%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS107+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:13:24 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : KRS107+1 : TPTP v9.0.0. Released v3.1.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 19:11:24 EDT 2025
% 0.20/0.34 % CPUTime :
% 0.20/0.40 % SZS status Unsatisfiable
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 tff(ra_Px1_type, type, (
% 0.20/0.40 ra_Px1: ( $i * $i ) > $o)).
% 0.20/0.40 tff(i2003_11_14_17_21_01226_type, type, (
% 0.20/0.40 i2003_11_14_17_21_01226: $i)).
% 0.20/0.40 tff(ca_Cx1xcomp_type, type, (
% 0.20/0.40 ca_Cx1xcomp: $i > $o)).
% 0.20/0.40 tff(tptp_fun_Y_4_type, type, (
% 0.20/0.40 tptp_fun_Y_4: $i > $i)).
% 0.20/0.40 tff(rrx3_type, type, (
% 0.20/0.40 rrx3: ( $i * $i ) > $o)).
% 0.20/0.40 tff(ca_Ax2_type, type, (
% 0.20/0.40 ca_Ax2: $i > $o)).
% 0.20/0.40 tff(tptp_fun_Y_0_type, type, (
% 0.20/0.40 tptp_fun_Y_0: $i > $i)).
% 0.20/0.40 tff(cc2_type, type, (
% 0.20/0.40 cc2: $i > $o)).
% 0.20/0.40 tff(cc1_type, type, (
% 0.20/0.40 cc1: $i > $o)).
% 0.20/0.40 tff(tptp_fun_Y_1_type, type, (
% 0.20/0.40 tptp_fun_Y_1: $i > $i)).
% 0.20/0.40 tff(rrx_type, type, (
% 0.20/0.40 rrx: ( $i * $i ) > $o)).
% 0.20/0.40 tff(rrx4_type, type, (
% 0.20/0.40 rrx4: ( $i * $i ) > $o)).
% 0.20/0.40 tff(ca_Cx1_type, type, (
% 0.20/0.40 ca_Cx1: $i > $o)).
% 0.20/0.40 tff(cUnsatisfiable_type, type, (
% 0.20/0.40 cUnsatisfiable: $i > $o)).
% 0.20/0.40 tff(tptp_fun_Y_3_type, type, (
% 0.20/0.40 tptp_fun_Y_3: $i > $i)).
% 0.20/0.40 tff(tptp_fun_Y0_2_type, type, (
% 0.20/0.40 tptp_fun_Y0_2: $i > $i)).
% 0.20/0.40 tff(1,plain,
% 0.20/0.40 (^[X: $i] : refl((~((~(ca_Cx1xcomp(X) | ra_Px1(X, tptp_fun_Y_4(X)))) | (~((~ca_Cx1xcomp(X)) | ![Y: $i] : (~ra_Px1(X, Y)))))) <=> (~((~(ca_Cx1xcomp(X) | ra_Px1(X, tptp_fun_Y_4(X)))) | (~((~ca_Cx1xcomp(X)) | ![Y: $i] : (~ra_Px1(X, Y)))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(2,plain,
% 0.20/0.40 (![X: $i] : (~((~(ca_Cx1xcomp(X) | ra_Px1(X, tptp_fun_Y_4(X)))) | (~((~ca_Cx1xcomp(X)) | ![Y: $i] : (~ra_Px1(X, Y)))))) <=> ![X: $i] : (~((~(ca_Cx1xcomp(X) | ra_Px1(X, tptp_fun_Y_4(X)))) | (~((~ca_Cx1xcomp(X)) | ![Y: $i] : (~ra_Px1(X, Y))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.40 tff(3,plain,
% 0.20/0.40 (^[X: $i] : rewrite((~((~(ca_Cx1xcomp(X) | ra_Px1(X, tptp_fun_Y_4(X)))) | (~((~ca_Cx1xcomp(X)) | ![Y: $i] : (~ra_Px1(X, Y)))))) <=> (~((~(ca_Cx1xcomp(X) | ra_Px1(X, tptp_fun_Y_4(X)))) | (~((~ca_Cx1xcomp(X)) | ![Y: $i] : (~ra_Px1(X, Y)))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(4,plain,
% 0.20/0.40 (![X: $i] : (~((~(ca_Cx1xcomp(X) | ra_Px1(X, tptp_fun_Y_4(X)))) | (~((~ca_Cx1xcomp(X)) | ![Y: $i] : (~ra_Px1(X, Y)))))) <=> ![X: $i] : (~((~(ca_Cx1xcomp(X) | ra_Px1(X, tptp_fun_Y_4(X)))) | (~((~ca_Cx1xcomp(X)) | ![Y: $i] : (~ra_Px1(X, Y))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.40 tff(5,plain,
% 0.20/0.40 (![X: $i] : (~((~(ca_Cx1xcomp(X) | ra_Px1(X, tptp_fun_Y_4(X)))) | (~((~ca_Cx1xcomp(X)) | ![Y: $i] : (~ra_Px1(X, Y)))))) <=> ![X: $i] : (~((~(ca_Cx1xcomp(X) | ra_Px1(X, tptp_fun_Y_4(X)))) | (~((~ca_Cx1xcomp(X)) | ![Y: $i] : (~ra_Px1(X, Y))))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[4, 2])).
% 0.20/0.40 tff(6,plain,
% 0.20/0.40 (^[X: $i] : trans(monotonicity(rewrite(((~ca_Cx1xcomp(X)) | ![Y: $i] : (~ra_Px1(X, Y))) <=> ((~ca_Cx1xcomp(X)) | ![Y: $i] : (~ra_Px1(X, Y)))), (((ca_Cx1xcomp(X) | ra_Px1(X, tptp_fun_Y_4(X))) & ((~ca_Cx1xcomp(X)) | ![Y: $i] : (~ra_Px1(X, Y)))) <=> ((ca_Cx1xcomp(X) | ra_Px1(X, tptp_fun_Y_4(X))) & ((~ca_Cx1xcomp(X)) | ![Y: $i] : (~ra_Px1(X, Y)))))), rewrite(((ca_Cx1xcomp(X) | ra_Px1(X, tptp_fun_Y_4(X))) & ((~ca_Cx1xcomp(X)) | ![Y: $i] : (~ra_Px1(X, Y)))) <=> (~((~(ca_Cx1xcomp(X) | ra_Px1(X, tptp_fun_Y_4(X)))) | (~((~ca_Cx1xcomp(X)) | ![Y: $i] : (~ra_Px1(X, Y))))))), (((ca_Cx1xcomp(X) | ra_Px1(X, tptp_fun_Y_4(X))) & ((~ca_Cx1xcomp(X)) | ![Y: $i] : (~ra_Px1(X, Y)))) <=> (~((~(ca_Cx1xcomp(X) | ra_Px1(X, tptp_fun_Y_4(X)))) | (~((~ca_Cx1xcomp(X)) | ![Y: $i] : (~ra_Px1(X, Y))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(7,plain,
% 0.20/0.40 (![X: $i] : ((ca_Cx1xcomp(X) | ra_Px1(X, tptp_fun_Y_4(X))) & ((~ca_Cx1xcomp(X)) | ![Y: $i] : (~ra_Px1(X, Y)))) <=> ![X: $i] : (~((~(ca_Cx1xcomp(X) | ra_Px1(X, tptp_fun_Y_4(X)))) | (~((~ca_Cx1xcomp(X)) | ![Y: $i] : (~ra_Px1(X, Y))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[6])).
% 0.20/0.40 tff(8,plain,
% 0.20/0.40 (^[X: $i] : rewrite(((ra_Px1(X, tptp_fun_Y_4(X)) | ca_Cx1xcomp(X)) & (![Y: $i] : (~ra_Px1(X, Y)) | (~ca_Cx1xcomp(X)))) <=> ((ca_Cx1xcomp(X) | ra_Px1(X, tptp_fun_Y_4(X))) & ((~ca_Cx1xcomp(X)) | ![Y: $i] : (~ra_Px1(X, Y)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(9,plain,
% 0.20/0.40 (![X: $i] : ((ra_Px1(X, tptp_fun_Y_4(X)) | ca_Cx1xcomp(X)) & (![Y: $i] : (~ra_Px1(X, Y)) | (~ca_Cx1xcomp(X)))) <=> ![X: $i] : ((ca_Cx1xcomp(X) | ra_Px1(X, tptp_fun_Y_4(X))) & ((~ca_Cx1xcomp(X)) | ![Y: $i] : (~ra_Px1(X, Y))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[8])).
% 0.20/0.40 tff(10,plain,
% 0.20/0.40 (![X: $i] : (~(?[Y: $i] : ra_Px1(X, Y) <=> ca_Cx1xcomp(X))) <=> ![X: $i] : (~(?[Y: $i] : ra_Px1(X, Y) <=> ca_Cx1xcomp(X)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(11,plain,
% 0.20/0.40 (^[X: $i] : trans(trans(monotonicity(rewrite((~?[Y: $i] : ra_Px1(X, Y)) <=> (~?[Y: $i] : ra_Px1(X, Y))), ((ca_Cx1xcomp(X) <=> (~?[Y: $i] : ra_Px1(X, Y))) <=> (ca_Cx1xcomp(X) <=> (~?[Y: $i] : ra_Px1(X, Y))))), rewrite((ca_Cx1xcomp(X) <=> (~?[Y: $i] : ra_Px1(X, Y))) <=> (~(?[Y: $i] : ra_Px1(X, Y) <=> ca_Cx1xcomp(X)))), ((ca_Cx1xcomp(X) <=> (~?[Y: $i] : ra_Px1(X, Y))) <=> (~(?[Y: $i] : ra_Px1(X, Y) <=> ca_Cx1xcomp(X))))), rewrite((~(?[Y: $i] : ra_Px1(X, Y) <=> ca_Cx1xcomp(X))) <=> (~(?[Y: $i] : ra_Px1(X, Y) <=> ca_Cx1xcomp(X)))), ((ca_Cx1xcomp(X) <=> (~?[Y: $i] : ra_Px1(X, Y))) <=> (~(?[Y: $i] : ra_Px1(X, Y) <=> ca_Cx1xcomp(X)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(12,plain,
% 0.20/0.40 (![X: $i] : (ca_Cx1xcomp(X) <=> (~?[Y: $i] : ra_Px1(X, Y))) <=> ![X: $i] : (~(?[Y: $i] : ra_Px1(X, Y) <=> ca_Cx1xcomp(X)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[11])).
% 0.20/0.40 tff(13,axiom,(![X: $i] : (ca_Cx1xcomp(X) <=> (~?[Y: $i] : ra_Px1(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_6')).
% 0.20/0.40 tff(14,plain,
% 0.20/0.40 (![X: $i] : (~(?[Y: $i] : ra_Px1(X, Y) <=> ca_Cx1xcomp(X)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.20/0.40 tff(15,plain,
% 0.20/0.40 (![X: $i] : (~(?[Y: $i] : ra_Px1(X, Y) <=> ca_Cx1xcomp(X)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.20/0.40 tff(16,plain,(
% 0.20/0.40 ![X: $i] : ((ra_Px1(X, tptp_fun_Y_4(X)) | ca_Cx1xcomp(X)) & (![Y: $i] : (~ra_Px1(X, Y)) | (~ca_Cx1xcomp(X))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[15])).
% 0.20/0.40 tff(17,plain,
% 0.20/0.40 (![X: $i] : ((ca_Cx1xcomp(X) | ra_Px1(X, tptp_fun_Y_4(X))) & ((~ca_Cx1xcomp(X)) | ![Y: $i] : (~ra_Px1(X, Y))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[16, 9])).
% 0.20/0.40 tff(18,plain,
% 0.20/0.40 (![X: $i] : (~((~(ca_Cx1xcomp(X) | ra_Px1(X, tptp_fun_Y_4(X)))) | (~((~ca_Cx1xcomp(X)) | ![Y: $i] : (~ra_Px1(X, Y))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[17, 7])).
% 0.20/0.40 tff(19,plain,
% 0.20/0.40 (![X: $i] : (~((~(ca_Cx1xcomp(X) | ra_Px1(X, tptp_fun_Y_4(X)))) | (~((~ca_Cx1xcomp(X)) | ![Y: $i] : (~ra_Px1(X, Y))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[18, 5])).
% 0.20/0.40 tff(20,plain,
% 0.20/0.40 ((~![X: $i] : (~((~(ca_Cx1xcomp(X) | ra_Px1(X, tptp_fun_Y_4(X)))) | (~((~ca_Cx1xcomp(X)) | ![Y: $i] : (~ra_Px1(X, Y))))))) | (~((~(ca_Cx1xcomp(i2003_11_14_17_21_01226) | ra_Px1(i2003_11_14_17_21_01226, tptp_fun_Y_4(i2003_11_14_17_21_01226)))) | (~((~ca_Cx1xcomp(i2003_11_14_17_21_01226)) | ![Y: $i] : (~ra_Px1(i2003_11_14_17_21_01226, Y))))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(21,plain,
% 0.20/0.40 (~((~(ca_Cx1xcomp(i2003_11_14_17_21_01226) | ra_Px1(i2003_11_14_17_21_01226, tptp_fun_Y_4(i2003_11_14_17_21_01226)))) | (~((~ca_Cx1xcomp(i2003_11_14_17_21_01226)) | ![Y: $i] : (~ra_Px1(i2003_11_14_17_21_01226, Y)))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.20/0.40 tff(22,plain,
% 0.20/0.40 (((~(ca_Cx1xcomp(i2003_11_14_17_21_01226) | ra_Px1(i2003_11_14_17_21_01226, tptp_fun_Y_4(i2003_11_14_17_21_01226)))) | (~((~ca_Cx1xcomp(i2003_11_14_17_21_01226)) | ![Y: $i] : (~ra_Px1(i2003_11_14_17_21_01226, Y))))) | ((~ca_Cx1xcomp(i2003_11_14_17_21_01226)) | ![Y: $i] : (~ra_Px1(i2003_11_14_17_21_01226, Y)))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(23,plain,
% 0.20/0.40 ((~ca_Cx1xcomp(i2003_11_14_17_21_01226)) | ![Y: $i] : (~ra_Px1(i2003_11_14_17_21_01226, Y))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.20/0.40 tff(24,assumption,(![Y: $i] : ((~ca_Ax2(Y)) | (~rrx3(i2003_11_14_17_21_01226, Y)))), introduced(assumption)).
% 0.20/0.40 tff(25,plain,
% 0.20/0.40 (^[X: $i] : refl((~(((~cc2(X)) | (~cc1(X))) <=> ca_Ax2(X))) <=> (~(((~cc2(X)) | (~cc1(X))) <=> ca_Ax2(X))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(26,plain,
% 0.20/0.40 (![X: $i] : (~(((~cc2(X)) | (~cc1(X))) <=> ca_Ax2(X))) <=> ![X: $i] : (~(((~cc2(X)) | (~cc1(X))) <=> ca_Ax2(X)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[25])).
% 0.20/0.40 tff(27,plain,
% 0.20/0.40 (^[X: $i] : trans(trans(monotonicity(rewrite((cc2(X) & cc1(X)) <=> (~((~cc2(X)) | (~cc1(X))))), ((ca_Ax2(X) <=> (cc2(X) & cc1(X))) <=> (ca_Ax2(X) <=> (~((~cc2(X)) | (~cc1(X))))))), rewrite((ca_Ax2(X) <=> (~((~cc2(X)) | (~cc1(X))))) <=> (~(((~cc2(X)) | (~cc1(X))) <=> ca_Ax2(X)))), ((ca_Ax2(X) <=> (cc2(X) & cc1(X))) <=> (~(((~cc2(X)) | (~cc1(X))) <=> ca_Ax2(X))))), rewrite((~(((~cc2(X)) | (~cc1(X))) <=> ca_Ax2(X))) <=> (~(((~cc2(X)) | (~cc1(X))) <=> ca_Ax2(X)))), ((ca_Ax2(X) <=> (cc2(X) & cc1(X))) <=> (~(((~cc2(X)) | (~cc1(X))) <=> ca_Ax2(X)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(28,plain,
% 0.20/0.40 (![X: $i] : (ca_Ax2(X) <=> (cc2(X) & cc1(X))) <=> ![X: $i] : (~(((~cc2(X)) | (~cc1(X))) <=> ca_Ax2(X)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[27])).
% 0.20/0.40 tff(29,plain,
% 0.20/0.40 (![X: $i] : (ca_Ax2(X) <=> (cc2(X) & cc1(X))) <=> ![X: $i] : (ca_Ax2(X) <=> (cc2(X) & cc1(X)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(30,axiom,(![X: $i] : (ca_Ax2(X) <=> (cc2(X) & cc1(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_3')).
% 0.20/0.40 tff(31,plain,
% 0.20/0.40 (![X: $i] : (ca_Ax2(X) <=> (cc2(X) & cc1(X)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.20/0.40 tff(32,plain,(
% 0.20/0.40 ![X: $i] : (ca_Ax2(X) <=> (cc2(X) & cc1(X)))),
% 0.20/0.40 inference(skolemize,[status(sab)],[31])).
% 0.20/0.40 tff(33,plain,
% 0.20/0.40 (![X: $i] : (~(((~cc2(X)) | (~cc1(X))) <=> ca_Ax2(X)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.20/0.40 tff(34,plain,
% 0.20/0.40 (![X: $i] : (~(((~cc2(X)) | (~cc1(X))) <=> ca_Ax2(X)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.20/0.40 tff(35,plain,
% 0.20/0.40 (((~![X: $i] : (~(((~cc2(X)) | (~cc1(X))) <=> ca_Ax2(X)))) | (~(((~cc1(tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~cc2(tptp_fun_Y_0(i2003_11_14_17_21_01226)))) <=> ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_01226))))) <=> ((~![X: $i] : (~(((~cc2(X)) | (~cc1(X))) <=> ca_Ax2(X)))) | (~(((~cc1(tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~cc2(tptp_fun_Y_0(i2003_11_14_17_21_01226)))) <=> ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_01226)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(36,plain,
% 0.20/0.40 ((~(((~cc1(tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~cc2(tptp_fun_Y_0(i2003_11_14_17_21_01226)))) <=> ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_01226)))) <=> (~(((~cc1(tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~cc2(tptp_fun_Y_0(i2003_11_14_17_21_01226)))) <=> ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_01226))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(37,plain,
% 0.20/0.40 ((((~cc2(tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~cc1(tptp_fun_Y_0(i2003_11_14_17_21_01226)))) <=> ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_01226))) <=> (((~cc1(tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~cc2(tptp_fun_Y_0(i2003_11_14_17_21_01226)))) <=> ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_01226)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(38,plain,
% 0.20/0.40 ((~(((~cc2(tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~cc1(tptp_fun_Y_0(i2003_11_14_17_21_01226)))) <=> ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_01226)))) <=> (~(((~cc1(tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~cc2(tptp_fun_Y_0(i2003_11_14_17_21_01226)))) <=> ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_01226))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[37])).
% 0.20/0.40 tff(39,plain,
% 0.20/0.40 ((~(((~cc2(tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~cc1(tptp_fun_Y_0(i2003_11_14_17_21_01226)))) <=> ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_01226)))) <=> (~(((~cc1(tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~cc2(tptp_fun_Y_0(i2003_11_14_17_21_01226)))) <=> ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_01226))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[38, 36])).
% 0.20/0.40 tff(40,plain,
% 0.20/0.40 (((~![X: $i] : (~(((~cc2(X)) | (~cc1(X))) <=> ca_Ax2(X)))) | (~(((~cc2(tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~cc1(tptp_fun_Y_0(i2003_11_14_17_21_01226)))) <=> ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_01226))))) <=> ((~![X: $i] : (~(((~cc2(X)) | (~cc1(X))) <=> ca_Ax2(X)))) | (~(((~cc1(tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~cc2(tptp_fun_Y_0(i2003_11_14_17_21_01226)))) <=> ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_01226)))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[39])).
% 0.20/0.40 tff(41,plain,
% 0.20/0.40 (((~![X: $i] : (~(((~cc2(X)) | (~cc1(X))) <=> ca_Ax2(X)))) | (~(((~cc2(tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~cc1(tptp_fun_Y_0(i2003_11_14_17_21_01226)))) <=> ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_01226))))) <=> ((~![X: $i] : (~(((~cc2(X)) | (~cc1(X))) <=> ca_Ax2(X)))) | (~(((~cc1(tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~cc2(tptp_fun_Y_0(i2003_11_14_17_21_01226)))) <=> ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_01226)))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[40, 35])).
% 0.20/0.40 tff(42,plain,
% 0.20/0.40 ((~![X: $i] : (~(((~cc2(X)) | (~cc1(X))) <=> ca_Ax2(X)))) | (~(((~cc2(tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~cc1(tptp_fun_Y_0(i2003_11_14_17_21_01226)))) <=> ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_01226))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(43,plain,
% 0.20/0.40 ((~![X: $i] : (~(((~cc2(X)) | (~cc1(X))) <=> ca_Ax2(X)))) | (~(((~cc1(tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~cc2(tptp_fun_Y_0(i2003_11_14_17_21_01226)))) <=> ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_01226))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.20/0.40 tff(44,plain,
% 0.20/0.40 (~(((~cc1(tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~cc2(tptp_fun_Y_0(i2003_11_14_17_21_01226)))) <=> ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_01226)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[43, 34])).
% 0.20/0.40 tff(45,plain,
% 0.20/0.40 (^[X: $i] : rewrite((~((~((~cUnsatisfiable(X)) | (~((~ca_Cx1(X)) | (~cc2(tptp_fun_Y_1(X))) | (~rrx4(X, tptp_fun_Y_1(X))) | (~rrx3(X, tptp_fun_Y_0(X))) | (~cc1(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~rrx4(X, Y)) | (~cc2(Y))) | (~ca_Cx1(X)) | ![Y: $i] : ((~rrx3(X, Y)) | (~cc1(Y))))))) <=> (~((~((~cUnsatisfiable(X)) | (~((~ca_Cx1(X)) | (~cc2(tptp_fun_Y_1(X))) | (~rrx4(X, tptp_fun_Y_1(X))) | (~rrx3(X, tptp_fun_Y_0(X))) | (~cc1(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | (~ca_Cx1(X)) | ![Y: $i] : ((~rrx4(X, Y)) | (~cc2(Y))) | ![Y: $i] : ((~rrx3(X, Y)) | (~cc1(Y))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(46,plain,
% 0.20/0.40 (![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~ca_Cx1(X)) | (~cc2(tptp_fun_Y_1(X))) | (~rrx4(X, tptp_fun_Y_1(X))) | (~rrx3(X, tptp_fun_Y_0(X))) | (~cc1(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~rrx4(X, Y)) | (~cc2(Y))) | (~ca_Cx1(X)) | ![Y: $i] : ((~rrx3(X, Y)) | (~cc1(Y))))))) <=> ![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~ca_Cx1(X)) | (~cc2(tptp_fun_Y_1(X))) | (~rrx4(X, tptp_fun_Y_1(X))) | (~rrx3(X, tptp_fun_Y_0(X))) | (~cc1(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | (~ca_Cx1(X)) | ![Y: $i] : ((~rrx4(X, Y)) | (~cc2(Y))) | ![Y: $i] : ((~rrx3(X, Y)) | (~cc1(Y)))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[45])).
% 0.20/0.40 tff(47,plain,
% 0.20/0.40 (^[X: $i] : refl((~((~((~cUnsatisfiable(X)) | (~((~ca_Cx1(X)) | (~cc2(tptp_fun_Y_1(X))) | (~rrx4(X, tptp_fun_Y_1(X))) | (~rrx3(X, tptp_fun_Y_0(X))) | (~cc1(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~rrx4(X, Y)) | (~cc2(Y))) | (~ca_Cx1(X)) | ![Y: $i] : ((~rrx3(X, Y)) | (~cc1(Y))))))) <=> (~((~((~cUnsatisfiable(X)) | (~((~ca_Cx1(X)) | (~cc2(tptp_fun_Y_1(X))) | (~rrx4(X, tptp_fun_Y_1(X))) | (~rrx3(X, tptp_fun_Y_0(X))) | (~cc1(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~rrx4(X, Y)) | (~cc2(Y))) | (~ca_Cx1(X)) | ![Y: $i] : ((~rrx3(X, Y)) | (~cc1(Y))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(48,plain,
% 0.20/0.40 (![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~ca_Cx1(X)) | (~cc2(tptp_fun_Y_1(X))) | (~rrx4(X, tptp_fun_Y_1(X))) | (~rrx3(X, tptp_fun_Y_0(X))) | (~cc1(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~rrx4(X, Y)) | (~cc2(Y))) | (~ca_Cx1(X)) | ![Y: $i] : ((~rrx3(X, Y)) | (~cc1(Y))))))) <=> ![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~ca_Cx1(X)) | (~cc2(tptp_fun_Y_1(X))) | (~rrx4(X, tptp_fun_Y_1(X))) | (~rrx3(X, tptp_fun_Y_0(X))) | (~cc1(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~rrx4(X, Y)) | (~cc2(Y))) | (~ca_Cx1(X)) | ![Y: $i] : ((~rrx3(X, Y)) | (~cc1(Y)))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[47])).
% 0.20/0.40 tff(49,plain,
% 0.20/0.40 (^[X: $i] : rewrite((~((~((~cUnsatisfiable(X)) | (~((~ca_Cx1(X)) | (~cc2(tptp_fun_Y_1(X))) | (~rrx4(X, tptp_fun_Y_1(X))) | (~rrx3(X, tptp_fun_Y_0(X))) | (~cc1(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~rrx4(X, Y)) | (~cc2(Y))) | (~ca_Cx1(X)) | ![Y: $i] : ((~rrx3(X, Y)) | (~cc1(Y))))))) <=> (~((~((~cUnsatisfiable(X)) | (~((~ca_Cx1(X)) | (~cc2(tptp_fun_Y_1(X))) | (~rrx4(X, tptp_fun_Y_1(X))) | (~rrx3(X, tptp_fun_Y_0(X))) | (~cc1(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~rrx4(X, Y)) | (~cc2(Y))) | (~ca_Cx1(X)) | ![Y: $i] : ((~rrx3(X, Y)) | (~cc1(Y))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(50,plain,
% 0.20/0.40 (![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~ca_Cx1(X)) | (~cc2(tptp_fun_Y_1(X))) | (~rrx4(X, tptp_fun_Y_1(X))) | (~rrx3(X, tptp_fun_Y_0(X))) | (~cc1(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~rrx4(X, Y)) | (~cc2(Y))) | (~ca_Cx1(X)) | ![Y: $i] : ((~rrx3(X, Y)) | (~cc1(Y))))))) <=> ![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~ca_Cx1(X)) | (~cc2(tptp_fun_Y_1(X))) | (~rrx4(X, tptp_fun_Y_1(X))) | (~rrx3(X, tptp_fun_Y_0(X))) | (~cc1(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~rrx4(X, Y)) | (~cc2(Y))) | (~ca_Cx1(X)) | ![Y: $i] : ((~rrx3(X, Y)) | (~cc1(Y)))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[49])).
% 0.20/0.40 tff(51,plain,
% 0.20/0.40 (![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~ca_Cx1(X)) | (~cc2(tptp_fun_Y_1(X))) | (~rrx4(X, tptp_fun_Y_1(X))) | (~rrx3(X, tptp_fun_Y_0(X))) | (~cc1(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~rrx4(X, Y)) | (~cc2(Y))) | (~ca_Cx1(X)) | ![Y: $i] : ((~rrx3(X, Y)) | (~cc1(Y))))))) <=> ![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~ca_Cx1(X)) | (~cc2(tptp_fun_Y_1(X))) | (~rrx4(X, tptp_fun_Y_1(X))) | (~rrx3(X, tptp_fun_Y_0(X))) | (~cc1(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~rrx4(X, Y)) | (~cc2(Y))) | (~ca_Cx1(X)) | ![Y: $i] : ((~rrx3(X, Y)) | (~cc1(Y)))))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[50, 48])).
% 0.20/0.40 tff(52,plain,
% 0.20/0.40 (^[X: $i] : trans(monotonicity(rewrite(((~cUnsatisfiable(X)) | (rrx3(X, tptp_fun_Y_0(X)) & cc1(tptp_fun_Y_0(X)) & rrx4(X, tptp_fun_Y_1(X)) & cc2(tptp_fun_Y_1(X)) & ca_Cx1(X))) <=> ((~cUnsatisfiable(X)) | (~((~ca_Cx1(X)) | (~cc2(tptp_fun_Y_1(X))) | (~rrx4(X, tptp_fun_Y_1(X))) | (~rrx3(X, tptp_fun_Y_0(X))) | (~cc1(tptp_fun_Y_0(X))))))), trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(rewrite((rrx3(X, Y) & cc1(Y)) <=> (~((~rrx3(X, Y)) | (~cc1(Y))))), ((~(rrx3(X, Y) & cc1(Y))) <=> (~(~((~rrx3(X, Y)) | (~cc1(Y))))))), rewrite((~(~((~rrx3(X, Y)) | (~cc1(Y))))) <=> ((~rrx3(X, Y)) | (~cc1(Y)))), ((~(rrx3(X, Y) & cc1(Y))) <=> ((~rrx3(X, Y)) | (~cc1(Y)))))), (![Y: $i] : (~(rrx3(X, Y) & cc1(Y))) <=> ![Y: $i] : ((~rrx3(X, Y)) | (~cc1(Y))))), quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(rewrite((rrx4(X, Y) & cc2(Y)) <=> (~((~rrx4(X, Y)) | (~cc2(Y))))), ((~(rrx4(X, Y) & cc2(Y))) <=> (~(~((~rrx4(X, Y)) | (~cc2(Y))))))), rewrite((~(~((~rrx4(X, Y)) | (~cc2(Y))))) <=> ((~rrx4(X, Y)) | (~cc2(Y)))), ((~(rrx4(X, Y) & cc2(Y))) <=> ((~rrx4(X, Y)) | (~cc2(Y)))))), (![Y: $i] : (~(rrx4(X, Y) & cc2(Y))) <=> ![Y: $i] : ((~rrx4(X, Y)) | (~cc2(Y))))), ((cUnsatisfiable(X) | ![Y: $i] : (~(rrx3(X, Y) & cc1(Y))) | ![Y: $i] : (~(rrx4(X, Y) & cc2(Y))) | (~ca_Cx1(X))) <=> (cUnsatisfiable(X) | ![Y: $i] : ((~rrx3(X, Y)) | (~cc1(Y))) | ![Y: $i] : ((~rrx4(X, Y)) | (~cc2(Y))) | (~ca_Cx1(X))))), rewrite((cUnsatisfiable(X) | ![Y: $i] : ((~rrx3(X, Y)) | (~cc1(Y))) | ![Y: $i] : ((~rrx4(X, Y)) | (~cc2(Y))) | (~ca_Cx1(X))) <=> (cUnsatisfiable(X) | ![Y: $i] : ((~rrx4(X, Y)) | (~cc2(Y))) | (~ca_Cx1(X)) | ![Y: $i] : ((~rrx3(X, Y)) | (~cc1(Y))))), ((cUnsatisfiable(X) | ![Y: $i] : (~(rrx3(X, Y) & cc1(Y))) | ![Y: $i] : (~(rrx4(X, Y) & cc2(Y))) | (~ca_Cx1(X))) <=> (cUnsatisfiable(X) | ![Y: $i] : ((~rrx4(X, Y)) | (~cc2(Y))) | (~ca_Cx1(X)) | ![Y: $i] : ((~rrx3(X, Y)) | (~cc1(Y)))))), ((((~cUnsatisfiable(X)) | (rrx3(X, tptp_fun_Y_0(X)) & cc1(tptp_fun_Y_0(X)) & rrx4(X, tptp_fun_Y_1(X)) & cc2(tptp_fun_Y_1(X)) & ca_Cx1(X))) & (cUnsatisfiable(X) | ![Y: $i] : (~(rrx3(X, Y) & cc1(Y))) | ![Y: $i] : (~(rrx4(X, Y) & cc2(Y))) | (~ca_Cx1(X)))) <=> (((~cUnsatisfiable(X)) | (~((~ca_Cx1(X)) | (~cc2(tptp_fun_Y_1(X))) | (~rrx4(X, tptp_fun_Y_1(X))) | (~rrx3(X, tptp_fun_Y_0(X))) | (~cc1(tptp_fun_Y_0(X)))))) & (cUnsatisfiable(X) | ![Y: $i] : ((~rrx4(X, Y)) | (~cc2(Y))) | (~ca_Cx1(X)) | ![Y: $i] : ((~rrx3(X, Y)) | (~cc1(Y))))))), rewrite((((~cUnsatisfiable(X)) | (~((~ca_Cx1(X)) | (~cc2(tptp_fun_Y_1(X))) | (~rrx4(X, tptp_fun_Y_1(X))) | (~rrx3(X, tptp_fun_Y_0(X))) | (~cc1(tptp_fun_Y_0(X)))))) & (cUnsatisfiable(X) | ![Y: $i] : ((~rrx4(X, Y)) | (~cc2(Y))) | (~ca_Cx1(X)) | ![Y: $i] : ((~rrx3(X, Y)) | (~cc1(Y))))) <=> (~((~((~cUnsatisfiable(X)) | (~((~ca_Cx1(X)) | (~cc2(tptp_fun_Y_1(X))) | (~rrx4(X, tptp_fun_Y_1(X))) | (~rrx3(X, tptp_fun_Y_0(X))) | (~cc1(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~rrx4(X, Y)) | (~cc2(Y))) | (~ca_Cx1(X)) | ![Y: $i] : ((~rrx3(X, Y)) | (~cc1(Y)))))))), ((((~cUnsatisfiable(X)) | (rrx3(X, tptp_fun_Y_0(X)) & cc1(tptp_fun_Y_0(X)) & rrx4(X, tptp_fun_Y_1(X)) & cc2(tptp_fun_Y_1(X)) & ca_Cx1(X))) & (cUnsatisfiable(X) | ![Y: $i] : (~(rrx3(X, Y) & cc1(Y))) | ![Y: $i] : (~(rrx4(X, Y) & cc2(Y))) | (~ca_Cx1(X)))) <=> (~((~((~cUnsatisfiable(X)) | (~((~ca_Cx1(X)) | (~cc2(tptp_fun_Y_1(X))) | (~rrx4(X, tptp_fun_Y_1(X))) | (~rrx3(X, tptp_fun_Y_0(X))) | (~cc1(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~rrx4(X, Y)) | (~cc2(Y))) | (~ca_Cx1(X)) | ![Y: $i] : ((~rrx3(X, Y)) | (~cc1(Y)))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(53,plain,
% 0.20/0.41 (![X: $i] : (((~cUnsatisfiable(X)) | (rrx3(X, tptp_fun_Y_0(X)) & cc1(tptp_fun_Y_0(X)) & rrx4(X, tptp_fun_Y_1(X)) & cc2(tptp_fun_Y_1(X)) & ca_Cx1(X))) & (cUnsatisfiable(X) | ![Y: $i] : (~(rrx3(X, Y) & cc1(Y))) | ![Y: $i] : (~(rrx4(X, Y) & cc2(Y))) | (~ca_Cx1(X)))) <=> ![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~ca_Cx1(X)) | (~cc2(tptp_fun_Y_1(X))) | (~rrx4(X, tptp_fun_Y_1(X))) | (~rrx3(X, tptp_fun_Y_0(X))) | (~cc1(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~rrx4(X, Y)) | (~cc2(Y))) | (~ca_Cx1(X)) | ![Y: $i] : ((~rrx3(X, Y)) | (~cc1(Y)))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[52])).
% 0.20/0.41 tff(54,plain,
% 0.20/0.41 (^[X: $i] : rewrite((((~cUnsatisfiable(X)) | ((rrx3(X, tptp_fun_Y_0(X)) & cc1(tptp_fun_Y_0(X))) & (rrx4(X, tptp_fun_Y_1(X)) & cc2(tptp_fun_Y_1(X))) & ca_Cx1(X))) & (cUnsatisfiable(X) | (![Y: $i] : (~(rrx3(X, Y) & cc1(Y))) | ![Y: $i] : (~(rrx4(X, Y) & cc2(Y))) | (~ca_Cx1(X))))) <=> (((~cUnsatisfiable(X)) | (rrx3(X, tptp_fun_Y_0(X)) & cc1(tptp_fun_Y_0(X)) & rrx4(X, tptp_fun_Y_1(X)) & cc2(tptp_fun_Y_1(X)) & ca_Cx1(X))) & (cUnsatisfiable(X) | ![Y: $i] : (~(rrx3(X, Y) & cc1(Y))) | ![Y: $i] : (~(rrx4(X, Y) & cc2(Y))) | (~ca_Cx1(X)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(55,plain,
% 0.20/0.41 (![X: $i] : (((~cUnsatisfiable(X)) | ((rrx3(X, tptp_fun_Y_0(X)) & cc1(tptp_fun_Y_0(X))) & (rrx4(X, tptp_fun_Y_1(X)) & cc2(tptp_fun_Y_1(X))) & ca_Cx1(X))) & (cUnsatisfiable(X) | (![Y: $i] : (~(rrx3(X, Y) & cc1(Y))) | ![Y: $i] : (~(rrx4(X, Y) & cc2(Y))) | (~ca_Cx1(X))))) <=> ![X: $i] : (((~cUnsatisfiable(X)) | (rrx3(X, tptp_fun_Y_0(X)) & cc1(tptp_fun_Y_0(X)) & rrx4(X, tptp_fun_Y_1(X)) & cc2(tptp_fun_Y_1(X)) & ca_Cx1(X))) & (cUnsatisfiable(X) | ![Y: $i] : (~(rrx3(X, Y) & cc1(Y))) | ![Y: $i] : (~(rrx4(X, Y) & cc2(Y))) | (~ca_Cx1(X))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[54])).
% 0.20/0.41 tff(56,plain,
% 0.20/0.41 (![X: $i] : (cUnsatisfiable(X) <=> (?[Y: $i] : (rrx3(X, Y) & cc1(Y)) & ?[Y: $i] : (rrx4(X, Y) & cc2(Y)) & ca_Cx1(X))) <=> ![X: $i] : (cUnsatisfiable(X) <=> (?[Y: $i] : (rrx3(X, Y) & cc1(Y)) & ?[Y: $i] : (rrx4(X, Y) & cc2(Y)) & ca_Cx1(X)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(57,plain,
% 0.20/0.41 (^[X: $i] : rewrite((cUnsatisfiable(X) <=> ((?[Y: $i] : (rrx3(X, Y) & cc1(Y)) & ?[Y: $i] : (rrx4(X, Y) & cc2(Y))) & ca_Cx1(X))) <=> (cUnsatisfiable(X) <=> (?[Y: $i] : (rrx3(X, Y) & cc1(Y)) & ?[Y: $i] : (rrx4(X, Y) & cc2(Y)) & ca_Cx1(X))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(58,plain,
% 0.20/0.41 (![X: $i] : (cUnsatisfiable(X) <=> ((?[Y: $i] : (rrx3(X, Y) & cc1(Y)) & ?[Y: $i] : (rrx4(X, Y) & cc2(Y))) & ca_Cx1(X))) <=> ![X: $i] : (cUnsatisfiable(X) <=> (?[Y: $i] : (rrx3(X, Y) & cc1(Y)) & ?[Y: $i] : (rrx4(X, Y) & cc2(Y)) & ca_Cx1(X)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[57])).
% 0.20/0.41 tff(59,axiom,(![X: $i] : (cUnsatisfiable(X) <=> ((?[Y: $i] : (rrx3(X, Y) & cc1(Y)) & ?[Y: $i] : (rrx4(X, Y) & cc2(Y))) & ca_Cx1(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_2')).
% 0.20/0.41 tff(60,plain,
% 0.20/0.41 (![X: $i] : (cUnsatisfiable(X) <=> (?[Y: $i] : (rrx3(X, Y) & cc1(Y)) & ?[Y: $i] : (rrx4(X, Y) & cc2(Y)) & ca_Cx1(X)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.20/0.41 tff(61,plain,
% 0.20/0.41 (![X: $i] : (cUnsatisfiable(X) <=> (?[Y: $i] : (rrx3(X, Y) & cc1(Y)) & ?[Y: $i] : (rrx4(X, Y) & cc2(Y)) & ca_Cx1(X)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.20/0.41 tff(62,plain,(
% 0.20/0.41 ![X: $i] : (((~cUnsatisfiable(X)) | ((rrx3(X, tptp_fun_Y_0(X)) & cc1(tptp_fun_Y_0(X))) & (rrx4(X, tptp_fun_Y_1(X)) & cc2(tptp_fun_Y_1(X))) & ca_Cx1(X))) & (cUnsatisfiable(X) | (![Y: $i] : (~(rrx3(X, Y) & cc1(Y))) | ![Y: $i] : (~(rrx4(X, Y) & cc2(Y))) | (~ca_Cx1(X)))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[61])).
% 0.20/0.41 tff(63,plain,
% 0.20/0.41 (![X: $i] : (((~cUnsatisfiable(X)) | (rrx3(X, tptp_fun_Y_0(X)) & cc1(tptp_fun_Y_0(X)) & rrx4(X, tptp_fun_Y_1(X)) & cc2(tptp_fun_Y_1(X)) & ca_Cx1(X))) & (cUnsatisfiable(X) | ![Y: $i] : (~(rrx3(X, Y) & cc1(Y))) | ![Y: $i] : (~(rrx4(X, Y) & cc2(Y))) | (~ca_Cx1(X))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[62, 55])).
% 0.20/0.41 tff(64,plain,
% 0.20/0.41 (![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~ca_Cx1(X)) | (~cc2(tptp_fun_Y_1(X))) | (~rrx4(X, tptp_fun_Y_1(X))) | (~rrx3(X, tptp_fun_Y_0(X))) | (~cc1(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~rrx4(X, Y)) | (~cc2(Y))) | (~ca_Cx1(X)) | ![Y: $i] : ((~rrx3(X, Y)) | (~cc1(Y)))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[63, 53])).
% 0.20/0.41 tff(65,plain,
% 0.20/0.41 (![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~ca_Cx1(X)) | (~cc2(tptp_fun_Y_1(X))) | (~rrx4(X, tptp_fun_Y_1(X))) | (~rrx3(X, tptp_fun_Y_0(X))) | (~cc1(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~rrx4(X, Y)) | (~cc2(Y))) | (~ca_Cx1(X)) | ![Y: $i] : ((~rrx3(X, Y)) | (~cc1(Y)))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[64, 51])).
% 0.20/0.41 tff(66,plain,
% 0.20/0.41 (![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~ca_Cx1(X)) | (~cc2(tptp_fun_Y_1(X))) | (~rrx4(X, tptp_fun_Y_1(X))) | (~rrx3(X, tptp_fun_Y_0(X))) | (~cc1(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | (~ca_Cx1(X)) | ![Y: $i] : ((~rrx4(X, Y)) | (~cc2(Y))) | ![Y: $i] : ((~rrx3(X, Y)) | (~cc1(Y)))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[65, 46])).
% 0.20/0.41 tff(67,plain,
% 0.20/0.41 (((~![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~ca_Cx1(X)) | (~cc2(tptp_fun_Y_1(X))) | (~rrx4(X, tptp_fun_Y_1(X))) | (~rrx3(X, tptp_fun_Y_0(X))) | (~cc1(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | (~ca_Cx1(X)) | ![Y: $i] : ((~rrx4(X, Y)) | (~cc2(Y))) | ![Y: $i] : ((~rrx3(X, Y)) | (~cc1(Y)))))))) | (~((~((~cUnsatisfiable(i2003_11_14_17_21_01226)) | (~((~ca_Cx1(i2003_11_14_17_21_01226)) | (~cc1(tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~rrx3(i2003_11_14_17_21_01226, tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~rrx4(i2003_11_14_17_21_01226, tptp_fun_Y_1(i2003_11_14_17_21_01226))) | (~cc2(tptp_fun_Y_1(i2003_11_14_17_21_01226))))))) | (~(cUnsatisfiable(i2003_11_14_17_21_01226) | (~ca_Cx1(i2003_11_14_17_21_01226)) | ![Y: $i] : ((~cc2(Y)) | (~rrx4(i2003_11_14_17_21_01226, Y))) | ![Y: $i] : ((~cc1(Y)) | (~rrx3(i2003_11_14_17_21_01226, Y)))))))) <=> ((~![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~ca_Cx1(X)) | (~cc2(tptp_fun_Y_1(X))) | (~rrx4(X, tptp_fun_Y_1(X))) | (~rrx3(X, tptp_fun_Y_0(X))) | (~cc1(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | (~ca_Cx1(X)) | ![Y: $i] : ((~rrx4(X, Y)) | (~cc2(Y))) | ![Y: $i] : ((~rrx3(X, Y)) | (~cc1(Y)))))))) | (~((~((~cUnsatisfiable(i2003_11_14_17_21_01226)) | (~((~ca_Cx1(i2003_11_14_17_21_01226)) | (~cc1(tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~rrx3(i2003_11_14_17_21_01226, tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~rrx4(i2003_11_14_17_21_01226, tptp_fun_Y_1(i2003_11_14_17_21_01226))) | (~cc2(tptp_fun_Y_1(i2003_11_14_17_21_01226))))))) | (~(cUnsatisfiable(i2003_11_14_17_21_01226) | (~ca_Cx1(i2003_11_14_17_21_01226)) | ![Y: $i] : ((~cc2(Y)) | (~rrx4(i2003_11_14_17_21_01226, Y))) | ![Y: $i] : ((~cc1(Y)) | (~rrx3(i2003_11_14_17_21_01226, Y))))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(68,plain,
% 0.20/0.41 ((~((~((~cUnsatisfiable(i2003_11_14_17_21_01226)) | (~((~ca_Cx1(i2003_11_14_17_21_01226)) | (~cc2(tptp_fun_Y_1(i2003_11_14_17_21_01226))) | (~rrx4(i2003_11_14_17_21_01226, tptp_fun_Y_1(i2003_11_14_17_21_01226))) | (~rrx3(i2003_11_14_17_21_01226, tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~cc1(tptp_fun_Y_0(i2003_11_14_17_21_01226))))))) | (~(cUnsatisfiable(i2003_11_14_17_21_01226) | (~ca_Cx1(i2003_11_14_17_21_01226)) | ![Y: $i] : ((~rrx4(i2003_11_14_17_21_01226, Y)) | (~cc2(Y))) | ![Y: $i] : ((~rrx3(i2003_11_14_17_21_01226, Y)) | (~cc1(Y))))))) <=> (~((~((~cUnsatisfiable(i2003_11_14_17_21_01226)) | (~((~ca_Cx1(i2003_11_14_17_21_01226)) | (~cc1(tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~rrx3(i2003_11_14_17_21_01226, tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~rrx4(i2003_11_14_17_21_01226, tptp_fun_Y_1(i2003_11_14_17_21_01226))) | (~cc2(tptp_fun_Y_1(i2003_11_14_17_21_01226))))))) | (~(cUnsatisfiable(i2003_11_14_17_21_01226) | (~ca_Cx1(i2003_11_14_17_21_01226)) | ![Y: $i] : ((~cc2(Y)) | (~rrx4(i2003_11_14_17_21_01226, Y))) | ![Y: $i] : ((~cc1(Y)) | (~rrx3(i2003_11_14_17_21_01226, Y)))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(69,plain,
% 0.20/0.41 (((~![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~ca_Cx1(X)) | (~cc2(tptp_fun_Y_1(X))) | (~rrx4(X, tptp_fun_Y_1(X))) | (~rrx3(X, tptp_fun_Y_0(X))) | (~cc1(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | (~ca_Cx1(X)) | ![Y: $i] : ((~rrx4(X, Y)) | (~cc2(Y))) | ![Y: $i] : ((~rrx3(X, Y)) | (~cc1(Y)))))))) | (~((~((~cUnsatisfiable(i2003_11_14_17_21_01226)) | (~((~ca_Cx1(i2003_11_14_17_21_01226)) | (~cc2(tptp_fun_Y_1(i2003_11_14_17_21_01226))) | (~rrx4(i2003_11_14_17_21_01226, tptp_fun_Y_1(i2003_11_14_17_21_01226))) | (~rrx3(i2003_11_14_17_21_01226, tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~cc1(tptp_fun_Y_0(i2003_11_14_17_21_01226))))))) | (~(cUnsatisfiable(i2003_11_14_17_21_01226) | (~ca_Cx1(i2003_11_14_17_21_01226)) | ![Y: $i] : ((~rrx4(i2003_11_14_17_21_01226, Y)) | (~cc2(Y))) | ![Y: $i] : ((~rrx3(i2003_11_14_17_21_01226, Y)) | (~cc1(Y)))))))) <=> ((~![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~ca_Cx1(X)) | (~cc2(tptp_fun_Y_1(X))) | (~rrx4(X, tptp_fun_Y_1(X))) | (~rrx3(X, tptp_fun_Y_0(X))) | (~cc1(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | (~ca_Cx1(X)) | ![Y: $i] : ((~rrx4(X, Y)) | (~cc2(Y))) | ![Y: $i] : ((~rrx3(X, Y)) | (~cc1(Y)))))))) | (~((~((~cUnsatisfiable(i2003_11_14_17_21_01226)) | (~((~ca_Cx1(i2003_11_14_17_21_01226)) | (~cc1(tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~rrx3(i2003_11_14_17_21_01226, tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~rrx4(i2003_11_14_17_21_01226, tptp_fun_Y_1(i2003_11_14_17_21_01226))) | (~cc2(tptp_fun_Y_1(i2003_11_14_17_21_01226))))))) | (~(cUnsatisfiable(i2003_11_14_17_21_01226) | (~ca_Cx1(i2003_11_14_17_21_01226)) | ![Y: $i] : ((~cc2(Y)) | (~rrx4(i2003_11_14_17_21_01226, Y))) | ![Y: $i] : ((~cc1(Y)) | (~rrx3(i2003_11_14_17_21_01226, Y))))))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[68])).
% 0.20/0.41 tff(70,plain,
% 0.20/0.41 (((~![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~ca_Cx1(X)) | (~cc2(tptp_fun_Y_1(X))) | (~rrx4(X, tptp_fun_Y_1(X))) | (~rrx3(X, tptp_fun_Y_0(X))) | (~cc1(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | (~ca_Cx1(X)) | ![Y: $i] : ((~rrx4(X, Y)) | (~cc2(Y))) | ![Y: $i] : ((~rrx3(X, Y)) | (~cc1(Y)))))))) | (~((~((~cUnsatisfiable(i2003_11_14_17_21_01226)) | (~((~ca_Cx1(i2003_11_14_17_21_01226)) | (~cc2(tptp_fun_Y_1(i2003_11_14_17_21_01226))) | (~rrx4(i2003_11_14_17_21_01226, tptp_fun_Y_1(i2003_11_14_17_21_01226))) | (~rrx3(i2003_11_14_17_21_01226, tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~cc1(tptp_fun_Y_0(i2003_11_14_17_21_01226))))))) | (~(cUnsatisfiable(i2003_11_14_17_21_01226) | (~ca_Cx1(i2003_11_14_17_21_01226)) | ![Y: $i] : ((~rrx4(i2003_11_14_17_21_01226, Y)) | (~cc2(Y))) | ![Y: $i] : ((~rrx3(i2003_11_14_17_21_01226, Y)) | (~cc1(Y)))))))) <=> ((~![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~ca_Cx1(X)) | (~cc2(tptp_fun_Y_1(X))) | (~rrx4(X, tptp_fun_Y_1(X))) | (~rrx3(X, tptp_fun_Y_0(X))) | (~cc1(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | (~ca_Cx1(X)) | ![Y: $i] : ((~rrx4(X, Y)) | (~cc2(Y))) | ![Y: $i] : ((~rrx3(X, Y)) | (~cc1(Y)))))))) | (~((~((~cUnsatisfiable(i2003_11_14_17_21_01226)) | (~((~ca_Cx1(i2003_11_14_17_21_01226)) | (~cc1(tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~rrx3(i2003_11_14_17_21_01226, tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~rrx4(i2003_11_14_17_21_01226, tptp_fun_Y_1(i2003_11_14_17_21_01226))) | (~cc2(tptp_fun_Y_1(i2003_11_14_17_21_01226))))))) | (~(cUnsatisfiable(i2003_11_14_17_21_01226) | (~ca_Cx1(i2003_11_14_17_21_01226)) | ![Y: $i] : ((~cc2(Y)) | (~rrx4(i2003_11_14_17_21_01226, Y))) | ![Y: $i] : ((~cc1(Y)) | (~rrx3(i2003_11_14_17_21_01226, Y))))))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[69, 67])).
% 0.20/0.41 tff(71,plain,
% 0.20/0.41 ((~![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~ca_Cx1(X)) | (~cc2(tptp_fun_Y_1(X))) | (~rrx4(X, tptp_fun_Y_1(X))) | (~rrx3(X, tptp_fun_Y_0(X))) | (~cc1(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | (~ca_Cx1(X)) | ![Y: $i] : ((~rrx4(X, Y)) | (~cc2(Y))) | ![Y: $i] : ((~rrx3(X, Y)) | (~cc1(Y)))))))) | (~((~((~cUnsatisfiable(i2003_11_14_17_21_01226)) | (~((~ca_Cx1(i2003_11_14_17_21_01226)) | (~cc2(tptp_fun_Y_1(i2003_11_14_17_21_01226))) | (~rrx4(i2003_11_14_17_21_01226, tptp_fun_Y_1(i2003_11_14_17_21_01226))) | (~rrx3(i2003_11_14_17_21_01226, tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~cc1(tptp_fun_Y_0(i2003_11_14_17_21_01226))))))) | (~(cUnsatisfiable(i2003_11_14_17_21_01226) | (~ca_Cx1(i2003_11_14_17_21_01226)) | ![Y: $i] : ((~rrx4(i2003_11_14_17_21_01226, Y)) | (~cc2(Y))) | ![Y: $i] : ((~rrx3(i2003_11_14_17_21_01226, Y)) | (~cc1(Y)))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(72,plain,
% 0.20/0.41 ((~![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~ca_Cx1(X)) | (~cc2(tptp_fun_Y_1(X))) | (~rrx4(X, tptp_fun_Y_1(X))) | (~rrx3(X, tptp_fun_Y_0(X))) | (~cc1(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | (~ca_Cx1(X)) | ![Y: $i] : ((~rrx4(X, Y)) | (~cc2(Y))) | ![Y: $i] : ((~rrx3(X, Y)) | (~cc1(Y)))))))) | (~((~((~cUnsatisfiable(i2003_11_14_17_21_01226)) | (~((~ca_Cx1(i2003_11_14_17_21_01226)) | (~cc1(tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~rrx3(i2003_11_14_17_21_01226, tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~rrx4(i2003_11_14_17_21_01226, tptp_fun_Y_1(i2003_11_14_17_21_01226))) | (~cc2(tptp_fun_Y_1(i2003_11_14_17_21_01226))))))) | (~(cUnsatisfiable(i2003_11_14_17_21_01226) | (~ca_Cx1(i2003_11_14_17_21_01226)) | ![Y: $i] : ((~cc2(Y)) | (~rrx4(i2003_11_14_17_21_01226, Y))) | ![Y: $i] : ((~cc1(Y)) | (~rrx3(i2003_11_14_17_21_01226, Y)))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.20/0.41 tff(73,plain,
% 0.20/0.41 (~((~((~cUnsatisfiable(i2003_11_14_17_21_01226)) | (~((~ca_Cx1(i2003_11_14_17_21_01226)) | (~cc1(tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~rrx3(i2003_11_14_17_21_01226, tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~rrx4(i2003_11_14_17_21_01226, tptp_fun_Y_1(i2003_11_14_17_21_01226))) | (~cc2(tptp_fun_Y_1(i2003_11_14_17_21_01226))))))) | (~(cUnsatisfiable(i2003_11_14_17_21_01226) | (~ca_Cx1(i2003_11_14_17_21_01226)) | ![Y: $i] : ((~cc2(Y)) | (~rrx4(i2003_11_14_17_21_01226, Y))) | ![Y: $i] : ((~cc1(Y)) | (~rrx3(i2003_11_14_17_21_01226, Y))))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[72, 66])).
% 0.20/0.41 tff(74,plain,
% 0.20/0.41 (((~((~cUnsatisfiable(i2003_11_14_17_21_01226)) | (~((~ca_Cx1(i2003_11_14_17_21_01226)) | (~cc1(tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~rrx3(i2003_11_14_17_21_01226, tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~rrx4(i2003_11_14_17_21_01226, tptp_fun_Y_1(i2003_11_14_17_21_01226))) | (~cc2(tptp_fun_Y_1(i2003_11_14_17_21_01226))))))) | (~(cUnsatisfiable(i2003_11_14_17_21_01226) | (~ca_Cx1(i2003_11_14_17_21_01226)) | ![Y: $i] : ((~cc2(Y)) | (~rrx4(i2003_11_14_17_21_01226, Y))) | ![Y: $i] : ((~cc1(Y)) | (~rrx3(i2003_11_14_17_21_01226, Y)))))) | ((~cUnsatisfiable(i2003_11_14_17_21_01226)) | (~((~ca_Cx1(i2003_11_14_17_21_01226)) | (~cc1(tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~rrx3(i2003_11_14_17_21_01226, tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~rrx4(i2003_11_14_17_21_01226, tptp_fun_Y_1(i2003_11_14_17_21_01226))) | (~cc2(tptp_fun_Y_1(i2003_11_14_17_21_01226))))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(75,plain,
% 0.20/0.41 ((~cUnsatisfiable(i2003_11_14_17_21_01226)) | (~((~ca_Cx1(i2003_11_14_17_21_01226)) | (~cc1(tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~rrx3(i2003_11_14_17_21_01226, tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~rrx4(i2003_11_14_17_21_01226, tptp_fun_Y_1(i2003_11_14_17_21_01226))) | (~cc2(tptp_fun_Y_1(i2003_11_14_17_21_01226)))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.20/0.41 tff(76,plain,
% 0.20/0.41 (cUnsatisfiable(i2003_11_14_17_21_01226) <=> cUnsatisfiable(i2003_11_14_17_21_01226)),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(77,axiom,(cUnsatisfiable(i2003_11_14_17_21_01226)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_12')).
% 0.20/0.41 tff(78,plain,
% 0.20/0.41 (cUnsatisfiable(i2003_11_14_17_21_01226)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.20/0.41 tff(79,plain,
% 0.20/0.41 ((~((~cUnsatisfiable(i2003_11_14_17_21_01226)) | (~((~ca_Cx1(i2003_11_14_17_21_01226)) | (~cc1(tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~rrx3(i2003_11_14_17_21_01226, tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~rrx4(i2003_11_14_17_21_01226, tptp_fun_Y_1(i2003_11_14_17_21_01226))) | (~cc2(tptp_fun_Y_1(i2003_11_14_17_21_01226))))))) | (~cUnsatisfiable(i2003_11_14_17_21_01226)) | (~((~ca_Cx1(i2003_11_14_17_21_01226)) | (~cc1(tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~rrx3(i2003_11_14_17_21_01226, tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~rrx4(i2003_11_14_17_21_01226, tptp_fun_Y_1(i2003_11_14_17_21_01226))) | (~cc2(tptp_fun_Y_1(i2003_11_14_17_21_01226)))))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(80,plain,
% 0.20/0.41 ((~((~cUnsatisfiable(i2003_11_14_17_21_01226)) | (~((~ca_Cx1(i2003_11_14_17_21_01226)) | (~cc1(tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~rrx3(i2003_11_14_17_21_01226, tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~rrx4(i2003_11_14_17_21_01226, tptp_fun_Y_1(i2003_11_14_17_21_01226))) | (~cc2(tptp_fun_Y_1(i2003_11_14_17_21_01226))))))) | (~((~ca_Cx1(i2003_11_14_17_21_01226)) | (~cc1(tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~rrx3(i2003_11_14_17_21_01226, tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~rrx4(i2003_11_14_17_21_01226, tptp_fun_Y_1(i2003_11_14_17_21_01226))) | (~cc2(tptp_fun_Y_1(i2003_11_14_17_21_01226)))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[79, 78])).
% 0.20/0.41 tff(81,plain,
% 0.20/0.41 (~((~ca_Cx1(i2003_11_14_17_21_01226)) | (~cc1(tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~rrx3(i2003_11_14_17_21_01226, tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~rrx4(i2003_11_14_17_21_01226, tptp_fun_Y_1(i2003_11_14_17_21_01226))) | (~cc2(tptp_fun_Y_1(i2003_11_14_17_21_01226))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[80, 75])).
% 0.20/0.41 tff(82,plain,
% 0.20/0.41 (((~ca_Cx1(i2003_11_14_17_21_01226)) | (~cc1(tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~rrx3(i2003_11_14_17_21_01226, tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~rrx4(i2003_11_14_17_21_01226, tptp_fun_Y_1(i2003_11_14_17_21_01226))) | (~cc2(tptp_fun_Y_1(i2003_11_14_17_21_01226)))) | rrx3(i2003_11_14_17_21_01226, tptp_fun_Y_0(i2003_11_14_17_21_01226))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(83,plain,
% 0.20/0.41 (rrx3(i2003_11_14_17_21_01226, tptp_fun_Y_0(i2003_11_14_17_21_01226))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.20/0.41 tff(84,plain,
% 0.20/0.41 (^[X: $i, Y: $i] : refl(((~rrx3(X, Y)) | rrx(X, Y)) <=> ((~rrx3(X, Y)) | rrx(X, Y)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(85,plain,
% 0.20/0.41 (![X: $i, Y: $i] : ((~rrx3(X, Y)) | rrx(X, Y)) <=> ![X: $i, Y: $i] : ((~rrx3(X, Y)) | rrx(X, Y))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[84])).
% 0.20/0.41 tff(86,plain,
% 0.20/0.41 (![X: $i, Y: $i] : ((~rrx3(X, Y)) | rrx(X, Y)) <=> ![X: $i, Y: $i] : ((~rrx3(X, Y)) | rrx(X, Y))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(87,plain,
% 0.20/0.41 (^[X: $i, Y: $i] : rewrite((rrx3(X, Y) => rrx(X, Y)) <=> ((~rrx3(X, Y)) | rrx(X, Y)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(88,plain,
% 0.20/0.41 (![X: $i, Y: $i] : (rrx3(X, Y) => rrx(X, Y)) <=> ![X: $i, Y: $i] : ((~rrx3(X, Y)) | rrx(X, Y))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[87])).
% 0.20/0.41 tff(89,axiom,(![X: $i, Y: $i] : (rrx3(X, Y) => rrx(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_20')).
% 0.20/0.41 tff(90,plain,
% 0.20/0.41 (![X: $i, Y: $i] : ((~rrx3(X, Y)) | rrx(X, Y))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.20/0.41 tff(91,plain,
% 0.20/0.41 (![X: $i, Y: $i] : ((~rrx3(X, Y)) | rrx(X, Y))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[90, 86])).
% 0.20/0.41 tff(92,plain,(
% 0.20/0.41 ![X: $i, Y: $i] : ((~rrx3(X, Y)) | rrx(X, Y))),
% 0.20/0.42 inference(skolemize,[status(sab)],[91])).
% 0.20/0.42 tff(93,plain,
% 0.20/0.42 (![X: $i, Y: $i] : ((~rrx3(X, Y)) | rrx(X, Y))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[92, 85])).
% 0.20/0.42 tff(94,plain,
% 0.20/0.42 (((~![X: $i, Y: $i] : ((~rrx3(X, Y)) | rrx(X, Y))) | ((~rrx3(i2003_11_14_17_21_01226, tptp_fun_Y_0(i2003_11_14_17_21_01226))) | rrx(i2003_11_14_17_21_01226, tptp_fun_Y_0(i2003_11_14_17_21_01226)))) <=> ((~![X: $i, Y: $i] : ((~rrx3(X, Y)) | rrx(X, Y))) | (~rrx3(i2003_11_14_17_21_01226, tptp_fun_Y_0(i2003_11_14_17_21_01226))) | rrx(i2003_11_14_17_21_01226, tptp_fun_Y_0(i2003_11_14_17_21_01226)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(95,plain,
% 0.20/0.42 ((~![X: $i, Y: $i] : ((~rrx3(X, Y)) | rrx(X, Y))) | ((~rrx3(i2003_11_14_17_21_01226, tptp_fun_Y_0(i2003_11_14_17_21_01226))) | rrx(i2003_11_14_17_21_01226, tptp_fun_Y_0(i2003_11_14_17_21_01226)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(96,plain,
% 0.20/0.42 ((~![X: $i, Y: $i] : ((~rrx3(X, Y)) | rrx(X, Y))) | (~rrx3(i2003_11_14_17_21_01226, tptp_fun_Y_0(i2003_11_14_17_21_01226))) | rrx(i2003_11_14_17_21_01226, tptp_fun_Y_0(i2003_11_14_17_21_01226))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.20/0.42 tff(97,plain,
% 0.20/0.42 (rrx(i2003_11_14_17_21_01226, tptp_fun_Y_0(i2003_11_14_17_21_01226))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[96, 93, 83])).
% 0.20/0.42 tff(98,plain,
% 0.20/0.42 (((~ca_Cx1(i2003_11_14_17_21_01226)) | (~cc1(tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~rrx3(i2003_11_14_17_21_01226, tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~rrx4(i2003_11_14_17_21_01226, tptp_fun_Y_1(i2003_11_14_17_21_01226))) | (~cc2(tptp_fun_Y_1(i2003_11_14_17_21_01226)))) | rrx4(i2003_11_14_17_21_01226, tptp_fun_Y_1(i2003_11_14_17_21_01226))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(99,plain,
% 0.20/0.42 (rrx4(i2003_11_14_17_21_01226, tptp_fun_Y_1(i2003_11_14_17_21_01226))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[98, 81])).
% 0.20/0.42 tff(100,plain,
% 0.20/0.42 (^[X: $i, Y: $i] : refl(((~rrx4(X, Y)) | rrx(X, Y)) <=> ((~rrx4(X, Y)) | rrx(X, Y)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(101,plain,
% 0.20/0.42 (![X: $i, Y: $i] : ((~rrx4(X, Y)) | rrx(X, Y)) <=> ![X: $i, Y: $i] : ((~rrx4(X, Y)) | rrx(X, Y))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[100])).
% 0.20/0.42 tff(102,plain,
% 0.20/0.42 (![X: $i, Y: $i] : ((~rrx4(X, Y)) | rrx(X, Y)) <=> ![X: $i, Y: $i] : ((~rrx4(X, Y)) | rrx(X, Y))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(103,plain,
% 0.20/0.42 (^[X: $i, Y: $i] : rewrite((rrx4(X, Y) => rrx(X, Y)) <=> ((~rrx4(X, Y)) | rrx(X, Y)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(104,plain,
% 0.20/0.42 (![X: $i, Y: $i] : (rrx4(X, Y) => rrx(X, Y)) <=> ![X: $i, Y: $i] : ((~rrx4(X, Y)) | rrx(X, Y))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[103])).
% 0.20/0.42 tff(105,axiom,(![X: $i, Y: $i] : (rrx4(X, Y) => rrx(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_17')).
% 0.20/0.42 tff(106,plain,
% 0.20/0.42 (![X: $i, Y: $i] : ((~rrx4(X, Y)) | rrx(X, Y))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.20/0.42 tff(107,plain,
% 0.20/0.42 (![X: $i, Y: $i] : ((~rrx4(X, Y)) | rrx(X, Y))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[106, 102])).
% 0.20/0.42 tff(108,plain,(
% 0.20/0.42 ![X: $i, Y: $i] : ((~rrx4(X, Y)) | rrx(X, Y))),
% 0.20/0.42 inference(skolemize,[status(sab)],[107])).
% 0.20/0.42 tff(109,plain,
% 0.20/0.42 (![X: $i, Y: $i] : ((~rrx4(X, Y)) | rrx(X, Y))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[108, 101])).
% 0.20/0.42 tff(110,plain,
% 0.20/0.42 (((~![X: $i, Y: $i] : ((~rrx4(X, Y)) | rrx(X, Y))) | ((~rrx4(i2003_11_14_17_21_01226, tptp_fun_Y_1(i2003_11_14_17_21_01226))) | rrx(i2003_11_14_17_21_01226, tptp_fun_Y_1(i2003_11_14_17_21_01226)))) <=> ((~![X: $i, Y: $i] : ((~rrx4(X, Y)) | rrx(X, Y))) | (~rrx4(i2003_11_14_17_21_01226, tptp_fun_Y_1(i2003_11_14_17_21_01226))) | rrx(i2003_11_14_17_21_01226, tptp_fun_Y_1(i2003_11_14_17_21_01226)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(111,plain,
% 0.20/0.42 ((~![X: $i, Y: $i] : ((~rrx4(X, Y)) | rrx(X, Y))) | ((~rrx4(i2003_11_14_17_21_01226, tptp_fun_Y_1(i2003_11_14_17_21_01226))) | rrx(i2003_11_14_17_21_01226, tptp_fun_Y_1(i2003_11_14_17_21_01226)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(112,plain,
% 0.20/0.42 ((~![X: $i, Y: $i] : ((~rrx4(X, Y)) | rrx(X, Y))) | (~rrx4(i2003_11_14_17_21_01226, tptp_fun_Y_1(i2003_11_14_17_21_01226))) | rrx(i2003_11_14_17_21_01226, tptp_fun_Y_1(i2003_11_14_17_21_01226))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.20/0.42 tff(113,plain,
% 0.20/0.42 (rrx(i2003_11_14_17_21_01226, tptp_fun_Y_1(i2003_11_14_17_21_01226))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[112, 109, 99])).
% 0.20/0.42 tff(114,plain,
% 0.20/0.42 (^[X: $i, Y: $i, Z: $i] : refl(((Y = Z) | (~rrx(X, Y)) | (~rrx(X, Z))) <=> ((Y = Z) | (~rrx(X, Y)) | (~rrx(X, Z))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(115,plain,
% 0.20/0.42 (![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rrx(X, Y)) | (~rrx(X, Z))) <=> ![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rrx(X, Y)) | (~rrx(X, Z)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[114])).
% 0.20/0.42 tff(116,plain,
% 0.20/0.42 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((rrx(X, Y) & rrx(X, Z)) <=> (~((~rrx(X, Y)) | (~rrx(X, Z))))), ((~(rrx(X, Y) & rrx(X, Z))) <=> (~(~((~rrx(X, Y)) | (~rrx(X, Z))))))), rewrite((~(~((~rrx(X, Y)) | (~rrx(X, Z))))) <=> ((~rrx(X, Y)) | (~rrx(X, Z)))), ((~(rrx(X, Y) & rrx(X, Z))) <=> ((~rrx(X, Y)) | (~rrx(X, Z))))), (((~(rrx(X, Y) & rrx(X, Z))) | (Y = Z)) <=> (((~rrx(X, Y)) | (~rrx(X, Z))) | (Y = Z)))), rewrite((((~rrx(X, Y)) | (~rrx(X, Z))) | (Y = Z)) <=> ((Y = Z) | (~rrx(X, Y)) | (~rrx(X, Z)))), (((~(rrx(X, Y) & rrx(X, Z))) | (Y = Z)) <=> ((Y = Z) | (~rrx(X, Y)) | (~rrx(X, Z)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(117,plain,
% 0.20/0.42 (![X: $i, Y: $i, Z: $i] : ((~(rrx(X, Y) & rrx(X, Z))) | (Y = Z)) <=> ![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rrx(X, Y)) | (~rrx(X, Z)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[116])).
% 0.20/0.42 tff(118,plain,
% 0.20/0.42 (![X: $i, Y: $i, Z: $i] : ((~(rrx(X, Y) & rrx(X, Z))) | (Y = Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(rrx(X, Y) & rrx(X, Z))) | (Y = Z))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(119,plain,
% 0.20/0.42 (^[X: $i, Y: $i, Z: $i] : rewrite(((rrx(X, Y) & rrx(X, Z)) => (Y = Z)) <=> ((~(rrx(X, Y) & rrx(X, Z))) | (Y = Z)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(120,plain,
% 0.20/0.42 (![X: $i, Y: $i, Z: $i] : ((rrx(X, Y) & rrx(X, Z)) => (Y = Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(rrx(X, Y) & rrx(X, Z))) | (Y = Z))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[119])).
% 0.20/0.42 tff(121,axiom,(![X: $i, Y: $i, Z: $i] : ((rrx(X, Y) & rrx(X, Z)) => (Y = Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_7')).
% 0.20/0.42 tff(122,plain,
% 0.20/0.42 (![X: $i, Y: $i, Z: $i] : ((~(rrx(X, Y) & rrx(X, Z))) | (Y = Z))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.20/0.42 tff(123,plain,
% 0.20/0.42 (![X: $i, Y: $i, Z: $i] : ((~(rrx(X, Y) & rrx(X, Z))) | (Y = Z))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[122, 118])).
% 0.20/0.42 tff(124,plain,(
% 0.20/0.42 ![X: $i, Y: $i, Z: $i] : ((~(rrx(X, Y) & rrx(X, Z))) | (Y = Z))),
% 0.20/0.42 inference(skolemize,[status(sab)],[123])).
% 0.20/0.42 tff(125,plain,
% 0.20/0.42 (![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rrx(X, Y)) | (~rrx(X, Z)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[124, 117])).
% 0.20/0.42 tff(126,plain,
% 0.20/0.42 (![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rrx(X, Y)) | (~rrx(X, Z)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[125, 115])).
% 0.20/0.42 tff(127,plain,
% 0.20/0.42 (((~![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rrx(X, Y)) | (~rrx(X, Z)))) | ((tptp_fun_Y_1(i2003_11_14_17_21_01226) = tptp_fun_Y_0(i2003_11_14_17_21_01226)) | (~rrx(i2003_11_14_17_21_01226, tptp_fun_Y_1(i2003_11_14_17_21_01226))) | (~rrx(i2003_11_14_17_21_01226, tptp_fun_Y_0(i2003_11_14_17_21_01226))))) <=> ((~![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rrx(X, Y)) | (~rrx(X, Z)))) | (tptp_fun_Y_1(i2003_11_14_17_21_01226) = tptp_fun_Y_0(i2003_11_14_17_21_01226)) | (~rrx(i2003_11_14_17_21_01226, tptp_fun_Y_1(i2003_11_14_17_21_01226))) | (~rrx(i2003_11_14_17_21_01226, tptp_fun_Y_0(i2003_11_14_17_21_01226))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(128,plain,
% 0.20/0.42 ((~![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rrx(X, Y)) | (~rrx(X, Z)))) | ((tptp_fun_Y_1(i2003_11_14_17_21_01226) = tptp_fun_Y_0(i2003_11_14_17_21_01226)) | (~rrx(i2003_11_14_17_21_01226, tptp_fun_Y_1(i2003_11_14_17_21_01226))) | (~rrx(i2003_11_14_17_21_01226, tptp_fun_Y_0(i2003_11_14_17_21_01226))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(129,plain,
% 0.20/0.42 ((~![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rrx(X, Y)) | (~rrx(X, Z)))) | (tptp_fun_Y_1(i2003_11_14_17_21_01226) = tptp_fun_Y_0(i2003_11_14_17_21_01226)) | (~rrx(i2003_11_14_17_21_01226, tptp_fun_Y_1(i2003_11_14_17_21_01226))) | (~rrx(i2003_11_14_17_21_01226, tptp_fun_Y_0(i2003_11_14_17_21_01226)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.20/0.42 tff(130,plain,
% 0.20/0.42 (tptp_fun_Y_1(i2003_11_14_17_21_01226) = tptp_fun_Y_0(i2003_11_14_17_21_01226)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[129, 126, 113, 97])).
% 0.20/0.42 tff(131,plain,
% 0.20/0.42 (cc2(tptp_fun_Y_1(i2003_11_14_17_21_01226)) <=> cc2(tptp_fun_Y_0(i2003_11_14_17_21_01226))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[130])).
% 0.20/0.42 tff(132,plain,
% 0.20/0.42 (((~ca_Cx1(i2003_11_14_17_21_01226)) | (~cc1(tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~rrx3(i2003_11_14_17_21_01226, tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~rrx4(i2003_11_14_17_21_01226, tptp_fun_Y_1(i2003_11_14_17_21_01226))) | (~cc2(tptp_fun_Y_1(i2003_11_14_17_21_01226)))) | cc2(tptp_fun_Y_1(i2003_11_14_17_21_01226))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(133,plain,
% 0.20/0.42 (cc2(tptp_fun_Y_1(i2003_11_14_17_21_01226))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[132, 81])).
% 0.20/0.42 tff(134,plain,
% 0.20/0.42 (cc2(tptp_fun_Y_0(i2003_11_14_17_21_01226))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[133, 131])).
% 0.20/0.42 tff(135,plain,
% 0.20/0.42 (((~ca_Cx1(i2003_11_14_17_21_01226)) | (~cc1(tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~rrx3(i2003_11_14_17_21_01226, tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~rrx4(i2003_11_14_17_21_01226, tptp_fun_Y_1(i2003_11_14_17_21_01226))) | (~cc2(tptp_fun_Y_1(i2003_11_14_17_21_01226)))) | cc1(tptp_fun_Y_0(i2003_11_14_17_21_01226))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(136,plain,
% 0.20/0.42 (cc1(tptp_fun_Y_0(i2003_11_14_17_21_01226))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[135, 81])).
% 0.20/0.42 tff(137,plain,
% 0.20/0.42 ((~((~cc1(tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~cc2(tptp_fun_Y_0(i2003_11_14_17_21_01226))))) | (~cc1(tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~cc2(tptp_fun_Y_0(i2003_11_14_17_21_01226)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(138,plain,
% 0.20/0.42 ((~((~cc1(tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~cc2(tptp_fun_Y_0(i2003_11_14_17_21_01226))))) | (~cc2(tptp_fun_Y_0(i2003_11_14_17_21_01226)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[137, 136])).
% 0.20/0.42 tff(139,plain,
% 0.20/0.42 (~((~cc1(tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~cc2(tptp_fun_Y_0(i2003_11_14_17_21_01226))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[138, 134])).
% 0.20/0.42 tff(140,plain,
% 0.20/0.42 ((((~cc1(tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~cc2(tptp_fun_Y_0(i2003_11_14_17_21_01226)))) <=> ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_01226))) | ((~cc1(tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~cc2(tptp_fun_Y_0(i2003_11_14_17_21_01226)))) | ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_01226))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(141,plain,
% 0.20/0.42 (ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_01226))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[140, 139, 44])).
% 0.20/0.42 tff(142,plain,
% 0.20/0.42 (((~![Y: $i] : ((~ca_Ax2(Y)) | (~rrx3(i2003_11_14_17_21_01226, Y)))) | ((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~rrx3(i2003_11_14_17_21_01226, tptp_fun_Y_0(i2003_11_14_17_21_01226))))) <=> ((~![Y: $i] : ((~ca_Ax2(Y)) | (~rrx3(i2003_11_14_17_21_01226, Y)))) | (~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~rrx3(i2003_11_14_17_21_01226, tptp_fun_Y_0(i2003_11_14_17_21_01226))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(143,plain,
% 0.20/0.42 ((~![Y: $i] : ((~ca_Ax2(Y)) | (~rrx3(i2003_11_14_17_21_01226, Y)))) | ((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~rrx3(i2003_11_14_17_21_01226, tptp_fun_Y_0(i2003_11_14_17_21_01226))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(144,plain,
% 0.20/0.42 ((~![Y: $i] : ((~ca_Ax2(Y)) | (~rrx3(i2003_11_14_17_21_01226, Y)))) | (~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~rrx3(i2003_11_14_17_21_01226, tptp_fun_Y_0(i2003_11_14_17_21_01226)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.20/0.42 tff(145,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[144, 83, 141, 24])).
% 0.20/0.42 tff(146,plain,(~![Y: $i] : ((~ca_Ax2(Y)) | (~rrx3(i2003_11_14_17_21_01226, Y)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.42 tff(147,plain,
% 0.21/0.42 (^[X: $i] : refl((~((~((~ca_Cx1xcomp(X)) | (~((~rrx3(X, tptp_fun_Y_3(X))) | (~ca_Ax2(tptp_fun_Y_3(X))))))) | (~(ca_Cx1xcomp(X) | ![Y: $i] : ((~rrx3(X, Y)) | (~ca_Ax2(Y))))))) <=> (~((~((~ca_Cx1xcomp(X)) | (~((~rrx3(X, tptp_fun_Y_3(X))) | (~ca_Ax2(tptp_fun_Y_3(X))))))) | (~(ca_Cx1xcomp(X) | ![Y: $i] : ((~rrx3(X, Y)) | (~ca_Ax2(Y))))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(148,plain,
% 0.21/0.42 (![X: $i] : (~((~((~ca_Cx1xcomp(X)) | (~((~rrx3(X, tptp_fun_Y_3(X))) | (~ca_Ax2(tptp_fun_Y_3(X))))))) | (~(ca_Cx1xcomp(X) | ![Y: $i] : ((~rrx3(X, Y)) | (~ca_Ax2(Y))))))) <=> ![X: $i] : (~((~((~ca_Cx1xcomp(X)) | (~((~rrx3(X, tptp_fun_Y_3(X))) | (~ca_Ax2(tptp_fun_Y_3(X))))))) | (~(ca_Cx1xcomp(X) | ![Y: $i] : ((~rrx3(X, Y)) | (~ca_Ax2(Y)))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[147])).
% 0.21/0.42 tff(149,plain,
% 0.21/0.42 (^[X: $i] : rewrite((~((~((~ca_Cx1xcomp(X)) | (~((~rrx3(X, tptp_fun_Y_3(X))) | (~ca_Ax2(tptp_fun_Y_3(X))))))) | (~(ca_Cx1xcomp(X) | ![Y: $i] : ((~rrx3(X, Y)) | (~ca_Ax2(Y))))))) <=> (~((~((~ca_Cx1xcomp(X)) | (~((~rrx3(X, tptp_fun_Y_3(X))) | (~ca_Ax2(tptp_fun_Y_3(X))))))) | (~(ca_Cx1xcomp(X) | ![Y: $i] : ((~rrx3(X, Y)) | (~ca_Ax2(Y))))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(150,plain,
% 0.21/0.42 (![X: $i] : (~((~((~ca_Cx1xcomp(X)) | (~((~rrx3(X, tptp_fun_Y_3(X))) | (~ca_Ax2(tptp_fun_Y_3(X))))))) | (~(ca_Cx1xcomp(X) | ![Y: $i] : ((~rrx3(X, Y)) | (~ca_Ax2(Y))))))) <=> ![X: $i] : (~((~((~ca_Cx1xcomp(X)) | (~((~rrx3(X, tptp_fun_Y_3(X))) | (~ca_Ax2(tptp_fun_Y_3(X))))))) | (~(ca_Cx1xcomp(X) | ![Y: $i] : ((~rrx3(X, Y)) | (~ca_Ax2(Y)))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[149])).
% 0.21/0.42 tff(151,plain,
% 0.21/0.42 (![X: $i] : (~((~((~ca_Cx1xcomp(X)) | (~((~rrx3(X, tptp_fun_Y_3(X))) | (~ca_Ax2(tptp_fun_Y_3(X))))))) | (~(ca_Cx1xcomp(X) | ![Y: $i] : ((~rrx3(X, Y)) | (~ca_Ax2(Y))))))) <=> ![X: $i] : (~((~((~ca_Cx1xcomp(X)) | (~((~rrx3(X, tptp_fun_Y_3(X))) | (~ca_Ax2(tptp_fun_Y_3(X))))))) | (~(ca_Cx1xcomp(X) | ![Y: $i] : ((~rrx3(X, Y)) | (~ca_Ax2(Y)))))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[150, 148])).
% 0.21/0.42 tff(152,plain,
% 0.21/0.42 (^[X: $i] : trans(monotonicity(rewrite(((~ca_Cx1xcomp(X)) | (rrx3(X, tptp_fun_Y_3(X)) & ca_Ax2(tptp_fun_Y_3(X)))) <=> ((~ca_Cx1xcomp(X)) | (~((~rrx3(X, tptp_fun_Y_3(X))) | (~ca_Ax2(tptp_fun_Y_3(X))))))), rewrite((ca_Cx1xcomp(X) | ![Y: $i] : (~(rrx3(X, Y) & ca_Ax2(Y)))) <=> (ca_Cx1xcomp(X) | ![Y: $i] : ((~rrx3(X, Y)) | (~ca_Ax2(Y))))), ((((~ca_Cx1xcomp(X)) | (rrx3(X, tptp_fun_Y_3(X)) & ca_Ax2(tptp_fun_Y_3(X)))) & (ca_Cx1xcomp(X) | ![Y: $i] : (~(rrx3(X, Y) & ca_Ax2(Y))))) <=> (((~ca_Cx1xcomp(X)) | (~((~rrx3(X, tptp_fun_Y_3(X))) | (~ca_Ax2(tptp_fun_Y_3(X)))))) & (ca_Cx1xcomp(X) | ![Y: $i] : ((~rrx3(X, Y)) | (~ca_Ax2(Y))))))), rewrite((((~ca_Cx1xcomp(X)) | (~((~rrx3(X, tptp_fun_Y_3(X))) | (~ca_Ax2(tptp_fun_Y_3(X)))))) & (ca_Cx1xcomp(X) | ![Y: $i] : ((~rrx3(X, Y)) | (~ca_Ax2(Y))))) <=> (~((~((~ca_Cx1xcomp(X)) | (~((~rrx3(X, tptp_fun_Y_3(X))) | (~ca_Ax2(tptp_fun_Y_3(X))))))) | (~(ca_Cx1xcomp(X) | ![Y: $i] : ((~rrx3(X, Y)) | (~ca_Ax2(Y)))))))), ((((~ca_Cx1xcomp(X)) | (rrx3(X, tptp_fun_Y_3(X)) & ca_Ax2(tptp_fun_Y_3(X)))) & (ca_Cx1xcomp(X) | ![Y: $i] : (~(rrx3(X, Y) & ca_Ax2(Y))))) <=> (~((~((~ca_Cx1xcomp(X)) | (~((~rrx3(X, tptp_fun_Y_3(X))) | (~ca_Ax2(tptp_fun_Y_3(X))))))) | (~(ca_Cx1xcomp(X) | ![Y: $i] : ((~rrx3(X, Y)) | (~ca_Ax2(Y)))))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(153,plain,
% 0.21/0.42 (![X: $i] : (((~ca_Cx1xcomp(X)) | (rrx3(X, tptp_fun_Y_3(X)) & ca_Ax2(tptp_fun_Y_3(X)))) & (ca_Cx1xcomp(X) | ![Y: $i] : (~(rrx3(X, Y) & ca_Ax2(Y))))) <=> ![X: $i] : (~((~((~ca_Cx1xcomp(X)) | (~((~rrx3(X, tptp_fun_Y_3(X))) | (~ca_Ax2(tptp_fun_Y_3(X))))))) | (~(ca_Cx1xcomp(X) | ![Y: $i] : ((~rrx3(X, Y)) | (~ca_Ax2(Y)))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[152])).
% 0.21/0.42 tff(154,plain,
% 0.21/0.42 (![X: $i] : (ca_Cx1xcomp(X) <=> ?[Y: $i] : (rrx3(X, Y) & ca_Ax2(Y))) <=> ![X: $i] : (ca_Cx1xcomp(X) <=> ?[Y: $i] : (rrx3(X, Y) & ca_Ax2(Y)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(155,axiom,(![X: $i] : (ca_Cx1xcomp(X) <=> ?[Y: $i] : (rrx3(X, Y) & ca_Ax2(Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_5')).
% 0.21/0.42 tff(156,plain,
% 0.21/0.42 (![X: $i] : (ca_Cx1xcomp(X) <=> ?[Y: $i] : (rrx3(X, Y) & ca_Ax2(Y)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.21/0.42 tff(157,plain,(
% 0.21/0.42 ![X: $i] : (((~ca_Cx1xcomp(X)) | (rrx3(X, tptp_fun_Y_3(X)) & ca_Ax2(tptp_fun_Y_3(X)))) & (ca_Cx1xcomp(X) | ![Y: $i] : (~(rrx3(X, Y) & ca_Ax2(Y)))))),
% 0.21/0.42 inference(skolemize,[status(sab)],[156])).
% 0.21/0.42 tff(158,plain,
% 0.21/0.42 (![X: $i] : (~((~((~ca_Cx1xcomp(X)) | (~((~rrx3(X, tptp_fun_Y_3(X))) | (~ca_Ax2(tptp_fun_Y_3(X))))))) | (~(ca_Cx1xcomp(X) | ![Y: $i] : ((~rrx3(X, Y)) | (~ca_Ax2(Y)))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[157, 153])).
% 0.21/0.42 tff(159,plain,
% 0.21/0.42 (![X: $i] : (~((~((~ca_Cx1xcomp(X)) | (~((~rrx3(X, tptp_fun_Y_3(X))) | (~ca_Ax2(tptp_fun_Y_3(X))))))) | (~(ca_Cx1xcomp(X) | ![Y: $i] : ((~rrx3(X, Y)) | (~ca_Ax2(Y)))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[158, 151])).
% 0.21/0.42 tff(160,plain,
% 0.21/0.42 (((~![X: $i] : (~((~((~ca_Cx1xcomp(X)) | (~((~rrx3(X, tptp_fun_Y_3(X))) | (~ca_Ax2(tptp_fun_Y_3(X))))))) | (~(ca_Cx1xcomp(X) | ![Y: $i] : ((~rrx3(X, Y)) | (~ca_Ax2(Y)))))))) | (~((~((~ca_Cx1xcomp(i2003_11_14_17_21_01226)) | (~((~ca_Ax2(tptp_fun_Y_3(i2003_11_14_17_21_01226))) | (~rrx3(i2003_11_14_17_21_01226, tptp_fun_Y_3(i2003_11_14_17_21_01226))))))) | (~(ca_Cx1xcomp(i2003_11_14_17_21_01226) | ![Y: $i] : ((~ca_Ax2(Y)) | (~rrx3(i2003_11_14_17_21_01226, Y)))))))) <=> ((~![X: $i] : (~((~((~ca_Cx1xcomp(X)) | (~((~rrx3(X, tptp_fun_Y_3(X))) | (~ca_Ax2(tptp_fun_Y_3(X))))))) | (~(ca_Cx1xcomp(X) | ![Y: $i] : ((~rrx3(X, Y)) | (~ca_Ax2(Y)))))))) | (~((~((~ca_Cx1xcomp(i2003_11_14_17_21_01226)) | (~((~ca_Ax2(tptp_fun_Y_3(i2003_11_14_17_21_01226))) | (~rrx3(i2003_11_14_17_21_01226, tptp_fun_Y_3(i2003_11_14_17_21_01226))))))) | (~(ca_Cx1xcomp(i2003_11_14_17_21_01226) | ![Y: $i] : ((~ca_Ax2(Y)) | (~rrx3(i2003_11_14_17_21_01226, Y))))))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(161,plain,
% 0.21/0.42 ((~((~((~ca_Cx1xcomp(i2003_11_14_17_21_01226)) | (~((~rrx3(i2003_11_14_17_21_01226, tptp_fun_Y_3(i2003_11_14_17_21_01226))) | (~ca_Ax2(tptp_fun_Y_3(i2003_11_14_17_21_01226))))))) | (~(ca_Cx1xcomp(i2003_11_14_17_21_01226) | ![Y: $i] : ((~rrx3(i2003_11_14_17_21_01226, Y)) | (~ca_Ax2(Y))))))) <=> (~((~((~ca_Cx1xcomp(i2003_11_14_17_21_01226)) | (~((~ca_Ax2(tptp_fun_Y_3(i2003_11_14_17_21_01226))) | (~rrx3(i2003_11_14_17_21_01226, tptp_fun_Y_3(i2003_11_14_17_21_01226))))))) | (~(ca_Cx1xcomp(i2003_11_14_17_21_01226) | ![Y: $i] : ((~ca_Ax2(Y)) | (~rrx3(i2003_11_14_17_21_01226, Y)))))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(162,plain,
% 0.21/0.42 (((~![X: $i] : (~((~((~ca_Cx1xcomp(X)) | (~((~rrx3(X, tptp_fun_Y_3(X))) | (~ca_Ax2(tptp_fun_Y_3(X))))))) | (~(ca_Cx1xcomp(X) | ![Y: $i] : ((~rrx3(X, Y)) | (~ca_Ax2(Y)))))))) | (~((~((~ca_Cx1xcomp(i2003_11_14_17_21_01226)) | (~((~rrx3(i2003_11_14_17_21_01226, tptp_fun_Y_3(i2003_11_14_17_21_01226))) | (~ca_Ax2(tptp_fun_Y_3(i2003_11_14_17_21_01226))))))) | (~(ca_Cx1xcomp(i2003_11_14_17_21_01226) | ![Y: $i] : ((~rrx3(i2003_11_14_17_21_01226, Y)) | (~ca_Ax2(Y)))))))) <=> ((~![X: $i] : (~((~((~ca_Cx1xcomp(X)) | (~((~rrx3(X, tptp_fun_Y_3(X))) | (~ca_Ax2(tptp_fun_Y_3(X))))))) | (~(ca_Cx1xcomp(X) | ![Y: $i] : ((~rrx3(X, Y)) | (~ca_Ax2(Y)))))))) | (~((~((~ca_Cx1xcomp(i2003_11_14_17_21_01226)) | (~((~ca_Ax2(tptp_fun_Y_3(i2003_11_14_17_21_01226))) | (~rrx3(i2003_11_14_17_21_01226, tptp_fun_Y_3(i2003_11_14_17_21_01226))))))) | (~(ca_Cx1xcomp(i2003_11_14_17_21_01226) | ![Y: $i] : ((~ca_Ax2(Y)) | (~rrx3(i2003_11_14_17_21_01226, Y))))))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[161])).
% 0.21/0.42 tff(163,plain,
% 0.21/0.42 (((~![X: $i] : (~((~((~ca_Cx1xcomp(X)) | (~((~rrx3(X, tptp_fun_Y_3(X))) | (~ca_Ax2(tptp_fun_Y_3(X))))))) | (~(ca_Cx1xcomp(X) | ![Y: $i] : ((~rrx3(X, Y)) | (~ca_Ax2(Y)))))))) | (~((~((~ca_Cx1xcomp(i2003_11_14_17_21_01226)) | (~((~rrx3(i2003_11_14_17_21_01226, tptp_fun_Y_3(i2003_11_14_17_21_01226))) | (~ca_Ax2(tptp_fun_Y_3(i2003_11_14_17_21_01226))))))) | (~(ca_Cx1xcomp(i2003_11_14_17_21_01226) | ![Y: $i] : ((~rrx3(i2003_11_14_17_21_01226, Y)) | (~ca_Ax2(Y)))))))) <=> ((~![X: $i] : (~((~((~ca_Cx1xcomp(X)) | (~((~rrx3(X, tptp_fun_Y_3(X))) | (~ca_Ax2(tptp_fun_Y_3(X))))))) | (~(ca_Cx1xcomp(X) | ![Y: $i] : ((~rrx3(X, Y)) | (~ca_Ax2(Y)))))))) | (~((~((~ca_Cx1xcomp(i2003_11_14_17_21_01226)) | (~((~ca_Ax2(tptp_fun_Y_3(i2003_11_14_17_21_01226))) | (~rrx3(i2003_11_14_17_21_01226, tptp_fun_Y_3(i2003_11_14_17_21_01226))))))) | (~(ca_Cx1xcomp(i2003_11_14_17_21_01226) | ![Y: $i] : ((~ca_Ax2(Y)) | (~rrx3(i2003_11_14_17_21_01226, Y))))))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[162, 160])).
% 0.21/0.43 tff(164,plain,
% 0.21/0.43 ((~![X: $i] : (~((~((~ca_Cx1xcomp(X)) | (~((~rrx3(X, tptp_fun_Y_3(X))) | (~ca_Ax2(tptp_fun_Y_3(X))))))) | (~(ca_Cx1xcomp(X) | ![Y: $i] : ((~rrx3(X, Y)) | (~ca_Ax2(Y)))))))) | (~((~((~ca_Cx1xcomp(i2003_11_14_17_21_01226)) | (~((~rrx3(i2003_11_14_17_21_01226, tptp_fun_Y_3(i2003_11_14_17_21_01226))) | (~ca_Ax2(tptp_fun_Y_3(i2003_11_14_17_21_01226))))))) | (~(ca_Cx1xcomp(i2003_11_14_17_21_01226) | ![Y: $i] : ((~rrx3(i2003_11_14_17_21_01226, Y)) | (~ca_Ax2(Y)))))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(165,plain,
% 0.21/0.43 ((~![X: $i] : (~((~((~ca_Cx1xcomp(X)) | (~((~rrx3(X, tptp_fun_Y_3(X))) | (~ca_Ax2(tptp_fun_Y_3(X))))))) | (~(ca_Cx1xcomp(X) | ![Y: $i] : ((~rrx3(X, Y)) | (~ca_Ax2(Y)))))))) | (~((~((~ca_Cx1xcomp(i2003_11_14_17_21_01226)) | (~((~ca_Ax2(tptp_fun_Y_3(i2003_11_14_17_21_01226))) | (~rrx3(i2003_11_14_17_21_01226, tptp_fun_Y_3(i2003_11_14_17_21_01226))))))) | (~(ca_Cx1xcomp(i2003_11_14_17_21_01226) | ![Y: $i] : ((~ca_Ax2(Y)) | (~rrx3(i2003_11_14_17_21_01226, Y)))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.21/0.43 tff(166,plain,
% 0.21/0.43 (~((~((~ca_Cx1xcomp(i2003_11_14_17_21_01226)) | (~((~ca_Ax2(tptp_fun_Y_3(i2003_11_14_17_21_01226))) | (~rrx3(i2003_11_14_17_21_01226, tptp_fun_Y_3(i2003_11_14_17_21_01226))))))) | (~(ca_Cx1xcomp(i2003_11_14_17_21_01226) | ![Y: $i] : ((~ca_Ax2(Y)) | (~rrx3(i2003_11_14_17_21_01226, Y))))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[165, 159])).
% 0.21/0.43 tff(167,plain,
% 0.21/0.43 (((~((~ca_Cx1xcomp(i2003_11_14_17_21_01226)) | (~((~ca_Ax2(tptp_fun_Y_3(i2003_11_14_17_21_01226))) | (~rrx3(i2003_11_14_17_21_01226, tptp_fun_Y_3(i2003_11_14_17_21_01226))))))) | (~(ca_Cx1xcomp(i2003_11_14_17_21_01226) | ![Y: $i] : ((~ca_Ax2(Y)) | (~rrx3(i2003_11_14_17_21_01226, Y)))))) | (ca_Cx1xcomp(i2003_11_14_17_21_01226) | ![Y: $i] : ((~ca_Ax2(Y)) | (~rrx3(i2003_11_14_17_21_01226, Y))))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(168,plain,
% 0.21/0.43 (ca_Cx1xcomp(i2003_11_14_17_21_01226) | ![Y: $i] : ((~ca_Ax2(Y)) | (~rrx3(i2003_11_14_17_21_01226, Y)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[167, 166])).
% 0.21/0.43 tff(169,plain,
% 0.21/0.43 ((~(ca_Cx1xcomp(i2003_11_14_17_21_01226) | ![Y: $i] : ((~ca_Ax2(Y)) | (~rrx3(i2003_11_14_17_21_01226, Y))))) | ca_Cx1xcomp(i2003_11_14_17_21_01226) | ![Y: $i] : ((~ca_Ax2(Y)) | (~rrx3(i2003_11_14_17_21_01226, Y)))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(170,plain,
% 0.21/0.43 (ca_Cx1xcomp(i2003_11_14_17_21_01226) | ![Y: $i] : ((~ca_Ax2(Y)) | (~rrx3(i2003_11_14_17_21_01226, Y)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[169, 168])).
% 0.21/0.43 tff(171,plain,
% 0.21/0.43 (ca_Cx1xcomp(i2003_11_14_17_21_01226)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[170, 146])).
% 0.21/0.43 tff(172,plain,
% 0.21/0.43 ((~((~ca_Cx1xcomp(i2003_11_14_17_21_01226)) | ![Y: $i] : (~ra_Px1(i2003_11_14_17_21_01226, Y)))) | (~ca_Cx1xcomp(i2003_11_14_17_21_01226)) | ![Y: $i] : (~ra_Px1(i2003_11_14_17_21_01226, Y))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(173,plain,
% 0.21/0.43 ((~((~ca_Cx1xcomp(i2003_11_14_17_21_01226)) | ![Y: $i] : (~ra_Px1(i2003_11_14_17_21_01226, Y)))) | ![Y: $i] : (~ra_Px1(i2003_11_14_17_21_01226, Y))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[172, 171])).
% 0.21/0.43 tff(174,plain,
% 0.21/0.43 (![Y: $i] : (~ra_Px1(i2003_11_14_17_21_01226, Y))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[173, 23])).
% 0.21/0.43 tff(175,plain,
% 0.21/0.43 (^[X: $i] : refl((~((~((~ca_Cx1(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(ca_Cx1(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))))) <=> (~((~((~ca_Cx1(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(ca_Cx1(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(176,plain,
% 0.21/0.43 (![X: $i] : (~((~((~ca_Cx1(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(ca_Cx1(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))))) <=> ![X: $i] : (~((~((~ca_Cx1(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(ca_Cx1(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[175])).
% 0.21/0.43 tff(177,plain,
% 0.21/0.43 (^[X: $i] : rewrite((~((~((~ca_Cx1(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(ca_Cx1(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))))) <=> (~((~((~ca_Cx1(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(ca_Cx1(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(178,plain,
% 0.21/0.43 (![X: $i] : (~((~((~ca_Cx1(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(ca_Cx1(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))))) <=> ![X: $i] : (~((~((~ca_Cx1(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(ca_Cx1(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[177])).
% 0.21/0.43 tff(179,plain,
% 0.21/0.43 (![X: $i] : (~((~((~ca_Cx1(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(ca_Cx1(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))))) <=> ![X: $i] : (~((~((~ca_Cx1(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(ca_Cx1(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[178, 176])).
% 0.21/0.43 tff(180,plain,
% 0.21/0.43 (^[X: $i] : trans(monotonicity(rewrite((ca_Cx1(X) | ![Y0: $i] : (~ra_Px1(X, Y0))) <=> (ca_Cx1(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))), ((((~ca_Cx1(X)) | ra_Px1(X, tptp_fun_Y0_2(X))) & (ca_Cx1(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))) <=> (((~ca_Cx1(X)) | ra_Px1(X, tptp_fun_Y0_2(X))) & (ca_Cx1(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))))), rewrite((((~ca_Cx1(X)) | ra_Px1(X, tptp_fun_Y0_2(X))) & (ca_Cx1(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))) <=> (~((~((~ca_Cx1(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(ca_Cx1(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))), ((((~ca_Cx1(X)) | ra_Px1(X, tptp_fun_Y0_2(X))) & (ca_Cx1(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))) <=> (~((~((~ca_Cx1(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(ca_Cx1(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(181,plain,
% 0.21/0.43 (![X: $i] : (((~ca_Cx1(X)) | ra_Px1(X, tptp_fun_Y0_2(X))) & (ca_Cx1(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))) <=> ![X: $i] : (~((~((~ca_Cx1(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(ca_Cx1(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[180])).
% 0.21/0.43 tff(182,plain,
% 0.21/0.43 (![X: $i] : (ca_Cx1(X) <=> ?[Y0: $i] : ra_Px1(X, Y0)) <=> ![X: $i] : (ca_Cx1(X) <=> ?[Y0: $i] : ra_Px1(X, Y0))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(183,axiom,(![X: $i] : (ca_Cx1(X) <=> ?[Y0: $i] : ra_Px1(X, Y0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_4')).
% 0.21/0.43 tff(184,plain,
% 0.21/0.43 (![X: $i] : (ca_Cx1(X) <=> ?[Y0: $i] : ra_Px1(X, Y0))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.21/0.43 tff(185,plain,(
% 0.21/0.43 ![X: $i] : (((~ca_Cx1(X)) | ra_Px1(X, tptp_fun_Y0_2(X))) & (ca_Cx1(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))),
% 0.21/0.43 inference(skolemize,[status(sab)],[184])).
% 0.21/0.43 tff(186,plain,
% 0.21/0.43 (![X: $i] : (~((~((~ca_Cx1(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(ca_Cx1(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[185, 181])).
% 0.21/0.43 tff(187,plain,
% 0.21/0.43 (![X: $i] : (~((~((~ca_Cx1(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(ca_Cx1(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[186, 179])).
% 0.21/0.43 tff(188,plain,
% 0.21/0.43 ((~![X: $i] : (~((~((~ca_Cx1(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(ca_Cx1(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))) | (~((~((~ca_Cx1(i2003_11_14_17_21_01226)) | ra_Px1(i2003_11_14_17_21_01226, tptp_fun_Y0_2(i2003_11_14_17_21_01226)))) | (~(ca_Cx1(i2003_11_14_17_21_01226) | ![Y0: $i] : (~ra_Px1(i2003_11_14_17_21_01226, Y0))))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(189,plain,
% 0.21/0.43 (~((~((~ca_Cx1(i2003_11_14_17_21_01226)) | ra_Px1(i2003_11_14_17_21_01226, tptp_fun_Y0_2(i2003_11_14_17_21_01226)))) | (~(ca_Cx1(i2003_11_14_17_21_01226) | ![Y0: $i] : (~ra_Px1(i2003_11_14_17_21_01226, Y0)))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[188, 187])).
% 0.21/0.43 tff(190,plain,
% 0.21/0.43 (((~((~ca_Cx1(i2003_11_14_17_21_01226)) | ra_Px1(i2003_11_14_17_21_01226, tptp_fun_Y0_2(i2003_11_14_17_21_01226)))) | (~(ca_Cx1(i2003_11_14_17_21_01226) | ![Y0: $i] : (~ra_Px1(i2003_11_14_17_21_01226, Y0))))) | ((~ca_Cx1(i2003_11_14_17_21_01226)) | ra_Px1(i2003_11_14_17_21_01226, tptp_fun_Y0_2(i2003_11_14_17_21_01226)))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(191,plain,
% 0.21/0.43 ((~ca_Cx1(i2003_11_14_17_21_01226)) | ra_Px1(i2003_11_14_17_21_01226, tptp_fun_Y0_2(i2003_11_14_17_21_01226))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[190, 189])).
% 0.21/0.43 tff(192,plain,
% 0.21/0.43 (((~ca_Cx1(i2003_11_14_17_21_01226)) | (~cc1(tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~rrx3(i2003_11_14_17_21_01226, tptp_fun_Y_0(i2003_11_14_17_21_01226))) | (~rrx4(i2003_11_14_17_21_01226, tptp_fun_Y_1(i2003_11_14_17_21_01226))) | (~cc2(tptp_fun_Y_1(i2003_11_14_17_21_01226)))) | ca_Cx1(i2003_11_14_17_21_01226)),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(193,plain,
% 0.21/0.43 (ca_Cx1(i2003_11_14_17_21_01226)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[192, 81])).
% 0.21/0.43 tff(194,plain,
% 0.21/0.43 ((~((~ca_Cx1(i2003_11_14_17_21_01226)) | ra_Px1(i2003_11_14_17_21_01226, tptp_fun_Y0_2(i2003_11_14_17_21_01226)))) | (~ca_Cx1(i2003_11_14_17_21_01226)) | ra_Px1(i2003_11_14_17_21_01226, tptp_fun_Y0_2(i2003_11_14_17_21_01226))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(195,plain,
% 0.21/0.43 ((~((~ca_Cx1(i2003_11_14_17_21_01226)) | ra_Px1(i2003_11_14_17_21_01226, tptp_fun_Y0_2(i2003_11_14_17_21_01226)))) | ra_Px1(i2003_11_14_17_21_01226, tptp_fun_Y0_2(i2003_11_14_17_21_01226))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[194, 193])).
% 0.21/0.43 tff(196,plain,
% 0.21/0.43 (ra_Px1(i2003_11_14_17_21_01226, tptp_fun_Y0_2(i2003_11_14_17_21_01226))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[195, 191])).
% 0.21/0.43 tff(197,plain,
% 0.21/0.43 ((~![Y: $i] : (~ra_Px1(i2003_11_14_17_21_01226, Y))) | (~ra_Px1(i2003_11_14_17_21_01226, tptp_fun_Y0_2(i2003_11_14_17_21_01226)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(198,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[197, 196, 174])).
% 0.21/0.43 % SZS output end Proof
% 0.21/0.43 % E exiting
%------------------------------------------------------------------------------