%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN559-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:39:34 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN559-1 : TPTP v9.0.0. Released v2.5.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 12:38:33 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.37 % SZS status Unsatisfiable
% 0.19/0.37 % SZS output start Proof
% 0.19/0.37 tff(p2_type, type, (
% 0.19/0.37 p2: ( $i * $i ) > $o)).
% 0.19/0.37 tff(f3_type, type, (
% 0.19/0.37 f3: ( $i * $i ) > $i)).
% 0.19/0.37 tff(c12_type, type, (
% 0.19/0.37 c12: $i)).
% 0.19/0.37 tff(f4_type, type, (
% 0.19/0.37 f4: $i > $i)).
% 0.19/0.37 tff(c11_type, type, (
% 0.19/0.37 c11: $i)).
% 0.19/0.37 tff(c15_type, type, (
% 0.19/0.37 c15: $i)).
% 0.19/0.37 tff(f5_type, type, (
% 0.19/0.37 f5: ( $i * $i ) > $i)).
% 0.19/0.37 tff(c10_type, type, (
% 0.19/0.37 c10: $i)).
% 0.19/0.37 tff(c14_type, type, (
% 0.19/0.37 c14: $i)).
% 0.19/0.37 tff(f6_type, type, (
% 0.19/0.37 f6: ( $i * $i ) > $i)).
% 0.19/0.37 tff(c13_type, type, (
% 0.19/0.37 c13: $i)).
% 0.19/0.37 tff(c9_type, type, (
% 0.19/0.37 c9: $i)).
% 0.19/0.37 tff(p8_type, type, (
% 0.19/0.37 p8: ( $i * $i ) > $o)).
% 0.19/0.37 tff(p7_type, type, (
% 0.19/0.37 p7: ( $i * $i ) > $o)).
% 0.19/0.37 tff(1,assumption,(~p2(f4(c11), f4(c11))), introduced(assumption)).
% 0.19/0.37 tff(2,plain,
% 0.19/0.37 (^[X0: $i] : refl(p2(X0, X0) <=> p2(X0, X0))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(3,plain,
% 0.19/0.37 (![X0: $i] : p2(X0, X0) <=> ![X0: $i] : p2(X0, X0)),
% 0.19/0.37 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.37 tff(4,plain,
% 0.19/0.37 (![X0: $i] : p2(X0, X0) <=> ![X0: $i] : p2(X0, X0)),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(5,axiom,(![X0: $i] : p2(X0, X0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_1')).
% 0.19/0.37 tff(6,plain,
% 0.19/0.37 (![X0: $i] : p2(X0, X0)),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.19/0.37 tff(7,plain,(
% 0.19/0.37 ![X0: $i] : p2(X0, X0)),
% 0.19/0.37 inference(skolemize,[status(sab)],[6])).
% 0.19/0.37 tff(8,plain,
% 0.19/0.37 (![X0: $i] : p2(X0, X0)),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.37 tff(9,plain,
% 0.19/0.37 ((~![X0: $i] : p2(X0, X0)) | p2(f4(c11), f4(c11))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(10,plain,
% 0.19/0.37 ($false),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.19/0.37 tff(11,plain,(p2(f4(c11), f4(c11))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.37 tff(12,assumption,(~p2(c12, c12)), introduced(assumption)).
% 0.19/0.37 tff(13,plain,
% 0.19/0.37 ((~![X0: $i] : p2(X0, X0)) | p2(c12, c12)),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(14,plain,
% 0.19/0.37 ($false),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[13, 8, 12])).
% 0.19/0.37 tff(15,plain,(p2(c12, c12)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.37 tff(16,plain,
% 0.19/0.37 (^[X6: $i, X4: $i, X3: $i, X5: $i] : refl(((~p2(X3, X5)) | (~p2(X4, X6)) | p2(f3(X3, X4), f3(X5, X6))) <=> ((~p2(X3, X5)) | (~p2(X4, X6)) | p2(f3(X3, X4), f3(X5, X6))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(17,plain,
% 0.19/0.37 (![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p2(X3, X5)) | (~p2(X4, X6)) | p2(f3(X3, X4), f3(X5, X6))) <=> ![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p2(X3, X5)) | (~p2(X4, X6)) | p2(f3(X3, X4), f3(X5, X6)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[16])).
% 0.19/0.37 tff(18,plain,
% 0.19/0.37 (![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p2(X3, X5)) | (~p2(X4, X6)) | p2(f3(X3, X4), f3(X5, X6))) <=> ![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p2(X3, X5)) | (~p2(X4, X6)) | p2(f3(X3, X4), f3(X5, X6)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(19,plain,
% 0.19/0.37 (^[X6: $i, X4: $i, X3: $i, X5: $i] : trans(monotonicity(rewrite((p2(f3(X3, X4), f3(X5, X6)) | (~p2(X3, X5))) <=> ((~p2(X3, X5)) | p2(f3(X3, X4), f3(X5, X6)))), (((p2(f3(X3, X4), f3(X5, X6)) | (~p2(X3, X5))) | (~p2(X4, X6))) <=> (((~p2(X3, X5)) | p2(f3(X3, X4), f3(X5, X6))) | (~p2(X4, X6))))), rewrite((((~p2(X3, X5)) | p2(f3(X3, X4), f3(X5, X6))) | (~p2(X4, X6))) <=> ((~p2(X3, X5)) | (~p2(X4, X6)) | p2(f3(X3, X4), f3(X5, X6)))), (((p2(f3(X3, X4), f3(X5, X6)) | (~p2(X3, X5))) | (~p2(X4, X6))) <=> ((~p2(X3, X5)) | (~p2(X4, X6)) | p2(f3(X3, X4), f3(X5, X6)))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(20,plain,
% 0.19/0.37 (![X6: $i, X4: $i, X3: $i, X5: $i] : ((p2(f3(X3, X4), f3(X5, X6)) | (~p2(X3, X5))) | (~p2(X4, X6))) <=> ![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p2(X3, X5)) | (~p2(X4, X6)) | p2(f3(X3, X4), f3(X5, X6)))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[19])).
% 0.19/0.37 tff(21,axiom,(![X6: $i, X4: $i, X3: $i, X5: $i] : ((p2(f3(X3, X4), f3(X5, X6)) | (~p2(X3, X5))) | (~p2(X4, X6)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_11')).
% 0.19/0.37 tff(22,plain,
% 0.19/0.37 (![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p2(X3, X5)) | (~p2(X4, X6)) | p2(f3(X3, X4), f3(X5, X6)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.19/0.37 tff(23,plain,
% 0.19/0.37 (![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p2(X3, X5)) | (~p2(X4, X6)) | p2(f3(X3, X4), f3(X5, X6)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.19/0.37 tff(24,plain,(
% 0.19/0.37 ![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p2(X3, X5)) | (~p2(X4, X6)) | p2(f3(X3, X4), f3(X5, X6)))),
% 0.19/0.37 inference(skolemize,[status(sab)],[23])).
% 0.19/0.37 tff(25,plain,
% 0.19/0.37 (![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p2(X3, X5)) | (~p2(X4, X6)) | p2(f3(X3, X4), f3(X5, X6)))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.19/0.37 tff(26,plain,
% 0.19/0.37 (((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p2(X3, X5)) | (~p2(X4, X6)) | p2(f3(X3, X4), f3(X5, X6)))) | ((~p2(f4(c11), f4(c11))) | (~p2(c12, c12)) | p2(f3(f4(c11), c12), f3(f4(c11), c12)))) <=> ((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p2(X3, X5)) | (~p2(X4, X6)) | p2(f3(X3, X4), f3(X5, X6)))) | (~p2(f4(c11), f4(c11))) | (~p2(c12, c12)) | p2(f3(f4(c11), c12), f3(f4(c11), c12)))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(27,plain,
% 0.19/0.37 ((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p2(X3, X5)) | (~p2(X4, X6)) | p2(f3(X3, X4), f3(X5, X6)))) | ((~p2(f4(c11), f4(c11))) | (~p2(c12, c12)) | p2(f3(f4(c11), c12), f3(f4(c11), c12)))),
% 0.19/0.37 inference(quant_inst,[status(thm)],[])).
% 0.19/0.37 tff(28,plain,
% 0.19/0.37 ((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p2(X3, X5)) | (~p2(X4, X6)) | p2(f3(X3, X4), f3(X5, X6)))) | (~p2(f4(c11), f4(c11))) | (~p2(c12, c12)) | p2(f3(f4(c11), c12), f3(f4(c11), c12))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.19/0.37 tff(29,plain,
% 0.19/0.37 ((~p2(f4(c11), f4(c11))) | (~p2(c12, c12)) | p2(f3(f4(c11), c12), f3(f4(c11), c12))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[28, 25])).
% 0.19/0.37 tff(30,plain,
% 0.19/0.37 (p2(f3(f4(c11), c12), f3(f4(c11), c12))),
% 0.19/0.37 inference(unit_resolution,[status(thm)],[29, 15, 11])).
% 0.19/0.37 tff(31,plain,
% 0.19/0.37 (^[X0: $i, X2: $i, X1: $i] : refl(((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2)) <=> ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2)))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(32,plain,
% 0.19/0.37 (![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2)) <=> ![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[31])).
% 0.19/0.37 tff(33,plain,
% 0.19/0.37 (![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2)) <=> ![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(34,plain,
% 0.19/0.37 (^[X0: $i, X2: $i, X1: $i] : trans(monotonicity(rewrite((p2(X1, X2) | (~p2(X0, X1))) <=> ((~p2(X0, X1)) | p2(X1, X2))), (((p2(X1, X2) | (~p2(X0, X1))) | (~p2(X0, X2))) <=> (((~p2(X0, X1)) | p2(X1, X2)) | (~p2(X0, X2))))), rewrite((((~p2(X0, X1)) | p2(X1, X2)) | (~p2(X0, X2))) <=> ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))), (((p2(X1, X2) | (~p2(X0, X1))) | (~p2(X0, X2))) <=> ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(35,plain,
% 0.19/0.37 (![X0: $i, X2: $i, X1: $i] : ((p2(X1, X2) | (~p2(X0, X1))) | (~p2(X0, X2))) <=> ![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[34])).
% 0.19/0.37 tff(36,axiom,(![X0: $i, X2: $i, X1: $i] : ((p2(X1, X2) | (~p2(X0, X1))) | (~p2(X0, X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_8')).
% 0.19/0.37 tff(37,plain,
% 0.19/0.37 (![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.19/0.37 tff(38,plain,
% 0.19/0.37 (![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.19/0.37 tff(39,plain,(
% 0.19/0.37 ![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))),
% 0.19/0.37 inference(skolemize,[status(sab)],[38])).
% 0.19/0.37 tff(40,plain,
% 0.19/0.37 (![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.19/0.37 tff(41,plain,
% 0.19/0.37 (p2(f3(f4(c11), c12), c15) <=> p2(f3(f4(c11), c12), c15)),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(42,axiom,(p2(f3(f4(c11), c12), c15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_6')).
% 0.19/0.37 tff(43,plain,
% 0.19/0.37 (p2(f3(f4(c11), c12), c15)),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.19/0.37 tff(44,plain,
% 0.19/0.37 (((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(f3(f4(c11), c12), c15)) | (~p2(f3(f4(c11), c12), f3(f4(c11), c12))) | p2(c15, f3(f4(c11), c12)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | (~p2(f3(f4(c11), c12), c15)) | (~p2(f3(f4(c11), c12), f3(f4(c11), c12))) | p2(c15, f3(f4(c11), c12)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(45,plain,
% 0.19/0.38 (((~p2(f3(f4(c11), c12), f3(f4(c11), c12))) | (~p2(f3(f4(c11), c12), c15)) | p2(c15, f3(f4(c11), c12))) <=> ((~p2(f3(f4(c11), c12), c15)) | (~p2(f3(f4(c11), c12), f3(f4(c11), c12))) | p2(c15, f3(f4(c11), c12)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(46,plain,
% 0.19/0.38 (((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(f3(f4(c11), c12), f3(f4(c11), c12))) | (~p2(f3(f4(c11), c12), c15)) | p2(c15, f3(f4(c11), c12)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(f3(f4(c11), c12), c15)) | (~p2(f3(f4(c11), c12), f3(f4(c11), c12))) | p2(c15, f3(f4(c11), c12))))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[45])).
% 0.19/0.38 tff(47,plain,
% 0.19/0.38 (((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(f3(f4(c11), c12), f3(f4(c11), c12))) | (~p2(f3(f4(c11), c12), c15)) | p2(c15, f3(f4(c11), c12)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | (~p2(f3(f4(c11), c12), c15)) | (~p2(f3(f4(c11), c12), f3(f4(c11), c12))) | p2(c15, f3(f4(c11), c12)))),
% 0.19/0.38 inference(transitivity,[status(thm)],[46, 44])).
% 0.19/0.38 tff(48,plain,
% 0.19/0.38 ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(f3(f4(c11), c12), f3(f4(c11), c12))) | (~p2(f3(f4(c11), c12), c15)) | p2(c15, f3(f4(c11), c12)))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(49,plain,
% 0.19/0.38 ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | (~p2(f3(f4(c11), c12), c15)) | (~p2(f3(f4(c11), c12), f3(f4(c11), c12))) | p2(c15, f3(f4(c11), c12))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.19/0.38 tff(50,plain,
% 0.19/0.38 (p2(c15, f3(f4(c11), c12))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[49, 43, 40, 30])).
% 0.19/0.38 tff(51,assumption,(~p2(c10, c10)), introduced(assumption)).
% 0.19/0.38 tff(52,plain,
% 0.19/0.38 ((~![X0: $i] : p2(X0, X0)) | p2(c10, c10)),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(53,plain,
% 0.19/0.38 ($false),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[52, 8, 51])).
% 0.19/0.38 tff(54,plain,(p2(c10, c10)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.38 tff(55,plain,
% 0.19/0.38 (p2(f6(c9, c13), c14) <=> p2(f6(c9, c13), c14)),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(56,axiom,(p2(f6(c9, c13), c14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_4')).
% 0.19/0.38 tff(57,plain,
% 0.19/0.38 (p2(f6(c9, c13), c14)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.19/0.38 tff(58,plain,
% 0.19/0.38 (((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(f6(c9, c13), c14)) | p2(c14, c14))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | (~p2(f6(c9, c13), c14)) | p2(c14, c14))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(59,plain,
% 0.19/0.38 (((~p2(f6(c9, c13), c14)) | (~p2(f6(c9, c13), c14)) | p2(c14, c14)) <=> ((~p2(f6(c9, c13), c14)) | p2(c14, c14))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(60,plain,
% 0.19/0.38 (((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(f6(c9, c13), c14)) | (~p2(f6(c9, c13), c14)) | p2(c14, c14))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(f6(c9, c13), c14)) | p2(c14, c14)))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[59])).
% 0.19/0.38 tff(61,plain,
% 0.19/0.38 (((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(f6(c9, c13), c14)) | (~p2(f6(c9, c13), c14)) | p2(c14, c14))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | (~p2(f6(c9, c13), c14)) | p2(c14, c14))),
% 0.19/0.38 inference(transitivity,[status(thm)],[60, 58])).
% 0.19/0.38 tff(62,plain,
% 0.19/0.38 ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(f6(c9, c13), c14)) | (~p2(f6(c9, c13), c14)) | p2(c14, c14))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(63,plain,
% 0.19/0.38 ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | (~p2(f6(c9, c13), c14)) | p2(c14, c14)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.19/0.38 tff(64,plain,
% 0.19/0.38 (p2(c14, c14)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[63, 57, 40])).
% 0.19/0.38 tff(65,plain,
% 0.19/0.38 (^[X9: $i, X12: $i, X11: $i, X10: $i] : refl(((~p2(X9, X11)) | (~p2(X10, X12)) | p2(f5(X9, X10), f5(X11, X12))) <=> ((~p2(X9, X11)) | (~p2(X10, X12)) | p2(f5(X9, X10), f5(X11, X12))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(66,plain,
% 0.19/0.38 (![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p2(X9, X11)) | (~p2(X10, X12)) | p2(f5(X9, X10), f5(X11, X12))) <=> ![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p2(X9, X11)) | (~p2(X10, X12)) | p2(f5(X9, X10), f5(X11, X12)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[65])).
% 0.19/0.38 tff(67,plain,
% 0.19/0.38 (![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p2(X9, X11)) | (~p2(X10, X12)) | p2(f5(X9, X10), f5(X11, X12))) <=> ![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p2(X9, X11)) | (~p2(X10, X12)) | p2(f5(X9, X10), f5(X11, X12)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(68,plain,
% 0.19/0.38 (^[X9: $i, X12: $i, X11: $i, X10: $i] : trans(monotonicity(rewrite((p2(f5(X9, X10), f5(X11, X12)) | (~p2(X9, X11))) <=> ((~p2(X9, X11)) | p2(f5(X9, X10), f5(X11, X12)))), (((p2(f5(X9, X10), f5(X11, X12)) | (~p2(X9, X11))) | (~p2(X10, X12))) <=> (((~p2(X9, X11)) | p2(f5(X9, X10), f5(X11, X12))) | (~p2(X10, X12))))), rewrite((((~p2(X9, X11)) | p2(f5(X9, X10), f5(X11, X12))) | (~p2(X10, X12))) <=> ((~p2(X9, X11)) | (~p2(X10, X12)) | p2(f5(X9, X10), f5(X11, X12)))), (((p2(f5(X9, X10), f5(X11, X12)) | (~p2(X9, X11))) | (~p2(X10, X12))) <=> ((~p2(X9, X11)) | (~p2(X10, X12)) | p2(f5(X9, X10), f5(X11, X12)))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(69,plain,
% 0.19/0.38 (![X9: $i, X12: $i, X11: $i, X10: $i] : ((p2(f5(X9, X10), f5(X11, X12)) | (~p2(X9, X11))) | (~p2(X10, X12))) <=> ![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p2(X9, X11)) | (~p2(X10, X12)) | p2(f5(X9, X10), f5(X11, X12)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[68])).
% 0.19/0.38 tff(70,axiom,(![X9: $i, X12: $i, X11: $i, X10: $i] : ((p2(f5(X9, X10), f5(X11, X12)) | (~p2(X9, X11))) | (~p2(X10, X12)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_13')).
% 0.19/0.38 tff(71,plain,
% 0.19/0.38 (![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p2(X9, X11)) | (~p2(X10, X12)) | p2(f5(X9, X10), f5(X11, X12)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.19/0.38 tff(72,plain,
% 0.19/0.38 (![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p2(X9, X11)) | (~p2(X10, X12)) | p2(f5(X9, X10), f5(X11, X12)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.19/0.38 tff(73,plain,(
% 0.19/0.38 ![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p2(X9, X11)) | (~p2(X10, X12)) | p2(f5(X9, X10), f5(X11, X12)))),
% 0.19/0.38 inference(skolemize,[status(sab)],[72])).
% 0.19/0.38 tff(74,plain,
% 0.19/0.38 (![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p2(X9, X11)) | (~p2(X10, X12)) | p2(f5(X9, X10), f5(X11, X12)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.19/0.38 tff(75,plain,
% 0.19/0.38 (((~![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p2(X9, X11)) | (~p2(X10, X12)) | p2(f5(X9, X10), f5(X11, X12)))) | ((~p2(c14, c14)) | (~p2(c10, c10)) | p2(f5(c14, c10), f5(c14, c10)))) <=> ((~![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p2(X9, X11)) | (~p2(X10, X12)) | p2(f5(X9, X10), f5(X11, X12)))) | (~p2(c14, c14)) | (~p2(c10, c10)) | p2(f5(c14, c10), f5(c14, c10)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(76,plain,
% 0.19/0.38 ((~![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p2(X9, X11)) | (~p2(X10, X12)) | p2(f5(X9, X10), f5(X11, X12)))) | ((~p2(c14, c14)) | (~p2(c10, c10)) | p2(f5(c14, c10), f5(c14, c10)))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(77,plain,
% 0.19/0.38 ((~![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p2(X9, X11)) | (~p2(X10, X12)) | p2(f5(X9, X10), f5(X11, X12)))) | (~p2(c14, c14)) | (~p2(c10, c10)) | p2(f5(c14, c10), f5(c14, c10))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.19/0.38 tff(78,plain,
% 0.19/0.38 ((~p2(c10, c10)) | p2(f5(c14, c10), f5(c14, c10))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[77, 74, 64])).
% 0.19/0.38 tff(79,plain,
% 0.19/0.38 (p2(f5(c14, c10), f5(c14, c10))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[78, 54])).
% 0.19/0.38 tff(80,plain,
% 0.19/0.38 (p2(f5(c14, c10), c15) <=> p2(f5(c14, c10), c15)),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(81,axiom,(p2(f5(c14, c10), c15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_5')).
% 0.19/0.38 tff(82,plain,
% 0.19/0.38 (p2(f5(c14, c10), c15)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.19/0.38 tff(83,plain,
% 0.19/0.38 (((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(f5(c14, c10), c15)) | (~p2(f5(c14, c10), f5(c14, c10))) | p2(c15, f5(c14, c10)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | (~p2(f5(c14, c10), c15)) | (~p2(f5(c14, c10), f5(c14, c10))) | p2(c15, f5(c14, c10)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(84,plain,
% 0.19/0.38 (((~p2(f5(c14, c10), f5(c14, c10))) | (~p2(f5(c14, c10), c15)) | p2(c15, f5(c14, c10))) <=> ((~p2(f5(c14, c10), c15)) | (~p2(f5(c14, c10), f5(c14, c10))) | p2(c15, f5(c14, c10)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(85,plain,
% 0.19/0.38 (((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(f5(c14, c10), f5(c14, c10))) | (~p2(f5(c14, c10), c15)) | p2(c15, f5(c14, c10)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(f5(c14, c10), c15)) | (~p2(f5(c14, c10), f5(c14, c10))) | p2(c15, f5(c14, c10))))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[84])).
% 0.19/0.38 tff(86,plain,
% 0.19/0.38 (((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(f5(c14, c10), f5(c14, c10))) | (~p2(f5(c14, c10), c15)) | p2(c15, f5(c14, c10)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | (~p2(f5(c14, c10), c15)) | (~p2(f5(c14, c10), f5(c14, c10))) | p2(c15, f5(c14, c10)))),
% 0.19/0.38 inference(transitivity,[status(thm)],[85, 83])).
% 0.19/0.38 tff(87,plain,
% 0.19/0.38 ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(f5(c14, c10), f5(c14, c10))) | (~p2(f5(c14, c10), c15)) | p2(c15, f5(c14, c10)))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(88,plain,
% 0.19/0.38 ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | (~p2(f5(c14, c10), c15)) | (~p2(f5(c14, c10), f5(c14, c10))) | p2(c15, f5(c14, c10))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.19/0.38 tff(89,plain,
% 0.19/0.38 (p2(c15, f5(c14, c10))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[88, 82, 40, 79])).
% 0.19/0.38 tff(90,plain,
% 0.19/0.38 (^[X25: $i, X26: $i] : refl(((~p2(f5(X25, c10), f3(f4(c11), c12))) | (~p2(f6(c9, X26), X25)) | (~p7(c10, X26)) | (~p8(X26, c9))) <=> ((~p2(f5(X25, c10), f3(f4(c11), c12))) | (~p2(f6(c9, X26), X25)) | (~p7(c10, X26)) | (~p8(X26, c9))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(91,plain,
% 0.19/0.38 (![X25: $i, X26: $i] : ((~p2(f5(X25, c10), f3(f4(c11), c12))) | (~p2(f6(c9, X26), X25)) | (~p7(c10, X26)) | (~p8(X26, c9))) <=> ![X25: $i, X26: $i] : ((~p2(f5(X25, c10), f3(f4(c11), c12))) | (~p2(f6(c9, X26), X25)) | (~p7(c10, X26)) | (~p8(X26, c9)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[90])).
% 0.19/0.38 tff(92,plain,
% 0.19/0.38 (![X25: $i, X26: $i] : ((~p2(f5(X25, c10), f3(f4(c11), c12))) | (~p2(f6(c9, X26), X25)) | (~p7(c10, X26)) | (~p8(X26, c9))) <=> ![X25: $i, X26: $i] : ((~p2(f5(X25, c10), f3(f4(c11), c12))) | (~p2(f6(c9, X26), X25)) | (~p7(c10, X26)) | (~p8(X26, c9)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(93,plain,
% 0.19/0.38 (^[X25: $i, X26: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~p8(X26, c9)) | (~p7(c10, X26))) <=> ((~p7(c10, X26)) | (~p8(X26, c9)))), ((((~p8(X26, c9)) | (~p7(c10, X26))) | (~p2(f6(c9, X26), X25))) <=> (((~p7(c10, X26)) | (~p8(X26, c9))) | (~p2(f6(c9, X26), X25))))), rewrite((((~p7(c10, X26)) | (~p8(X26, c9))) | (~p2(f6(c9, X26), X25))) <=> ((~p2(f6(c9, X26), X25)) | (~p7(c10, X26)) | (~p8(X26, c9)))), ((((~p8(X26, c9)) | (~p7(c10, X26))) | (~p2(f6(c9, X26), X25))) <=> ((~p2(f6(c9, X26), X25)) | (~p7(c10, X26)) | (~p8(X26, c9))))), (((((~p8(X26, c9)) | (~p7(c10, X26))) | (~p2(f6(c9, X26), X25))) | (~p2(f5(X25, c10), f3(f4(c11), c12)))) <=> (((~p2(f6(c9, X26), X25)) | (~p7(c10, X26)) | (~p8(X26, c9))) | (~p2(f5(X25, c10), f3(f4(c11), c12)))))), rewrite((((~p2(f6(c9, X26), X25)) | (~p7(c10, X26)) | (~p8(X26, c9))) | (~p2(f5(X25, c10), f3(f4(c11), c12)))) <=> ((~p2(f5(X25, c10), f3(f4(c11), c12))) | (~p2(f6(c9, X26), X25)) | (~p7(c10, X26)) | (~p8(X26, c9)))), (((((~p8(X26, c9)) | (~p7(c10, X26))) | (~p2(f6(c9, X26), X25))) | (~p2(f5(X25, c10), f3(f4(c11), c12)))) <=> ((~p2(f5(X25, c10), f3(f4(c11), c12))) | (~p2(f6(c9, X26), X25)) | (~p7(c10, X26)) | (~p8(X26, c9)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(94,plain,
% 0.19/0.39 (![X25: $i, X26: $i] : ((((~p8(X26, c9)) | (~p7(c10, X26))) | (~p2(f6(c9, X26), X25))) | (~p2(f5(X25, c10), f3(f4(c11), c12)))) <=> ![X25: $i, X26: $i] : ((~p2(f5(X25, c10), f3(f4(c11), c12))) | (~p2(f6(c9, X26), X25)) | (~p7(c10, X26)) | (~p8(X26, c9)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[93])).
% 0.19/0.39 tff(95,axiom,(![X25: $i, X26: $i] : ((((~p8(X26, c9)) | (~p7(c10, X26))) | (~p2(f6(c9, X26), X25))) | (~p2(f5(X25, c10), f3(f4(c11), c12))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_p8_14')).
% 0.19/0.39 tff(96,plain,
% 0.19/0.39 (![X25: $i, X26: $i] : ((~p2(f5(X25, c10), f3(f4(c11), c12))) | (~p2(f6(c9, X26), X25)) | (~p7(c10, X26)) | (~p8(X26, c9)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.19/0.39 tff(97,plain,
% 0.19/0.39 (![X25: $i, X26: $i] : ((~p2(f5(X25, c10), f3(f4(c11), c12))) | (~p2(f6(c9, X26), X25)) | (~p7(c10, X26)) | (~p8(X26, c9)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.19/0.39 tff(98,plain,(
% 0.19/0.39 ![X25: $i, X26: $i] : ((~p2(f5(X25, c10), f3(f4(c11), c12))) | (~p2(f6(c9, X26), X25)) | (~p7(c10, X26)) | (~p8(X26, c9)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[97])).
% 0.19/0.39 tff(99,plain,
% 0.19/0.39 (![X25: $i, X26: $i] : ((~p2(f5(X25, c10), f3(f4(c11), c12))) | (~p2(f6(c9, X26), X25)) | (~p7(c10, X26)) | (~p8(X26, c9)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[98, 91])).
% 0.19/0.39 tff(100,plain,
% 0.19/0.39 (p7(c10, c13) <=> p7(c10, c13)),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(101,axiom,(p7(c10, c13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p7_3')).
% 0.19/0.39 tff(102,plain,
% 0.19/0.39 (p7(c10, c13)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.19/0.39 tff(103,plain,
% 0.19/0.39 (p8(c13, c9) <=> p8(c13, c9)),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(104,axiom,(p8(c13, c9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p8_2')).
% 0.19/0.39 tff(105,plain,
% 0.19/0.39 (p8(c13, c9)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.19/0.39 tff(106,plain,
% 0.19/0.39 (((~![X25: $i, X26: $i] : ((~p2(f5(X25, c10), f3(f4(c11), c12))) | (~p2(f6(c9, X26), X25)) | (~p7(c10, X26)) | (~p8(X26, c9)))) | ((~p2(f5(c14, c10), f3(f4(c11), c12))) | (~p2(f6(c9, c13), c14)) | (~p7(c10, c13)) | (~p8(c13, c9)))) <=> ((~![X25: $i, X26: $i] : ((~p2(f5(X25, c10), f3(f4(c11), c12))) | (~p2(f6(c9, X26), X25)) | (~p7(c10, X26)) | (~p8(X26, c9)))) | (~p2(f5(c14, c10), f3(f4(c11), c12))) | (~p2(f6(c9, c13), c14)) | (~p7(c10, c13)) | (~p8(c13, c9)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(107,plain,
% 0.19/0.39 ((~![X25: $i, X26: $i] : ((~p2(f5(X25, c10), f3(f4(c11), c12))) | (~p2(f6(c9, X26), X25)) | (~p7(c10, X26)) | (~p8(X26, c9)))) | ((~p2(f5(c14, c10), f3(f4(c11), c12))) | (~p2(f6(c9, c13), c14)) | (~p7(c10, c13)) | (~p8(c13, c9)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(108,plain,
% 0.19/0.39 ((~![X25: $i, X26: $i] : ((~p2(f5(X25, c10), f3(f4(c11), c12))) | (~p2(f6(c9, X26), X25)) | (~p7(c10, X26)) | (~p8(X26, c9)))) | (~p2(f5(c14, c10), f3(f4(c11), c12))) | (~p2(f6(c9, c13), c14)) | (~p7(c10, c13)) | (~p8(c13, c9))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.19/0.39 tff(109,plain,
% 0.19/0.39 (~p2(f5(c14, c10), f3(f4(c11), c12))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[108, 105, 102, 57, 99])).
% 0.19/0.39 tff(110,plain,
% 0.19/0.39 (((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | (p2(f5(c14, c10), f3(f4(c11), c12)) | (~p2(c15, f5(c14, c10))) | (~p2(c15, f3(f4(c11), c12))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | p2(f5(c14, c10), f3(f4(c11), c12)) | (~p2(c15, f5(c14, c10))) | (~p2(c15, f3(f4(c11), c12))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(111,plain,
% 0.19/0.39 (((~p2(c15, f3(f4(c11), c12))) | (~p2(c15, f5(c14, c10))) | p2(f5(c14, c10), f3(f4(c11), c12))) <=> (p2(f5(c14, c10), f3(f4(c11), c12)) | (~p2(c15, f5(c14, c10))) | (~p2(c15, f3(f4(c11), c12))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(112,plain,
% 0.19/0.39 (((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(c15, f3(f4(c11), c12))) | (~p2(c15, f5(c14, c10))) | p2(f5(c14, c10), f3(f4(c11), c12)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | (p2(f5(c14, c10), f3(f4(c11), c12)) | (~p2(c15, f5(c14, c10))) | (~p2(c15, f3(f4(c11), c12)))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[111])).
% 0.19/0.39 tff(113,plain,
% 0.19/0.39 (((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(c15, f3(f4(c11), c12))) | (~p2(c15, f5(c14, c10))) | p2(f5(c14, c10), f3(f4(c11), c12)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | p2(f5(c14, c10), f3(f4(c11), c12)) | (~p2(c15, f5(c14, c10))) | (~p2(c15, f3(f4(c11), c12))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[112, 110])).
% 0.19/0.39 tff(114,plain,
% 0.19/0.39 ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(c15, f3(f4(c11), c12))) | (~p2(c15, f5(c14, c10))) | p2(f5(c14, c10), f3(f4(c11), c12)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(115,plain,
% 0.19/0.39 ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | p2(f5(c14, c10), f3(f4(c11), c12)) | (~p2(c15, f5(c14, c10))) | (~p2(c15, f3(f4(c11), c12)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.19/0.39 tff(116,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[115, 40, 109, 89, 50])).
% 0.19/0.39 % SZS output end Proof
% 0.19/0.39 % E exiting
%------------------------------------------------------------------------------