%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN579-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:39:37 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.41s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SYN579-1 : TPTP v9.0.0. Released v2.5.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.14/0.34 % Computer : n012.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Jun 20 12:37:55 EDT 2025
% 0.14/0.34 % CPUTime :
% 0.21/0.41 % SZS status Unsatisfiable
% 0.21/0.41 % SZS output start Proof
% 0.21/0.41 tff(p9_type, type, (
% 0.21/0.41 p9: ( $i * $i ) > $o)).
% 0.21/0.41 tff(f6_type, type, (
% 0.21/0.41 f6: $i > $i)).
% 0.21/0.41 tff(c14_type, type, (
% 0.21/0.41 c14: $i)).
% 0.21/0.41 tff(f8_type, type, (
% 0.21/0.41 f8: ( $i * $i ) > $i)).
% 0.21/0.41 tff(c12_type, type, (
% 0.21/0.41 c12: $i)).
% 0.21/0.41 tff(p7_type, type, (
% 0.21/0.41 p7: ( $i * $i ) > $o)).
% 0.21/0.41 tff(p3_type, type, (
% 0.21/0.41 p3: ( $i * $i ) > $o)).
% 0.21/0.41 tff(c16_type, type, (
% 0.21/0.41 c16: $i)).
% 0.21/0.41 tff(f5_type, type, (
% 0.21/0.41 f5: $i > $i)).
% 0.21/0.41 tff(p2_type, type, (
% 0.21/0.41 p2: ( $i * $i ) > $o)).
% 0.21/0.41 tff(c13_type, type, (
% 0.21/0.41 c13: $i)).
% 0.21/0.41 tff(p11_type, type, (
% 0.21/0.41 p11: ( $i * $i ) > $o)).
% 0.21/0.41 tff(c15_type, type, (
% 0.21/0.41 c15: $i)).
% 0.21/0.41 tff(1,assumption,(~p7(c12, c12)), introduced(assumption)).
% 0.21/0.41 tff(2,plain,
% 0.21/0.41 (^[X21: $i] : refl(p7(X21, X21) <=> p7(X21, X21))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(3,plain,
% 0.21/0.41 (![X21: $i] : p7(X21, X21) <=> ![X21: $i] : p7(X21, X21)),
% 0.21/0.41 inference(quant_intro,[status(thm)],[2])).
% 0.21/0.41 tff(4,plain,
% 0.21/0.41 (![X21: $i] : p7(X21, X21) <=> ![X21: $i] : p7(X21, X21)),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(5,axiom,(![X21: $i] : p7(X21, X21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p7_2')).
% 0.21/0.41 tff(6,plain,
% 0.21/0.41 (![X21: $i] : p7(X21, X21)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.21/0.41 tff(7,plain,(
% 0.21/0.41 ![X21: $i] : p7(X21, X21)),
% 0.21/0.41 inference(skolemize,[status(sab)],[6])).
% 0.21/0.41 tff(8,plain,
% 0.21/0.41 (![X21: $i] : p7(X21, X21)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.21/0.41 tff(9,plain,
% 0.21/0.41 ((~![X21: $i] : p7(X21, X21)) | p7(c12, c12)),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(10,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.21/0.41 tff(11,plain,(p7(c12, c12)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.41 tff(12,assumption,(~p2(c16, c16)), introduced(assumption)).
% 0.21/0.41 tff(13,plain,
% 0.21/0.41 (^[X7: $i] : refl(p2(X7, X7) <=> p2(X7, X7))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(14,plain,
% 0.21/0.41 (![X7: $i] : p2(X7, X7) <=> ![X7: $i] : p2(X7, X7)),
% 0.21/0.41 inference(quant_intro,[status(thm)],[13])).
% 0.21/0.41 tff(15,plain,
% 0.21/0.41 (![X7: $i] : p2(X7, X7) <=> ![X7: $i] : p2(X7, X7)),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(16,axiom,(![X7: $i] : p2(X7, X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_4')).
% 0.21/0.41 tff(17,plain,
% 0.21/0.41 (![X7: $i] : p2(X7, X7)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.21/0.41 tff(18,plain,(
% 0.21/0.41 ![X7: $i] : p2(X7, X7)),
% 0.21/0.41 inference(skolemize,[status(sab)],[17])).
% 0.21/0.41 tff(19,plain,
% 0.21/0.41 (![X7: $i] : p2(X7, X7)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.21/0.41 tff(20,plain,
% 0.21/0.41 ((~![X7: $i] : p2(X7, X7)) | p2(c16, c16)),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(21,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[20, 19, 12])).
% 0.21/0.41 tff(22,plain,(p2(c16, c16)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.41 tff(23,plain,
% 0.21/0.41 (^[X18: $i, X19: $i] : refl(((~p2(X18, X19)) | p3(f6(X18), f6(X19))) <=> ((~p2(X18, X19)) | p3(f6(X18), f6(X19))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(24,plain,
% 0.21/0.41 (![X18: $i, X19: $i] : ((~p2(X18, X19)) | p3(f6(X18), f6(X19))) <=> ![X18: $i, X19: $i] : ((~p2(X18, X19)) | p3(f6(X18), f6(X19)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[23])).
% 0.21/0.41 tff(25,plain,
% 0.21/0.41 (![X18: $i, X19: $i] : ((~p2(X18, X19)) | p3(f6(X18), f6(X19))) <=> ![X18: $i, X19: $i] : ((~p2(X18, X19)) | p3(f6(X18), f6(X19)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(26,plain,
% 0.21/0.41 (^[X18: $i, X19: $i] : rewrite((p3(f6(X18), f6(X19)) | (~p2(X18, X19))) <=> ((~p2(X18, X19)) | p3(f6(X18), f6(X19))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(27,plain,
% 0.21/0.41 (![X18: $i, X19: $i] : (p3(f6(X18), f6(X19)) | (~p2(X18, X19))) <=> ![X18: $i, X19: $i] : ((~p2(X18, X19)) | p3(f6(X18), f6(X19)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[26])).
% 0.21/0.41 tff(28,axiom,(![X18: $i, X19: $i] : (p3(f6(X18), f6(X19)) | (~p2(X18, X19)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p3_13')).
% 0.21/0.41 tff(29,plain,
% 0.21/0.41 (![X18: $i, X19: $i] : ((~p2(X18, X19)) | p3(f6(X18), f6(X19)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.21/0.41 tff(30,plain,
% 0.21/0.41 (![X18: $i, X19: $i] : ((~p2(X18, X19)) | p3(f6(X18), f6(X19)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.21/0.41 tff(31,plain,(
% 0.21/0.41 ![X18: $i, X19: $i] : ((~p2(X18, X19)) | p3(f6(X18), f6(X19)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[30])).
% 0.21/0.41 tff(32,plain,
% 0.21/0.41 (![X18: $i, X19: $i] : ((~p2(X18, X19)) | p3(f6(X18), f6(X19)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.21/0.41 tff(33,plain,
% 0.21/0.41 (((~![X18: $i, X19: $i] : ((~p2(X18, X19)) | p3(f6(X18), f6(X19)))) | ((~p2(c16, c16)) | p3(f6(c16), f6(c16)))) <=> ((~![X18: $i, X19: $i] : ((~p2(X18, X19)) | p3(f6(X18), f6(X19)))) | (~p2(c16, c16)) | p3(f6(c16), f6(c16)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(34,plain,
% 0.21/0.41 ((~![X18: $i, X19: $i] : ((~p2(X18, X19)) | p3(f6(X18), f6(X19)))) | ((~p2(c16, c16)) | p3(f6(c16), f6(c16)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(35,plain,
% 0.21/0.41 ((~![X18: $i, X19: $i] : ((~p2(X18, X19)) | p3(f6(X18), f6(X19)))) | (~p2(c16, c16)) | p3(f6(c16), f6(c16))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.21/0.41 tff(36,plain,
% 0.21/0.41 ((~p2(c16, c16)) | p3(f6(c16), f6(c16))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[35, 32])).
% 0.21/0.41 tff(37,plain,
% 0.21/0.41 (p3(f6(c16), f6(c16))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[36, 22])).
% 0.21/0.41 tff(38,plain,
% 0.21/0.41 (p2(c16, f5(c14)) <=> p2(c16, f5(c14))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(39,axiom,(p2(c16, f5(c14))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_7')).
% 0.21/0.41 tff(40,plain,
% 0.21/0.41 (p2(c16, f5(c14))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.21/0.41 tff(41,plain,
% 0.21/0.41 (((~![X18: $i, X19: $i] : ((~p2(X18, X19)) | p3(f6(X18), f6(X19)))) | ((~p2(c16, f5(c14))) | p3(f6(c16), f6(f5(c14))))) <=> ((~![X18: $i, X19: $i] : ((~p2(X18, X19)) | p3(f6(X18), f6(X19)))) | (~p2(c16, f5(c14))) | p3(f6(c16), f6(f5(c14))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(42,plain,
% 0.21/0.41 ((~![X18: $i, X19: $i] : ((~p2(X18, X19)) | p3(f6(X18), f6(X19)))) | ((~p2(c16, f5(c14))) | p3(f6(c16), f6(f5(c14))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(43,plain,
% 0.21/0.41 ((~![X18: $i, X19: $i] : ((~p2(X18, X19)) | p3(f6(X18), f6(X19)))) | (~p2(c16, f5(c14))) | p3(f6(c16), f6(f5(c14)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.21/0.41 tff(44,plain,
% 0.21/0.41 (p3(f6(c16), f6(f5(c14)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[43, 40, 32])).
% 0.21/0.41 tff(45,plain,
% 0.21/0.41 (^[X14: $i, X12: $i, X13: $i] : refl(((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14)) <=> ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14)))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(46,plain,
% 0.21/0.41 (![X14: $i, X12: $i, X13: $i] : ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14)) <=> ![X14: $i, X12: $i, X13: $i] : ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[45])).
% 0.21/0.41 tff(47,plain,
% 0.21/0.41 (![X14: $i, X12: $i, X13: $i] : ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14)) <=> ![X14: $i, X12: $i, X13: $i] : ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(48,plain,
% 0.21/0.41 (^[X14: $i, X12: $i, X13: $i] : trans(monotonicity(rewrite((p3(X13, X14) | (~p3(X12, X13))) <=> ((~p3(X12, X13)) | p3(X13, X14))), (((p3(X13, X14) | (~p3(X12, X13))) | (~p3(X12, X14))) <=> (((~p3(X12, X13)) | p3(X13, X14)) | (~p3(X12, X14))))), rewrite((((~p3(X12, X13)) | p3(X13, X14)) | (~p3(X12, X14))) <=> ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14))), (((p3(X13, X14) | (~p3(X12, X13))) | (~p3(X12, X14))) <=> ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(49,plain,
% 0.21/0.41 (![X14: $i, X12: $i, X13: $i] : ((p3(X13, X14) | (~p3(X12, X13))) | (~p3(X12, X14))) <=> ![X14: $i, X12: $i, X13: $i] : ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[48])).
% 0.21/0.41 tff(50,axiom,(![X14: $i, X12: $i, X13: $i] : ((p3(X13, X14) | (~p3(X12, X13))) | (~p3(X12, X14)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p3_17')).
% 0.21/0.41 tff(51,plain,
% 0.21/0.41 (![X14: $i, X12: $i, X13: $i] : ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.21/0.41 tff(52,plain,
% 0.21/0.41 (![X14: $i, X12: $i, X13: $i] : ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.21/0.41 tff(53,plain,(
% 0.21/0.41 ![X14: $i, X12: $i, X13: $i] : ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14))),
% 0.21/0.41 inference(skolemize,[status(sab)],[52])).
% 0.21/0.41 tff(54,plain,
% 0.21/0.41 (![X14: $i, X12: $i, X13: $i] : ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[53, 46])).
% 0.21/0.41 tff(55,plain,
% 0.21/0.41 (((~![X14: $i, X12: $i, X13: $i] : ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14))) | ((~p3(f6(c16), f6(c16))) | (~p3(f6(c16), f6(f5(c14)))) | p3(f6(f5(c14)), f6(c16)))) <=> ((~![X14: $i, X12: $i, X13: $i] : ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14))) | (~p3(f6(c16), f6(c16))) | (~p3(f6(c16), f6(f5(c14)))) | p3(f6(f5(c14)), f6(c16)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(56,plain,
% 0.21/0.41 ((~![X14: $i, X12: $i, X13: $i] : ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14))) | ((~p3(f6(c16), f6(c16))) | (~p3(f6(c16), f6(f5(c14)))) | p3(f6(f5(c14)), f6(c16)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(57,plain,
% 0.21/0.41 ((~![X14: $i, X12: $i, X13: $i] : ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14))) | (~p3(f6(c16), f6(c16))) | (~p3(f6(c16), f6(f5(c14)))) | p3(f6(f5(c14)), f6(c16))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.21/0.41 tff(58,plain,
% 0.21/0.41 (p3(f6(f5(c14)), f6(c16))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[57, 54, 44, 37])).
% 0.21/0.41 tff(59,plain,
% 0.21/0.41 (^[X20: $i] : refl(p3(f6(f5(X20)), f6(X20)) <=> p3(f6(f5(X20)), f6(X20)))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(60,plain,
% 0.21/0.41 (![X20: $i] : p3(f6(f5(X20)), f6(X20)) <=> ![X20: $i] : p3(f6(f5(X20)), f6(X20))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[59])).
% 0.21/0.41 tff(61,plain,
% 0.21/0.41 (![X20: $i] : p3(f6(f5(X20)), f6(X20)) <=> ![X20: $i] : p3(f6(f5(X20)), f6(X20))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(62,axiom,(![X20: $i] : p3(f6(f5(X20)), f6(X20))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p3_9')).
% 0.21/0.41 tff(63,plain,
% 0.21/0.41 (![X20: $i] : p3(f6(f5(X20)), f6(X20))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.21/0.41 tff(64,plain,(
% 0.21/0.41 ![X20: $i] : p3(f6(f5(X20)), f6(X20))),
% 0.21/0.41 inference(skolemize,[status(sab)],[63])).
% 0.21/0.41 tff(65,plain,
% 0.21/0.41 (![X20: $i] : p3(f6(f5(X20)), f6(X20))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.21/0.41 tff(66,plain,
% 0.21/0.41 ((~![X20: $i] : p3(f6(f5(X20)), f6(X20))) | p3(f6(f5(c14)), f6(c14))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(67,plain,
% 0.21/0.41 (p3(f6(f5(c14)), f6(c14))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.21/0.41 tff(68,plain,
% 0.21/0.41 (((~![X14: $i, X12: $i, X13: $i] : ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14))) | ((~p3(f6(f5(c14)), f6(c14))) | (~p3(f6(f5(c14)), f6(c16))) | p3(f6(c16), f6(c14)))) <=> ((~![X14: $i, X12: $i, X13: $i] : ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14))) | (~p3(f6(f5(c14)), f6(c14))) | (~p3(f6(f5(c14)), f6(c16))) | p3(f6(c16), f6(c14)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(69,plain,
% 0.21/0.41 ((~![X14: $i, X12: $i, X13: $i] : ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14))) | ((~p3(f6(f5(c14)), f6(c14))) | (~p3(f6(f5(c14)), f6(c16))) | p3(f6(c16), f6(c14)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(70,plain,
% 0.21/0.41 ((~![X14: $i, X12: $i, X13: $i] : ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14))) | (~p3(f6(f5(c14)), f6(c14))) | (~p3(f6(f5(c14)), f6(c16))) | p3(f6(c16), f6(c14))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.21/0.41 tff(71,plain,
% 0.21/0.41 (p3(f6(c16), f6(c14))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[70, 54, 67, 58])).
% 0.21/0.41 tff(72,plain,
% 0.21/0.41 (^[X32: $i] : refl((p9(X32, f6(c16)) | (~p9(X32, c13))) <=> (p9(X32, f6(c16)) | (~p9(X32, c13))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(73,plain,
% 0.21/0.41 (![X32: $i] : (p9(X32, f6(c16)) | (~p9(X32, c13))) <=> ![X32: $i] : (p9(X32, f6(c16)) | (~p9(X32, c13)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[72])).
% 0.21/0.41 tff(74,plain,
% 0.21/0.41 (![X32: $i] : (p9(X32, f6(c16)) | (~p9(X32, c13))) <=> ![X32: $i] : (p9(X32, f6(c16)) | (~p9(X32, c13)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(75,axiom,(![X32: $i] : (p9(X32, f6(c16)) | (~p9(X32, c13)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p9_11')).
% 0.21/0.41 tff(76,plain,
% 0.21/0.41 (![X32: $i] : (p9(X32, f6(c16)) | (~p9(X32, c13)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.21/0.42 tff(77,plain,(
% 0.21/0.42 ![X32: $i] : (p9(X32, f6(c16)) | (~p9(X32, c13)))),
% 0.21/0.42 inference(skolemize,[status(sab)],[76])).
% 0.21/0.42 tff(78,plain,
% 0.21/0.42 (![X32: $i] : (p9(X32, f6(c16)) | (~p9(X32, c13)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[77, 73])).
% 0.21/0.42 tff(79,plain,
% 0.21/0.42 (p9(c12, c13) <=> p9(c12, c13)),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(80,axiom,(p9(c12, c13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p9_5')).
% 0.21/0.42 tff(81,plain,
% 0.21/0.42 (p9(c12, c13)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.21/0.42 tff(82,plain,
% 0.21/0.42 (((~![X32: $i] : (p9(X32, f6(c16)) | (~p9(X32, c13)))) | (p9(c12, f6(c16)) | (~p9(c12, c13)))) <=> ((~![X32: $i] : (p9(X32, f6(c16)) | (~p9(X32, c13)))) | p9(c12, f6(c16)) | (~p9(c12, c13)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(83,plain,
% 0.21/0.42 ((~![X32: $i] : (p9(X32, f6(c16)) | (~p9(X32, c13)))) | (p9(c12, f6(c16)) | (~p9(c12, c13)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(84,plain,
% 0.21/0.42 ((~![X32: $i] : (p9(X32, f6(c16)) | (~p9(X32, c13)))) | p9(c12, f6(c16)) | (~p9(c12, c13))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.21/0.42 tff(85,plain,
% 0.21/0.42 (p9(c12, f6(c16))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[84, 81, 78])).
% 0.21/0.42 tff(86,plain,
% 0.21/0.42 (^[X31: $i, X30: $i, X29: $i, X28: $i] : refl(((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29)) <=> ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29)))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(87,plain,
% 0.21/0.42 (![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29)) <=> ![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[86])).
% 0.21/0.42 tff(88,plain,
% 0.21/0.42 (![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29)) <=> ![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(89,plain,
% 0.21/0.42 (^[X31: $i, X30: $i, X29: $i, X28: $i] : trans(monotonicity(trans(monotonicity(rewrite((p9(X28, X29) | (~p7(X31, X28))) <=> ((~p7(X31, X28)) | p9(X28, X29))), (((p9(X28, X29) | (~p7(X31, X28))) | (~p9(X31, X30))) <=> (((~p7(X31, X28)) | p9(X28, X29)) | (~p9(X31, X30))))), rewrite((((~p7(X31, X28)) | p9(X28, X29)) | (~p9(X31, X30))) <=> ((~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))), (((p9(X28, X29) | (~p7(X31, X28))) | (~p9(X31, X30))) <=> ((~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29)))), ((((p9(X28, X29) | (~p7(X31, X28))) | (~p9(X31, X30))) | (~p3(X30, X29))) <=> (((~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29)) | (~p3(X30, X29))))), rewrite((((~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29)) | (~p3(X30, X29))) <=> ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))), ((((p9(X28, X29) | (~p7(X31, X28))) | (~p9(X31, X30))) | (~p3(X30, X29))) <=> ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(90,plain,
% 0.21/0.42 (![X31: $i, X30: $i, X29: $i, X28: $i] : (((p9(X28, X29) | (~p7(X31, X28))) | (~p9(X31, X30))) | (~p3(X30, X29))) <=> ![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[89])).
% 0.21/0.42 tff(91,axiom,(![X31: $i, X30: $i, X29: $i, X28: $i] : (((p9(X28, X29) | (~p7(X31, X28))) | (~p9(X31, X30))) | (~p3(X30, X29)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p9_20')).
% 0.21/0.42 tff(92,plain,
% 0.21/0.42 (![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.21/0.42 tff(93,plain,
% 0.21/0.42 (![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[92, 88])).
% 0.21/0.42 tff(94,plain,(
% 0.21/0.42 ![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))),
% 0.21/0.42 inference(skolemize,[status(sab)],[93])).
% 0.21/0.42 tff(95,plain,
% 0.21/0.42 (![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[94, 87])).
% 0.21/0.42 tff(96,plain,
% 0.21/0.42 (((~![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))) | (p9(c12, f6(c14)) | (~p7(c12, c12)) | (~p9(c12, f6(c16))) | (~p3(f6(c16), f6(c14))))) <=> ((~![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))) | p9(c12, f6(c14)) | (~p7(c12, c12)) | (~p9(c12, f6(c16))) | (~p3(f6(c16), f6(c14))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(97,plain,
% 0.21/0.42 (((~p3(f6(c16), f6(c14))) | (~p9(c12, f6(c16))) | (~p7(c12, c12)) | p9(c12, f6(c14))) <=> (p9(c12, f6(c14)) | (~p7(c12, c12)) | (~p9(c12, f6(c16))) | (~p3(f6(c16), f6(c14))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(98,plain,
% 0.21/0.42 (((~![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))) | ((~p3(f6(c16), f6(c14))) | (~p9(c12, f6(c16))) | (~p7(c12, c12)) | p9(c12, f6(c14)))) <=> ((~![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))) | (p9(c12, f6(c14)) | (~p7(c12, c12)) | (~p9(c12, f6(c16))) | (~p3(f6(c16), f6(c14)))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[97])).
% 0.21/0.42 tff(99,plain,
% 0.21/0.42 (((~![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))) | ((~p3(f6(c16), f6(c14))) | (~p9(c12, f6(c16))) | (~p7(c12, c12)) | p9(c12, f6(c14)))) <=> ((~![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))) | p9(c12, f6(c14)) | (~p7(c12, c12)) | (~p9(c12, f6(c16))) | (~p3(f6(c16), f6(c14))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[98, 96])).
% 0.21/0.42 tff(100,plain,
% 0.21/0.42 ((~![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))) | ((~p3(f6(c16), f6(c14))) | (~p9(c12, f6(c16))) | (~p7(c12, c12)) | p9(c12, f6(c14)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(101,plain,
% 0.21/0.42 ((~![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))) | p9(c12, f6(c14)) | (~p7(c12, c12)) | (~p9(c12, f6(c16))) | (~p3(f6(c16), f6(c14)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.21/0.42 tff(102,plain,
% 0.21/0.42 (p9(c12, f6(c14))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[101, 95, 85, 71, 11])).
% 0.21/0.42 tff(103,plain,
% 0.21/0.42 (^[X34: $i, X33: $i] : refl(((~p9(c12, X33)) | (~p11(X34, c15)) | (~p9(f8(X33, X34), f6(X34))) | (~p9(f8(X33, X34), X33))) <=> ((~p9(c12, X33)) | (~p11(X34, c15)) | (~p9(f8(X33, X34), f6(X34))) | (~p9(f8(X33, X34), X33))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(104,plain,
% 0.21/0.42 (![X34: $i, X33: $i] : ((~p9(c12, X33)) | (~p11(X34, c15)) | (~p9(f8(X33, X34), f6(X34))) | (~p9(f8(X33, X34), X33))) <=> ![X34: $i, X33: $i] : ((~p9(c12, X33)) | (~p11(X34, c15)) | (~p9(f8(X33, X34), f6(X34))) | (~p9(f8(X33, X34), X33)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[103])).
% 0.21/0.42 tff(105,plain,
% 0.21/0.42 (![X34: $i, X33: $i] : ((~p9(c12, X33)) | (~p11(X34, c15)) | (~p9(f8(X33, X34), f6(X34))) | (~p9(f8(X33, X34), X33))) <=> ![X34: $i, X33: $i] : ((~p9(c12, X33)) | (~p11(X34, c15)) | (~p9(f8(X33, X34), f6(X34))) | (~p9(f8(X33, X34), X33)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(106,plain,
% 0.21/0.42 (^[X34: $i, X33: $i] : trans(monotonicity(rewrite((((~p11(X34, c15)) | (~p9(c12, X33))) | (~p9(f8(X33, X34), X33))) <=> ((~p9(c12, X33)) | (~p11(X34, c15)) | (~p9(f8(X33, X34), X33)))), (((((~p11(X34, c15)) | (~p9(c12, X33))) | (~p9(f8(X33, X34), X33))) | (~p9(f8(X33, X34), f6(X34)))) <=> (((~p9(c12, X33)) | (~p11(X34, c15)) | (~p9(f8(X33, X34), X33))) | (~p9(f8(X33, X34), f6(X34)))))), rewrite((((~p9(c12, X33)) | (~p11(X34, c15)) | (~p9(f8(X33, X34), X33))) | (~p9(f8(X33, X34), f6(X34)))) <=> ((~p9(c12, X33)) | (~p11(X34, c15)) | (~p9(f8(X33, X34), f6(X34))) | (~p9(f8(X33, X34), X33)))), (((((~p11(X34, c15)) | (~p9(c12, X33))) | (~p9(f8(X33, X34), X33))) | (~p9(f8(X33, X34), f6(X34)))) <=> ((~p9(c12, X33)) | (~p11(X34, c15)) | (~p9(f8(X33, X34), f6(X34))) | (~p9(f8(X33, X34), X33)))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(107,plain,
% 0.21/0.42 (![X34: $i, X33: $i] : ((((~p11(X34, c15)) | (~p9(c12, X33))) | (~p9(f8(X33, X34), X33))) | (~p9(f8(X33, X34), f6(X34)))) <=> ![X34: $i, X33: $i] : ((~p9(c12, X33)) | (~p11(X34, c15)) | (~p9(f8(X33, X34), f6(X34))) | (~p9(f8(X33, X34), X33)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[106])).
% 0.21/0.42 tff(108,axiom,(![X34: $i, X33: $i] : ((((~p11(X34, c15)) | (~p9(c12, X33))) | (~p9(f8(X33, X34), X33))) | (~p9(f8(X33, X34), f6(X34))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_p11_23')).
% 0.21/0.42 tff(109,plain,
% 0.21/0.42 (![X34: $i, X33: $i] : ((~p9(c12, X33)) | (~p11(X34, c15)) | (~p9(f8(X33, X34), f6(X34))) | (~p9(f8(X33, X34), X33)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.21/0.42 tff(110,plain,
% 0.21/0.42 (![X34: $i, X33: $i] : ((~p9(c12, X33)) | (~p11(X34, c15)) | (~p9(f8(X33, X34), f6(X34))) | (~p9(f8(X33, X34), X33)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[109, 105])).
% 0.21/0.42 tff(111,plain,(
% 0.21/0.42 ![X34: $i, X33: $i] : ((~p9(c12, X33)) | (~p11(X34, c15)) | (~p9(f8(X33, X34), f6(X34))) | (~p9(f8(X33, X34), X33)))),
% 0.21/0.42 inference(skolemize,[status(sab)],[110])).
% 0.21/0.42 tff(112,plain,
% 0.21/0.42 (![X34: $i, X33: $i] : ((~p9(c12, X33)) | (~p11(X34, c15)) | (~p9(f8(X33, X34), f6(X34))) | (~p9(f8(X33, X34), X33)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[111, 104])).
% 0.21/0.42 tff(113,plain,
% 0.21/0.42 (p11(c14, c15) <=> p11(c14, c15)),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(114,axiom,(p11(c14, c15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p11_6')).
% 0.21/0.42 tff(115,plain,
% 0.21/0.42 (p11(c14, c15)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.21/0.42 tff(116,plain,
% 0.21/0.42 (((~![X34: $i, X33: $i] : ((~p9(c12, X33)) | (~p11(X34, c15)) | (~p9(f8(X33, X34), f6(X34))) | (~p9(f8(X33, X34), X33)))) | ((~p9(c12, f6(c14))) | (~p11(c14, c15)) | (~p9(f8(f6(c14), c14), f6(c14))))) <=> ((~![X34: $i, X33: $i] : ((~p9(c12, X33)) | (~p11(X34, c15)) | (~p9(f8(X33, X34), f6(X34))) | (~p9(f8(X33, X34), X33)))) | (~p9(c12, f6(c14))) | (~p11(c14, c15)) | (~p9(f8(f6(c14), c14), f6(c14))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(117,plain,
% 0.21/0.42 (((~p9(c12, f6(c14))) | (~p11(c14, c15)) | (~p9(f8(f6(c14), c14), f6(c14))) | (~p9(f8(f6(c14), c14), f6(c14)))) <=> ((~p9(c12, f6(c14))) | (~p11(c14, c15)) | (~p9(f8(f6(c14), c14), f6(c14))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(118,plain,
% 0.21/0.42 (((~![X34: $i, X33: $i] : ((~p9(c12, X33)) | (~p11(X34, c15)) | (~p9(f8(X33, X34), f6(X34))) | (~p9(f8(X33, X34), X33)))) | ((~p9(c12, f6(c14))) | (~p11(c14, c15)) | (~p9(f8(f6(c14), c14), f6(c14))) | (~p9(f8(f6(c14), c14), f6(c14))))) <=> ((~![X34: $i, X33: $i] : ((~p9(c12, X33)) | (~p11(X34, c15)) | (~p9(f8(X33, X34), f6(X34))) | (~p9(f8(X33, X34), X33)))) | ((~p9(c12, f6(c14))) | (~p11(c14, c15)) | (~p9(f8(f6(c14), c14), f6(c14)))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[117])).
% 0.21/0.42 tff(119,plain,
% 0.21/0.42 (((~![X34: $i, X33: $i] : ((~p9(c12, X33)) | (~p11(X34, c15)) | (~p9(f8(X33, X34), f6(X34))) | (~p9(f8(X33, X34), X33)))) | ((~p9(c12, f6(c14))) | (~p11(c14, c15)) | (~p9(f8(f6(c14), c14), f6(c14))) | (~p9(f8(f6(c14), c14), f6(c14))))) <=> ((~![X34: $i, X33: $i] : ((~p9(c12, X33)) | (~p11(X34, c15)) | (~p9(f8(X33, X34), f6(X34))) | (~p9(f8(X33, X34), X33)))) | (~p9(c12, f6(c14))) | (~p11(c14, c15)) | (~p9(f8(f6(c14), c14), f6(c14))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[118, 116])).
% 0.21/0.42 tff(120,plain,
% 0.21/0.42 ((~![X34: $i, X33: $i] : ((~p9(c12, X33)) | (~p11(X34, c15)) | (~p9(f8(X33, X34), f6(X34))) | (~p9(f8(X33, X34), X33)))) | ((~p9(c12, f6(c14))) | (~p11(c14, c15)) | (~p9(f8(f6(c14), c14), f6(c14))) | (~p9(f8(f6(c14), c14), f6(c14))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(121,plain,
% 0.21/0.42 ((~![X34: $i, X33: $i] : ((~p9(c12, X33)) | (~p11(X34, c15)) | (~p9(f8(X33, X34), f6(X34))) | (~p9(f8(X33, X34), X33)))) | (~p9(c12, f6(c14))) | (~p11(c14, c15)) | (~p9(f8(f6(c14), c14), f6(c14)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.21/0.42 tff(122,plain,
% 0.21/0.42 (~p9(f8(f6(c14), c14), f6(c14))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[121, 115, 112, 102])).
% 0.21/0.43 tff(123,plain,
% 0.21/0.43 (^[X34: $i, X33: $i] : refl(((~p9(c12, X33)) | (~p11(X34, c15)) | p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33)) <=> ((~p9(c12, X33)) | (~p11(X34, c15)) | p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33)))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(124,plain,
% 0.21/0.43 (![X34: $i, X33: $i] : ((~p9(c12, X33)) | (~p11(X34, c15)) | p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33)) <=> ![X34: $i, X33: $i] : ((~p9(c12, X33)) | (~p11(X34, c15)) | p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[123])).
% 0.21/0.43 tff(125,plain,
% 0.21/0.43 (![X34: $i, X33: $i] : ((~p9(c12, X33)) | (~p11(X34, c15)) | p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33)) <=> ![X34: $i, X33: $i] : ((~p9(c12, X33)) | (~p11(X34, c15)) | p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(126,plain,
% 0.21/0.43 (^[X34: $i, X33: $i] : trans(monotonicity(trans(monotonicity(rewrite((p9(f8(X33, X34), X33) | p9(f8(X33, X34), f6(X34))) <=> (p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33))), (((p9(f8(X33, X34), X33) | p9(f8(X33, X34), f6(X34))) | (~p11(X34, c15))) <=> ((p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33)) | (~p11(X34, c15))))), rewrite(((p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33)) | (~p11(X34, c15))) <=> ((~p11(X34, c15)) | p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33))), (((p9(f8(X33, X34), X33) | p9(f8(X33, X34), f6(X34))) | (~p11(X34, c15))) <=> ((~p11(X34, c15)) | p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33)))), ((((p9(f8(X33, X34), X33) | p9(f8(X33, X34), f6(X34))) | (~p11(X34, c15))) | (~p9(c12, X33))) <=> (((~p11(X34, c15)) | p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33)) | (~p9(c12, X33))))), rewrite((((~p11(X34, c15)) | p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33)) | (~p9(c12, X33))) <=> ((~p9(c12, X33)) | (~p11(X34, c15)) | p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33))), ((((p9(f8(X33, X34), X33) | p9(f8(X33, X34), f6(X34))) | (~p11(X34, c15))) | (~p9(c12, X33))) <=> ((~p9(c12, X33)) | (~p11(X34, c15)) | p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(127,plain,
% 0.21/0.43 (![X34: $i, X33: $i] : (((p9(f8(X33, X34), X33) | p9(f8(X33, X34), f6(X34))) | (~p11(X34, c15))) | (~p9(c12, X33))) <=> ![X34: $i, X33: $i] : ((~p9(c12, X33)) | (~p11(X34, c15)) | p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[126])).
% 0.21/0.43 tff(128,axiom,(![X34: $i, X33: $i] : (((p9(f8(X33, X34), X33) | p9(f8(X33, X34), f6(X34))) | (~p11(X34, c15))) | (~p9(c12, X33)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p9_22')).
% 0.21/0.43 tff(129,plain,
% 0.21/0.43 (![X34: $i, X33: $i] : ((~p9(c12, X33)) | (~p11(X34, c15)) | p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.21/0.43 tff(130,plain,
% 0.21/0.43 (![X34: $i, X33: $i] : ((~p9(c12, X33)) | (~p11(X34, c15)) | p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[129, 125])).
% 0.21/0.43 tff(131,plain,(
% 0.21/0.43 ![X34: $i, X33: $i] : ((~p9(c12, X33)) | (~p11(X34, c15)) | p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33))),
% 0.21/0.43 inference(skolemize,[status(sab)],[130])).
% 0.21/0.43 tff(132,plain,
% 0.21/0.43 (![X34: $i, X33: $i] : ((~p9(c12, X33)) | (~p11(X34, c15)) | p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[131, 124])).
% 0.21/0.43 tff(133,plain,
% 0.21/0.43 (((~![X34: $i, X33: $i] : ((~p9(c12, X33)) | (~p11(X34, c15)) | p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33))) | ((~p9(c12, f6(c14))) | (~p11(c14, c15)) | p9(f8(f6(c14), c14), f6(c14)))) <=> ((~![X34: $i, X33: $i] : ((~p9(c12, X33)) | (~p11(X34, c15)) | p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33))) | (~p9(c12, f6(c14))) | (~p11(c14, c15)) | p9(f8(f6(c14), c14), f6(c14)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(134,plain,
% 0.21/0.43 (((~p9(c12, f6(c14))) | (~p11(c14, c15)) | p9(f8(f6(c14), c14), f6(c14)) | p9(f8(f6(c14), c14), f6(c14))) <=> ((~p9(c12, f6(c14))) | (~p11(c14, c15)) | p9(f8(f6(c14), c14), f6(c14)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(135,plain,
% 0.21/0.43 (((~![X34: $i, X33: $i] : ((~p9(c12, X33)) | (~p11(X34, c15)) | p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33))) | ((~p9(c12, f6(c14))) | (~p11(c14, c15)) | p9(f8(f6(c14), c14), f6(c14)) | p9(f8(f6(c14), c14), f6(c14)))) <=> ((~![X34: $i, X33: $i] : ((~p9(c12, X33)) | (~p11(X34, c15)) | p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33))) | ((~p9(c12, f6(c14))) | (~p11(c14, c15)) | p9(f8(f6(c14), c14), f6(c14))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[134])).
% 0.21/0.43 tff(136,plain,
% 0.21/0.43 (((~![X34: $i, X33: $i] : ((~p9(c12, X33)) | (~p11(X34, c15)) | p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33))) | ((~p9(c12, f6(c14))) | (~p11(c14, c15)) | p9(f8(f6(c14), c14), f6(c14)) | p9(f8(f6(c14), c14), f6(c14)))) <=> ((~![X34: $i, X33: $i] : ((~p9(c12, X33)) | (~p11(X34, c15)) | p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33))) | (~p9(c12, f6(c14))) | (~p11(c14, c15)) | p9(f8(f6(c14), c14), f6(c14)))),
% 0.21/0.43 inference(transitivity,[status(thm)],[135, 133])).
% 0.21/0.43 tff(137,plain,
% 0.21/0.43 ((~![X34: $i, X33: $i] : ((~p9(c12, X33)) | (~p11(X34, c15)) | p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33))) | ((~p9(c12, f6(c14))) | (~p11(c14, c15)) | p9(f8(f6(c14), c14), f6(c14)) | p9(f8(f6(c14), c14), f6(c14)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(138,plain,
% 0.21/0.43 ((~![X34: $i, X33: $i] : ((~p9(c12, X33)) | (~p11(X34, c15)) | p9(f8(X33, X34), f6(X34)) | p9(f8(X33, X34), X33))) | (~p9(c12, f6(c14))) | (~p11(c14, c15)) | p9(f8(f6(c14), c14), f6(c14))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.21/0.43 tff(139,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[138, 115, 132, 102, 122])).
% 0.21/0.43 % SZS output end Proof
% 0.21/0.43 % E exiting
%------------------------------------------------------------------------------