%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN596-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:39:39 AM UTC 2025
% Result : Unsatisfiable 0.11s 0.37s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SYN596-1 : TPTP v9.0.0. Released v2.5.0.
% 0.07/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n010.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 12:39:57 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.37 % SZS status Unsatisfiable
% 0.11/0.37 % SZS output start Proof
% 0.11/0.37 tff(p2_type, type, (
% 0.11/0.37 p2: ( $i * $i ) > $o)).
% 0.11/0.37 tff(c20_type, type, (
% 0.11/0.37 c20: $i)).
% 0.11/0.37 tff(p10_type, type, (
% 0.11/0.37 p10: ( $i * $i ) > $o)).
% 0.11/0.37 tff(f11_type, type, (
% 0.11/0.37 f11: ( $i * $i * $i ) > $i)).
% 0.11/0.37 tff(c24_type, type, (
% 0.11/0.37 c24: $i)).
% 0.11/0.37 tff(c23_type, type, (
% 0.11/0.37 c23: $i)).
% 0.11/0.37 tff(f13_type, type, (
% 0.11/0.37 f13: ( $i * $i ) > $i)).
% 0.11/0.37 tff(f14_type, type, (
% 0.11/0.37 f14: ( $i * $i ) > $i)).
% 0.11/0.37 tff(c22_type, type, (
% 0.11/0.37 c22: $i)).
% 0.11/0.37 tff(f4_type, type, (
% 0.11/0.37 f4: $i > $i)).
% 0.11/0.37 tff(f15_type, type, (
% 0.11/0.37 f15: $i > $i)).
% 0.11/0.37 tff(c21_type, type, (
% 0.11/0.37 c21: $i)).
% 0.11/0.37 tff(p9_type, type, (
% 0.11/0.37 p9: ( $i * $i ) > $o)).
% 0.11/0.37 tff(p18_type, type, (
% 0.11/0.37 p18: ( $i * $i ) > $o)).
% 0.11/0.37 tff(1,assumption,(~p2(c20, c20)), introduced(assumption)).
% 0.11/0.37 tff(2,plain,
% 0.11/0.37 (^[X28: $i] : refl(p2(X28, X28) <=> p2(X28, X28))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(3,plain,
% 0.11/0.37 (![X28: $i] : p2(X28, X28) <=> ![X28: $i] : p2(X28, X28)),
% 0.11/0.37 inference(quant_intro,[status(thm)],[2])).
% 0.11/0.37 tff(4,plain,
% 0.11/0.37 (![X28: $i] : p2(X28, X28) <=> ![X28: $i] : p2(X28, X28)),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(5,axiom,(![X28: $i] : p2(X28, X28)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_4')).
% 0.11/0.37 tff(6,plain,
% 0.11/0.37 (![X28: $i] : p2(X28, X28)),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.11/0.37 tff(7,plain,(
% 0.11/0.37 ![X28: $i] : p2(X28, X28)),
% 0.11/0.37 inference(skolemize,[status(sab)],[6])).
% 0.11/0.37 tff(8,plain,
% 0.11/0.37 (![X28: $i] : p2(X28, X28)),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.11/0.37 tff(9,plain,
% 0.11/0.37 ((~![X28: $i] : p2(X28, X28)) | p2(c20, c20)),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(10,plain,
% 0.11/0.37 ($false),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.11/0.37 tff(11,plain,(p2(c20, c20)), inference(lemma,lemma(discharge,[]))).
% 0.11/0.37 tff(12,assumption,(~p10(c24, c24)), introduced(assumption)).
% 0.11/0.37 tff(13,plain,
% 0.11/0.37 (^[X0: $i] : refl(p10(X0, X0) <=> p10(X0, X0))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(14,plain,
% 0.11/0.37 (![X0: $i] : p10(X0, X0) <=> ![X0: $i] : p10(X0, X0)),
% 0.11/0.37 inference(quant_intro,[status(thm)],[13])).
% 0.11/0.37 tff(15,plain,
% 0.11/0.37 (![X0: $i] : p10(X0, X0) <=> ![X0: $i] : p10(X0, X0)),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(16,axiom,(![X0: $i] : p10(X0, X0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p10_1')).
% 0.11/0.37 tff(17,plain,
% 0.11/0.37 (![X0: $i] : p10(X0, X0)),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.11/0.37 tff(18,plain,(
% 0.11/0.37 ![X0: $i] : p10(X0, X0)),
% 0.11/0.37 inference(skolemize,[status(sab)],[17])).
% 0.11/0.37 tff(19,plain,
% 0.11/0.37 (![X0: $i] : p10(X0, X0)),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.11/0.37 tff(20,plain,
% 0.11/0.37 ((~![X0: $i] : p10(X0, X0)) | p10(c24, c24)),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(21,plain,
% 0.11/0.37 ($false),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[20, 19, 12])).
% 0.11/0.37 tff(22,plain,(p10(c24, c24)), inference(lemma,lemma(discharge,[]))).
% 0.11/0.37 tff(23,assumption,(~p9(c23, c23)), introduced(assumption)).
% 0.11/0.37 tff(24,plain,
% 0.11/0.37 (^[X50: $i] : refl(p9(X50, X50) <=> p9(X50, X50))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(25,plain,
% 0.11/0.37 (![X50: $i] : p9(X50, X50) <=> ![X50: $i] : p9(X50, X50)),
% 0.11/0.37 inference(quant_intro,[status(thm)],[24])).
% 0.11/0.37 tff(26,plain,
% 0.11/0.37 (![X50: $i] : p9(X50, X50) <=> ![X50: $i] : p9(X50, X50)),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(27,axiom,(![X50: $i] : p9(X50, X50)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p9_2')).
% 0.11/0.37 tff(28,plain,
% 0.11/0.37 (![X50: $i] : p9(X50, X50)),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.11/0.37 tff(29,plain,(
% 0.11/0.37 ![X50: $i] : p9(X50, X50)),
% 0.11/0.37 inference(skolemize,[status(sab)],[28])).
% 0.11/0.37 tff(30,plain,
% 0.11/0.37 (![X50: $i] : p9(X50, X50)),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.11/0.37 tff(31,plain,
% 0.11/0.37 ((~![X50: $i] : p9(X50, X50)) | p9(c23, c23)),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(32,plain,
% 0.11/0.37 ($false),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[31, 30, 23])).
% 0.11/0.37 tff(33,plain,(p9(c23, c23)), inference(lemma,lemma(discharge,[]))).
% 0.11/0.37 tff(34,assumption,(~p2(f13(f15(c20), f14(f4(c20), c22)), f13(f15(c20), f14(f4(c20), c22)))), introduced(assumption)).
% 0.11/0.37 tff(35,plain,
% 0.11/0.37 ((~![X28: $i] : p2(X28, X28)) | p2(f13(f15(c20), f14(f4(c20), c22)), f13(f15(c20), f14(f4(c20), c22)))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(36,plain,
% 0.11/0.37 ($false),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[35, 8, 34])).
% 0.11/0.37 tff(37,plain,(p2(f13(f15(c20), f14(f4(c20), c22)), f13(f15(c20), f14(f4(c20), c22)))), inference(lemma,lemma(discharge,[]))).
% 0.11/0.37 tff(38,plain,
% 0.11/0.37 (^[X6: $i, X4: $i, X3: $i, X7: $i, X5: $i, X8: $i] : refl(((~p10(X5, X8)) | (~p9(X4, X7)) | (~p2(X3, X6)) | p10(f11(X3, X4, X5), f11(X6, X7, X8))) <=> ((~p10(X5, X8)) | (~p9(X4, X7)) | (~p2(X3, X6)) | p10(f11(X3, X4, X5), f11(X6, X7, X8))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(39,plain,
% 0.11/0.37 (![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i, X8: $i] : ((~p10(X5, X8)) | (~p9(X4, X7)) | (~p2(X3, X6)) | p10(f11(X3, X4, X5), f11(X6, X7, X8))) <=> ![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i, X8: $i] : ((~p10(X5, X8)) | (~p9(X4, X7)) | (~p2(X3, X6)) | p10(f11(X3, X4, X5), f11(X6, X7, X8)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[38])).
% 0.11/0.37 tff(40,plain,
% 0.11/0.37 (![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i, X8: $i] : ((~p10(X5, X8)) | (~p9(X4, X7)) | (~p2(X3, X6)) | p10(f11(X3, X4, X5), f11(X6, X7, X8))) <=> ![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i, X8: $i] : ((~p10(X5, X8)) | (~p9(X4, X7)) | (~p2(X3, X6)) | p10(f11(X3, X4, X5), f11(X6, X7, X8)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(41,plain,
% 0.11/0.37 (^[X6: $i, X4: $i, X3: $i, X7: $i, X5: $i, X8: $i] : trans(monotonicity(trans(monotonicity(rewrite((p10(f11(X3, X4, X5), f11(X6, X7, X8)) | (~p2(X3, X6))) <=> ((~p2(X3, X6)) | p10(f11(X3, X4, X5), f11(X6, X7, X8)))), (((p10(f11(X3, X4, X5), f11(X6, X7, X8)) | (~p2(X3, X6))) | (~p9(X4, X7))) <=> (((~p2(X3, X6)) | p10(f11(X3, X4, X5), f11(X6, X7, X8))) | (~p9(X4, X7))))), rewrite((((~p2(X3, X6)) | p10(f11(X3, X4, X5), f11(X6, X7, X8))) | (~p9(X4, X7))) <=> ((~p9(X4, X7)) | (~p2(X3, X6)) | p10(f11(X3, X4, X5), f11(X6, X7, X8)))), (((p10(f11(X3, X4, X5), f11(X6, X7, X8)) | (~p2(X3, X6))) | (~p9(X4, X7))) <=> ((~p9(X4, X7)) | (~p2(X3, X6)) | p10(f11(X3, X4, X5), f11(X6, X7, X8))))), ((((p10(f11(X3, X4, X5), f11(X6, X7, X8)) | (~p2(X3, X6))) | (~p9(X4, X7))) | (~p10(X5, X8))) <=> (((~p9(X4, X7)) | (~p2(X3, X6)) | p10(f11(X3, X4, X5), f11(X6, X7, X8))) | (~p10(X5, X8))))), rewrite((((~p9(X4, X7)) | (~p2(X3, X6)) | p10(f11(X3, X4, X5), f11(X6, X7, X8))) | (~p10(X5, X8))) <=> ((~p10(X5, X8)) | (~p9(X4, X7)) | (~p2(X3, X6)) | p10(f11(X3, X4, X5), f11(X6, X7, X8)))), ((((p10(f11(X3, X4, X5), f11(X6, X7, X8)) | (~p2(X3, X6))) | (~p9(X4, X7))) | (~p10(X5, X8))) <=> ((~p10(X5, X8)) | (~p9(X4, X7)) | (~p2(X3, X6)) | p10(f11(X3, X4, X5), f11(X6, X7, X8)))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(42,plain,
% 0.11/0.37 (![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i, X8: $i] : (((p10(f11(X3, X4, X5), f11(X6, X7, X8)) | (~p2(X3, X6))) | (~p9(X4, X7))) | (~p10(X5, X8))) <=> ![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i, X8: $i] : ((~p10(X5, X8)) | (~p9(X4, X7)) | (~p2(X3, X6)) | p10(f11(X3, X4, X5), f11(X6, X7, X8)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[41])).
% 0.11/0.37 tff(43,axiom,(![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i, X8: $i] : (((p10(f11(X3, X4, X5), f11(X6, X7, X8)) | (~p2(X3, X6))) | (~p9(X4, X7))) | (~p10(X5, X8)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p10_27')).
% 0.11/0.37 tff(44,plain,
% 0.11/0.37 (![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i, X8: $i] : ((~p10(X5, X8)) | (~p9(X4, X7)) | (~p2(X3, X6)) | p10(f11(X3, X4, X5), f11(X6, X7, X8)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.11/0.37 tff(45,plain,
% 0.11/0.37 (![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i, X8: $i] : ((~p10(X5, X8)) | (~p9(X4, X7)) | (~p2(X3, X6)) | p10(f11(X3, X4, X5), f11(X6, X7, X8)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.11/0.37 tff(46,plain,(
% 0.11/0.37 ![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i, X8: $i] : ((~p10(X5, X8)) | (~p9(X4, X7)) | (~p2(X3, X6)) | p10(f11(X3, X4, X5), f11(X6, X7, X8)))),
% 0.11/0.37 inference(skolemize,[status(sab)],[45])).
% 0.11/0.37 tff(47,plain,
% 0.11/0.37 (![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i, X8: $i] : ((~p10(X5, X8)) | (~p9(X4, X7)) | (~p2(X3, X6)) | p10(f11(X3, X4, X5), f11(X6, X7, X8)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[46, 39])).
% 0.11/0.37 tff(48,plain,
% 0.11/0.37 (((~![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i, X8: $i] : ((~p10(X5, X8)) | (~p9(X4, X7)) | (~p2(X3, X6)) | p10(f11(X3, X4, X5), f11(X6, X7, X8)))) | ((~p10(c24, c24)) | (~p9(c23, c23)) | (~p2(f13(f15(c20), f14(f4(c20), c22)), f13(f15(c20), f14(f4(c20), c22)))) | p10(f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24)))) <=> ((~![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i, X8: $i] : ((~p10(X5, X8)) | (~p9(X4, X7)) | (~p2(X3, X6)) | p10(f11(X3, X4, X5), f11(X6, X7, X8)))) | (~p10(c24, c24)) | (~p9(c23, c23)) | (~p2(f13(f15(c20), f14(f4(c20), c22)), f13(f15(c20), f14(f4(c20), c22)))) | p10(f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24)))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(49,plain,
% 0.18/0.37 ((~![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i, X8: $i] : ((~p10(X5, X8)) | (~p9(X4, X7)) | (~p2(X3, X6)) | p10(f11(X3, X4, X5), f11(X6, X7, X8)))) | ((~p10(c24, c24)) | (~p9(c23, c23)) | (~p2(f13(f15(c20), f14(f4(c20), c22)), f13(f15(c20), f14(f4(c20), c22)))) | p10(f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24)))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(50,plain,
% 0.18/0.37 ((~![X6: $i, X4: $i, X3: $i, X7: $i, X5: $i, X8: $i] : ((~p10(X5, X8)) | (~p9(X4, X7)) | (~p2(X3, X6)) | p10(f11(X3, X4, X5), f11(X6, X7, X8)))) | (~p10(c24, c24)) | (~p9(c23, c23)) | (~p2(f13(f15(c20), f14(f4(c20), c22)), f13(f15(c20), f14(f4(c20), c22)))) | p10(f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.18/0.37 tff(51,plain,
% 0.18/0.37 ((~p10(c24, c24)) | (~p9(c23, c23)) | (~p2(f13(f15(c20), f14(f4(c20), c22)), f13(f15(c20), f14(f4(c20), c22)))) | p10(f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[50, 47])).
% 0.18/0.37 tff(52,plain,
% 0.18/0.37 ((~p10(c24, c24)) | (~p9(c23, c23)) | p10(f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[51, 37])).
% 0.18/0.37 tff(53,plain,
% 0.18/0.37 (p10(f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[52, 33, 22])).
% 0.18/0.37 tff(54,plain,
% 0.18/0.37 (p10(f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24)) <=> p10(f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(55,axiom,(p10(f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p10_28')).
% 0.18/0.37 tff(56,plain,
% 0.18/0.37 (p10(f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.18/0.37 tff(57,plain,
% 0.18/0.37 (^[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)))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(58,plain,
% 0.18/0.37 (![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))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[57])).
% 0.18/0.37 tff(59,plain,
% 0.18/0.37 (![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))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(60,plain,
% 0.18/0.37 (^[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))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(61,plain,
% 0.18/0.37 (![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))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[60])).
% 0.18/0.38 tff(62,axiom,(![X0: $i, X2: $i, X1: $i] : ((p10(X1, X2) | (~p10(X0, X1))) | (~p10(X0, X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p10_15')).
% 0.18/0.38 tff(63,plain,
% 0.18/0.38 (![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.18/0.38 tff(64,plain,
% 0.18/0.38 (![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.18/0.38 tff(65,plain,(
% 0.18/0.38 ![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))),
% 0.18/0.38 inference(skolemize,[status(sab)],[64])).
% 0.18/0.38 tff(66,plain,
% 0.18/0.38 (![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.18/0.38 tff(67,plain,
% 0.18/0.38 (((~![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))) | ((~p10(f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24))) | p10(f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24)) | (~p10(f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))) | (~p10(f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24))) | p10(f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24)) | (~p10(f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(68,plain,
% 0.18/0.38 (((~p10(f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24))) | (~p10(f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24))) | p10(f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24))) <=> ((~p10(f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24))) | p10(f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24)) | (~p10(f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(69,plain,
% 0.18/0.38 (((~![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))) | ((~p10(f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24))) | (~p10(f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24))) | p10(f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))) | ((~p10(f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24))) | p10(f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24)) | (~p10(f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24)))))),
% 0.18/0.38 inference(monotonicity,[status(thm)],[68])).
% 0.18/0.38 tff(70,plain,
% 0.18/0.38 (((~![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))) | ((~p10(f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24))) | (~p10(f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24))) | p10(f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))) | (~p10(f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24))) | p10(f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24)) | (~p10(f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24))))),
% 0.18/0.38 inference(transitivity,[status(thm)],[69, 67])).
% 0.18/0.38 tff(71,plain,
% 0.18/0.38 ((~![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))) | ((~p10(f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24))) | (~p10(f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24))) | p10(f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24)))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(72,plain,
% 0.18/0.38 ((~![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))) | (~p10(f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24))) | p10(f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24)) | (~p10(f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.18/0.38 tff(73,plain,
% 0.18/0.38 (p10(f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[72, 66, 56, 53])).
% 0.18/0.38 tff(74,plain,
% 0.18/0.38 (^[X25: $i, X27: $i, X26: $i, X24: $i] : refl(((~p10(X26, X25)) | (~p2(X27, X24)) | (~p18(X27, X26)) | p18(X24, X25)) <=> ((~p10(X26, X25)) | (~p2(X27, X24)) | (~p18(X27, X26)) | p18(X24, X25)))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(75,plain,
% 0.18/0.38 (![X25: $i, X27: $i, X26: $i, X24: $i] : ((~p10(X26, X25)) | (~p2(X27, X24)) | (~p18(X27, X26)) | p18(X24, X25)) <=> ![X25: $i, X27: $i, X26: $i, X24: $i] : ((~p10(X26, X25)) | (~p2(X27, X24)) | (~p18(X27, X26)) | p18(X24, X25))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[74])).
% 0.18/0.38 tff(76,plain,
% 0.18/0.38 (![X25: $i, X27: $i, X26: $i, X24: $i] : ((~p10(X26, X25)) | (~p2(X27, X24)) | (~p18(X27, X26)) | p18(X24, X25)) <=> ![X25: $i, X27: $i, X26: $i, X24: $i] : ((~p10(X26, X25)) | (~p2(X27, X24)) | (~p18(X27, X26)) | p18(X24, X25))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(77,plain,
% 0.18/0.38 (^[X25: $i, X27: $i, X26: $i, X24: $i] : trans(monotonicity(trans(monotonicity(rewrite((p18(X24, X25) | (~p18(X27, X26))) <=> ((~p18(X27, X26)) | p18(X24, X25))), (((p18(X24, X25) | (~p18(X27, X26))) | (~p2(X27, X24))) <=> (((~p18(X27, X26)) | p18(X24, X25)) | (~p2(X27, X24))))), rewrite((((~p18(X27, X26)) | p18(X24, X25)) | (~p2(X27, X24))) <=> ((~p2(X27, X24)) | (~p18(X27, X26)) | p18(X24, X25))), (((p18(X24, X25) | (~p18(X27, X26))) | (~p2(X27, X24))) <=> ((~p2(X27, X24)) | (~p18(X27, X26)) | p18(X24, X25)))), ((((p18(X24, X25) | (~p18(X27, X26))) | (~p2(X27, X24))) | (~p10(X26, X25))) <=> (((~p2(X27, X24)) | (~p18(X27, X26)) | p18(X24, X25)) | (~p10(X26, X25))))), rewrite((((~p2(X27, X24)) | (~p18(X27, X26)) | p18(X24, X25)) | (~p10(X26, X25))) <=> ((~p10(X26, X25)) | (~p2(X27, X24)) | (~p18(X27, X26)) | p18(X24, X25))), ((((p18(X24, X25) | (~p18(X27, X26))) | (~p2(X27, X24))) | (~p10(X26, X25))) <=> ((~p10(X26, X25)) | (~p2(X27, X24)) | (~p18(X27, X26)) | p18(X24, X25))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(78,plain,
% 0.18/0.38 (![X25: $i, X27: $i, X26: $i, X24: $i] : (((p18(X24, X25) | (~p18(X27, X26))) | (~p2(X27, X24))) | (~p10(X26, X25))) <=> ![X25: $i, X27: $i, X26: $i, X24: $i] : ((~p10(X26, X25)) | (~p2(X27, X24)) | (~p18(X27, X26)) | p18(X24, X25))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[77])).
% 0.18/0.38 tff(79,axiom,(![X25: $i, X27: $i, X26: $i, X24: $i] : (((p18(X24, X25) | (~p18(X27, X26))) | (~p2(X27, X24))) | (~p10(X26, X25)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p18_23')).
% 0.18/0.38 tff(80,plain,
% 0.18/0.38 (![X25: $i, X27: $i, X26: $i, X24: $i] : ((~p10(X26, X25)) | (~p2(X27, X24)) | (~p18(X27, X26)) | p18(X24, X25))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.18/0.38 tff(81,plain,
% 0.18/0.38 (![X25: $i, X27: $i, X26: $i, X24: $i] : ((~p10(X26, X25)) | (~p2(X27, X24)) | (~p18(X27, X26)) | p18(X24, X25))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.18/0.38 tff(82,plain,(
% 0.18/0.38 ![X25: $i, X27: $i, X26: $i, X24: $i] : ((~p10(X26, X25)) | (~p2(X27, X24)) | (~p18(X27, X26)) | p18(X24, X25))),
% 0.18/0.39 inference(skolemize,[status(sab)],[81])).
% 0.18/0.39 tff(83,plain,
% 0.18/0.39 (![X25: $i, X27: $i, X26: $i, X24: $i] : ((~p10(X26, X25)) | (~p2(X27, X24)) | (~p18(X27, X26)) | p18(X24, X25))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[82, 75])).
% 0.18/0.39 tff(84,plain,
% 0.18/0.39 ((~p18(c20, f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24))) <=> (~p18(c20, f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(85,axiom,(~p18(c20, f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_p18_21')).
% 0.18/0.39 tff(86,plain,
% 0.18/0.39 (~p18(c20, f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.18/0.39 tff(87,plain,
% 0.18/0.39 (p18(c20, f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24)) <=> p18(c20, f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(88,axiom,(p18(c20, f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p18_20')).
% 0.18/0.39 tff(89,plain,
% 0.18/0.39 (p18(c20, f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.18/0.39 tff(90,plain,
% 0.18/0.39 (((~![X25: $i, X27: $i, X26: $i, X24: $i] : ((~p10(X26, X25)) | (~p2(X27, X24)) | (~p18(X27, X26)) | p18(X24, X25))) | (p18(c20, f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24)) | (~p10(f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24))) | (~p2(c20, c20)) | (~p18(c20, f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24))))) <=> ((~![X25: $i, X27: $i, X26: $i, X24: $i] : ((~p10(X26, X25)) | (~p2(X27, X24)) | (~p18(X27, X26)) | p18(X24, X25))) | p18(c20, f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24)) | (~p10(f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24))) | (~p2(c20, c20)) | (~p18(c20, f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(91,plain,
% 0.18/0.39 (((~p10(f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24))) | (~p2(c20, c20)) | (~p18(c20, f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24))) | p18(c20, f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24))) <=> (p18(c20, f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24)) | (~p10(f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24))) | (~p2(c20, c20)) | (~p18(c20, f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(92,plain,
% 0.18/0.39 (((~![X25: $i, X27: $i, X26: $i, X24: $i] : ((~p10(X26, X25)) | (~p2(X27, X24)) | (~p18(X27, X26)) | p18(X24, X25))) | ((~p10(f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24))) | (~p2(c20, c20)) | (~p18(c20, f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24))) | p18(c20, f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24)))) <=> ((~![X25: $i, X27: $i, X26: $i, X24: $i] : ((~p10(X26, X25)) | (~p2(X27, X24)) | (~p18(X27, X26)) | p18(X24, X25))) | (p18(c20, f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24)) | (~p10(f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24))) | (~p2(c20, c20)) | (~p18(c20, f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24)))))),
% 0.18/0.39 inference(monotonicity,[status(thm)],[91])).
% 0.18/0.39 tff(93,plain,
% 0.18/0.39 (((~![X25: $i, X27: $i, X26: $i, X24: $i] : ((~p10(X26, X25)) | (~p2(X27, X24)) | (~p18(X27, X26)) | p18(X24, X25))) | ((~p10(f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24))) | (~p2(c20, c20)) | (~p18(c20, f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24))) | p18(c20, f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24)))) <=> ((~![X25: $i, X27: $i, X26: $i, X24: $i] : ((~p10(X26, X25)) | (~p2(X27, X24)) | (~p18(X27, X26)) | p18(X24, X25))) | p18(c20, f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24)) | (~p10(f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24))) | (~p2(c20, c20)) | (~p18(c20, f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24))))),
% 0.18/0.39 inference(transitivity,[status(thm)],[92, 90])).
% 0.18/0.39 tff(94,plain,
% 0.18/0.39 ((~![X25: $i, X27: $i, X26: $i, X24: $i] : ((~p10(X26, X25)) | (~p2(X27, X24)) | (~p18(X27, X26)) | p18(X24, X25))) | ((~p10(f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24))) | (~p2(c20, c20)) | (~p18(c20, f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24))) | p18(c20, f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24)))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(95,plain,
% 0.18/0.39 ((~![X25: $i, X27: $i, X26: $i, X24: $i] : ((~p10(X26, X25)) | (~p2(X27, X24)) | (~p18(X27, X26)) | p18(X24, X25))) | p18(c20, f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24)) | (~p10(f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24))) | (~p2(c20, c20)) | (~p18(c20, f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.18/0.39 tff(96,plain,
% 0.18/0.39 ($false),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[95, 89, 86, 83, 73, 11])).
% 0.18/0.39 % SZS output end Proof
% 0.18/0.39 % E exiting
%------------------------------------------------------------------------------