))), f12(f13(f6(c24), f16(c26, c27))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.20/0.42 tff(192,plain,
% 0.20/0.42 (p20(f12(f13(f6(c24), f16(c26, f14(f15(f7(c25)))))), f12(f13(f6(c24), f16(c26, c27))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[191, 188, 178, 174, 165])).
% 0.20/0.42 tff(193,plain,
% 0.20/0.42 ((~p20(f12(f13(f6(c22), f14(f15(f7(c25))))), f12(f13(f6(c22), c27)))) <=> (~p20(f12(f13(f6(c22), f14(f15(f7(c25))))), f12(f13(f6(c22), c27))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(194,axiom,(~p20(f12(f13(f6(c22), f14(f15(f7(c25))))), f12(f13(f6(c22), c27)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_p20_33')).
% 0.20/0.42 tff(195,plain,
% 0.20/0.42 (~p20(f12(f13(f6(c22), f14(f15(f7(c25))))), f12(f13(f6(c22), c27)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[194, 193])).
% 0.20/0.42 tff(196,plain,
% 0.20/0.42 (((~![X39: $i, X38: $i, X37: $i, X36: $i] : ((~p11(X38, X36)) | (~p20(X38, X39)) | (~p11(X39, X37)) | p20(X36, X37))) | (p20(f12(f13(f6(c22), f14(f15(f7(c25))))), f12(f13(f6(c22), c27))) | (~p11(f12(f13(f6(c24), f16(c26, f14(f15(f7(c25)))))), f12(f13(f6(c22), f14(f15(f7(c25))))))) | (~p20(f12(f13(f6(c24), f16(c26, f14(f15(f7(c25)))))), f12(f13(f6(c24), f16(c26, c27))))) | (~p11(f12(f13(f6(c24), f16(c26, c27))), f12(f13(f6(c22), c27)))))) <=> ((~![X39: $i, X38: $i, X37: $i, X36: $i] : ((~p11(X38, X36)) | (~p20(X38, X39)) | (~p11(X39, X37)) | p20(X36, X37))) | p20(f12(f13(f6(c22), f14(f15(f7(c25))))), f12(f13(f6(c22), c27))) | (~p11(f12(f13(f6(c24), f16(c26, f14(f15(f7(c25)))))), f12(f13(f6(c22), f14(f15(f7(c25))))))) | (~p20(f12(f13(f6(c24), f16(c26, f14(f15(f7(c25)))))), f12(f13(f6(c24), f16(c26, c27))))) | (~p11(f12(f13(f6(c24), f16(c26, c27))), f12(f13(f6(c22), c27)))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(197,plain,
% 0.20/0.42 (((~p11(f12(f13(f6(c24), f16(c26, f14(f15(f7(c25)))))), f12(f13(f6(c22), f14(f15(f7(c25))))))) | (~p20(f12(f13(f6(c24), f16(c26, f14(f15(f7(c25)))))), f12(f13(f6(c24), f16(c26, c27))))) | (~p11(f12(f13(f6(c24), f16(c26, c27))), f12(f13(f6(c22), c27)))) | p20(f12(f13(f6(c22), f14(f15(f7(c25))))), f12(f13(f6(c22), c27)))) <=> (p20(f12(f13(f6(c22), f14(f15(f7(c25))))), f12(f13(f6(c22), c27))) | (~p11(f12(f13(f6(c24), f16(c26, f14(f15(f7(c25)))))), f12(f13(f6(c22), f14(f15(f7(c25))))))) | (~p20(f12(f13(f6(c24), f16(c26, f14(f15(f7(c25)))))), f12(f13(f6(c24), f16(c26, c27))))) | (~p11(f12(f13(f6(c24), f16(c26, c27))), f12(f13(f6(c22), c27)))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(198,plain,
% 0.20/0.43 (((~![X39: $i, X38: $i, X37: $i, X36: $i] : ((~p11(X38, X36)) | (~p20(X38, X39)) | (~p11(X39, X37)) | p20(X36, X37))) | ((~p11(f12(f13(f6(c24), f16(c26, f14(f15(f7(c25)))))), f12(f13(f6(c22), f14(f15(f7(c25))))))) | (~p20(f12(f13(f6(c24), f16(c26, f14(f15(f7(c25)))))), f12(f13(f6(c24), f16(c26, c27))))) | (~p11(f12(f13(f6(c24), f16(c26, c27))), f12(f13(f6(c22), c27)))) | p20(f12(f13(f6(c22), f14(f15(f7(c25))))), f12(f13(f6(c22), c27))))) <=> ((~![X39: $i, X38: $i, X37: $i, X36: $i] : ((~p11(X38, X36)) | (~p20(X38, X39)) | (~p11(X39, X37)) | p20(X36, X37))) | (p20(f12(f13(f6(c22), f14(f15(f7(c25))))), f12(f13(f6(c22), c27))) | (~p11(f12(f13(f6(c24), f16(c26, f14(f15(f7(c25)))))), f12(f13(f6(c22), f14(f15(f7(c25))))))) | (~p20(f12(f13(f6(c24), f16(c26, f14(f15(f7(c25)))))), f12(f13(f6(c24), f16(c26, c27))))) | (~p11(f12(f13(f6(c24), f16(c26, c27))), f12(f13(f6(c22), c27))))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[197])).
% 0.20/0.43 tff(199,plain,
% 0.20/0.43 (((~![X39: $i, X38: $i, X37: $i, X36: $i] : ((~p11(X38, X36)) | (~p20(X38, X39)) | (~p11(X39, X37)) | p20(X36, X37))) | ((~p11(f12(f13(f6(c24), f16(c26, f14(f15(f7(c25)))))), f12(f13(f6(c22), f14(f15(f7(c25))))))) | (~p20(f12(f13(f6(c24), f16(c26, f14(f15(f7(c25)))))), f12(f13(f6(c24), f16(c26, c27))))) | (~p11(f12(f13(f6(c24), f16(c26, c27))), f12(f13(f6(c22), c27)))) | p20(f12(f13(f6(c22), f14(f15(f7(c25))))), f12(f13(f6(c22), c27))))) <=> ((~![X39: $i, X38: $i, X37: $i, X36: $i] : ((~p11(X38, X36)) | (~p20(X38, X39)) | (~p11(X39, X37)) | p20(X36, X37))) | p20(f12(f13(f6(c22), f14(f15(f7(c25))))), f12(f13(f6(c22), c27))) | (~p11(f12(f13(f6(c24), f16(c26, f14(f15(f7(c25)))))), f12(f13(f6(c22), f14(f15(f7(c25))))))) | (~p20(f12(f13(f6(c24), f16(c26, f14(f15(f7(c25)))))), f12(f13(f6(c24), f16(c26, c27))))) | (~p11(f12(f13(f6(c24), f16(c26, c27))), f12(f13(f6(c22), c27)))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[198, 196])).
% 0.20/0.43 tff(200,plain,
% 0.20/0.43 ((~![X39: $i, X38: $i, X37: $i, X36: $i] : ((~p11(X38, X36)) | (~p20(X38, X39)) | (~p11(X39, X37)) | p20(X36, X37))) | ((~p11(f12(f13(f6(c24), f16(c26, f14(f15(f7(c25)))))), f12(f13(f6(c22), f14(f15(f7(c25))))))) | (~p20(f12(f13(f6(c24), f16(c26, f14(f15(f7(c25)))))), f12(f13(f6(c24), f16(c26, c27))))) | (~p11(f12(f13(f6(c24), f16(c26, c27))), f12(f13(f6(c22), c27)))) | p20(f12(f13(f6(c22), f14(f15(f7(c25))))), f12(f13(f6(c22), c27))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(201,plain,
% 0.20/0.43 ((~![X39: $i, X38: $i, X37: $i, X36: $i] : ((~p11(X38, X36)) | (~p20(X38, X39)) | (~p11(X39, X37)) | p20(X36, X37))) | p20(f12(f13(f6(c22), f14(f15(f7(c25))))), f12(f13(f6(c22), c27))) | (~p11(f12(f13(f6(c24), f16(c26, f14(f15(f7(c25)))))), f12(f13(f6(c22), f14(f15(f7(c25))))))) | (~p20(f12(f13(f6(c24), f16(c26, f14(f15(f7(c25)))))), f12(f13(f6(c24), f16(c26, c27))))) | (~p11(f12(f13(f6(c24), f16(c26, c27))), f12(f13(f6(c22), c27))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.20/0.43 tff(202,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[201, 188, 195, 192, 144, 74])).
% 0.20/0.43 % SZS output end Proof
% 0.20/0.43 % E exiting
%------------------------------------------------------------------------------