%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS104+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:13:23 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.41s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KRS104+1 : TPTP v9.0.0. Released v3.1.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n012.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 19:10:26 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.41 % SZS status Unsatisfiable
% 0.19/0.41 % SZS output start Proof
% 0.19/0.41 tff(ra_Px2_type, type, (
% 0.19/0.41 ra_Px2: ( $i * $i ) > $o)).
% 0.19/0.41 tff(tptp_fun_Y0_4_type, type, (
% 0.19/0.41 tptp_fun_Y0_4: $i > $i)).
% 0.19/0.41 tff(i2003_11_14_17_20_50869_type, type, (
% 0.19/0.41 i2003_11_14_17_20_50869: $i)).
% 0.19/0.41 tff(cc_type, type, (
% 0.19/0.41 cc: $i > $o)).
% 0.19/0.41 tff(cb_type, type, (
% 0.19/0.41 cb: $i > $o)).
% 0.19/0.41 tff(ca_Cx8xcomp_type, type, (
% 0.19/0.41 ca_Cx8xcomp: $i > $o)).
% 0.19/0.41 tff(ra_Px8_type, type, (
% 0.19/0.41 ra_Px8: ( $i * $i ) > $o)).
% 0.19/0.41 tff(tptp_fun_Y_12_type, type, (
% 0.19/0.41 tptp_fun_Y_12: $i > $i)).
% 0.19/0.41 tff(ca_Cx8_type, type, (
% 0.19/0.41 ca_Cx8: $i > $o)).
% 0.19/0.41 tff(ca_Cx7_type, type, (
% 0.19/0.41 ca_Cx7: $i > $o)).
% 0.19/0.41 tff(ca_Cx6_type, type, (
% 0.19/0.41 ca_Cx6: $i > $o)).
% 0.19/0.41 tff(cUnsatisfiablexcomp_type, type, (
% 0.19/0.41 cUnsatisfiablexcomp: $i > $o)).
% 0.19/0.41 tff(ra_Px5_type, type, (
% 0.19/0.41 ra_Px5: ( $i * $i ) > $o)).
% 0.19/0.41 tff(tptp_fun_Y0_1_type, type, (
% 0.19/0.41 tptp_fun_Y0_1: $i > $i)).
% 0.19/0.41 tff(cUnsatisfiable_type, type, (
% 0.19/0.41 cUnsatisfiable: $i > $o)).
% 0.19/0.41 tff(tptp_fun_Y_0_type, type, (
% 0.19/0.41 tptp_fun_Y_0: $i > $i)).
% 0.19/0.41 tff(ra_Px7_type, type, (
% 0.19/0.41 ra_Px7: ( $i * $i ) > $o)).
% 0.19/0.41 tff(tptp_fun_Y0_10_type, type, (
% 0.19/0.41 tptp_fun_Y0_10: $i > $i)).
% 0.19/0.41 tff(tptp_fun_Y_11_type, type, (
% 0.19/0.41 tptp_fun_Y_11: $i > $i)).
% 0.19/0.41 tff(ca_Cx7xcomp_type, type, (
% 0.19/0.41 ca_Cx7xcomp: $i > $o)).
% 0.19/0.41 tff(ca_type, type, (
% 0.19/0.41 ca: $i > $o)).
% 0.19/0.41 tff(ca_Cx1_type, type, (
% 0.19/0.41 ca_Cx1: $i > $o)).
% 0.19/0.41 tff(ccxcomp_type, type, (
% 0.19/0.41 ccxcomp: $i > $o)).
% 0.19/0.41 tff(cbxcomp_type, type, (
% 0.19/0.41 cbxcomp: $i > $o)).
% 0.19/0.41 tff(ra_Px3_type, type, (
% 0.19/0.41 ra_Px3: ( $i * $i ) > $o)).
% 0.19/0.41 tff(tptp_fun_Y0_2_type, type, (
% 0.19/0.41 tptp_fun_Y0_2: $i > $i)).
% 0.19/0.41 tff(tptp_fun_Y0_13_type, type, (
% 0.19/0.41 tptp_fun_Y0_13: $i > $i)).
% 0.19/0.41 tff(ra_Px6_type, type, (
% 0.19/0.41 ra_Px6: ( $i * $i ) > $o)).
% 0.19/0.41 tff(tptp_fun_Y_8_type, type, (
% 0.19/0.41 tptp_fun_Y_8: $i > $i)).
% 0.19/0.41 tff(ca_Cx6xcomp_type, type, (
% 0.19/0.41 ca_Cx6xcomp: $i > $o)).
% 0.19/0.41 tff(tptp_fun_Y0_9_type, type, (
% 0.19/0.41 tptp_fun_Y0_9: $i > $i)).
% 0.19/0.41 tff(tptp_fun_Y_5_type, type, (
% 0.19/0.41 tptp_fun_Y_5: $i > $i)).
% 0.19/0.41 tff(tptp_fun_Y_3_type, type, (
% 0.19/0.41 tptp_fun_Y_3: $i > $i)).
% 0.19/0.41 tff(1,plain,
% 0.19/0.41 (^[X: $i] : refl((~((~((~cc(X)) | ra_Px2(X, tptp_fun_Y0_4(X)))) | (~(cc(X) | ![Y0: $i] : (~ra_Px2(X, Y0)))))) <=> (~((~((~cc(X)) | ra_Px2(X, tptp_fun_Y0_4(X)))) | (~(cc(X) | ![Y0: $i] : (~ra_Px2(X, Y0)))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(2,plain,
% 0.19/0.41 (![X: $i] : (~((~((~cc(X)) | ra_Px2(X, tptp_fun_Y0_4(X)))) | (~(cc(X) | ![Y0: $i] : (~ra_Px2(X, Y0)))))) <=> ![X: $i] : (~((~((~cc(X)) | ra_Px2(X, tptp_fun_Y0_4(X)))) | (~(cc(X) | ![Y0: $i] : (~ra_Px2(X, Y0))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.41 tff(3,plain,
% 0.19/0.41 (^[X: $i] : rewrite((~((~((~cc(X)) | ra_Px2(X, tptp_fun_Y0_4(X)))) | (~(cc(X) | ![Y0: $i] : (~ra_Px2(X, Y0)))))) <=> (~((~((~cc(X)) | ra_Px2(X, tptp_fun_Y0_4(X)))) | (~(cc(X) | ![Y0: $i] : (~ra_Px2(X, Y0)))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(4,plain,
% 0.19/0.41 (![X: $i] : (~((~((~cc(X)) | ra_Px2(X, tptp_fun_Y0_4(X)))) | (~(cc(X) | ![Y0: $i] : (~ra_Px2(X, Y0)))))) <=> ![X: $i] : (~((~((~cc(X)) | ra_Px2(X, tptp_fun_Y0_4(X)))) | (~(cc(X) | ![Y0: $i] : (~ra_Px2(X, Y0))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.41 tff(5,plain,
% 0.19/0.41 (![X: $i] : (~((~((~cc(X)) | ra_Px2(X, tptp_fun_Y0_4(X)))) | (~(cc(X) | ![Y0: $i] : (~ra_Px2(X, Y0)))))) <=> ![X: $i] : (~((~((~cc(X)) | ra_Px2(X, tptp_fun_Y0_4(X)))) | (~(cc(X) | ![Y0: $i] : (~ra_Px2(X, Y0))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[4, 2])).
% 0.19/0.41 tff(6,plain,
% 0.19/0.41 (^[X: $i] : trans(monotonicity(rewrite((cc(X) | ![Y0: $i] : (~ra_Px2(X, Y0))) <=> (cc(X) | ![Y0: $i] : (~ra_Px2(X, Y0)))), ((((~cc(X)) | ra_Px2(X, tptp_fun_Y0_4(X))) & (cc(X) | ![Y0: $i] : (~ra_Px2(X, Y0)))) <=> (((~cc(X)) | ra_Px2(X, tptp_fun_Y0_4(X))) & (cc(X) | ![Y0: $i] : (~ra_Px2(X, Y0)))))), rewrite((((~cc(X)) | ra_Px2(X, tptp_fun_Y0_4(X))) & (cc(X) | ![Y0: $i] : (~ra_Px2(X, Y0)))) <=> (~((~((~cc(X)) | ra_Px2(X, tptp_fun_Y0_4(X)))) | (~(cc(X) | ![Y0: $i] : (~ra_Px2(X, Y0))))))), ((((~cc(X)) | ra_Px2(X, tptp_fun_Y0_4(X))) & (cc(X) | ![Y0: $i] : (~ra_Px2(X, Y0)))) <=> (~((~((~cc(X)) | ra_Px2(X, tptp_fun_Y0_4(X)))) | (~(cc(X) | ![Y0: $i] : (~ra_Px2(X, Y0))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(7,plain,
% 0.19/0.41 (![X: $i] : (((~cc(X)) | ra_Px2(X, tptp_fun_Y0_4(X))) & (cc(X) | ![Y0: $i] : (~ra_Px2(X, Y0)))) <=> ![X: $i] : (~((~((~cc(X)) | ra_Px2(X, tptp_fun_Y0_4(X)))) | (~(cc(X) | ![Y0: $i] : (~ra_Px2(X, Y0))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[6])).
% 0.19/0.41 tff(8,plain,
% 0.19/0.41 (![X: $i] : (cc(X) <=> ?[Y0: $i] : ra_Px2(X, Y0)) <=> ![X: $i] : (cc(X) <=> ?[Y0: $i] : ra_Px2(X, Y0))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(9,axiom,(![X: $i] : (cc(X) <=> ?[Y0: $i] : ra_Px2(X, Y0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_9')).
% 0.19/0.41 tff(10,plain,
% 0.19/0.41 (![X: $i] : (cc(X) <=> ?[Y0: $i] : ra_Px2(X, Y0))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.19/0.41 tff(11,plain,(
% 0.19/0.41 ![X: $i] : (((~cc(X)) | ra_Px2(X, tptp_fun_Y0_4(X))) & (cc(X) | ![Y0: $i] : (~ra_Px2(X, Y0))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[10])).
% 0.19/0.41 tff(12,plain,
% 0.19/0.41 (![X: $i] : (~((~((~cc(X)) | ra_Px2(X, tptp_fun_Y0_4(X)))) | (~(cc(X) | ![Y0: $i] : (~ra_Px2(X, Y0))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.19/0.41 tff(13,plain,
% 0.19/0.41 (![X: $i] : (~((~((~cc(X)) | ra_Px2(X, tptp_fun_Y0_4(X)))) | (~(cc(X) | ![Y0: $i] : (~ra_Px2(X, Y0))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.19/0.41 tff(14,plain,
% 0.19/0.41 ((~![X: $i] : (~((~((~cc(X)) | ra_Px2(X, tptp_fun_Y0_4(X)))) | (~(cc(X) | ![Y0: $i] : (~ra_Px2(X, Y0))))))) | (~((~((~cc(i2003_11_14_17_20_50869)) | ra_Px2(i2003_11_14_17_20_50869, tptp_fun_Y0_4(i2003_11_14_17_20_50869)))) | (~(cc(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px2(i2003_11_14_17_20_50869, Y0))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(15,plain,
% 0.19/0.41 (~((~((~cc(i2003_11_14_17_20_50869)) | ra_Px2(i2003_11_14_17_20_50869, tptp_fun_Y0_4(i2003_11_14_17_20_50869)))) | (~(cc(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px2(i2003_11_14_17_20_50869, Y0)))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.19/0.41 tff(16,plain,
% 0.19/0.41 (((~((~cc(i2003_11_14_17_20_50869)) | ra_Px2(i2003_11_14_17_20_50869, tptp_fun_Y0_4(i2003_11_14_17_20_50869)))) | (~(cc(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px2(i2003_11_14_17_20_50869, Y0))))) | ((~cc(i2003_11_14_17_20_50869)) | ra_Px2(i2003_11_14_17_20_50869, tptp_fun_Y0_4(i2003_11_14_17_20_50869)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(17,plain,
% 0.19/0.41 ((~cc(i2003_11_14_17_20_50869)) | ra_Px2(i2003_11_14_17_20_50869, tptp_fun_Y0_4(i2003_11_14_17_20_50869))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.19/0.41 tff(18,plain,
% 0.19/0.41 (^[X: $i] : refl((~(((~cb(X)) | (~cc(X))) <=> ca_Cx8xcomp(X))) <=> (~(((~cb(X)) | (~cc(X))) <=> ca_Cx8xcomp(X))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(19,plain,
% 0.19/0.41 (![X: $i] : (~(((~cb(X)) | (~cc(X))) <=> ca_Cx8xcomp(X))) <=> ![X: $i] : (~(((~cb(X)) | (~cc(X))) <=> ca_Cx8xcomp(X)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[18])).
% 0.19/0.41 tff(20,plain,
% 0.19/0.41 (^[X: $i] : trans(trans(monotonicity(rewrite((cc(X) & cb(X)) <=> (~((~cb(X)) | (~cc(X))))), ((ca_Cx8xcomp(X) <=> (cc(X) & cb(X))) <=> (ca_Cx8xcomp(X) <=> (~((~cb(X)) | (~cc(X))))))), rewrite((ca_Cx8xcomp(X) <=> (~((~cb(X)) | (~cc(X))))) <=> (~(((~cb(X)) | (~cc(X))) <=> ca_Cx8xcomp(X)))), ((ca_Cx8xcomp(X) <=> (cc(X) & cb(X))) <=> (~(((~cb(X)) | (~cc(X))) <=> ca_Cx8xcomp(X))))), rewrite((~(((~cb(X)) | (~cc(X))) <=> ca_Cx8xcomp(X))) <=> (~(((~cb(X)) | (~cc(X))) <=> ca_Cx8xcomp(X)))), ((ca_Cx8xcomp(X) <=> (cc(X) & cb(X))) <=> (~(((~cb(X)) | (~cc(X))) <=> ca_Cx8xcomp(X)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(21,plain,
% 0.19/0.41 (![X: $i] : (ca_Cx8xcomp(X) <=> (cc(X) & cb(X))) <=> ![X: $i] : (~(((~cb(X)) | (~cc(X))) <=> ca_Cx8xcomp(X)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[20])).
% 0.19/0.41 tff(22,plain,
% 0.19/0.41 (![X: $i] : (ca_Cx8xcomp(X) <=> (cc(X) & cb(X))) <=> ![X: $i] : (ca_Cx8xcomp(X) <=> (cc(X) & cb(X)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(23,axiom,(![X: $i] : (ca_Cx8xcomp(X) <=> (cc(X) & cb(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_22')).
% 0.19/0.41 tff(24,plain,
% 0.19/0.41 (![X: $i] : (ca_Cx8xcomp(X) <=> (cc(X) & cb(X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.19/0.41 tff(25,plain,(
% 0.19/0.41 ![X: $i] : (ca_Cx8xcomp(X) <=> (cc(X) & cb(X)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[24])).
% 0.19/0.41 tff(26,plain,
% 0.19/0.41 (![X: $i] : (~(((~cb(X)) | (~cc(X))) <=> ca_Cx8xcomp(X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.19/0.41 tff(27,plain,
% 0.19/0.41 (![X: $i] : (~(((~cb(X)) | (~cc(X))) <=> ca_Cx8xcomp(X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.19/0.41 tff(28,plain,
% 0.19/0.41 ((~![X: $i] : (~(((~cb(X)) | (~cc(X))) <=> ca_Cx8xcomp(X)))) | (~(((~cb(i2003_11_14_17_20_50869)) | (~cc(i2003_11_14_17_20_50869))) <=> ca_Cx8xcomp(i2003_11_14_17_20_50869)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(29,plain,
% 0.19/0.41 (~(((~cb(i2003_11_14_17_20_50869)) | (~cc(i2003_11_14_17_20_50869))) <=> ca_Cx8xcomp(i2003_11_14_17_20_50869))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.19/0.41 tff(30,plain,
% 0.19/0.41 (^[X: $i] : refl((~(((~ca_Cx6(X)) | (~ca_Cx7(X)) | (~ca_Cx8(X))) <=> cUnsatisfiablexcomp(X))) <=> (~(((~ca_Cx6(X)) | (~ca_Cx7(X)) | (~ca_Cx8(X))) <=> cUnsatisfiablexcomp(X))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(31,plain,
% 0.19/0.41 (![X: $i] : (~(((~ca_Cx6(X)) | (~ca_Cx7(X)) | (~ca_Cx8(X))) <=> cUnsatisfiablexcomp(X))) <=> ![X: $i] : (~(((~ca_Cx6(X)) | (~ca_Cx7(X)) | (~ca_Cx8(X))) <=> cUnsatisfiablexcomp(X)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[30])).
% 0.19/0.41 tff(32,plain,
% 0.19/0.41 (^[X: $i] : trans(trans(monotonicity(rewrite((ca_Cx7(X) & ca_Cx8(X) & ca_Cx6(X)) <=> (~((~ca_Cx6(X)) | (~ca_Cx7(X)) | (~ca_Cx8(X))))), ((cUnsatisfiablexcomp(X) <=> (ca_Cx7(X) & ca_Cx8(X) & ca_Cx6(X))) <=> (cUnsatisfiablexcomp(X) <=> (~((~ca_Cx6(X)) | (~ca_Cx7(X)) | (~ca_Cx8(X))))))), rewrite((cUnsatisfiablexcomp(X) <=> (~((~ca_Cx6(X)) | (~ca_Cx7(X)) | (~ca_Cx8(X))))) <=> (~(((~ca_Cx6(X)) | (~ca_Cx7(X)) | (~ca_Cx8(X))) <=> cUnsatisfiablexcomp(X)))), ((cUnsatisfiablexcomp(X) <=> (ca_Cx7(X) & ca_Cx8(X) & ca_Cx6(X))) <=> (~(((~ca_Cx6(X)) | (~ca_Cx7(X)) | (~ca_Cx8(X))) <=> cUnsatisfiablexcomp(X))))), rewrite((~(((~ca_Cx6(X)) | (~ca_Cx7(X)) | (~ca_Cx8(X))) <=> cUnsatisfiablexcomp(X))) <=> (~(((~ca_Cx6(X)) | (~ca_Cx7(X)) | (~ca_Cx8(X))) <=> cUnsatisfiablexcomp(X)))), ((cUnsatisfiablexcomp(X) <=> (ca_Cx7(X) & ca_Cx8(X) & ca_Cx6(X))) <=> (~(((~ca_Cx6(X)) | (~ca_Cx7(X)) | (~ca_Cx8(X))) <=> cUnsatisfiablexcomp(X)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(33,plain,
% 0.19/0.41 (![X: $i] : (cUnsatisfiablexcomp(X) <=> (ca_Cx7(X) & ca_Cx8(X) & ca_Cx6(X))) <=> ![X: $i] : (~(((~ca_Cx6(X)) | (~ca_Cx7(X)) | (~ca_Cx8(X))) <=> cUnsatisfiablexcomp(X)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[32])).
% 0.19/0.41 tff(34,plain,
% 0.19/0.41 (![X: $i] : (cUnsatisfiablexcomp(X) <=> (ca_Cx7(X) & ca_Cx8(X) & ca_Cx6(X))) <=> ![X: $i] : (cUnsatisfiablexcomp(X) <=> (ca_Cx7(X) & ca_Cx8(X) & ca_Cx6(X)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(35,plain,
% 0.19/0.41 (^[X: $i] : rewrite((cUnsatisfiablexcomp(X) <=> ((ca_Cx7(X) & ca_Cx8(X)) & ca_Cx6(X))) <=> (cUnsatisfiablexcomp(X) <=> (ca_Cx7(X) & ca_Cx8(X) & ca_Cx6(X))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(36,plain,
% 0.19/0.41 (![X: $i] : (cUnsatisfiablexcomp(X) <=> ((ca_Cx7(X) & ca_Cx8(X)) & ca_Cx6(X))) <=> ![X: $i] : (cUnsatisfiablexcomp(X) <=> (ca_Cx7(X) & ca_Cx8(X) & ca_Cx6(X)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[35])).
% 0.19/0.41 tff(37,axiom,(![X: $i] : (cUnsatisfiablexcomp(X) <=> ((ca_Cx7(X) & ca_Cx8(X)) & ca_Cx6(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_3')).
% 0.19/0.41 tff(38,plain,
% 0.19/0.41 (![X: $i] : (cUnsatisfiablexcomp(X) <=> (ca_Cx7(X) & ca_Cx8(X) & ca_Cx6(X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.19/0.41 tff(39,plain,
% 0.19/0.41 (![X: $i] : (cUnsatisfiablexcomp(X) <=> (ca_Cx7(X) & ca_Cx8(X) & ca_Cx6(X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.19/0.41 tff(40,plain,(
% 0.19/0.41 ![X: $i] : (cUnsatisfiablexcomp(X) <=> (ca_Cx7(X) & ca_Cx8(X) & ca_Cx6(X)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[39])).
% 0.19/0.41 tff(41,plain,
% 0.19/0.41 (![X: $i] : (~(((~ca_Cx6(X)) | (~ca_Cx7(X)) | (~ca_Cx8(X))) <=> cUnsatisfiablexcomp(X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.19/0.41 tff(42,plain,
% 0.19/0.41 (![X: $i] : (~(((~ca_Cx6(X)) | (~ca_Cx7(X)) | (~ca_Cx8(X))) <=> cUnsatisfiablexcomp(X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[41, 31])).
% 0.19/0.41 tff(43,plain,
% 0.19/0.41 ((~![X: $i] : (~(((~ca_Cx6(X)) | (~ca_Cx7(X)) | (~ca_Cx8(X))) <=> cUnsatisfiablexcomp(X)))) | (~(((~ca_Cx6(i2003_11_14_17_20_50869)) | (~ca_Cx7(i2003_11_14_17_20_50869)) | (~ca_Cx8(i2003_11_14_17_20_50869))) <=> cUnsatisfiablexcomp(i2003_11_14_17_20_50869)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(44,plain,
% 0.19/0.41 (~(((~ca_Cx6(i2003_11_14_17_20_50869)) | (~ca_Cx7(i2003_11_14_17_20_50869)) | (~ca_Cx8(i2003_11_14_17_20_50869))) <=> cUnsatisfiablexcomp(i2003_11_14_17_20_50869))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.19/0.41 tff(45,plain,
% 0.19/0.41 (^[X: $i] : refl((~((~((~cUnsatisfiablexcomp(X)) | ra_Px5(X, tptp_fun_Y0_1(X)))) | (~(cUnsatisfiablexcomp(X) | ![Y0: $i] : (~ra_Px5(X, Y0)))))) <=> (~((~((~cUnsatisfiablexcomp(X)) | ra_Px5(X, tptp_fun_Y0_1(X)))) | (~(cUnsatisfiablexcomp(X) | ![Y0: $i] : (~ra_Px5(X, Y0)))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(46,plain,
% 0.19/0.41 (![X: $i] : (~((~((~cUnsatisfiablexcomp(X)) | ra_Px5(X, tptp_fun_Y0_1(X)))) | (~(cUnsatisfiablexcomp(X) | ![Y0: $i] : (~ra_Px5(X, Y0)))))) <=> ![X: $i] : (~((~((~cUnsatisfiablexcomp(X)) | ra_Px5(X, tptp_fun_Y0_1(X)))) | (~(cUnsatisfiablexcomp(X) | ![Y0: $i] : (~ra_Px5(X, Y0))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[45])).
% 0.19/0.41 tff(47,plain,
% 0.19/0.41 (^[X: $i] : rewrite((~((~((~cUnsatisfiablexcomp(X)) | ra_Px5(X, tptp_fun_Y0_1(X)))) | (~(cUnsatisfiablexcomp(X) | ![Y0: $i] : (~ra_Px5(X, Y0)))))) <=> (~((~((~cUnsatisfiablexcomp(X)) | ra_Px5(X, tptp_fun_Y0_1(X)))) | (~(cUnsatisfiablexcomp(X) | ![Y0: $i] : (~ra_Px5(X, Y0)))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(48,plain,
% 0.19/0.41 (![X: $i] : (~((~((~cUnsatisfiablexcomp(X)) | ra_Px5(X, tptp_fun_Y0_1(X)))) | (~(cUnsatisfiablexcomp(X) | ![Y0: $i] : (~ra_Px5(X, Y0)))))) <=> ![X: $i] : (~((~((~cUnsatisfiablexcomp(X)) | ra_Px5(X, tptp_fun_Y0_1(X)))) | (~(cUnsatisfiablexcomp(X) | ![Y0: $i] : (~ra_Px5(X, Y0))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[47])).
% 0.19/0.41 tff(49,plain,
% 0.19/0.41 (![X: $i] : (~((~((~cUnsatisfiablexcomp(X)) | ra_Px5(X, tptp_fun_Y0_1(X)))) | (~(cUnsatisfiablexcomp(X) | ![Y0: $i] : (~ra_Px5(X, Y0)))))) <=> ![X: $i] : (~((~((~cUnsatisfiablexcomp(X)) | ra_Px5(X, tptp_fun_Y0_1(X)))) | (~(cUnsatisfiablexcomp(X) | ![Y0: $i] : (~ra_Px5(X, Y0))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[48, 46])).
% 0.19/0.41 tff(50,plain,
% 0.19/0.41 (^[X: $i] : trans(monotonicity(rewrite((cUnsatisfiablexcomp(X) | ![Y0: $i] : (~ra_Px5(X, Y0))) <=> (cUnsatisfiablexcomp(X) | ![Y0: $i] : (~ra_Px5(X, Y0)))), ((((~cUnsatisfiablexcomp(X)) | ra_Px5(X, tptp_fun_Y0_1(X))) & (cUnsatisfiablexcomp(X) | ![Y0: $i] : (~ra_Px5(X, Y0)))) <=> (((~cUnsatisfiablexcomp(X)) | ra_Px5(X, tptp_fun_Y0_1(X))) & (cUnsatisfiablexcomp(X) | ![Y0: $i] : (~ra_Px5(X, Y0)))))), rewrite((((~cUnsatisfiablexcomp(X)) | ra_Px5(X, tptp_fun_Y0_1(X))) & (cUnsatisfiablexcomp(X) | ![Y0: $i] : (~ra_Px5(X, Y0)))) <=> (~((~((~cUnsatisfiablexcomp(X)) | ra_Px5(X, tptp_fun_Y0_1(X)))) | (~(cUnsatisfiablexcomp(X) | ![Y0: $i] : (~ra_Px5(X, Y0))))))), ((((~cUnsatisfiablexcomp(X)) | ra_Px5(X, tptp_fun_Y0_1(X))) & (cUnsatisfiablexcomp(X) | ![Y0: $i] : (~ra_Px5(X, Y0)))) <=> (~((~((~cUnsatisfiablexcomp(X)) | ra_Px5(X, tptp_fun_Y0_1(X)))) | (~(cUnsatisfiablexcomp(X) | ![Y0: $i] : (~ra_Px5(X, Y0))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(51,plain,
% 0.19/0.41 (![X: $i] : (((~cUnsatisfiablexcomp(X)) | ra_Px5(X, tptp_fun_Y0_1(X))) & (cUnsatisfiablexcomp(X) | ![Y0: $i] : (~ra_Px5(X, Y0)))) <=> ![X: $i] : (~((~((~cUnsatisfiablexcomp(X)) | ra_Px5(X, tptp_fun_Y0_1(X)))) | (~(cUnsatisfiablexcomp(X) | ![Y0: $i] : (~ra_Px5(X, Y0))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[50])).
% 0.19/0.41 tff(52,plain,
% 0.19/0.41 (![X: $i] : (cUnsatisfiablexcomp(X) <=> ?[Y0: $i] : ra_Px5(X, Y0)) <=> ![X: $i] : (cUnsatisfiablexcomp(X) <=> ?[Y0: $i] : ra_Px5(X, Y0))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(53,axiom,(![X: $i] : (cUnsatisfiablexcomp(X) <=> ?[Y0: $i] : ra_Px5(X, Y0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_4')).
% 0.19/0.41 tff(54,plain,
% 0.19/0.41 (![X: $i] : (cUnsatisfiablexcomp(X) <=> ?[Y0: $i] : ra_Px5(X, Y0))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.19/0.41 tff(55,plain,(
% 0.19/0.41 ![X: $i] : (((~cUnsatisfiablexcomp(X)) | ra_Px5(X, tptp_fun_Y0_1(X))) & (cUnsatisfiablexcomp(X) | ![Y0: $i] : (~ra_Px5(X, Y0))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[54])).
% 0.19/0.41 tff(56,plain,
% 0.19/0.41 (![X: $i] : (~((~((~cUnsatisfiablexcomp(X)) | ra_Px5(X, tptp_fun_Y0_1(X)))) | (~(cUnsatisfiablexcomp(X) | ![Y0: $i] : (~ra_Px5(X, Y0))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.19/0.41 tff(57,plain,
% 0.19/0.41 (![X: $i] : (~((~((~cUnsatisfiablexcomp(X)) | ra_Px5(X, tptp_fun_Y0_1(X)))) | (~(cUnsatisfiablexcomp(X) | ![Y0: $i] : (~ra_Px5(X, Y0))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[56, 49])).
% 0.19/0.41 tff(58,plain,
% 0.19/0.41 ((~![X: $i] : (~((~((~cUnsatisfiablexcomp(X)) | ra_Px5(X, tptp_fun_Y0_1(X)))) | (~(cUnsatisfiablexcomp(X) | ![Y0: $i] : (~ra_Px5(X, Y0))))))) | (~((~((~cUnsatisfiablexcomp(i2003_11_14_17_20_50869)) | ra_Px5(i2003_11_14_17_20_50869, tptp_fun_Y0_1(i2003_11_14_17_20_50869)))) | (~(cUnsatisfiablexcomp(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px5(i2003_11_14_17_20_50869, Y0))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(59,plain,
% 0.19/0.41 (~((~((~cUnsatisfiablexcomp(i2003_11_14_17_20_50869)) | ra_Px5(i2003_11_14_17_20_50869, tptp_fun_Y0_1(i2003_11_14_17_20_50869)))) | (~(cUnsatisfiablexcomp(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px5(i2003_11_14_17_20_50869, Y0)))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.19/0.41 tff(60,plain,
% 0.19/0.41 (((~((~cUnsatisfiablexcomp(i2003_11_14_17_20_50869)) | ra_Px5(i2003_11_14_17_20_50869, tptp_fun_Y0_1(i2003_11_14_17_20_50869)))) | (~(cUnsatisfiablexcomp(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px5(i2003_11_14_17_20_50869, Y0))))) | ((~cUnsatisfiablexcomp(i2003_11_14_17_20_50869)) | ra_Px5(i2003_11_14_17_20_50869, tptp_fun_Y0_1(i2003_11_14_17_20_50869)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(61,plain,
% 0.19/0.41 ((~cUnsatisfiablexcomp(i2003_11_14_17_20_50869)) | ra_Px5(i2003_11_14_17_20_50869, tptp_fun_Y0_1(i2003_11_14_17_20_50869))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.19/0.41 tff(62,assumption,(ra_Px5(i2003_11_14_17_20_50869, tptp_fun_Y0_1(i2003_11_14_17_20_50869))), introduced(assumption)).
% 0.19/0.41 tff(63,plain,
% 0.19/0.41 (^[X: $i] : rewrite((~((~(cUnsatisfiable(X) | ra_Px5(X, tptp_fun_Y_0(X)))) | (~(![Y: $i] : (~ra_Px5(X, Y)) | (~cUnsatisfiable(X)))))) <=> (~((~(cUnsatisfiable(X) | ra_Px5(X, tptp_fun_Y_0(X)))) | (~((~cUnsatisfiable(X)) | ![Y: $i] : (~ra_Px5(X, Y)))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(64,plain,
% 0.19/0.41 (![X: $i] : (~((~(cUnsatisfiable(X) | ra_Px5(X, tptp_fun_Y_0(X)))) | (~(![Y: $i] : (~ra_Px5(X, Y)) | (~cUnsatisfiable(X)))))) <=> ![X: $i] : (~((~(cUnsatisfiable(X) | ra_Px5(X, tptp_fun_Y_0(X)))) | (~((~cUnsatisfiable(X)) | ![Y: $i] : (~ra_Px5(X, Y))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[63])).
% 0.19/0.41 tff(65,plain,
% 0.19/0.41 (^[X: $i] : refl((~((~(cUnsatisfiable(X) | ra_Px5(X, tptp_fun_Y_0(X)))) | (~(![Y: $i] : (~ra_Px5(X, Y)) | (~cUnsatisfiable(X)))))) <=> (~((~(cUnsatisfiable(X) | ra_Px5(X, tptp_fun_Y_0(X)))) | (~(![Y: $i] : (~ra_Px5(X, Y)) | (~cUnsatisfiable(X)))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(66,plain,
% 0.19/0.41 (![X: $i] : (~((~(cUnsatisfiable(X) | ra_Px5(X, tptp_fun_Y_0(X)))) | (~(![Y: $i] : (~ra_Px5(X, Y)) | (~cUnsatisfiable(X)))))) <=> ![X: $i] : (~((~(cUnsatisfiable(X) | ra_Px5(X, tptp_fun_Y_0(X)))) | (~(![Y: $i] : (~ra_Px5(X, Y)) | (~cUnsatisfiable(X))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[65])).
% 0.19/0.41 tff(67,plain,
% 0.19/0.41 (^[X: $i] : rewrite((~((~(cUnsatisfiable(X) | ra_Px5(X, tptp_fun_Y_0(X)))) | (~(![Y: $i] : (~ra_Px5(X, Y)) | (~cUnsatisfiable(X)))))) <=> (~((~(cUnsatisfiable(X) | ra_Px5(X, tptp_fun_Y_0(X)))) | (~(![Y: $i] : (~ra_Px5(X, Y)) | (~cUnsatisfiable(X)))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(68,plain,
% 0.19/0.41 (![X: $i] : (~((~(cUnsatisfiable(X) | ra_Px5(X, tptp_fun_Y_0(X)))) | (~(![Y: $i] : (~ra_Px5(X, Y)) | (~cUnsatisfiable(X)))))) <=> ![X: $i] : (~((~(cUnsatisfiable(X) | ra_Px5(X, tptp_fun_Y_0(X)))) | (~(![Y: $i] : (~ra_Px5(X, Y)) | (~cUnsatisfiable(X))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[67])).
% 0.19/0.41 tff(69,plain,
% 0.19/0.41 (![X: $i] : (~((~(cUnsatisfiable(X) | ra_Px5(X, tptp_fun_Y_0(X)))) | (~(![Y: $i] : (~ra_Px5(X, Y)) | (~cUnsatisfiable(X)))))) <=> ![X: $i] : (~((~(cUnsatisfiable(X) | ra_Px5(X, tptp_fun_Y_0(X)))) | (~(![Y: $i] : (~ra_Px5(X, Y)) | (~cUnsatisfiable(X))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[68, 66])).
% 0.19/0.41 tff(70,plain,
% 0.19/0.41 (^[X: $i] : trans(monotonicity(rewrite((![Y: $i] : (~ra_Px5(X, Y)) | (~cUnsatisfiable(X))) <=> (![Y: $i] : (~ra_Px5(X, Y)) | (~cUnsatisfiable(X)))), (((cUnsatisfiable(X) | ra_Px5(X, tptp_fun_Y_0(X))) & (![Y: $i] : (~ra_Px5(X, Y)) | (~cUnsatisfiable(X)))) <=> ((cUnsatisfiable(X) | ra_Px5(X, tptp_fun_Y_0(X))) & (![Y: $i] : (~ra_Px5(X, Y)) | (~cUnsatisfiable(X)))))), rewrite(((cUnsatisfiable(X) | ra_Px5(X, tptp_fun_Y_0(X))) & (![Y: $i] : (~ra_Px5(X, Y)) | (~cUnsatisfiable(X)))) <=> (~((~(cUnsatisfiable(X) | ra_Px5(X, tptp_fun_Y_0(X)))) | (~(![Y: $i] : (~ra_Px5(X, Y)) | (~cUnsatisfiable(X))))))), (((cUnsatisfiable(X) | ra_Px5(X, tptp_fun_Y_0(X))) & (![Y: $i] : (~ra_Px5(X, Y)) | (~cUnsatisfiable(X)))) <=> (~((~(cUnsatisfiable(X) | ra_Px5(X, tptp_fun_Y_0(X)))) | (~(![Y: $i] : (~ra_Px5(X, Y)) | (~cUnsatisfiable(X))))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(71,plain,
% 0.19/0.41 (![X: $i] : ((cUnsatisfiable(X) | ra_Px5(X, tptp_fun_Y_0(X))) & (![Y: $i] : (~ra_Px5(X, Y)) | (~cUnsatisfiable(X)))) <=> ![X: $i] : (~((~(cUnsatisfiable(X) | ra_Px5(X, tptp_fun_Y_0(X)))) | (~(![Y: $i] : (~ra_Px5(X, Y)) | (~cUnsatisfiable(X))))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[70])).
% 0.19/0.41 tff(72,plain,
% 0.19/0.41 (^[X: $i] : rewrite(((ra_Px5(X, tptp_fun_Y_0(X)) | cUnsatisfiable(X)) & (![Y: $i] : (~ra_Px5(X, Y)) | (~cUnsatisfiable(X)))) <=> ((cUnsatisfiable(X) | ra_Px5(X, tptp_fun_Y_0(X))) & (![Y: $i] : (~ra_Px5(X, Y)) | (~cUnsatisfiable(X)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(73,plain,
% 0.19/0.41 (![X: $i] : ((ra_Px5(X, tptp_fun_Y_0(X)) | cUnsatisfiable(X)) & (![Y: $i] : (~ra_Px5(X, Y)) | (~cUnsatisfiable(X)))) <=> ![X: $i] : ((cUnsatisfiable(X) | ra_Px5(X, tptp_fun_Y_0(X))) & (![Y: $i] : (~ra_Px5(X, Y)) | (~cUnsatisfiable(X))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[72])).
% 0.19/0.41 tff(74,plain,
% 0.19/0.41 (![X: $i] : (~(?[Y: $i] : ra_Px5(X, Y) <=> cUnsatisfiable(X))) <=> ![X: $i] : (~(?[Y: $i] : ra_Px5(X, Y) <=> cUnsatisfiable(X)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(75,plain,
% 0.19/0.41 (^[X: $i] : trans(trans(monotonicity(rewrite((~?[Y: $i] : ra_Px5(X, Y)) <=> (~?[Y: $i] : ra_Px5(X, Y))), ((cUnsatisfiable(X) <=> (~?[Y: $i] : ra_Px5(X, Y))) <=> (cUnsatisfiable(X) <=> (~?[Y: $i] : ra_Px5(X, Y))))), rewrite((cUnsatisfiable(X) <=> (~?[Y: $i] : ra_Px5(X, Y))) <=> (~(?[Y: $i] : ra_Px5(X, Y) <=> cUnsatisfiable(X)))), ((cUnsatisfiable(X) <=> (~?[Y: $i] : ra_Px5(X, Y))) <=> (~(?[Y: $i] : ra_Px5(X, Y) <=> cUnsatisfiable(X))))), rewrite((~(?[Y: $i] : ra_Px5(X, Y) <=> cUnsatisfiable(X))) <=> (~(?[Y: $i] : ra_Px5(X, Y) <=> cUnsatisfiable(X)))), ((cUnsatisfiable(X) <=> (~?[Y: $i] : ra_Px5(X, Y))) <=> (~(?[Y: $i] : ra_Px5(X, Y) <=> cUnsatisfiable(X)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(76,plain,
% 0.19/0.41 (![X: $i] : (cUnsatisfiable(X) <=> (~?[Y: $i] : ra_Px5(X, Y))) <=> ![X: $i] : (~(?[Y: $i] : ra_Px5(X, Y) <=> cUnsatisfiable(X)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[75])).
% 0.19/0.41 tff(77,axiom,(![X: $i] : (cUnsatisfiable(X) <=> (~?[Y: $i] : ra_Px5(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_2')).
% 0.19/0.41 tff(78,plain,
% 0.19/0.41 (![X: $i] : (~(?[Y: $i] : ra_Px5(X, Y) <=> cUnsatisfiable(X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.19/0.41 tff(79,plain,
% 0.19/0.41 (![X: $i] : (~(?[Y: $i] : ra_Px5(X, Y) <=> cUnsatisfiable(X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.19/0.41 tff(80,plain,(
% 0.19/0.41 ![X: $i] : ((ra_Px5(X, tptp_fun_Y_0(X)) | cUnsatisfiable(X)) & (![Y: $i] : (~ra_Px5(X, Y)) | (~cUnsatisfiable(X))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[79])).
% 0.19/0.41 tff(81,plain,
% 0.19/0.41 (![X: $i] : ((cUnsatisfiable(X) | ra_Px5(X, tptp_fun_Y_0(X))) & (![Y: $i] : (~ra_Px5(X, Y)) | (~cUnsatisfiable(X))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[80, 73])).
% 0.19/0.41 tff(82,plain,
% 0.19/0.41 (![X: $i] : (~((~(cUnsatisfiable(X) | ra_Px5(X, tptp_fun_Y_0(X)))) | (~(![Y: $i] : (~ra_Px5(X, Y)) | (~cUnsatisfiable(X))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[81, 71])).
% 0.19/0.41 tff(83,plain,
% 0.19/0.41 (![X: $i] : (~((~(cUnsatisfiable(X) | ra_Px5(X, tptp_fun_Y_0(X)))) | (~(![Y: $i] : (~ra_Px5(X, Y)) | (~cUnsatisfiable(X))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[82, 69])).
% 0.19/0.42 tff(84,plain,
% 0.19/0.42 (![X: $i] : (~((~(cUnsatisfiable(X) | ra_Px5(X, tptp_fun_Y_0(X)))) | (~((~cUnsatisfiable(X)) | ![Y: $i] : (~ra_Px5(X, Y))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[83, 64])).
% 0.19/0.42 tff(85,plain,
% 0.19/0.42 ((~![X: $i] : (~((~(cUnsatisfiable(X) | ra_Px5(X, tptp_fun_Y_0(X)))) | (~((~cUnsatisfiable(X)) | ![Y: $i] : (~ra_Px5(X, Y))))))) | (~((~(cUnsatisfiable(i2003_11_14_17_20_50869) | ra_Px5(i2003_11_14_17_20_50869, tptp_fun_Y_0(i2003_11_14_17_20_50869)))) | (~((~cUnsatisfiable(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px5(i2003_11_14_17_20_50869, Y))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(86,plain,
% 0.19/0.42 (~((~(cUnsatisfiable(i2003_11_14_17_20_50869) | ra_Px5(i2003_11_14_17_20_50869, tptp_fun_Y_0(i2003_11_14_17_20_50869)))) | (~((~cUnsatisfiable(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px5(i2003_11_14_17_20_50869, Y)))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.19/0.42 tff(87,plain,
% 0.19/0.42 (((~(cUnsatisfiable(i2003_11_14_17_20_50869) | ra_Px5(i2003_11_14_17_20_50869, tptp_fun_Y_0(i2003_11_14_17_20_50869)))) | (~((~cUnsatisfiable(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px5(i2003_11_14_17_20_50869, Y))))) | ((~cUnsatisfiable(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px5(i2003_11_14_17_20_50869, Y)))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(88,plain,
% 0.19/0.42 ((~cUnsatisfiable(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px5(i2003_11_14_17_20_50869, Y))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[87, 86])).
% 0.19/0.42 tff(89,plain,
% 0.19/0.42 (cUnsatisfiable(i2003_11_14_17_20_50869) <=> cUnsatisfiable(i2003_11_14_17_20_50869)),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(90,axiom,(cUnsatisfiable(i2003_11_14_17_20_50869)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_23')).
% 0.19/0.42 tff(91,plain,
% 0.19/0.42 (cUnsatisfiable(i2003_11_14_17_20_50869)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.19/0.42 tff(92,plain,
% 0.19/0.42 ((~((~cUnsatisfiable(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px5(i2003_11_14_17_20_50869, Y)))) | (~cUnsatisfiable(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px5(i2003_11_14_17_20_50869, Y))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(93,plain,
% 0.19/0.42 ((~((~cUnsatisfiable(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px5(i2003_11_14_17_20_50869, Y)))) | ![Y: $i] : (~ra_Px5(i2003_11_14_17_20_50869, Y))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.19/0.42 tff(94,plain,
% 0.19/0.42 (![Y: $i] : (~ra_Px5(i2003_11_14_17_20_50869, Y))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[93, 88])).
% 0.19/0.42 tff(95,plain,
% 0.19/0.42 ((~![Y: $i] : (~ra_Px5(i2003_11_14_17_20_50869, Y))) | (~ra_Px5(i2003_11_14_17_20_50869, tptp_fun_Y0_1(i2003_11_14_17_20_50869)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(96,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[95, 94, 62])).
% 0.19/0.42 tff(97,plain,(~ra_Px5(i2003_11_14_17_20_50869, tptp_fun_Y0_1(i2003_11_14_17_20_50869))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(98,plain,
% 0.19/0.42 ((~((~cUnsatisfiablexcomp(i2003_11_14_17_20_50869)) | ra_Px5(i2003_11_14_17_20_50869, tptp_fun_Y0_1(i2003_11_14_17_20_50869)))) | (~cUnsatisfiablexcomp(i2003_11_14_17_20_50869)) | ra_Px5(i2003_11_14_17_20_50869, tptp_fun_Y0_1(i2003_11_14_17_20_50869))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(99,plain,
% 0.19/0.42 ((~((~cUnsatisfiablexcomp(i2003_11_14_17_20_50869)) | ra_Px5(i2003_11_14_17_20_50869, tptp_fun_Y0_1(i2003_11_14_17_20_50869)))) | (~cUnsatisfiablexcomp(i2003_11_14_17_20_50869))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.19/0.42 tff(100,plain,
% 0.19/0.42 (~cUnsatisfiablexcomp(i2003_11_14_17_20_50869)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[99, 61])).
% 0.19/0.42 tff(101,plain,
% 0.19/0.42 ((((~ca_Cx6(i2003_11_14_17_20_50869)) | (~ca_Cx7(i2003_11_14_17_20_50869)) | (~ca_Cx8(i2003_11_14_17_20_50869))) <=> cUnsatisfiablexcomp(i2003_11_14_17_20_50869)) | ((~ca_Cx6(i2003_11_14_17_20_50869)) | (~ca_Cx7(i2003_11_14_17_20_50869)) | (~ca_Cx8(i2003_11_14_17_20_50869))) | cUnsatisfiablexcomp(i2003_11_14_17_20_50869)),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(102,plain,
% 0.19/0.42 ((~ca_Cx6(i2003_11_14_17_20_50869)) | (~ca_Cx7(i2003_11_14_17_20_50869)) | (~ca_Cx8(i2003_11_14_17_20_50869))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[101, 100, 44])).
% 0.19/0.42 tff(103,plain,
% 0.19/0.42 (^[X: $i] : refl((~((~((~ca_Cx7(X)) | ra_Px7(X, tptp_fun_Y0_10(X)))) | (~(ca_Cx7(X) | ![Y0: $i] : (~ra_Px7(X, Y0)))))) <=> (~((~((~ca_Cx7(X)) | ra_Px7(X, tptp_fun_Y0_10(X)))) | (~(ca_Cx7(X) | ![Y0: $i] : (~ra_Px7(X, Y0)))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(104,plain,
% 0.19/0.42 (![X: $i] : (~((~((~ca_Cx7(X)) | ra_Px7(X, tptp_fun_Y0_10(X)))) | (~(ca_Cx7(X) | ![Y0: $i] : (~ra_Px7(X, Y0)))))) <=> ![X: $i] : (~((~((~ca_Cx7(X)) | ra_Px7(X, tptp_fun_Y0_10(X)))) | (~(ca_Cx7(X) | ![Y0: $i] : (~ra_Px7(X, Y0))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[103])).
% 0.19/0.42 tff(105,plain,
% 0.19/0.42 (^[X: $i] : rewrite((~((~((~ca_Cx7(X)) | ra_Px7(X, tptp_fun_Y0_10(X)))) | (~(ca_Cx7(X) | ![Y0: $i] : (~ra_Px7(X, Y0)))))) <=> (~((~((~ca_Cx7(X)) | ra_Px7(X, tptp_fun_Y0_10(X)))) | (~(ca_Cx7(X) | ![Y0: $i] : (~ra_Px7(X, Y0)))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(106,plain,
% 0.19/0.42 (![X: $i] : (~((~((~ca_Cx7(X)) | ra_Px7(X, tptp_fun_Y0_10(X)))) | (~(ca_Cx7(X) | ![Y0: $i] : (~ra_Px7(X, Y0)))))) <=> ![X: $i] : (~((~((~ca_Cx7(X)) | ra_Px7(X, tptp_fun_Y0_10(X)))) | (~(ca_Cx7(X) | ![Y0: $i] : (~ra_Px7(X, Y0))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[105])).
% 0.19/0.42 tff(107,plain,
% 0.19/0.42 (![X: $i] : (~((~((~ca_Cx7(X)) | ra_Px7(X, tptp_fun_Y0_10(X)))) | (~(ca_Cx7(X) | ![Y0: $i] : (~ra_Px7(X, Y0)))))) <=> ![X: $i] : (~((~((~ca_Cx7(X)) | ra_Px7(X, tptp_fun_Y0_10(X)))) | (~(ca_Cx7(X) | ![Y0: $i] : (~ra_Px7(X, Y0))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[106, 104])).
% 0.19/0.42 tff(108,plain,
% 0.19/0.42 (^[X: $i] : trans(monotonicity(rewrite((ca_Cx7(X) | ![Y0: $i] : (~ra_Px7(X, Y0))) <=> (ca_Cx7(X) | ![Y0: $i] : (~ra_Px7(X, Y0)))), ((((~ca_Cx7(X)) | ra_Px7(X, tptp_fun_Y0_10(X))) & (ca_Cx7(X) | ![Y0: $i] : (~ra_Px7(X, Y0)))) <=> (((~ca_Cx7(X)) | ra_Px7(X, tptp_fun_Y0_10(X))) & (ca_Cx7(X) | ![Y0: $i] : (~ra_Px7(X, Y0)))))), rewrite((((~ca_Cx7(X)) | ra_Px7(X, tptp_fun_Y0_10(X))) & (ca_Cx7(X) | ![Y0: $i] : (~ra_Px7(X, Y0)))) <=> (~((~((~ca_Cx7(X)) | ra_Px7(X, tptp_fun_Y0_10(X)))) | (~(ca_Cx7(X) | ![Y0: $i] : (~ra_Px7(X, Y0))))))), ((((~ca_Cx7(X)) | ra_Px7(X, tptp_fun_Y0_10(X))) & (ca_Cx7(X) | ![Y0: $i] : (~ra_Px7(X, Y0)))) <=> (~((~((~ca_Cx7(X)) | ra_Px7(X, tptp_fun_Y0_10(X)))) | (~(ca_Cx7(X) | ![Y0: $i] : (~ra_Px7(X, Y0))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(109,plain,
% 0.19/0.42 (![X: $i] : (((~ca_Cx7(X)) | ra_Px7(X, tptp_fun_Y0_10(X))) & (ca_Cx7(X) | ![Y0: $i] : (~ra_Px7(X, Y0)))) <=> ![X: $i] : (~((~((~ca_Cx7(X)) | ra_Px7(X, tptp_fun_Y0_10(X)))) | (~(ca_Cx7(X) | ![Y0: $i] : (~ra_Px7(X, Y0))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[108])).
% 0.19/0.42 tff(110,plain,
% 0.19/0.42 (![X: $i] : (ca_Cx7(X) <=> ?[Y0: $i] : ra_Px7(X, Y0)) <=> ![X: $i] : (ca_Cx7(X) <=> ?[Y0: $i] : ra_Px7(X, Y0))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(111,axiom,(![X: $i] : (ca_Cx7(X) <=> ?[Y0: $i] : ra_Px7(X, Y0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_17')).
% 0.19/0.42 tff(112,plain,
% 0.19/0.42 (![X: $i] : (ca_Cx7(X) <=> ?[Y0: $i] : ra_Px7(X, Y0))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.19/0.42 tff(113,plain,(
% 0.19/0.42 ![X: $i] : (((~ca_Cx7(X)) | ra_Px7(X, tptp_fun_Y0_10(X))) & (ca_Cx7(X) | ![Y0: $i] : (~ra_Px7(X, Y0))))),
% 0.19/0.42 inference(skolemize,[status(sab)],[112])).
% 0.19/0.42 tff(114,plain,
% 0.19/0.42 (![X: $i] : (~((~((~ca_Cx7(X)) | ra_Px7(X, tptp_fun_Y0_10(X)))) | (~(ca_Cx7(X) | ![Y0: $i] : (~ra_Px7(X, Y0))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[113, 109])).
% 0.19/0.42 tff(115,plain,
% 0.19/0.42 (![X: $i] : (~((~((~ca_Cx7(X)) | ra_Px7(X, tptp_fun_Y0_10(X)))) | (~(ca_Cx7(X) | ![Y0: $i] : (~ra_Px7(X, Y0))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[114, 107])).
% 0.19/0.42 tff(116,plain,
% 0.19/0.42 ((~![X: $i] : (~((~((~ca_Cx7(X)) | ra_Px7(X, tptp_fun_Y0_10(X)))) | (~(ca_Cx7(X) | ![Y0: $i] : (~ra_Px7(X, Y0))))))) | (~((~((~ca_Cx7(i2003_11_14_17_20_50869)) | ra_Px7(i2003_11_14_17_20_50869, tptp_fun_Y0_10(i2003_11_14_17_20_50869)))) | (~(ca_Cx7(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px7(i2003_11_14_17_20_50869, Y0))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(117,plain,
% 0.19/0.42 (~((~((~ca_Cx7(i2003_11_14_17_20_50869)) | ra_Px7(i2003_11_14_17_20_50869, tptp_fun_Y0_10(i2003_11_14_17_20_50869)))) | (~(ca_Cx7(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px7(i2003_11_14_17_20_50869, Y0)))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[116, 115])).
% 0.19/0.42 tff(118,plain,
% 0.19/0.42 (((~((~ca_Cx7(i2003_11_14_17_20_50869)) | ra_Px7(i2003_11_14_17_20_50869, tptp_fun_Y0_10(i2003_11_14_17_20_50869)))) | (~(ca_Cx7(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px7(i2003_11_14_17_20_50869, Y0))))) | (ca_Cx7(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px7(i2003_11_14_17_20_50869, Y0)))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(119,plain,
% 0.19/0.42 (ca_Cx7(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px7(i2003_11_14_17_20_50869, Y0))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[118, 117])).
% 0.19/0.42 tff(120,plain,
% 0.19/0.42 (^[X: $i] : refl((~(((~cbxcomp(X)) | (~ccxcomp(X))) <=> ca_Cx1(X))) <=> (~(((~cbxcomp(X)) | (~ccxcomp(X))) <=> ca_Cx1(X))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(121,plain,
% 0.19/0.42 (![X: $i] : (~(((~cbxcomp(X)) | (~ccxcomp(X))) <=> ca_Cx1(X))) <=> ![X: $i] : (~(((~cbxcomp(X)) | (~ccxcomp(X))) <=> ca_Cx1(X)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[120])).
% 0.19/0.42 tff(122,plain,
% 0.19/0.42 (^[X: $i] : trans(trans(monotonicity(rewrite((cbxcomp(X) & ccxcomp(X)) <=> (~((~cbxcomp(X)) | (~ccxcomp(X))))), ((ca_Cx1(X) <=> (cbxcomp(X) & ccxcomp(X))) <=> (ca_Cx1(X) <=> (~((~cbxcomp(X)) | (~ccxcomp(X))))))), rewrite((ca_Cx1(X) <=> (~((~cbxcomp(X)) | (~ccxcomp(X))))) <=> (~(((~cbxcomp(X)) | (~ccxcomp(X))) <=> ca_Cx1(X)))), ((ca_Cx1(X) <=> (cbxcomp(X) & ccxcomp(X))) <=> (~(((~cbxcomp(X)) | (~ccxcomp(X))) <=> ca_Cx1(X))))), rewrite((~(((~cbxcomp(X)) | (~ccxcomp(X))) <=> ca_Cx1(X))) <=> (~(((~cbxcomp(X)) | (~ccxcomp(X))) <=> ca_Cx1(X)))), ((ca_Cx1(X) <=> (cbxcomp(X) & ccxcomp(X))) <=> (~(((~cbxcomp(X)) | (~ccxcomp(X))) <=> ca_Cx1(X)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(123,plain,
% 0.19/0.42 (![X: $i] : (ca_Cx1(X) <=> (cbxcomp(X) & ccxcomp(X))) <=> ![X: $i] : (~(((~cbxcomp(X)) | (~ccxcomp(X))) <=> ca_Cx1(X)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[122])).
% 0.19/0.42 tff(124,plain,
% 0.19/0.42 (![X: $i] : (ca_Cx1(X) <=> (cbxcomp(X) & ccxcomp(X))) <=> ![X: $i] : (ca_Cx1(X) <=> (cbxcomp(X) & ccxcomp(X)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(125,axiom,(![X: $i] : (ca_Cx1(X) <=> (cbxcomp(X) & ccxcomp(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_11')).
% 0.19/0.42 tff(126,plain,
% 0.19/0.42 (![X: $i] : (ca_Cx1(X) <=> (cbxcomp(X) & ccxcomp(X)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.19/0.42 tff(127,plain,(
% 0.19/0.42 ![X: $i] : (ca_Cx1(X) <=> (cbxcomp(X) & ccxcomp(X)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[126])).
% 0.19/0.42 tff(128,plain,
% 0.19/0.42 (![X: $i] : (~(((~cbxcomp(X)) | (~ccxcomp(X))) <=> ca_Cx1(X)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[127, 123])).
% 0.19/0.42 tff(129,plain,
% 0.19/0.42 (![X: $i] : (~(((~cbxcomp(X)) | (~ccxcomp(X))) <=> ca_Cx1(X)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[128, 121])).
% 0.19/0.42 tff(130,plain,
% 0.19/0.42 ((~![X: $i] : (~(((~cbxcomp(X)) | (~ccxcomp(X))) <=> ca_Cx1(X)))) | (~(((~cbxcomp(i2003_11_14_17_20_50869)) | (~ccxcomp(i2003_11_14_17_20_50869))) <=> ca_Cx1(i2003_11_14_17_20_50869)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(131,plain,
% 0.19/0.42 (~(((~cbxcomp(i2003_11_14_17_20_50869)) | (~ccxcomp(i2003_11_14_17_20_50869))) <=> ca_Cx1(i2003_11_14_17_20_50869))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[130, 129])).
% 0.19/0.42 tff(132,assumption,(~cb(i2003_11_14_17_20_50869)), introduced(assumption)).
% 0.19/0.42 tff(133,plain,
% 0.19/0.42 (((~cb(i2003_11_14_17_20_50869)) | (~cc(i2003_11_14_17_20_50869))) | cb(i2003_11_14_17_20_50869)),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(134,plain,
% 0.19/0.42 ((~cb(i2003_11_14_17_20_50869)) | (~cc(i2003_11_14_17_20_50869))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[133, 132])).
% 0.19/0.42 tff(135,plain,
% 0.19/0.42 ((((~cb(i2003_11_14_17_20_50869)) | (~cc(i2003_11_14_17_20_50869))) <=> ca_Cx8xcomp(i2003_11_14_17_20_50869)) | (~((~cb(i2003_11_14_17_20_50869)) | (~cc(i2003_11_14_17_20_50869)))) | (~ca_Cx8xcomp(i2003_11_14_17_20_50869))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(136,plain,
% 0.19/0.42 ((((~cb(i2003_11_14_17_20_50869)) | (~cc(i2003_11_14_17_20_50869))) <=> ca_Cx8xcomp(i2003_11_14_17_20_50869)) | (~ca_Cx8xcomp(i2003_11_14_17_20_50869))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[135, 134])).
% 0.19/0.42 tff(137,plain,
% 0.19/0.42 (~ca_Cx8xcomp(i2003_11_14_17_20_50869)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[136, 29])).
% 0.19/0.42 tff(138,plain,
% 0.19/0.42 (^[X: $i] : refl((~((~((~ca_Cx8xcomp(X)) | ra_Px8(X, tptp_fun_Y0_13(X)))) | (~(ca_Cx8xcomp(X) | ![Y0: $i] : (~ra_Px8(X, Y0)))))) <=> (~((~((~ca_Cx8xcomp(X)) | ra_Px8(X, tptp_fun_Y0_13(X)))) | (~(ca_Cx8xcomp(X) | ![Y0: $i] : (~ra_Px8(X, Y0)))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(139,plain,
% 0.19/0.42 (![X: $i] : (~((~((~ca_Cx8xcomp(X)) | ra_Px8(X, tptp_fun_Y0_13(X)))) | (~(ca_Cx8xcomp(X) | ![Y0: $i] : (~ra_Px8(X, Y0)))))) <=> ![X: $i] : (~((~((~ca_Cx8xcomp(X)) | ra_Px8(X, tptp_fun_Y0_13(X)))) | (~(ca_Cx8xcomp(X) | ![Y0: $i] : (~ra_Px8(X, Y0))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[138])).
% 0.19/0.42 tff(140,plain,
% 0.19/0.42 (^[X: $i] : rewrite((~((~((~ca_Cx8xcomp(X)) | ra_Px8(X, tptp_fun_Y0_13(X)))) | (~(ca_Cx8xcomp(X) | ![Y0: $i] : (~ra_Px8(X, Y0)))))) <=> (~((~((~ca_Cx8xcomp(X)) | ra_Px8(X, tptp_fun_Y0_13(X)))) | (~(ca_Cx8xcomp(X) | ![Y0: $i] : (~ra_Px8(X, Y0)))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(141,plain,
% 0.19/0.42 (![X: $i] : (~((~((~ca_Cx8xcomp(X)) | ra_Px8(X, tptp_fun_Y0_13(X)))) | (~(ca_Cx8xcomp(X) | ![Y0: $i] : (~ra_Px8(X, Y0)))))) <=> ![X: $i] : (~((~((~ca_Cx8xcomp(X)) | ra_Px8(X, tptp_fun_Y0_13(X)))) | (~(ca_Cx8xcomp(X) | ![Y0: $i] : (~ra_Px8(X, Y0))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[140])).
% 0.19/0.42 tff(142,plain,
% 0.19/0.42 (![X: $i] : (~((~((~ca_Cx8xcomp(X)) | ra_Px8(X, tptp_fun_Y0_13(X)))) | (~(ca_Cx8xcomp(X) | ![Y0: $i] : (~ra_Px8(X, Y0)))))) <=> ![X: $i] : (~((~((~ca_Cx8xcomp(X)) | ra_Px8(X, tptp_fun_Y0_13(X)))) | (~(ca_Cx8xcomp(X) | ![Y0: $i] : (~ra_Px8(X, Y0))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[141, 139])).
% 0.19/0.42 tff(143,plain,
% 0.19/0.42 (^[X: $i] : trans(monotonicity(rewrite((ca_Cx8xcomp(X) | ![Y0: $i] : (~ra_Px8(X, Y0))) <=> (ca_Cx8xcomp(X) | ![Y0: $i] : (~ra_Px8(X, Y0)))), ((((~ca_Cx8xcomp(X)) | ra_Px8(X, tptp_fun_Y0_13(X))) & (ca_Cx8xcomp(X) | ![Y0: $i] : (~ra_Px8(X, Y0)))) <=> (((~ca_Cx8xcomp(X)) | ra_Px8(X, tptp_fun_Y0_13(X))) & (ca_Cx8xcomp(X) | ![Y0: $i] : (~ra_Px8(X, Y0)))))), rewrite((((~ca_Cx8xcomp(X)) | ra_Px8(X, tptp_fun_Y0_13(X))) & (ca_Cx8xcomp(X) | ![Y0: $i] : (~ra_Px8(X, Y0)))) <=> (~((~((~ca_Cx8xcomp(X)) | ra_Px8(X, tptp_fun_Y0_13(X)))) | (~(ca_Cx8xcomp(X) | ![Y0: $i] : (~ra_Px8(X, Y0))))))), ((((~ca_Cx8xcomp(X)) | ra_Px8(X, tptp_fun_Y0_13(X))) & (ca_Cx8xcomp(X) | ![Y0: $i] : (~ra_Px8(X, Y0)))) <=> (~((~((~ca_Cx8xcomp(X)) | ra_Px8(X, tptp_fun_Y0_13(X)))) | (~(ca_Cx8xcomp(X) | ![Y0: $i] : (~ra_Px8(X, Y0))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(144,plain,
% 0.19/0.42 (![X: $i] : (((~ca_Cx8xcomp(X)) | ra_Px8(X, tptp_fun_Y0_13(X))) & (ca_Cx8xcomp(X) | ![Y0: $i] : (~ra_Px8(X, Y0)))) <=> ![X: $i] : (~((~((~ca_Cx8xcomp(X)) | ra_Px8(X, tptp_fun_Y0_13(X)))) | (~(ca_Cx8xcomp(X) | ![Y0: $i] : (~ra_Px8(X, Y0))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[143])).
% 0.19/0.42 tff(145,plain,
% 0.19/0.42 (![X: $i] : (ca_Cx8xcomp(X) <=> ?[Y0: $i] : ra_Px8(X, Y0)) <=> ![X: $i] : (ca_Cx8xcomp(X) <=> ?[Y0: $i] : ra_Px8(X, Y0))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(146,axiom,(![X: $i] : (ca_Cx8xcomp(X) <=> ?[Y0: $i] : ra_Px8(X, Y0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_21')).
% 0.19/0.42 tff(147,plain,
% 0.19/0.42 (![X: $i] : (ca_Cx8xcomp(X) <=> ?[Y0: $i] : ra_Px8(X, Y0))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.19/0.42 tff(148,plain,(
% 0.19/0.42 ![X: $i] : (((~ca_Cx8xcomp(X)) | ra_Px8(X, tptp_fun_Y0_13(X))) & (ca_Cx8xcomp(X) | ![Y0: $i] : (~ra_Px8(X, Y0))))),
% 0.19/0.42 inference(skolemize,[status(sab)],[147])).
% 0.19/0.42 tff(149,plain,
% 0.19/0.42 (![X: $i] : (~((~((~ca_Cx8xcomp(X)) | ra_Px8(X, tptp_fun_Y0_13(X)))) | (~(ca_Cx8xcomp(X) | ![Y0: $i] : (~ra_Px8(X, Y0))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[148, 144])).
% 0.19/0.42 tff(150,plain,
% 0.19/0.42 (![X: $i] : (~((~((~ca_Cx8xcomp(X)) | ra_Px8(X, tptp_fun_Y0_13(X)))) | (~(ca_Cx8xcomp(X) | ![Y0: $i] : (~ra_Px8(X, Y0))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[149, 142])).
% 0.19/0.42 tff(151,plain,
% 0.19/0.42 ((~![X: $i] : (~((~((~ca_Cx8xcomp(X)) | ra_Px8(X, tptp_fun_Y0_13(X)))) | (~(ca_Cx8xcomp(X) | ![Y0: $i] : (~ra_Px8(X, Y0))))))) | (~((~((~ca_Cx8xcomp(i2003_11_14_17_20_50869)) | ra_Px8(i2003_11_14_17_20_50869, tptp_fun_Y0_13(i2003_11_14_17_20_50869)))) | (~(ca_Cx8xcomp(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px8(i2003_11_14_17_20_50869, Y0))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(152,plain,
% 0.19/0.42 (~((~((~ca_Cx8xcomp(i2003_11_14_17_20_50869)) | ra_Px8(i2003_11_14_17_20_50869, tptp_fun_Y0_13(i2003_11_14_17_20_50869)))) | (~(ca_Cx8xcomp(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px8(i2003_11_14_17_20_50869, Y0)))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[151, 150])).
% 0.19/0.42 tff(153,plain,
% 0.19/0.42 (((~((~ca_Cx8xcomp(i2003_11_14_17_20_50869)) | ra_Px8(i2003_11_14_17_20_50869, tptp_fun_Y0_13(i2003_11_14_17_20_50869)))) | (~(ca_Cx8xcomp(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px8(i2003_11_14_17_20_50869, Y0))))) | (ca_Cx8xcomp(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px8(i2003_11_14_17_20_50869, Y0)))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(154,plain,
% 0.19/0.42 (ca_Cx8xcomp(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px8(i2003_11_14_17_20_50869, Y0))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[153, 152])).
% 0.19/0.42 tff(155,plain,
% 0.19/0.42 ((~(ca_Cx8xcomp(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px8(i2003_11_14_17_20_50869, Y0)))) | ca_Cx8xcomp(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px8(i2003_11_14_17_20_50869, Y0))),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(156,plain,
% 0.19/0.42 (ca_Cx8xcomp(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px8(i2003_11_14_17_20_50869, Y0))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[155, 154])).
% 0.19/0.42 tff(157,plain,
% 0.19/0.42 (![Y0: $i] : (~ra_Px8(i2003_11_14_17_20_50869, Y0))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[156, 137])).
% 0.19/0.42 tff(158,assumption,(![Y0: $i] : (~ra_Px8(i2003_11_14_17_20_50869, Y0))), introduced(assumption)).
% 0.19/0.42 tff(159,assumption,(ra_Px8(i2003_11_14_17_20_50869, tptp_fun_Y_12(i2003_11_14_17_20_50869))), introduced(assumption)).
% 0.19/0.42 tff(160,plain,
% 0.19/0.42 ((~![Y0: $i] : (~ra_Px8(i2003_11_14_17_20_50869, Y0))) | (~ra_Px8(i2003_11_14_17_20_50869, tptp_fun_Y_12(i2003_11_14_17_20_50869)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(161,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[160, 159, 158])).
% 0.19/0.42 tff(162,plain,((~ra_Px8(i2003_11_14_17_20_50869, tptp_fun_Y_12(i2003_11_14_17_20_50869))) | (~![Y0: $i] : (~ra_Px8(i2003_11_14_17_20_50869, Y0)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(163,plain,
% 0.19/0.42 (~ra_Px8(i2003_11_14_17_20_50869, tptp_fun_Y_12(i2003_11_14_17_20_50869))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[162, 157])).
% 0.19/0.42 tff(164,plain,
% 0.19/0.42 (^[X: $i] : rewrite((~((~(ca_Cx8(X) | ra_Px8(X, tptp_fun_Y_12(X)))) | (~(![Y: $i] : (~ra_Px8(X, Y)) | (~ca_Cx8(X)))))) <=> (~((~(ca_Cx8(X) | ra_Px8(X, tptp_fun_Y_12(X)))) | (~((~ca_Cx8(X)) | ![Y: $i] : (~ra_Px8(X, Y)))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(165,plain,
% 0.19/0.42 (![X: $i] : (~((~(ca_Cx8(X) | ra_Px8(X, tptp_fun_Y_12(X)))) | (~(![Y: $i] : (~ra_Px8(X, Y)) | (~ca_Cx8(X)))))) <=> ![X: $i] : (~((~(ca_Cx8(X) | ra_Px8(X, tptp_fun_Y_12(X)))) | (~((~ca_Cx8(X)) | ![Y: $i] : (~ra_Px8(X, Y))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[164])).
% 0.19/0.42 tff(166,plain,
% 0.19/0.42 (^[X: $i] : refl((~((~(ca_Cx8(X) | ra_Px8(X, tptp_fun_Y_12(X)))) | (~(![Y: $i] : (~ra_Px8(X, Y)) | (~ca_Cx8(X)))))) <=> (~((~(ca_Cx8(X) | ra_Px8(X, tptp_fun_Y_12(X)))) | (~(![Y: $i] : (~ra_Px8(X, Y)) | (~ca_Cx8(X)))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(167,plain,
% 0.19/0.42 (![X: $i] : (~((~(ca_Cx8(X) | ra_Px8(X, tptp_fun_Y_12(X)))) | (~(![Y: $i] : (~ra_Px8(X, Y)) | (~ca_Cx8(X)))))) <=> ![X: $i] : (~((~(ca_Cx8(X) | ra_Px8(X, tptp_fun_Y_12(X)))) | (~(![Y: $i] : (~ra_Px8(X, Y)) | (~ca_Cx8(X))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[166])).
% 0.19/0.42 tff(168,plain,
% 0.19/0.42 (^[X: $i] : rewrite((~((~(ca_Cx8(X) | ra_Px8(X, tptp_fun_Y_12(X)))) | (~(![Y: $i] : (~ra_Px8(X, Y)) | (~ca_Cx8(X)))))) <=> (~((~(ca_Cx8(X) | ra_Px8(X, tptp_fun_Y_12(X)))) | (~(![Y: $i] : (~ra_Px8(X, Y)) | (~ca_Cx8(X)))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(169,plain,
% 0.19/0.43 (![X: $i] : (~((~(ca_Cx8(X) | ra_Px8(X, tptp_fun_Y_12(X)))) | (~(![Y: $i] : (~ra_Px8(X, Y)) | (~ca_Cx8(X)))))) <=> ![X: $i] : (~((~(ca_Cx8(X) | ra_Px8(X, tptp_fun_Y_12(X)))) | (~(![Y: $i] : (~ra_Px8(X, Y)) | (~ca_Cx8(X))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[168])).
% 0.19/0.43 tff(170,plain,
% 0.19/0.43 (![X: $i] : (~((~(ca_Cx8(X) | ra_Px8(X, tptp_fun_Y_12(X)))) | (~(![Y: $i] : (~ra_Px8(X, Y)) | (~ca_Cx8(X)))))) <=> ![X: $i] : (~((~(ca_Cx8(X) | ra_Px8(X, tptp_fun_Y_12(X)))) | (~(![Y: $i] : (~ra_Px8(X, Y)) | (~ca_Cx8(X))))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[169, 167])).
% 0.19/0.43 tff(171,plain,
% 0.19/0.43 (^[X: $i] : trans(monotonicity(rewrite((![Y: $i] : (~ra_Px8(X, Y)) | (~ca_Cx8(X))) <=> (![Y: $i] : (~ra_Px8(X, Y)) | (~ca_Cx8(X)))), (((ca_Cx8(X) | ra_Px8(X, tptp_fun_Y_12(X))) & (![Y: $i] : (~ra_Px8(X, Y)) | (~ca_Cx8(X)))) <=> ((ca_Cx8(X) | ra_Px8(X, tptp_fun_Y_12(X))) & (![Y: $i] : (~ra_Px8(X, Y)) | (~ca_Cx8(X)))))), rewrite(((ca_Cx8(X) | ra_Px8(X, tptp_fun_Y_12(X))) & (![Y: $i] : (~ra_Px8(X, Y)) | (~ca_Cx8(X)))) <=> (~((~(ca_Cx8(X) | ra_Px8(X, tptp_fun_Y_12(X)))) | (~(![Y: $i] : (~ra_Px8(X, Y)) | (~ca_Cx8(X))))))), (((ca_Cx8(X) | ra_Px8(X, tptp_fun_Y_12(X))) & (![Y: $i] : (~ra_Px8(X, Y)) | (~ca_Cx8(X)))) <=> (~((~(ca_Cx8(X) | ra_Px8(X, tptp_fun_Y_12(X)))) | (~(![Y: $i] : (~ra_Px8(X, Y)) | (~ca_Cx8(X))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(172,plain,
% 0.19/0.43 (![X: $i] : ((ca_Cx8(X) | ra_Px8(X, tptp_fun_Y_12(X))) & (![Y: $i] : (~ra_Px8(X, Y)) | (~ca_Cx8(X)))) <=> ![X: $i] : (~((~(ca_Cx8(X) | ra_Px8(X, tptp_fun_Y_12(X)))) | (~(![Y: $i] : (~ra_Px8(X, Y)) | (~ca_Cx8(X))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[171])).
% 0.19/0.43 tff(173,plain,
% 0.19/0.43 (^[X: $i] : rewrite(((ra_Px8(X, tptp_fun_Y_12(X)) | ca_Cx8(X)) & (![Y: $i] : (~ra_Px8(X, Y)) | (~ca_Cx8(X)))) <=> ((ca_Cx8(X) | ra_Px8(X, tptp_fun_Y_12(X))) & (![Y: $i] : (~ra_Px8(X, Y)) | (~ca_Cx8(X)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(174,plain,
% 0.19/0.43 (![X: $i] : ((ra_Px8(X, tptp_fun_Y_12(X)) | ca_Cx8(X)) & (![Y: $i] : (~ra_Px8(X, Y)) | (~ca_Cx8(X)))) <=> ![X: $i] : ((ca_Cx8(X) | ra_Px8(X, tptp_fun_Y_12(X))) & (![Y: $i] : (~ra_Px8(X, Y)) | (~ca_Cx8(X))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[173])).
% 0.19/0.43 tff(175,plain,
% 0.19/0.43 (![X: $i] : (~(?[Y: $i] : ra_Px8(X, Y) <=> ca_Cx8(X))) <=> ![X: $i] : (~(?[Y: $i] : ra_Px8(X, Y) <=> ca_Cx8(X)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(176,plain,
% 0.19/0.43 (^[X: $i] : trans(trans(monotonicity(rewrite((~?[Y: $i] : ra_Px8(X, Y)) <=> (~?[Y: $i] : ra_Px8(X, Y))), ((ca_Cx8(X) <=> (~?[Y: $i] : ra_Px8(X, Y))) <=> (ca_Cx8(X) <=> (~?[Y: $i] : ra_Px8(X, Y))))), rewrite((ca_Cx8(X) <=> (~?[Y: $i] : ra_Px8(X, Y))) <=> (~(?[Y: $i] : ra_Px8(X, Y) <=> ca_Cx8(X)))), ((ca_Cx8(X) <=> (~?[Y: $i] : ra_Px8(X, Y))) <=> (~(?[Y: $i] : ra_Px8(X, Y) <=> ca_Cx8(X))))), rewrite((~(?[Y: $i] : ra_Px8(X, Y) <=> ca_Cx8(X))) <=> (~(?[Y: $i] : ra_Px8(X, Y) <=> ca_Cx8(X)))), ((ca_Cx8(X) <=> (~?[Y: $i] : ra_Px8(X, Y))) <=> (~(?[Y: $i] : ra_Px8(X, Y) <=> ca_Cx8(X)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(177,plain,
% 0.19/0.43 (![X: $i] : (ca_Cx8(X) <=> (~?[Y: $i] : ra_Px8(X, Y))) <=> ![X: $i] : (~(?[Y: $i] : ra_Px8(X, Y) <=> ca_Cx8(X)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[176])).
% 0.19/0.43 tff(178,axiom,(![X: $i] : (ca_Cx8(X) <=> (~?[Y: $i] : ra_Px8(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_20')).
% 0.19/0.43 tff(179,plain,
% 0.19/0.43 (![X: $i] : (~(?[Y: $i] : ra_Px8(X, Y) <=> ca_Cx8(X)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.19/0.43 tff(180,plain,
% 0.19/0.43 (![X: $i] : (~(?[Y: $i] : ra_Px8(X, Y) <=> ca_Cx8(X)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[179, 175])).
% 0.19/0.43 tff(181,plain,(
% 0.19/0.43 ![X: $i] : ((ra_Px8(X, tptp_fun_Y_12(X)) | ca_Cx8(X)) & (![Y: $i] : (~ra_Px8(X, Y)) | (~ca_Cx8(X))))),
% 0.19/0.43 inference(skolemize,[status(sab)],[180])).
% 0.19/0.43 tff(182,plain,
% 0.19/0.43 (![X: $i] : ((ca_Cx8(X) | ra_Px8(X, tptp_fun_Y_12(X))) & (![Y: $i] : (~ra_Px8(X, Y)) | (~ca_Cx8(X))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[181, 174])).
% 0.19/0.43 tff(183,plain,
% 0.19/0.43 (![X: $i] : (~((~(ca_Cx8(X) | ra_Px8(X, tptp_fun_Y_12(X)))) | (~(![Y: $i] : (~ra_Px8(X, Y)) | (~ca_Cx8(X))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[182, 172])).
% 0.19/0.43 tff(184,plain,
% 0.19/0.43 (![X: $i] : (~((~(ca_Cx8(X) | ra_Px8(X, tptp_fun_Y_12(X)))) | (~(![Y: $i] : (~ra_Px8(X, Y)) | (~ca_Cx8(X))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[183, 170])).
% 0.19/0.43 tff(185,plain,
% 0.19/0.43 (![X: $i] : (~((~(ca_Cx8(X) | ra_Px8(X, tptp_fun_Y_12(X)))) | (~((~ca_Cx8(X)) | ![Y: $i] : (~ra_Px8(X, Y))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[184, 165])).
% 0.19/0.43 tff(186,plain,
% 0.19/0.43 ((~![X: $i] : (~((~(ca_Cx8(X) | ra_Px8(X, tptp_fun_Y_12(X)))) | (~((~ca_Cx8(X)) | ![Y: $i] : (~ra_Px8(X, Y))))))) | (~((~(ca_Cx8(i2003_11_14_17_20_50869) | ra_Px8(i2003_11_14_17_20_50869, tptp_fun_Y_12(i2003_11_14_17_20_50869)))) | (~((~ca_Cx8(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px8(i2003_11_14_17_20_50869, Y))))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(187,plain,
% 0.19/0.43 (~((~(ca_Cx8(i2003_11_14_17_20_50869) | ra_Px8(i2003_11_14_17_20_50869, tptp_fun_Y_12(i2003_11_14_17_20_50869)))) | (~((~ca_Cx8(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px8(i2003_11_14_17_20_50869, Y)))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[186, 185])).
% 0.19/0.43 tff(188,plain,
% 0.19/0.43 (((~(ca_Cx8(i2003_11_14_17_20_50869) | ra_Px8(i2003_11_14_17_20_50869, tptp_fun_Y_12(i2003_11_14_17_20_50869)))) | (~((~ca_Cx8(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px8(i2003_11_14_17_20_50869, Y))))) | (ca_Cx8(i2003_11_14_17_20_50869) | ra_Px8(i2003_11_14_17_20_50869, tptp_fun_Y_12(i2003_11_14_17_20_50869)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(189,plain,
% 0.19/0.43 (ca_Cx8(i2003_11_14_17_20_50869) | ra_Px8(i2003_11_14_17_20_50869, tptp_fun_Y_12(i2003_11_14_17_20_50869))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[188, 187])).
% 0.19/0.43 tff(190,plain,
% 0.19/0.43 ((~(ca_Cx8(i2003_11_14_17_20_50869) | ra_Px8(i2003_11_14_17_20_50869, tptp_fun_Y_12(i2003_11_14_17_20_50869)))) | ca_Cx8(i2003_11_14_17_20_50869) | ra_Px8(i2003_11_14_17_20_50869, tptp_fun_Y_12(i2003_11_14_17_20_50869))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(191,plain,
% 0.19/0.43 (ca_Cx8(i2003_11_14_17_20_50869) | ra_Px8(i2003_11_14_17_20_50869, tptp_fun_Y_12(i2003_11_14_17_20_50869))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[190, 189])).
% 0.19/0.43 tff(192,plain,
% 0.19/0.43 (ca_Cx8(i2003_11_14_17_20_50869)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[191, 163])).
% 0.19/0.43 tff(193,plain,
% 0.19/0.43 (((~ca(i2003_11_14_17_20_50869)) | (~cb(i2003_11_14_17_20_50869))) | cb(i2003_11_14_17_20_50869)),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(194,plain,
% 0.19/0.43 ((~ca(i2003_11_14_17_20_50869)) | (~cb(i2003_11_14_17_20_50869))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[193, 132])).
% 0.19/0.43 tff(195,plain,
% 0.19/0.43 (^[X: $i] : refl((~(((~ca(X)) | (~cb(X))) <=> ca_Cx6xcomp(X))) <=> (~(((~ca(X)) | (~cb(X))) <=> ca_Cx6xcomp(X))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(196,plain,
% 0.19/0.43 (![X: $i] : (~(((~ca(X)) | (~cb(X))) <=> ca_Cx6xcomp(X))) <=> ![X: $i] : (~(((~ca(X)) | (~cb(X))) <=> ca_Cx6xcomp(X)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[195])).
% 0.19/0.43 tff(197,plain,
% 0.19/0.43 (^[X: $i] : trans(trans(monotonicity(rewrite((ca(X) & cb(X)) <=> (~((~ca(X)) | (~cb(X))))), ((ca_Cx6xcomp(X) <=> (ca(X) & cb(X))) <=> (ca_Cx6xcomp(X) <=> (~((~ca(X)) | (~cb(X))))))), rewrite((ca_Cx6xcomp(X) <=> (~((~ca(X)) | (~cb(X))))) <=> (~(((~ca(X)) | (~cb(X))) <=> ca_Cx6xcomp(X)))), ((ca_Cx6xcomp(X) <=> (ca(X) & cb(X))) <=> (~(((~ca(X)) | (~cb(X))) <=> ca_Cx6xcomp(X))))), rewrite((~(((~ca(X)) | (~cb(X))) <=> ca_Cx6xcomp(X))) <=> (~(((~ca(X)) | (~cb(X))) <=> ca_Cx6xcomp(X)))), ((ca_Cx6xcomp(X) <=> (ca(X) & cb(X))) <=> (~(((~ca(X)) | (~cb(X))) <=> ca_Cx6xcomp(X)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(198,plain,
% 0.19/0.43 (![X: $i] : (ca_Cx6xcomp(X) <=> (ca(X) & cb(X))) <=> ![X: $i] : (~(((~ca(X)) | (~cb(X))) <=> ca_Cx6xcomp(X)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[197])).
% 0.19/0.43 tff(199,plain,
% 0.19/0.43 (![X: $i] : (ca_Cx6xcomp(X) <=> (ca(X) & cb(X))) <=> ![X: $i] : (ca_Cx6xcomp(X) <=> (ca(X) & cb(X)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(200,axiom,(![X: $i] : (ca_Cx6xcomp(X) <=> (ca(X) & cb(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_15')).
% 0.19/0.43 tff(201,plain,
% 0.19/0.43 (![X: $i] : (ca_Cx6xcomp(X) <=> (ca(X) & cb(X)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.19/0.43 tff(202,plain,(
% 0.19/0.43 ![X: $i] : (ca_Cx6xcomp(X) <=> (ca(X) & cb(X)))),
% 0.19/0.43 inference(skolemize,[status(sab)],[201])).
% 0.19/0.43 tff(203,plain,
% 0.19/0.43 (![X: $i] : (~(((~ca(X)) | (~cb(X))) <=> ca_Cx6xcomp(X)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[202, 198])).
% 0.19/0.43 tff(204,plain,
% 0.19/0.43 (![X: $i] : (~(((~ca(X)) | (~cb(X))) <=> ca_Cx6xcomp(X)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[203, 196])).
% 0.19/0.43 tff(205,plain,
% 0.19/0.43 ((~![X: $i] : (~(((~ca(X)) | (~cb(X))) <=> ca_Cx6xcomp(X)))) | (~(((~ca(i2003_11_14_17_20_50869)) | (~cb(i2003_11_14_17_20_50869))) <=> ca_Cx6xcomp(i2003_11_14_17_20_50869)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(206,plain,
% 0.19/0.43 (~(((~ca(i2003_11_14_17_20_50869)) | (~cb(i2003_11_14_17_20_50869))) <=> ca_Cx6xcomp(i2003_11_14_17_20_50869))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[205, 204])).
% 0.19/0.43 tff(207,plain,
% 0.19/0.43 ((((~ca(i2003_11_14_17_20_50869)) | (~cb(i2003_11_14_17_20_50869))) <=> ca_Cx6xcomp(i2003_11_14_17_20_50869)) | (~((~ca(i2003_11_14_17_20_50869)) | (~cb(i2003_11_14_17_20_50869)))) | (~ca_Cx6xcomp(i2003_11_14_17_20_50869))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(208,plain,
% 0.19/0.43 ((~((~ca(i2003_11_14_17_20_50869)) | (~cb(i2003_11_14_17_20_50869)))) | (~ca_Cx6xcomp(i2003_11_14_17_20_50869))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[207, 206])).
% 0.19/0.43 tff(209,plain,
% 0.19/0.43 (~ca_Cx6xcomp(i2003_11_14_17_20_50869)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[208, 194])).
% 0.19/0.43 tff(210,plain,
% 0.19/0.43 (^[X: $i] : refl((~((~((~ca_Cx6xcomp(X)) | ra_Px6(X, tptp_fun_Y0_9(X)))) | (~(ca_Cx6xcomp(X) | ![Y0: $i] : (~ra_Px6(X, Y0)))))) <=> (~((~((~ca_Cx6xcomp(X)) | ra_Px6(X, tptp_fun_Y0_9(X)))) | (~(ca_Cx6xcomp(X) | ![Y0: $i] : (~ra_Px6(X, Y0)))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(211,plain,
% 0.19/0.43 (![X: $i] : (~((~((~ca_Cx6xcomp(X)) | ra_Px6(X, tptp_fun_Y0_9(X)))) | (~(ca_Cx6xcomp(X) | ![Y0: $i] : (~ra_Px6(X, Y0)))))) <=> ![X: $i] : (~((~((~ca_Cx6xcomp(X)) | ra_Px6(X, tptp_fun_Y0_9(X)))) | (~(ca_Cx6xcomp(X) | ![Y0: $i] : (~ra_Px6(X, Y0))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[210])).
% 0.19/0.43 tff(212,plain,
% 0.19/0.43 (^[X: $i] : rewrite((~((~((~ca_Cx6xcomp(X)) | ra_Px6(X, tptp_fun_Y0_9(X)))) | (~(ca_Cx6xcomp(X) | ![Y0: $i] : (~ra_Px6(X, Y0)))))) <=> (~((~((~ca_Cx6xcomp(X)) | ra_Px6(X, tptp_fun_Y0_9(X)))) | (~(ca_Cx6xcomp(X) | ![Y0: $i] : (~ra_Px6(X, Y0)))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(213,plain,
% 0.19/0.43 (![X: $i] : (~((~((~ca_Cx6xcomp(X)) | ra_Px6(X, tptp_fun_Y0_9(X)))) | (~(ca_Cx6xcomp(X) | ![Y0: $i] : (~ra_Px6(X, Y0)))))) <=> ![X: $i] : (~((~((~ca_Cx6xcomp(X)) | ra_Px6(X, tptp_fun_Y0_9(X)))) | (~(ca_Cx6xcomp(X) | ![Y0: $i] : (~ra_Px6(X, Y0))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[212])).
% 0.19/0.43 tff(214,plain,
% 0.19/0.43 (![X: $i] : (~((~((~ca_Cx6xcomp(X)) | ra_Px6(X, tptp_fun_Y0_9(X)))) | (~(ca_Cx6xcomp(X) | ![Y0: $i] : (~ra_Px6(X, Y0)))))) <=> ![X: $i] : (~((~((~ca_Cx6xcomp(X)) | ra_Px6(X, tptp_fun_Y0_9(X)))) | (~(ca_Cx6xcomp(X) | ![Y0: $i] : (~ra_Px6(X, Y0))))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[213, 211])).
% 0.19/0.43 tff(215,plain,
% 0.19/0.43 (^[X: $i] : trans(monotonicity(rewrite((ca_Cx6xcomp(X) | ![Y0: $i] : (~ra_Px6(X, Y0))) <=> (ca_Cx6xcomp(X) | ![Y0: $i] : (~ra_Px6(X, Y0)))), ((((~ca_Cx6xcomp(X)) | ra_Px6(X, tptp_fun_Y0_9(X))) & (ca_Cx6xcomp(X) | ![Y0: $i] : (~ra_Px6(X, Y0)))) <=> (((~ca_Cx6xcomp(X)) | ra_Px6(X, tptp_fun_Y0_9(X))) & (ca_Cx6xcomp(X) | ![Y0: $i] : (~ra_Px6(X, Y0)))))), rewrite((((~ca_Cx6xcomp(X)) | ra_Px6(X, tptp_fun_Y0_9(X))) & (ca_Cx6xcomp(X) | ![Y0: $i] : (~ra_Px6(X, Y0)))) <=> (~((~((~ca_Cx6xcomp(X)) | ra_Px6(X, tptp_fun_Y0_9(X)))) | (~(ca_Cx6xcomp(X) | ![Y0: $i] : (~ra_Px6(X, Y0))))))), ((((~ca_Cx6xcomp(X)) | ra_Px6(X, tptp_fun_Y0_9(X))) & (ca_Cx6xcomp(X) | ![Y0: $i] : (~ra_Px6(X, Y0)))) <=> (~((~((~ca_Cx6xcomp(X)) | ra_Px6(X, tptp_fun_Y0_9(X)))) | (~(ca_Cx6xcomp(X) | ![Y0: $i] : (~ra_Px6(X, Y0))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(216,plain,
% 0.19/0.43 (![X: $i] : (((~ca_Cx6xcomp(X)) | ra_Px6(X, tptp_fun_Y0_9(X))) & (ca_Cx6xcomp(X) | ![Y0: $i] : (~ra_Px6(X, Y0)))) <=> ![X: $i] : (~((~((~ca_Cx6xcomp(X)) | ra_Px6(X, tptp_fun_Y0_9(X)))) | (~(ca_Cx6xcomp(X) | ![Y0: $i] : (~ra_Px6(X, Y0))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[215])).
% 0.19/0.43 tff(217,plain,
% 0.19/0.43 (![X: $i] : (ca_Cx6xcomp(X) <=> ?[Y0: $i] : ra_Px6(X, Y0)) <=> ![X: $i] : (ca_Cx6xcomp(X) <=> ?[Y0: $i] : ra_Px6(X, Y0))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(218,axiom,(![X: $i] : (ca_Cx6xcomp(X) <=> ?[Y0: $i] : ra_Px6(X, Y0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_16')).
% 0.19/0.43 tff(219,plain,
% 0.19/0.43 (![X: $i] : (ca_Cx6xcomp(X) <=> ?[Y0: $i] : ra_Px6(X, Y0))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.19/0.43 tff(220,plain,(
% 0.19/0.43 ![X: $i] : (((~ca_Cx6xcomp(X)) | ra_Px6(X, tptp_fun_Y0_9(X))) & (ca_Cx6xcomp(X) | ![Y0: $i] : (~ra_Px6(X, Y0))))),
% 0.19/0.43 inference(skolemize,[status(sab)],[219])).
% 0.19/0.43 tff(221,plain,
% 0.19/0.43 (![X: $i] : (~((~((~ca_Cx6xcomp(X)) | ra_Px6(X, tptp_fun_Y0_9(X)))) | (~(ca_Cx6xcomp(X) | ![Y0: $i] : (~ra_Px6(X, Y0))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[220, 216])).
% 0.19/0.43 tff(222,plain,
% 0.19/0.43 (![X: $i] : (~((~((~ca_Cx6xcomp(X)) | ra_Px6(X, tptp_fun_Y0_9(X)))) | (~(ca_Cx6xcomp(X) | ![Y0: $i] : (~ra_Px6(X, Y0))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[221, 214])).
% 0.19/0.43 tff(223,plain,
% 0.19/0.43 ((~![X: $i] : (~((~((~ca_Cx6xcomp(X)) | ra_Px6(X, tptp_fun_Y0_9(X)))) | (~(ca_Cx6xcomp(X) | ![Y0: $i] : (~ra_Px6(X, Y0))))))) | (~((~((~ca_Cx6xcomp(i2003_11_14_17_20_50869)) | ra_Px6(i2003_11_14_17_20_50869, tptp_fun_Y0_9(i2003_11_14_17_20_50869)))) | (~(ca_Cx6xcomp(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px6(i2003_11_14_17_20_50869, Y0))))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(224,plain,
% 0.19/0.43 (~((~((~ca_Cx6xcomp(i2003_11_14_17_20_50869)) | ra_Px6(i2003_11_14_17_20_50869, tptp_fun_Y0_9(i2003_11_14_17_20_50869)))) | (~(ca_Cx6xcomp(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px6(i2003_11_14_17_20_50869, Y0)))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[223, 222])).
% 0.19/0.43 tff(225,plain,
% 0.19/0.43 (((~((~ca_Cx6xcomp(i2003_11_14_17_20_50869)) | ra_Px6(i2003_11_14_17_20_50869, tptp_fun_Y0_9(i2003_11_14_17_20_50869)))) | (~(ca_Cx6xcomp(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px6(i2003_11_14_17_20_50869, Y0))))) | (ca_Cx6xcomp(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px6(i2003_11_14_17_20_50869, Y0)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(226,plain,
% 0.19/0.43 (ca_Cx6xcomp(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px6(i2003_11_14_17_20_50869, Y0))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[225, 224])).
% 0.19/0.43 tff(227,plain,
% 0.19/0.43 ((~(ca_Cx6xcomp(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px6(i2003_11_14_17_20_50869, Y0)))) | ca_Cx6xcomp(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px6(i2003_11_14_17_20_50869, Y0))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(228,plain,
% 0.19/0.43 (ca_Cx6xcomp(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px6(i2003_11_14_17_20_50869, Y0))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[227, 226])).
% 0.19/0.43 tff(229,plain,
% 0.19/0.43 (![Y0: $i] : (~ra_Px6(i2003_11_14_17_20_50869, Y0))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[228, 209])).
% 0.19/0.43 tff(230,assumption,(ra_Px6(i2003_11_14_17_20_50869, tptp_fun_Y_8(i2003_11_14_17_20_50869))), introduced(assumption)).
% 0.19/0.43 tff(231,assumption,(![Y0: $i] : (~ra_Px6(i2003_11_14_17_20_50869, Y0))), introduced(assumption)).
% 0.19/0.43 tff(232,plain,
% 0.19/0.43 ((~![Y0: $i] : (~ra_Px6(i2003_11_14_17_20_50869, Y0))) | (~ra_Px6(i2003_11_14_17_20_50869, tptp_fun_Y_8(i2003_11_14_17_20_50869)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(233,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[232, 231, 230])).
% 0.19/0.43 tff(234,plain,((~ra_Px6(i2003_11_14_17_20_50869, tptp_fun_Y_8(i2003_11_14_17_20_50869))) | (~![Y0: $i] : (~ra_Px6(i2003_11_14_17_20_50869, Y0)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(235,plain,
% 0.19/0.43 (~ra_Px6(i2003_11_14_17_20_50869, tptp_fun_Y_8(i2003_11_14_17_20_50869))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[234, 229])).
% 0.19/0.43 tff(236,plain,
% 0.19/0.43 (^[X: $i] : rewrite((~((~(ca_Cx6(X) | ra_Px6(X, tptp_fun_Y_8(X)))) | (~(![Y: $i] : (~ra_Px6(X, Y)) | (~ca_Cx6(X)))))) <=> (~((~(ca_Cx6(X) | ra_Px6(X, tptp_fun_Y_8(X)))) | (~((~ca_Cx6(X)) | ![Y: $i] : (~ra_Px6(X, Y)))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(237,plain,
% 0.19/0.43 (![X: $i] : (~((~(ca_Cx6(X) | ra_Px6(X, tptp_fun_Y_8(X)))) | (~(![Y: $i] : (~ra_Px6(X, Y)) | (~ca_Cx6(X)))))) <=> ![X: $i] : (~((~(ca_Cx6(X) | ra_Px6(X, tptp_fun_Y_8(X)))) | (~((~ca_Cx6(X)) | ![Y: $i] : (~ra_Px6(X, Y))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[236])).
% 0.19/0.43 tff(238,plain,
% 0.19/0.43 (^[X: $i] : refl((~((~(ca_Cx6(X) | ra_Px6(X, tptp_fun_Y_8(X)))) | (~(![Y: $i] : (~ra_Px6(X, Y)) | (~ca_Cx6(X)))))) <=> (~((~(ca_Cx6(X) | ra_Px6(X, tptp_fun_Y_8(X)))) | (~(![Y: $i] : (~ra_Px6(X, Y)) | (~ca_Cx6(X)))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(239,plain,
% 0.19/0.43 (![X: $i] : (~((~(ca_Cx6(X) | ra_Px6(X, tptp_fun_Y_8(X)))) | (~(![Y: $i] : (~ra_Px6(X, Y)) | (~ca_Cx6(X)))))) <=> ![X: $i] : (~((~(ca_Cx6(X) | ra_Px6(X, tptp_fun_Y_8(X)))) | (~(![Y: $i] : (~ra_Px6(X, Y)) | (~ca_Cx6(X))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[238])).
% 0.19/0.43 tff(240,plain,
% 0.19/0.43 (^[X: $i] : rewrite((~((~(ca_Cx6(X) | ra_Px6(X, tptp_fun_Y_8(X)))) | (~(![Y: $i] : (~ra_Px6(X, Y)) | (~ca_Cx6(X)))))) <=> (~((~(ca_Cx6(X) | ra_Px6(X, tptp_fun_Y_8(X)))) | (~(![Y: $i] : (~ra_Px6(X, Y)) | (~ca_Cx6(X)))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(241,plain,
% 0.19/0.43 (![X: $i] : (~((~(ca_Cx6(X) | ra_Px6(X, tptp_fun_Y_8(X)))) | (~(![Y: $i] : (~ra_Px6(X, Y)) | (~ca_Cx6(X)))))) <=> ![X: $i] : (~((~(ca_Cx6(X) | ra_Px6(X, tptp_fun_Y_8(X)))) | (~(![Y: $i] : (~ra_Px6(X, Y)) | (~ca_Cx6(X))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[240])).
% 0.19/0.43 tff(242,plain,
% 0.19/0.43 (![X: $i] : (~((~(ca_Cx6(X) | ra_Px6(X, tptp_fun_Y_8(X)))) | (~(![Y: $i] : (~ra_Px6(X, Y)) | (~ca_Cx6(X)))))) <=> ![X: $i] : (~((~(ca_Cx6(X) | ra_Px6(X, tptp_fun_Y_8(X)))) | (~(![Y: $i] : (~ra_Px6(X, Y)) | (~ca_Cx6(X))))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[241, 239])).
% 0.19/0.43 tff(243,plain,
% 0.19/0.43 (^[X: $i] : trans(monotonicity(rewrite((![Y: $i] : (~ra_Px6(X, Y)) | (~ca_Cx6(X))) <=> (![Y: $i] : (~ra_Px6(X, Y)) | (~ca_Cx6(X)))), (((ca_Cx6(X) | ra_Px6(X, tptp_fun_Y_8(X))) & (![Y: $i] : (~ra_Px6(X, Y)) | (~ca_Cx6(X)))) <=> ((ca_Cx6(X) | ra_Px6(X, tptp_fun_Y_8(X))) & (![Y: $i] : (~ra_Px6(X, Y)) | (~ca_Cx6(X)))))), rewrite(((ca_Cx6(X) | ra_Px6(X, tptp_fun_Y_8(X))) & (![Y: $i] : (~ra_Px6(X, Y)) | (~ca_Cx6(X)))) <=> (~((~(ca_Cx6(X) | ra_Px6(X, tptp_fun_Y_8(X)))) | (~(![Y: $i] : (~ra_Px6(X, Y)) | (~ca_Cx6(X))))))), (((ca_Cx6(X) | ra_Px6(X, tptp_fun_Y_8(X))) & (![Y: $i] : (~ra_Px6(X, Y)) | (~ca_Cx6(X)))) <=> (~((~(ca_Cx6(X) | ra_Px6(X, tptp_fun_Y_8(X)))) | (~(![Y: $i] : (~ra_Px6(X, Y)) | (~ca_Cx6(X))))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(244,plain,
% 0.19/0.43 (![X: $i] : ((ca_Cx6(X) | ra_Px6(X, tptp_fun_Y_8(X))) & (![Y: $i] : (~ra_Px6(X, Y)) | (~ca_Cx6(X)))) <=> ![X: $i] : (~((~(ca_Cx6(X) | ra_Px6(X, tptp_fun_Y_8(X)))) | (~(![Y: $i] : (~ra_Px6(X, Y)) | (~ca_Cx6(X))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[243])).
% 0.19/0.43 tff(245,plain,
% 0.19/0.43 (^[X: $i] : rewrite(((ra_Px6(X, tptp_fun_Y_8(X)) | ca_Cx6(X)) & (![Y: $i] : (~ra_Px6(X, Y)) | (~ca_Cx6(X)))) <=> ((ca_Cx6(X) | ra_Px6(X, tptp_fun_Y_8(X))) & (![Y: $i] : (~ra_Px6(X, Y)) | (~ca_Cx6(X)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(246,plain,
% 0.19/0.43 (![X: $i] : ((ra_Px6(X, tptp_fun_Y_8(X)) | ca_Cx6(X)) & (![Y: $i] : (~ra_Px6(X, Y)) | (~ca_Cx6(X)))) <=> ![X: $i] : ((ca_Cx6(X) | ra_Px6(X, tptp_fun_Y_8(X))) & (![Y: $i] : (~ra_Px6(X, Y)) | (~ca_Cx6(X))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[245])).
% 0.19/0.43 tff(247,plain,
% 0.19/0.43 (![X: $i] : (~(?[Y: $i] : ra_Px6(X, Y) <=> ca_Cx6(X))) <=> ![X: $i] : (~(?[Y: $i] : ra_Px6(X, Y) <=> ca_Cx6(X)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(248,plain,
% 0.19/0.43 (^[X: $i] : trans(trans(monotonicity(rewrite((~?[Y: $i] : ra_Px6(X, Y)) <=> (~?[Y: $i] : ra_Px6(X, Y))), ((ca_Cx6(X) <=> (~?[Y: $i] : ra_Px6(X, Y))) <=> (ca_Cx6(X) <=> (~?[Y: $i] : ra_Px6(X, Y))))), rewrite((ca_Cx6(X) <=> (~?[Y: $i] : ra_Px6(X, Y))) <=> (~(?[Y: $i] : ra_Px6(X, Y) <=> ca_Cx6(X)))), ((ca_Cx6(X) <=> (~?[Y: $i] : ra_Px6(X, Y))) <=> (~(?[Y: $i] : ra_Px6(X, Y) <=> ca_Cx6(X))))), rewrite((~(?[Y: $i] : ra_Px6(X, Y) <=> ca_Cx6(X))) <=> (~(?[Y: $i] : ra_Px6(X, Y) <=> ca_Cx6(X)))), ((ca_Cx6(X) <=> (~?[Y: $i] : ra_Px6(X, Y))) <=> (~(?[Y: $i] : ra_Px6(X, Y) <=> ca_Cx6(X)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(249,plain,
% 0.19/0.43 (![X: $i] : (ca_Cx6(X) <=> (~?[Y: $i] : ra_Px6(X, Y))) <=> ![X: $i] : (~(?[Y: $i] : ra_Px6(X, Y) <=> ca_Cx6(X)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[248])).
% 0.19/0.43 tff(250,axiom,(![X: $i] : (ca_Cx6(X) <=> (~?[Y: $i] : ra_Px6(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_14')).
% 0.19/0.43 tff(251,plain,
% 0.19/0.43 (![X: $i] : (~(?[Y: $i] : ra_Px6(X, Y) <=> ca_Cx6(X)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[250, 249])).
% 0.19/0.43 tff(252,plain,
% 0.19/0.43 (![X: $i] : (~(?[Y: $i] : ra_Px6(X, Y) <=> ca_Cx6(X)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[251, 247])).
% 0.19/0.43 tff(253,plain,(
% 0.19/0.43 ![X: $i] : ((ra_Px6(X, tptp_fun_Y_8(X)) | ca_Cx6(X)) & (![Y: $i] : (~ra_Px6(X, Y)) | (~ca_Cx6(X))))),
% 0.19/0.43 inference(skolemize,[status(sab)],[252])).
% 0.19/0.43 tff(254,plain,
% 0.19/0.43 (![X: $i] : ((ca_Cx6(X) | ra_Px6(X, tptp_fun_Y_8(X))) & (![Y: $i] : (~ra_Px6(X, Y)) | (~ca_Cx6(X))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[253, 246])).
% 0.19/0.43 tff(255,plain,
% 0.19/0.43 (![X: $i] : (~((~(ca_Cx6(X) | ra_Px6(X, tptp_fun_Y_8(X)))) | (~(![Y: $i] : (~ra_Px6(X, Y)) | (~ca_Cx6(X))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[254, 244])).
% 0.19/0.43 tff(256,plain,
% 0.19/0.43 (![X: $i] : (~((~(ca_Cx6(X) | ra_Px6(X, tptp_fun_Y_8(X)))) | (~(![Y: $i] : (~ra_Px6(X, Y)) | (~ca_Cx6(X))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[255, 242])).
% 0.19/0.43 tff(257,plain,
% 0.19/0.43 (![X: $i] : (~((~(ca_Cx6(X) | ra_Px6(X, tptp_fun_Y_8(X)))) | (~((~ca_Cx6(X)) | ![Y: $i] : (~ra_Px6(X, Y))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[256, 237])).
% 0.19/0.43 tff(258,plain,
% 0.19/0.43 ((~![X: $i] : (~((~(ca_Cx6(X) | ra_Px6(X, tptp_fun_Y_8(X)))) | (~((~ca_Cx6(X)) | ![Y: $i] : (~ra_Px6(X, Y))))))) | (~((~(ca_Cx6(i2003_11_14_17_20_50869) | ra_Px6(i2003_11_14_17_20_50869, tptp_fun_Y_8(i2003_11_14_17_20_50869)))) | (~((~ca_Cx6(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px6(i2003_11_14_17_20_50869, Y))))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(259,plain,
% 0.19/0.43 (~((~(ca_Cx6(i2003_11_14_17_20_50869) | ra_Px6(i2003_11_14_17_20_50869, tptp_fun_Y_8(i2003_11_14_17_20_50869)))) | (~((~ca_Cx6(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px6(i2003_11_14_17_20_50869, Y)))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[258, 257])).
% 0.19/0.43 tff(260,plain,
% 0.19/0.43 (((~(ca_Cx6(i2003_11_14_17_20_50869) | ra_Px6(i2003_11_14_17_20_50869, tptp_fun_Y_8(i2003_11_14_17_20_50869)))) | (~((~ca_Cx6(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px6(i2003_11_14_17_20_50869, Y))))) | (ca_Cx6(i2003_11_14_17_20_50869) | ra_Px6(i2003_11_14_17_20_50869, tptp_fun_Y_8(i2003_11_14_17_20_50869)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(261,plain,
% 0.19/0.43 (ca_Cx6(i2003_11_14_17_20_50869) | ra_Px6(i2003_11_14_17_20_50869, tptp_fun_Y_8(i2003_11_14_17_20_50869))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[260, 259])).
% 0.19/0.43 tff(262,plain,
% 0.19/0.43 ((~(ca_Cx6(i2003_11_14_17_20_50869) | ra_Px6(i2003_11_14_17_20_50869, tptp_fun_Y_8(i2003_11_14_17_20_50869)))) | ca_Cx6(i2003_11_14_17_20_50869) | ra_Px6(i2003_11_14_17_20_50869, tptp_fun_Y_8(i2003_11_14_17_20_50869))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(263,plain,
% 0.19/0.43 (ca_Cx6(i2003_11_14_17_20_50869) | ra_Px6(i2003_11_14_17_20_50869, tptp_fun_Y_8(i2003_11_14_17_20_50869))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[262, 261])).
% 0.19/0.43 tff(264,plain,
% 0.19/0.43 (ca_Cx6(i2003_11_14_17_20_50869)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[263, 235])).
% 0.19/0.43 tff(265,plain,
% 0.19/0.43 ((~((~ca_Cx6(i2003_11_14_17_20_50869)) | (~ca_Cx7(i2003_11_14_17_20_50869)) | (~ca_Cx8(i2003_11_14_17_20_50869)))) | (~ca_Cx6(i2003_11_14_17_20_50869)) | (~ca_Cx7(i2003_11_14_17_20_50869)) | (~ca_Cx8(i2003_11_14_17_20_50869))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(266,plain,
% 0.19/0.43 ((~((~ca_Cx6(i2003_11_14_17_20_50869)) | (~ca_Cx7(i2003_11_14_17_20_50869)) | (~ca_Cx8(i2003_11_14_17_20_50869)))) | (~ca_Cx7(i2003_11_14_17_20_50869)) | (~ca_Cx8(i2003_11_14_17_20_50869))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[265, 264])).
% 0.19/0.43 tff(267,plain,
% 0.19/0.43 (~ca_Cx7(i2003_11_14_17_20_50869)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[266, 102, 192])).
% 0.19/0.43 tff(268,plain,
% 0.19/0.44 ((~(ca_Cx7(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px7(i2003_11_14_17_20_50869, Y0)))) | ca_Cx7(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px7(i2003_11_14_17_20_50869, Y0))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(269,plain,
% 0.19/0.44 (![Y0: $i] : (~ra_Px7(i2003_11_14_17_20_50869, Y0))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[268, 267, 119])).
% 0.19/0.44 tff(270,assumption,(ra_Px7(i2003_11_14_17_20_50869, tptp_fun_Y_11(i2003_11_14_17_20_50869))), introduced(assumption)).
% 0.19/0.44 tff(271,assumption,(![Y0: $i] : (~ra_Px7(i2003_11_14_17_20_50869, Y0))), introduced(assumption)).
% 0.19/0.44 tff(272,plain,
% 0.19/0.44 ((~![Y0: $i] : (~ra_Px7(i2003_11_14_17_20_50869, Y0))) | (~ra_Px7(i2003_11_14_17_20_50869, tptp_fun_Y_11(i2003_11_14_17_20_50869)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(273,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[272, 271, 270])).
% 0.19/0.44 tff(274,plain,((~ra_Px7(i2003_11_14_17_20_50869, tptp_fun_Y_11(i2003_11_14_17_20_50869))) | (~![Y0: $i] : (~ra_Px7(i2003_11_14_17_20_50869, Y0)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(275,plain,
% 0.19/0.44 (~ra_Px7(i2003_11_14_17_20_50869, tptp_fun_Y_11(i2003_11_14_17_20_50869))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[274, 269])).
% 0.19/0.44 tff(276,assumption,((~(ca_Cx7xcomp(i2003_11_14_17_20_50869) | ra_Px7(i2003_11_14_17_20_50869, tptp_fun_Y_11(i2003_11_14_17_20_50869)))) | (~((~ca_Cx7xcomp(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px7(i2003_11_14_17_20_50869, Y))))), introduced(assumption)).
% 0.19/0.44 tff(277,plain,
% 0.19/0.44 (^[X: $i] : rewrite((~((~(ca_Cx7xcomp(X) | ra_Px7(X, tptp_fun_Y_11(X)))) | (~(![Y: $i] : (~ra_Px7(X, Y)) | (~ca_Cx7xcomp(X)))))) <=> (~((~(ca_Cx7xcomp(X) | ra_Px7(X, tptp_fun_Y_11(X)))) | (~((~ca_Cx7xcomp(X)) | ![Y: $i] : (~ra_Px7(X, Y)))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(278,plain,
% 0.19/0.44 (![X: $i] : (~((~(ca_Cx7xcomp(X) | ra_Px7(X, tptp_fun_Y_11(X)))) | (~(![Y: $i] : (~ra_Px7(X, Y)) | (~ca_Cx7xcomp(X)))))) <=> ![X: $i] : (~((~(ca_Cx7xcomp(X) | ra_Px7(X, tptp_fun_Y_11(X)))) | (~((~ca_Cx7xcomp(X)) | ![Y: $i] : (~ra_Px7(X, Y))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[277])).
% 0.19/0.44 tff(279,plain,
% 0.19/0.44 (^[X: $i] : refl((~((~(ca_Cx7xcomp(X) | ra_Px7(X, tptp_fun_Y_11(X)))) | (~(![Y: $i] : (~ra_Px7(X, Y)) | (~ca_Cx7xcomp(X)))))) <=> (~((~(ca_Cx7xcomp(X) | ra_Px7(X, tptp_fun_Y_11(X)))) | (~(![Y: $i] : (~ra_Px7(X, Y)) | (~ca_Cx7xcomp(X)))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(280,plain,
% 0.19/0.44 (![X: $i] : (~((~(ca_Cx7xcomp(X) | ra_Px7(X, tptp_fun_Y_11(X)))) | (~(![Y: $i] : (~ra_Px7(X, Y)) | (~ca_Cx7xcomp(X)))))) <=> ![X: $i] : (~((~(ca_Cx7xcomp(X) | ra_Px7(X, tptp_fun_Y_11(X)))) | (~(![Y: $i] : (~ra_Px7(X, Y)) | (~ca_Cx7xcomp(X))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[279])).
% 0.19/0.44 tff(281,plain,
% 0.19/0.44 (^[X: $i] : rewrite((~((~(ca_Cx7xcomp(X) | ra_Px7(X, tptp_fun_Y_11(X)))) | (~(![Y: $i] : (~ra_Px7(X, Y)) | (~ca_Cx7xcomp(X)))))) <=> (~((~(ca_Cx7xcomp(X) | ra_Px7(X, tptp_fun_Y_11(X)))) | (~(![Y: $i] : (~ra_Px7(X, Y)) | (~ca_Cx7xcomp(X)))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(282,plain,
% 0.19/0.44 (![X: $i] : (~((~(ca_Cx7xcomp(X) | ra_Px7(X, tptp_fun_Y_11(X)))) | (~(![Y: $i] : (~ra_Px7(X, Y)) | (~ca_Cx7xcomp(X)))))) <=> ![X: $i] : (~((~(ca_Cx7xcomp(X) | ra_Px7(X, tptp_fun_Y_11(X)))) | (~(![Y: $i] : (~ra_Px7(X, Y)) | (~ca_Cx7xcomp(X))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[281])).
% 0.19/0.44 tff(283,plain,
% 0.19/0.44 (![X: $i] : (~((~(ca_Cx7xcomp(X) | ra_Px7(X, tptp_fun_Y_11(X)))) | (~(![Y: $i] : (~ra_Px7(X, Y)) | (~ca_Cx7xcomp(X)))))) <=> ![X: $i] : (~((~(ca_Cx7xcomp(X) | ra_Px7(X, tptp_fun_Y_11(X)))) | (~(![Y: $i] : (~ra_Px7(X, Y)) | (~ca_Cx7xcomp(X))))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[282, 280])).
% 0.19/0.44 tff(284,plain,
% 0.19/0.44 (^[X: $i] : trans(monotonicity(rewrite((![Y: $i] : (~ra_Px7(X, Y)) | (~ca_Cx7xcomp(X))) <=> (![Y: $i] : (~ra_Px7(X, Y)) | (~ca_Cx7xcomp(X)))), (((ca_Cx7xcomp(X) | ra_Px7(X, tptp_fun_Y_11(X))) & (![Y: $i] : (~ra_Px7(X, Y)) | (~ca_Cx7xcomp(X)))) <=> ((ca_Cx7xcomp(X) | ra_Px7(X, tptp_fun_Y_11(X))) & (![Y: $i] : (~ra_Px7(X, Y)) | (~ca_Cx7xcomp(X)))))), rewrite(((ca_Cx7xcomp(X) | ra_Px7(X, tptp_fun_Y_11(X))) & (![Y: $i] : (~ra_Px7(X, Y)) | (~ca_Cx7xcomp(X)))) <=> (~((~(ca_Cx7xcomp(X) | ra_Px7(X, tptp_fun_Y_11(X)))) | (~(![Y: $i] : (~ra_Px7(X, Y)) | (~ca_Cx7xcomp(X))))))), (((ca_Cx7xcomp(X) | ra_Px7(X, tptp_fun_Y_11(X))) & (![Y: $i] : (~ra_Px7(X, Y)) | (~ca_Cx7xcomp(X)))) <=> (~((~(ca_Cx7xcomp(X) | ra_Px7(X, tptp_fun_Y_11(X)))) | (~(![Y: $i] : (~ra_Px7(X, Y)) | (~ca_Cx7xcomp(X))))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(285,plain,
% 0.19/0.44 (![X: $i] : ((ca_Cx7xcomp(X) | ra_Px7(X, tptp_fun_Y_11(X))) & (![Y: $i] : (~ra_Px7(X, Y)) | (~ca_Cx7xcomp(X)))) <=> ![X: $i] : (~((~(ca_Cx7xcomp(X) | ra_Px7(X, tptp_fun_Y_11(X)))) | (~(![Y: $i] : (~ra_Px7(X, Y)) | (~ca_Cx7xcomp(X))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[284])).
% 0.19/0.44 tff(286,plain,
% 0.19/0.44 (^[X: $i] : rewrite(((ra_Px7(X, tptp_fun_Y_11(X)) | ca_Cx7xcomp(X)) & (![Y: $i] : (~ra_Px7(X, Y)) | (~ca_Cx7xcomp(X)))) <=> ((ca_Cx7xcomp(X) | ra_Px7(X, tptp_fun_Y_11(X))) & (![Y: $i] : (~ra_Px7(X, Y)) | (~ca_Cx7xcomp(X)))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(287,plain,
% 0.19/0.44 (![X: $i] : ((ra_Px7(X, tptp_fun_Y_11(X)) | ca_Cx7xcomp(X)) & (![Y: $i] : (~ra_Px7(X, Y)) | (~ca_Cx7xcomp(X)))) <=> ![X: $i] : ((ca_Cx7xcomp(X) | ra_Px7(X, tptp_fun_Y_11(X))) & (![Y: $i] : (~ra_Px7(X, Y)) | (~ca_Cx7xcomp(X))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[286])).
% 0.19/0.44 tff(288,plain,
% 0.19/0.44 (![X: $i] : (~(?[Y: $i] : ra_Px7(X, Y) <=> ca_Cx7xcomp(X))) <=> ![X: $i] : (~(?[Y: $i] : ra_Px7(X, Y) <=> ca_Cx7xcomp(X)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(289,plain,
% 0.19/0.44 (^[X: $i] : trans(trans(monotonicity(rewrite((~?[Y: $i] : ra_Px7(X, Y)) <=> (~?[Y: $i] : ra_Px7(X, Y))), ((ca_Cx7xcomp(X) <=> (~?[Y: $i] : ra_Px7(X, Y))) <=> (ca_Cx7xcomp(X) <=> (~?[Y: $i] : ra_Px7(X, Y))))), rewrite((ca_Cx7xcomp(X) <=> (~?[Y: $i] : ra_Px7(X, Y))) <=> (~(?[Y: $i] : ra_Px7(X, Y) <=> ca_Cx7xcomp(X)))), ((ca_Cx7xcomp(X) <=> (~?[Y: $i] : ra_Px7(X, Y))) <=> (~(?[Y: $i] : ra_Px7(X, Y) <=> ca_Cx7xcomp(X))))), rewrite((~(?[Y: $i] : ra_Px7(X, Y) <=> ca_Cx7xcomp(X))) <=> (~(?[Y: $i] : ra_Px7(X, Y) <=> ca_Cx7xcomp(X)))), ((ca_Cx7xcomp(X) <=> (~?[Y: $i] : ra_Px7(X, Y))) <=> (~(?[Y: $i] : ra_Px7(X, Y) <=> ca_Cx7xcomp(X)))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(290,plain,
% 0.19/0.44 (![X: $i] : (ca_Cx7xcomp(X) <=> (~?[Y: $i] : ra_Px7(X, Y))) <=> ![X: $i] : (~(?[Y: $i] : ra_Px7(X, Y) <=> ca_Cx7xcomp(X)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[289])).
% 0.19/0.44 tff(291,axiom,(![X: $i] : (ca_Cx7xcomp(X) <=> (~?[Y: $i] : ra_Px7(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_19')).
% 0.19/0.44 tff(292,plain,
% 0.19/0.44 (![X: $i] : (~(?[Y: $i] : ra_Px7(X, Y) <=> ca_Cx7xcomp(X)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[291, 290])).
% 0.19/0.44 tff(293,plain,
% 0.19/0.44 (![X: $i] : (~(?[Y: $i] : ra_Px7(X, Y) <=> ca_Cx7xcomp(X)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[292, 288])).
% 0.19/0.44 tff(294,plain,(
% 0.19/0.44 ![X: $i] : ((ra_Px7(X, tptp_fun_Y_11(X)) | ca_Cx7xcomp(X)) & (![Y: $i] : (~ra_Px7(X, Y)) | (~ca_Cx7xcomp(X))))),
% 0.19/0.44 inference(skolemize,[status(sab)],[293])).
% 0.19/0.44 tff(295,plain,
% 0.19/0.44 (![X: $i] : ((ca_Cx7xcomp(X) | ra_Px7(X, tptp_fun_Y_11(X))) & (![Y: $i] : (~ra_Px7(X, Y)) | (~ca_Cx7xcomp(X))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[294, 287])).
% 0.19/0.44 tff(296,plain,
% 0.19/0.44 (![X: $i] : (~((~(ca_Cx7xcomp(X) | ra_Px7(X, tptp_fun_Y_11(X)))) | (~(![Y: $i] : (~ra_Px7(X, Y)) | (~ca_Cx7xcomp(X))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[295, 285])).
% 0.19/0.44 tff(297,plain,
% 0.19/0.44 (![X: $i] : (~((~(ca_Cx7xcomp(X) | ra_Px7(X, tptp_fun_Y_11(X)))) | (~(![Y: $i] : (~ra_Px7(X, Y)) | (~ca_Cx7xcomp(X))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[296, 283])).
% 0.19/0.44 tff(298,plain,
% 0.19/0.44 (![X: $i] : (~((~(ca_Cx7xcomp(X) | ra_Px7(X, tptp_fun_Y_11(X)))) | (~((~ca_Cx7xcomp(X)) | ![Y: $i] : (~ra_Px7(X, Y))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[297, 278])).
% 0.19/0.44 tff(299,plain,
% 0.19/0.44 ((~![X: $i] : (~((~(ca_Cx7xcomp(X) | ra_Px7(X, tptp_fun_Y_11(X)))) | (~((~ca_Cx7xcomp(X)) | ![Y: $i] : (~ra_Px7(X, Y))))))) | (~((~(ca_Cx7xcomp(i2003_11_14_17_20_50869) | ra_Px7(i2003_11_14_17_20_50869, tptp_fun_Y_11(i2003_11_14_17_20_50869)))) | (~((~ca_Cx7xcomp(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px7(i2003_11_14_17_20_50869, Y))))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(300,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[299, 298, 276])).
% 0.19/0.44 tff(301,plain,(~((~(ca_Cx7xcomp(i2003_11_14_17_20_50869) | ra_Px7(i2003_11_14_17_20_50869, tptp_fun_Y_11(i2003_11_14_17_20_50869)))) | (~((~ca_Cx7xcomp(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px7(i2003_11_14_17_20_50869, Y)))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(302,plain,
% 0.19/0.44 (((~(ca_Cx7xcomp(i2003_11_14_17_20_50869) | ra_Px7(i2003_11_14_17_20_50869, tptp_fun_Y_11(i2003_11_14_17_20_50869)))) | (~((~ca_Cx7xcomp(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px7(i2003_11_14_17_20_50869, Y))))) | (ca_Cx7xcomp(i2003_11_14_17_20_50869) | ra_Px7(i2003_11_14_17_20_50869, tptp_fun_Y_11(i2003_11_14_17_20_50869)))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(303,plain,
% 0.19/0.44 (ca_Cx7xcomp(i2003_11_14_17_20_50869) | ra_Px7(i2003_11_14_17_20_50869, tptp_fun_Y_11(i2003_11_14_17_20_50869))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[302, 301])).
% 0.19/0.44 tff(304,plain,
% 0.19/0.44 ((~(ca_Cx7xcomp(i2003_11_14_17_20_50869) | ra_Px7(i2003_11_14_17_20_50869, tptp_fun_Y_11(i2003_11_14_17_20_50869)))) | ca_Cx7xcomp(i2003_11_14_17_20_50869) | ra_Px7(i2003_11_14_17_20_50869, tptp_fun_Y_11(i2003_11_14_17_20_50869))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(305,plain,
% 0.19/0.44 (ca_Cx7xcomp(i2003_11_14_17_20_50869) | ra_Px7(i2003_11_14_17_20_50869, tptp_fun_Y_11(i2003_11_14_17_20_50869))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[304, 303])).
% 0.19/0.44 tff(306,plain,
% 0.19/0.44 (ca_Cx7xcomp(i2003_11_14_17_20_50869)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[305, 275])).
% 0.19/0.44 tff(307,assumption,(((~ca(i2003_11_14_17_20_50869)) | (~cc(i2003_11_14_17_20_50869))) <=> ca_Cx7xcomp(i2003_11_14_17_20_50869)), introduced(assumption)).
% 0.19/0.44 tff(308,plain,
% 0.19/0.44 (^[X: $i] : refl((~(((~ca(X)) | (~cc(X))) <=> ca_Cx7xcomp(X))) <=> (~(((~ca(X)) | (~cc(X))) <=> ca_Cx7xcomp(X))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(309,plain,
% 0.19/0.44 (![X: $i] : (~(((~ca(X)) | (~cc(X))) <=> ca_Cx7xcomp(X))) <=> ![X: $i] : (~(((~ca(X)) | (~cc(X))) <=> ca_Cx7xcomp(X)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[308])).
% 0.19/0.44 tff(310,plain,
% 0.19/0.44 (^[X: $i] : trans(trans(monotonicity(rewrite((cc(X) & ca(X)) <=> (~((~ca(X)) | (~cc(X))))), ((ca_Cx7xcomp(X) <=> (cc(X) & ca(X))) <=> (ca_Cx7xcomp(X) <=> (~((~ca(X)) | (~cc(X))))))), rewrite((ca_Cx7xcomp(X) <=> (~((~ca(X)) | (~cc(X))))) <=> (~(((~ca(X)) | (~cc(X))) <=> ca_Cx7xcomp(X)))), ((ca_Cx7xcomp(X) <=> (cc(X) & ca(X))) <=> (~(((~ca(X)) | (~cc(X))) <=> ca_Cx7xcomp(X))))), rewrite((~(((~ca(X)) | (~cc(X))) <=> ca_Cx7xcomp(X))) <=> (~(((~ca(X)) | (~cc(X))) <=> ca_Cx7xcomp(X)))), ((ca_Cx7xcomp(X) <=> (cc(X) & ca(X))) <=> (~(((~ca(X)) | (~cc(X))) <=> ca_Cx7xcomp(X)))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(311,plain,
% 0.19/0.44 (![X: $i] : (ca_Cx7xcomp(X) <=> (cc(X) & ca(X))) <=> ![X: $i] : (~(((~ca(X)) | (~cc(X))) <=> ca_Cx7xcomp(X)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[310])).
% 0.19/0.44 tff(312,plain,
% 0.19/0.44 (![X: $i] : (ca_Cx7xcomp(X) <=> (cc(X) & ca(X))) <=> ![X: $i] : (ca_Cx7xcomp(X) <=> (cc(X) & ca(X)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(313,axiom,(![X: $i] : (ca_Cx7xcomp(X) <=> (cc(X) & ca(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_18')).
% 0.19/0.44 tff(314,plain,
% 0.19/0.44 (![X: $i] : (ca_Cx7xcomp(X) <=> (cc(X) & ca(X)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[313, 312])).
% 0.19/0.44 tff(315,plain,(
% 0.19/0.44 ![X: $i] : (ca_Cx7xcomp(X) <=> (cc(X) & ca(X)))),
% 0.19/0.44 inference(skolemize,[status(sab)],[314])).
% 0.19/0.44 tff(316,plain,
% 0.19/0.44 (![X: $i] : (~(((~ca(X)) | (~cc(X))) <=> ca_Cx7xcomp(X)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[315, 311])).
% 0.19/0.44 tff(317,plain,
% 0.19/0.44 (![X: $i] : (~(((~ca(X)) | (~cc(X))) <=> ca_Cx7xcomp(X)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[316, 309])).
% 0.19/0.44 tff(318,plain,
% 0.19/0.44 ((~![X: $i] : (~(((~ca(X)) | (~cc(X))) <=> ca_Cx7xcomp(X)))) | (~(((~ca(i2003_11_14_17_20_50869)) | (~cc(i2003_11_14_17_20_50869))) <=> ca_Cx7xcomp(i2003_11_14_17_20_50869)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(319,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[318, 317, 307])).
% 0.19/0.44 tff(320,plain,(~(((~ca(i2003_11_14_17_20_50869)) | (~cc(i2003_11_14_17_20_50869))) <=> ca_Cx7xcomp(i2003_11_14_17_20_50869))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(321,plain,
% 0.19/0.44 ((((~ca(i2003_11_14_17_20_50869)) | (~cc(i2003_11_14_17_20_50869))) <=> ca_Cx7xcomp(i2003_11_14_17_20_50869)) | (~((~ca(i2003_11_14_17_20_50869)) | (~cc(i2003_11_14_17_20_50869)))) | (~ca_Cx7xcomp(i2003_11_14_17_20_50869))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(322,plain,
% 0.19/0.44 ((~((~ca(i2003_11_14_17_20_50869)) | (~cc(i2003_11_14_17_20_50869)))) | (~ca_Cx7xcomp(i2003_11_14_17_20_50869))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[321, 320])).
% 0.19/0.44 tff(323,plain,
% 0.19/0.44 (~((~ca(i2003_11_14_17_20_50869)) | (~cc(i2003_11_14_17_20_50869)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[322, 306])).
% 0.19/0.44 tff(324,plain,
% 0.19/0.44 (((~ca(i2003_11_14_17_20_50869)) | (~cc(i2003_11_14_17_20_50869))) | cc(i2003_11_14_17_20_50869)),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(325,plain,
% 0.19/0.44 (cc(i2003_11_14_17_20_50869)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[324, 323])).
% 0.19/0.44 tff(326,plain,
% 0.19/0.44 ((~((~cc(i2003_11_14_17_20_50869)) | ra_Px2(i2003_11_14_17_20_50869, tptp_fun_Y0_4(i2003_11_14_17_20_50869)))) | (~cc(i2003_11_14_17_20_50869)) | ra_Px2(i2003_11_14_17_20_50869, tptp_fun_Y0_4(i2003_11_14_17_20_50869))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(327,plain,
% 0.19/0.44 (ra_Px2(i2003_11_14_17_20_50869, tptp_fun_Y0_4(i2003_11_14_17_20_50869))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[326, 325, 17])).
% 0.19/0.44 tff(328,plain,
% 0.19/0.44 (((~ca(i2003_11_14_17_20_50869)) | (~cc(i2003_11_14_17_20_50869))) | ca(i2003_11_14_17_20_50869)),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(329,plain,
% 0.19/0.44 (ca(i2003_11_14_17_20_50869)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[328, 323])).
% 0.19/0.44 tff(330,plain,
% 0.19/0.44 (^[X: $i] : refl((ca_Cx1(X) | (~ca(X))) <=> (ca_Cx1(X) | (~ca(X))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(331,plain,
% 0.19/0.44 (![X: $i] : (ca_Cx1(X) | (~ca(X))) <=> ![X: $i] : (ca_Cx1(X) | (~ca(X)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[330])).
% 0.19/0.44 tff(332,plain,
% 0.19/0.44 (![X: $i] : (ca_Cx1(X) | (~ca(X))) <=> ![X: $i] : (ca_Cx1(X) | (~ca(X)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(333,plain,
% 0.19/0.44 (^[X: $i] : rewrite((ca(X) => ca_Cx1(X)) <=> (ca_Cx1(X) | (~ca(X))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(334,plain,
% 0.19/0.44 (![X: $i] : (ca(X) => ca_Cx1(X)) <=> ![X: $i] : (ca_Cx1(X) | (~ca(X)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[333])).
% 0.19/0.44 tff(335,axiom,(![X: $i] : (ca(X) => ca_Cx1(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_5')).
% 0.19/0.44 tff(336,plain,
% 0.19/0.44 (![X: $i] : (ca_Cx1(X) | (~ca(X)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[335, 334])).
% 0.19/0.44 tff(337,plain,
% 0.19/0.44 (![X: $i] : (ca_Cx1(X) | (~ca(X)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[336, 332])).
% 0.19/0.44 tff(338,plain,(
% 0.19/0.44 ![X: $i] : (ca_Cx1(X) | (~ca(X)))),
% 0.19/0.44 inference(skolemize,[status(sab)],[337])).
% 0.19/0.44 tff(339,plain,
% 0.19/0.44 (![X: $i] : (ca_Cx1(X) | (~ca(X)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[338, 331])).
% 0.19/0.44 tff(340,plain,
% 0.19/0.44 (((~![X: $i] : (ca_Cx1(X) | (~ca(X)))) | (ca_Cx1(i2003_11_14_17_20_50869) | (~ca(i2003_11_14_17_20_50869)))) <=> ((~![X: $i] : (ca_Cx1(X) | (~ca(X)))) | ca_Cx1(i2003_11_14_17_20_50869) | (~ca(i2003_11_14_17_20_50869)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(341,plain,
% 0.19/0.44 ((~![X: $i] : (ca_Cx1(X) | (~ca(X)))) | (ca_Cx1(i2003_11_14_17_20_50869) | (~ca(i2003_11_14_17_20_50869)))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(342,plain,
% 0.19/0.44 ((~![X: $i] : (ca_Cx1(X) | (~ca(X)))) | ca_Cx1(i2003_11_14_17_20_50869) | (~ca(i2003_11_14_17_20_50869))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[341, 340])).
% 0.19/0.44 tff(343,plain,
% 0.19/0.44 (ca_Cx1(i2003_11_14_17_20_50869) | (~ca(i2003_11_14_17_20_50869))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[342, 339])).
% 0.19/0.44 tff(344,plain,
% 0.19/0.44 (ca_Cx1(i2003_11_14_17_20_50869)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[343, 329])).
% 0.19/0.44 tff(345,plain,
% 0.19/0.44 ((((~cbxcomp(i2003_11_14_17_20_50869)) | (~ccxcomp(i2003_11_14_17_20_50869))) <=> ca_Cx1(i2003_11_14_17_20_50869)) | (~((~cbxcomp(i2003_11_14_17_20_50869)) | (~ccxcomp(i2003_11_14_17_20_50869)))) | (~ca_Cx1(i2003_11_14_17_20_50869))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(346,plain,
% 0.19/0.44 (~((~cbxcomp(i2003_11_14_17_20_50869)) | (~ccxcomp(i2003_11_14_17_20_50869)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[345, 344, 131])).
% 0.19/0.44 tff(347,plain,
% 0.19/0.44 (((~cbxcomp(i2003_11_14_17_20_50869)) | (~ccxcomp(i2003_11_14_17_20_50869))) | ccxcomp(i2003_11_14_17_20_50869)),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(348,plain,
% 0.19/0.44 (ccxcomp(i2003_11_14_17_20_50869)),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[347, 346])).
% 0.19/0.44 tff(349,plain,
% 0.19/0.44 (^[X: $i] : rewrite((~((~(ccxcomp(X) | ra_Px2(X, tptp_fun_Y_5(X)))) | (~(![Y: $i] : (~ra_Px2(X, Y)) | (~ccxcomp(X)))))) <=> (~((~(ccxcomp(X) | ra_Px2(X, tptp_fun_Y_5(X)))) | (~((~ccxcomp(X)) | ![Y: $i] : (~ra_Px2(X, Y)))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(350,plain,
% 0.19/0.44 (![X: $i] : (~((~(ccxcomp(X) | ra_Px2(X, tptp_fun_Y_5(X)))) | (~(![Y: $i] : (~ra_Px2(X, Y)) | (~ccxcomp(X)))))) <=> ![X: $i] : (~((~(ccxcomp(X) | ra_Px2(X, tptp_fun_Y_5(X)))) | (~((~ccxcomp(X)) | ![Y: $i] : (~ra_Px2(X, Y))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[349])).
% 0.19/0.44 tff(351,plain,
% 0.19/0.44 (^[X: $i] : refl((~((~(ccxcomp(X) | ra_Px2(X, tptp_fun_Y_5(X)))) | (~(![Y: $i] : (~ra_Px2(X, Y)) | (~ccxcomp(X)))))) <=> (~((~(ccxcomp(X) | ra_Px2(X, tptp_fun_Y_5(X)))) | (~(![Y: $i] : (~ra_Px2(X, Y)) | (~ccxcomp(X)))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(352,plain,
% 0.19/0.44 (![X: $i] : (~((~(ccxcomp(X) | ra_Px2(X, tptp_fun_Y_5(X)))) | (~(![Y: $i] : (~ra_Px2(X, Y)) | (~ccxcomp(X)))))) <=> ![X: $i] : (~((~(ccxcomp(X) | ra_Px2(X, tptp_fun_Y_5(X)))) | (~(![Y: $i] : (~ra_Px2(X, Y)) | (~ccxcomp(X))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[351])).
% 0.19/0.44 tff(353,plain,
% 0.19/0.44 (^[X: $i] : rewrite((~((~(ccxcomp(X) | ra_Px2(X, tptp_fun_Y_5(X)))) | (~(![Y: $i] : (~ra_Px2(X, Y)) | (~ccxcomp(X)))))) <=> (~((~(ccxcomp(X) | ra_Px2(X, tptp_fun_Y_5(X)))) | (~(![Y: $i] : (~ra_Px2(X, Y)) | (~ccxcomp(X)))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(354,plain,
% 0.19/0.44 (![X: $i] : (~((~(ccxcomp(X) | ra_Px2(X, tptp_fun_Y_5(X)))) | (~(![Y: $i] : (~ra_Px2(X, Y)) | (~ccxcomp(X)))))) <=> ![X: $i] : (~((~(ccxcomp(X) | ra_Px2(X, tptp_fun_Y_5(X)))) | (~(![Y: $i] : (~ra_Px2(X, Y)) | (~ccxcomp(X))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[353])).
% 0.19/0.44 tff(355,plain,
% 0.19/0.44 (![X: $i] : (~((~(ccxcomp(X) | ra_Px2(X, tptp_fun_Y_5(X)))) | (~(![Y: $i] : (~ra_Px2(X, Y)) | (~ccxcomp(X)))))) <=> ![X: $i] : (~((~(ccxcomp(X) | ra_Px2(X, tptp_fun_Y_5(X)))) | (~(![Y: $i] : (~ra_Px2(X, Y)) | (~ccxcomp(X))))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[354, 352])).
% 0.19/0.44 tff(356,plain,
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% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(357,plain,
% 0.19/0.44 (![X: $i] : ((ccxcomp(X) | ra_Px2(X, tptp_fun_Y_5(X))) & (![Y: $i] : (~ra_Px2(X, Y)) | (~ccxcomp(X)))) <=> ![X: $i] : (~((~(ccxcomp(X) | ra_Px2(X, tptp_fun_Y_5(X)))) | (~(![Y: $i] : (~ra_Px2(X, Y)) | (~ccxcomp(X))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[356])).
% 0.19/0.44 tff(358,plain,
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% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(359,plain,
% 0.19/0.44 (![X: $i] : ((ra_Px2(X, tptp_fun_Y_5(X)) | ccxcomp(X)) & (![Y: $i] : (~ra_Px2(X, Y)) | (~ccxcomp(X)))) <=> ![X: $i] : ((ccxcomp(X) | ra_Px2(X, tptp_fun_Y_5(X))) & (![Y: $i] : (~ra_Px2(X, Y)) | (~ccxcomp(X))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[358])).
% 0.19/0.44 tff(360,plain,
% 0.19/0.44 (![X: $i] : (~(?[Y: $i] : ra_Px2(X, Y) <=> ccxcomp(X))) <=> ![X: $i] : (~(?[Y: $i] : ra_Px2(X, Y) <=> ccxcomp(X)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(361,plain,
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% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(362,plain,
% 0.19/0.44 (![X: $i] : (ccxcomp(X) <=> (~?[Y: $i] : ra_Px2(X, Y))) <=> ![X: $i] : (~(?[Y: $i] : ra_Px2(X, Y) <=> ccxcomp(X)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[361])).
% 0.19/0.44 tff(363,axiom,(![X: $i] : (ccxcomp(X) <=> (~?[Y: $i] : ra_Px2(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_10')).
% 0.19/0.44 tff(364,plain,
% 0.19/0.44 (![X: $i] : (~(?[Y: $i] : ra_Px2(X, Y) <=> ccxcomp(X)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[363, 362])).
% 0.19/0.44 tff(365,plain,
% 0.19/0.44 (![X: $i] : (~(?[Y: $i] : ra_Px2(X, Y) <=> ccxcomp(X)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[364, 360])).
% 0.19/0.44 tff(366,plain,(
% 0.19/0.44 ![X: $i] : ((ra_Px2(X, tptp_fun_Y_5(X)) | ccxcomp(X)) & (![Y: $i] : (~ra_Px2(X, Y)) | (~ccxcomp(X))))),
% 0.19/0.44 inference(skolemize,[status(sab)],[365])).
% 0.19/0.44 tff(367,plain,
% 0.19/0.44 (![X: $i] : ((ccxcomp(X) | ra_Px2(X, tptp_fun_Y_5(X))) & (![Y: $i] : (~ra_Px2(X, Y)) | (~ccxcomp(X))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[366, 359])).
% 0.19/0.44 tff(368,plain,
% 0.19/0.44 (![X: $i] : (~((~(ccxcomp(X) | ra_Px2(X, tptp_fun_Y_5(X)))) | (~(![Y: $i] : (~ra_Px2(X, Y)) | (~ccxcomp(X))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[367, 357])).
% 0.19/0.44 tff(369,plain,
% 0.19/0.44 (![X: $i] : (~((~(ccxcomp(X) | ra_Px2(X, tptp_fun_Y_5(X)))) | (~(![Y: $i] : (~ra_Px2(X, Y)) | (~ccxcomp(X))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[368, 355])).
% 0.19/0.44 tff(370,plain,
% 0.19/0.44 (![X: $i] : (~((~(ccxcomp(X) | ra_Px2(X, tptp_fun_Y_5(X)))) | (~((~ccxcomp(X)) | ![Y: $i] : (~ra_Px2(X, Y))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[369, 350])).
% 0.19/0.44 tff(371,plain,
% 0.19/0.44 ((~![X: $i] : (~((~(ccxcomp(X) | ra_Px2(X, tptp_fun_Y_5(X)))) | (~((~ccxcomp(X)) | ![Y: $i] : (~ra_Px2(X, Y))))))) | (~((~(ccxcomp(i2003_11_14_17_20_50869) | ra_Px2(i2003_11_14_17_20_50869, tptp_fun_Y_5(i2003_11_14_17_20_50869)))) | (~((~ccxcomp(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px2(i2003_11_14_17_20_50869, Y))))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(372,plain,
% 0.19/0.44 (~((~(ccxcomp(i2003_11_14_17_20_50869) | ra_Px2(i2003_11_14_17_20_50869, tptp_fun_Y_5(i2003_11_14_17_20_50869)))) | (~((~ccxcomp(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px2(i2003_11_14_17_20_50869, Y)))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[371, 370])).
% 0.19/0.44 tff(373,plain,
% 0.19/0.44 (((~(ccxcomp(i2003_11_14_17_20_50869) | ra_Px2(i2003_11_14_17_20_50869, tptp_fun_Y_5(i2003_11_14_17_20_50869)))) | (~((~ccxcomp(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px2(i2003_11_14_17_20_50869, Y))))) | ((~ccxcomp(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px2(i2003_11_14_17_20_50869, Y)))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(374,plain,
% 0.19/0.44 ((~ccxcomp(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px2(i2003_11_14_17_20_50869, Y))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[373, 372])).
% 0.19/0.44 tff(375,plain,
% 0.19/0.44 ((~((~ccxcomp(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px2(i2003_11_14_17_20_50869, Y)))) | (~ccxcomp(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px2(i2003_11_14_17_20_50869, Y))),
% 0.19/0.44 inference(tautology,[status(thm)],[])).
% 0.19/0.44 tff(376,plain,
% 0.19/0.44 ((~ccxcomp(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px2(i2003_11_14_17_20_50869, Y))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[375, 374])).
% 0.19/0.44 tff(377,plain,
% 0.19/0.44 (![Y: $i] : (~ra_Px2(i2003_11_14_17_20_50869, Y))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[376, 348])).
% 0.19/0.45 tff(378,plain,
% 0.19/0.45 ((~![Y: $i] : (~ra_Px2(i2003_11_14_17_20_50869, Y))) | (~ra_Px2(i2003_11_14_17_20_50869, tptp_fun_Y0_4(i2003_11_14_17_20_50869)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(379,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[378, 377, 327])).
% 0.19/0.45 tff(380,plain,(cb(i2003_11_14_17_20_50869)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(381,plain,
% 0.19/0.45 (^[X: $i] : refl((~((~((~cb(X)) | ra_Px3(X, tptp_fun_Y0_2(X)))) | (~(cb(X) | ![Y0: $i] : (~ra_Px3(X, Y0)))))) <=> (~((~((~cb(X)) | ra_Px3(X, tptp_fun_Y0_2(X)))) | (~(cb(X) | ![Y0: $i] : (~ra_Px3(X, Y0)))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(382,plain,
% 0.19/0.45 (![X: $i] : (~((~((~cb(X)) | ra_Px3(X, tptp_fun_Y0_2(X)))) | (~(cb(X) | ![Y0: $i] : (~ra_Px3(X, Y0)))))) <=> ![X: $i] : (~((~((~cb(X)) | ra_Px3(X, tptp_fun_Y0_2(X)))) | (~(cb(X) | ![Y0: $i] : (~ra_Px3(X, Y0))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[381])).
% 0.19/0.45 tff(383,plain,
% 0.19/0.45 (^[X: $i] : rewrite((~((~((~cb(X)) | ra_Px3(X, tptp_fun_Y0_2(X)))) | (~(cb(X) | ![Y0: $i] : (~ra_Px3(X, Y0)))))) <=> (~((~((~cb(X)) | ra_Px3(X, tptp_fun_Y0_2(X)))) | (~(cb(X) | ![Y0: $i] : (~ra_Px3(X, Y0)))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(384,plain,
% 0.19/0.45 (![X: $i] : (~((~((~cb(X)) | ra_Px3(X, tptp_fun_Y0_2(X)))) | (~(cb(X) | ![Y0: $i] : (~ra_Px3(X, Y0)))))) <=> ![X: $i] : (~((~((~cb(X)) | ra_Px3(X, tptp_fun_Y0_2(X)))) | (~(cb(X) | ![Y0: $i] : (~ra_Px3(X, Y0))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[383])).
% 0.19/0.45 tff(385,plain,
% 0.19/0.45 (![X: $i] : (~((~((~cb(X)) | ra_Px3(X, tptp_fun_Y0_2(X)))) | (~(cb(X) | ![Y0: $i] : (~ra_Px3(X, Y0)))))) <=> ![X: $i] : (~((~((~cb(X)) | ra_Px3(X, tptp_fun_Y0_2(X)))) | (~(cb(X) | ![Y0: $i] : (~ra_Px3(X, Y0))))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[384, 382])).
% 0.19/0.45 tff(386,plain,
% 0.19/0.45 (^[X: $i] : trans(monotonicity(rewrite((cb(X) | ![Y0: $i] : (~ra_Px3(X, Y0))) <=> (cb(X) | ![Y0: $i] : (~ra_Px3(X, Y0)))), ((((~cb(X)) | ra_Px3(X, tptp_fun_Y0_2(X))) & (cb(X) | ![Y0: $i] : (~ra_Px3(X, Y0)))) <=> (((~cb(X)) | ra_Px3(X, tptp_fun_Y0_2(X))) & (cb(X) | ![Y0: $i] : (~ra_Px3(X, Y0)))))), rewrite((((~cb(X)) | ra_Px3(X, tptp_fun_Y0_2(X))) & (cb(X) | ![Y0: $i] : (~ra_Px3(X, Y0)))) <=> (~((~((~cb(X)) | ra_Px3(X, tptp_fun_Y0_2(X)))) | (~(cb(X) | ![Y0: $i] : (~ra_Px3(X, Y0))))))), ((((~cb(X)) | ra_Px3(X, tptp_fun_Y0_2(X))) & (cb(X) | ![Y0: $i] : (~ra_Px3(X, Y0)))) <=> (~((~((~cb(X)) | ra_Px3(X, tptp_fun_Y0_2(X)))) | (~(cb(X) | ![Y0: $i] : (~ra_Px3(X, Y0))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(387,plain,
% 0.19/0.45 (![X: $i] : (((~cb(X)) | ra_Px3(X, tptp_fun_Y0_2(X))) & (cb(X) | ![Y0: $i] : (~ra_Px3(X, Y0)))) <=> ![X: $i] : (~((~((~cb(X)) | ra_Px3(X, tptp_fun_Y0_2(X)))) | (~(cb(X) | ![Y0: $i] : (~ra_Px3(X, Y0))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[386])).
% 0.19/0.45 tff(388,plain,
% 0.19/0.45 (![X: $i] : (cb(X) <=> ?[Y0: $i] : ra_Px3(X, Y0)) <=> ![X: $i] : (cb(X) <=> ?[Y0: $i] : ra_Px3(X, Y0))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(389,axiom,(![X: $i] : (cb(X) <=> ?[Y0: $i] : ra_Px3(X, Y0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_6')).
% 0.19/0.45 tff(390,plain,
% 0.19/0.45 (![X: $i] : (cb(X) <=> ?[Y0: $i] : ra_Px3(X, Y0))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[389, 388])).
% 0.19/0.45 tff(391,plain,(
% 0.19/0.45 ![X: $i] : (((~cb(X)) | ra_Px3(X, tptp_fun_Y0_2(X))) & (cb(X) | ![Y0: $i] : (~ra_Px3(X, Y0))))),
% 0.19/0.45 inference(skolemize,[status(sab)],[390])).
% 0.19/0.45 tff(392,plain,
% 0.19/0.45 (![X: $i] : (~((~((~cb(X)) | ra_Px3(X, tptp_fun_Y0_2(X)))) | (~(cb(X) | ![Y0: $i] : (~ra_Px3(X, Y0))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[391, 387])).
% 0.19/0.45 tff(393,plain,
% 0.19/0.45 (![X: $i] : (~((~((~cb(X)) | ra_Px3(X, tptp_fun_Y0_2(X)))) | (~(cb(X) | ![Y0: $i] : (~ra_Px3(X, Y0))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[392, 385])).
% 0.19/0.45 tff(394,plain,
% 0.19/0.45 ((~![X: $i] : (~((~((~cb(X)) | ra_Px3(X, tptp_fun_Y0_2(X)))) | (~(cb(X) | ![Y0: $i] : (~ra_Px3(X, Y0))))))) | (~((~((~cb(i2003_11_14_17_20_50869)) | ra_Px3(i2003_11_14_17_20_50869, tptp_fun_Y0_2(i2003_11_14_17_20_50869)))) | (~(cb(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px3(i2003_11_14_17_20_50869, Y0))))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(395,plain,
% 0.19/0.45 (~((~((~cb(i2003_11_14_17_20_50869)) | ra_Px3(i2003_11_14_17_20_50869, tptp_fun_Y0_2(i2003_11_14_17_20_50869)))) | (~(cb(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px3(i2003_11_14_17_20_50869, Y0)))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[394, 393])).
% 0.19/0.45 tff(396,plain,
% 0.19/0.45 (((~((~cb(i2003_11_14_17_20_50869)) | ra_Px3(i2003_11_14_17_20_50869, tptp_fun_Y0_2(i2003_11_14_17_20_50869)))) | (~(cb(i2003_11_14_17_20_50869) | ![Y0: $i] : (~ra_Px3(i2003_11_14_17_20_50869, Y0))))) | ((~cb(i2003_11_14_17_20_50869)) | ra_Px3(i2003_11_14_17_20_50869, tptp_fun_Y0_2(i2003_11_14_17_20_50869)))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(397,plain,
% 0.19/0.45 ((~cb(i2003_11_14_17_20_50869)) | ra_Px3(i2003_11_14_17_20_50869, tptp_fun_Y0_2(i2003_11_14_17_20_50869))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[396, 395])).
% 0.19/0.45 tff(398,plain,
% 0.19/0.45 ((~((~cb(i2003_11_14_17_20_50869)) | ra_Px3(i2003_11_14_17_20_50869, tptp_fun_Y0_2(i2003_11_14_17_20_50869)))) | (~cb(i2003_11_14_17_20_50869)) | ra_Px3(i2003_11_14_17_20_50869, tptp_fun_Y0_2(i2003_11_14_17_20_50869))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(399,plain,
% 0.19/0.45 ((~cb(i2003_11_14_17_20_50869)) | ra_Px3(i2003_11_14_17_20_50869, tptp_fun_Y0_2(i2003_11_14_17_20_50869))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[398, 397])).
% 0.19/0.45 tff(400,plain,
% 0.19/0.45 (ra_Px3(i2003_11_14_17_20_50869, tptp_fun_Y0_2(i2003_11_14_17_20_50869))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[399, 380])).
% 0.19/0.45 tff(401,assumption,(ra_Px3(i2003_11_14_17_20_50869, tptp_fun_Y0_2(i2003_11_14_17_20_50869))), introduced(assumption)).
% 0.19/0.45 tff(402,assumption,(![Y: $i] : (~ra_Px3(i2003_11_14_17_20_50869, Y))), introduced(assumption)).
% 0.19/0.45 tff(403,plain,
% 0.19/0.45 ((~![Y: $i] : (~ra_Px3(i2003_11_14_17_20_50869, Y))) | (~ra_Px3(i2003_11_14_17_20_50869, tptp_fun_Y0_2(i2003_11_14_17_20_50869)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(404,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[403, 402, 401])).
% 0.19/0.45 tff(405,plain,((~ra_Px3(i2003_11_14_17_20_50869, tptp_fun_Y0_2(i2003_11_14_17_20_50869))) | (~![Y: $i] : (~ra_Px3(i2003_11_14_17_20_50869, Y)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(406,plain,
% 0.19/0.45 (~![Y: $i] : (~ra_Px3(i2003_11_14_17_20_50869, Y))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[405, 400])).
% 0.19/0.45 tff(407,plain,
% 0.19/0.45 (^[X: $i] : rewrite((~((~(cbxcomp(X) | ra_Px3(X, tptp_fun_Y_3(X)))) | (~(![Y: $i] : (~ra_Px3(X, Y)) | (~cbxcomp(X)))))) <=> (~((~(cbxcomp(X) | ra_Px3(X, tptp_fun_Y_3(X)))) | (~((~cbxcomp(X)) | ![Y: $i] : (~ra_Px3(X, Y)))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(408,plain,
% 0.19/0.45 (![X: $i] : (~((~(cbxcomp(X) | ra_Px3(X, tptp_fun_Y_3(X)))) | (~(![Y: $i] : (~ra_Px3(X, Y)) | (~cbxcomp(X)))))) <=> ![X: $i] : (~((~(cbxcomp(X) | ra_Px3(X, tptp_fun_Y_3(X)))) | (~((~cbxcomp(X)) | ![Y: $i] : (~ra_Px3(X, Y))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[407])).
% 0.19/0.45 tff(409,plain,
% 0.19/0.45 (^[X: $i] : refl((~((~(cbxcomp(X) | ra_Px3(X, tptp_fun_Y_3(X)))) | (~(![Y: $i] : (~ra_Px3(X, Y)) | (~cbxcomp(X)))))) <=> (~((~(cbxcomp(X) | ra_Px3(X, tptp_fun_Y_3(X)))) | (~(![Y: $i] : (~ra_Px3(X, Y)) | (~cbxcomp(X)))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(410,plain,
% 0.19/0.45 (![X: $i] : (~((~(cbxcomp(X) | ra_Px3(X, tptp_fun_Y_3(X)))) | (~(![Y: $i] : (~ra_Px3(X, Y)) | (~cbxcomp(X)))))) <=> ![X: $i] : (~((~(cbxcomp(X) | ra_Px3(X, tptp_fun_Y_3(X)))) | (~(![Y: $i] : (~ra_Px3(X, Y)) | (~cbxcomp(X))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[409])).
% 0.19/0.45 tff(411,plain,
% 0.19/0.45 (^[X: $i] : rewrite((~((~(cbxcomp(X) | ra_Px3(X, tptp_fun_Y_3(X)))) | (~(![Y: $i] : (~ra_Px3(X, Y)) | (~cbxcomp(X)))))) <=> (~((~(cbxcomp(X) | ra_Px3(X, tptp_fun_Y_3(X)))) | (~(![Y: $i] : (~ra_Px3(X, Y)) | (~cbxcomp(X)))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(412,plain,
% 0.19/0.45 (![X: $i] : (~((~(cbxcomp(X) | ra_Px3(X, tptp_fun_Y_3(X)))) | (~(![Y: $i] : (~ra_Px3(X, Y)) | (~cbxcomp(X)))))) <=> ![X: $i] : (~((~(cbxcomp(X) | ra_Px3(X, tptp_fun_Y_3(X)))) | (~(![Y: $i] : (~ra_Px3(X, Y)) | (~cbxcomp(X))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[411])).
% 0.19/0.45 tff(413,plain,
% 0.19/0.45 (![X: $i] : (~((~(cbxcomp(X) | ra_Px3(X, tptp_fun_Y_3(X)))) | (~(![Y: $i] : (~ra_Px3(X, Y)) | (~cbxcomp(X)))))) <=> ![X: $i] : (~((~(cbxcomp(X) | ra_Px3(X, tptp_fun_Y_3(X)))) | (~(![Y: $i] : (~ra_Px3(X, Y)) | (~cbxcomp(X))))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[412, 410])).
% 0.19/0.45 tff(414,plain,
% 0.19/0.45 (^[X: $i] : trans(monotonicity(rewrite((![Y: $i] : (~ra_Px3(X, Y)) | (~cbxcomp(X))) <=> (![Y: $i] : (~ra_Px3(X, Y)) | (~cbxcomp(X)))), (((cbxcomp(X) | ra_Px3(X, tptp_fun_Y_3(X))) & (![Y: $i] : (~ra_Px3(X, Y)) | (~cbxcomp(X)))) <=> ((cbxcomp(X) | ra_Px3(X, tptp_fun_Y_3(X))) & (![Y: $i] : (~ra_Px3(X, Y)) | (~cbxcomp(X)))))), rewrite(((cbxcomp(X) | ra_Px3(X, tptp_fun_Y_3(X))) & (![Y: $i] : (~ra_Px3(X, Y)) | (~cbxcomp(X)))) <=> (~((~(cbxcomp(X) | ra_Px3(X, tptp_fun_Y_3(X)))) | (~(![Y: $i] : (~ra_Px3(X, Y)) | (~cbxcomp(X))))))), (((cbxcomp(X) | ra_Px3(X, tptp_fun_Y_3(X))) & (![Y: $i] : (~ra_Px3(X, Y)) | (~cbxcomp(X)))) <=> (~((~(cbxcomp(X) | ra_Px3(X, tptp_fun_Y_3(X)))) | (~(![Y: $i] : (~ra_Px3(X, Y)) | (~cbxcomp(X))))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(415,plain,
% 0.19/0.45 (![X: $i] : ((cbxcomp(X) | ra_Px3(X, tptp_fun_Y_3(X))) & (![Y: $i] : (~ra_Px3(X, Y)) | (~cbxcomp(X)))) <=> ![X: $i] : (~((~(cbxcomp(X) | ra_Px3(X, tptp_fun_Y_3(X)))) | (~(![Y: $i] : (~ra_Px3(X, Y)) | (~cbxcomp(X))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[414])).
% 0.19/0.45 tff(416,plain,
% 0.19/0.45 (^[X: $i] : rewrite(((ra_Px3(X, tptp_fun_Y_3(X)) | cbxcomp(X)) & (![Y: $i] : (~ra_Px3(X, Y)) | (~cbxcomp(X)))) <=> ((cbxcomp(X) | ra_Px3(X, tptp_fun_Y_3(X))) & (![Y: $i] : (~ra_Px3(X, Y)) | (~cbxcomp(X)))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(417,plain,
% 0.19/0.45 (![X: $i] : ((ra_Px3(X, tptp_fun_Y_3(X)) | cbxcomp(X)) & (![Y: $i] : (~ra_Px3(X, Y)) | (~cbxcomp(X)))) <=> ![X: $i] : ((cbxcomp(X) | ra_Px3(X, tptp_fun_Y_3(X))) & (![Y: $i] : (~ra_Px3(X, Y)) | (~cbxcomp(X))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[416])).
% 0.19/0.45 tff(418,plain,
% 0.19/0.45 (![X: $i] : (~(?[Y: $i] : ra_Px3(X, Y) <=> cbxcomp(X))) <=> ![X: $i] : (~(?[Y: $i] : ra_Px3(X, Y) <=> cbxcomp(X)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(419,plain,
% 0.19/0.45 (^[X: $i] : trans(trans(monotonicity(rewrite((~?[Y: $i] : ra_Px3(X, Y)) <=> (~?[Y: $i] : ra_Px3(X, Y))), ((cbxcomp(X) <=> (~?[Y: $i] : ra_Px3(X, Y))) <=> (cbxcomp(X) <=> (~?[Y: $i] : ra_Px3(X, Y))))), rewrite((cbxcomp(X) <=> (~?[Y: $i] : ra_Px3(X, Y))) <=> (~(?[Y: $i] : ra_Px3(X, Y) <=> cbxcomp(X)))), ((cbxcomp(X) <=> (~?[Y: $i] : ra_Px3(X, Y))) <=> (~(?[Y: $i] : ra_Px3(X, Y) <=> cbxcomp(X))))), rewrite((~(?[Y: $i] : ra_Px3(X, Y) <=> cbxcomp(X))) <=> (~(?[Y: $i] : ra_Px3(X, Y) <=> cbxcomp(X)))), ((cbxcomp(X) <=> (~?[Y: $i] : ra_Px3(X, Y))) <=> (~(?[Y: $i] : ra_Px3(X, Y) <=> cbxcomp(X)))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(420,plain,
% 0.19/0.45 (![X: $i] : (cbxcomp(X) <=> (~?[Y: $i] : ra_Px3(X, Y))) <=> ![X: $i] : (~(?[Y: $i] : ra_Px3(X, Y) <=> cbxcomp(X)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[419])).
% 0.19/0.45 tff(421,axiom,(![X: $i] : (cbxcomp(X) <=> (~?[Y: $i] : ra_Px3(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_8')).
% 0.19/0.45 tff(422,plain,
% 0.19/0.45 (![X: $i] : (~(?[Y: $i] : ra_Px3(X, Y) <=> cbxcomp(X)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[421, 420])).
% 0.19/0.45 tff(423,plain,
% 0.19/0.45 (![X: $i] : (~(?[Y: $i] : ra_Px3(X, Y) <=> cbxcomp(X)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[422, 418])).
% 0.19/0.45 tff(424,plain,(
% 0.19/0.45 ![X: $i] : ((ra_Px3(X, tptp_fun_Y_3(X)) | cbxcomp(X)) & (![Y: $i] : (~ra_Px3(X, Y)) | (~cbxcomp(X))))),
% 0.19/0.45 inference(skolemize,[status(sab)],[423])).
% 0.19/0.45 tff(425,plain,
% 0.19/0.45 (![X: $i] : ((cbxcomp(X) | ra_Px3(X, tptp_fun_Y_3(X))) & (![Y: $i] : (~ra_Px3(X, Y)) | (~cbxcomp(X))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[424, 417])).
% 0.19/0.45 tff(426,plain,
% 0.19/0.45 (![X: $i] : (~((~(cbxcomp(X) | ra_Px3(X, tptp_fun_Y_3(X)))) | (~(![Y: $i] : (~ra_Px3(X, Y)) | (~cbxcomp(X))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[425, 415])).
% 0.19/0.45 tff(427,plain,
% 0.19/0.45 (![X: $i] : (~((~(cbxcomp(X) | ra_Px3(X, tptp_fun_Y_3(X)))) | (~(![Y: $i] : (~ra_Px3(X, Y)) | (~cbxcomp(X))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[426, 413])).
% 0.19/0.45 tff(428,plain,
% 0.19/0.45 (![X: $i] : (~((~(cbxcomp(X) | ra_Px3(X, tptp_fun_Y_3(X)))) | (~((~cbxcomp(X)) | ![Y: $i] : (~ra_Px3(X, Y))))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[427, 408])).
% 0.19/0.45 tff(429,plain,
% 0.19/0.45 ((~![X: $i] : (~((~(cbxcomp(X) | ra_Px3(X, tptp_fun_Y_3(X)))) | (~((~cbxcomp(X)) | ![Y: $i] : (~ra_Px3(X, Y))))))) | (~((~(cbxcomp(i2003_11_14_17_20_50869) | ra_Px3(i2003_11_14_17_20_50869, tptp_fun_Y_3(i2003_11_14_17_20_50869)))) | (~((~cbxcomp(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px3(i2003_11_14_17_20_50869, Y))))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(430,plain,
% 0.19/0.45 (~((~(cbxcomp(i2003_11_14_17_20_50869) | ra_Px3(i2003_11_14_17_20_50869, tptp_fun_Y_3(i2003_11_14_17_20_50869)))) | (~((~cbxcomp(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px3(i2003_11_14_17_20_50869, Y)))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[429, 428])).
% 0.19/0.45 tff(431,plain,
% 0.19/0.45 (((~(cbxcomp(i2003_11_14_17_20_50869) | ra_Px3(i2003_11_14_17_20_50869, tptp_fun_Y_3(i2003_11_14_17_20_50869)))) | (~((~cbxcomp(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px3(i2003_11_14_17_20_50869, Y))))) | ((~cbxcomp(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px3(i2003_11_14_17_20_50869, Y)))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(432,plain,
% 0.19/0.45 ((~cbxcomp(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px3(i2003_11_14_17_20_50869, Y))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[431, 430])).
% 0.19/0.45 tff(433,plain,
% 0.19/0.45 ((~((~cbxcomp(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px3(i2003_11_14_17_20_50869, Y)))) | (~cbxcomp(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px3(i2003_11_14_17_20_50869, Y))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(434,plain,
% 0.19/0.45 ((~cbxcomp(i2003_11_14_17_20_50869)) | ![Y: $i] : (~ra_Px3(i2003_11_14_17_20_50869, Y))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[433, 432])).
% 0.19/0.45 tff(435,plain,
% 0.19/0.45 (~cbxcomp(i2003_11_14_17_20_50869)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[434, 406])).
% 0.19/0.45 tff(436,plain,
% 0.19/0.45 (((~cbxcomp(i2003_11_14_17_20_50869)) | (~ccxcomp(i2003_11_14_17_20_50869))) | cbxcomp(i2003_11_14_17_20_50869)),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(437,plain,
% 0.19/0.45 ((~cbxcomp(i2003_11_14_17_20_50869)) | (~ccxcomp(i2003_11_14_17_20_50869))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[436, 435])).
% 0.19/0.45 tff(438,plain,
% 0.19/0.45 ((((~cbxcomp(i2003_11_14_17_20_50869)) | (~ccxcomp(i2003_11_14_17_20_50869))) <=> ca_Cx1(i2003_11_14_17_20_50869)) | (~ca_Cx1(i2003_11_14_17_20_50869))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[345, 437])).
% 0.19/0.45 tff(439,plain,
% 0.19/0.45 (~ca_Cx1(i2003_11_14_17_20_50869)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[438, 131])).
% 0.19/0.45 tff(440,plain,
% 0.19/0.45 (~ca(i2003_11_14_17_20_50869)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[343, 439])).
% 0.19/0.45 tff(441,plain,
% 0.19/0.45 ((~ca(i2003_11_14_17_20_50869)) | (~cc(i2003_11_14_17_20_50869))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[328, 440])).
% 0.19/0.45 tff(442,plain,
% 0.19/0.45 (~ca_Cx7xcomp(i2003_11_14_17_20_50869)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[322, 441])).
% 0.19/0.45 tff(443,plain,
% 0.19/0.45 (ra_Px7(i2003_11_14_17_20_50869, tptp_fun_Y_11(i2003_11_14_17_20_50869))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[305, 442])).
% 0.19/0.45 tff(444,plain,
% 0.19/0.45 (~![Y0: $i] : (~ra_Px7(i2003_11_14_17_20_50869, Y0))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[274, 443])).
% 0.19/0.45 tff(445,plain,
% 0.19/0.45 (ca_Cx7(i2003_11_14_17_20_50869)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[268, 444, 119])).
% 0.19/0.45 tff(446,plain,
% 0.19/0.45 (((~ca(i2003_11_14_17_20_50869)) | (~cb(i2003_11_14_17_20_50869))) | ca(i2003_11_14_17_20_50869)),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(447,plain,
% 0.19/0.45 ((~ca(i2003_11_14_17_20_50869)) | (~cb(i2003_11_14_17_20_50869))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[446, 440])).
% 0.19/0.45 tff(448,plain,
% 0.19/0.45 (~ca_Cx6xcomp(i2003_11_14_17_20_50869)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[208, 447])).
% 0.19/0.45 tff(449,plain,
% 0.19/0.45 (![Y0: $i] : (~ra_Px6(i2003_11_14_17_20_50869, Y0))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[228, 448])).
% 0.19/0.45 tff(450,plain,
% 0.19/0.45 (~ra_Px6(i2003_11_14_17_20_50869, tptp_fun_Y_8(i2003_11_14_17_20_50869))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[234, 449])).
% 0.19/0.46 tff(451,plain,
% 0.19/0.46 (ca_Cx6(i2003_11_14_17_20_50869)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[263, 450])).
% 0.19/0.46 tff(452,plain,
% 0.19/0.46 ((~((~ca_Cx6(i2003_11_14_17_20_50869)) | (~ca_Cx7(i2003_11_14_17_20_50869)) | (~ca_Cx8(i2003_11_14_17_20_50869)))) | (~ca_Cx8(i2003_11_14_17_20_50869))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[265, 451, 445])).
% 0.19/0.46 tff(453,plain,
% 0.19/0.46 (~ca_Cx8(i2003_11_14_17_20_50869)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[452, 102])).
% 0.19/0.46 tff(454,plain,
% 0.19/0.46 (ra_Px8(i2003_11_14_17_20_50869, tptp_fun_Y_12(i2003_11_14_17_20_50869))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[191, 453])).
% 0.19/0.46 tff(455,plain,
% 0.19/0.46 (~![Y0: $i] : (~ra_Px8(i2003_11_14_17_20_50869, Y0))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[162, 454])).
% 0.19/0.46 tff(456,plain,
% 0.19/0.46 (ca_Cx8xcomp(i2003_11_14_17_20_50869)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[156, 455])).
% 0.19/0.46 tff(457,plain,
% 0.19/0.46 (~((~cb(i2003_11_14_17_20_50869)) | (~cc(i2003_11_14_17_20_50869)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[135, 456, 29])).
% 0.19/0.46 tff(458,plain,
% 0.19/0.46 (((~cb(i2003_11_14_17_20_50869)) | (~cc(i2003_11_14_17_20_50869))) | cc(i2003_11_14_17_20_50869)),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(459,plain,
% 0.19/0.46 (cc(i2003_11_14_17_20_50869)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[458, 457])).
% 0.19/0.46 tff(460,plain,
% 0.19/0.46 (ra_Px2(i2003_11_14_17_20_50869, tptp_fun_Y0_4(i2003_11_14_17_20_50869))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[326, 459, 17])).
% 0.19/0.46 tff(461,plain,
% 0.19/0.46 (^[X: $i] : refl((ccxcomp(X) | (~cb(X))) <=> (ccxcomp(X) | (~cb(X))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(462,plain,
% 0.19/0.46 (![X: $i] : (ccxcomp(X) | (~cb(X))) <=> ![X: $i] : (ccxcomp(X) | (~cb(X)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[461])).
% 0.19/0.46 tff(463,plain,
% 0.19/0.46 (![X: $i] : (ccxcomp(X) | (~cb(X))) <=> ![X: $i] : (ccxcomp(X) | (~cb(X)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(464,plain,
% 0.19/0.46 (^[X: $i] : rewrite((cb(X) => ccxcomp(X)) <=> (ccxcomp(X) | (~cb(X))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(465,plain,
% 0.19/0.46 (![X: $i] : (cb(X) => ccxcomp(X)) <=> ![X: $i] : (ccxcomp(X) | (~cb(X)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[464])).
% 0.19/0.46 tff(466,axiom,(![X: $i] : (cb(X) => ccxcomp(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_7')).
% 0.19/0.46 tff(467,plain,
% 0.19/0.46 (![X: $i] : (ccxcomp(X) | (~cb(X)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[466, 465])).
% 0.19/0.46 tff(468,plain,
% 0.19/0.46 (![X: $i] : (ccxcomp(X) | (~cb(X)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[467, 463])).
% 0.19/0.46 tff(469,plain,(
% 0.19/0.46 ![X: $i] : (ccxcomp(X) | (~cb(X)))),
% 0.19/0.46 inference(skolemize,[status(sab)],[468])).
% 0.19/0.46 tff(470,plain,
% 0.19/0.46 (![X: $i] : (ccxcomp(X) | (~cb(X)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[469, 462])).
% 0.19/0.46 tff(471,plain,
% 0.19/0.46 (((~![X: $i] : (ccxcomp(X) | (~cb(X)))) | (ccxcomp(i2003_11_14_17_20_50869) | (~cb(i2003_11_14_17_20_50869)))) <=> ((~![X: $i] : (ccxcomp(X) | (~cb(X)))) | ccxcomp(i2003_11_14_17_20_50869) | (~cb(i2003_11_14_17_20_50869)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(472,plain,
% 0.19/0.46 ((~![X: $i] : (ccxcomp(X) | (~cb(X)))) | (ccxcomp(i2003_11_14_17_20_50869) | (~cb(i2003_11_14_17_20_50869)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(473,plain,
% 0.19/0.46 ((~![X: $i] : (ccxcomp(X) | (~cb(X)))) | ccxcomp(i2003_11_14_17_20_50869) | (~cb(i2003_11_14_17_20_50869))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[472, 471])).
% 0.19/0.46 tff(474,plain,
% 0.19/0.46 (ccxcomp(i2003_11_14_17_20_50869)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[473, 470, 380])).
% 0.19/0.46 tff(475,plain,
% 0.19/0.46 (![Y: $i] : (~ra_Px2(i2003_11_14_17_20_50869, Y))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[376, 474])).
% 0.19/0.46 tff(476,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[378, 475, 460])).
% 0.19/0.46 % SZS output end Proof
% 0.19/0.46 % E exiting
%------------------------------------------------------------------------------