%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN597-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN597-1 : TPTP v9.0.0. Released v2.5.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n006.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 12:37:50 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(p3_type, type, (
% 0.11/0.37 p3: ( $i * $i ) > $o)).
% 0.11/0.37 tff(p12_type, type, (
% 0.11/0.37 p12: ( $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,(~p9(c23, c23)), introduced(assumption)).
% 0.11/0.37 tff(13,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(14,plain,
% 0.11/0.37 (![X50: $i] : p9(X50, X50) <=> ![X50: $i] : p9(X50, X50)),
% 0.11/0.37 inference(quant_intro,[status(thm)],[13])).
% 0.11/0.37 tff(15,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(16,axiom,(![X50: $i] : p9(X50, X50)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p9_2')).
% 0.11/0.37 tff(17,plain,
% 0.11/0.37 (![X50: $i] : p9(X50, X50)),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.11/0.37 tff(18,plain,(
% 0.11/0.37 ![X50: $i] : p9(X50, X50)),
% 0.11/0.37 inference(skolemize,[status(sab)],[17])).
% 0.11/0.37 tff(19,plain,
% 0.11/0.37 (![X50: $i] : p9(X50, X50)),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.11/0.37 tff(20,plain,
% 0.11/0.37 ((~![X50: $i] : p9(X50, X50)) | p9(c23, c23)),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(21,plain,
% 0.11/0.37 ($false),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[20, 19, 12])).
% 0.11/0.37 tff(22,plain,(p9(c23, c23)), inference(lemma,lemma(discharge,[]))).
% 0.11/0.37 tff(23,assumption,(~p3(f15(c20), f15(c20))), introduced(assumption)).
% 0.11/0.37 tff(24,plain,
% 0.11/0.37 (^[X35: $i] : refl(p3(X35, X35) <=> p3(X35, X35))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(25,plain,
% 0.11/0.37 (![X35: $i] : p3(X35, X35) <=> ![X35: $i] : p3(X35, X35)),
% 0.11/0.37 inference(quant_intro,[status(thm)],[24])).
% 0.11/0.37 tff(26,plain,
% 0.11/0.37 (![X35: $i] : p3(X35, X35) <=> ![X35: $i] : p3(X35, X35)),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(27,axiom,(![X35: $i] : p3(X35, X35)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p3_3')).
% 0.11/0.37 tff(28,plain,
% 0.11/0.37 (![X35: $i] : p3(X35, X35)),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.11/0.37 tff(29,plain,(
% 0.11/0.37 ![X35: $i] : p3(X35, X35)),
% 0.11/0.37 inference(skolemize,[status(sab)],[28])).
% 0.11/0.37 tff(30,plain,
% 0.11/0.37 (![X35: $i] : p3(X35, X35)),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.11/0.37 tff(31,plain,
% 0.11/0.37 ((~![X35: $i] : p3(X35, X35)) | p3(f15(c20), f15(c20))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(32,plain,
% 0.11/0.37 ($false),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[31, 30, 23])).
% 0.11/0.37 tff(33,plain,(p3(f15(c20), f15(c20))), inference(lemma,lemma(discharge,[]))).
% 0.11/0.37 tff(34,assumption,(~p3(f4(c20), f4(c20))), introduced(assumption)).
% 0.11/0.37 tff(35,plain,
% 0.11/0.37 ((~![X35: $i] : p3(X35, X35)) | p3(f4(c20), f4(c20))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(36,plain,
% 0.11/0.37 ($false),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[35, 30, 34])).
% 0.11/0.37 tff(37,plain,(p3(f4(c20), f4(c20))), inference(lemma,lemma(discharge,[]))).
% 0.11/0.37 tff(38,plain,
% 0.11/0.37 (^[X14: $i, X12: $i, X13: $i, X15: $i] : refl(((~p3(X13, X15)) | (~p3(X12, X14)) | p12(f14(X12, X13), f14(X14, X15))) <=> ((~p3(X13, X15)) | (~p3(X12, X14)) | p12(f14(X12, X13), f14(X14, X15))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(39,plain,
% 0.11/0.37 (![X14: $i, X12: $i, X13: $i, X15: $i] : ((~p3(X13, X15)) | (~p3(X12, X14)) | p12(f14(X12, X13), f14(X14, X15))) <=> ![X14: $i, X12: $i, X13: $i, X15: $i] : ((~p3(X13, X15)) | (~p3(X12, X14)) | p12(f14(X12, X13), f14(X14, X15)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[38])).
% 0.11/0.37 tff(40,plain,
% 0.11/0.37 (![X14: $i, X12: $i, X13: $i, X15: $i] : ((~p3(X13, X15)) | (~p3(X12, X14)) | p12(f14(X12, X13), f14(X14, X15))) <=> ![X14: $i, X12: $i, X13: $i, X15: $i] : ((~p3(X13, X15)) | (~p3(X12, X14)) | p12(f14(X12, X13), f14(X14, X15)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(41,plain,
% 0.11/0.37 (^[X14: $i, X12: $i, X13: $i, X15: $i] : trans(monotonicity(rewrite((p12(f14(X12, X13), f14(X14, X15)) | (~p3(X12, X14))) <=> ((~p3(X12, X14)) | p12(f14(X12, X13), f14(X14, X15)))), (((p12(f14(X12, X13), f14(X14, X15)) | (~p3(X12, X14))) | (~p3(X13, X15))) <=> (((~p3(X12, X14)) | p12(f14(X12, X13), f14(X14, X15))) | (~p3(X13, X15))))), rewrite((((~p3(X12, X14)) | p12(f14(X12, X13), f14(X14, X15))) | (~p3(X13, X15))) <=> ((~p3(X13, X15)) | (~p3(X12, X14)) | p12(f14(X12, X13), f14(X14, X15)))), (((p12(f14(X12, X13), f14(X14, X15)) | (~p3(X12, X14))) | (~p3(X13, X15))) <=> ((~p3(X13, X15)) | (~p3(X12, X14)) | p12(f14(X12, X13), f14(X14, X15)))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(42,plain,
% 0.11/0.37 (![X14: $i, X12: $i, X13: $i, X15: $i] : ((p12(f14(X12, X13), f14(X14, X15)) | (~p3(X12, X14))) | (~p3(X13, X15))) <=> ![X14: $i, X12: $i, X13: $i, X15: $i] : ((~p3(X13, X15)) | (~p3(X12, X14)) | p12(f14(X12, X13), f14(X14, X15)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[41])).
% 0.11/0.37 tff(43,axiom,(![X14: $i, X12: $i, X13: $i, X15: $i] : ((p12(f14(X12, X13), f14(X14, X15)) | (~p3(X12, X14))) | (~p3(X13, X15)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p12_27')).
% 0.11/0.37 tff(44,plain,
% 0.11/0.37 (![X14: $i, X12: $i, X13: $i, X15: $i] : ((~p3(X13, X15)) | (~p3(X12, X14)) | p12(f14(X12, X13), f14(X14, X15)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.11/0.37 tff(45,plain,
% 0.11/0.37 (![X14: $i, X12: $i, X13: $i, X15: $i] : ((~p3(X13, X15)) | (~p3(X12, X14)) | p12(f14(X12, X13), f14(X14, X15)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.11/0.37 tff(46,plain,(
% 0.11/0.37 ![X14: $i, X12: $i, X13: $i, X15: $i] : ((~p3(X13, X15)) | (~p3(X12, X14)) | p12(f14(X12, X13), f14(X14, X15)))),
% 0.11/0.37 inference(skolemize,[status(sab)],[45])).
% 0.11/0.37 tff(47,plain,
% 0.11/0.37 (![X14: $i, X12: $i, X13: $i, X15: $i] : ((~p3(X13, X15)) | (~p3(X12, X14)) | p12(f14(X12, X13), f14(X14, X15)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[46, 39])).
% 0.11/0.37 tff(48,plain,
% 0.11/0.37 (p3(c21, c22) <=> p3(c21, c22)),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(49,axiom,(p3(c21, c22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p3_7')).
% 0.11/0.37 tff(50,plain,
% 0.11/0.37 (p3(c21, c22)),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.11/0.37 tff(51,plain,
% 0.11/0.37 (((~![X14: $i, X12: $i, X13: $i, X15: $i] : ((~p3(X13, X15)) | (~p3(X12, X14)) | p12(f14(X12, X13), f14(X14, X15)))) | ((~p3(c21, c22)) | (~p3(f4(c20), f4(c20))) | p12(f14(f4(c20), c21), f14(f4(c20), c22)))) <=> ((~![X14: $i, X12: $i, X13: $i, X15: $i] : ((~p3(X13, X15)) | (~p3(X12, X14)) | p12(f14(X12, X13), f14(X14, X15)))) | (~p3(c21, c22)) | (~p3(f4(c20), f4(c20))) | p12(f14(f4(c20), c21), f14(f4(c20), c22)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(52,plain,
% 0.11/0.37 ((~![X14: $i, X12: $i, X13: $i, X15: $i] : ((~p3(X13, X15)) | (~p3(X12, X14)) | p12(f14(X12, X13), f14(X14, X15)))) | ((~p3(c21, c22)) | (~p3(f4(c20), f4(c20))) | p12(f14(f4(c20), c21), f14(f4(c20), c22)))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(53,plain,
% 0.11/0.37 ((~![X14: $i, X12: $i, X13: $i, X15: $i] : ((~p3(X13, X15)) | (~p3(X12, X14)) | p12(f14(X12, X13), f14(X14, X15)))) | (~p3(c21, c22)) | (~p3(f4(c20), f4(c20))) | p12(f14(f4(c20), c21), f14(f4(c20), c22))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.11/0.37 tff(54,plain,
% 0.11/0.37 ((~p3(f4(c20), f4(c20))) | p12(f14(f4(c20), c21), f14(f4(c20), c22))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[53, 50, 47])).
% 0.11/0.37 tff(55,plain,
% 0.11/0.37 (p12(f14(f4(c20), c21), f14(f4(c20), c22))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[54, 37])).
% 0.11/0.37 tff(56,plain,
% 0.11/0.37 (^[X31: $i, X32: $i, X34: $i, X33: $i] : refl(((~p12(X32, X34)) | (~p3(X31, X33)) | p2(f13(X31, X32), f13(X33, X34))) <=> ((~p12(X32, X34)) | (~p3(X31, X33)) | p2(f13(X31, X32), f13(X33, X34))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(57,plain,
% 0.11/0.37 (![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p12(X32, X34)) | (~p3(X31, X33)) | p2(f13(X31, X32), f13(X33, X34))) <=> ![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p12(X32, X34)) | (~p3(X31, X33)) | p2(f13(X31, X32), f13(X33, X34)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[56])).
% 0.11/0.37 tff(58,plain,
% 0.11/0.37 (![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p12(X32, X34)) | (~p3(X31, X33)) | p2(f13(X31, X32), f13(X33, X34))) <=> ![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p12(X32, X34)) | (~p3(X31, X33)) | p2(f13(X31, X32), f13(X33, X34)))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(59,plain,
% 0.11/0.37 (^[X31: $i, X32: $i, X34: $i, X33: $i] : trans(monotonicity(rewrite((p2(f13(X31, X32), f13(X33, X34)) | (~p12(X32, X34))) <=> ((~p12(X32, X34)) | p2(f13(X31, X32), f13(X33, X34)))), (((p2(f13(X31, X32), f13(X33, X34)) | (~p12(X32, X34))) | (~p3(X31, X33))) <=> (((~p12(X32, X34)) | p2(f13(X31, X32), f13(X33, X34))) | (~p3(X31, X33))))), rewrite((((~p12(X32, X34)) | p2(f13(X31, X32), f13(X33, X34))) | (~p3(X31, X33))) <=> ((~p12(X32, X34)) | (~p3(X31, X33)) | p2(f13(X31, X32), f13(X33, X34)))), (((p2(f13(X31, X32), f13(X33, X34)) | (~p12(X32, X34))) | (~p3(X31, X33))) <=> ((~p12(X32, X34)) | (~p3(X31, X33)) | p2(f13(X31, X32), f13(X33, X34)))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(60,plain,
% 0.11/0.37 (![X31: $i, X32: $i, X34: $i, X33: $i] : ((p2(f13(X31, X32), f13(X33, X34)) | (~p12(X32, X34))) | (~p3(X31, X33))) <=> ![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p12(X32, X34)) | (~p3(X31, X33)) | p2(f13(X31, X32), f13(X33, X34)))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[59])).
% 0.11/0.37 tff(61,axiom,(![X31: $i, X32: $i, X34: $i, X33: $i] : ((p2(f13(X31, X32), f13(X33, X34)) | (~p12(X32, X34))) | (~p3(X31, X33)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_26')).
% 0.11/0.37 tff(62,plain,
% 0.11/0.37 (![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p12(X32, X34)) | (~p3(X31, X33)) | p2(f13(X31, X32), f13(X33, X34)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.11/0.37 tff(63,plain,
% 0.11/0.37 (![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p12(X32, X34)) | (~p3(X31, X33)) | p2(f13(X31, X32), f13(X33, X34)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.11/0.37 tff(64,plain,(
% 0.11/0.37 ![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p12(X32, X34)) | (~p3(X31, X33)) | p2(f13(X31, X32), f13(X33, X34)))),
% 0.11/0.37 inference(skolemize,[status(sab)],[63])).
% 0.11/0.37 tff(65,plain,
% 0.11/0.37 (![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p12(X32, X34)) | (~p3(X31, X33)) | p2(f13(X31, X32), f13(X33, X34)))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[64, 57])).
% 0.11/0.37 tff(66,plain,
% 0.11/0.37 (((~![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p12(X32, X34)) | (~p3(X31, X33)) | p2(f13(X31, X32), f13(X33, X34)))) | ((~p3(f15(c20), f15(c20))) | (~p12(f14(f4(c20), c21), f14(f4(c20), c22))) | p2(f13(f15(c20), f14(f4(c20), c21)), f13(f15(c20), f14(f4(c20), c22))))) <=> ((~![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p12(X32, X34)) | (~p3(X31, X33)) | p2(f13(X31, X32), f13(X33, X34)))) | (~p3(f15(c20), f15(c20))) | (~p12(f14(f4(c20), c21), f14(f4(c20), c22))) | p2(f13(f15(c20), f14(f4(c20), c21)), f13(f15(c20), f14(f4(c20), c22))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(67,plain,
% 0.11/0.37 (((~p12(f14(f4(c20), c21), f14(f4(c20), c22))) | (~p3(f15(c20), f15(c20))) | p2(f13(f15(c20), f14(f4(c20), c21)), f13(f15(c20), f14(f4(c20), c22)))) <=> ((~p3(f15(c20), f15(c20))) | (~p12(f14(f4(c20), c21), f14(f4(c20), c22))) | p2(f13(f15(c20), f14(f4(c20), c21)), f13(f15(c20), f14(f4(c20), c22))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(68,plain,
% 0.11/0.38 (((~![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p12(X32, X34)) | (~p3(X31, X33)) | p2(f13(X31, X32), f13(X33, X34)))) | ((~p12(f14(f4(c20), c21), f14(f4(c20), c22))) | (~p3(f15(c20), f15(c20))) | p2(f13(f15(c20), f14(f4(c20), c21)), f13(f15(c20), f14(f4(c20), c22))))) <=> ((~![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p12(X32, X34)) | (~p3(X31, X33)) | p2(f13(X31, X32), f13(X33, X34)))) | ((~p3(f15(c20), f15(c20))) | (~p12(f14(f4(c20), c21), f14(f4(c20), c22))) | p2(f13(f15(c20), f14(f4(c20), c21)), f13(f15(c20), f14(f4(c20), c22)))))),
% 0.11/0.38 inference(monotonicity,[status(thm)],[67])).
% 0.11/0.38 tff(69,plain,
% 0.11/0.38 (((~![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p12(X32, X34)) | (~p3(X31, X33)) | p2(f13(X31, X32), f13(X33, X34)))) | ((~p12(f14(f4(c20), c21), f14(f4(c20), c22))) | (~p3(f15(c20), f15(c20))) | p2(f13(f15(c20), f14(f4(c20), c21)), f13(f15(c20), f14(f4(c20), c22))))) <=> ((~![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p12(X32, X34)) | (~p3(X31, X33)) | p2(f13(X31, X32), f13(X33, X34)))) | (~p3(f15(c20), f15(c20))) | (~p12(f14(f4(c20), c21), f14(f4(c20), c22))) | p2(f13(f15(c20), f14(f4(c20), c21)), f13(f15(c20), f14(f4(c20), c22))))),
% 0.11/0.38 inference(transitivity,[status(thm)],[68, 66])).
% 0.11/0.38 tff(70,plain,
% 0.11/0.38 ((~![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p12(X32, X34)) | (~p3(X31, X33)) | p2(f13(X31, X32), f13(X33, X34)))) | ((~p12(f14(f4(c20), c21), f14(f4(c20), c22))) | (~p3(f15(c20), f15(c20))) | p2(f13(f15(c20), f14(f4(c20), c21)), f13(f15(c20), f14(f4(c20), c22))))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(71,plain,
% 0.11/0.38 ((~![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p12(X32, X34)) | (~p3(X31, X33)) | p2(f13(X31, X32), f13(X33, X34)))) | (~p3(f15(c20), f15(c20))) | (~p12(f14(f4(c20), c21), f14(f4(c20), c22))) | p2(f13(f15(c20), f14(f4(c20), c21)), f13(f15(c20), f14(f4(c20), c22)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.11/0.38 tff(72,plain,
% 0.11/0.38 ((~p3(f15(c20), f15(c20))) | (~p12(f14(f4(c20), c21), f14(f4(c20), c22))) | p2(f13(f15(c20), f14(f4(c20), c21)), f13(f15(c20), f14(f4(c20), c22)))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[71, 65])).
% 0.11/0.38 tff(73,plain,
% 0.11/0.38 (p2(f13(f15(c20), f14(f4(c20), c21)), f13(f15(c20), f14(f4(c20), c22)))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[72, 55, 33])).
% 0.11/0.38 tff(74,assumption,(~p10(c24, c24)), introduced(assumption)).
% 0.11/0.38 tff(75,plain,
% 0.11/0.38 (^[X0: $i] : refl(p10(X0, X0) <=> p10(X0, X0))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(76,plain,
% 0.11/0.38 (![X0: $i] : p10(X0, X0) <=> ![X0: $i] : p10(X0, X0)),
% 0.11/0.38 inference(quant_intro,[status(thm)],[75])).
% 0.11/0.38 tff(77,plain,
% 0.11/0.38 (![X0: $i] : p10(X0, X0) <=> ![X0: $i] : p10(X0, X0)),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(78,axiom,(![X0: $i] : p10(X0, X0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p10_1')).
% 0.11/0.38 tff(79,plain,
% 0.11/0.38 (![X0: $i] : p10(X0, X0)),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.11/0.38 tff(80,plain,(
% 0.11/0.38 ![X0: $i] : p10(X0, X0)),
% 0.11/0.38 inference(skolemize,[status(sab)],[79])).
% 0.11/0.38 tff(81,plain,
% 0.11/0.38 (![X0: $i] : p10(X0, X0)),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.11/0.38 tff(82,plain,
% 0.11/0.38 ((~![X0: $i] : p10(X0, X0)) | p10(c24, c24)),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(83,plain,
% 0.11/0.38 ($false),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[82, 81, 74])).
% 0.11/0.38 tff(84,plain,(p10(c24, c24)), inference(lemma,lemma(discharge,[]))).
% 0.11/0.38 tff(85,plain,
% 0.11/0.38 (^[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))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(86,plain,
% 0.11/0.38 (![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)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[85])).
% 0.11/0.38 tff(87,plain,
% 0.11/0.38 (![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)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(88,plain,
% 0.11/0.38 (^[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)))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(89,plain,
% 0.11/0.38 (![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)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[88])).
% 0.11/0.38 tff(90,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_28')).
% 0.11/0.38 tff(91,plain,
% 0.11/0.38 (![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)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.11/0.38 tff(92,plain,
% 0.11/0.38 (![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)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[91, 87])).
% 0.11/0.38 tff(93,plain,(
% 0.11/0.38 ![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)))),
% 0.11/0.38 inference(skolemize,[status(sab)],[92])).
% 0.11/0.38 tff(94,plain,
% 0.11/0.38 (![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)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[93, 86])).
% 0.11/0.38 tff(95,plain,
% 0.11/0.38 (((~![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), c21)), f13(f15(c20), f14(f4(c20), c22)))) | p10(f11(f13(f15(c20), f14(f4(c20), c21)), 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), c21)), f13(f15(c20), f14(f4(c20), c22)))) | p10(f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(96,plain,
% 0.11/0.38 ((~![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), c21)), f13(f15(c20), f14(f4(c20), c22)))) | p10(f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24)))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(97,plain,
% 0.11/0.38 ((~![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), c21)), f13(f15(c20), f14(f4(c20), c22)))) | p10(f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.11/0.38 tff(98,plain,
% 0.11/0.38 ((~p10(c24, c24)) | (~p9(c23, c23)) | (~p2(f13(f15(c20), f14(f4(c20), c21)), f13(f15(c20), f14(f4(c20), c22)))) | p10(f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[97, 94])).
% 0.11/0.38 tff(99,plain,
% 0.11/0.38 ((~p9(c23, c23)) | p10(f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[98, 84, 73])).
% 0.11/0.38 tff(100,plain,
% 0.11/0.38 (p10(f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[99, 22])).
% 0.11/0.38 tff(101,plain,
% 0.11/0.38 (^[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)))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(102,plain,
% 0.11/0.38 (![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))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[101])).
% 0.11/0.38 tff(103,plain,
% 0.11/0.38 (![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))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(104,plain,
% 0.11/0.38 (^[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))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(105,plain,
% 0.11/0.38 (![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))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[104])).
% 0.11/0.38 tff(106,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_24')).
% 0.11/0.38 tff(107,plain,
% 0.11/0.38 (![X25: $i, X27: $i, X26: $i, X24: $i] : ((~p10(X26, X25)) | (~p2(X27, X24)) | (~p18(X27, X26)) | p18(X24, X25))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.11/0.38 tff(108,plain,
% 0.11/0.38 (![X25: $i, X27: $i, X26: $i, X24: $i] : ((~p10(X26, X25)) | (~p2(X27, X24)) | (~p18(X27, X26)) | p18(X24, X25))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[107, 103])).
% 0.11/0.39 tff(109,plain,(
% 0.11/0.39 ![X25: $i, X27: $i, X26: $i, X24: $i] : ((~p10(X26, X25)) | (~p2(X27, X24)) | (~p18(X27, X26)) | p18(X24, X25))),
% 0.11/0.39 inference(skolemize,[status(sab)],[108])).
% 0.11/0.39 tff(110,plain,
% 0.11/0.39 (![X25: $i, X27: $i, X26: $i, X24: $i] : ((~p10(X26, X25)) | (~p2(X27, X24)) | (~p18(X27, X26)) | p18(X24, X25))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[109, 102])).
% 0.11/0.39 tff(111,plain,
% 0.11/0.39 ((~p18(c20, f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24))) <=> (~p18(c20, f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24)))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(112,axiom,(~p18(c20, f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_p18_22')).
% 0.11/0.39 tff(113,plain,
% 0.11/0.39 (~p18(c20, f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.11/0.39 tff(114,plain,
% 0.11/0.39 (p18(c20, f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24)) <=> p18(c20, f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(115,axiom,(p18(c20, f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p18_21')).
% 0.11/0.39 tff(116,plain,
% 0.11/0.39 (p18(c20, f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.11/0.39 tff(117,plain,
% 0.11/0.39 (((~![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))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(118,plain,
% 0.11/0.39 (((~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))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(119,plain,
% 0.11/0.39 (((~![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)))))),
% 0.11/0.39 inference(monotonicity,[status(thm)],[118])).
% 0.11/0.39 tff(120,plain,
% 0.11/0.39 (((~![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))))),
% 0.11/0.39 inference(transitivity,[status(thm)],[119, 117])).
% 0.11/0.39 tff(121,plain,
% 0.11/0.39 ((~![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)))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(122,plain,
% 0.11/0.39 ((~![X25: $i, X27: $i, X26: $i, X24: $i] : ((~p10(X26, X25)) | (~p2(X27, X24)) | (~p18(X27, X26)) | p18(X24, X25))) | p18(c20, f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24)) | (~p10(f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24), f11(f13(f15(c20), f14(f4(c20), c22)), c23, c24))) | (~p2(c20, c20)) | (~p18(c20, f11(f13(f15(c20), f14(f4(c20), c21)), c23, c24)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.11/0.39 tff(123,plain,
% 0.11/0.39 ($false),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[122, 116, 113, 110, 100, 11])).
% 0.11/0.39 % SZS output end Proof
% 0.11/0.39 % E exiting
%------------------------------------------------------------------------------