%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS147+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 0.23s 0.43s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : KRS147+1 : TPTP v9.0.0. Released v3.1.0.
% 0.04/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n016.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Jun 19 19:12:02 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.23/0.43 % SZS status Theorem
% 0.23/0.43 % SZS output start Proof
% 0.23/0.43 tff(rR1_type, type, (
% 0.23/0.43 rR1: ( $i * $i ) > $o)).
% 0.23/0.43 tff(tptp_fun_Y_3_type, type, (
% 0.23/0.43 tptp_fun_Y_3: $i > $i)).
% 0.23/0.43 tff(iV8467_type, type, (
% 0.23/0.43 iV8467: $i)).
% 0.23/0.43 tff(cC2_type, type, (
% 0.23/0.43 cC2: $i > $o)).
% 0.23/0.43 tff(cC48_type, type, (
% 0.23/0.43 cC48: $i > $o)).
% 0.23/0.43 tff(iV8468_type, type, (
% 0.23/0.43 iV8468: $i)).
% 0.23/0.43 tff(cC14_type, type, (
% 0.23/0.43 cC14: $i > $o)).
% 0.23/0.43 tff(cTOP_type, type, (
% 0.23/0.43 cTOP: $i > $o)).
% 0.23/0.43 tff(tptp_fun_Y_1_type, type, (
% 0.23/0.43 tptp_fun_Y_1: $i > $i)).
% 0.23/0.43 tff(iV8470_type, type, (
% 0.23/0.43 iV8470: $i)).
% 0.23/0.43 tff(cowlThing_type, type, (
% 0.23/0.43 cowlThing: $i > $o)).
% 0.23/0.43 tff(tptp_fun_X_21_type, type, (
% 0.23/0.43 tptp_fun_X_21: $i)).
% 0.23/0.43 tff(cowlNothing_type, type, (
% 0.23/0.43 cowlNothing: $i > $o)).
% 0.23/0.43 tff(cC58_type, type, (
% 0.23/0.43 cC58: $i > $o)).
% 0.23/0.43 tff(iV8472_type, type, (
% 0.23/0.43 iV8472: $i)).
% 0.23/0.43 tff(tptp_fun_Y_6_type, type, (
% 0.23/0.43 tptp_fun_Y_6: $i > $i)).
% 0.23/0.43 tff(iV8476_type, type, (
% 0.23/0.43 iV8476: $i)).
% 0.23/0.43 tff(cC60_type, type, (
% 0.23/0.43 cC60: $i > $o)).
% 0.23/0.43 tff(cC34_type, type, (
% 0.23/0.43 cC34: $i > $o)).
% 0.23/0.43 tff(cC32_type, type, (
% 0.23/0.43 cC32: $i > $o)).
% 0.23/0.43 tff(tptp_fun_Y_7_type, type, (
% 0.23/0.43 tptp_fun_Y_7: $i > $i)).
% 0.23/0.43 tff(iV8474_type, type, (
% 0.23/0.43 iV8474: $i)).
% 0.23/0.43 tff(cC62_type, type, (
% 0.23/0.43 cC62: $i > $o)).
% 0.23/0.43 tff(tptp_fun_Y_12_type, type, (
% 0.23/0.43 tptp_fun_Y_12: $i > $i)).
% 0.23/0.43 tff(cC20_type, type, (
% 0.23/0.43 cC20: $i > $o)).
% 0.23/0.43 tff(cC8_type, type, (
% 0.23/0.43 cC8: $i > $o)).
% 0.23/0.43 tff(cC6_type, type, (
% 0.23/0.43 cC6: $i > $o)).
% 0.23/0.43 tff(tptp_fun_Y_16_type, type, (
% 0.23/0.43 tptp_fun_Y_16: $i > $i)).
% 0.23/0.43 tff(iV8469_type, type, (
% 0.23/0.43 iV8469: $i)).
% 0.23/0.43 tff(cC82_type, type, (
% 0.23/0.43 cC82: $i > $o)).
% 0.23/0.43 tff(cC80_type, type, (
% 0.23/0.43 cC80: $i > $o)).
% 0.23/0.43 tff(tptp_fun_Y_17_type, type, (
% 0.23/0.43 tptp_fun_Y_17: $i > $i)).
% 0.23/0.43 tff(iV8471_type, type, (
% 0.23/0.43 iV8471: $i)).
% 0.23/0.43 tff(cC78_type, type, (
% 0.23/0.43 cC78: $i > $o)).
% 0.23/0.43 tff(xsd_string_type, type, (
% 0.23/0.43 xsd_string: $i > $o)).
% 0.23/0.43 tff(tptp_fun_X_22_type, type, (
% 0.23/0.43 tptp_fun_X_22: $i)).
% 0.23/0.43 tff(xsd_integer_type, type, (
% 0.23/0.43 xsd_integer: $i > $o)).
% 0.23/0.43 tff(cC4_type, type, (
% 0.23/0.43 cC4: $i > $o)).
% 0.23/0.43 tff(cC10_type, type, (
% 0.23/0.43 cC10: $i > $o)).
% 0.23/0.43 tff(1,assumption,(![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y)))), introduced(assumption)).
% 0.23/0.43 tff(2,plain,
% 0.23/0.43 ((~cC2(iV8468)) <=> (~cC2(iV8468))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(3,axiom,(~cC2(iV8468)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_63')).
% 0.23/0.43 tff(4,plain,
% 0.23/0.43 (~cC2(iV8468)),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.23/0.43 tff(5,plain,
% 0.23/0.43 (rR1(iV8467, iV8468) <=> rR1(iV8467, iV8468)),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(6,axiom,(rR1(iV8467, iV8468)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_57')).
% 0.23/0.43 tff(7,plain,
% 0.23/0.43 (rR1(iV8467, iV8468)),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.23/0.43 tff(8,plain,
% 0.23/0.43 (((~![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y)))) | (cC2(iV8468) | (~rR1(iV8467, iV8468)))) <=> ((~![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y)))) | cC2(iV8468) | (~rR1(iV8467, iV8468)))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(9,plain,
% 0.23/0.43 ((~![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y)))) | (cC2(iV8468) | (~rR1(iV8467, iV8468)))),
% 0.23/0.43 inference(quant_inst,[status(thm)],[])).
% 0.23/0.43 tff(10,plain,
% 0.23/0.43 ((~![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y)))) | cC2(iV8468) | (~rR1(iV8467, iV8468))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.23/0.43 tff(11,plain,
% 0.23/0.43 ($false),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[10, 7, 4, 1])).
% 0.23/0.43 tff(12,plain,(~![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y)))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.43 tff(13,assumption,((~(cC14(iV8467) | ![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y))))) | (~((~cC14(iV8467)) | (~((~cTOP(tptp_fun_Y_1(iV8467))) | (~rR1(iV8467, tptp_fun_Y_1(iV8467)))))))), introduced(assumption)).
% 0.23/0.43 tff(14,plain,
% 0.23/0.43 (^[X: $i] : refl((~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_1(X))) | (~cTOP(tptp_fun_Y_1(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y))))))) <=> (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_1(X))) | (~cTOP(tptp_fun_Y_1(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y))))))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(15,plain,
% 0.23/0.43 (![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_1(X))) | (~cTOP(tptp_fun_Y_1(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y))))))) <=> ![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_1(X))) | (~cTOP(tptp_fun_Y_1(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[14])).
% 0.23/0.43 tff(16,plain,
% 0.23/0.43 (^[X: $i] : rewrite((~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_1(X))) | (~cTOP(tptp_fun_Y_1(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y))))))) <=> (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_1(X))) | (~cTOP(tptp_fun_Y_1(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y))))))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(17,plain,
% 0.23/0.43 (![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_1(X))) | (~cTOP(tptp_fun_Y_1(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y))))))) <=> ![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_1(X))) | (~cTOP(tptp_fun_Y_1(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[16])).
% 0.23/0.43 tff(18,plain,
% 0.23/0.43 (![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_1(X))) | (~cTOP(tptp_fun_Y_1(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y))))))) <=> ![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_1(X))) | (~cTOP(tptp_fun_Y_1(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))),
% 0.23/0.43 inference(transitivity,[status(thm)],[17, 15])).
% 0.23/0.43 tff(19,plain,
% 0.23/0.43 (^[X: $i] : trans(monotonicity(rewrite(((~cC14(X)) | (rR1(X, tptp_fun_Y_1(X)) & cTOP(tptp_fun_Y_1(X)))) <=> ((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_1(X))) | (~cTOP(tptp_fun_Y_1(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_1(X)) & cTOP(tptp_fun_Y_1(X)))) & (cC14(X) | ![Y: $i] : (~(rR1(X, Y) & cTOP(Y))))) <=> (((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_1(X))) | (~cTOP(tptp_fun_Y_1(X)))))) & (cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y))))))), rewrite((((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_1(X))) | (~cTOP(tptp_fun_Y_1(X)))))) & (cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y))))) <=> (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_1(X))) | (~cTOP(tptp_fun_Y_1(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))), ((((~cC14(X)) | (rR1(X, tptp_fun_Y_1(X)) & cTOP(tptp_fun_Y_1(X)))) & (cC14(X) | ![Y: $i] : (~(rR1(X, Y) & cTOP(Y))))) <=> (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_1(X))) | (~cTOP(tptp_fun_Y_1(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(20,plain,
% 0.23/0.43 (![X: $i] : (((~cC14(X)) | (rR1(X, tptp_fun_Y_1(X)) & cTOP(tptp_fun_Y_1(X)))) & (cC14(X) | ![Y: $i] : (~(rR1(X, Y) & cTOP(Y))))) <=> ![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_1(X))) | (~cTOP(tptp_fun_Y_1(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[19])).
% 0.23/0.43 tff(21,plain,
% 0.23/0.43 (![X: $i] : (cC14(X) <=> ?[Y: $i] : (rR1(X, Y) & cTOP(Y))) <=> ![X: $i] : (cC14(X) <=> ?[Y: $i] : (rR1(X, Y) & cTOP(Y)))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(22,axiom,(![X: $i] : (cC14(X) <=> ?[Y: $i] : (rR1(X, Y) & cTOP(Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_4')).
% 0.23/0.43 tff(23,plain,
% 0.23/0.43 (![X: $i] : (cC14(X) <=> ?[Y: $i] : (rR1(X, Y) & cTOP(Y)))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.23/0.43 tff(24,plain,(
% 0.23/0.43 ![X: $i] : (((~cC14(X)) | (rR1(X, tptp_fun_Y_1(X)) & cTOP(tptp_fun_Y_1(X)))) & (cC14(X) | ![Y: $i] : (~(rR1(X, Y) & cTOP(Y)))))),
% 0.23/0.43 inference(skolemize,[status(sab)],[23])).
% 0.23/0.43 tff(25,plain,
% 0.23/0.43 (![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_1(X))) | (~cTOP(tptp_fun_Y_1(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.23/0.43 tff(26,plain,
% 0.23/0.43 (![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_1(X))) | (~cTOP(tptp_fun_Y_1(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.23/0.43 tff(27,plain,
% 0.23/0.43 (((~![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_1(X))) | (~cTOP(tptp_fun_Y_1(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_1(iV8467))) | (~rR1(iV8467, tptp_fun_Y_1(iV8467)))))))))) <=> ((~![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_1(X))) | (~cTOP(tptp_fun_Y_1(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_1(iV8467))) | (~rR1(iV8467, tptp_fun_Y_1(iV8467))))))))))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(28,plain,
% 0.23/0.44 ((~((~((~cC14(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_1(iV8467))) | (~cTOP(tptp_fun_Y_1(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_1(iV8467))) | (~rR1(iV8467, tptp_fun_Y_1(iV8467)))))))))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(29,plain,
% 0.23/0.44 (((~![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_1(X))) | (~cTOP(tptp_fun_Y_1(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))) | (~((~((~cC14(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_1(iV8467))) | (~cTOP(tptp_fun_Y_1(iV8467))))))) | (~(cC14(iV8467) | ![Y: $i] : ((~rR1(iV8467, Y)) | (~cTOP(Y)))))))) <=> ((~![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_1(X))) | (~cTOP(tptp_fun_Y_1(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_1(iV8467))) | (~rR1(iV8467, tptp_fun_Y_1(iV8467))))))))))),
% 0.23/0.44 inference(monotonicity,[status(thm)],[28])).
% 0.23/0.44 tff(30,plain,
% 0.23/0.44 (((~![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_1(X))) | (~cTOP(tptp_fun_Y_1(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))) | (~((~((~cC14(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_1(iV8467))) | (~cTOP(tptp_fun_Y_1(iV8467))))))) | (~(cC14(iV8467) | ![Y: $i] : ((~rR1(iV8467, Y)) | (~cTOP(Y)))))))) <=> ((~![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_1(X))) | (~cTOP(tptp_fun_Y_1(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_1(iV8467))) | (~rR1(iV8467, tptp_fun_Y_1(iV8467))))))))))),
% 0.23/0.44 inference(transitivity,[status(thm)],[29, 27])).
% 0.23/0.44 tff(31,plain,
% 0.23/0.44 ((~![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_1(X))) | (~cTOP(tptp_fun_Y_1(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))) | (~((~((~cC14(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_1(iV8467))) | (~cTOP(tptp_fun_Y_1(iV8467))))))) | (~(cC14(iV8467) | ![Y: $i] : ((~rR1(iV8467, Y)) | (~cTOP(Y)))))))),
% 0.23/0.44 inference(quant_inst,[status(thm)],[])).
% 0.23/0.44 tff(32,plain,
% 0.23/0.44 ((~![X: $i] : (~((~((~cC14(X)) | (~((~rR1(X, tptp_fun_Y_1(X))) | (~cTOP(tptp_fun_Y_1(X))))))) | (~(cC14(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cTOP(Y)))))))) | (~((~(cC14(iV8467) | ![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y))))) | (~((~cC14(iV8467)) | (~((~cTOP(tptp_fun_Y_1(iV8467))) | (~rR1(iV8467, tptp_fun_Y_1(iV8467)))))))))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.23/0.44 tff(33,plain,
% 0.23/0.44 ($false),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[32, 26, 13])).
% 0.23/0.44 tff(34,plain,(~((~(cC14(iV8467) | ![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y))))) | (~((~cC14(iV8467)) | (~((~cTOP(tptp_fun_Y_1(iV8467))) | (~rR1(iV8467, tptp_fun_Y_1(iV8467))))))))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.44 tff(35,plain,
% 0.23/0.44 (((~(cC14(iV8467) | ![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y))))) | (~((~cC14(iV8467)) | (~((~cTOP(tptp_fun_Y_1(iV8467))) | (~rR1(iV8467, tptp_fun_Y_1(iV8467)))))))) | (cC14(iV8467) | ![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y))))),
% 0.23/0.44 inference(tautology,[status(thm)],[])).
% 0.23/0.44 tff(36,plain,
% 0.23/0.44 (cC14(iV8467) | ![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y)))),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.23/0.44 tff(37,assumption,(![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y)))), introduced(assumption)).
% 0.23/0.44 tff(38,plain,
% 0.23/0.44 (cTOP(iV8470) <=> cTOP(iV8470)),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(39,axiom,(cTOP(iV8470)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_68')).
% 0.23/0.44 tff(40,plain,
% 0.23/0.44 (cTOP(iV8470)),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.23/0.44 tff(41,plain,
% 0.23/0.44 (rR1(iV8467, iV8470) <=> rR1(iV8467, iV8470)),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(42,axiom,(rR1(iV8467, iV8470)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_62')).
% 0.23/0.44 tff(43,plain,
% 0.23/0.44 (rR1(iV8467, iV8470)),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.23/0.44 tff(44,plain,
% 0.23/0.44 (((~![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y)))) | ((~cTOP(iV8470)) | (~rR1(iV8467, iV8470)))) <=> ((~![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y)))) | (~cTOP(iV8470)) | (~rR1(iV8467, iV8470)))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(45,plain,
% 0.23/0.44 ((~![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y)))) | ((~cTOP(iV8470)) | (~rR1(iV8467, iV8470)))),
% 0.23/0.44 inference(quant_inst,[status(thm)],[])).
% 0.23/0.44 tff(46,plain,
% 0.23/0.44 ((~![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y)))) | (~cTOP(iV8470)) | (~rR1(iV8467, iV8470))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.23/0.44 tff(47,plain,
% 0.23/0.44 ($false),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[46, 43, 40, 37])).
% 0.23/0.44 tff(48,plain,(~![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y)))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.44 tff(49,plain,
% 0.23/0.44 ((~(cC14(iV8467) | ![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y))))) | cC14(iV8467) | ![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y)))),
% 0.23/0.44 inference(tautology,[status(thm)],[])).
% 0.23/0.44 tff(50,plain,
% 0.23/0.44 ((~(cC14(iV8467) | ![Y: $i] : ((~cTOP(Y)) | (~rR1(iV8467, Y))))) | cC14(iV8467)),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.23/0.44 tff(51,plain,
% 0.23/0.44 (cC14(iV8467)),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[50, 36])).
% 0.23/0.44 tff(52,assumption,(cowlNothing(X!21) | (~cowlThing(X!21))), introduced(assumption)).
% 0.23/0.44 tff(53,plain,
% 0.23/0.44 (^[X: $i] : refl((~(cowlNothing(X) | (~cowlThing(X)))) <=> (~(cowlNothing(X) | (~cowlThing(X)))))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(54,plain,
% 0.23/0.44 (![X: $i] : (~(cowlNothing(X) | (~cowlThing(X)))) <=> ![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[53])).
% 0.23/0.44 tff(55,plain,
% 0.23/0.44 (^[X: $i] : rewrite((cowlThing(X) & (~cowlNothing(X))) <=> (~(cowlNothing(X) | (~cowlThing(X)))))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(56,plain,
% 0.23/0.44 (![X: $i] : (cowlThing(X) & (~cowlNothing(X))) <=> ![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[55])).
% 0.23/0.44 tff(57,plain,
% 0.23/0.44 (![X: $i] : (cowlThing(X) & (~cowlNothing(X))) <=> ![X: $i] : (cowlThing(X) & (~cowlNothing(X)))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(58,axiom,(![X: $i] : (cowlThing(X) & (~cowlNothing(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_0')).
% 0.23/0.44 tff(59,plain,
% 0.23/0.44 (![X: $i] : (cowlThing(X) & (~cowlNothing(X)))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.23/0.44 tff(60,plain,(
% 0.23/0.44 ![X: $i] : (cowlThing(X) & (~cowlNothing(X)))),
% 0.23/0.44 inference(skolemize,[status(sab)],[59])).
% 0.23/0.44 tff(61,plain,
% 0.23/0.44 (![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.23/0.44 tff(62,plain,
% 0.23/0.44 (![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[61, 54])).
% 0.23/0.44 tff(63,plain,
% 0.23/0.44 ((~![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))) | (~(cowlNothing(X!21) | (~cowlThing(X!21))))),
% 0.23/0.44 inference(quant_inst,[status(thm)],[])).
% 0.23/0.44 tff(64,plain,
% 0.23/0.44 ($false),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[63, 62, 52])).
% 0.23/0.44 tff(65,plain,(~(cowlNothing(X!21) | (~cowlThing(X!21)))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.44 tff(66,plain,
% 0.23/0.44 ((cowlNothing(X!21) | (~cowlThing(X!21))) | cowlThing(X!21)),
% 0.23/0.44 inference(tautology,[status(thm)],[])).
% 0.23/0.44 tff(67,plain,
% 0.23/0.44 (cowlThing(X!21)),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.23/0.44 tff(68,assumption,((~(cC58(iV8472) | ![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y))))) | (~((~cC58(iV8472)) | (~((~cC2(tptp_fun_Y_6(iV8472))) | (~rR1(iV8472, tptp_fun_Y_6(iV8472)))))))), introduced(assumption)).
% 0.23/0.44 tff(69,plain,
% 0.23/0.44 (^[X: $i] : refl((~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_6(X))) | (~cC2(tptp_fun_Y_6(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y))))))) <=> (~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_6(X))) | (~cC2(tptp_fun_Y_6(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y))))))))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(70,plain,
% 0.23/0.44 (![X: $i] : (~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_6(X))) | (~cC2(tptp_fun_Y_6(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_6(X))) | (~cC2(tptp_fun_Y_6(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y)))))))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[69])).
% 0.23/0.44 tff(71,plain,
% 0.23/0.44 (^[X: $i] : rewrite((~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_6(X))) | (~cC2(tptp_fun_Y_6(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y))))))) <=> (~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_6(X))) | (~cC2(tptp_fun_Y_6(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y))))))))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(72,plain,
% 0.23/0.44 (![X: $i] : (~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_6(X))) | (~cC2(tptp_fun_Y_6(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_6(X))) | (~cC2(tptp_fun_Y_6(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y)))))))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[71])).
% 0.23/0.44 tff(73,plain,
% 0.23/0.44 (![X: $i] : (~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_6(X))) | (~cC2(tptp_fun_Y_6(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_6(X))) | (~cC2(tptp_fun_Y_6(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y)))))))),
% 0.23/0.44 inference(transitivity,[status(thm)],[72, 70])).
% 0.23/0.44 tff(74,plain,
% 0.23/0.44 (^[X: $i] : trans(monotonicity(rewrite(((~cC58(X)) | (rR1(X, tptp_fun_Y_6(X)) & cC2(tptp_fun_Y_6(X)))) <=> ((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_6(X))) | (~cC2(tptp_fun_Y_6(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_6(X)) & cC2(tptp_fun_Y_6(X)))) & (cC58(X) | ![Y: $i] : (~(rR1(X, Y) & cC2(Y))))) <=> (((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_6(X))) | (~cC2(tptp_fun_Y_6(X)))))) & (cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y))))))), rewrite((((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_6(X))) | (~cC2(tptp_fun_Y_6(X)))))) & (cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y))))) <=> (~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_6(X))) | (~cC2(tptp_fun_Y_6(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y)))))))), ((((~cC58(X)) | (rR1(X, tptp_fun_Y_6(X)) & cC2(tptp_fun_Y_6(X)))) & (cC58(X) | ![Y: $i] : (~(rR1(X, Y) & cC2(Y))))) <=> (~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_6(X))) | (~cC2(tptp_fun_Y_6(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y)))))))))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(75,plain,
% 0.23/0.44 (![X: $i] : (((~cC58(X)) | (rR1(X, tptp_fun_Y_6(X)) & cC2(tptp_fun_Y_6(X)))) & (cC58(X) | ![Y: $i] : (~(rR1(X, Y) & cC2(Y))))) <=> ![X: $i] : (~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_6(X))) | (~cC2(tptp_fun_Y_6(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y)))))))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[74])).
% 0.23/0.44 tff(76,plain,
% 0.23/0.44 (![X: $i] : (cC58(X) <=> ?[Y: $i] : (rR1(X, Y) & cC2(Y))) <=> ![X: $i] : (cC58(X) <=> ?[Y: $i] : (rR1(X, Y) & cC2(Y)))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(77,axiom,(![X: $i] : (cC58(X) <=> ?[Y: $i] : (rR1(X, Y) & cC2(Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_27')).
% 0.23/0.44 tff(78,plain,
% 0.23/0.44 (![X: $i] : (cC58(X) <=> ?[Y: $i] : (rR1(X, Y) & cC2(Y)))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.23/0.44 tff(79,plain,(
% 0.23/0.44 ![X: $i] : (((~cC58(X)) | (rR1(X, tptp_fun_Y_6(X)) & cC2(tptp_fun_Y_6(X)))) & (cC58(X) | ![Y: $i] : (~(rR1(X, Y) & cC2(Y)))))),
% 0.23/0.44 inference(skolemize,[status(sab)],[78])).
% 0.23/0.44 tff(80,plain,
% 0.23/0.44 (![X: $i] : (~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_6(X))) | (~cC2(tptp_fun_Y_6(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y)))))))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.23/0.44 tff(81,plain,
% 0.23/0.44 (![X: $i] : (~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_6(X))) | (~cC2(tptp_fun_Y_6(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y)))))))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[80, 73])).
% 0.23/0.44 tff(82,plain,
% 0.23/0.44 (((~![X: $i] : (~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_6(X))) | (~cC2(tptp_fun_Y_6(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_6(iV8472))) | (~rR1(iV8472, tptp_fun_Y_6(iV8472)))))))))) <=> ((~![X: $i] : (~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_6(X))) | (~cC2(tptp_fun_Y_6(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_6(iV8472))) | (~rR1(iV8472, tptp_fun_Y_6(iV8472))))))))))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(83,plain,
% 0.23/0.44 ((~((~((~cC58(iV8472)) | (~((~rR1(iV8472, tptp_fun_Y_6(iV8472))) | (~cC2(tptp_fun_Y_6(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_6(iV8472))) | (~rR1(iV8472, tptp_fun_Y_6(iV8472)))))))))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(84,plain,
% 0.23/0.44 (((~![X: $i] : (~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_6(X))) | (~cC2(tptp_fun_Y_6(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y)))))))) | (~((~((~cC58(iV8472)) | (~((~rR1(iV8472, tptp_fun_Y_6(iV8472))) | (~cC2(tptp_fun_Y_6(iV8472))))))) | (~(cC58(iV8472) | ![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y)))))))) <=> ((~![X: $i] : (~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_6(X))) | (~cC2(tptp_fun_Y_6(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_6(iV8472))) | (~rR1(iV8472, tptp_fun_Y_6(iV8472))))))))))),
% 0.23/0.44 inference(monotonicity,[status(thm)],[83])).
% 0.23/0.44 tff(85,plain,
% 0.23/0.44 (((~![X: $i] : (~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_6(X))) | (~cC2(tptp_fun_Y_6(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y)))))))) | (~((~((~cC58(iV8472)) | (~((~rR1(iV8472, tptp_fun_Y_6(iV8472))) | (~cC2(tptp_fun_Y_6(iV8472))))))) | (~(cC58(iV8472) | ![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y)))))))) <=> ((~![X: $i] : (~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_6(X))) | (~cC2(tptp_fun_Y_6(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_6(iV8472))) | (~rR1(iV8472, tptp_fun_Y_6(iV8472))))))))))),
% 0.23/0.44 inference(transitivity,[status(thm)],[84, 82])).
% 0.23/0.44 tff(86,plain,
% 0.23/0.44 ((~![X: $i] : (~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_6(X))) | (~cC2(tptp_fun_Y_6(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y)))))))) | (~((~((~cC58(iV8472)) | (~((~rR1(iV8472, tptp_fun_Y_6(iV8472))) | (~cC2(tptp_fun_Y_6(iV8472))))))) | (~(cC58(iV8472) | ![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y)))))))),
% 0.23/0.44 inference(quant_inst,[status(thm)],[])).
% 0.23/0.44 tff(87,plain,
% 0.23/0.44 ((~![X: $i] : (~((~((~cC58(X)) | (~((~rR1(X, tptp_fun_Y_6(X))) | (~cC2(tptp_fun_Y_6(X))))))) | (~(cC58(X) | ![Y: $i] : ((~cC2(Y)) | (~rR1(X, Y)))))))) | (~((~(cC58(iV8472) | ![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y))))) | (~((~cC58(iV8472)) | (~((~cC2(tptp_fun_Y_6(iV8472))) | (~rR1(iV8472, tptp_fun_Y_6(iV8472)))))))))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.23/0.44 tff(88,plain,
% 0.23/0.44 ($false),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[87, 81, 68])).
% 0.23/0.44 tff(89,plain,(~((~(cC58(iV8472) | ![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y))))) | (~((~cC58(iV8472)) | (~((~cC2(tptp_fun_Y_6(iV8472))) | (~rR1(iV8472, tptp_fun_Y_6(iV8472))))))))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.44 tff(90,plain,
% 0.23/0.44 (((~(cC58(iV8472) | ![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y))))) | (~((~cC58(iV8472)) | (~((~cC2(tptp_fun_Y_6(iV8472))) | (~rR1(iV8472, tptp_fun_Y_6(iV8472)))))))) | (cC58(iV8472) | ![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y))))),
% 0.23/0.44 inference(tautology,[status(thm)],[])).
% 0.23/0.44 tff(91,plain,
% 0.23/0.44 (cC58(iV8472) | ![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y)))),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[90, 89])).
% 0.23/0.44 tff(92,assumption,(![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y)))), introduced(assumption)).
% 0.23/0.44 tff(93,plain,
% 0.23/0.44 (cC2(iV8476) <=> cC2(iV8476)),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(94,axiom,(cC2(iV8476)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_84')).
% 0.23/0.44 tff(95,plain,
% 0.23/0.44 (cC2(iV8476)),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.23/0.44 tff(96,plain,
% 0.23/0.44 (rR1(iV8472, iV8476) <=> rR1(iV8472, iV8476)),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(97,axiom,(rR1(iV8472, iV8476)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_76')).
% 0.23/0.44 tff(98,plain,
% 0.23/0.44 (rR1(iV8472, iV8476)),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.23/0.44 tff(99,plain,
% 0.23/0.44 (((~![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y)))) | ((~cC2(iV8476)) | (~rR1(iV8472, iV8476)))) <=> ((~![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y)))) | (~cC2(iV8476)) | (~rR1(iV8472, iV8476)))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(100,plain,
% 0.23/0.44 ((~![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y)))) | ((~cC2(iV8476)) | (~rR1(iV8472, iV8476)))),
% 0.23/0.44 inference(quant_inst,[status(thm)],[])).
% 0.23/0.44 tff(101,plain,
% 0.23/0.44 ((~![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y)))) | (~cC2(iV8476)) | (~rR1(iV8472, iV8476))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.23/0.44 tff(102,plain,
% 0.23/0.44 ($false),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[101, 98, 95, 92])).
% 0.23/0.44 tff(103,plain,(~![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y)))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.44 tff(104,plain,
% 0.23/0.44 ((~(cC58(iV8472) | ![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y))))) | cC58(iV8472) | ![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y)))),
% 0.23/0.44 inference(tautology,[status(thm)],[])).
% 0.23/0.44 tff(105,plain,
% 0.23/0.44 ((~(cC58(iV8472) | ![Y: $i] : ((~cC2(Y)) | (~rR1(iV8472, Y))))) | cC58(iV8472)),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[104, 103])).
% 0.23/0.44 tff(106,plain,
% 0.23/0.44 (cC58(iV8472)),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[105, 91])).
% 0.23/0.44 tff(107,plain,
% 0.23/0.44 ((~cC2(iV8472)) <=> (~cC2(iV8472))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(108,axiom,(~cC2(iV8472)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_74')).
% 0.23/0.44 tff(109,plain,
% 0.23/0.44 (~cC2(iV8472)),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.23/0.44 tff(110,plain,
% 0.23/0.44 ((~(cC2(iV8472) | (~cC58(iV8472)))) | cC2(iV8472) | (~cC58(iV8472))),
% 0.23/0.44 inference(tautology,[status(thm)],[])).
% 0.23/0.44 tff(111,plain,
% 0.23/0.44 ((~(cC2(iV8472) | (~cC58(iV8472)))) | (~cC58(iV8472))),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.23/0.44 tff(112,plain,
% 0.23/0.44 (~(cC2(iV8472) | (~cC58(iV8472)))),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[111, 106])).
% 0.23/0.44 tff(113,plain,
% 0.23/0.44 (^[X: $i] : refl((~((cC2(X) | (~cC58(X))) <=> cC60(X))) <=> (~((cC2(X) | (~cC58(X))) <=> cC60(X))))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(114,plain,
% 0.23/0.44 (![X: $i] : (~((cC2(X) | (~cC58(X))) <=> cC60(X))) <=> ![X: $i] : (~((cC2(X) | (~cC58(X))) <=> cC60(X)))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[113])).
% 0.23/0.44 tff(115,plain,
% 0.23/0.44 (^[X: $i] : trans(trans(monotonicity(rewrite((cC58(X) & (~cC2(X))) <=> (~(cC2(X) | (~cC58(X))))), ((cC60(X) <=> (cC58(X) & (~cC2(X)))) <=> (cC60(X) <=> (~(cC2(X) | (~cC58(X))))))), rewrite((cC60(X) <=> (~(cC2(X) | (~cC58(X))))) <=> (~((cC2(X) | (~cC58(X))) <=> cC60(X)))), ((cC60(X) <=> (cC58(X) & (~cC2(X)))) <=> (~((cC2(X) | (~cC58(X))) <=> cC60(X))))), rewrite((~((cC2(X) | (~cC58(X))) <=> cC60(X))) <=> (~((cC2(X) | (~cC58(X))) <=> cC60(X)))), ((cC60(X) <=> (cC58(X) & (~cC2(X)))) <=> (~((cC2(X) | (~cC58(X))) <=> cC60(X)))))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(116,plain,
% 0.23/0.44 (![X: $i] : (cC60(X) <=> (cC58(X) & (~cC2(X)))) <=> ![X: $i] : (~((cC2(X) | (~cC58(X))) <=> cC60(X)))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[115])).
% 0.23/0.44 tff(117,plain,
% 0.23/0.44 (![X: $i] : (cC60(X) <=> (cC58(X) & (~cC2(X)))) <=> ![X: $i] : (cC60(X) <=> (cC58(X) & (~cC2(X))))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(118,axiom,(![X: $i] : (cC60(X) <=> (cC58(X) & (~cC2(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_29')).
% 0.23/0.44 tff(119,plain,
% 0.23/0.44 (![X: $i] : (cC60(X) <=> (cC58(X) & (~cC2(X))))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.23/0.45 tff(120,plain,(
% 0.23/0.45 ![X: $i] : (cC60(X) <=> (cC58(X) & (~cC2(X))))),
% 0.23/0.45 inference(skolemize,[status(sab)],[119])).
% 0.23/0.45 tff(121,plain,
% 0.23/0.45 (![X: $i] : (~((cC2(X) | (~cC58(X))) <=> cC60(X)))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[120, 116])).
% 0.23/0.45 tff(122,plain,
% 0.23/0.45 (![X: $i] : (~((cC2(X) | (~cC58(X))) <=> cC60(X)))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[121, 114])).
% 0.23/0.45 tff(123,plain,
% 0.23/0.45 ((~![X: $i] : (~((cC2(X) | (~cC58(X))) <=> cC60(X)))) | (~((cC2(iV8472) | (~cC58(iV8472))) <=> cC60(iV8472)))),
% 0.23/0.45 inference(quant_inst,[status(thm)],[])).
% 0.23/0.45 tff(124,plain,
% 0.23/0.45 (~((cC2(iV8472) | (~cC58(iV8472))) <=> cC60(iV8472))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[123, 122])).
% 0.23/0.45 tff(125,plain,
% 0.23/0.45 (((cC2(iV8472) | (~cC58(iV8472))) <=> cC60(iV8472)) | (cC2(iV8472) | (~cC58(iV8472))) | cC60(iV8472)),
% 0.23/0.45 inference(tautology,[status(thm)],[])).
% 0.23/0.45 tff(126,plain,
% 0.23/0.45 ((cC2(iV8472) | (~cC58(iV8472))) | cC60(iV8472)),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[125, 124])).
% 0.23/0.45 tff(127,plain,
% 0.23/0.45 (cC60(iV8472)),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[126, 112])).
% 0.23/0.45 tff(128,assumption,((~(cC34(iV8467) | ![Y: $i] : (cC32(Y) | (~rR1(iV8467, Y))))) | (~((~cC34(iV8467)) | (~(cC32(tptp_fun_Y_7(iV8467)) | (~rR1(iV8467, tptp_fun_Y_7(iV8467)))))))), introduced(assumption)).
% 0.23/0.45 tff(129,plain,
% 0.23/0.45 (^[X: $i] : refl((~((~((~cC34(X)) | (~(cC32(tptp_fun_Y_7(X)) | (~rR1(X, tptp_fun_Y_7(X))))))) | (~(cC34(X) | ![Y: $i] : (cC32(Y) | (~rR1(X, Y))))))) <=> (~((~((~cC34(X)) | (~(cC32(tptp_fun_Y_7(X)) | (~rR1(X, tptp_fun_Y_7(X))))))) | (~(cC34(X) | ![Y: $i] : (cC32(Y) | (~rR1(X, Y))))))))),
% 0.23/0.45 inference(bind,[status(th)],[])).
% 0.23/0.45 tff(130,plain,
% 0.23/0.45 (![X: $i] : (~((~((~cC34(X)) | (~(cC32(tptp_fun_Y_7(X)) | (~rR1(X, tptp_fun_Y_7(X))))))) | (~(cC34(X) | ![Y: $i] : (cC32(Y) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC34(X)) | (~(cC32(tptp_fun_Y_7(X)) | (~rR1(X, tptp_fun_Y_7(X))))))) | (~(cC34(X) | ![Y: $i] : (cC32(Y) | (~rR1(X, Y)))))))),
% 0.23/0.45 inference(quant_intro,[status(thm)],[129])).
% 0.23/0.45 tff(131,plain,
% 0.23/0.45 (^[X: $i] : rewrite((~((~((~cC34(X)) | (~(cC32(tptp_fun_Y_7(X)) | (~rR1(X, tptp_fun_Y_7(X))))))) | (~(cC34(X) | ![Y: $i] : (cC32(Y) | (~rR1(X, Y))))))) <=> (~((~((~cC34(X)) | (~(cC32(tptp_fun_Y_7(X)) | (~rR1(X, tptp_fun_Y_7(X))))))) | (~(cC34(X) | ![Y: $i] : (cC32(Y) | (~rR1(X, Y))))))))),
% 0.23/0.45 inference(bind,[status(th)],[])).
% 0.23/0.45 tff(132,plain,
% 0.23/0.45 (![X: $i] : (~((~((~cC34(X)) | (~(cC32(tptp_fun_Y_7(X)) | (~rR1(X, tptp_fun_Y_7(X))))))) | (~(cC34(X) | ![Y: $i] : (cC32(Y) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC34(X)) | (~(cC32(tptp_fun_Y_7(X)) | (~rR1(X, tptp_fun_Y_7(X))))))) | (~(cC34(X) | ![Y: $i] : (cC32(Y) | (~rR1(X, Y)))))))),
% 0.23/0.45 inference(quant_intro,[status(thm)],[131])).
% 0.23/0.45 tff(133,plain,
% 0.23/0.45 (![X: $i] : (~((~((~cC34(X)) | (~(cC32(tptp_fun_Y_7(X)) | (~rR1(X, tptp_fun_Y_7(X))))))) | (~(cC34(X) | ![Y: $i] : (cC32(Y) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC34(X)) | (~(cC32(tptp_fun_Y_7(X)) | (~rR1(X, tptp_fun_Y_7(X))))))) | (~(cC34(X) | ![Y: $i] : (cC32(Y) | (~rR1(X, Y)))))))),
% 0.23/0.45 inference(transitivity,[status(thm)],[132, 130])).
% 0.23/0.45 tff(134,plain,
% 0.23/0.45 (^[X: $i] : trans(monotonicity(rewrite(((~cC34(X)) | (rR1(X, tptp_fun_Y_7(X)) & (~cC32(tptp_fun_Y_7(X))))) <=> ((~cC34(X)) | (~(cC32(tptp_fun_Y_7(X)) | (~rR1(X, tptp_fun_Y_7(X))))))), rewrite((cC34(X) | ![Y: $i] : (~(rR1(X, Y) & (~cC32(Y))))) <=> (cC34(X) | ![Y: $i] : (cC32(Y) | (~rR1(X, Y))))), ((((~cC34(X)) | (rR1(X, tptp_fun_Y_7(X)) & (~cC32(tptp_fun_Y_7(X))))) & (cC34(X) | ![Y: $i] : (~(rR1(X, Y) & (~cC32(Y)))))) <=> (((~cC34(X)) | (~(cC32(tptp_fun_Y_7(X)) | (~rR1(X, tptp_fun_Y_7(X)))))) & (cC34(X) | ![Y: $i] : (cC32(Y) | (~rR1(X, Y))))))), rewrite((((~cC34(X)) | (~(cC32(tptp_fun_Y_7(X)) | (~rR1(X, tptp_fun_Y_7(X)))))) & (cC34(X) | ![Y: $i] : (cC32(Y) | (~rR1(X, Y))))) <=> (~((~((~cC34(X)) | (~(cC32(tptp_fun_Y_7(X)) | (~rR1(X, tptp_fun_Y_7(X))))))) | (~(cC34(X) | ![Y: $i] : (cC32(Y) | (~rR1(X, Y)))))))), ((((~cC34(X)) | (rR1(X, tptp_fun_Y_7(X)) & (~cC32(tptp_fun_Y_7(X))))) & (cC34(X) | ![Y: $i] : (~(rR1(X, Y) & (~cC32(Y)))))) <=> (~((~((~cC34(X)) | (~(cC32(tptp_fun_Y_7(X)) | (~rR1(X, tptp_fun_Y_7(X))))))) | (~(cC34(X) | ![Y: $i] : (cC32(Y) | (~rR1(X, Y)))))))))),
% 0.23/0.45 inference(bind,[status(th)],[])).
% 0.23/0.45 tff(135,plain,
% 0.23/0.45 (![X: $i] : (((~cC34(X)) | (rR1(X, tptp_fun_Y_7(X)) & (~cC32(tptp_fun_Y_7(X))))) & (cC34(X) | ![Y: $i] : (~(rR1(X, Y) & (~cC32(Y)))))) <=> ![X: $i] : (~((~((~cC34(X)) | (~(cC32(tptp_fun_Y_7(X)) | (~rR1(X, tptp_fun_Y_7(X))))))) | (~(cC34(X) | ![Y: $i] : (cC32(Y) | (~rR1(X, Y)))))))),
% 0.23/0.45 inference(quant_intro,[status(thm)],[134])).
% 0.23/0.45 tff(136,plain,
% 0.23/0.45 (![X: $i] : (cC34(X) <=> ?[Y: $i] : (rR1(X, Y) & (~cC32(Y)))) <=> ![X: $i] : (cC34(X) <=> ?[Y: $i] : (rR1(X, Y) & (~cC32(Y))))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(137,axiom,(![X: $i] : (cC34(X) <=> ?[Y: $i] : (rR1(X, Y) & (~cC32(Y))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_14')).
% 0.23/0.45 tff(138,plain,
% 0.23/0.45 (![X: $i] : (cC34(X) <=> ?[Y: $i] : (rR1(X, Y) & (~cC32(Y))))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.23/0.45 tff(139,plain,(
% 0.23/0.45 ![X: $i] : (((~cC34(X)) | (rR1(X, tptp_fun_Y_7(X)) & (~cC32(tptp_fun_Y_7(X))))) & (cC34(X) | ![Y: $i] : (~(rR1(X, Y) & (~cC32(Y))))))),
% 0.23/0.45 inference(skolemize,[status(sab)],[138])).
% 0.23/0.45 tff(140,plain,
% 0.23/0.45 (![X: $i] : (~((~((~cC34(X)) | (~(cC32(tptp_fun_Y_7(X)) | (~rR1(X, tptp_fun_Y_7(X))))))) | (~(cC34(X) | ![Y: $i] : (cC32(Y) | (~rR1(X, Y)))))))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[139, 135])).
% 0.23/0.45 tff(141,plain,
% 0.23/0.45 (![X: $i] : (~((~((~cC34(X)) | (~(cC32(tptp_fun_Y_7(X)) | (~rR1(X, tptp_fun_Y_7(X))))))) | (~(cC34(X) | ![Y: $i] : (cC32(Y) | (~rR1(X, Y)))))))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[140, 133])).
% 0.23/0.45 tff(142,plain,
% 0.23/0.45 (((~![X: $i] : (~((~((~cC34(X)) | (~(cC32(tptp_fun_Y_7(X)) | (~rR1(X, tptp_fun_Y_7(X))))))) | (~(cC34(X) | ![Y: $i] : (cC32(Y) | (~rR1(X, Y)))))))) | (~((~(cC34(iV8467) | ![Y: $i] : (cC32(Y) | (~rR1(iV8467, Y))))) | (~((~cC34(iV8467)) | (~(cC32(tptp_fun_Y_7(iV8467)) | (~rR1(iV8467, tptp_fun_Y_7(iV8467)))))))))) <=> ((~![X: $i] : (~((~((~cC34(X)) | (~(cC32(tptp_fun_Y_7(X)) | (~rR1(X, tptp_fun_Y_7(X))))))) | (~(cC34(X) | ![Y: $i] : (cC32(Y) | (~rR1(X, Y)))))))) | (~((~(cC34(iV8467) | ![Y: $i] : (cC32(Y) | (~rR1(iV8467, Y))))) | (~((~cC34(iV8467)) | (~(cC32(tptp_fun_Y_7(iV8467)) | (~rR1(iV8467, tptp_fun_Y_7(iV8467))))))))))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(143,plain,
% 0.23/0.45 ((~((~((~cC34(iV8467)) | (~(cC32(tptp_fun_Y_7(iV8467)) | (~rR1(iV8467, tptp_fun_Y_7(iV8467))))))) | (~(cC34(iV8467) | ![Y: $i] : (cC32(Y) | (~rR1(iV8467, Y))))))) <=> (~((~(cC34(iV8467) | ![Y: $i] : (cC32(Y) | (~rR1(iV8467, Y))))) | (~((~cC34(iV8467)) | (~(cC32(tptp_fun_Y_7(iV8467)) | (~rR1(iV8467, tptp_fun_Y_7(iV8467)))))))))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(144,plain,
% 0.23/0.45 (((~![X: $i] : (~((~((~cC34(X)) | (~(cC32(tptp_fun_Y_7(X)) | (~rR1(X, tptp_fun_Y_7(X))))))) | (~(cC34(X) | ![Y: $i] : (cC32(Y) | (~rR1(X, Y)))))))) | (~((~((~cC34(iV8467)) | (~(cC32(tptp_fun_Y_7(iV8467)) | (~rR1(iV8467, tptp_fun_Y_7(iV8467))))))) | (~(cC34(iV8467) | ![Y: $i] : (cC32(Y) | (~rR1(iV8467, Y)))))))) <=> ((~![X: $i] : (~((~((~cC34(X)) | (~(cC32(tptp_fun_Y_7(X)) | (~rR1(X, tptp_fun_Y_7(X))))))) | (~(cC34(X) | ![Y: $i] : (cC32(Y) | (~rR1(X, Y)))))))) | (~((~(cC34(iV8467) | ![Y: $i] : (cC32(Y) | (~rR1(iV8467, Y))))) | (~((~cC34(iV8467)) | (~(cC32(tptp_fun_Y_7(iV8467)) | (~rR1(iV8467, tptp_fun_Y_7(iV8467))))))))))),
% 0.23/0.45 inference(monotonicity,[status(thm)],[143])).
% 0.23/0.45 tff(145,plain,
% 0.23/0.45 (((~![X: $i] : (~((~((~cC34(X)) | (~(cC32(tptp_fun_Y_7(X)) | (~rR1(X, tptp_fun_Y_7(X))))))) | (~(cC34(X) | ![Y: $i] : (cC32(Y) | (~rR1(X, Y)))))))) | (~((~((~cC34(iV8467)) | (~(cC32(tptp_fun_Y_7(iV8467)) | (~rR1(iV8467, tptp_fun_Y_7(iV8467))))))) | (~(cC34(iV8467) | ![Y: $i] : (cC32(Y) | (~rR1(iV8467, Y)))))))) <=> ((~![X: $i] : (~((~((~cC34(X)) | (~(cC32(tptp_fun_Y_7(X)) | (~rR1(X, tptp_fun_Y_7(X))))))) | (~(cC34(X) | ![Y: $i] : (cC32(Y) | (~rR1(X, Y)))))))) | (~((~(cC34(iV8467) | ![Y: $i] : (cC32(Y) | (~rR1(iV8467, Y))))) | (~((~cC34(iV8467)) | (~(cC32(tptp_fun_Y_7(iV8467)) | (~rR1(iV8467, tptp_fun_Y_7(iV8467))))))))))),
% 0.23/0.45 inference(transitivity,[status(thm)],[144, 142])).
% 0.23/0.45 tff(146,plain,
% 0.23/0.45 ((~![X: $i] : (~((~((~cC34(X)) | (~(cC32(tptp_fun_Y_7(X)) | (~rR1(X, tptp_fun_Y_7(X))))))) | (~(cC34(X) | ![Y: $i] : (cC32(Y) | (~rR1(X, Y)))))))) | (~((~((~cC34(iV8467)) | (~(cC32(tptp_fun_Y_7(iV8467)) | (~rR1(iV8467, tptp_fun_Y_7(iV8467))))))) | (~(cC34(iV8467) | ![Y: $i] : (cC32(Y) | (~rR1(iV8467, Y)))))))),
% 0.23/0.45 inference(quant_inst,[status(thm)],[])).
% 0.23/0.45 tff(147,plain,
% 0.23/0.45 ((~![X: $i] : (~((~((~cC34(X)) | (~(cC32(tptp_fun_Y_7(X)) | (~rR1(X, tptp_fun_Y_7(X))))))) | (~(cC34(X) | ![Y: $i] : (cC32(Y) | (~rR1(X, Y)))))))) | (~((~(cC34(iV8467) | ![Y: $i] : (cC32(Y) | (~rR1(iV8467, Y))))) | (~((~cC34(iV8467)) | (~(cC32(tptp_fun_Y_7(iV8467)) | (~rR1(iV8467, tptp_fun_Y_7(iV8467)))))))))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.23/0.45 tff(148,plain,
% 0.23/0.45 ($false),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[147, 141, 128])).
% 0.23/0.45 tff(149,plain,(~((~(cC34(iV8467) | ![Y: $i] : (cC32(Y) | (~rR1(iV8467, Y))))) | (~((~cC34(iV8467)) | (~(cC32(tptp_fun_Y_7(iV8467)) | (~rR1(iV8467, tptp_fun_Y_7(iV8467))))))))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.45 tff(150,plain,
% 0.23/0.45 (((~(cC34(iV8467) | ![Y: $i] : (cC32(Y) | (~rR1(iV8467, Y))))) | (~((~cC34(iV8467)) | (~(cC32(tptp_fun_Y_7(iV8467)) | (~rR1(iV8467, tptp_fun_Y_7(iV8467)))))))) | (cC34(iV8467) | ![Y: $i] : (cC32(Y) | (~rR1(iV8467, Y))))),
% 0.23/0.45 inference(tautology,[status(thm)],[])).
% 0.23/0.45 tff(151,plain,
% 0.23/0.45 (cC34(iV8467) | ![Y: $i] : (cC32(Y) | (~rR1(iV8467, Y)))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[150, 149])).
% 0.23/0.45 tff(152,assumption,(![Y: $i] : (cC32(Y) | (~rR1(iV8467, Y)))), introduced(assumption)).
% 0.23/0.45 tff(153,plain,
% 0.23/0.45 ((~cC32(iV8474)) <=> (~cC32(iV8474))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(154,axiom,(~cC32(iV8474)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_80')).
% 0.23/0.45 tff(155,plain,
% 0.23/0.45 (~cC32(iV8474)),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.23/0.45 tff(156,plain,
% 0.23/0.45 (rR1(iV8467, iV8474) <=> rR1(iV8467, iV8474)),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(157,axiom,(rR1(iV8467, iV8474)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_61')).
% 0.23/0.45 tff(158,plain,
% 0.23/0.45 (rR1(iV8467, iV8474)),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.23/0.45 tff(159,plain,
% 0.23/0.45 (((~![Y: $i] : (cC32(Y) | (~rR1(iV8467, Y)))) | (cC32(iV8474) | (~rR1(iV8467, iV8474)))) <=> ((~![Y: $i] : (cC32(Y) | (~rR1(iV8467, Y)))) | cC32(iV8474) | (~rR1(iV8467, iV8474)))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(160,plain,
% 0.23/0.45 ((~![Y: $i] : (cC32(Y) | (~rR1(iV8467, Y)))) | (cC32(iV8474) | (~rR1(iV8467, iV8474)))),
% 0.23/0.45 inference(quant_inst,[status(thm)],[])).
% 0.23/0.45 tff(161,plain,
% 0.23/0.45 ((~![Y: $i] : (cC32(Y) | (~rR1(iV8467, Y)))) | cC32(iV8474) | (~rR1(iV8467, iV8474))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.23/0.45 tff(162,plain,
% 0.23/0.45 ($false),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[161, 158, 155, 152])).
% 0.23/0.45 tff(163,plain,(~![Y: $i] : (cC32(Y) | (~rR1(iV8467, Y)))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.45 tff(164,plain,
% 0.23/0.45 ((~(cC34(iV8467) | ![Y: $i] : (cC32(Y) | (~rR1(iV8467, Y))))) | cC34(iV8467) | ![Y: $i] : (cC32(Y) | (~rR1(iV8467, Y)))),
% 0.23/0.45 inference(tautology,[status(thm)],[])).
% 0.23/0.45 tff(165,plain,
% 0.23/0.45 ((~(cC34(iV8467) | ![Y: $i] : (cC32(Y) | (~rR1(iV8467, Y))))) | cC34(iV8467)),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[164, 163])).
% 0.23/0.45 tff(166,plain,
% 0.23/0.45 (cC34(iV8467)),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[165, 151])).
% 0.23/0.45 tff(167,assumption,((~((~cC62(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_12(iV8467))) | (~cC60(tptp_fun_Y_12(iV8467))))))) | (~(cC62(iV8467) | ![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y)))))), introduced(assumption)).
% 0.23/0.45 tff(168,plain,
% 0.23/0.45 (^[X: $i] : refl((~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_12(X))) | (~cC60(tptp_fun_Y_12(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y))))))) <=> (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_12(X))) | (~cC60(tptp_fun_Y_12(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y))))))))),
% 0.23/0.45 inference(bind,[status(th)],[])).
% 0.23/0.45 tff(169,plain,
% 0.23/0.45 (![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_12(X))) | (~cC60(tptp_fun_Y_12(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y))))))) <=> ![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_12(X))) | (~cC60(tptp_fun_Y_12(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))),
% 0.23/0.45 inference(quant_intro,[status(thm)],[168])).
% 0.23/0.45 tff(170,plain,
% 0.23/0.45 (^[X: $i] : rewrite((~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_12(X))) | (~cC60(tptp_fun_Y_12(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y))))))) <=> (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_12(X))) | (~cC60(tptp_fun_Y_12(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y))))))))),
% 0.23/0.45 inference(bind,[status(th)],[])).
% 0.23/0.45 tff(171,plain,
% 0.23/0.45 (![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_12(X))) | (~cC60(tptp_fun_Y_12(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y))))))) <=> ![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_12(X))) | (~cC60(tptp_fun_Y_12(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))),
% 0.23/0.45 inference(quant_intro,[status(thm)],[170])).
% 0.23/0.45 tff(172,plain,
% 0.23/0.45 (![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_12(X))) | (~cC60(tptp_fun_Y_12(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y))))))) <=> ![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_12(X))) | (~cC60(tptp_fun_Y_12(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))),
% 0.23/0.45 inference(transitivity,[status(thm)],[171, 169])).
% 0.23/0.45 tff(173,plain,
% 0.23/0.45 (^[X: $i] : trans(monotonicity(rewrite(((~cC62(X)) | (rR1(X, tptp_fun_Y_12(X)) & cC60(tptp_fun_Y_12(X)))) <=> ((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_12(X))) | (~cC60(tptp_fun_Y_12(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_12(X)) & cC60(tptp_fun_Y_12(X)))) & (cC62(X) | ![Y: $i] : (~(rR1(X, Y) & cC60(Y))))) <=> (((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_12(X))) | (~cC60(tptp_fun_Y_12(X)))))) & (cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y))))))), rewrite((((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_12(X))) | (~cC60(tptp_fun_Y_12(X)))))) & (cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y))))) <=> (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_12(X))) | (~cC60(tptp_fun_Y_12(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))), ((((~cC62(X)) | (rR1(X, tptp_fun_Y_12(X)) & cC60(tptp_fun_Y_12(X)))) & (cC62(X) | ![Y: $i] : (~(rR1(X, Y) & cC60(Y))))) <=> (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_12(X))) | (~cC60(tptp_fun_Y_12(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))))),
% 0.23/0.45 inference(bind,[status(th)],[])).
% 0.23/0.45 tff(174,plain,
% 0.23/0.45 (![X: $i] : (((~cC62(X)) | (rR1(X, tptp_fun_Y_12(X)) & cC60(tptp_fun_Y_12(X)))) & (cC62(X) | ![Y: $i] : (~(rR1(X, Y) & cC60(Y))))) <=> ![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_12(X))) | (~cC60(tptp_fun_Y_12(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))),
% 0.23/0.45 inference(quant_intro,[status(thm)],[173])).
% 0.23/0.45 tff(175,plain,
% 0.23/0.45 (![X: $i] : (cC62(X) <=> ?[Y: $i] : (rR1(X, Y) & cC60(Y))) <=> ![X: $i] : (cC62(X) <=> ?[Y: $i] : (rR1(X, Y) & cC60(Y)))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(176,axiom,(![X: $i] : (cC62(X) <=> ?[Y: $i] : (rR1(X, Y) & cC60(Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_30')).
% 0.23/0.45 tff(177,plain,
% 0.23/0.45 (![X: $i] : (cC62(X) <=> ?[Y: $i] : (rR1(X, Y) & cC60(Y)))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.23/0.45 tff(178,plain,(
% 0.23/0.45 ![X: $i] : (((~cC62(X)) | (rR1(X, tptp_fun_Y_12(X)) & cC60(tptp_fun_Y_12(X)))) & (cC62(X) | ![Y: $i] : (~(rR1(X, Y) & cC60(Y)))))),
% 0.23/0.45 inference(skolemize,[status(sab)],[177])).
% 0.23/0.45 tff(179,plain,
% 0.23/0.45 (![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_12(X))) | (~cC60(tptp_fun_Y_12(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[178, 174])).
% 0.23/0.45 tff(180,plain,
% 0.23/0.45 (![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_12(X))) | (~cC60(tptp_fun_Y_12(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[179, 172])).
% 0.23/0.45 tff(181,plain,
% 0.23/0.45 (((~![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_12(X))) | (~cC60(tptp_fun_Y_12(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))) | (~((~((~cC62(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_12(iV8467))) | (~cC60(tptp_fun_Y_12(iV8467))))))) | (~(cC62(iV8467) | ![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y)))))))) <=> ((~![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_12(X))) | (~cC60(tptp_fun_Y_12(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))) | (~((~((~cC62(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_12(iV8467))) | (~cC60(tptp_fun_Y_12(iV8467))))))) | (~(cC62(iV8467) | ![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y))))))))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(182,plain,
% 0.23/0.46 ((~((~((~cC62(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_12(iV8467))) | (~cC60(tptp_fun_Y_12(iV8467))))))) | (~(cC62(iV8467) | ![Y: $i] : ((~rR1(iV8467, Y)) | (~cC60(Y))))))) <=> (~((~((~cC62(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_12(iV8467))) | (~cC60(tptp_fun_Y_12(iV8467))))))) | (~(cC62(iV8467) | ![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y)))))))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(183,plain,
% 0.23/0.46 (((~![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_12(X))) | (~cC60(tptp_fun_Y_12(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))) | (~((~((~cC62(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_12(iV8467))) | (~cC60(tptp_fun_Y_12(iV8467))))))) | (~(cC62(iV8467) | ![Y: $i] : ((~rR1(iV8467, Y)) | (~cC60(Y)))))))) <=> ((~![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_12(X))) | (~cC60(tptp_fun_Y_12(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))) | (~((~((~cC62(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_12(iV8467))) | (~cC60(tptp_fun_Y_12(iV8467))))))) | (~(cC62(iV8467) | ![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y))))))))),
% 0.23/0.46 inference(monotonicity,[status(thm)],[182])).
% 0.23/0.46 tff(184,plain,
% 0.23/0.46 (((~![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_12(X))) | (~cC60(tptp_fun_Y_12(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))) | (~((~((~cC62(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_12(iV8467))) | (~cC60(tptp_fun_Y_12(iV8467))))))) | (~(cC62(iV8467) | ![Y: $i] : ((~rR1(iV8467, Y)) | (~cC60(Y)))))))) <=> ((~![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_12(X))) | (~cC60(tptp_fun_Y_12(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))) | (~((~((~cC62(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_12(iV8467))) | (~cC60(tptp_fun_Y_12(iV8467))))))) | (~(cC62(iV8467) | ![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y))))))))),
% 0.23/0.46 inference(transitivity,[status(thm)],[183, 181])).
% 0.23/0.46 tff(185,plain,
% 0.23/0.46 ((~![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_12(X))) | (~cC60(tptp_fun_Y_12(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))) | (~((~((~cC62(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_12(iV8467))) | (~cC60(tptp_fun_Y_12(iV8467))))))) | (~(cC62(iV8467) | ![Y: $i] : ((~rR1(iV8467, Y)) | (~cC60(Y)))))))),
% 0.23/0.46 inference(quant_inst,[status(thm)],[])).
% 0.23/0.46 tff(186,plain,
% 0.23/0.46 ((~![X: $i] : (~((~((~cC62(X)) | (~((~rR1(X, tptp_fun_Y_12(X))) | (~cC60(tptp_fun_Y_12(X))))))) | (~(cC62(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC60(Y)))))))) | (~((~((~cC62(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_12(iV8467))) | (~cC60(tptp_fun_Y_12(iV8467))))))) | (~(cC62(iV8467) | ![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y)))))))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.23/0.46 tff(187,plain,
% 0.23/0.46 ($false),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[186, 180, 167])).
% 0.23/0.46 tff(188,plain,(~((~((~cC62(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_12(iV8467))) | (~cC60(tptp_fun_Y_12(iV8467))))))) | (~(cC62(iV8467) | ![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y))))))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.46 tff(189,plain,
% 0.23/0.46 (((~((~cC62(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_12(iV8467))) | (~cC60(tptp_fun_Y_12(iV8467))))))) | (~(cC62(iV8467) | ![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y)))))) | (cC62(iV8467) | ![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y))))),
% 0.23/0.46 inference(tautology,[status(thm)],[])).
% 0.23/0.46 tff(190,plain,
% 0.23/0.46 (cC62(iV8467) | ![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y)))),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[189, 188])).
% 0.23/0.46 tff(191,assumption,(![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y)))), introduced(assumption)).
% 0.23/0.46 tff(192,plain,
% 0.23/0.46 (rR1(iV8467, iV8472) <=> rR1(iV8467, iV8472)),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(193,axiom,(rR1(iV8467, iV8472)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_60')).
% 0.23/0.46 tff(194,plain,
% 0.23/0.46 (rR1(iV8467, iV8472)),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.23/0.46 tff(195,plain,
% 0.23/0.46 (((~![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y)))) | ((~cC60(iV8472)) | (~rR1(iV8467, iV8472)))) <=> ((~![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y)))) | (~cC60(iV8472)) | (~rR1(iV8467, iV8472)))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(196,plain,
% 0.23/0.46 ((~![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y)))) | ((~cC60(iV8472)) | (~rR1(iV8467, iV8472)))),
% 0.23/0.46 inference(quant_inst,[status(thm)],[])).
% 0.23/0.46 tff(197,plain,
% 0.23/0.46 ((~![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y)))) | (~cC60(iV8472)) | (~rR1(iV8467, iV8472))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[196, 195])).
% 0.23/0.46 tff(198,plain,
% 0.23/0.46 ($false),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[197, 194, 127, 191])).
% 0.23/0.46 tff(199,plain,(~![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y)))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.46 tff(200,plain,
% 0.23/0.46 ((~(cC62(iV8467) | ![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y))))) | cC62(iV8467) | ![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y)))),
% 0.23/0.46 inference(tautology,[status(thm)],[])).
% 0.23/0.46 tff(201,plain,
% 0.23/0.46 ((~(cC62(iV8467) | ![Y: $i] : ((~cC60(Y)) | (~rR1(iV8467, Y))))) | cC62(iV8467)),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[200, 199])).
% 0.23/0.46 tff(202,plain,
% 0.23/0.46 (cC62(iV8467)),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[201, 190])).
% 0.23/0.46 tff(203,assumption,((~(cC20(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y))))) | (~((~cC20(iV8467)) | (~(cC2(tptp_fun_Y_3(iV8467)) | (~rR1(iV8467, tptp_fun_Y_3(iV8467)))))))), introduced(assumption)).
% 0.23/0.46 tff(204,plain,
% 0.23/0.46 (^[X: $i] : refl((~((~((~cC20(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC20(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y))))))) <=> (~((~((~cC20(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC20(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y))))))))),
% 0.23/0.46 inference(bind,[status(th)],[])).
% 0.23/0.46 tff(205,plain,
% 0.23/0.46 (![X: $i] : (~((~((~cC20(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC20(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC20(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC20(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))),
% 0.23/0.46 inference(quant_intro,[status(thm)],[204])).
% 0.23/0.46 tff(206,plain,
% 0.23/0.46 (^[X: $i] : rewrite((~((~((~cC20(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC20(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y))))))) <=> (~((~((~cC20(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC20(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y))))))))),
% 0.23/0.46 inference(bind,[status(th)],[])).
% 0.23/0.46 tff(207,plain,
% 0.23/0.46 (![X: $i] : (~((~((~cC20(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC20(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC20(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC20(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))),
% 0.23/0.46 inference(quant_intro,[status(thm)],[206])).
% 0.23/0.46 tff(208,plain,
% 0.23/0.46 (![X: $i] : (~((~((~cC20(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC20(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC20(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC20(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))),
% 0.23/0.46 inference(transitivity,[status(thm)],[207, 205])).
% 0.23/0.46 tff(209,plain,
% 0.23/0.46 (^[X: $i] : trans(monotonicity(rewrite(((~cC20(X)) | (rR1(X, tptp_fun_Y_3(X)) & (~cC2(tptp_fun_Y_3(X))))) <=> ((~cC20(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))), rewrite((cC20(X) | ![Y: $i] : (~(rR1(X, Y) & (~cC2(Y))))) <=> (cC20(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y))))), ((((~cC20(X)) | (rR1(X, tptp_fun_Y_3(X)) & (~cC2(tptp_fun_Y_3(X))))) & (cC20(X) | ![Y: $i] : (~(rR1(X, Y) & (~cC2(Y)))))) <=> (((~cC20(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X)))))) & (cC20(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y))))))), rewrite((((~cC20(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X)))))) & (cC20(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y))))) <=> (~((~((~cC20(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC20(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))), ((((~cC20(X)) | (rR1(X, tptp_fun_Y_3(X)) & (~cC2(tptp_fun_Y_3(X))))) & (cC20(X) | ![Y: $i] : (~(rR1(X, Y) & (~cC2(Y)))))) <=> (~((~((~cC20(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC20(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))))),
% 0.23/0.46 inference(bind,[status(th)],[])).
% 0.23/0.46 tff(210,plain,
% 0.23/0.46 (![X: $i] : (((~cC20(X)) | (rR1(X, tptp_fun_Y_3(X)) & (~cC2(tptp_fun_Y_3(X))))) & (cC20(X) | ![Y: $i] : (~(rR1(X, Y) & (~cC2(Y)))))) <=> ![X: $i] : (~((~((~cC20(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC20(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))),
% 0.23/0.46 inference(quant_intro,[status(thm)],[209])).
% 0.23/0.46 tff(211,plain,
% 0.23/0.46 (![X: $i] : (cC20(X) <=> ?[Y: $i] : (rR1(X, Y) & (~cC2(Y)))) <=> ![X: $i] : (cC20(X) <=> ?[Y: $i] : (rR1(X, Y) & (~cC2(Y))))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(212,axiom,(![X: $i] : (cC20(X) <=> ?[Y: $i] : (rR1(X, Y) & (~cC2(Y))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_7')).
% 0.23/0.46 tff(213,plain,
% 0.23/0.46 (![X: $i] : (cC20(X) <=> ?[Y: $i] : (rR1(X, Y) & (~cC2(Y))))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.23/0.46 tff(214,plain,(
% 0.23/0.46 ![X: $i] : (((~cC20(X)) | (rR1(X, tptp_fun_Y_3(X)) & (~cC2(tptp_fun_Y_3(X))))) & (cC20(X) | ![Y: $i] : (~(rR1(X, Y) & (~cC2(Y))))))),
% 0.23/0.46 inference(skolemize,[status(sab)],[213])).
% 0.23/0.46 tff(215,plain,
% 0.23/0.46 (![X: $i] : (~((~((~cC20(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC20(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[214, 210])).
% 0.23/0.46 tff(216,plain,
% 0.23/0.46 (![X: $i] : (~((~((~cC20(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC20(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[215, 208])).
% 0.23/0.46 tff(217,plain,
% 0.23/0.46 (((~![X: $i] : (~((~((~cC20(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC20(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))) | (~((~(cC20(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y))))) | (~((~cC20(iV8467)) | (~(cC2(tptp_fun_Y_3(iV8467)) | (~rR1(iV8467, tptp_fun_Y_3(iV8467)))))))))) <=> ((~![X: $i] : (~((~((~cC20(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC20(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))) | (~((~(cC20(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y))))) | (~((~cC20(iV8467)) | (~(cC2(tptp_fun_Y_3(iV8467)) | (~rR1(iV8467, tptp_fun_Y_3(iV8467))))))))))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(218,plain,
% 0.23/0.46 ((~((~((~cC20(iV8467)) | (~(cC2(tptp_fun_Y_3(iV8467)) | (~rR1(iV8467, tptp_fun_Y_3(iV8467))))))) | (~(cC20(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y))))))) <=> (~((~(cC20(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y))))) | (~((~cC20(iV8467)) | (~(cC2(tptp_fun_Y_3(iV8467)) | (~rR1(iV8467, tptp_fun_Y_3(iV8467)))))))))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(219,plain,
% 0.23/0.46 (((~![X: $i] : (~((~((~cC20(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC20(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))) | (~((~((~cC20(iV8467)) | (~(cC2(tptp_fun_Y_3(iV8467)) | (~rR1(iV8467, tptp_fun_Y_3(iV8467))))))) | (~(cC20(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y)))))))) <=> ((~![X: $i] : (~((~((~cC20(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC20(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))) | (~((~(cC20(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y))))) | (~((~cC20(iV8467)) | (~(cC2(tptp_fun_Y_3(iV8467)) | (~rR1(iV8467, tptp_fun_Y_3(iV8467))))))))))),
% 0.23/0.46 inference(monotonicity,[status(thm)],[218])).
% 0.23/0.46 tff(220,plain,
% 0.23/0.46 (((~![X: $i] : (~((~((~cC20(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC20(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))) | (~((~((~cC20(iV8467)) | (~(cC2(tptp_fun_Y_3(iV8467)) | (~rR1(iV8467, tptp_fun_Y_3(iV8467))))))) | (~(cC20(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y)))))))) <=> ((~![X: $i] : (~((~((~cC20(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC20(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))) | (~((~(cC20(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y))))) | (~((~cC20(iV8467)) | (~(cC2(tptp_fun_Y_3(iV8467)) | (~rR1(iV8467, tptp_fun_Y_3(iV8467))))))))))),
% 0.23/0.46 inference(transitivity,[status(thm)],[219, 217])).
% 0.23/0.46 tff(221,plain,
% 0.23/0.46 ((~![X: $i] : (~((~((~cC20(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC20(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))) | (~((~((~cC20(iV8467)) | (~(cC2(tptp_fun_Y_3(iV8467)) | (~rR1(iV8467, tptp_fun_Y_3(iV8467))))))) | (~(cC20(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y)))))))),
% 0.23/0.46 inference(quant_inst,[status(thm)],[])).
% 0.23/0.46 tff(222,plain,
% 0.23/0.46 ((~![X: $i] : (~((~((~cC20(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC20(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))) | (~((~(cC20(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y))))) | (~((~cC20(iV8467)) | (~(cC2(tptp_fun_Y_3(iV8467)) | (~rR1(iV8467, tptp_fun_Y_3(iV8467)))))))))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[221, 220])).
% 0.23/0.46 tff(223,plain,
% 0.23/0.46 ($false),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[222, 216, 203])).
% 0.23/0.46 tff(224,plain,(~((~(cC20(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y))))) | (~((~cC20(iV8467)) | (~(cC2(tptp_fun_Y_3(iV8467)) | (~rR1(iV8467, tptp_fun_Y_3(iV8467))))))))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.46 tff(225,plain,
% 0.23/0.46 (((~(cC20(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y))))) | (~((~cC20(iV8467)) | (~(cC2(tptp_fun_Y_3(iV8467)) | (~rR1(iV8467, tptp_fun_Y_3(iV8467)))))))) | (cC20(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y))))),
% 0.23/0.46 inference(tautology,[status(thm)],[])).
% 0.23/0.46 tff(226,plain,
% 0.23/0.46 (cC20(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y)))),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[225, 224])).
% 0.23/0.46 tff(227,plain,
% 0.23/0.46 ((~(cC20(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y))))) | cC20(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y)))),
% 0.23/0.46 inference(tautology,[status(thm)],[])).
% 0.23/0.46 tff(228,plain,
% 0.23/0.46 ((~(cC20(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y))))) | cC20(iV8467)),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[227, 12])).
% 0.23/0.46 tff(229,plain,
% 0.23/0.46 (cC20(iV8467)),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[228, 226])).
% 0.23/0.46 tff(230,assumption,((~(cC8(iV8467) | ![Y: $i] : (cC6(Y) | (~rR1(iV8467, Y))))) | (~((~cC8(iV8467)) | (~(cC6(tptp_fun_Y_16(iV8467)) | (~rR1(iV8467, tptp_fun_Y_16(iV8467)))))))), introduced(assumption)).
% 0.23/0.46 tff(231,plain,
% 0.23/0.46 (^[X: $i] : refl((~((~((~cC8(X)) | (~(cC6(tptp_fun_Y_16(X)) | (~rR1(X, tptp_fun_Y_16(X))))))) | (~(cC8(X) | ![Y: $i] : (cC6(Y) | (~rR1(X, Y))))))) <=> (~((~((~cC8(X)) | (~(cC6(tptp_fun_Y_16(X)) | (~rR1(X, tptp_fun_Y_16(X))))))) | (~(cC8(X) | ![Y: $i] : (cC6(Y) | (~rR1(X, Y))))))))),
% 0.23/0.46 inference(bind,[status(th)],[])).
% 0.23/0.46 tff(232,plain,
% 0.23/0.46 (![X: $i] : (~((~((~cC8(X)) | (~(cC6(tptp_fun_Y_16(X)) | (~rR1(X, tptp_fun_Y_16(X))))))) | (~(cC8(X) | ![Y: $i] : (cC6(Y) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC8(X)) | (~(cC6(tptp_fun_Y_16(X)) | (~rR1(X, tptp_fun_Y_16(X))))))) | (~(cC8(X) | ![Y: $i] : (cC6(Y) | (~rR1(X, Y)))))))),
% 0.23/0.46 inference(quant_intro,[status(thm)],[231])).
% 0.23/0.46 tff(233,plain,
% 0.23/0.46 (^[X: $i] : rewrite((~((~((~cC8(X)) | (~(cC6(tptp_fun_Y_16(X)) | (~rR1(X, tptp_fun_Y_16(X))))))) | (~(cC8(X) | ![Y: $i] : (cC6(Y) | (~rR1(X, Y))))))) <=> (~((~((~cC8(X)) | (~(cC6(tptp_fun_Y_16(X)) | (~rR1(X, tptp_fun_Y_16(X))))))) | (~(cC8(X) | ![Y: $i] : (cC6(Y) | (~rR1(X, Y))))))))),
% 0.23/0.46 inference(bind,[status(th)],[])).
% 0.23/0.46 tff(234,plain,
% 0.23/0.46 (![X: $i] : (~((~((~cC8(X)) | (~(cC6(tptp_fun_Y_16(X)) | (~rR1(X, tptp_fun_Y_16(X))))))) | (~(cC8(X) | ![Y: $i] : (cC6(Y) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC8(X)) | (~(cC6(tptp_fun_Y_16(X)) | (~rR1(X, tptp_fun_Y_16(X))))))) | (~(cC8(X) | ![Y: $i] : (cC6(Y) | (~rR1(X, Y)))))))),
% 0.23/0.46 inference(quant_intro,[status(thm)],[233])).
% 0.23/0.46 tff(235,plain,
% 0.23/0.46 (![X: $i] : (~((~((~cC8(X)) | (~(cC6(tptp_fun_Y_16(X)) | (~rR1(X, tptp_fun_Y_16(X))))))) | (~(cC8(X) | ![Y: $i] : (cC6(Y) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC8(X)) | (~(cC6(tptp_fun_Y_16(X)) | (~rR1(X, tptp_fun_Y_16(X))))))) | (~(cC8(X) | ![Y: $i] : (cC6(Y) | (~rR1(X, Y)))))))),
% 0.23/0.47 inference(transitivity,[status(thm)],[234, 232])).
% 0.23/0.47 tff(236,plain,
% 0.23/0.47 (^[X: $i] : trans(monotonicity(rewrite(((~cC8(X)) | (rR1(X, tptp_fun_Y_16(X)) & (~cC6(tptp_fun_Y_16(X))))) <=> ((~cC8(X)) | (~(cC6(tptp_fun_Y_16(X)) | (~rR1(X, tptp_fun_Y_16(X))))))), rewrite((cC8(X) | ![Y: $i] : (~(rR1(X, Y) & (~cC6(Y))))) <=> (cC8(X) | ![Y: $i] : (cC6(Y) | (~rR1(X, Y))))), ((((~cC8(X)) | (rR1(X, tptp_fun_Y_16(X)) & (~cC6(tptp_fun_Y_16(X))))) & (cC8(X) | ![Y: $i] : (~(rR1(X, Y) & (~cC6(Y)))))) <=> (((~cC8(X)) | (~(cC6(tptp_fun_Y_16(X)) | (~rR1(X, tptp_fun_Y_16(X)))))) & (cC8(X) | ![Y: $i] : (cC6(Y) | (~rR1(X, Y))))))), rewrite((((~cC8(X)) | (~(cC6(tptp_fun_Y_16(X)) | (~rR1(X, tptp_fun_Y_16(X)))))) & (cC8(X) | ![Y: $i] : (cC6(Y) | (~rR1(X, Y))))) <=> (~((~((~cC8(X)) | (~(cC6(tptp_fun_Y_16(X)) | (~rR1(X, tptp_fun_Y_16(X))))))) | (~(cC8(X) | ![Y: $i] : (cC6(Y) | (~rR1(X, Y)))))))), ((((~cC8(X)) | (rR1(X, tptp_fun_Y_16(X)) & (~cC6(tptp_fun_Y_16(X))))) & (cC8(X) | ![Y: $i] : (~(rR1(X, Y) & (~cC6(Y)))))) <=> (~((~((~cC8(X)) | (~(cC6(tptp_fun_Y_16(X)) | (~rR1(X, tptp_fun_Y_16(X))))))) | (~(cC8(X) | ![Y: $i] : (cC6(Y) | (~rR1(X, Y)))))))))),
% 0.23/0.47 inference(bind,[status(th)],[])).
% 0.23/0.47 tff(237,plain,
% 0.23/0.47 (![X: $i] : (((~cC8(X)) | (rR1(X, tptp_fun_Y_16(X)) & (~cC6(tptp_fun_Y_16(X))))) & (cC8(X) | ![Y: $i] : (~(rR1(X, Y) & (~cC6(Y)))))) <=> ![X: $i] : (~((~((~cC8(X)) | (~(cC6(tptp_fun_Y_16(X)) | (~rR1(X, tptp_fun_Y_16(X))))))) | (~(cC8(X) | ![Y: $i] : (cC6(Y) | (~rR1(X, Y)))))))),
% 0.23/0.47 inference(quant_intro,[status(thm)],[236])).
% 0.23/0.47 tff(238,plain,
% 0.23/0.47 (![X: $i] : (cC8(X) <=> ?[Y: $i] : (rR1(X, Y) & (~cC6(Y)))) <=> ![X: $i] : (cC8(X) <=> ?[Y: $i] : (rR1(X, Y) & (~cC6(Y))))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(239,axiom,(![X: $i] : (cC8(X) <=> ?[Y: $i] : (rR1(X, Y) & (~cC6(Y))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_39')).
% 0.23/0.47 tff(240,plain,
% 0.23/0.47 (![X: $i] : (cC8(X) <=> ?[Y: $i] : (rR1(X, Y) & (~cC6(Y))))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[239, 238])).
% 0.23/0.47 tff(241,plain,(
% 0.23/0.47 ![X: $i] : (((~cC8(X)) | (rR1(X, tptp_fun_Y_16(X)) & (~cC6(tptp_fun_Y_16(X))))) & (cC8(X) | ![Y: $i] : (~(rR1(X, Y) & (~cC6(Y))))))),
% 0.23/0.47 inference(skolemize,[status(sab)],[240])).
% 0.23/0.47 tff(242,plain,
% 0.23/0.47 (![X: $i] : (~((~((~cC8(X)) | (~(cC6(tptp_fun_Y_16(X)) | (~rR1(X, tptp_fun_Y_16(X))))))) | (~(cC8(X) | ![Y: $i] : (cC6(Y) | (~rR1(X, Y)))))))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[241, 237])).
% 0.23/0.47 tff(243,plain,
% 0.23/0.47 (![X: $i] : (~((~((~cC8(X)) | (~(cC6(tptp_fun_Y_16(X)) | (~rR1(X, tptp_fun_Y_16(X))))))) | (~(cC8(X) | ![Y: $i] : (cC6(Y) | (~rR1(X, Y)))))))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[242, 235])).
% 0.23/0.47 tff(244,plain,
% 0.23/0.47 (((~![X: $i] : (~((~((~cC8(X)) | (~(cC6(tptp_fun_Y_16(X)) | (~rR1(X, tptp_fun_Y_16(X))))))) | (~(cC8(X) | ![Y: $i] : (cC6(Y) | (~rR1(X, Y)))))))) | (~((~(cC8(iV8467) | ![Y: $i] : (cC6(Y) | (~rR1(iV8467, Y))))) | (~((~cC8(iV8467)) | (~(cC6(tptp_fun_Y_16(iV8467)) | (~rR1(iV8467, tptp_fun_Y_16(iV8467)))))))))) <=> ((~![X: $i] : (~((~((~cC8(X)) | (~(cC6(tptp_fun_Y_16(X)) | (~rR1(X, tptp_fun_Y_16(X))))))) | (~(cC8(X) | ![Y: $i] : (cC6(Y) | (~rR1(X, Y)))))))) | (~((~(cC8(iV8467) | ![Y: $i] : (cC6(Y) | (~rR1(iV8467, Y))))) | (~((~cC8(iV8467)) | (~(cC6(tptp_fun_Y_16(iV8467)) | (~rR1(iV8467, tptp_fun_Y_16(iV8467))))))))))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(245,plain,
% 0.23/0.47 ((~((~((~cC8(iV8467)) | (~(cC6(tptp_fun_Y_16(iV8467)) | (~rR1(iV8467, tptp_fun_Y_16(iV8467))))))) | (~(cC8(iV8467) | ![Y: $i] : (cC6(Y) | (~rR1(iV8467, Y))))))) <=> (~((~(cC8(iV8467) | ![Y: $i] : (cC6(Y) | (~rR1(iV8467, Y))))) | (~((~cC8(iV8467)) | (~(cC6(tptp_fun_Y_16(iV8467)) | (~rR1(iV8467, tptp_fun_Y_16(iV8467)))))))))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(246,plain,
% 0.23/0.47 (((~![X: $i] : (~((~((~cC8(X)) | (~(cC6(tptp_fun_Y_16(X)) | (~rR1(X, tptp_fun_Y_16(X))))))) | (~(cC8(X) | ![Y: $i] : (cC6(Y) | (~rR1(X, Y)))))))) | (~((~((~cC8(iV8467)) | (~(cC6(tptp_fun_Y_16(iV8467)) | (~rR1(iV8467, tptp_fun_Y_16(iV8467))))))) | (~(cC8(iV8467) | ![Y: $i] : (cC6(Y) | (~rR1(iV8467, Y)))))))) <=> ((~![X: $i] : (~((~((~cC8(X)) | (~(cC6(tptp_fun_Y_16(X)) | (~rR1(X, tptp_fun_Y_16(X))))))) | (~(cC8(X) | ![Y: $i] : (cC6(Y) | (~rR1(X, Y)))))))) | (~((~(cC8(iV8467) | ![Y: $i] : (cC6(Y) | (~rR1(iV8467, Y))))) | (~((~cC8(iV8467)) | (~(cC6(tptp_fun_Y_16(iV8467)) | (~rR1(iV8467, tptp_fun_Y_16(iV8467))))))))))),
% 0.23/0.47 inference(monotonicity,[status(thm)],[245])).
% 0.23/0.47 tff(247,plain,
% 0.23/0.47 (((~![X: $i] : (~((~((~cC8(X)) | (~(cC6(tptp_fun_Y_16(X)) | (~rR1(X, tptp_fun_Y_16(X))))))) | (~(cC8(X) | ![Y: $i] : (cC6(Y) | (~rR1(X, Y)))))))) | (~((~((~cC8(iV8467)) | (~(cC6(tptp_fun_Y_16(iV8467)) | (~rR1(iV8467, tptp_fun_Y_16(iV8467))))))) | (~(cC8(iV8467) | ![Y: $i] : (cC6(Y) | (~rR1(iV8467, Y)))))))) <=> ((~![X: $i] : (~((~((~cC8(X)) | (~(cC6(tptp_fun_Y_16(X)) | (~rR1(X, tptp_fun_Y_16(X))))))) | (~(cC8(X) | ![Y: $i] : (cC6(Y) | (~rR1(X, Y)))))))) | (~((~(cC8(iV8467) | ![Y: $i] : (cC6(Y) | (~rR1(iV8467, Y))))) | (~((~cC8(iV8467)) | (~(cC6(tptp_fun_Y_16(iV8467)) | (~rR1(iV8467, tptp_fun_Y_16(iV8467))))))))))),
% 0.23/0.47 inference(transitivity,[status(thm)],[246, 244])).
% 0.23/0.47 tff(248,plain,
% 0.23/0.47 ((~![X: $i] : (~((~((~cC8(X)) | (~(cC6(tptp_fun_Y_16(X)) | (~rR1(X, tptp_fun_Y_16(X))))))) | (~(cC8(X) | ![Y: $i] : (cC6(Y) | (~rR1(X, Y)))))))) | (~((~((~cC8(iV8467)) | (~(cC6(tptp_fun_Y_16(iV8467)) | (~rR1(iV8467, tptp_fun_Y_16(iV8467))))))) | (~(cC8(iV8467) | ![Y: $i] : (cC6(Y) | (~rR1(iV8467, Y)))))))),
% 0.23/0.47 inference(quant_inst,[status(thm)],[])).
% 0.23/0.47 tff(249,plain,
% 0.23/0.47 ((~![X: $i] : (~((~((~cC8(X)) | (~(cC6(tptp_fun_Y_16(X)) | (~rR1(X, tptp_fun_Y_16(X))))))) | (~(cC8(X) | ![Y: $i] : (cC6(Y) | (~rR1(X, Y)))))))) | (~((~(cC8(iV8467) | ![Y: $i] : (cC6(Y) | (~rR1(iV8467, Y))))) | (~((~cC8(iV8467)) | (~(cC6(tptp_fun_Y_16(iV8467)) | (~rR1(iV8467, tptp_fun_Y_16(iV8467)))))))))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[248, 247])).
% 0.23/0.47 tff(250,plain,
% 0.23/0.47 ($false),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[249, 243, 230])).
% 0.23/0.47 tff(251,plain,(~((~(cC8(iV8467) | ![Y: $i] : (cC6(Y) | (~rR1(iV8467, Y))))) | (~((~cC8(iV8467)) | (~(cC6(tptp_fun_Y_16(iV8467)) | (~rR1(iV8467, tptp_fun_Y_16(iV8467))))))))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.47 tff(252,plain,
% 0.23/0.47 (((~(cC8(iV8467) | ![Y: $i] : (cC6(Y) | (~rR1(iV8467, Y))))) | (~((~cC8(iV8467)) | (~(cC6(tptp_fun_Y_16(iV8467)) | (~rR1(iV8467, tptp_fun_Y_16(iV8467)))))))) | (cC8(iV8467) | ![Y: $i] : (cC6(Y) | (~rR1(iV8467, Y))))),
% 0.23/0.47 inference(tautology,[status(thm)],[])).
% 0.23/0.47 tff(253,plain,
% 0.23/0.47 (cC8(iV8467) | ![Y: $i] : (cC6(Y) | (~rR1(iV8467, Y)))),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[252, 251])).
% 0.23/0.47 tff(254,assumption,(![Y: $i] : (cC6(Y) | (~rR1(iV8467, Y)))), introduced(assumption)).
% 0.23/0.47 tff(255,plain,
% 0.23/0.47 ((~cC6(iV8469)) <=> (~cC6(iV8469))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(256,axiom,(~cC6(iV8469)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_65')).
% 0.23/0.47 tff(257,plain,
% 0.23/0.47 (~cC6(iV8469)),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[256, 255])).
% 0.23/0.47 tff(258,plain,
% 0.23/0.47 (rR1(iV8467, iV8469) <=> rR1(iV8467, iV8469)),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(259,axiom,(rR1(iV8467, iV8469)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_58')).
% 0.23/0.47 tff(260,plain,
% 0.23/0.47 (rR1(iV8467, iV8469)),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[259, 258])).
% 0.23/0.47 tff(261,plain,
% 0.23/0.47 (((~![Y: $i] : (cC6(Y) | (~rR1(iV8467, Y)))) | (cC6(iV8469) | (~rR1(iV8467, iV8469)))) <=> ((~![Y: $i] : (cC6(Y) | (~rR1(iV8467, Y)))) | cC6(iV8469) | (~rR1(iV8467, iV8469)))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(262,plain,
% 0.23/0.47 ((~![Y: $i] : (cC6(Y) | (~rR1(iV8467, Y)))) | (cC6(iV8469) | (~rR1(iV8467, iV8469)))),
% 0.23/0.47 inference(quant_inst,[status(thm)],[])).
% 0.23/0.47 tff(263,plain,
% 0.23/0.47 ((~![Y: $i] : (cC6(Y) | (~rR1(iV8467, Y)))) | cC6(iV8469) | (~rR1(iV8467, iV8469))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[262, 261])).
% 0.23/0.47 tff(264,plain,
% 0.23/0.47 ($false),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[263, 260, 257, 254])).
% 0.23/0.47 tff(265,plain,(~![Y: $i] : (cC6(Y) | (~rR1(iV8467, Y)))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.47 tff(266,plain,
% 0.23/0.47 ((~(cC8(iV8467) | ![Y: $i] : (cC6(Y) | (~rR1(iV8467, Y))))) | cC8(iV8467) | ![Y: $i] : (cC6(Y) | (~rR1(iV8467, Y)))),
% 0.23/0.47 inference(tautology,[status(thm)],[])).
% 0.23/0.47 tff(267,plain,
% 0.23/0.47 ((~(cC8(iV8467) | ![Y: $i] : (cC6(Y) | (~rR1(iV8467, Y))))) | cC8(iV8467)),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[266, 265])).
% 0.23/0.47 tff(268,plain,
% 0.23/0.47 (cC8(iV8467)),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[267, 253])).
% 0.23/0.47 tff(269,assumption,((~(cC82(iV8467) | ![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y))))) | (~((~cC82(iV8467)) | (~((~cC80(tptp_fun_Y_17(iV8467))) | (~rR1(iV8467, tptp_fun_Y_17(iV8467)))))))), introduced(assumption)).
% 0.23/0.47 tff(270,plain,
% 0.23/0.47 (^[X: $i] : refl((~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_17(X))) | (~cC80(tptp_fun_Y_17(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y))))))) <=> (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_17(X))) | (~cC80(tptp_fun_Y_17(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y))))))))),
% 0.23/0.47 inference(bind,[status(th)],[])).
% 0.23/0.47 tff(271,plain,
% 0.23/0.47 (![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_17(X))) | (~cC80(tptp_fun_Y_17(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y))))))) <=> ![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_17(X))) | (~cC80(tptp_fun_Y_17(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))),
% 0.23/0.47 inference(quant_intro,[status(thm)],[270])).
% 0.23/0.47 tff(272,plain,
% 0.23/0.47 (^[X: $i] : rewrite((~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_17(X))) | (~cC80(tptp_fun_Y_17(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y))))))) <=> (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_17(X))) | (~cC80(tptp_fun_Y_17(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y))))))))),
% 0.23/0.47 inference(bind,[status(th)],[])).
% 0.23/0.47 tff(273,plain,
% 0.23/0.47 (![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_17(X))) | (~cC80(tptp_fun_Y_17(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y))))))) <=> ![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_17(X))) | (~cC80(tptp_fun_Y_17(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))),
% 0.23/0.47 inference(quant_intro,[status(thm)],[272])).
% 0.23/0.47 tff(274,plain,
% 0.23/0.47 (![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_17(X))) | (~cC80(tptp_fun_Y_17(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y))))))) <=> ![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_17(X))) | (~cC80(tptp_fun_Y_17(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))),
% 0.23/0.47 inference(transitivity,[status(thm)],[273, 271])).
% 0.23/0.47 tff(275,plain,
% 0.23/0.47 (^[X: $i] : trans(monotonicity(rewrite(((~cC82(X)) | (rR1(X, tptp_fun_Y_17(X)) & cC80(tptp_fun_Y_17(X)))) <=> ((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_17(X))) | (~cC80(tptp_fun_Y_17(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_17(X)) & cC80(tptp_fun_Y_17(X)))) & (cC82(X) | ![Y: $i] : (~(rR1(X, Y) & cC80(Y))))) <=> (((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_17(X))) | (~cC80(tptp_fun_Y_17(X)))))) & (cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y))))))), rewrite((((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_17(X))) | (~cC80(tptp_fun_Y_17(X)))))) & (cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y))))) <=> (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_17(X))) | (~cC80(tptp_fun_Y_17(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))), ((((~cC82(X)) | (rR1(X, tptp_fun_Y_17(X)) & cC80(tptp_fun_Y_17(X)))) & (cC82(X) | ![Y: $i] : (~(rR1(X, Y) & cC80(Y))))) <=> (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_17(X))) | (~cC80(tptp_fun_Y_17(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))))),
% 0.23/0.47 inference(bind,[status(th)],[])).
% 0.23/0.47 tff(276,plain,
% 0.23/0.47 (![X: $i] : (((~cC82(X)) | (rR1(X, tptp_fun_Y_17(X)) & cC80(tptp_fun_Y_17(X)))) & (cC82(X) | ![Y: $i] : (~(rR1(X, Y) & cC80(Y))))) <=> ![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_17(X))) | (~cC80(tptp_fun_Y_17(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))),
% 0.23/0.47 inference(quant_intro,[status(thm)],[275])).
% 0.23/0.47 tff(277,plain,
% 0.23/0.47 (![X: $i] : (cC82(X) <=> ?[Y: $i] : (rR1(X, Y) & cC80(Y))) <=> ![X: $i] : (cC82(X) <=> ?[Y: $i] : (rR1(X, Y) & cC80(Y)))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(278,axiom,(![X: $i] : (cC82(X) <=> ?[Y: $i] : (rR1(X, Y) & cC80(Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_41')).
% 0.23/0.47 tff(279,plain,
% 0.23/0.47 (![X: $i] : (cC82(X) <=> ?[Y: $i] : (rR1(X, Y) & cC80(Y)))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[278, 277])).
% 0.23/0.47 tff(280,plain,(
% 0.23/0.47 ![X: $i] : (((~cC82(X)) | (rR1(X, tptp_fun_Y_17(X)) & cC80(tptp_fun_Y_17(X)))) & (cC82(X) | ![Y: $i] : (~(rR1(X, Y) & cC80(Y)))))),
% 0.23/0.47 inference(skolemize,[status(sab)],[279])).
% 0.23/0.47 tff(281,plain,
% 0.23/0.47 (![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_17(X))) | (~cC80(tptp_fun_Y_17(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[280, 276])).
% 0.23/0.47 tff(282,plain,
% 0.23/0.47 (![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_17(X))) | (~cC80(tptp_fun_Y_17(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[281, 274])).
% 0.23/0.47 tff(283,plain,
% 0.23/0.47 (((~![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_17(X))) | (~cC80(tptp_fun_Y_17(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_17(iV8467))) | (~rR1(iV8467, tptp_fun_Y_17(iV8467)))))))))) <=> ((~![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_17(X))) | (~cC80(tptp_fun_Y_17(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_17(iV8467))) | (~rR1(iV8467, tptp_fun_Y_17(iV8467))))))))))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(284,plain,
% 0.23/0.47 ((~((~((~cC82(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_17(iV8467))) | (~cC80(tptp_fun_Y_17(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_17(iV8467))) | (~rR1(iV8467, tptp_fun_Y_17(iV8467)))))))))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(285,plain,
% 0.23/0.47 (((~![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_17(X))) | (~cC80(tptp_fun_Y_17(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))) | (~((~((~cC82(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_17(iV8467))) | (~cC80(tptp_fun_Y_17(iV8467))))))) | (~(cC82(iV8467) | ![Y: $i] : ((~rR1(iV8467, Y)) | (~cC80(Y)))))))) <=> ((~![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_17(X))) | (~cC80(tptp_fun_Y_17(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_17(iV8467))) | (~rR1(iV8467, tptp_fun_Y_17(iV8467))))))))))),
% 0.23/0.47 inference(monotonicity,[status(thm)],[284])).
% 0.23/0.47 tff(286,plain,
% 0.23/0.47 (((~![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_17(X))) | (~cC80(tptp_fun_Y_17(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))) | (~((~((~cC82(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_17(iV8467))) | (~cC80(tptp_fun_Y_17(iV8467))))))) | (~(cC82(iV8467) | ![Y: $i] : ((~rR1(iV8467, Y)) | (~cC80(Y)))))))) <=> ((~![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_17(X))) | (~cC80(tptp_fun_Y_17(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_17(iV8467))) | (~rR1(iV8467, tptp_fun_Y_17(iV8467))))))))))),
% 0.23/0.47 inference(transitivity,[status(thm)],[285, 283])).
% 0.23/0.47 tff(287,plain,
% 0.23/0.47 ((~![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_17(X))) | (~cC80(tptp_fun_Y_17(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))) | (~((~((~cC82(iV8467)) | (~((~rR1(iV8467, tptp_fun_Y_17(iV8467))) | (~cC80(tptp_fun_Y_17(iV8467))))))) | (~(cC82(iV8467) | ![Y: $i] : ((~rR1(iV8467, Y)) | (~cC80(Y)))))))),
% 0.23/0.47 inference(quant_inst,[status(thm)],[])).
% 0.23/0.47 tff(288,plain,
% 0.23/0.47 ((~![X: $i] : (~((~((~cC82(X)) | (~((~rR1(X, tptp_fun_Y_17(X))) | (~cC80(tptp_fun_Y_17(X))))))) | (~(cC82(X) | ![Y: $i] : ((~rR1(X, Y)) | (~cC80(Y)))))))) | (~((~(cC82(iV8467) | ![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y))))) | (~((~cC82(iV8467)) | (~((~cC80(tptp_fun_Y_17(iV8467))) | (~rR1(iV8467, tptp_fun_Y_17(iV8467)))))))))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[287, 286])).
% 0.23/0.48 tff(289,plain,
% 0.23/0.48 ($false),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[288, 282, 269])).
% 0.23/0.48 tff(290,plain,(~((~(cC82(iV8467) | ![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y))))) | (~((~cC82(iV8467)) | (~((~cC80(tptp_fun_Y_17(iV8467))) | (~rR1(iV8467, tptp_fun_Y_17(iV8467))))))))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.48 tff(291,plain,
% 0.23/0.48 (((~(cC82(iV8467) | ![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y))))) | (~((~cC82(iV8467)) | (~((~cC80(tptp_fun_Y_17(iV8467))) | (~rR1(iV8467, tptp_fun_Y_17(iV8467)))))))) | (cC82(iV8467) | ![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y))))),
% 0.23/0.48 inference(tautology,[status(thm)],[])).
% 0.23/0.48 tff(292,plain,
% 0.23/0.48 (cC82(iV8467) | ![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y)))),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[291, 290])).
% 0.23/0.48 tff(293,assumption,(![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y)))), introduced(assumption)).
% 0.23/0.48 tff(294,plain,
% 0.23/0.48 (^[X: $i] : refl((~((cC2(X) | cC78(X)) <=> cC80(X))) <=> (~((cC2(X) | cC78(X)) <=> cC80(X))))),
% 0.23/0.48 inference(bind,[status(th)],[])).
% 0.23/0.48 tff(295,plain,
% 0.23/0.48 (![X: $i] : (~((cC2(X) | cC78(X)) <=> cC80(X))) <=> ![X: $i] : (~((cC2(X) | cC78(X)) <=> cC80(X)))),
% 0.23/0.48 inference(quant_intro,[status(thm)],[294])).
% 0.23/0.48 tff(296,plain,
% 0.23/0.48 (^[X: $i] : trans(trans(monotonicity(rewrite(((~cC2(X)) & (~cC78(X))) <=> (~(cC2(X) | cC78(X)))), ((cC80(X) <=> ((~cC2(X)) & (~cC78(X)))) <=> (cC80(X) <=> (~(cC2(X) | cC78(X)))))), rewrite((cC80(X) <=> (~(cC2(X) | cC78(X)))) <=> (~((cC2(X) | cC78(X)) <=> cC80(X)))), ((cC80(X) <=> ((~cC2(X)) & (~cC78(X)))) <=> (~((cC2(X) | cC78(X)) <=> cC80(X))))), rewrite((~((cC2(X) | cC78(X)) <=> cC80(X))) <=> (~((cC2(X) | cC78(X)) <=> cC80(X)))), ((cC80(X) <=> ((~cC2(X)) & (~cC78(X)))) <=> (~((cC2(X) | cC78(X)) <=> cC80(X)))))),
% 0.23/0.48 inference(bind,[status(th)],[])).
% 0.23/0.48 tff(297,plain,
% 0.23/0.48 (![X: $i] : (cC80(X) <=> ((~cC2(X)) & (~cC78(X)))) <=> ![X: $i] : (~((cC2(X) | cC78(X)) <=> cC80(X)))),
% 0.23/0.48 inference(quant_intro,[status(thm)],[296])).
% 0.23/0.48 tff(298,plain,
% 0.23/0.48 (![X: $i] : (cC80(X) <=> ((~cC2(X)) & (~cC78(X)))) <=> ![X: $i] : (cC80(X) <=> ((~cC2(X)) & (~cC78(X))))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(299,axiom,(![X: $i] : (cC80(X) <=> ((~cC2(X)) & (~cC78(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_40')).
% 0.23/0.48 tff(300,plain,
% 0.23/0.48 (![X: $i] : (cC80(X) <=> ((~cC2(X)) & (~cC78(X))))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[299, 298])).
% 0.23/0.48 tff(301,plain,(
% 0.23/0.48 ![X: $i] : (cC80(X) <=> ((~cC2(X)) & (~cC78(X))))),
% 0.23/0.48 inference(skolemize,[status(sab)],[300])).
% 0.23/0.48 tff(302,plain,
% 0.23/0.48 (![X: $i] : (~((cC2(X) | cC78(X)) <=> cC80(X)))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[301, 297])).
% 0.23/0.48 tff(303,plain,
% 0.23/0.48 (![X: $i] : (~((cC2(X) | cC78(X)) <=> cC80(X)))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[302, 295])).
% 0.23/0.48 tff(304,plain,
% 0.23/0.48 ((~![X: $i] : (~((cC2(X) | cC78(X)) <=> cC80(X)))) | (~((cC2(iV8471) | cC78(iV8471)) <=> cC80(iV8471)))),
% 0.23/0.48 inference(quant_inst,[status(thm)],[])).
% 0.23/0.48 tff(305,plain,
% 0.23/0.48 (~((cC2(iV8471) | cC78(iV8471)) <=> cC80(iV8471))),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[304, 303])).
% 0.23/0.48 tff(306,plain,
% 0.23/0.48 ((~cC78(iV8471)) <=> (~cC78(iV8471))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(307,axiom,(~cC78(iV8471)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_71')).
% 0.23/0.48 tff(308,plain,
% 0.23/0.48 (~cC78(iV8471)),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[307, 306])).
% 0.23/0.48 tff(309,plain,
% 0.23/0.48 ((~cC2(iV8471)) <=> (~cC2(iV8471))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(310,axiom,(~cC2(iV8471)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_70')).
% 0.23/0.48 tff(311,plain,
% 0.23/0.48 (~cC2(iV8471)),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[310, 309])).
% 0.23/0.48 tff(312,plain,
% 0.23/0.48 ((~(cC2(iV8471) | cC78(iV8471))) | cC2(iV8471) | cC78(iV8471)),
% 0.23/0.48 inference(tautology,[status(thm)],[])).
% 0.23/0.48 tff(313,plain,
% 0.23/0.48 (~(cC2(iV8471) | cC78(iV8471))),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[312, 311, 308])).
% 0.23/0.48 tff(314,plain,
% 0.23/0.48 (((cC2(iV8471) | cC78(iV8471)) <=> cC80(iV8471)) | (cC2(iV8471) | cC78(iV8471)) | cC80(iV8471)),
% 0.23/0.48 inference(tautology,[status(thm)],[])).
% 0.23/0.48 tff(315,plain,
% 0.23/0.48 (((cC2(iV8471) | cC78(iV8471)) <=> cC80(iV8471)) | cC80(iV8471)),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[314, 313])).
% 0.23/0.48 tff(316,plain,
% 0.23/0.48 (cC80(iV8471)),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[315, 305])).
% 0.23/0.48 tff(317,plain,
% 0.23/0.48 (rR1(iV8467, iV8471) <=> rR1(iV8467, iV8471)),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(318,axiom,(rR1(iV8467, iV8471)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_55')).
% 0.23/0.48 tff(319,plain,
% 0.23/0.48 (rR1(iV8467, iV8471)),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[318, 317])).
% 0.23/0.48 tff(320,plain,
% 0.23/0.48 (((~![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y)))) | ((~cC80(iV8471)) | (~rR1(iV8467, iV8471)))) <=> ((~![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y)))) | (~cC80(iV8471)) | (~rR1(iV8467, iV8471)))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(321,plain,
% 0.23/0.48 ((~![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y)))) | ((~cC80(iV8471)) | (~rR1(iV8467, iV8471)))),
% 0.23/0.48 inference(quant_inst,[status(thm)],[])).
% 0.23/0.48 tff(322,plain,
% 0.23/0.48 ((~![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y)))) | (~cC80(iV8471)) | (~rR1(iV8467, iV8471))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[321, 320])).
% 0.23/0.48 tff(323,plain,
% 0.23/0.48 ($false),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[322, 319, 316, 293])).
% 0.23/0.48 tff(324,plain,(~![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y)))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.48 tff(325,plain,
% 0.23/0.48 ((~(cC82(iV8467) | ![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y))))) | cC82(iV8467) | ![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y)))),
% 0.23/0.48 inference(tautology,[status(thm)],[])).
% 0.23/0.48 tff(326,plain,
% 0.23/0.48 ((~(cC82(iV8467) | ![Y: $i] : ((~cC80(Y)) | (~rR1(iV8467, Y))))) | cC82(iV8467)),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[325, 324])).
% 0.23/0.48 tff(327,plain,
% 0.23/0.48 (cC82(iV8467)),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[326, 292])).
% 0.23/0.48 tff(328,assumption,(xsd_integer(X!22) <=> xsd_string(X!22)), introduced(assumption)).
% 0.23/0.48 tff(329,plain,
% 0.23/0.48 (^[X: $i] : refl((~(xsd_integer(X) <=> xsd_string(X))) <=> (~(xsd_integer(X) <=> xsd_string(X))))),
% 0.23/0.48 inference(bind,[status(th)],[])).
% 0.23/0.48 tff(330,plain,
% 0.23/0.48 (![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) <=> ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X)))),
% 0.23/0.48 inference(quant_intro,[status(thm)],[329])).
% 0.23/0.48 tff(331,plain,
% 0.23/0.48 (![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) <=> ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X)))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(332,plain,
% 0.23/0.48 (^[X: $i] : trans(rewrite((xsd_string(X) <=> (~xsd_integer(X))) <=> (~(xsd_integer(X) <=> xsd_string(X)))), rewrite((~(xsd_integer(X) <=> xsd_string(X))) <=> (~(xsd_integer(X) <=> xsd_string(X)))), ((xsd_string(X) <=> (~xsd_integer(X))) <=> (~(xsd_integer(X) <=> xsd_string(X)))))),
% 0.23/0.48 inference(bind,[status(th)],[])).
% 0.23/0.48 tff(333,plain,
% 0.23/0.48 (![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) <=> ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X)))),
% 0.23/0.48 inference(quant_intro,[status(thm)],[332])).
% 0.23/0.48 tff(334,axiom,(![X: $i] : (xsd_string(X) <=> (~xsd_integer(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_1')).
% 0.23/0.48 tff(335,plain,
% 0.23/0.48 (![X: $i] : (~(xsd_integer(X) <=> xsd_string(X)))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[334, 333])).
% 0.23/0.48 tff(336,plain,
% 0.23/0.48 (![X: $i] : (~(xsd_integer(X) <=> xsd_string(X)))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[335, 331])).
% 0.23/0.48 tff(337,plain,(
% 0.23/0.48 ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X)))),
% 0.23/0.48 inference(skolemize,[status(sab)],[336])).
% 0.23/0.48 tff(338,plain,
% 0.23/0.48 (![X: $i] : (~(xsd_integer(X) <=> xsd_string(X)))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[337, 330])).
% 0.23/0.48 tff(339,plain,
% 0.23/0.48 ((~![X: $i] : (~(xsd_integer(X) <=> xsd_string(X)))) | (~(xsd_integer(X!22) <=> xsd_string(X!22)))),
% 0.23/0.48 inference(quant_inst,[status(thm)],[])).
% 0.23/0.48 tff(340,plain,
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% 0.23/0.48 inference(unit_resolution,[status(thm)],[339, 338, 328])).
% 0.23/0.48 tff(341,plain,(~(xsd_integer(X!22) <=> xsd_string(X!22))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.48 tff(342,assumption,((~(cC4(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y))))) | (~((~cC4(iV8467)) | (~(cC2(tptp_fun_Y_3(iV8467)) | (~rR1(iV8467, tptp_fun_Y_3(iV8467)))))))), introduced(assumption)).
% 0.23/0.48 tff(343,plain,
% 0.23/0.48 (^[X: $i] : refl((~((~((~cC4(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC4(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y))))))) <=> (~((~((~cC4(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC4(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y))))))))),
% 0.23/0.48 inference(bind,[status(th)],[])).
% 0.23/0.48 tff(344,plain,
% 0.23/0.48 (![X: $i] : (~((~((~cC4(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC4(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC4(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC4(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))),
% 0.23/0.48 inference(quant_intro,[status(thm)],[343])).
% 0.23/0.48 tff(345,plain,
% 0.23/0.48 (^[X: $i] : rewrite((~((~((~cC4(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC4(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y))))))) <=> (~((~((~cC4(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC4(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y))))))))),
% 0.23/0.48 inference(bind,[status(th)],[])).
% 0.23/0.48 tff(346,plain,
% 0.23/0.48 (![X: $i] : (~((~((~cC4(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC4(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC4(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC4(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))),
% 0.23/0.48 inference(quant_intro,[status(thm)],[345])).
% 0.23/0.48 tff(347,plain,
% 0.23/0.48 (![X: $i] : (~((~((~cC4(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC4(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC4(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC4(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))),
% 0.23/0.48 inference(transitivity,[status(thm)],[346, 344])).
% 0.23/0.48 tff(348,plain,
% 0.23/0.48 (^[X: $i] : trans(monotonicity(rewrite(((~cC4(X)) | (rR1(X, tptp_fun_Y_3(X)) & (~cC2(tptp_fun_Y_3(X))))) <=> ((~cC4(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))), rewrite((cC4(X) | ![Y: $i] : (~(rR1(X, Y) & (~cC2(Y))))) <=> (cC4(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y))))), ((((~cC4(X)) | (rR1(X, tptp_fun_Y_3(X)) & (~cC2(tptp_fun_Y_3(X))))) & (cC4(X) | ![Y: $i] : (~(rR1(X, Y) & (~cC2(Y)))))) <=> (((~cC4(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X)))))) & (cC4(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y))))))), rewrite((((~cC4(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X)))))) & (cC4(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y))))) <=> (~((~((~cC4(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC4(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))), ((((~cC4(X)) | (rR1(X, tptp_fun_Y_3(X)) & (~cC2(tptp_fun_Y_3(X))))) & (cC4(X) | ![Y: $i] : (~(rR1(X, Y) & (~cC2(Y)))))) <=> (~((~((~cC4(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC4(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))))),
% 0.23/0.48 inference(bind,[status(th)],[])).
% 0.23/0.48 tff(349,plain,
% 0.23/0.48 (![X: $i] : (((~cC4(X)) | (rR1(X, tptp_fun_Y_3(X)) & (~cC2(tptp_fun_Y_3(X))))) & (cC4(X) | ![Y: $i] : (~(rR1(X, Y) & (~cC2(Y)))))) <=> ![X: $i] : (~((~((~cC4(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC4(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))),
% 0.23/0.48 inference(quant_intro,[status(thm)],[348])).
% 0.23/0.48 tff(350,plain,
% 0.23/0.48 (![X: $i] : (cC4(X) <=> ?[Y: $i] : (rR1(X, Y) & (~cC2(Y)))) <=> ![X: $i] : (cC4(X) <=> ?[Y: $i] : (rR1(X, Y) & (~cC2(Y))))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(351,axiom,(![X: $i] : (cC4(X) <=> ?[Y: $i] : (rR1(X, Y) & (~cC2(Y))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_17')).
% 0.23/0.48 tff(352,plain,
% 0.23/0.48 (![X: $i] : (cC4(X) <=> ?[Y: $i] : (rR1(X, Y) & (~cC2(Y))))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[351, 350])).
% 0.23/0.48 tff(353,plain,(
% 0.23/0.48 ![X: $i] : (((~cC4(X)) | (rR1(X, tptp_fun_Y_3(X)) & (~cC2(tptp_fun_Y_3(X))))) & (cC4(X) | ![Y: $i] : (~(rR1(X, Y) & (~cC2(Y))))))),
% 0.23/0.48 inference(skolemize,[status(sab)],[352])).
% 0.23/0.48 tff(354,plain,
% 0.23/0.48 (![X: $i] : (~((~((~cC4(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC4(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[353, 349])).
% 0.23/0.48 tff(355,plain,
% 0.23/0.48 (![X: $i] : (~((~((~cC4(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC4(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[354, 347])).
% 0.23/0.48 tff(356,plain,
% 0.23/0.48 (((~![X: $i] : (~((~((~cC4(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC4(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))) | (~((~(cC4(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y))))) | (~((~cC4(iV8467)) | (~(cC2(tptp_fun_Y_3(iV8467)) | (~rR1(iV8467, tptp_fun_Y_3(iV8467)))))))))) <=> ((~![X: $i] : (~((~((~cC4(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC4(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))) | (~((~(cC4(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y))))) | (~((~cC4(iV8467)) | (~(cC2(tptp_fun_Y_3(iV8467)) | (~rR1(iV8467, tptp_fun_Y_3(iV8467))))))))))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(357,plain,
% 0.23/0.48 ((~((~((~cC4(iV8467)) | (~(cC2(tptp_fun_Y_3(iV8467)) | (~rR1(iV8467, tptp_fun_Y_3(iV8467))))))) | (~(cC4(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y))))))) <=> (~((~(cC4(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y))))) | (~((~cC4(iV8467)) | (~(cC2(tptp_fun_Y_3(iV8467)) | (~rR1(iV8467, tptp_fun_Y_3(iV8467)))))))))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(358,plain,
% 0.23/0.48 (((~![X: $i] : (~((~((~cC4(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC4(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))) | (~((~((~cC4(iV8467)) | (~(cC2(tptp_fun_Y_3(iV8467)) | (~rR1(iV8467, tptp_fun_Y_3(iV8467))))))) | (~(cC4(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y)))))))) <=> ((~![X: $i] : (~((~((~cC4(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC4(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))) | (~((~(cC4(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y))))) | (~((~cC4(iV8467)) | (~(cC2(tptp_fun_Y_3(iV8467)) | (~rR1(iV8467, tptp_fun_Y_3(iV8467))))))))))),
% 0.23/0.48 inference(monotonicity,[status(thm)],[357])).
% 0.23/0.48 tff(359,plain,
% 0.23/0.48 (((~![X: $i] : (~((~((~cC4(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC4(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))) | (~((~((~cC4(iV8467)) | (~(cC2(tptp_fun_Y_3(iV8467)) | (~rR1(iV8467, tptp_fun_Y_3(iV8467))))))) | (~(cC4(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y)))))))) <=> ((~![X: $i] : (~((~((~cC4(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC4(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))) | (~((~(cC4(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y))))) | (~((~cC4(iV8467)) | (~(cC2(tptp_fun_Y_3(iV8467)) | (~rR1(iV8467, tptp_fun_Y_3(iV8467))))))))))),
% 0.23/0.48 inference(transitivity,[status(thm)],[358, 356])).
% 0.23/0.48 tff(360,plain,
% 0.23/0.48 ((~![X: $i] : (~((~((~cC4(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC4(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))) | (~((~((~cC4(iV8467)) | (~(cC2(tptp_fun_Y_3(iV8467)) | (~rR1(iV8467, tptp_fun_Y_3(iV8467))))))) | (~(cC4(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y)))))))),
% 0.23/0.48 inference(quant_inst,[status(thm)],[])).
% 0.23/0.48 tff(361,plain,
% 0.23/0.48 ((~![X: $i] : (~((~((~cC4(X)) | (~(cC2(tptp_fun_Y_3(X)) | (~rR1(X, tptp_fun_Y_3(X))))))) | (~(cC4(X) | ![Y: $i] : (cC2(Y) | (~rR1(X, Y)))))))) | (~((~(cC4(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y))))) | (~((~cC4(iV8467)) | (~(cC2(tptp_fun_Y_3(iV8467)) | (~rR1(iV8467, tptp_fun_Y_3(iV8467)))))))))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[360, 359])).
% 0.23/0.48 tff(362,plain,
% 0.23/0.48 ($false),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[361, 355, 342])).
% 0.23/0.48 tff(363,plain,(~((~(cC4(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y))))) | (~((~cC4(iV8467)) | (~(cC2(tptp_fun_Y_3(iV8467)) | (~rR1(iV8467, tptp_fun_Y_3(iV8467))))))))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.48 tff(364,plain,
% 0.23/0.48 (((~(cC4(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y))))) | (~((~cC4(iV8467)) | (~(cC2(tptp_fun_Y_3(iV8467)) | (~rR1(iV8467, tptp_fun_Y_3(iV8467)))))))) | (cC4(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y))))),
% 0.23/0.48 inference(tautology,[status(thm)],[])).
% 0.23/0.48 tff(365,plain,
% 0.23/0.48 (cC4(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y)))),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[364, 363])).
% 0.23/0.48 tff(366,plain,
% 0.23/0.48 ((~(cC4(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y))))) | cC4(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y)))),
% 0.23/0.48 inference(tautology,[status(thm)],[])).
% 0.23/0.48 tff(367,plain,
% 0.23/0.48 ((~(cC4(iV8467) | ![Y: $i] : (cC2(Y) | (~rR1(iV8467, Y))))) | cC4(iV8467)),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[366, 12])).
% 0.23/0.48 tff(368,plain,
% 0.23/0.48 (cC4(iV8467)),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[367, 365])).
% 0.23/0.48 tff(369,assumption,(((~cC4(iV8467)) | (~cC8(iV8467))) <=> cC10(iV8467)), introduced(assumption)).
% 0.23/0.48 tff(370,plain,
% 0.23/0.48 (^[X: $i] : refl((~(((~cC4(X)) | (~cC8(X))) <=> cC10(X))) <=> (~(((~cC4(X)) | (~cC8(X))) <=> cC10(X))))),
% 0.23/0.48 inference(bind,[status(th)],[])).
% 0.23/0.48 tff(371,plain,
% 0.23/0.48 (![X: $i] : (~(((~cC4(X)) | (~cC8(X))) <=> cC10(X))) <=> ![X: $i] : (~(((~cC4(X)) | (~cC8(X))) <=> cC10(X)))),
% 0.23/0.48 inference(quant_intro,[status(thm)],[370])).
% 0.23/0.48 tff(372,plain,
% 0.23/0.48 (^[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)))))),
% 0.23/0.48 inference(bind,[status(th)],[])).
% 0.23/0.48 tff(373,plain,
% 0.23/0.48 (![X: $i] : (cC10(X) <=> (cC4(X) & cC8(X))) <=> ![X: $i] : (~(((~cC4(X)) | (~cC8(X))) <=> cC10(X)))),
% 0.23/0.48 inference(quant_intro,[status(thm)],[372])).
% 0.23/0.48 tff(374,plain,
% 0.23/0.48 (![X: $i] : (cC10(X) <=> (cC4(X) & cC8(X))) <=> ![X: $i] : (cC10(X) <=> (cC4(X) & cC8(X)))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(375,axiom,(![X: $i] : (cC10(X) <=> (cC4(X) & cC8(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_2')).
% 0.23/0.48 tff(376,plain,
% 0.23/0.48 (![X: $i] : (cC10(X) <=> (cC4(X) & cC8(X)))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[375, 374])).
% 0.23/0.48 tff(377,plain,(
% 0.23/0.48 ![X: $i] : (cC10(X) <=> (cC4(X) & cC8(X)))),
% 0.23/0.48 inference(skolemize,[status(sab)],[376])).
% 0.23/0.48 tff(378,plain,
% 0.23/0.48 (![X: $i] : (~(((~cC4(X)) | (~cC8(X))) <=> cC10(X)))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[377, 373])).
% 0.23/0.48 tff(379,plain,
% 0.23/0.48 (![X: $i] : (~(((~cC4(X)) | (~cC8(X))) <=> cC10(X)))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[378, 371])).
% 0.23/0.48 tff(380,plain,
% 0.23/0.48 ((~![X: $i] : (~(((~cC4(X)) | (~cC8(X))) <=> cC10(X)))) | (~(((~cC4(iV8467)) | (~cC8(iV8467))) <=> cC10(iV8467)))),
% 0.23/0.48 inference(quant_inst,[status(thm)],[])).
% 0.23/0.48 tff(381,plain,
% 0.23/0.48 ($false),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[380, 379, 369])).
% 0.23/0.48 tff(382,plain,(~(((~cC4(iV8467)) | (~cC8(iV8467))) <=> cC10(iV8467))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.48 tff(383,plain,
% 0.23/0.48 ((~((~cC4(iV8467)) | (~cC8(iV8467)))) | (~cC4(iV8467)) | (~cC8(iV8467))),
% 0.23/0.48 inference(tautology,[status(thm)],[])).
% 0.23/0.48 tff(384,plain,
% 0.23/0.48 (~((~cC4(iV8467)) | (~cC8(iV8467)))),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[383, 368, 268])).
% 0.23/0.48 tff(385,plain,
% 0.23/0.48 ((((~cC4(iV8467)) | (~cC8(iV8467))) <=> cC10(iV8467)) | ((~cC4(iV8467)) | (~cC8(iV8467))) | cC10(iV8467)),
% 0.23/0.48 inference(tautology,[status(thm)],[])).
% 0.23/0.48 tff(386,plain,
% 0.23/0.48 ((((~cC4(iV8467)) | (~cC8(iV8467))) <=> cC10(iV8467)) | cC10(iV8467)),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[385, 384])).
% 0.23/0.48 tff(387,plain,
% 0.23/0.48 (cC10(iV8467)),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[386, 382])).
% 0.23/0.48 tff(388,plain,
% 0.23/0.48 ((cowlNothing(X!21) | (~cowlThing(X!21))) | (~cowlNothing(X!21))),
% 0.23/0.48 inference(tautology,[status(thm)],[])).
% 0.23/0.48 tff(389,plain,
% 0.23/0.48 (~cowlNothing(X!21)),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[388, 65])).
% 0.23/0.48 tff(390,plain,
% 0.23/0.48 (cowlThing(iV8472) <=> cowlThing(iV8472)),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(391,axiom,(cowlThing(iV8472)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_75')).
% 0.23/0.48 tff(392,plain,
% 0.23/0.48 (cowlThing(iV8472)),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[391, 390])).
% 0.23/0.49 tff(393,plain,
% 0.23/0.49 (cowlThing(iV8471) <=> cowlThing(iV8471)),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(394,axiom,(cowlThing(iV8471)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_72')).
% 0.23/0.49 tff(395,plain,
% 0.23/0.49 (cowlThing(iV8471)),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[394, 393])).
% 0.23/0.49 tff(396,plain,
% 0.23/0.49 (cowlThing(iV8467) <=> cowlThing(iV8467)),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(397,axiom,(cowlThing(iV8467)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_52')).
% 0.23/0.49 tff(398,plain,
% 0.23/0.49 (cowlThing(iV8467)),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[397, 396])).
% 0.23/0.49 tff(399,plain,
% 0.23/0.49 (((cowlNothing(X!21) | (~cowlThing(X!21))) | (xsd_integer(X!22) <=> xsd_string(X!22)) | (~cC10(iV8467)) | (~cC48(iV8467)) | (~cC4(iV8467)) | (~cC82(iV8467)) | (~cC14(iV8467)) | (~cC8(iV8467)) | (~cC20(iV8467)) | (~cowlThing(iV8467)) | (~cC62(iV8467)) | (~cC34(iV8467)) | (~cowlThing(iV8471)) | (~cC80(iV8471)) | (~cC60(iV8472)) | (~cowlThing(iV8472)) | (~cC58(iV8472))) <=> (cowlNothing(X!21) | (xsd_integer(X!22) <=> xsd_string(X!22)) | (~cC10(iV8467)) | (~cC48(iV8467)) | (~cC4(iV8467)) | (~cC82(iV8467)) | (~cC14(iV8467)) | (~cC8(iV8467)) | (~cC20(iV8467)) | (~cowlThing(iV8467)) | (~cC62(iV8467)) | (~cC34(iV8467)) | (~cowlThing(iV8471)) | (~cC80(iV8471)) | (~cC60(iV8472)) | (~cowlThing(iV8472)) | (~cC58(iV8472)) | (~cowlThing(X!21)))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(400,plain,
% 0.23/0.49 ((~(~(cowlNothing(X!21) | (~cowlThing(X!21))))) <=> (cowlNothing(X!21) | (~cowlThing(X!21)))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(401,plain,
% 0.23/0.49 ((cowlThing(X!21) & (~cowlNothing(X!21))) <=> (~(cowlNothing(X!21) | (~cowlThing(X!21))))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(402,plain,
% 0.23/0.49 ((~(cowlThing(X!21) & (~cowlNothing(X!21)))) <=> (~(~(cowlNothing(X!21) | (~cowlThing(X!21)))))),
% 0.23/0.49 inference(monotonicity,[status(thm)],[401])).
% 0.23/0.49 tff(403,plain,
% 0.23/0.49 ((~(cowlThing(X!21) & (~cowlNothing(X!21)))) <=> (cowlNothing(X!21) | (~cowlThing(X!21)))),
% 0.23/0.49 inference(transitivity,[status(thm)],[402, 400])).
% 0.23/0.49 tff(404,plain,
% 0.23/0.49 (((~(cowlThing(X!21) & (~cowlNothing(X!21)))) | (xsd_integer(X!22) <=> xsd_string(X!22)) | (~cC10(iV8467)) | (~cC48(iV8467)) | (~cC4(iV8467)) | (~cC82(iV8467)) | (~cC14(iV8467)) | (~cC8(iV8467)) | (~cC20(iV8467)) | (~cowlThing(iV8467)) | (~cC62(iV8467)) | (~cC34(iV8467)) | (~cowlThing(iV8471)) | (~cC80(iV8471)) | (~cC60(iV8472)) | (~cowlThing(iV8472)) | (~cC58(iV8472))) <=> ((cowlNothing(X!21) | (~cowlThing(X!21))) | (xsd_integer(X!22) <=> xsd_string(X!22)) | (~cC10(iV8467)) | (~cC48(iV8467)) | (~cC4(iV8467)) | (~cC82(iV8467)) | (~cC14(iV8467)) | (~cC8(iV8467)) | (~cC20(iV8467)) | (~cowlThing(iV8467)) | (~cC62(iV8467)) | (~cC34(iV8467)) | (~cowlThing(iV8471)) | (~cC80(iV8471)) | (~cC60(iV8472)) | (~cowlThing(iV8472)) | (~cC58(iV8472)))),
% 0.23/0.49 inference(monotonicity,[status(thm)],[403])).
% 0.23/0.49 tff(405,plain,
% 0.23/0.49 (((~(cowlThing(X!21) & (~cowlNothing(X!21)))) | (xsd_integer(X!22) <=> xsd_string(X!22)) | (~cC10(iV8467)) | (~cC48(iV8467)) | (~cC4(iV8467)) | (~cC82(iV8467)) | (~cC14(iV8467)) | (~cC8(iV8467)) | (~cC20(iV8467)) | (~cowlThing(iV8467)) | (~cC62(iV8467)) | (~cC34(iV8467)) | (~cowlThing(iV8471)) | (~cC80(iV8471)) | (~cC60(iV8472)) | (~cowlThing(iV8472)) | (~cC58(iV8472))) <=> (cowlNothing(X!21) | (xsd_integer(X!22) <=> xsd_string(X!22)) | (~cC10(iV8467)) | (~cC48(iV8467)) | (~cC4(iV8467)) | (~cC82(iV8467)) | (~cC14(iV8467)) | (~cC8(iV8467)) | (~cC20(iV8467)) | (~cowlThing(iV8467)) | (~cC62(iV8467)) | (~cC34(iV8467)) | (~cowlThing(iV8471)) | (~cC80(iV8471)) | (~cC60(iV8472)) | (~cowlThing(iV8472)) | (~cC58(iV8472)) | (~cowlThing(X!21)))),
% 0.23/0.49 inference(transitivity,[status(thm)],[404, 399])).
% 0.23/0.49 tff(406,plain,
% 0.23/0.49 (((~(cowlThing(X!21) & (~cowlNothing(X!21)))) | (xsd_integer(X!22) <=> xsd_string(X!22)) | (~cC10(iV8467)) | (~cC48(iV8467)) | (~cC4(iV8467)) | (~cC82(iV8467)) | (~cC14(iV8467)) | (~cC8(iV8467)) | (~cC20(iV8467)) | (~cowlThing(iV8467)) | (~cC62(iV8467)) | (~cC34(iV8467)) | (~cowlThing(iV8471)) | (~cC80(iV8471)) | (~cC60(iV8472)) | (~cowlThing(iV8472)) | (~cC58(iV8472))) <=> ((~(cowlThing(X!21) & (~cowlNothing(X!21)))) | (xsd_integer(X!22) <=> xsd_string(X!22)) | (~cC10(iV8467)) | (~cC48(iV8467)) | (~cC4(iV8467)) | (~cC82(iV8467)) | (~cC14(iV8467)) | (~cC8(iV8467)) | (~cC20(iV8467)) | (~cowlThing(iV8467)) | (~cC62(iV8467)) | (~cC34(iV8467)) | (~cowlThing(iV8471)) | (~cC80(iV8471)) | (~cC60(iV8472)) | (~cowlThing(iV8472)) | (~cC58(iV8472)))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(407,plain,
% 0.23/0.49 ((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & cC10(iV8467) & cC48(iV8467) & cC4(iV8467) & cC82(iV8467) & cC14(iV8467) & cC8(iV8467) & cC20(iV8467) & cowlThing(iV8467) & cC62(iV8467) & cC34(iV8467) & cowlThing(iV8471) & cC80(iV8471) & cC60(iV8472) & cowlThing(iV8472) & cC58(iV8472)) <=> (![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & cC10(iV8467) & cC48(iV8467) & cC4(iV8467) & cC82(iV8467) & cC14(iV8467) & cC8(iV8467) & cC20(iV8467) & cowlThing(iV8467) & cC62(iV8467) & cC34(iV8467) & cowlThing(iV8471) & cC80(iV8471) & cC60(iV8472) & cowlThing(iV8472) & cC58(iV8472))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(408,plain,
% 0.23/0.49 ((~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & cC10(iV8467) & cC48(iV8467) & cC4(iV8467) & cC82(iV8467) & cC14(iV8467) & cC8(iV8467) & cC20(iV8467) & cowlThing(iV8467) & cC62(iV8467) & cC34(iV8467) & cowlThing(iV8471) & cC80(iV8471) & cC60(iV8472) & cowlThing(iV8472) & cC58(iV8472))) <=> (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & cC10(iV8467) & cC48(iV8467) & cC4(iV8467) & cC82(iV8467) & cC14(iV8467) & cC8(iV8467) & cC20(iV8467) & cowlThing(iV8467) & cC62(iV8467) & cC34(iV8467) & cowlThing(iV8471) & cC80(iV8471) & cC60(iV8472) & cowlThing(iV8472) & cC58(iV8472)))),
% 0.23/0.49 inference(monotonicity,[status(thm)],[407])).
% 0.23/0.49 tff(409,plain,
% 0.23/0.49 ((~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & cC10(iV8467) & cC48(iV8467) & cC4(iV8467) & cC82(iV8467) & cC14(iV8467) & cC8(iV8467) & cC20(iV8467) & cowlThing(iV8467) & cC62(iV8467) & cC34(iV8467) & cowlThing(iV8471) & cC80(iV8471) & cC60(iV8472) & cowlThing(iV8472) & cC58(iV8472))) <=> (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & cC10(iV8467) & cC48(iV8467) & cC4(iV8467) & cC82(iV8467) & cC14(iV8467) & cC8(iV8467) & cC20(iV8467) & cowlThing(iV8467) & cC62(iV8467) & cC34(iV8467) & cowlThing(iV8471) & cC80(iV8471) & cC60(iV8472) & cowlThing(iV8472) & cC58(iV8472)))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(410,plain,
% 0.23/0.49 ((~((((((((((((((((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X)))) & cC10(iV8467)) & cC48(iV8467)) & cC4(iV8467)) & cC82(iV8467)) & cC14(iV8467)) & cC8(iV8467)) & cC20(iV8467)) & cowlThing(iV8467)) & cC62(iV8467)) & cC34(iV8467)) & cowlThing(iV8471)) & cC80(iV8471)) & cC60(iV8472)) & cowlThing(iV8472)) & cC58(iV8472))) <=> (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & cC10(iV8467) & cC48(iV8467) & cC4(iV8467) & cC82(iV8467) & cC14(iV8467) & cC8(iV8467) & cC20(iV8467) & cowlThing(iV8467) & cC62(iV8467) & cC34(iV8467) & cowlThing(iV8471) & cC80(iV8471) & cC60(iV8472) & cowlThing(iV8472) & cC58(iV8472)))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(411,axiom,(~((((((((((((((((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X)))) & cC10(iV8467)) & cC48(iV8467)) & cC4(iV8467)) & cC82(iV8467)) & cC14(iV8467)) & cC8(iV8467)) & cC20(iV8467)) & cowlThing(iV8467)) & cC62(iV8467)) & cC34(iV8467)) & cowlThing(iV8471)) & cC80(iV8471)) & cC60(iV8472)) & cowlThing(iV8472)) & cC58(iV8472))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','the_axiom')).
% 0.23/0.49 tff(412,plain,
% 0.23/0.49 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & cC10(iV8467) & cC48(iV8467) & cC4(iV8467) & cC82(iV8467) & cC14(iV8467) & cC8(iV8467) & cC20(iV8467) & cowlThing(iV8467) & cC62(iV8467) & cC34(iV8467) & cowlThing(iV8471) & cC80(iV8471) & cC60(iV8472) & cowlThing(iV8472) & cC58(iV8472))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[411, 410])).
% 0.23/0.50 tff(413,plain,
% 0.23/0.50 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & cC10(iV8467) & cC48(iV8467) & cC4(iV8467) & cC82(iV8467) & cC14(iV8467) & cC8(iV8467) & cC20(iV8467) & cowlThing(iV8467) & cC62(iV8467) & cC34(iV8467) & cowlThing(iV8471) & cC80(iV8471) & cC60(iV8472) & cowlThing(iV8472) & cC58(iV8472))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[412, 408])).
% 0.23/0.50 tff(414,plain,
% 0.23/0.50 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & cC10(iV8467) & cC48(iV8467) & cC4(iV8467) & cC82(iV8467) & cC14(iV8467) & cC8(iV8467) & cC20(iV8467) & cowlThing(iV8467) & cC62(iV8467) & cC34(iV8467) & cowlThing(iV8471) & cC80(iV8471) & cC60(iV8472) & cowlThing(iV8472) & cC58(iV8472))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[413, 409])).
% 0.23/0.50 tff(415,plain,
% 0.23/0.50 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & cC10(iV8467) & cC48(iV8467) & cC4(iV8467) & cC82(iV8467) & cC14(iV8467) & cC8(iV8467) & cC20(iV8467) & cowlThing(iV8467) & cC62(iV8467) & cC34(iV8467) & cowlThing(iV8471) & cC80(iV8471) & cC60(iV8472) & cowlThing(iV8472) & cC58(iV8472))),
% 0.23/0.50 inference(modus_ponens,[status(thm)],[414, 408])).
% 0.23/0.50 unexpected number of arguments: (let ((a!1 (forall ((X $i)) (and (cowlThing X) (not (cowlNothing X)))))
% 0.23/0.50 (a!2 (not (and (cowlThing X!21) (not (cowlNothing X!21)))))
% 0.23/0.50 (a!3 (forall ((X $i)) (not (= (xsd_integer X) (xsd_string X)))))
% 0.23/0.50 (a!5 (refl (~ (not (cC10 iV8467)) (not (cC10 iV8467)))))
% 0.23/0.50 (a!6 (refl (~ (not (cC48 iV8467)) (not (cC48 iV8467)))))
% 0.23/0.50 (a!7 (refl (~ (not (cC4 iV8467)) (not (cC4 iV8467)))))
% 0.23/0.50 (a!8 (refl (~ (not (cC82 iV8467)) (not (cC82 iV8467)))))
% 0.23/0.50 (a!9 (refl (~ (not (cC14 iV8467)) (not (cC14 iV8467)))))
% 0.23/0.50 (a!10 (refl (~ (not (cC8 iV8467)) (not (cC8 iV8467)))))
% 0.23/0.50 (a!11 (refl (~ (not (cC20 iV8467)) (not (cC20 iV8467)))))
% 0.23/0.50 (a!12 (refl (~ (not (cowlThing iV8467)) (not (cowlThing iV8467)))))
% 0.23/0.50 (a!13 (refl (~ (not (cC62 iV8467)) (not (cC62 iV8467)))))
% 0.23/0.50 (a!14 (refl (~ (not (cC34 iV8467)) (not (cC34 iV8467)))))
% 0.23/0.50 (a!15 (refl (~ (not (cowlThing iV8471)) (not (cowlThing iV8471)))))
% 0.23/0.50 (a!16 (refl (~ (not (cC80 iV8471)) (not (cC80 iV8471)))))
% 0.23/0.50 (a!17 (refl (~ (not (cC60 iV8472)) (not (cC60 iV8472)))))
% 0.23/0.50 (a!18 (refl (~ (not (cowlThing iV8472)) (not (cowlThing iV8472)))))
% 0.23/0.50 (a!19 (refl (~ (not (cC58 iV8472)) (not (cC58 iV8472))))))
% 0.23/0.50 (let ((a!4 (sk (~ (not a!3) (= (xsd_integer X!22) (xsd_string X!22)))))
% 0.23/0.50 (a!20 (~ (not (and a!1
% 0.23/0.50 a!3
% 0.23/0.50 (cC10 iV8467)
% 0.23/0.50 (cC48 iV8467)
% 0.23/0.50 (cC4 iV8467)
% 0.23/0.50 (cC82 iV8467)
% 0.23/0.50 (cC14 iV8467)
% 0.23/0.50 (cC8 iV8467)
% 0.23/0.50 (cC20 iV8467)
% 0.23/0.50 (cowlThing iV8467)
% 0.23/0.50 (cC62 iV8467)
% 0.23/0.50 (cC34 iV8467)
% 0.23/0.50 (cowlThing iV8471)
% 0.23/0.50 (cC80 iV8471)
% 0.23/0.50 (cC60 iV8472)
% 0.23/0.50 (cowlThing iV8472)
% 0.23/0.50 (cC58 iV8472)))
% 0.23/0.50 (or a!2
% 0.23/0.50 (= (xsd_integer X!22) (xsd_string X!22))
% 0.23/0.50 (not (cC10 iV8467))
% 0.23/0.50 (not (cC48 iV8467))
% 0.23/0.50 (not (cC4 iV8467))
% 0.23/0.50 (not (cC82 iV8467))
% 0.23/0.50 (not (cC14 iV8467))
% 0.23/0.50 (not (cC8 iV8467))
% 0.23/0.50 (not (cC20 iV8467))
% 0.23/0.50 (not (cowlThing iV8467))
% 0.23/0.50 (not (cC62 iV8467))
% 0.23/0.50 (not (cC34 iV8467))
% 0.23/0.50 (not (cowlThing iV8471))
% 0.23/0.50 (not (cC80 iV8471))
% 0.23/0.50 (not (cC60 iV8472))
% 0.23/0.50 (not (cowlThing iV8472))
% 0.23/0.50 (not (cC58 iV8472))))))
% 0.23/0.50 (nnf-neg (sk (~ (not a!1) a!2))
% 0.23/0.50 a!4
% 0.23/0.50 a!5
% 0.23/0.50 a!6
% 0.23/0.50 a!7
% 0.23/0.50 a!8
% 0.23/0.50 a!9
% 0.23/0.50 a!10
% 0.23/0.50 a!11
% 0.23/0.50 a!12
% 0.23/0.50 a!13
% 0.23/0.50 a!14
% 0.23/0.50 a!15
% 0.23/0.50 a!16
% 0.23/0.50 a!17
% 0.23/0.50 a!18
% 0.23/0.50 a!19
% 0.23/0.50 a!20)))
% 0.23/0.50 Proof display could not be completed: unexpected number of arguments
% 0.23/0.50 % E exiting
%------------------------------------------------------------------------------