%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS155+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:13:29 AM UTC 2025
% Result : Theorem 0.21s 0.42s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KRS155+1 : TPTP v9.0.0. Released v3.1.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 19:16:04 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.21/0.42 % SZS status Theorem
% 0.21/0.42 % SZS output start Proof
% 0.21/0.42 tff(xsd_string_type, type, (
% 0.21/0.42 xsd_string: $i > $o)).
% 0.21/0.42 tff(tptp_fun_X_70_type, type, (
% 0.21/0.42 tptp_fun_X_70: $i)).
% 0.21/0.42 tff(xsd_integer_type, type, (
% 0.21/0.42 xsd_integer: $i > $o)).
% 0.21/0.42 tff(cowlThing_type, type, (
% 0.21/0.42 cowlThing: $i > $o)).
% 0.21/0.42 tff(tptp_fun_X_69_type, type, (
% 0.21/0.42 tptp_fun_X_69: $i)).
% 0.21/0.42 tff(cowlNothing_type, type, (
% 0.21/0.42 cowlNothing: $i > $o)).
% 0.21/0.42 tff(cC60_type, type, (
% 0.21/0.42 cC60: $i > $o)).
% 0.21/0.42 tff(iV8472_type, type, (
% 0.21/0.42 iV8472: $i)).
% 0.21/0.42 tff(cC58_type, type, (
% 0.21/0.42 cC58: $i > $o)).
% 0.21/0.42 tff(cC2xcomp_type, type, (
% 0.21/0.42 cC2xcomp: $i > $o)).
% 0.21/0.42 tff(rR1_type, type, (
% 0.21/0.42 rR1: ( $i * $i ) > $o)).
% 0.21/0.42 tff(cC2_type, type, (
% 0.21/0.42 cC2: $i > $o)).
% 0.21/0.42 tff(tptp_fun_Y_18_type, type, (
% 0.21/0.42 tptp_fun_Y_18: $i > $i)).
% 0.21/0.42 tff(iV8476_type, type, (
% 0.21/0.42 iV8476: $i)).
% 0.21/0.42 tff(cC48_type, type, (
% 0.21/0.42 cC48: $i > $o)).
% 0.21/0.42 tff(iV8467_type, type, (
% 0.21/0.42 iV8467: $i)).
% 0.21/0.42 tff(tptp_fun_Y_9_type, type, (
% 0.21/0.42 tptp_fun_Y_9: $i > $i)).
% 0.21/0.42 tff(iV8468_type, type, (
% 0.21/0.42 iV8468: $i)).
% 0.21/0.42 tff(cC4_type, type, (
% 0.21/0.42 cC4: $i > $o)).
% 0.21/0.42 tff(cC34_type, type, (
% 0.21/0.42 cC34: $i > $o)).
% 0.21/0.42 tff(cC32xcomp_type, type, (
% 0.21/0.42 cC32xcomp: $i > $o)).
% 0.21/0.42 tff(tptp_fun_Y_22_type, type, (
% 0.21/0.42 tptp_fun_Y_22: $i > $i)).
% 0.21/0.42 tff(iV8474_type, type, (
% 0.21/0.42 iV8474: $i)).
% 0.21/0.42 tff(cC14_type, type, (
% 0.21/0.42 cC14: $i > $o)).
% 0.21/0.42 tff(cTOP_type, type, (
% 0.21/0.42 cTOP: $i > $o)).
% 0.21/0.42 tff(tptp_fun_Y_2_type, type, (
% 0.21/0.42 tptp_fun_Y_2: $i > $i)).
% 0.21/0.42 tff(iV8470_type, type, (
% 0.21/0.42 iV8470: $i)).
% 0.21/0.42 tff(cC62_type, type, (
% 0.21/0.42 cC62: $i > $o)).
% 0.21/0.42 tff(tptp_fun_Y_44_type, type, (
% 0.21/0.42 tptp_fun_Y_44: $i > $i)).
% 0.21/0.42 tff(cC82_type, type, (
% 0.21/0.42 cC82: $i > $o)).
% 0.21/0.42 tff(cC80_type, type, (
% 0.21/0.42 cC80: $i > $o)).
% 0.21/0.42 tff(tptp_fun_Y_58_type, type, (
% 0.21/0.42 tptp_fun_Y_58: $i > $i)).
% 0.21/0.42 tff(iV8471_type, type, (
% 0.21/0.42 iV8471: $i)).
% 0.21/0.42 tff(cC78xcomp_type, type, (
% 0.21/0.42 cC78xcomp: $i > $o)).
% 0.21/0.42 tff(cC8_type, type, (
% 0.21/0.42 cC8: $i > $o)).
% 0.21/0.42 tff(cC6xcomp_type, type, (
% 0.21/0.42 cC6xcomp: $i > $o)).
% 0.21/0.42 tff(tptp_fun_Y_56_type, type, (
% 0.21/0.42 tptp_fun_Y_56: $i > $i)).
% 0.21/0.42 tff(iV8469_type, type, (
% 0.21/0.42 iV8469: $i)).
% 0.21/0.42 tff(cC20_type, type, (
% 0.21/0.42 cC20: $i > $o)).
% 0.21/0.42 tff(cC10_type, type, (
% 0.21/0.42 cC10: $i > $o)).
% 0.21/0.42 tff(1,assumption,(cowlNothing(X!69) | (~cowlThing(X!69))), introduced(assumption)).
% 0.21/0.42 tff(2,plain,
% 0.21/0.42 (^[X: $i] : refl((~(cowlNothing(X) | (~cowlThing(X)))) <=> (~(cowlNothing(X) | (~cowlThing(X)))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(3,plain,
% 0.21/0.42 (![X: $i] : (~(cowlNothing(X) | (~cowlThing(X)))) <=> ![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[2])).
% 0.21/0.42 tff(4,plain,
% 0.21/0.42 (^[X: $i] : rewrite((cowlThing(X) & (~cowlNothing(X))) <=> (~(cowlNothing(X) | (~cowlThing(X)))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(5,plain,
% 0.21/0.42 (![X: $i] : (cowlThing(X) & (~cowlNothing(X))) <=> ![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[4])).
% 0.21/0.42 tff(6,plain,
% 0.21/0.42 (![X: $i] : (cowlThing(X) & (~cowlNothing(X))) <=> ![X: $i] : (cowlThing(X) & (~cowlNothing(X)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(7,axiom,(![X: $i] : (cowlThing(X) & (~cowlNothing(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_0')).
% 0.21/0.42 tff(8,plain,
% 0.21/0.42 (![X: $i] : (cowlThing(X) & (~cowlNothing(X)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.21/0.42 tff(9,plain,(
% 0.21/0.42 ![X: $i] : (cowlThing(X) & (~cowlNothing(X)))),
% 0.21/0.42 inference(skolemize,[status(sab)],[8])).
% 0.21/0.42 tff(10,plain,
% 0.21/0.42 (![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.21/0.42 tff(11,plain,
% 0.21/0.42 (![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.21/0.42 tff(12,plain,
% 0.21/0.42 ((~![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))) | (~(cowlNothing(X!69) | (~cowlThing(X!69))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(13,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[12, 11, 1])).
% 0.21/0.42 tff(14,plain,(~(cowlNothing(X!69) | (~cowlThing(X!69)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.42 tff(15,plain,
% 0.21/0.42 ((cowlNothing(X!69) | (~cowlThing(X!69))) | cowlThing(X!69)),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(16,plain,
% 0.21/0.42 (cowlThing(X!69)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[15, 14])).
% 0.21/0.42 tff(17,assumption,((~(cC58(iV8472) | ![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y))))) | (~((~cC58(iV8472)) | (~((~cC2(tptp_fun_Y_18(iV8472))) | (~rR1(iV8472, tptp_fun_Y_18(iV8472)))))))), introduced(assumption)).
% 0.21/0.43 tff(18,plain,
% 0.21/0.43 (^[X: $i] : refl((~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_18(X))) | (~cC2(tptp_fun_Y_18(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y))))))) <=> (~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_18(X))) | (~cC2(tptp_fun_Y_18(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(19,plain,
% 0.21/0.43 (![X: $i] : (~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_18(X))) | (~cC2(tptp_fun_Y_18(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_18(X))) | (~cC2(tptp_fun_Y_18(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y)))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[18])).
% 0.21/0.43 tff(20,plain,
% 0.21/0.43 (^[X: $i] : rewrite((~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_18(X))) | (~cC2(tptp_fun_Y_18(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y))))))) <=> (~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_18(X))) | (~cC2(tptp_fun_Y_18(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(21,plain,
% 0.21/0.43 (![X: $i] : (~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_18(X))) | (~cC2(tptp_fun_Y_18(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_18(X))) | (~cC2(tptp_fun_Y_18(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y)))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[20])).
% 0.21/0.43 tff(22,plain,
% 0.21/0.43 (![X: $i] : (~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_18(X))) | (~cC2(tptp_fun_Y_18(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_18(X))) | (~cC2(tptp_fun_Y_18(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y)))))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[21, 19])).
% 0.21/0.43 tff(23,plain,
% 0.21/0.43 (^[X: $i] : trans(monotonicity(rewrite(((~cC58(X)) | (rR1(X, tptp_fun_Y_18(X)) & cC2(tptp_fun_Y_18(X)))) <=> ((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_18(X))) | (~cC2(tptp_fun_Y_18(X))))))), rewrite((cC58(X) | ![Y: $i] : (~(rR1(X, Y) & cC2(Y)))) <=> (cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y))))), ((((~cC58(X)) | (rR1(X, tptp_fun_Y_18(X)) & cC2(tptp_fun_Y_18(X)))) & (cC58(X) | ![Y: $i] : (~(rR1(X, Y) & cC2(Y))))) <=> (((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_18(X))) | (~cC2(tptp_fun_Y_18(X)))))) & (cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y))))))), rewrite((((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_18(X))) | (~cC2(tptp_fun_Y_18(X)))))) & (cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y))))) <=> (~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_18(X))) | (~cC2(tptp_fun_Y_18(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y)))))))), ((((~cC58(X)) | (rR1(X, tptp_fun_Y_18(X)) & cC2(tptp_fun_Y_18(X)))) & (cC58(X) | ![Y: $i] : (~(rR1(X, Y) & cC2(Y))))) <=> (~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_18(X))) | (~cC2(tptp_fun_Y_18(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y)))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(24,plain,
% 0.21/0.43 (![X: $i] : (((~cC58(X)) | (rR1(X, tptp_fun_Y_18(X)) & cC2(tptp_fun_Y_18(X)))) & (cC58(X) | ![Y: $i] : (~(rR1(X, Y) & cC2(Y))))) <=> ![X: $i] : (~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_18(X))) | (~cC2(tptp_fun_Y_18(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y)))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[23])).
% 0.21/0.43 tff(25,plain,
% 0.21/0.43 (![X: $i] : (cC58(X) <=> ?[Y: $i] : (rR1(X, Y) & cC2(Y))) <=> ![X: $i] : (cC58(X) <=> ?[Y: $i] : (rR1(X, Y) & cC2(Y)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(26,axiom,(![X: $i] : (cC58(X) <=> ?[Y: $i] : (rR1(X, Y) & cC2(Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_57')).
% 0.21/0.43 tff(27,plain,
% 0.21/0.43 (![X: $i] : (cC58(X) <=> ?[Y: $i] : (rR1(X, Y) & cC2(Y)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.21/0.43 tff(28,plain,(
% 0.21/0.43 ![X: $i] : (((~cC58(X)) | (rR1(X, tptp_fun_Y_18(X)) & cC2(tptp_fun_Y_18(X)))) & (cC58(X) | ![Y: $i] : (~(rR1(X, Y) & cC2(Y)))))),
% 0.21/0.43 inference(skolemize,[status(sab)],[27])).
% 0.21/0.43 tff(29,plain,
% 0.21/0.43 (![X: $i] : (~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_18(X))) | (~cC2(tptp_fun_Y_18(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y)))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.21/0.43 tff(30,plain,
% 0.21/0.43 (![X: $i] : (~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_18(X))) | (~cC2(tptp_fun_Y_18(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y)))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.21/0.43 tff(31,plain,
% 0.21/0.43 (((~![X: $i] : (~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_18(X))) | (~cC2(tptp_fun_Y_18(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y)))))))) | (~((~(cC58(iV8472) | ![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y))))) | (~((~cC58(iV8472)) | (~((~cC2(tptp_fun_Y_18(iV8472))) | (~rR1(iV8472, tptp_fun_Y_18(iV8472)))))))))) <=> ((~![X: $i] : (~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_18(X))) | (~cC2(tptp_fun_Y_18(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y)))))))) | (~((~(cC58(iV8472) | ![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y))))) | (~((~cC58(iV8472)) | (~((~cC2(tptp_fun_Y_18(iV8472))) | (~rR1(iV8472, tptp_fun_Y_18(iV8472))))))))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(32,plain,
% 0.21/0.43 ((~((~((~cC58(iV8472)) | (~((~rR1(iV8472, tptp_fun_Y_18(iV8472))) | (~cC2(tptp_fun_Y_18(iV8472))))))) | (~(cC58(iV8472) | ![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y))))))) <=> (~((~(cC58(iV8472) | ![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y))))) | (~((~cC58(iV8472)) | (~((~cC2(tptp_fun_Y_18(iV8472))) | (~rR1(iV8472, tptp_fun_Y_18(iV8472)))))))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(33,plain,
% 0.21/0.43 (((~![X: $i] : (~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_18(X))) | (~cC2(tptp_fun_Y_18(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y)))))))) | (~((~((~cC58(iV8472)) | (~((~rR1(iV8472, tptp_fun_Y_18(iV8472))) | (~cC2(tptp_fun_Y_18(iV8472))))))) | (~(cC58(iV8472) | ![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y)))))))) <=> ((~![X: $i] : (~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_18(X))) | (~cC2(tptp_fun_Y_18(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y)))))))) | (~((~(cC58(iV8472) | ![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y))))) | (~((~cC58(iV8472)) | (~((~cC2(tptp_fun_Y_18(iV8472))) | (~rR1(iV8472, tptp_fun_Y_18(iV8472))))))))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[32])).
% 0.21/0.43 tff(34,plain,
% 0.21/0.43 (((~![X: $i] : (~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_18(X))) | (~cC2(tptp_fun_Y_18(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y)))))))) | (~((~((~cC58(iV8472)) | (~((~rR1(iV8472, tptp_fun_Y_18(iV8472))) | (~cC2(tptp_fun_Y_18(iV8472))))))) | (~(cC58(iV8472) | ![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y)))))))) <=> ((~![X: $i] : (~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_18(X))) | (~cC2(tptp_fun_Y_18(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y)))))))) | (~((~(cC58(iV8472) | ![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y))))) | (~((~cC58(iV8472)) | (~((~cC2(tptp_fun_Y_18(iV8472))) | (~rR1(iV8472, tptp_fun_Y_18(iV8472))))))))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[33, 31])).
% 0.21/0.43 tff(35,plain,
% 0.21/0.43 ((~![X: $i] : (~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_18(X))) | (~cC2(tptp_fun_Y_18(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y)))))))) | (~((~((~cC58(iV8472)) | (~((~rR1(iV8472, tptp_fun_Y_18(iV8472))) | (~cC2(tptp_fun_Y_18(iV8472))))))) | (~(cC58(iV8472) | ![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y)))))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(36,plain,
% 0.21/0.43 ((~![X: $i] : (~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_18(X))) | (~cC2(tptp_fun_Y_18(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y)))))))) | (~((~(cC58(iV8472) | ![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y))))) | (~((~cC58(iV8472)) | (~((~cC2(tptp_fun_Y_18(iV8472))) | (~rR1(iV8472, tptp_fun_Y_18(iV8472)))))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.21/0.43 tff(37,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[36, 30, 17])).
% 0.21/0.43 tff(38,plain,(~((~(cC58(iV8472) | ![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y))))) | (~((~cC58(iV8472)) | (~((~cC2(tptp_fun_Y_18(iV8472))) | (~rR1(iV8472, tptp_fun_Y_18(iV8472))))))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(39,plain,
% 0.21/0.43 (((~(cC58(iV8472) | ![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y))))) | (~((~cC58(iV8472)) | (~((~cC2(tptp_fun_Y_18(iV8472))) | (~rR1(iV8472, tptp_fun_Y_18(iV8472)))))))) | (cC58(iV8472) | ![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y))))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(40,plain,
% 0.21/0.43 (cC58(iV8472) | ![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.21/0.43 tff(41,assumption,(![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y)))), introduced(assumption)).
% 0.21/0.43 tff(42,plain,
% 0.21/0.43 (cC2(iV8476) <=> cC2(iV8476)),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(43,axiom,(cC2(iV8476)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_132')).
% 0.21/0.43 tff(44,plain,
% 0.21/0.43 (cC2(iV8476)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.21/0.43 tff(45,plain,
% 0.21/0.43 (rR1(iV8472, iV8476) <=> rR1(iV8472, iV8476)),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(46,axiom,(rR1(iV8472, iV8476)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_124')).
% 0.21/0.43 tff(47,plain,
% 0.21/0.43 (rR1(iV8472, iV8476)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.21/0.43 tff(48,plain,
% 0.21/0.43 (((~![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y)))) | ((~cC2(iV8476)) | (~rR1(iV8472, iV8476)))) <=> ((~![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y)))) | (~cC2(iV8476)) | (~rR1(iV8472, iV8476)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(49,plain,
% 0.21/0.43 ((~![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y)))) | ((~cC2(iV8476)) | (~rR1(iV8472, iV8476)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(50,plain,
% 0.21/0.43 ((~![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y)))) | (~cC2(iV8476)) | (~rR1(iV8472, iV8476))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.21/0.43 tff(51,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[50, 47, 44, 41])).
% 0.21/0.43 tff(52,plain,(~![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(53,plain,
% 0.21/0.43 ((~(cC58(iV8472) | ![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y))))) | cC58(iV8472) | ![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y)))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(54,plain,
% 0.21/0.43 ((~(cC58(iV8472) | ![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y))))) | cC58(iV8472)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.21/0.43 tff(55,plain,
% 0.21/0.43 (cC58(iV8472)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[54, 40])).
% 0.21/0.43 tff(56,plain,
% 0.21/0.43 (cC2xcomp(iV8472) <=> cC2xcomp(iV8472)),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(57,axiom,(cC2xcomp(iV8472)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_122')).
% 0.21/0.43 tff(58,plain,
% 0.21/0.43 (cC2xcomp(iV8472)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.21/0.43 tff(59,plain,
% 0.21/0.43 ((~((~cC2xcomp(iV8472)) | (~cC58(iV8472)))) | (~cC2xcomp(iV8472)) | (~cC58(iV8472))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(60,plain,
% 0.21/0.43 ((~((~cC2xcomp(iV8472)) | (~cC58(iV8472)))) | (~cC58(iV8472))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.21/0.43 tff(61,plain,
% 0.21/0.43 (~((~cC2xcomp(iV8472)) | (~cC58(iV8472)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[60, 55])).
% 0.21/0.43 tff(62,plain,
% 0.21/0.43 (^[X: $i] : refl((~(((~cC2xcomp(X)) | (~cC58(X))) <=> cC60(X))) <=> (~(((~cC2xcomp(X)) | (~cC58(X))) <=> cC60(X))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(63,plain,
% 0.21/0.43 (![X: $i] : (~(((~cC2xcomp(X)) | (~cC58(X))) <=> cC60(X))) <=> ![X: $i] : (~(((~cC2xcomp(X)) | (~cC58(X))) <=> cC60(X)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[62])).
% 0.21/0.43 tff(64,plain,
% 0.21/0.43 (^[X: $i] : trans(trans(monotonicity(rewrite((cC2xcomp(X) & cC58(X)) <=> (~((~cC2xcomp(X)) | (~cC58(X))))), ((cC60(X) <=> (cC2xcomp(X) & cC58(X))) <=> (cC60(X) <=> (~((~cC2xcomp(X)) | (~cC58(X))))))), rewrite((cC60(X) <=> (~((~cC2xcomp(X)) | (~cC58(X))))) <=> (~(((~cC2xcomp(X)) | (~cC58(X))) <=> cC60(X)))), ((cC60(X) <=> (cC2xcomp(X) & cC58(X))) <=> (~(((~cC2xcomp(X)) | (~cC58(X))) <=> cC60(X))))), rewrite((~(((~cC2xcomp(X)) | (~cC58(X))) <=> cC60(X))) <=> (~(((~cC2xcomp(X)) | (~cC58(X))) <=> cC60(X)))), ((cC60(X) <=> (cC2xcomp(X) & cC58(X))) <=> (~(((~cC2xcomp(X)) | (~cC58(X))) <=> cC60(X)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(65,plain,
% 0.21/0.43 (![X: $i] : (cC60(X) <=> (cC2xcomp(X) & cC58(X))) <=> ![X: $i] : (~(((~cC2xcomp(X)) | (~cC58(X))) <=> cC60(X)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[64])).
% 0.21/0.43 tff(66,plain,
% 0.21/0.43 (![X: $i] : (cC60(X) <=> (cC2xcomp(X) & cC58(X))) <=> ![X: $i] : (cC60(X) <=> (cC2xcomp(X) & cC58(X)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(67,axiom,(![X: $i] : (cC60(X) <=> (cC2xcomp(X) & cC58(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_61')).
% 0.21/0.43 tff(68,plain,
% 0.21/0.43 (![X: $i] : (cC60(X) <=> (cC2xcomp(X) & cC58(X)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.21/0.43 tff(69,plain,(
% 0.21/0.43 ![X: $i] : (cC60(X) <=> (cC2xcomp(X) & cC58(X)))),
% 0.21/0.43 inference(skolemize,[status(sab)],[68])).
% 0.21/0.43 tff(70,plain,
% 0.21/0.43 (![X: $i] : (~(((~cC2xcomp(X)) | (~cC58(X))) <=> cC60(X)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.21/0.43 tff(71,plain,
% 0.21/0.43 (![X: $i] : (~(((~cC2xcomp(X)) | (~cC58(X))) <=> cC60(X)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.21/0.43 tff(72,plain,
% 0.21/0.43 ((~![X: $i] : (~(((~cC2xcomp(X)) | (~cC58(X))) <=> cC60(X)))) | (~(((~cC2xcomp(iV8472)) | (~cC58(iV8472))) <=> cC60(iV8472)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(73,plain,
% 0.21/0.43 (~(((~cC2xcomp(iV8472)) | (~cC58(iV8472))) <=> cC60(iV8472))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.21/0.43 tff(74,plain,
% 0.21/0.43 ((((~cC2xcomp(iV8472)) | (~cC58(iV8472))) <=> cC60(iV8472)) | ((~cC2xcomp(iV8472)) | (~cC58(iV8472))) | cC60(iV8472)),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(75,plain,
% 0.21/0.43 (((~cC2xcomp(iV8472)) | (~cC58(iV8472))) | cC60(iV8472)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.21/0.43 tff(76,plain,
% 0.21/0.43 (cC60(iV8472)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[75, 61])).
% 0.21/0.43 tff(77,assumption,((~(cC48(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y))))) | (~((~cC48(iV8467)) | (~((~cC2xcomp(tptp_fun_Y_9(iV8467))) | (~rR1(iV8467, tptp_fun_Y_9(iV8467)))))))), introduced(assumption)).
% 0.21/0.43 tff(78,plain,
% 0.21/0.43 (^[X: $i] : refl((~((~((~cC48(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC48(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))))) <=> (~((~((~cC48(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC48(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(79,plain,
% 0.21/0.43 (![X: $i] : (~((~((~cC48(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC48(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC48(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC48(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[78])).
% 0.21/0.43 tff(80,plain,
% 0.21/0.43 (^[X: $i] : rewrite((~((~((~cC48(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC48(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))))) <=> (~((~((~cC48(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC48(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(81,plain,
% 0.21/0.43 (![X: $i] : (~((~((~cC48(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC48(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC48(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC48(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[80])).
% 0.21/0.43 tff(82,plain,
% 0.21/0.43 (![X: $i] : (~((~((~cC48(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC48(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC48(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC48(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[81, 79])).
% 0.21/0.43 tff(83,plain,
% 0.21/0.43 (^[X: $i] : trans(monotonicity(rewrite(((~cC48(X)) | (rR1(X, tptp_fun_Y_9(X)) & cC2xcomp(tptp_fun_Y_9(X)))) <=> ((~cC48(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))), rewrite((cC48(X) | ![Y: $i] : (~(rR1(X, Y) & cC2xcomp(Y)))) <=> (cC48(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))), ((((~cC48(X)) | (rR1(X, tptp_fun_Y_9(X)) & cC2xcomp(tptp_fun_Y_9(X)))) & (cC48(X) | ![Y: $i] : (~(rR1(X, Y) & cC2xcomp(Y))))) <=> (((~cC48(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X)))))) & (cC48(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))))), rewrite((((~cC48(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X)))))) & (cC48(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))) <=> (~((~((~cC48(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC48(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))), ((((~cC48(X)) | (rR1(X, tptp_fun_Y_9(X)) & cC2xcomp(tptp_fun_Y_9(X)))) & (cC48(X) | ![Y: $i] : (~(rR1(X, Y) & cC2xcomp(Y))))) <=> (~((~((~cC48(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC48(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(84,plain,
% 0.21/0.43 (![X: $i] : (((~cC48(X)) | (rR1(X, tptp_fun_Y_9(X)) & cC2xcomp(tptp_fun_Y_9(X)))) & (cC48(X) | ![Y: $i] : (~(rR1(X, Y) & cC2xcomp(Y))))) <=> ![X: $i] : (~((~((~cC48(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC48(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[83])).
% 0.21/0.43 tff(85,plain,
% 0.21/0.43 (![X: $i] : (cC48(X) <=> ?[Y: $i] : (rR1(X, Y) & cC2xcomp(Y))) <=> ![X: $i] : (cC48(X) <=> ?[Y: $i] : (rR1(X, Y) & cC2xcomp(Y)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(86,axiom,(![X: $i] : (cC48(X) <=> ?[Y: $i] : (rR1(X, Y) & cC2xcomp(Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_44')).
% 0.21/0.43 tff(87,plain,
% 0.21/0.43 (![X: $i] : (cC48(X) <=> ?[Y: $i] : (rR1(X, Y) & cC2xcomp(Y)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.21/0.43 tff(88,plain,(
% 0.21/0.43 ![X: $i] : (((~cC48(X)) | (rR1(X, tptp_fun_Y_9(X)) & cC2xcomp(tptp_fun_Y_9(X)))) & (cC48(X) | ![Y: $i] : (~(rR1(X, Y) & cC2xcomp(Y)))))),
% 0.21/0.43 inference(skolemize,[status(sab)],[87])).
% 0.21/0.43 tff(89,plain,
% 0.21/0.43 (![X: $i] : (~((~((~cC48(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC48(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[88, 84])).
% 0.21/0.43 tff(90,plain,
% 0.21/0.43 (![X: $i] : (~((~((~cC48(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC48(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[89, 82])).
% 0.21/0.43 tff(91,plain,
% 0.21/0.43 (((~![X: $i] : (~((~((~cC48(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC48(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))) | (~((~(cC48(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y))))) | (~((~cC48(iV8467)) | (~((~cC2xcomp(tptp_fun_Y_9(iV8467))) | (~rR1(iV8467, tptp_fun_Y_9(iV8467)))))))))) <=> ((~![X: $i] : (~((~((~cC48(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC48(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))) | (~((~(cC48(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y))))) | (~((~cC48(iV8467)) | (~((~cC2xcomp(tptp_fun_Y_9(iV8467))) | (~rR1(iV8467, tptp_fun_Y_9(iV8467))))))))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(92,plain,
% 0.21/0.43 ((~((~((~cC48(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_9(iV8467))) | (~cC2xcomp(tptp_fun_Y_9(iV8467))))))) | (~(cC48(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y))))))) <=> (~((~(cC48(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y))))) | (~((~cC48(iV8467)) | (~((~cC2xcomp(tptp_fun_Y_9(iV8467))) | (~rR1(iV8467, tptp_fun_Y_9(iV8467)))))))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(93,plain,
% 0.21/0.43 (((~![X: $i] : (~((~((~cC48(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC48(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))) | (~((~((~cC48(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_9(iV8467))) | (~cC2xcomp(tptp_fun_Y_9(iV8467))))))) | (~(cC48(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y)))))))) <=> ((~![X: $i] : (~((~((~cC48(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC48(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))) | (~((~(cC48(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y))))) | (~((~cC48(iV8467)) | (~((~cC2xcomp(tptp_fun_Y_9(iV8467))) | (~rR1(iV8467, tptp_fun_Y_9(iV8467))))))))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[92])).
% 0.21/0.44 tff(94,plain,
% 0.21/0.44 (((~![X: $i] : (~((~((~cC48(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC48(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))) | (~((~((~cC48(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_9(iV8467))) | (~cC2xcomp(tptp_fun_Y_9(iV8467))))))) | (~(cC48(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y)))))))) <=> ((~![X: $i] : (~((~((~cC48(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC48(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))) | (~((~(cC48(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y))))) | (~((~cC48(iV8467)) | (~((~cC2xcomp(tptp_fun_Y_9(iV8467))) | (~rR1(iV8467, tptp_fun_Y_9(iV8467))))))))))),
% 0.21/0.44 inference(transitivity,[status(thm)],[93, 91])).
% 0.21/0.44 tff(95,plain,
% 0.21/0.44 ((~![X: $i] : (~((~((~cC48(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC48(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))) | (~((~((~cC48(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_9(iV8467))) | (~cC2xcomp(tptp_fun_Y_9(iV8467))))))) | (~(cC48(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y)))))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(96,plain,
% 0.21/0.44 ((~![X: $i] : (~((~((~cC48(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC48(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))) | (~((~(cC48(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y))))) | (~((~cC48(iV8467)) | (~((~cC2xcomp(tptp_fun_Y_9(iV8467))) | (~rR1(iV8467, tptp_fun_Y_9(iV8467)))))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.21/0.44 tff(97,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[96, 90, 77])).
% 0.21/0.44 tff(98,plain,(~((~(cC48(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y))))) | (~((~cC48(iV8467)) | (~((~cC2xcomp(tptp_fun_Y_9(iV8467))) | (~rR1(iV8467, tptp_fun_Y_9(iV8467))))))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44 tff(99,plain,
% 0.21/0.44 (((~(cC48(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y))))) | (~((~cC48(iV8467)) | (~((~cC2xcomp(tptp_fun_Y_9(iV8467))) | (~rR1(iV8467, tptp_fun_Y_9(iV8467)))))))) | (cC48(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y))))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(100,plain,
% 0.21/0.44 (cC48(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.21/0.44 tff(101,assumption,(![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y)))), introduced(assumption)).
% 0.21/0.44 tff(102,plain,
% 0.21/0.44 (cC2xcomp(iV8468) <=> cC2xcomp(iV8468)),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(103,axiom,(cC2xcomp(iV8468)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_111')).
% 0.21/0.44 tff(104,plain,
% 0.21/0.44 (cC2xcomp(iV8468)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.21/0.44 tff(105,plain,
% 0.21/0.44 (rR1(iV8467, iV8468) <=> rR1(iV8467, iV8468)),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(106,axiom,(rR1(iV8467, iV8468)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_107')).
% 0.21/0.44 tff(107,plain,
% 0.21/0.44 (rR1(iV8467, iV8468)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.21/0.44 tff(108,plain,
% 0.21/0.44 (((~![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y)))) | ((~cC2xcomp(iV8468)) | (~rR1(iV8467, iV8468)))) <=> ((~![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y)))) | (~cC2xcomp(iV8468)) | (~rR1(iV8467, iV8468)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(109,plain,
% 0.21/0.44 ((~![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y)))) | ((~cC2xcomp(iV8468)) | (~rR1(iV8467, iV8468)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(110,plain,
% 0.21/0.44 ((~![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y)))) | (~cC2xcomp(iV8468)) | (~rR1(iV8467, iV8468))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.21/0.44 tff(111,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[110, 107, 104, 101])).
% 0.21/0.44 tff(112,plain,(~![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44 tff(113,plain,
% 0.21/0.44 ((~(cC48(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y))))) | cC48(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y)))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(114,plain,
% 0.21/0.44 ((~(cC48(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y))))) | cC48(iV8467)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[113, 112])).
% 0.21/0.44 tff(115,plain,
% 0.21/0.44 (cC48(iV8467)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[114, 100])).
% 0.21/0.44 tff(116,assumption,((~((~cC4(iV8467)) | (~((~cC2xcomp(tptp_fun_Y_9(iV8467))) | (~rR1(iV8467, tptp_fun_Y_9(iV8467))))))) | (~(cC4(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y)))))), introduced(assumption)).
% 0.21/0.44 tff(117,plain,
% 0.21/0.44 (^[X: $i] : refl((~((~((~cC4(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC4(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))))) <=> (~((~((~cC4(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC4(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(118,plain,
% 0.21/0.44 (![X: $i] : (~((~((~cC4(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC4(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC4(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC4(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[117])).
% 0.21/0.44 tff(119,plain,
% 0.21/0.44 (^[X: $i] : rewrite((~((~((~cC4(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC4(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))))) <=> (~((~((~cC4(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC4(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(120,plain,
% 0.21/0.44 (![X: $i] : (~((~((~cC4(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC4(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC4(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC4(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[119])).
% 0.21/0.44 tff(121,plain,
% 0.21/0.44 (![X: $i] : (~((~((~cC4(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC4(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC4(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC4(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.21/0.44 inference(transitivity,[status(thm)],[120, 118])).
% 0.21/0.44 tff(122,plain,
% 0.21/0.44 (^[X: $i] : trans(monotonicity(rewrite(((~cC4(X)) | (rR1(X, tptp_fun_Y_9(X)) & cC2xcomp(tptp_fun_Y_9(X)))) <=> ((~cC4(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))), rewrite((cC4(X) | ![Y: $i] : (~(rR1(X, Y) & cC2xcomp(Y)))) <=> (cC4(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))), ((((~cC4(X)) | (rR1(X, tptp_fun_Y_9(X)) & cC2xcomp(tptp_fun_Y_9(X)))) & (cC4(X) | ![Y: $i] : (~(rR1(X, Y) & cC2xcomp(Y))))) <=> (((~cC4(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X)))))) & (cC4(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))))), rewrite((((~cC4(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X)))))) & (cC4(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))) <=> (~((~((~cC4(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC4(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))), ((((~cC4(X)) | (rR1(X, tptp_fun_Y_9(X)) & cC2xcomp(tptp_fun_Y_9(X)))) & (cC4(X) | ![Y: $i] : (~(rR1(X, Y) & cC2xcomp(Y))))) <=> (~((~((~cC4(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC4(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(123,plain,
% 0.21/0.44 (![X: $i] : (((~cC4(X)) | (rR1(X, tptp_fun_Y_9(X)) & cC2xcomp(tptp_fun_Y_9(X)))) & (cC4(X) | ![Y: $i] : (~(rR1(X, Y) & cC2xcomp(Y))))) <=> ![X: $i] : (~((~((~cC4(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC4(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[122])).
% 0.21/0.44 tff(124,plain,
% 0.21/0.44 (![X: $i] : (cC4(X) <=> ?[Y: $i] : (rR1(X, Y) & cC2xcomp(Y))) <=> ![X: $i] : (cC4(X) <=> ?[Y: $i] : (rR1(X, Y) & cC2xcomp(Y)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(125,axiom,(![X: $i] : (cC4(X) <=> ?[Y: $i] : (rR1(X, Y) & cC2xcomp(Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_35')).
% 0.21/0.44 tff(126,plain,
% 0.21/0.44 (![X: $i] : (cC4(X) <=> ?[Y: $i] : (rR1(X, Y) & cC2xcomp(Y)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.21/0.44 tff(127,plain,(
% 0.21/0.44 ![X: $i] : (((~cC4(X)) | (rR1(X, tptp_fun_Y_9(X)) & cC2xcomp(tptp_fun_Y_9(X)))) & (cC4(X) | ![Y: $i] : (~(rR1(X, Y) & cC2xcomp(Y)))))),
% 0.21/0.44 inference(skolemize,[status(sab)],[126])).
% 0.21/0.44 tff(128,plain,
% 0.21/0.44 (![X: $i] : (~((~((~cC4(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC4(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[127, 123])).
% 0.21/0.44 tff(129,plain,
% 0.21/0.44 (![X: $i] : (~((~((~cC4(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC4(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[128, 121])).
% 0.21/0.44 tff(130,plain,
% 0.21/0.44 (((~![X: $i] : (~((~((~cC4(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC4(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))) | (~((~((~cC4(iV8467)) | (~((~cC2xcomp(tptp_fun_Y_9(iV8467))) | (~rR1(iV8467, tptp_fun_Y_9(iV8467))))))) | (~(cC4(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y)))))))) <=> ((~![X: $i] : (~((~((~cC4(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC4(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))) | (~((~((~cC4(iV8467)) | (~((~cC2xcomp(tptp_fun_Y_9(iV8467))) | (~rR1(iV8467, tptp_fun_Y_9(iV8467))))))) | (~(cC4(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y))))))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(131,plain,
% 0.21/0.44 ((~((~((~cC4(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_9(iV8467))) | (~cC2xcomp(tptp_fun_Y_9(iV8467))))))) | (~(cC4(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y))))))) <=> (~((~((~cC4(iV8467)) | (~((~cC2xcomp(tptp_fun_Y_9(iV8467))) | (~rR1(iV8467, tptp_fun_Y_9(iV8467))))))) | (~(cC4(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y)))))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(132,plain,
% 0.21/0.44 (((~![X: $i] : (~((~((~cC4(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC4(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))) | (~((~((~cC4(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_9(iV8467))) | (~cC2xcomp(tptp_fun_Y_9(iV8467))))))) | (~(cC4(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y)))))))) <=> ((~![X: $i] : (~((~((~cC4(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC4(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))) | (~((~((~cC4(iV8467)) | (~((~cC2xcomp(tptp_fun_Y_9(iV8467))) | (~rR1(iV8467, tptp_fun_Y_9(iV8467))))))) | (~(cC4(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y))))))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[131])).
% 0.21/0.44 tff(133,plain,
% 0.21/0.44 (((~![X: $i] : (~((~((~cC4(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC4(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))) | (~((~((~cC4(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_9(iV8467))) | (~cC2xcomp(tptp_fun_Y_9(iV8467))))))) | (~(cC4(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y)))))))) <=> ((~![X: $i] : (~((~((~cC4(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC4(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))) | (~((~((~cC4(iV8467)) | (~((~cC2xcomp(tptp_fun_Y_9(iV8467))) | (~rR1(iV8467, tptp_fun_Y_9(iV8467))))))) | (~(cC4(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y))))))))),
% 0.21/0.44 inference(transitivity,[status(thm)],[132, 130])).
% 0.21/0.44 tff(134,plain,
% 0.21/0.44 ((~![X: $i] : (~((~((~cC4(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC4(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))) | (~((~((~cC4(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_9(iV8467))) | (~cC2xcomp(tptp_fun_Y_9(iV8467))))))) | (~(cC4(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y)))))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(135,plain,
% 0.21/0.44 ((~![X: $i] : (~((~((~cC4(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC4(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))) | (~((~((~cC4(iV8467)) | (~((~cC2xcomp(tptp_fun_Y_9(iV8467))) | (~rR1(iV8467, tptp_fun_Y_9(iV8467))))))) | (~(cC4(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y)))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.21/0.44 tff(136,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[135, 129, 116])).
% 0.21/0.44 tff(137,plain,(~((~((~cC4(iV8467)) | (~((~cC2xcomp(tptp_fun_Y_9(iV8467))) | (~rR1(iV8467, tptp_fun_Y_9(iV8467))))))) | (~(cC4(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y))))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44 tff(138,plain,
% 0.21/0.44 (((~((~cC4(iV8467)) | (~((~cC2xcomp(tptp_fun_Y_9(iV8467))) | (~rR1(iV8467, tptp_fun_Y_9(iV8467))))))) | (~(cC4(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y)))))) | (cC4(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y))))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(139,plain,
% 0.21/0.44 (cC4(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[138, 137])).
% 0.21/0.44 tff(140,plain,
% 0.21/0.44 ((~(cC4(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y))))) | cC4(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y)))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(141,plain,
% 0.21/0.44 ((~(cC4(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y))))) | cC4(iV8467)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[140, 112])).
% 0.21/0.44 tff(142,plain,
% 0.21/0.44 (cC4(iV8467)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[141, 139])).
% 0.21/0.44 tff(143,assumption,((~((~cC34(iV8467)) | (~((~cC32xcomp(tptp_fun_Y_22(iV8467))) | (~rR1(iV8467, tptp_fun_Y_22(iV8467))))))) | (~(cC34(iV8467) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(iV8467, Y)))))), introduced(assumption)).
% 0.21/0.44 tff(144,plain,
% 0.21/0.44 (^[X: $i] : refl((~((~((~cC34(X)) | (~((~rR1(X, tptp_fun_Y_22(X))) | (~cC32xcomp(tptp_fun_Y_22(X))))))) | (~(cC34(X) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(X, Y))))))) <=> (~((~((~cC34(X)) | (~((~rR1(X, tptp_fun_Y_22(X))) | (~cC32xcomp(tptp_fun_Y_22(X))))))) | (~(cC34(X) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(X, Y))))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(145,plain,
% 0.21/0.44 (![X: $i] : (~((~((~cC34(X)) | (~((~rR1(X, tptp_fun_Y_22(X))) | (~cC32xcomp(tptp_fun_Y_22(X))))))) | (~(cC34(X) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC34(X)) | (~((~rR1(X, tptp_fun_Y_22(X))) | (~cC32xcomp(tptp_fun_Y_22(X))))))) | (~(cC34(X) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[144])).
% 0.21/0.44 tff(146,plain,
% 0.21/0.44 (^[X: $i] : rewrite((~((~((~cC34(X)) | (~((~rR1(X, tptp_fun_Y_22(X))) | (~cC32xcomp(tptp_fun_Y_22(X))))))) | (~(cC34(X) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(X, Y))))))) <=> (~((~((~cC34(X)) | (~((~rR1(X, tptp_fun_Y_22(X))) | (~cC32xcomp(tptp_fun_Y_22(X))))))) | (~(cC34(X) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(X, Y))))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(147,plain,
% 0.21/0.44 (![X: $i] : (~((~((~cC34(X)) | (~((~rR1(X, tptp_fun_Y_22(X))) | (~cC32xcomp(tptp_fun_Y_22(X))))))) | (~(cC34(X) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC34(X)) | (~((~rR1(X, tptp_fun_Y_22(X))) | (~cC32xcomp(tptp_fun_Y_22(X))))))) | (~(cC34(X) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[146])).
% 0.21/0.44 tff(148,plain,
% 0.21/0.44 (![X: $i] : (~((~((~cC34(X)) | (~((~rR1(X, tptp_fun_Y_22(X))) | (~cC32xcomp(tptp_fun_Y_22(X))))))) | (~(cC34(X) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC34(X)) | (~((~rR1(X, tptp_fun_Y_22(X))) | (~cC32xcomp(tptp_fun_Y_22(X))))))) | (~(cC34(X) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.21/0.44 inference(transitivity,[status(thm)],[147, 145])).
% 0.21/0.44 tff(149,plain,
% 0.21/0.44 (^[X: $i] : trans(monotonicity(rewrite(((~cC34(X)) | (rR1(X, tptp_fun_Y_22(X)) & cC32xcomp(tptp_fun_Y_22(X)))) <=> ((~cC34(X)) | (~((~rR1(X, tptp_fun_Y_22(X))) | (~cC32xcomp(tptp_fun_Y_22(X))))))), rewrite((cC34(X) | ![Y: $i] : (~(rR1(X, Y) & cC32xcomp(Y)))) <=> (cC34(X) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(X, Y))))), ((((~cC34(X)) | (rR1(X, tptp_fun_Y_22(X)) & cC32xcomp(tptp_fun_Y_22(X)))) & (cC34(X) | ![Y: $i] : (~(rR1(X, Y) & cC32xcomp(Y))))) <=> (((~cC34(X)) | (~((~rR1(X, tptp_fun_Y_22(X))) | (~cC32xcomp(tptp_fun_Y_22(X)))))) & (cC34(X) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(X, Y))))))), rewrite((((~cC34(X)) | (~((~rR1(X, tptp_fun_Y_22(X))) | (~cC32xcomp(tptp_fun_Y_22(X)))))) & (cC34(X) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(X, Y))))) <=> (~((~((~cC34(X)) | (~((~rR1(X, tptp_fun_Y_22(X))) | (~cC32xcomp(tptp_fun_Y_22(X))))))) | (~(cC34(X) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(X, Y)))))))), ((((~cC34(X)) | (rR1(X, tptp_fun_Y_22(X)) & cC32xcomp(tptp_fun_Y_22(X)))) & (cC34(X) | ![Y: $i] : (~(rR1(X, Y) & cC32xcomp(Y))))) <=> (~((~((~cC34(X)) | (~((~rR1(X, tptp_fun_Y_22(X))) | (~cC32xcomp(tptp_fun_Y_22(X))))))) | (~(cC34(X) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(X, Y)))))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(150,plain,
% 0.21/0.45 (![X: $i] : (((~cC34(X)) | (rR1(X, tptp_fun_Y_22(X)) & cC32xcomp(tptp_fun_Y_22(X)))) & (cC34(X) | ![Y: $i] : (~(rR1(X, Y) & cC32xcomp(Y))))) <=> ![X: $i] : (~((~((~cC34(X)) | (~((~rR1(X, tptp_fun_Y_22(X))) | (~cC32xcomp(tptp_fun_Y_22(X))))))) | (~(cC34(X) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[149])).
% 0.21/0.45 tff(151,plain,
% 0.21/0.45 (![X: $i] : (cC34(X) <=> ?[Y: $i] : (rR1(X, Y) & cC32xcomp(Y))) <=> ![X: $i] : (cC34(X) <=> ?[Y: $i] : (rR1(X, Y) & cC32xcomp(Y)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(152,axiom,(![X: $i] : (cC34(X) <=> ?[Y: $i] : (rR1(X, Y) & cC32xcomp(Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_29')).
% 0.21/0.45 tff(153,plain,
% 0.21/0.45 (![X: $i] : (cC34(X) <=> ?[Y: $i] : (rR1(X, Y) & cC32xcomp(Y)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.21/0.45 tff(154,plain,(
% 0.21/0.45 ![X: $i] : (((~cC34(X)) | (rR1(X, tptp_fun_Y_22(X)) & cC32xcomp(tptp_fun_Y_22(X)))) & (cC34(X) | ![Y: $i] : (~(rR1(X, Y) & cC32xcomp(Y)))))),
% 0.21/0.45 inference(skolemize,[status(sab)],[153])).
% 0.21/0.45 tff(155,plain,
% 0.21/0.45 (![X: $i] : (~((~((~cC34(X)) | (~((~rR1(X, tptp_fun_Y_22(X))) | (~cC32xcomp(tptp_fun_Y_22(X))))))) | (~(cC34(X) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[154, 150])).
% 0.21/0.45 tff(156,plain,
% 0.21/0.45 (![X: $i] : (~((~((~cC34(X)) | (~((~rR1(X, tptp_fun_Y_22(X))) | (~cC32xcomp(tptp_fun_Y_22(X))))))) | (~(cC34(X) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[155, 148])).
% 0.21/0.45 tff(157,plain,
% 0.21/0.45 (((~![X: $i] : (~((~((~cC34(X)) | (~((~rR1(X, tptp_fun_Y_22(X))) | (~cC32xcomp(tptp_fun_Y_22(X))))))) | (~(cC34(X) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(X, Y)))))))) | (~((~((~cC34(iV8467)) | (~((~cC32xcomp(tptp_fun_Y_22(iV8467))) | (~rR1(iV8467, tptp_fun_Y_22(iV8467))))))) | (~(cC34(iV8467) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(iV8467, Y)))))))) <=> ((~![X: $i] : (~((~((~cC34(X)) | (~((~rR1(X, tptp_fun_Y_22(X))) | (~cC32xcomp(tptp_fun_Y_22(X))))))) | (~(cC34(X) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(X, Y)))))))) | (~((~((~cC34(iV8467)) | (~((~cC32xcomp(tptp_fun_Y_22(iV8467))) | (~rR1(iV8467, tptp_fun_Y_22(iV8467))))))) | (~(cC34(iV8467) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(iV8467, Y))))))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(158,plain,
% 0.21/0.45 ((~((~((~cC34(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_22(iV8467))) | (~cC32xcomp(tptp_fun_Y_22(iV8467))))))) | (~(cC34(iV8467) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(iV8467, Y))))))) <=> (~((~((~cC34(iV8467)) | (~((~cC32xcomp(tptp_fun_Y_22(iV8467))) | (~rR1(iV8467, tptp_fun_Y_22(iV8467))))))) | (~(cC34(iV8467) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(iV8467, Y)))))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(159,plain,
% 0.21/0.45 (((~![X: $i] : (~((~((~cC34(X)) | (~((~rR1(X, tptp_fun_Y_22(X))) | (~cC32xcomp(tptp_fun_Y_22(X))))))) | (~(cC34(X) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(X, Y)))))))) | (~((~((~cC34(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_22(iV8467))) | (~cC32xcomp(tptp_fun_Y_22(iV8467))))))) | (~(cC34(iV8467) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(iV8467, Y)))))))) <=> ((~![X: $i] : (~((~((~cC34(X)) | (~((~rR1(X, tptp_fun_Y_22(X))) | (~cC32xcomp(tptp_fun_Y_22(X))))))) | (~(cC34(X) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(X, Y)))))))) | (~((~((~cC34(iV8467)) | (~((~cC32xcomp(tptp_fun_Y_22(iV8467))) | (~rR1(iV8467, tptp_fun_Y_22(iV8467))))))) | (~(cC34(iV8467) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(iV8467, Y))))))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[158])).
% 0.21/0.45 tff(160,plain,
% 0.21/0.45 (((~![X: $i] : (~((~((~cC34(X)) | (~((~rR1(X, tptp_fun_Y_22(X))) | (~cC32xcomp(tptp_fun_Y_22(X))))))) | (~(cC34(X) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(X, Y)))))))) | (~((~((~cC34(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_22(iV8467))) | (~cC32xcomp(tptp_fun_Y_22(iV8467))))))) | (~(cC34(iV8467) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(iV8467, Y)))))))) <=> ((~![X: $i] : (~((~((~cC34(X)) | (~((~rR1(X, tptp_fun_Y_22(X))) | (~cC32xcomp(tptp_fun_Y_22(X))))))) | (~(cC34(X) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(X, Y)))))))) | (~((~((~cC34(iV8467)) | (~((~cC32xcomp(tptp_fun_Y_22(iV8467))) | (~rR1(iV8467, tptp_fun_Y_22(iV8467))))))) | (~(cC34(iV8467) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(iV8467, Y))))))))),
% 0.21/0.45 inference(transitivity,[status(thm)],[159, 157])).
% 0.21/0.45 tff(161,plain,
% 0.21/0.45 ((~![X: $i] : (~((~((~cC34(X)) | (~((~rR1(X, tptp_fun_Y_22(X))) | (~cC32xcomp(tptp_fun_Y_22(X))))))) | (~(cC34(X) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(X, Y)))))))) | (~((~((~cC34(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_22(iV8467))) | (~cC32xcomp(tptp_fun_Y_22(iV8467))))))) | (~(cC34(iV8467) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(iV8467, Y)))))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(162,plain,
% 0.21/0.45 ((~![X: $i] : (~((~((~cC34(X)) | (~((~rR1(X, tptp_fun_Y_22(X))) | (~cC32xcomp(tptp_fun_Y_22(X))))))) | (~(cC34(X) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(X, Y)))))))) | (~((~((~cC34(iV8467)) | (~((~cC32xcomp(tptp_fun_Y_22(iV8467))) | (~rR1(iV8467, tptp_fun_Y_22(iV8467))))))) | (~(cC34(iV8467) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(iV8467, Y)))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.21/0.45 tff(163,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[162, 156, 143])).
% 0.21/0.45 tff(164,plain,(~((~((~cC34(iV8467)) | (~((~cC32xcomp(tptp_fun_Y_22(iV8467))) | (~rR1(iV8467, tptp_fun_Y_22(iV8467))))))) | (~(cC34(iV8467) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(iV8467, Y))))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.45 tff(165,plain,
% 0.21/0.45 (((~((~cC34(iV8467)) | (~((~cC32xcomp(tptp_fun_Y_22(iV8467))) | (~rR1(iV8467, tptp_fun_Y_22(iV8467))))))) | (~(cC34(iV8467) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(iV8467, Y)))))) | (cC34(iV8467) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(iV8467, Y))))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(166,plain,
% 0.21/0.45 (cC34(iV8467) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(iV8467, Y)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[165, 164])).
% 0.21/0.45 tff(167,assumption,(![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(iV8467, Y)))), introduced(assumption)).
% 0.21/0.45 tff(168,plain,
% 0.21/0.45 (cC32xcomp(iV8474) <=> cC32xcomp(iV8474)),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(169,axiom,(cC32xcomp(iV8474)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_127')).
% 0.21/0.45 tff(170,plain,
% 0.21/0.45 (cC32xcomp(iV8474)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.21/0.45 tff(171,plain,
% 0.21/0.45 (rR1(iV8467, iV8474) <=> rR1(iV8467, iV8474)),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(172,axiom,(rR1(iV8467, iV8474)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_106')).
% 0.21/0.45 tff(173,plain,
% 0.21/0.45 (rR1(iV8467, iV8474)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.21/0.45 tff(174,plain,
% 0.21/0.45 (((~![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(iV8467, Y)))) | ((~cC32xcomp(iV8474)) | (~rR1(iV8467, iV8474)))) <=> ((~![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(iV8467, Y)))) | (~cC32xcomp(iV8474)) | (~rR1(iV8467, iV8474)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(175,plain,
% 0.21/0.45 ((~![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(iV8467, Y)))) | ((~cC32xcomp(iV8474)) | (~rR1(iV8467, iV8474)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(176,plain,
% 0.21/0.45 ((~![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(iV8467, Y)))) | (~cC32xcomp(iV8474)) | (~rR1(iV8467, iV8474))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.21/0.45 tff(177,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[176, 173, 170, 167])).
% 0.21/0.45 tff(178,plain,(~![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(iV8467, Y)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.45 tff(179,plain,
% 0.21/0.45 ((~(cC34(iV8467) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(iV8467, Y))))) | cC34(iV8467) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(iV8467, Y)))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(180,plain,
% 0.21/0.45 ((~(cC34(iV8467) | ![Y: $i] : ((~cC32xcomp(Y)) | (~rR1(iV8467, Y))))) | cC34(iV8467)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[179, 178])).
% 0.21/0.45 tff(181,plain,
% 0.21/0.45 (cC34(iV8467)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[180, 166])).
% 0.21/0.45 tff(182,assumption,((~(cC14(iV8467) | ![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y))))) | (~((~cC14(iV8467)) | (~((~cTOP(tptp_fun_Y_2(iV8467))) | (~rR1(iV8467, tptp_fun_Y_2(iV8467)))))))), introduced(assumption)).
% 0.21/0.45 tff(183,plain,
% 0.21/0.45 (^[X: $i] : refl((~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_2(X))) | (~cTOP(tptp_fun_Y_2(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y))))))) <=> (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_2(X))) | (~cTOP(tptp_fun_Y_2(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y))))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(184,plain,
% 0.21/0.45 (![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_2(X))) | (~cTOP(tptp_fun_Y_2(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y))))))) <=> ![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_2(X))) | (~cTOP(tptp_fun_Y_2(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[183])).
% 0.21/0.45 tff(185,plain,
% 0.21/0.45 (^[X: $i] : rewrite((~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_2(X))) | (~cTOP(tptp_fun_Y_2(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y))))))) <=> (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_2(X))) | (~cTOP(tptp_fun_Y_2(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y))))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(186,plain,
% 0.21/0.45 (![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_2(X))) | (~cTOP(tptp_fun_Y_2(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y))))))) <=> ![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_2(X))) | (~cTOP(tptp_fun_Y_2(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[185])).
% 0.21/0.45 tff(187,plain,
% 0.21/0.45 (![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_2(X))) | (~cTOP(tptp_fun_Y_2(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y))))))) <=> ![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_2(X))) | (~cTOP(tptp_fun_Y_2(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))),
% 0.21/0.45 inference(transitivity,[status(thm)],[186, 184])).
% 0.21/0.45 tff(188,plain,
% 0.21/0.45 (^[X: $i] : trans(monotonicity(rewrite(((~cC14(X)) | (rR1(X, tptp_fun_Y_2(X)) & cTOP(tptp_fun_Y_2(X)))) <=> ((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_2(X))) | (~cTOP(tptp_fun_Y_2(X))))))), rewrite((cC14(X) | ![Y: $i] : (~(rR1(X, Y) & cTOP(Y)))) <=> (cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y))))), ((((~cC14(X)) | (rR1(X, tptp_fun_Y_2(X)) & cTOP(tptp_fun_Y_2(X)))) & (cC14(X) | ![Y: $i] : (~(rR1(X, Y) & cTOP(Y))))) <=> (((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_2(X))) | (~cTOP(tptp_fun_Y_2(X)))))) & (cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y))))))), rewrite((((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_2(X))) | (~cTOP(tptp_fun_Y_2(X)))))) & (cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y))))) <=> (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_2(X))) | (~cTOP(tptp_fun_Y_2(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))), ((((~cC14(X)) | (rR1(X, tptp_fun_Y_2(X)) & cTOP(tptp_fun_Y_2(X)))) & (cC14(X) | ![Y: $i] : (~(rR1(X, Y) & cTOP(Y))))) <=> (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_2(X))) | (~cTOP(tptp_fun_Y_2(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(189,plain,
% 0.21/0.45 (![X: $i] : (((~cC14(X)) | (rR1(X, tptp_fun_Y_2(X)) & cTOP(tptp_fun_Y_2(X)))) & (cC14(X) | ![Y: $i] : (~(rR1(X, Y) & cTOP(Y))))) <=> ![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_2(X))) | (~cTOP(tptp_fun_Y_2(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[188])).
% 0.21/0.45 tff(190,plain,
% 0.21/0.45 (![X: $i] : (cC14(X) <=> ?[Y: $i] : (rR1(X, Y) & cTOP(Y))) <=> ![X: $i] : (cC14(X) <=> ?[Y: $i] : (rR1(X, Y) & cTOP(Y)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(191,axiom,(![X: $i] : (cC14(X) <=> ?[Y: $i] : (rR1(X, Y) & cTOP(Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_5')).
% 0.21/0.45 tff(192,plain,
% 0.21/0.45 (![X: $i] : (cC14(X) <=> ?[Y: $i] : (rR1(X, Y) & cTOP(Y)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.21/0.45 tff(193,plain,(
% 0.21/0.45 ![X: $i] : (((~cC14(X)) | (rR1(X, tptp_fun_Y_2(X)) & cTOP(tptp_fun_Y_2(X)))) & (cC14(X) | ![Y: $i] : (~(rR1(X, Y) & cTOP(Y)))))),
% 0.21/0.45 inference(skolemize,[status(sab)],[192])).
% 0.21/0.45 tff(194,plain,
% 0.21/0.45 (![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_2(X))) | (~cTOP(tptp_fun_Y_2(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[193, 189])).
% 0.21/0.45 tff(195,plain,
% 0.21/0.45 (![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_2(X))) | (~cTOP(tptp_fun_Y_2(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[194, 187])).
% 0.21/0.45 tff(196,plain,
% 0.21/0.45 (((~![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_2(X))) | (~cTOP(tptp_fun_Y_2(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))) | (~((~(cC14(iV8467) | ![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y))))) | (~((~cC14(iV8467)) | (~((~cTOP(tptp_fun_Y_2(iV8467))) | (~rR1(iV8467, tptp_fun_Y_2(iV8467)))))))))) <=> ((~![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_2(X))) | (~cTOP(tptp_fun_Y_2(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))) | (~((~(cC14(iV8467) | ![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y))))) | (~((~cC14(iV8467)) | (~((~cTOP(tptp_fun_Y_2(iV8467))) | (~rR1(iV8467, tptp_fun_Y_2(iV8467))))))))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(197,plain,
% 0.21/0.45 ((~((~((~cC14(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_2(iV8467))) | (~cTOP(tptp_fun_Y_2(iV8467))))))) | (~(cC14(iV8467) | ![Y: $i] : ((~rR1(iV8467, Y)) | (~cTOP(Y))))))) <=> (~((~(cC14(iV8467) | ![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y))))) | (~((~cC14(iV8467)) | (~((~cTOP(tptp_fun_Y_2(iV8467))) | (~rR1(iV8467, tptp_fun_Y_2(iV8467)))))))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(198,plain,
% 0.21/0.45 (((~![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_2(X))) | (~cTOP(tptp_fun_Y_2(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))) | (~((~((~cC14(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_2(iV8467))) | (~cTOP(tptp_fun_Y_2(iV8467))))))) | (~(cC14(iV8467) | ![Y: $i] : ((~rR1(iV8467, Y)) | (~cTOP(Y)))))))) <=> ((~![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_2(X))) | (~cTOP(tptp_fun_Y_2(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))) | (~((~(cC14(iV8467) | ![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y))))) | (~((~cC14(iV8467)) | (~((~cTOP(tptp_fun_Y_2(iV8467))) | (~rR1(iV8467, tptp_fun_Y_2(iV8467))))))))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[197])).
% 0.21/0.45 tff(199,plain,
% 0.21/0.45 (((~![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_2(X))) | (~cTOP(tptp_fun_Y_2(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))) | (~((~((~cC14(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_2(iV8467))) | (~cTOP(tptp_fun_Y_2(iV8467))))))) | (~(cC14(iV8467) | ![Y: $i] : ((~rR1(iV8467, Y)) | (~cTOP(Y)))))))) <=> ((~![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_2(X))) | (~cTOP(tptp_fun_Y_2(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))) | (~((~(cC14(iV8467) | ![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y))))) | (~((~cC14(iV8467)) | (~((~cTOP(tptp_fun_Y_2(iV8467))) | (~rR1(iV8467, tptp_fun_Y_2(iV8467))))))))))),
% 0.21/0.45 inference(transitivity,[status(thm)],[198, 196])).
% 0.21/0.45 tff(200,plain,
% 0.21/0.45 ((~![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_2(X))) | (~cTOP(tptp_fun_Y_2(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))) | (~((~((~cC14(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_2(iV8467))) | (~cTOP(tptp_fun_Y_2(iV8467))))))) | (~(cC14(iV8467) | ![Y: $i] : ((~rR1(iV8467, Y)) | (~cTOP(Y)))))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(201,plain,
% 0.21/0.45 ((~![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_2(X))) | (~cTOP(tptp_fun_Y_2(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))) | (~((~(cC14(iV8467) | ![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y))))) | (~((~cC14(iV8467)) | (~((~cTOP(tptp_fun_Y_2(iV8467))) | (~rR1(iV8467, tptp_fun_Y_2(iV8467)))))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.21/0.45 tff(202,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[201, 195, 182])).
% 0.21/0.45 tff(203,plain,(~((~(cC14(iV8467) | ![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y))))) | (~((~cC14(iV8467)) | (~((~cTOP(tptp_fun_Y_2(iV8467))) | (~rR1(iV8467, tptp_fun_Y_2(iV8467))))))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.45 tff(204,plain,
% 0.21/0.45 (((~(cC14(iV8467) | ![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y))))) | (~((~cC14(iV8467)) | (~((~cTOP(tptp_fun_Y_2(iV8467))) | (~rR1(iV8467, tptp_fun_Y_2(iV8467)))))))) | (cC14(iV8467) | ![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y))))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(205,plain,
% 0.21/0.45 (cC14(iV8467) | ![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[204, 203])).
% 0.21/0.45 tff(206,assumption,(![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y)))), introduced(assumption)).
% 0.21/0.45 tff(207,plain,
% 0.21/0.45 (cTOP(iV8470) <=> cTOP(iV8470)),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(208,axiom,(cTOP(iV8470)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_116')).
% 0.21/0.45 tff(209,plain,
% 0.21/0.45 (cTOP(iV8470)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.21/0.45 tff(210,plain,
% 0.21/0.45 (rR1(iV8467, iV8470) <=> rR1(iV8467, iV8470)),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(211,axiom,(rR1(iV8467, iV8470)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_104')).
% 0.21/0.45 tff(212,plain,
% 0.21/0.45 (rR1(iV8467, iV8470)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[211, 210])).
% 0.21/0.45 tff(213,plain,
% 0.21/0.45 (((~![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y)))) | ((~cTOP(iV8470)) | (~rR1(iV8467, iV8470)))) <=> ((~![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y)))) | (~cTOP(iV8470)) | (~rR1(iV8467, iV8470)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(214,plain,
% 0.21/0.45 ((~![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y)))) | ((~cTOP(iV8470)) | (~rR1(iV8467, iV8470)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(215,plain,
% 0.21/0.45 ((~![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y)))) | (~cTOP(iV8470)) | (~rR1(iV8467, iV8470))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[214, 213])).
% 0.21/0.45 tff(216,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[215, 212, 209, 206])).
% 0.21/0.45 tff(217,plain,(~![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.45 tff(218,plain,
% 0.21/0.45 ((~(cC14(iV8467) | ![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y))))) | cC14(iV8467) | ![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y)))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(219,plain,
% 0.21/0.45 ((~(cC14(iV8467) | ![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y))))) | cC14(iV8467)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[218, 217])).
% 0.21/0.45 tff(220,plain,
% 0.21/0.45 (cC14(iV8467)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[219, 205])).
% 0.21/0.45 tff(221,assumption,((~((~cC62(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_44(iV8467))) | (~cC60(tptp_fun_Y_44(iV8467))))))) | (~(cC62(iV8467) | ![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y)))))), introduced(assumption)).
% 0.21/0.45 tff(222,plain,
% 0.21/0.45 (^[X: $i] : refl((~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_44(X))) | (~cC60(tptp_fun_Y_44(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y))))))) <=> (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_44(X))) | (~cC60(tptp_fun_Y_44(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y))))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(223,plain,
% 0.21/0.45 (![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_44(X))) | (~cC60(tptp_fun_Y_44(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y))))))) <=> ![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_44(X))) | (~cC60(tptp_fun_Y_44(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[222])).
% 0.21/0.45 tff(224,plain,
% 0.21/0.45 (^[X: $i] : rewrite((~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_44(X))) | (~cC60(tptp_fun_Y_44(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y))))))) <=> (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_44(X))) | (~cC60(tptp_fun_Y_44(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y))))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(225,plain,
% 0.21/0.45 (![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_44(X))) | (~cC60(tptp_fun_Y_44(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y))))))) <=> ![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_44(X))) | (~cC60(tptp_fun_Y_44(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[224])).
% 0.21/0.45 tff(226,plain,
% 0.21/0.45 (![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_44(X))) | (~cC60(tptp_fun_Y_44(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y))))))) <=> ![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_44(X))) | (~cC60(tptp_fun_Y_44(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))),
% 0.21/0.45 inference(transitivity,[status(thm)],[225, 223])).
% 0.21/0.45 tff(227,plain,
% 0.21/0.45 (^[X: $i] : trans(monotonicity(rewrite(((~cC62(X)) | (rR1(X, tptp_fun_Y_44(X)) & cC60(tptp_fun_Y_44(X)))) <=> ((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_44(X))) | (~cC60(tptp_fun_Y_44(X))))))), rewrite((cC62(X) | ![Y: $i] : (~(rR1(X, Y) & cC60(Y)))) <=> (cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y))))), ((((~cC62(X)) | (rR1(X, tptp_fun_Y_44(X)) & cC60(tptp_fun_Y_44(X)))) & (cC62(X) | ![Y: $i] : (~(rR1(X, Y) & cC60(Y))))) <=> (((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_44(X))) | (~cC60(tptp_fun_Y_44(X)))))) & (cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y))))))), rewrite((((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_44(X))) | (~cC60(tptp_fun_Y_44(X)))))) & (cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y))))) <=> (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_44(X))) | (~cC60(tptp_fun_Y_44(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))), ((((~cC62(X)) | (rR1(X, tptp_fun_Y_44(X)) & cC60(tptp_fun_Y_44(X)))) & (cC62(X) | ![Y: $i] : (~(rR1(X, Y) & cC60(Y))))) <=> (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_44(X))) | (~cC60(tptp_fun_Y_44(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(228,plain,
% 0.21/0.45 (![X: $i] : (((~cC62(X)) | (rR1(X, tptp_fun_Y_44(X)) & cC60(tptp_fun_Y_44(X)))) & (cC62(X) | ![Y: $i] : (~(rR1(X, Y) & cC60(Y))))) <=> ![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_44(X))) | (~cC60(tptp_fun_Y_44(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[227])).
% 0.21/0.45 tff(229,plain,
% 0.21/0.45 (![X: $i] : (cC62(X) <=> ?[Y: $i] : (rR1(X, Y) & cC60(Y))) <=> ![X: $i] : (cC62(X) <=> ?[Y: $i] : (rR1(X, Y) & cC60(Y)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(230,axiom,(![X: $i] : (cC62(X) <=> ?[Y: $i] : (rR1(X, Y) & cC60(Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_62')).
% 0.21/0.45 tff(231,plain,
% 0.21/0.45 (![X: $i] : (cC62(X) <=> ?[Y: $i] : (rR1(X, Y) & cC60(Y)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[230, 229])).
% 0.21/0.45 tff(232,plain,(
% 0.21/0.45 ![X: $i] : (((~cC62(X)) | (rR1(X, tptp_fun_Y_44(X)) & cC60(tptp_fun_Y_44(X)))) & (cC62(X) | ![Y: $i] : (~(rR1(X, Y) & cC60(Y)))))),
% 0.21/0.45 inference(skolemize,[status(sab)],[231])).
% 0.21/0.45 tff(233,plain,
% 0.21/0.45 (![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_44(X))) | (~cC60(tptp_fun_Y_44(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[232, 228])).
% 0.21/0.45 tff(234,plain,
% 0.21/0.45 (![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_44(X))) | (~cC60(tptp_fun_Y_44(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[233, 226])).
% 0.21/0.45 tff(235,plain,
% 0.21/0.45 (((~![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_44(X))) | (~cC60(tptp_fun_Y_44(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))) | (~((~((~cC62(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_44(iV8467))) | (~cC60(tptp_fun_Y_44(iV8467))))))) | (~(cC62(iV8467) | ![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y)))))))) <=> ((~![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_44(X))) | (~cC60(tptp_fun_Y_44(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))) | (~((~((~cC62(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_44(iV8467))) | (~cC60(tptp_fun_Y_44(iV8467))))))) | (~(cC62(iV8467) | ![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y))))))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(236,plain,
% 0.21/0.46 ((~((~((~cC62(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_44(iV8467))) | (~cC60(tptp_fun_Y_44(iV8467))))))) | (~(cC62(iV8467) | ![Y: $i] : ((~rR1(iV8467, Y)) | (~cC60(Y))))))) <=> (~((~((~cC62(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_44(iV8467))) | (~cC60(tptp_fun_Y_44(iV8467))))))) | (~(cC62(iV8467) | ![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y)))))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(237,plain,
% 0.21/0.46 (((~![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_44(X))) | (~cC60(tptp_fun_Y_44(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))) | (~((~((~cC62(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_44(iV8467))) | (~cC60(tptp_fun_Y_44(iV8467))))))) | (~(cC62(iV8467) | ![Y: $i] : ((~rR1(iV8467, Y)) | (~cC60(Y)))))))) <=> ((~![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_44(X))) | (~cC60(tptp_fun_Y_44(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))) | (~((~((~cC62(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_44(iV8467))) | (~cC60(tptp_fun_Y_44(iV8467))))))) | (~(cC62(iV8467) | ![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y))))))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[236])).
% 0.21/0.46 tff(238,plain,
% 0.21/0.46 (((~![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_44(X))) | (~cC60(tptp_fun_Y_44(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))) | (~((~((~cC62(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_44(iV8467))) | (~cC60(tptp_fun_Y_44(iV8467))))))) | (~(cC62(iV8467) | ![Y: $i] : ((~rR1(iV8467, Y)) | (~cC60(Y)))))))) <=> ((~![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_44(X))) | (~cC60(tptp_fun_Y_44(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))) | (~((~((~cC62(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_44(iV8467))) | (~cC60(tptp_fun_Y_44(iV8467))))))) | (~(cC62(iV8467) | ![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y))))))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[237, 235])).
% 0.21/0.46 tff(239,plain,
% 0.21/0.46 ((~![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_44(X))) | (~cC60(tptp_fun_Y_44(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))) | (~((~((~cC62(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_44(iV8467))) | (~cC60(tptp_fun_Y_44(iV8467))))))) | (~(cC62(iV8467) | ![Y: $i] : ((~rR1(iV8467, Y)) | (~cC60(Y)))))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(240,plain,
% 0.21/0.46 ((~![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_44(X))) | (~cC60(tptp_fun_Y_44(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))) | (~((~((~cC62(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_44(iV8467))) | (~cC60(tptp_fun_Y_44(iV8467))))))) | (~(cC62(iV8467) | ![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y)))))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[239, 238])).
% 0.21/0.46 tff(241,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[240, 234, 221])).
% 0.21/0.46 tff(242,plain,(~((~((~cC62(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_44(iV8467))) | (~cC60(tptp_fun_Y_44(iV8467))))))) | (~(cC62(iV8467) | ![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y))))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.46 tff(243,plain,
% 0.21/0.46 (((~((~cC62(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_44(iV8467))) | (~cC60(tptp_fun_Y_44(iV8467))))))) | (~(cC62(iV8467) | ![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y)))))) | (cC62(iV8467) | ![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y))))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(244,plain,
% 0.21/0.46 (cC62(iV8467) | ![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[243, 242])).
% 0.21/0.46 tff(245,assumption,(![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y)))), introduced(assumption)).
% 0.21/0.46 tff(246,plain,
% 0.21/0.46 (rR1(iV8467, iV8472) <=> rR1(iV8467, iV8472)),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(247,axiom,(rR1(iV8467, iV8472)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_110')).
% 0.21/0.46 tff(248,plain,
% 0.21/0.46 (rR1(iV8467, iV8472)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[247, 246])).
% 0.21/0.46 tff(249,plain,
% 0.21/0.46 (((~![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y)))) | ((~cC60(iV8472)) | (~rR1(iV8467, iV8472)))) <=> ((~![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y)))) | (~cC60(iV8472)) | (~rR1(iV8467, iV8472)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(250,plain,
% 0.21/0.46 ((~![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y)))) | ((~cC60(iV8472)) | (~rR1(iV8467, iV8472)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(251,plain,
% 0.21/0.46 ((~![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y)))) | (~cC60(iV8472)) | (~rR1(iV8467, iV8472))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[250, 249])).
% 0.21/0.46 tff(252,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[251, 248, 76, 245])).
% 0.21/0.46 tff(253,plain,(~![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.46 tff(254,plain,
% 0.21/0.46 ((~(cC62(iV8467) | ![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y))))) | cC62(iV8467) | ![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y)))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(255,plain,
% 0.21/0.46 ((~(cC62(iV8467) | ![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y))))) | cC62(iV8467)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[254, 253])).
% 0.21/0.46 tff(256,plain,
% 0.21/0.46 (cC62(iV8467)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[255, 244])).
% 0.21/0.46 tff(257,assumption,((~(cC82(iV8467) | ![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y))))) | (~((~cC82(iV8467)) | (~((~cC80(tptp_fun_Y_58(iV8467))) | (~rR1(iV8467, tptp_fun_Y_58(iV8467)))))))), introduced(assumption)).
% 0.21/0.46 tff(258,plain,
% 0.21/0.46 (^[X: $i] : refl((~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_58(X))) | (~cC80(tptp_fun_Y_58(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y))))))) <=> (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_58(X))) | (~cC80(tptp_fun_Y_58(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y))))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(259,plain,
% 0.21/0.46 (![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_58(X))) | (~cC80(tptp_fun_Y_58(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y))))))) <=> ![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_58(X))) | (~cC80(tptp_fun_Y_58(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[258])).
% 0.21/0.46 tff(260,plain,
% 0.21/0.46 (^[X: $i] : rewrite((~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_58(X))) | (~cC80(tptp_fun_Y_58(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y))))))) <=> (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_58(X))) | (~cC80(tptp_fun_Y_58(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y))))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(261,plain,
% 0.21/0.46 (![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_58(X))) | (~cC80(tptp_fun_Y_58(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y))))))) <=> ![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_58(X))) | (~cC80(tptp_fun_Y_58(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[260])).
% 0.21/0.46 tff(262,plain,
% 0.21/0.46 (![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_58(X))) | (~cC80(tptp_fun_Y_58(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y))))))) <=> ![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_58(X))) | (~cC80(tptp_fun_Y_58(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[261, 259])).
% 0.21/0.46 tff(263,plain,
% 0.21/0.46 (^[X: $i] : trans(monotonicity(rewrite(((~cC82(X)) | (rR1(X, tptp_fun_Y_58(X)) & cC80(tptp_fun_Y_58(X)))) <=> ((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_58(X))) | (~cC80(tptp_fun_Y_58(X))))))), rewrite((cC82(X) | ![Y: $i] : (~(rR1(X, Y) & cC80(Y)))) <=> (cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y))))), ((((~cC82(X)) | (rR1(X, tptp_fun_Y_58(X)) & cC80(tptp_fun_Y_58(X)))) & (cC82(X) | ![Y: $i] : (~(rR1(X, Y) & cC80(Y))))) <=> (((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_58(X))) | (~cC80(tptp_fun_Y_58(X)))))) & (cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y))))))), rewrite((((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_58(X))) | (~cC80(tptp_fun_Y_58(X)))))) & (cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y))))) <=> (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_58(X))) | (~cC80(tptp_fun_Y_58(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))), ((((~cC82(X)) | (rR1(X, tptp_fun_Y_58(X)) & cC80(tptp_fun_Y_58(X)))) & (cC82(X) | ![Y: $i] : (~(rR1(X, Y) & cC80(Y))))) <=> (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_58(X))) | (~cC80(tptp_fun_Y_58(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(264,plain,
% 0.21/0.46 (![X: $i] : (((~cC82(X)) | (rR1(X, tptp_fun_Y_58(X)) & cC80(tptp_fun_Y_58(X)))) & (cC82(X) | ![Y: $i] : (~(rR1(X, Y) & cC80(Y))))) <=> ![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_58(X))) | (~cC80(tptp_fun_Y_58(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[263])).
% 0.21/0.46 tff(265,plain,
% 0.21/0.46 (![X: $i] : (cC82(X) <=> ?[Y: $i] : (rR1(X, Y) & cC80(Y))) <=> ![X: $i] : (cC82(X) <=> ?[Y: $i] : (rR1(X, Y) & cC80(Y)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(266,axiom,(![X: $i] : (cC82(X) <=> ?[Y: $i] : (rR1(X, Y) & cC80(Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_82')).
% 0.21/0.46 tff(267,plain,
% 0.21/0.46 (![X: $i] : (cC82(X) <=> ?[Y: $i] : (rR1(X, Y) & cC80(Y)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[266, 265])).
% 0.21/0.46 tff(268,plain,(
% 0.21/0.46 ![X: $i] : (((~cC82(X)) | (rR1(X, tptp_fun_Y_58(X)) & cC80(tptp_fun_Y_58(X)))) & (cC82(X) | ![Y: $i] : (~(rR1(X, Y) & cC80(Y)))))),
% 0.21/0.46 inference(skolemize,[status(sab)],[267])).
% 0.21/0.46 tff(269,plain,
% 0.21/0.46 (![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_58(X))) | (~cC80(tptp_fun_Y_58(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[268, 264])).
% 0.21/0.46 tff(270,plain,
% 0.21/0.46 (![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_58(X))) | (~cC80(tptp_fun_Y_58(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[269, 262])).
% 0.21/0.46 tff(271,plain,
% 0.21/0.46 (((~![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_58(X))) | (~cC80(tptp_fun_Y_58(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))) | (~((~(cC82(iV8467) | ![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y))))) | (~((~cC82(iV8467)) | (~((~cC80(tptp_fun_Y_58(iV8467))) | (~rR1(iV8467, tptp_fun_Y_58(iV8467)))))))))) <=> ((~![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_58(X))) | (~cC80(tptp_fun_Y_58(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))) | (~((~(cC82(iV8467) | ![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y))))) | (~((~cC82(iV8467)) | (~((~cC80(tptp_fun_Y_58(iV8467))) | (~rR1(iV8467, tptp_fun_Y_58(iV8467))))))))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(272,plain,
% 0.21/0.46 ((~((~((~cC82(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_58(iV8467))) | (~cC80(tptp_fun_Y_58(iV8467))))))) | (~(cC82(iV8467) | ![Y: $i] : ((~rR1(iV8467, Y)) | (~cC80(Y))))))) <=> (~((~(cC82(iV8467) | ![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y))))) | (~((~cC82(iV8467)) | (~((~cC80(tptp_fun_Y_58(iV8467))) | (~rR1(iV8467, tptp_fun_Y_58(iV8467)))))))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(273,plain,
% 0.21/0.46 (((~![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_58(X))) | (~cC80(tptp_fun_Y_58(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))) | (~((~((~cC82(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_58(iV8467))) | (~cC80(tptp_fun_Y_58(iV8467))))))) | (~(cC82(iV8467) | ![Y: $i] : ((~rR1(iV8467, Y)) | (~cC80(Y)))))))) <=> ((~![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_58(X))) | (~cC80(tptp_fun_Y_58(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))) | (~((~(cC82(iV8467) | ![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y))))) | (~((~cC82(iV8467)) | (~((~cC80(tptp_fun_Y_58(iV8467))) | (~rR1(iV8467, tptp_fun_Y_58(iV8467))))))))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[272])).
% 0.21/0.46 tff(274,plain,
% 0.21/0.46 (((~![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_58(X))) | (~cC80(tptp_fun_Y_58(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))) | (~((~((~cC82(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_58(iV8467))) | (~cC80(tptp_fun_Y_58(iV8467))))))) | (~(cC82(iV8467) | ![Y: $i] : ((~rR1(iV8467, Y)) | (~cC80(Y)))))))) <=> ((~![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_58(X))) | (~cC80(tptp_fun_Y_58(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))) | (~((~(cC82(iV8467) | ![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y))))) | (~((~cC82(iV8467)) | (~((~cC80(tptp_fun_Y_58(iV8467))) | (~rR1(iV8467, tptp_fun_Y_58(iV8467))))))))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[273, 271])).
% 0.21/0.46 tff(275,plain,
% 0.21/0.46 ((~![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_58(X))) | (~cC80(tptp_fun_Y_58(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))) | (~((~((~cC82(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_58(iV8467))) | (~cC80(tptp_fun_Y_58(iV8467))))))) | (~(cC82(iV8467) | ![Y: $i] : ((~rR1(iV8467, Y)) | (~cC80(Y)))))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(276,plain,
% 0.21/0.46 ((~![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_58(X))) | (~cC80(tptp_fun_Y_58(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))) | (~((~(cC82(iV8467) | ![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y))))) | (~((~cC82(iV8467)) | (~((~cC80(tptp_fun_Y_58(iV8467))) | (~rR1(iV8467, tptp_fun_Y_58(iV8467)))))))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[275, 274])).
% 0.21/0.46 tff(277,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[276, 270, 257])).
% 0.21/0.46 tff(278,plain,(~((~(cC82(iV8467) | ![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y))))) | (~((~cC82(iV8467)) | (~((~cC80(tptp_fun_Y_58(iV8467))) | (~rR1(iV8467, tptp_fun_Y_58(iV8467))))))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.46 tff(279,plain,
% 0.21/0.46 (((~(cC82(iV8467) | ![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y))))) | (~((~cC82(iV8467)) | (~((~cC80(tptp_fun_Y_58(iV8467))) | (~rR1(iV8467, tptp_fun_Y_58(iV8467)))))))) | (cC82(iV8467) | ![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y))))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(280,plain,
% 0.21/0.46 (cC82(iV8467) | ![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[279, 278])).
% 0.21/0.46 tff(281,assumption,(![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y)))), introduced(assumption)).
% 0.21/0.46 tff(282,plain,
% 0.21/0.46 (^[X: $i] : refl((~(((~cC2xcomp(X)) | (~cC78xcomp(X))) <=> cC80(X))) <=> (~(((~cC2xcomp(X)) | (~cC78xcomp(X))) <=> cC80(X))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(283,plain,
% 0.21/0.46 (![X: $i] : (~(((~cC2xcomp(X)) | (~cC78xcomp(X))) <=> cC80(X))) <=> ![X: $i] : (~(((~cC2xcomp(X)) | (~cC78xcomp(X))) <=> cC80(X)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[282])).
% 0.21/0.46 tff(284,plain,
% 0.21/0.46 (^[X: $i] : trans(trans(monotonicity(rewrite((cC78xcomp(X) & cC2xcomp(X)) <=> (~((~cC2xcomp(X)) | (~cC78xcomp(X))))), ((cC80(X) <=> (cC78xcomp(X) & cC2xcomp(X))) <=> (cC80(X) <=> (~((~cC2xcomp(X)) | (~cC78xcomp(X))))))), rewrite((cC80(X) <=> (~((~cC2xcomp(X)) | (~cC78xcomp(X))))) <=> (~(((~cC2xcomp(X)) | (~cC78xcomp(X))) <=> cC80(X)))), ((cC80(X) <=> (cC78xcomp(X) & cC2xcomp(X))) <=> (~(((~cC2xcomp(X)) | (~cC78xcomp(X))) <=> cC80(X))))), rewrite((~(((~cC2xcomp(X)) | (~cC78xcomp(X))) <=> cC80(X))) <=> (~(((~cC2xcomp(X)) | (~cC78xcomp(X))) <=> cC80(X)))), ((cC80(X) <=> (cC78xcomp(X) & cC2xcomp(X))) <=> (~(((~cC2xcomp(X)) | (~cC78xcomp(X))) <=> cC80(X)))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(285,plain,
% 0.21/0.46 (![X: $i] : (cC80(X) <=> (cC78xcomp(X) & cC2xcomp(X))) <=> ![X: $i] : (~(((~cC2xcomp(X)) | (~cC78xcomp(X))) <=> cC80(X)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[284])).
% 0.21/0.46 tff(286,plain,
% 0.21/0.46 (![X: $i] : (cC80(X) <=> (cC78xcomp(X) & cC2xcomp(X))) <=> ![X: $i] : (cC80(X) <=> (cC78xcomp(X) & cC2xcomp(X)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(287,axiom,(![X: $i] : (cC80(X) <=> (cC78xcomp(X) & cC2xcomp(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_80')).
% 0.21/0.46 tff(288,plain,
% 0.21/0.46 (![X: $i] : (cC80(X) <=> (cC78xcomp(X) & cC2xcomp(X)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[287, 286])).
% 0.21/0.46 tff(289,plain,(
% 0.21/0.46 ![X: $i] : (cC80(X) <=> (cC78xcomp(X) & cC2xcomp(X)))),
% 0.21/0.46 inference(skolemize,[status(sab)],[288])).
% 0.21/0.46 tff(290,plain,
% 0.21/0.46 (![X: $i] : (~(((~cC2xcomp(X)) | (~cC78xcomp(X))) <=> cC80(X)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[289, 285])).
% 0.21/0.46 tff(291,plain,
% 0.21/0.46 (![X: $i] : (~(((~cC2xcomp(X)) | (~cC78xcomp(X))) <=> cC80(X)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[290, 283])).
% 0.21/0.46 tff(292,plain,
% 0.21/0.46 ((~![X: $i] : (~(((~cC2xcomp(X)) | (~cC78xcomp(X))) <=> cC80(X)))) | (~(((~cC2xcomp(iV8471)) | (~cC78xcomp(iV8471))) <=> cC80(iV8471)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(293,plain,
% 0.21/0.46 (~(((~cC2xcomp(iV8471)) | (~cC78xcomp(iV8471))) <=> cC80(iV8471))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[292, 291])).
% 0.21/0.46 tff(294,plain,
% 0.21/0.46 (cC2xcomp(iV8471) <=> cC2xcomp(iV8471)),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(295,axiom,(cC2xcomp(iV8471)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_119')).
% 0.21/0.46 tff(296,plain,
% 0.21/0.46 (cC2xcomp(iV8471)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[295, 294])).
% 0.21/0.46 tff(297,plain,
% 0.21/0.46 (cC78xcomp(iV8471) <=> cC78xcomp(iV8471)),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(298,axiom,(cC78xcomp(iV8471)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_118')).
% 0.21/0.46 tff(299,plain,
% 0.21/0.46 (cC78xcomp(iV8471)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[298, 297])).
% 0.21/0.46 tff(300,plain,
% 0.21/0.46 ((~((~cC2xcomp(iV8471)) | (~cC78xcomp(iV8471)))) | (~cC2xcomp(iV8471)) | (~cC78xcomp(iV8471))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(301,plain,
% 0.21/0.46 (~((~cC2xcomp(iV8471)) | (~cC78xcomp(iV8471)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[300, 299, 296])).
% 0.21/0.46 tff(302,plain,
% 0.21/0.46 ((((~cC2xcomp(iV8471)) | (~cC78xcomp(iV8471))) <=> cC80(iV8471)) | ((~cC2xcomp(iV8471)) | (~cC78xcomp(iV8471))) | cC80(iV8471)),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(303,plain,
% 0.21/0.46 ((((~cC2xcomp(iV8471)) | (~cC78xcomp(iV8471))) <=> cC80(iV8471)) | cC80(iV8471)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[302, 301])).
% 0.21/0.46 tff(304,plain,
% 0.21/0.46 (cC80(iV8471)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[303, 293])).
% 0.21/0.46 tff(305,plain,
% 0.21/0.46 (rR1(iV8467, iV8471) <=> rR1(iV8467, iV8471)),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(306,axiom,(rR1(iV8467, iV8471)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_103')).
% 0.21/0.46 tff(307,plain,
% 0.21/0.46 (rR1(iV8467, iV8471)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[306, 305])).
% 0.21/0.46 tff(308,plain,
% 0.21/0.46 (((~![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y)))) | ((~cC80(iV8471)) | (~rR1(iV8467, iV8471)))) <=> ((~![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y)))) | (~cC80(iV8471)) | (~rR1(iV8467, iV8471)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(309,plain,
% 0.21/0.46 ((~![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y)))) | ((~cC80(iV8471)) | (~rR1(iV8467, iV8471)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(310,plain,
% 0.21/0.46 ((~![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y)))) | (~cC80(iV8471)) | (~rR1(iV8467, iV8471))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[309, 308])).
% 0.21/0.46 tff(311,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[310, 307, 304, 281])).
% 0.21/0.46 tff(312,plain,(~![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.46 tff(313,plain,
% 0.21/0.46 ((~(cC82(iV8467) | ![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y))))) | cC82(iV8467) | ![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y)))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(314,plain,
% 0.21/0.46 ((~(cC82(iV8467) | ![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y))))) | cC82(iV8467)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[313, 312])).
% 0.21/0.46 tff(315,plain,
% 0.21/0.46 (cC82(iV8467)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[314, 280])).
% 0.21/0.46 tff(316,assumption,((~(cC8(iV8467) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(iV8467, Y))))) | (~((~cC8(iV8467)) | (~((~cC6xcomp(tptp_fun_Y_56(iV8467))) | (~rR1(iV8467, tptp_fun_Y_56(iV8467)))))))), introduced(assumption)).
% 0.21/0.46 tff(317,plain,
% 0.21/0.46 (^[X: $i] : refl((~((~((~cC8(X)) | (~((~rR1(X, tptp_fun_Y_56(X))) | (~cC6xcomp(tptp_fun_Y_56(X))))))) | (~(cC8(X) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(X, Y))))))) <=> (~((~((~cC8(X)) | (~((~rR1(X, tptp_fun_Y_56(X))) | (~cC6xcomp(tptp_fun_Y_56(X))))))) | (~(cC8(X) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(X, Y))))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(318,plain,
% 0.21/0.46 (![X: $i] : (~((~((~cC8(X)) | (~((~rR1(X, tptp_fun_Y_56(X))) | (~cC6xcomp(tptp_fun_Y_56(X))))))) | (~(cC8(X) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC8(X)) | (~((~rR1(X, tptp_fun_Y_56(X))) | (~cC6xcomp(tptp_fun_Y_56(X))))))) | (~(cC8(X) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[317])).
% 0.21/0.46 tff(319,plain,
% 0.21/0.46 (^[X: $i] : rewrite((~((~((~cC8(X)) | (~((~rR1(X, tptp_fun_Y_56(X))) | (~cC6xcomp(tptp_fun_Y_56(X))))))) | (~(cC8(X) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(X, Y))))))) <=> (~((~((~cC8(X)) | (~((~rR1(X, tptp_fun_Y_56(X))) | (~cC6xcomp(tptp_fun_Y_56(X))))))) | (~(cC8(X) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(X, Y))))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(320,plain,
% 0.21/0.46 (![X: $i] : (~((~((~cC8(X)) | (~((~rR1(X, tptp_fun_Y_56(X))) | (~cC6xcomp(tptp_fun_Y_56(X))))))) | (~(cC8(X) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC8(X)) | (~((~rR1(X, tptp_fun_Y_56(X))) | (~cC6xcomp(tptp_fun_Y_56(X))))))) | (~(cC8(X) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[319])).
% 0.21/0.46 tff(321,plain,
% 0.21/0.46 (![X: $i] : (~((~((~cC8(X)) | (~((~rR1(X, tptp_fun_Y_56(X))) | (~cC6xcomp(tptp_fun_Y_56(X))))))) | (~(cC8(X) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC8(X)) | (~((~rR1(X, tptp_fun_Y_56(X))) | (~cC6xcomp(tptp_fun_Y_56(X))))))) | (~(cC8(X) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[320, 318])).
% 0.21/0.46 tff(322,plain,
% 0.21/0.46 (^[X: $i] : trans(monotonicity(rewrite(((~cC8(X)) | (rR1(X, tptp_fun_Y_56(X)) & cC6xcomp(tptp_fun_Y_56(X)))) <=> ((~cC8(X)) | (~((~rR1(X, tptp_fun_Y_56(X))) | (~cC6xcomp(tptp_fun_Y_56(X))))))), rewrite((cC8(X) | ![Y: $i] : (~(rR1(X, Y) & cC6xcomp(Y)))) <=> (cC8(X) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(X, Y))))), ((((~cC8(X)) | (rR1(X, tptp_fun_Y_56(X)) & cC6xcomp(tptp_fun_Y_56(X)))) & (cC8(X) | ![Y: $i] : (~(rR1(X, Y) & cC6xcomp(Y))))) <=> (((~cC8(X)) | (~((~rR1(X, tptp_fun_Y_56(X))) | (~cC6xcomp(tptp_fun_Y_56(X)))))) & (cC8(X) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(X, Y))))))), rewrite((((~cC8(X)) | (~((~rR1(X, tptp_fun_Y_56(X))) | (~cC6xcomp(tptp_fun_Y_56(X)))))) & (cC8(X) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(X, Y))))) <=> (~((~((~cC8(X)) | (~((~rR1(X, tptp_fun_Y_56(X))) | (~cC6xcomp(tptp_fun_Y_56(X))))))) | (~(cC8(X) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(X, Y)))))))), ((((~cC8(X)) | (rR1(X, tptp_fun_Y_56(X)) & cC6xcomp(tptp_fun_Y_56(X)))) & (cC8(X) | ![Y: $i] : (~(rR1(X, Y) & cC6xcomp(Y))))) <=> (~((~((~cC8(X)) | (~((~rR1(X, tptp_fun_Y_56(X))) | (~cC6xcomp(tptp_fun_Y_56(X))))))) | (~(cC8(X) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(X, Y)))))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(323,plain,
% 0.21/0.46 (![X: $i] : (((~cC8(X)) | (rR1(X, tptp_fun_Y_56(X)) & cC6xcomp(tptp_fun_Y_56(X)))) & (cC8(X) | ![Y: $i] : (~(rR1(X, Y) & cC6xcomp(Y))))) <=> ![X: $i] : (~((~((~cC8(X)) | (~((~rR1(X, tptp_fun_Y_56(X))) | (~cC6xcomp(tptp_fun_Y_56(X))))))) | (~(cC8(X) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[322])).
% 0.21/0.46 tff(324,plain,
% 0.21/0.46 (![X: $i] : (cC8(X) <=> ?[Y: $i] : (rR1(X, Y) & cC6xcomp(Y))) <=> ![X: $i] : (cC8(X) <=> ?[Y: $i] : (rR1(X, Y) & cC6xcomp(Y)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(325,axiom,(![X: $i] : (cC8(X) <=> ?[Y: $i] : (rR1(X, Y) & cC6xcomp(Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_79')).
% 0.21/0.46 tff(326,plain,
% 0.21/0.46 (![X: $i] : (cC8(X) <=> ?[Y: $i] : (rR1(X, Y) & cC6xcomp(Y)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[325, 324])).
% 0.21/0.46 tff(327,plain,(
% 0.21/0.46 ![X: $i] : (((~cC8(X)) | (rR1(X, tptp_fun_Y_56(X)) & cC6xcomp(tptp_fun_Y_56(X)))) & (cC8(X) | ![Y: $i] : (~(rR1(X, Y) & cC6xcomp(Y)))))),
% 0.21/0.46 inference(skolemize,[status(sab)],[326])).
% 0.21/0.46 tff(328,plain,
% 0.21/0.46 (![X: $i] : (~((~((~cC8(X)) | (~((~rR1(X, tptp_fun_Y_56(X))) | (~cC6xcomp(tptp_fun_Y_56(X))))))) | (~(cC8(X) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[327, 323])).
% 0.21/0.46 tff(329,plain,
% 0.21/0.46 (![X: $i] : (~((~((~cC8(X)) | (~((~rR1(X, tptp_fun_Y_56(X))) | (~cC6xcomp(tptp_fun_Y_56(X))))))) | (~(cC8(X) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[328, 321])).
% 0.21/0.46 tff(330,plain,
% 0.21/0.46 (((~![X: $i] : (~((~((~cC8(X)) | (~((~rR1(X, tptp_fun_Y_56(X))) | (~cC6xcomp(tptp_fun_Y_56(X))))))) | (~(cC8(X) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(X, Y)))))))) | (~((~(cC8(iV8467) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(iV8467, Y))))) | (~((~cC8(iV8467)) | (~((~cC6xcomp(tptp_fun_Y_56(iV8467))) | (~rR1(iV8467, tptp_fun_Y_56(iV8467)))))))))) <=> ((~![X: $i] : (~((~((~cC8(X)) | (~((~rR1(X, tptp_fun_Y_56(X))) | (~cC6xcomp(tptp_fun_Y_56(X))))))) | (~(cC8(X) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(X, Y)))))))) | (~((~(cC8(iV8467) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(iV8467, Y))))) | (~((~cC8(iV8467)) | (~((~cC6xcomp(tptp_fun_Y_56(iV8467))) | (~rR1(iV8467, tptp_fun_Y_56(iV8467))))))))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(331,plain,
% 0.21/0.46 ((~((~((~cC8(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_56(iV8467))) | (~cC6xcomp(tptp_fun_Y_56(iV8467))))))) | (~(cC8(iV8467) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(iV8467, Y))))))) <=> (~((~(cC8(iV8467) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(iV8467, Y))))) | (~((~cC8(iV8467)) | (~((~cC6xcomp(tptp_fun_Y_56(iV8467))) | (~rR1(iV8467, tptp_fun_Y_56(iV8467)))))))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(332,plain,
% 0.21/0.46 (((~![X: $i] : (~((~((~cC8(X)) | (~((~rR1(X, tptp_fun_Y_56(X))) | (~cC6xcomp(tptp_fun_Y_56(X))))))) | (~(cC8(X) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(X, Y)))))))) | (~((~((~cC8(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_56(iV8467))) | (~cC6xcomp(tptp_fun_Y_56(iV8467))))))) | (~(cC8(iV8467) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(iV8467, Y)))))))) <=> ((~![X: $i] : (~((~((~cC8(X)) | (~((~rR1(X, tptp_fun_Y_56(X))) | (~cC6xcomp(tptp_fun_Y_56(X))))))) | (~(cC8(X) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(X, Y)))))))) | (~((~(cC8(iV8467) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(iV8467, Y))))) | (~((~cC8(iV8467)) | (~((~cC6xcomp(tptp_fun_Y_56(iV8467))) | (~rR1(iV8467, tptp_fun_Y_56(iV8467))))))))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[331])).
% 0.21/0.46 tff(333,plain,
% 0.21/0.46 (((~![X: $i] : (~((~((~cC8(X)) | (~((~rR1(X, tptp_fun_Y_56(X))) | (~cC6xcomp(tptp_fun_Y_56(X))))))) | (~(cC8(X) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(X, Y)))))))) | (~((~((~cC8(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_56(iV8467))) | (~cC6xcomp(tptp_fun_Y_56(iV8467))))))) | (~(cC8(iV8467) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(iV8467, Y)))))))) <=> ((~![X: $i] : (~((~((~cC8(X)) | (~((~rR1(X, tptp_fun_Y_56(X))) | (~cC6xcomp(tptp_fun_Y_56(X))))))) | (~(cC8(X) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(X, Y)))))))) | (~((~(cC8(iV8467) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(iV8467, Y))))) | (~((~cC8(iV8467)) | (~((~cC6xcomp(tptp_fun_Y_56(iV8467))) | (~rR1(iV8467, tptp_fun_Y_56(iV8467))))))))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[332, 330])).
% 0.21/0.46 tff(334,plain,
% 0.21/0.46 ((~![X: $i] : (~((~((~cC8(X)) | (~((~rR1(X, tptp_fun_Y_56(X))) | (~cC6xcomp(tptp_fun_Y_56(X))))))) | (~(cC8(X) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(X, Y)))))))) | (~((~((~cC8(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_56(iV8467))) | (~cC6xcomp(tptp_fun_Y_56(iV8467))))))) | (~(cC8(iV8467) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(iV8467, Y)))))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(335,plain,
% 0.21/0.46 ((~![X: $i] : (~((~((~cC8(X)) | (~((~rR1(X, tptp_fun_Y_56(X))) | (~cC6xcomp(tptp_fun_Y_56(X))))))) | (~(cC8(X) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(X, Y)))))))) | (~((~(cC8(iV8467) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(iV8467, Y))))) | (~((~cC8(iV8467)) | (~((~cC6xcomp(tptp_fun_Y_56(iV8467))) | (~rR1(iV8467, tptp_fun_Y_56(iV8467)))))))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[334, 333])).
% 0.21/0.46 tff(336,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[335, 329, 316])).
% 0.21/0.46 tff(337,plain,(~((~(cC8(iV8467) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(iV8467, Y))))) | (~((~cC8(iV8467)) | (~((~cC6xcomp(tptp_fun_Y_56(iV8467))) | (~rR1(iV8467, tptp_fun_Y_56(iV8467))))))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.47 tff(338,plain,
% 0.21/0.47 (((~(cC8(iV8467) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(iV8467, Y))))) | (~((~cC8(iV8467)) | (~((~cC6xcomp(tptp_fun_Y_56(iV8467))) | (~rR1(iV8467, tptp_fun_Y_56(iV8467)))))))) | (cC8(iV8467) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(iV8467, Y))))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(339,plain,
% 0.21/0.47 (cC8(iV8467) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(iV8467, Y)))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[338, 337])).
% 0.21/0.47 tff(340,assumption,(![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(iV8467, Y)))), introduced(assumption)).
% 0.21/0.47 tff(341,plain,
% 0.21/0.47 (cC6xcomp(iV8469) <=> cC6xcomp(iV8469)),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(342,axiom,(cC6xcomp(iV8469)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_113')).
% 0.21/0.47 tff(343,plain,
% 0.21/0.47 (cC6xcomp(iV8469)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[342, 341])).
% 0.21/0.47 tff(344,plain,
% 0.21/0.47 (rR1(iV8467, iV8469) <=> rR1(iV8467, iV8469)),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(345,axiom,(rR1(iV8467, iV8469)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_105')).
% 0.21/0.47 tff(346,plain,
% 0.21/0.47 (rR1(iV8467, iV8469)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[345, 344])).
% 0.21/0.47 tff(347,plain,
% 0.21/0.47 (((~![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(iV8467, Y)))) | ((~cC6xcomp(iV8469)) | (~rR1(iV8467, iV8469)))) <=> ((~![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(iV8467, Y)))) | (~cC6xcomp(iV8469)) | (~rR1(iV8467, iV8469)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(348,plain,
% 0.21/0.47 ((~![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(iV8467, Y)))) | ((~cC6xcomp(iV8469)) | (~rR1(iV8467, iV8469)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(349,plain,
% 0.21/0.47 ((~![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(iV8467, Y)))) | (~cC6xcomp(iV8469)) | (~rR1(iV8467, iV8469))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[348, 347])).
% 0.21/0.47 tff(350,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[349, 346, 343, 340])).
% 0.21/0.47 tff(351,plain,(~![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(iV8467, Y)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.47 tff(352,plain,
% 0.21/0.47 ((~(cC8(iV8467) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(iV8467, Y))))) | cC8(iV8467) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(iV8467, Y)))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(353,plain,
% 0.21/0.47 ((~(cC8(iV8467) | ![Y: $i] : ((~cC6xcomp(Y)) | (~rR1(iV8467, Y))))) | cC8(iV8467)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[352, 351])).
% 0.21/0.47 tff(354,plain,
% 0.21/0.47 (cC8(iV8467)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[353, 339])).
% 0.21/0.47 tff(355,assumption,((~((~cC20(iV8467)) | (~((~cC2xcomp(tptp_fun_Y_9(iV8467))) | (~rR1(iV8467, tptp_fun_Y_9(iV8467))))))) | (~(cC20(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y)))))), introduced(assumption)).
% 0.21/0.47 tff(356,plain,
% 0.21/0.47 (^[X: $i] : refl((~((~((~cC20(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC20(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))))) <=> (~((~((~cC20(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC20(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(357,plain,
% 0.21/0.47 (![X: $i] : (~((~((~cC20(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC20(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC20(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC20(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[356])).
% 0.21/0.47 tff(358,plain,
% 0.21/0.47 (^[X: $i] : rewrite((~((~((~cC20(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC20(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))))) <=> (~((~((~cC20(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC20(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(359,plain,
% 0.21/0.47 (![X: $i] : (~((~((~cC20(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC20(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC20(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC20(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[358])).
% 0.21/0.47 tff(360,plain,
% 0.21/0.47 (![X: $i] : (~((~((~cC20(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC20(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC20(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC20(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[359, 357])).
% 0.21/0.47 tff(361,plain,
% 0.21/0.47 (^[X: $i] : trans(monotonicity(rewrite(((~cC20(X)) | (rR1(X, tptp_fun_Y_9(X)) & cC2xcomp(tptp_fun_Y_9(X)))) <=> ((~cC20(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))), rewrite((cC20(X) | ![Y: $i] : (~(rR1(X, Y) & cC2xcomp(Y)))) <=> (cC20(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))), ((((~cC20(X)) | (rR1(X, tptp_fun_Y_9(X)) & cC2xcomp(tptp_fun_Y_9(X)))) & (cC20(X) | ![Y: $i] : (~(rR1(X, Y) & cC2xcomp(Y))))) <=> (((~cC20(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X)))))) & (cC20(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))))), rewrite((((~cC20(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X)))))) & (cC20(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y))))) <=> (~((~((~cC20(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC20(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))), ((((~cC20(X)) | (rR1(X, tptp_fun_Y_9(X)) & cC2xcomp(tptp_fun_Y_9(X)))) & (cC20(X) | ![Y: $i] : (~(rR1(X, Y) & cC2xcomp(Y))))) <=> (~((~((~cC20(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC20(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(362,plain,
% 0.21/0.47 (![X: $i] : (((~cC20(X)) | (rR1(X, tptp_fun_Y_9(X)) & cC2xcomp(tptp_fun_Y_9(X)))) & (cC20(X) | ![Y: $i] : (~(rR1(X, Y) & cC2xcomp(Y))))) <=> ![X: $i] : (~((~((~cC20(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC20(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[361])).
% 0.21/0.47 tff(363,plain,
% 0.21/0.47 (![X: $i] : (cC20(X) <=> ?[Y: $i] : (rR1(X, Y) & cC2xcomp(Y))) <=> ![X: $i] : (cC20(X) <=> ?[Y: $i] : (rR1(X, Y) & cC2xcomp(Y)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(364,axiom,(![X: $i] : (cC20(X) <=> ?[Y: $i] : (rR1(X, Y) & cC2xcomp(Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_13')).
% 0.21/0.47 tff(365,plain,
% 0.21/0.47 (![X: $i] : (cC20(X) <=> ?[Y: $i] : (rR1(X, Y) & cC2xcomp(Y)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[364, 363])).
% 0.21/0.47 tff(366,plain,(
% 0.21/0.47 ![X: $i] : (((~cC20(X)) | (rR1(X, tptp_fun_Y_9(X)) & cC2xcomp(tptp_fun_Y_9(X)))) & (cC20(X) | ![Y: $i] : (~(rR1(X, Y) & cC2xcomp(Y)))))),
% 0.21/0.47 inference(skolemize,[status(sab)],[365])).
% 0.21/0.47 tff(367,plain,
% 0.21/0.47 (![X: $i] : (~((~((~cC20(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC20(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[366, 362])).
% 0.21/0.47 tff(368,plain,
% 0.21/0.47 (![X: $i] : (~((~((~cC20(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC20(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[367, 360])).
% 0.21/0.47 tff(369,plain,
% 0.21/0.47 (((~![X: $i] : (~((~((~cC20(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC20(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))) | (~((~((~cC20(iV8467)) | (~((~cC2xcomp(tptp_fun_Y_9(iV8467))) | (~rR1(iV8467, tptp_fun_Y_9(iV8467))))))) | (~(cC20(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y)))))))) <=> ((~![X: $i] : (~((~((~cC20(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC20(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))) | (~((~((~cC20(iV8467)) | (~((~cC2xcomp(tptp_fun_Y_9(iV8467))) | (~rR1(iV8467, tptp_fun_Y_9(iV8467))))))) | (~(cC20(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y))))))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(370,plain,
% 0.21/0.47 ((~((~((~cC20(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_9(iV8467))) | (~cC2xcomp(tptp_fun_Y_9(iV8467))))))) | (~(cC20(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y))))))) <=> (~((~((~cC20(iV8467)) | (~((~cC2xcomp(tptp_fun_Y_9(iV8467))) | (~rR1(iV8467, tptp_fun_Y_9(iV8467))))))) | (~(cC20(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y)))))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(371,plain,
% 0.21/0.47 (((~![X: $i] : (~((~((~cC20(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC20(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))) | (~((~((~cC20(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_9(iV8467))) | (~cC2xcomp(tptp_fun_Y_9(iV8467))))))) | (~(cC20(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y)))))))) <=> ((~![X: $i] : (~((~((~cC20(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC20(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))) | (~((~((~cC20(iV8467)) | (~((~cC2xcomp(tptp_fun_Y_9(iV8467))) | (~rR1(iV8467, tptp_fun_Y_9(iV8467))))))) | (~(cC20(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y))))))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[370])).
% 0.21/0.47 tff(372,plain,
% 0.21/0.47 (((~![X: $i] : (~((~((~cC20(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC20(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))) | (~((~((~cC20(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_9(iV8467))) | (~cC2xcomp(tptp_fun_Y_9(iV8467))))))) | (~(cC20(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y)))))))) <=> ((~![X: $i] : (~((~((~cC20(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC20(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))) | (~((~((~cC20(iV8467)) | (~((~cC2xcomp(tptp_fun_Y_9(iV8467))) | (~rR1(iV8467, tptp_fun_Y_9(iV8467))))))) | (~(cC20(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y))))))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[371, 369])).
% 0.21/0.47 tff(373,plain,
% 0.21/0.47 ((~![X: $i] : (~((~((~cC20(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC20(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))) | (~((~((~cC20(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_9(iV8467))) | (~cC2xcomp(tptp_fun_Y_9(iV8467))))))) | (~(cC20(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y)))))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(374,plain,
% 0.21/0.47 ((~![X: $i] : (~((~((~cC20(X)) | (~((~rR1(X, tptp_fun_Y_9(X))) | (~cC2xcomp(tptp_fun_Y_9(X))))))) | (~(cC20(X) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(X, Y)))))))) | (~((~((~cC20(iV8467)) | (~((~cC2xcomp(tptp_fun_Y_9(iV8467))) | (~rR1(iV8467, tptp_fun_Y_9(iV8467))))))) | (~(cC20(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y)))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[373, 372])).
% 0.21/0.47 tff(375,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[374, 368, 355])).
% 0.21/0.47 tff(376,plain,(~((~((~cC20(iV8467)) | (~((~cC2xcomp(tptp_fun_Y_9(iV8467))) | (~rR1(iV8467, tptp_fun_Y_9(iV8467))))))) | (~(cC20(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y))))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.47 tff(377,plain,
% 0.21/0.47 (((~((~cC20(iV8467)) | (~((~cC2xcomp(tptp_fun_Y_9(iV8467))) | (~rR1(iV8467, tptp_fun_Y_9(iV8467))))))) | (~(cC20(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y)))))) | (cC20(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y))))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(378,plain,
% 0.21/0.47 (cC20(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y)))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[377, 376])).
% 0.21/0.47 tff(379,plain,
% 0.21/0.47 ((~(cC20(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y))))) | cC20(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y)))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(380,plain,
% 0.21/0.47 ((~(cC20(iV8467) | ![Y: $i] : ((~cC2xcomp(Y)) | (~rR1(iV8467, Y))))) | cC20(iV8467)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[379, 112])).
% 0.21/0.47 tff(381,plain,
% 0.21/0.47 (cC20(iV8467)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[380, 378])).
% 0.21/0.47 tff(382,plain,
% 0.21/0.47 ((cowlNothing(X!69) | (~cowlThing(X!69))) | (~cowlNothing(X!69))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(383,plain,
% 0.21/0.47 (~cowlNothing(X!69)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[382, 14])).
% 0.21/0.47 tff(384,assumption,(((~cC4(iV8467)) | (~cC8(iV8467))) <=> cC10(iV8467)), introduced(assumption)).
% 0.21/0.47 tff(385,plain,
% 0.21/0.47 (^[X: $i] : refl((~(((~cC4(X)) | (~cC8(X))) <=> cC10(X))) <=> (~(((~cC4(X)) | (~cC8(X))) <=> cC10(X))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(386,plain,
% 0.21/0.47 (![X: $i] : (~(((~cC4(X)) | (~cC8(X))) <=> cC10(X))) <=> ![X: $i] : (~(((~cC4(X)) | (~cC8(X))) <=> cC10(X)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[385])).
% 0.21/0.47 tff(387,plain,
% 0.21/0.47 (^[X: $i] : trans(trans(monotonicity(rewrite((cC4(X) & cC8(X)) <=> (~((~cC4(X)) | (~cC8(X))))), ((cC10(X) <=> (cC4(X) & cC8(X))) <=> (cC10(X) <=> (~((~cC4(X)) | (~cC8(X))))))), rewrite((cC10(X) <=> (~((~cC4(X)) | (~cC8(X))))) <=> (~(((~cC4(X)) | (~cC8(X))) <=> cC10(X)))), ((cC10(X) <=> (cC4(X) & cC8(X))) <=> (~(((~cC4(X)) | (~cC8(X))) <=> cC10(X))))), rewrite((~(((~cC4(X)) | (~cC8(X))) <=> cC10(X))) <=> (~(((~cC4(X)) | (~cC8(X))) <=> cC10(X)))), ((cC10(X) <=> (cC4(X) & cC8(X))) <=> (~(((~cC4(X)) | (~cC8(X))) <=> cC10(X)))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(388,plain,
% 0.21/0.47 (![X: $i] : (cC10(X) <=> (cC4(X) & cC8(X))) <=> ![X: $i] : (~(((~cC4(X)) | (~cC8(X))) <=> cC10(X)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[387])).
% 0.21/0.47 tff(389,plain,
% 0.21/0.47 (![X: $i] : (cC10(X) <=> (cC4(X) & cC8(X))) <=> ![X: $i] : (cC10(X) <=> (cC4(X) & cC8(X)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(390,axiom,(![X: $i] : (cC10(X) <=> (cC4(X) & cC8(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_2')).
% 0.21/0.47 tff(391,plain,
% 0.21/0.47 (![X: $i] : (cC10(X) <=> (cC4(X) & cC8(X)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[390, 389])).
% 0.21/0.47 tff(392,plain,(
% 0.21/0.47 ![X: $i] : (cC10(X) <=> (cC4(X) & cC8(X)))),
% 0.21/0.47 inference(skolemize,[status(sab)],[391])).
% 0.21/0.47 tff(393,plain,
% 0.21/0.47 (![X: $i] : (~(((~cC4(X)) | (~cC8(X))) <=> cC10(X)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[392, 388])).
% 0.21/0.47 tff(394,plain,
% 0.21/0.47 (![X: $i] : (~(((~cC4(X)) | (~cC8(X))) <=> cC10(X)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[393, 386])).
% 0.21/0.47 tff(395,plain,
% 0.21/0.47 ((~![X: $i] : (~(((~cC4(X)) | (~cC8(X))) <=> cC10(X)))) | (~(((~cC4(iV8467)) | (~cC8(iV8467))) <=> cC10(iV8467)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(396,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[395, 394, 384])).
% 0.21/0.47 tff(397,plain,(~(((~cC4(iV8467)) | (~cC8(iV8467))) <=> cC10(iV8467))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.47 tff(398,plain,
% 0.21/0.47 ((~((~cC4(iV8467)) | (~cC8(iV8467)))) | (~cC4(iV8467)) | (~cC8(iV8467))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(399,plain,
% 0.21/0.47 (~((~cC4(iV8467)) | (~cC8(iV8467)))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[398, 142, 354])).
% 0.21/0.47 tff(400,plain,
% 0.21/0.47 ((((~cC4(iV8467)) | (~cC8(iV8467))) <=> cC10(iV8467)) | ((~cC4(iV8467)) | (~cC8(iV8467))) | cC10(iV8467)),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(401,plain,
% 0.21/0.47 ((((~cC4(iV8467)) | (~cC8(iV8467))) <=> cC10(iV8467)) | cC10(iV8467)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[400, 399])).
% 0.21/0.47 tff(402,plain,
% 0.21/0.47 (cC10(iV8467)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[401, 397])).
% 0.21/0.47 tff(403,plain,
% 0.21/0.47 (cowlThing(iV8472) <=> cowlThing(iV8472)),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(404,axiom,(cowlThing(iV8472)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_123')).
% 0.21/0.47 tff(405,plain,
% 0.21/0.47 (cowlThing(iV8472)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[404, 403])).
% 0.21/0.47 tff(406,plain,
% 0.21/0.47 (cowlThing(iV8471) <=> cowlThing(iV8471)),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(407,axiom,(cowlThing(iV8471)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_120')).
% 0.21/0.47 tff(408,plain,
% 0.21/0.47 (cowlThing(iV8471)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[407, 406])).
% 0.21/0.47 tff(409,plain,
% 0.21/0.47 (cowlThing(iV8467) <=> cowlThing(iV8467)),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(410,axiom,(cowlThing(iV8467)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_102')).
% 0.21/0.47 tff(411,plain,
% 0.21/0.47 (cowlThing(iV8467)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[410, 409])).
% 0.21/0.47 tff(412,plain,
% 0.21/0.47 (((cowlNothing(X!69) | (~cowlThing(X!69))) | (xsd_integer(X!70) <=> xsd_string(X!70)) | (~cC20(iV8467)) | (~cC4(iV8467)) | (~cC8(iV8467)) | (~cC82(iV8467)) | (~cC62(iV8467)) | (~cC14(iV8467)) | (~cC34(iV8467)) | (~cC10(iV8467)) | (~cowlThing(iV8467)) | (~cC48(iV8467)) | (~cowlThing(iV8471)) | (~cC80(iV8471)) | (~cC58(iV8472)) | (~cC60(iV8472)) | (~cowlThing(iV8472))) <=> (cowlNothing(X!69) | (xsd_integer(X!70) <=> xsd_string(X!70)) | (~cC20(iV8467)) | (~cC4(iV8467)) | (~cC8(iV8467)) | (~cC82(iV8467)) | (~cC62(iV8467)) | (~cC14(iV8467)) | (~cC34(iV8467)) | (~cC10(iV8467)) | (~cowlThing(iV8467)) | (~cC48(iV8467)) | (~cowlThing(iV8471)) | (~cC80(iV8471)) | (~cC58(iV8472)) | (~cC60(iV8472)) | (~cowlThing(iV8472)) | (~cowlThing(X!69)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(413,plain,
% 0.21/0.47 ((~(~(cowlNothing(X!69) | (~cowlThing(X!69))))) <=> (cowlNothing(X!69) | (~cowlThing(X!69)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(414,plain,
% 0.21/0.47 ((cowlThing(X!69) & (~cowlNothing(X!69))) <=> (~(cowlNothing(X!69) | (~cowlThing(X!69))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(415,plain,
% 0.21/0.47 ((~(cowlThing(X!69) & (~cowlNothing(X!69)))) <=> (~(~(cowlNothing(X!69) | (~cowlThing(X!69)))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[414])).
% 0.21/0.47 tff(416,plain,
% 0.21/0.47 ((~(cowlThing(X!69) & (~cowlNothing(X!69)))) <=> (cowlNothing(X!69) | (~cowlThing(X!69)))),
% 0.21/0.47 inference(transitivity,[status(thm)],[415, 413])).
% 0.21/0.47 tff(417,plain,
% 0.21/0.47 (((~(cowlThing(X!69) & (~cowlNothing(X!69)))) | (xsd_integer(X!70) <=> xsd_string(X!70)) | (~cC20(iV8467)) | (~cC4(iV8467)) | (~cC8(iV8467)) | (~cC82(iV8467)) | (~cC62(iV8467)) | (~cC14(iV8467)) | (~cC34(iV8467)) | (~cC10(iV8467)) | (~cowlThing(iV8467)) | (~cC48(iV8467)) | (~cowlThing(iV8471)) | (~cC80(iV8471)) | (~cC58(iV8472)) | (~cC60(iV8472)) | (~cowlThing(iV8472))) <=> ((cowlNothing(X!69) | (~cowlThing(X!69))) | (xsd_integer(X!70) <=> xsd_string(X!70)) | (~cC20(iV8467)) | (~cC4(iV8467)) | (~cC8(iV8467)) | (~cC82(iV8467)) | (~cC62(iV8467)) | (~cC14(iV8467)) | (~cC34(iV8467)) | (~cC10(iV8467)) | (~cowlThing(iV8467)) | (~cC48(iV8467)) | (~cowlThing(iV8471)) | (~cC80(iV8471)) | (~cC58(iV8472)) | (~cC60(iV8472)) | (~cowlThing(iV8472)))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[416])).
% 0.21/0.47 tff(418,plain,
% 0.21/0.47 (((~(cowlThing(X!69) & (~cowlNothing(X!69)))) | (xsd_integer(X!70) <=> xsd_string(X!70)) | (~cC20(iV8467)) | (~cC4(iV8467)) | (~cC8(iV8467)) | (~cC82(iV8467)) | (~cC62(iV8467)) | (~cC14(iV8467)) | (~cC34(iV8467)) | (~cC10(iV8467)) | (~cowlThing(iV8467)) | (~cC48(iV8467)) | (~cowlThing(iV8471)) | (~cC80(iV8471)) | (~cC58(iV8472)) | (~cC60(iV8472)) | (~cowlThing(iV8472))) <=> (cowlNothing(X!69) | (xsd_integer(X!70) <=> xsd_string(X!70)) | (~cC20(iV8467)) | (~cC4(iV8467)) | (~cC8(iV8467)) | (~cC82(iV8467)) | (~cC62(iV8467)) | (~cC14(iV8467)) | (~cC34(iV8467)) | (~cC10(iV8467)) | (~cowlThing(iV8467)) | (~cC48(iV8467)) | (~cowlThing(iV8471)) | (~cC80(iV8471)) | (~cC58(iV8472)) | (~cC60(iV8472)) | (~cowlThing(iV8472)) | (~cowlThing(X!69)))),
% 0.21/0.47 inference(transitivity,[status(thm)],[417, 412])).
% 0.21/0.47 tff(419,plain,
% 0.21/0.47 (((~(cowlThing(X!69) & (~cowlNothing(X!69)))) | (xsd_integer(X!70) <=> xsd_string(X!70)) | (~cC20(iV8467)) | (~cC4(iV8467)) | (~cC8(iV8467)) | (~cC82(iV8467)) | (~cC62(iV8467)) | (~cC14(iV8467)) | (~cC34(iV8467)) | (~cC10(iV8467)) | (~cowlThing(iV8467)) | (~cC48(iV8467)) | (~cowlThing(iV8471)) | (~cC80(iV8471)) | (~cC58(iV8472)) | (~cC60(iV8472)) | (~cowlThing(iV8472))) <=> ((~(cowlThing(X!69) & (~cowlNothing(X!69)))) | (xsd_integer(X!70) <=> xsd_string(X!70)) | (~cC20(iV8467)) | (~cC4(iV8467)) | (~cC8(iV8467)) | (~cC82(iV8467)) | (~cC62(iV8467)) | (~cC14(iV8467)) | (~cC34(iV8467)) | (~cC10(iV8467)) | (~cowlThing(iV8467)) | (~cC48(iV8467)) | (~cowlThing(iV8471)) | (~cC80(iV8471)) | (~cC58(iV8472)) | (~cC60(iV8472)) | (~cowlThing(iV8472)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(420,plain,
% 0.21/0.47 ((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & cC20(iV8467) & cC4(iV8467) & cC8(iV8467) & cC82(iV8467) & cC62(iV8467) & cC14(iV8467) & cC34(iV8467) & cC10(iV8467) & cowlThing(iV8467) & cC48(iV8467) & cowlThing(iV8471) & cC80(iV8471) & cC58(iV8472) & cC60(iV8472) & cowlThing(iV8472)) <=> (![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & cC20(iV8467) & cC4(iV8467) & cC8(iV8467) & cC82(iV8467) & cC62(iV8467) & cC14(iV8467) & cC34(iV8467) & cC10(iV8467) & cowlThing(iV8467) & cC48(iV8467) & cowlThing(iV8471) & cC80(iV8471) & cC58(iV8472) & cC60(iV8472) & cowlThing(iV8472))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(421,plain,
% 0.21/0.47 ((~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & cC20(iV8467) & cC4(iV8467) & cC8(iV8467) & cC82(iV8467) & cC62(iV8467) & cC14(iV8467) & cC34(iV8467) & cC10(iV8467) & cowlThing(iV8467) & cC48(iV8467) & cowlThing(iV8471) & cC80(iV8471) & cC58(iV8472) & cC60(iV8472) & cowlThing(iV8472))) <=> (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & cC20(iV8467) & cC4(iV8467) & cC8(iV8467) & cC82(iV8467) & cC62(iV8467) & cC14(iV8467) & cC34(iV8467) & cC10(iV8467) & cowlThing(iV8467) & cC48(iV8467) & cowlThing(iV8471) & cC80(iV8471) & cC58(iV8472) & cC60(iV8472) & cowlThing(iV8472)))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[420])).
% 0.21/0.47 tff(422,plain,
% 0.21/0.47 ((~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & cC20(iV8467) & cC4(iV8467) & cC8(iV8467) & cC82(iV8467) & cC62(iV8467) & cC14(iV8467) & cC34(iV8467) & cC10(iV8467) & cowlThing(iV8467) & cC48(iV8467) & cowlThing(iV8471) & cC80(iV8471) & cC58(iV8472) & cC60(iV8472) & cowlThing(iV8472))) <=> (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & cC20(iV8467) & cC4(iV8467) & cC8(iV8467) & cC82(iV8467) & cC62(iV8467) & cC14(iV8467) & cC34(iV8467) & cC10(iV8467) & cowlThing(iV8467) & cC48(iV8467) & cowlThing(iV8471) & cC80(iV8471) & cC58(iV8472) & cC60(iV8472) & cowlThing(iV8472)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(423,plain,
% 0.21/0.47 ((~((((((((((((((((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X)))) & cC20(iV8467)) & cC4(iV8467)) & cC8(iV8467)) & cC82(iV8467)) & cC62(iV8467)) & cC14(iV8467)) & cC34(iV8467)) & cC10(iV8467)) & cowlThing(iV8467)) & cC48(iV8467)) & cowlThing(iV8471)) & cC80(iV8471)) & cC58(iV8472)) & cC60(iV8472)) & cowlThing(iV8472))) <=> (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & cC20(iV8467) & cC4(iV8467) & cC8(iV8467) & cC82(iV8467) & cC62(iV8467) & cC14(iV8467) & cC34(iV8467) & cC10(iV8467) & cowlThing(iV8467) & cC48(iV8467) & cowlThing(iV8471) & cC80(iV8471) & cC58(iV8472) & cC60(iV8472) & cowlThing(iV8472)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(424,axiom,(~((((((((((((((((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X)))) & cC20(iV8467)) & cC4(iV8467)) & cC8(iV8467)) & cC82(iV8467)) & cC62(iV8467)) & cC14(iV8467)) & cC34(iV8467)) & cC10(iV8467)) & cowlThing(iV8467)) & cC48(iV8467)) & cowlThing(iV8471)) & cC80(iV8471)) & cC58(iV8472)) & cC60(iV8472)) & cowlThing(iV8472))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','the_axiom')).
% 0.21/0.47 tff(425,plain,
% 0.21/0.47 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & cC20(iV8467) & cC4(iV8467) & cC8(iV8467) & cC82(iV8467) & cC62(iV8467) & cC14(iV8467) & cC34(iV8467) & cC10(iV8467) & cowlThing(iV8467) & cC48(iV8467) & cowlThing(iV8471) & cC80(iV8471) & cC58(iV8472) & cC60(iV8472) & cowlThing(iV8472))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[424, 423])).
% 0.21/0.47 tff(426,plain,
% 0.21/0.47 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & cC20(iV8467) & cC4(iV8467) & cC8(iV8467) & cC82(iV8467) & cC62(iV8467) & cC14(iV8467) & cC34(iV8467) & cC10(iV8467) & cowlThing(iV8467) & cC48(iV8467) & cowlThing(iV8471) & cC80(iV8471) & cC58(iV8472) & cC60(iV8472) & cowlThing(iV8472))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[425, 421])).
% 0.21/0.47 tff(427,plain,
% 0.21/0.47 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & cC20(iV8467) & cC4(iV8467) & cC8(iV8467) & cC82(iV8467) & cC62(iV8467) & cC14(iV8467) & cC34(iV8467) & cC10(iV8467) & cowlThing(iV8467) & cC48(iV8467) & cowlThing(iV8471) & cC80(iV8471) & cC58(iV8472) & cC60(iV8472) & cowlThing(iV8472))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[426, 422])).
% 0.21/0.48 tff(428,plain,
% 0.21/0.48 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & cC20(iV8467) & cC4(iV8467) & cC8(iV8467) & cC82(iV8467) & cC62(iV8467) & cC14(iV8467) & cC34(iV8467) & cC10(iV8467) & cowlThing(iV8467) & cC48(iV8467) & cowlThing(iV8471) & cC80(iV8471) & cC58(iV8472) & cC60(iV8472) & cowlThing(iV8472))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[427, 421])).
% 0.21/0.48 unexpected number of arguments: (let ((a!1 (forall ((X $i)) (and (cowlThing X) (not (cowlNothing X)))))
% 0.21/0.48 (a!2 (not (and (cowlThing X!69) (not (cowlNothing X!69)))))
% 0.21/0.48 (a!3 (forall ((X $i)) (not (= (xsd_integer X) (xsd_string X)))))
% 0.21/0.48 (a!5 (refl (~ (not (cC20 iV8467)) (not (cC20 iV8467)))))
% 0.21/0.48 (a!6 (refl (~ (not (cC4 iV8467)) (not (cC4 iV8467)))))
% 0.21/0.48 (a!7 (refl (~ (not (cC8 iV8467)) (not (cC8 iV8467)))))
% 0.21/0.48 (a!8 (refl (~ (not (cC82 iV8467)) (not (cC82 iV8467)))))
% 0.21/0.48 (a!9 (refl (~ (not (cC62 iV8467)) (not (cC62 iV8467)))))
% 0.21/0.48 (a!10 (refl (~ (not (cC14 iV8467)) (not (cC14 iV8467)))))
% 0.21/0.48 (a!11 (refl (~ (not (cC34 iV8467)) (not (cC34 iV8467)))))
% 0.21/0.48 (a!12 (refl (~ (not (cC10 iV8467)) (not (cC10 iV8467)))))
% 0.21/0.48 (a!13 (refl (~ (not (cowlThing iV8467)) (not (cowlThing iV8467)))))
% 0.21/0.48 (a!14 (refl (~ (not (cC48 iV8467)) (not (cC48 iV8467)))))
% 0.21/0.48 (a!15 (refl (~ (not (cowlThing iV8471)) (not (cowlThing iV8471)))))
% 0.21/0.48 (a!16 (refl (~ (not (cC80 iV8471)) (not (cC80 iV8471)))))
% 0.21/0.48 (a!17 (refl (~ (not (cC58 iV8472)) (not (cC58 iV8472)))))
% 0.21/0.48 (a!18 (refl (~ (not (cC60 iV8472)) (not (cC60 iV8472)))))
% 0.21/0.48 (a!19 (refl (~ (not (cowlThing iV8472)) (not (cowlThing iV8472))))))
% 0.21/0.48 (let ((a!4 (sk (~ (not a!3) (= (xsd_integer X!70) (xsd_string X!70)))))
% 0.21/0.48 (a!20 (~ (not (and a!1
% 0.21/0.48 a!3
% 0.21/0.48 (cC20 iV8467)
% 0.21/0.48 (cC4 iV8467)
% 0.21/0.48 (cC8 iV8467)
% 0.21/0.48 (cC82 iV8467)
% 0.21/0.48 (cC62 iV8467)
% 0.21/0.48 (cC14 iV8467)
% 0.21/0.48 (cC34 iV8467)
% 0.21/0.48 (cC10 iV8467)
% 0.21/0.48 (cowlThing iV8467)
% 0.21/0.48 (cC48 iV8467)
% 0.21/0.48 (cowlThing iV8471)
% 0.21/0.48 (cC80 iV8471)
% 0.21/0.48 (cC58 iV8472)
% 0.21/0.48 (cC60 iV8472)
% 0.21/0.48 (cowlThing iV8472)))
% 0.21/0.48 (or a!2
% 0.21/0.48 (= (xsd_integer X!70) (xsd_string X!70))
% 0.21/0.48 (not (cC20 iV8467))
% 0.21/0.48 (not (cC4 iV8467))
% 0.21/0.48 (not (cC8 iV8467))
% 0.21/0.48 (not (cC82 iV8467))
% 0.21/0.48 (not (cC62 iV8467))
% 0.21/0.48 (not (cC14 iV8467))
% 0.21/0.48 (not (cC34 iV8467))
% 0.21/0.48 (not (cC10 iV8467))
% 0.21/0.48 (not (cowlThing iV8467))
% 0.21/0.48 (not (cC48 iV8467))
% 0.21/0.48 (not (cowlThing iV8471))
% 0.21/0.48 (not (cC80 iV8471))
% 0.21/0.48 (not (cC58 iV8472))
% 0.21/0.48 (not (cC60 iV8472))
% 0.21/0.48 (not (cowlThing iV8472))))))
% 0.21/0.48 (nnf-neg (sk (~ (not a!1) a!2))
% 0.21/0.48 a!4
% 0.21/0.48 a!5
% 0.21/0.48 a!6
% 0.21/0.48 a!7
% 0.21/0.48 a!8
% 0.21/0.48 a!9
% 0.21/0.48 a!10
% 0.21/0.48 a!11
% 0.21/0.48 a!12
% 0.21/0.48 a!13
% 0.21/0.48 a!14
% 0.21/0.48 a!15
% 0.21/0.48 a!16
% 0.21/0.48 a!17
% 0.21/0.48 a!18
% 0.21/0.48 a!19
% 0.21/0.48 a!20)))
% 0.21/0.48 Proof display could not be completed: unexpected number of arguments
% 0.21/0.48 % E exiting
%------------------------------------------------------------------------------