%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS116+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:13:25 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KRS116+1 : TPTP v9.0.0. Released v3.1.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 19:11:20 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.38 % SZS status Unsatisfiable
% 0.20/0.38 % SZS output start Proof
% 0.20/0.38 tff(caxcomp_type, type, (
% 0.20/0.38 caxcomp: $i > $o)).
% 0.20/0.38 tff(i2003_11_14_17_21_33997_type, type, (
% 0.20/0.38 i2003_11_14_17_21_33997: $i)).
% 0.20/0.38 tff(ra_Px1_type, type, (
% 0.20/0.38 ra_Px1: ( $i * $i ) > $o)).
% 0.20/0.38 tff(tptp_fun_Y0_2_type, type, (
% 0.20/0.38 tptp_fun_Y0_2: $i > $i)).
% 0.20/0.38 tff(ca_type, type, (
% 0.20/0.38 ca: $i > $o)).
% 0.20/0.38 tff(tptp_fun_Y_1_type, type, (
% 0.20/0.38 tptp_fun_Y_1: $i > $i)).
% 0.20/0.38 tff(cUnsatisfiable_type, type, (
% 0.20/0.38 cUnsatisfiable: $i > $o)).
% 0.20/0.38 tff(rinvS_type, type, (
% 0.20/0.38 rinvS: ( $i * $i ) > $o)).
% 0.20/0.38 tff(tptp_fun_Y_0_type, type, (
% 0.20/0.38 tptp_fun_Y_0: $i > $i)).
% 0.20/0.38 tff(ca_Vx6_type, type, (
% 0.20/0.38 ca_Vx6: $i > $o)).
% 0.20/0.38 tff(tptp_fun_Y_10_type, type, (
% 0.20/0.38 tptp_fun_Y_10: $i > $i)).
% 0.20/0.38 tff(rinvP_type, type, (
% 0.20/0.38 rinvP: ( $i * $i ) > $o)).
% 0.20/0.38 tff(tptp_fun_Y_5_type, type, (
% 0.20/0.38 tptp_fun_Y_5: $i > $i)).
% 0.20/0.38 tff(ca_Vx7_type, type, (
% 0.20/0.38 ca_Vx7: $i > $o)).
% 0.20/0.38 tff(tptp_fun_Y_11_type, type, (
% 0.20/0.38 tptp_fun_Y_11: $i > $i)).
% 0.20/0.38 tff(rinvR_type, type, (
% 0.20/0.38 rinvR: ( $i * $i ) > $o)).
% 0.20/0.38 tff(tptp_fun_Y_4_type, type, (
% 0.20/0.38 tptp_fun_Y_4: $i > $i)).
% 0.20/0.38 tff(cc_type, type, (
% 0.20/0.38 cc: $i > $o)).
% 0.20/0.38 tff(tptp_fun_Y_3_type, type, (
% 0.20/0.38 tptp_fun_Y_3: $i > $i)).
% 0.20/0.38 tff(rr_type, type, (
% 0.20/0.38 rr: ( $i * $i ) > $o)).
% 0.20/0.38 tff(ca_Vx5_type, type, (
% 0.20/0.38 ca_Vx5: $i > $o)).
% 0.20/0.38 tff(tptp_fun_Y_8_type, type, (
% 0.20/0.38 tptp_fun_Y_8: $i > $i)).
% 0.20/0.38 tff(rp_type, type, (
% 0.20/0.38 rp: ( $i * $i ) > $o)).
% 0.20/0.38 tff(cowlThing_type, type, (
% 0.20/0.38 cowlThing: $i > $o)).
% 0.20/0.38 tff(ca_Vx3_type, type, (
% 0.20/0.38 ca_Vx3: $i > $o)).
% 0.20/0.38 tff(ca_Vx4_type, type, (
% 0.20/0.38 ca_Vx4: $i > $o)).
% 0.20/0.38 tff(ca_Ax2_type, type, (
% 0.20/0.38 ca_Ax2: $i > $o)).
% 0.20/0.38 tff(tptp_fun_Y_6_type, type, (
% 0.20/0.38 tptp_fun_Y_6: $i > $i)).
% 0.20/0.38 tff(tptp_fun_Y_7_type, type, (
% 0.20/0.38 tptp_fun_Y_7: $i > $i)).
% 0.20/0.38 tff(tptp_fun_Y_9_type, type, (
% 0.20/0.38 tptp_fun_Y_9: $i > $i)).
% 0.20/0.38 tff(rs_type, type, (
% 0.20/0.38 rs: ( $i * $i ) > $o)).
% 0.20/0.38 tff(1,assumption,((~((~caxcomp(i2003_11_14_17_21_33997)) | ra_Px1(i2003_11_14_17_21_33997, tptp_fun_Y0_2(i2003_11_14_17_21_33997)))) | (~(caxcomp(i2003_11_14_17_21_33997) | ![Y0: $i] : (~ra_Px1(i2003_11_14_17_21_33997, Y0))))), introduced(assumption)).
% 0.20/0.38 tff(2,plain,
% 0.20/0.38 (^[X: $i] : refl((~((~((~caxcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(caxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))))) <=> (~((~((~caxcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(caxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(3,plain,
% 0.20/0.38 (![X: $i] : (~((~((~caxcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(caxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))))) <=> ![X: $i] : (~((~((~caxcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(caxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.38 tff(4,plain,
% 0.20/0.38 (^[X: $i] : rewrite((~((~((~caxcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(caxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))))) <=> (~((~((~caxcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(caxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(5,plain,
% 0.20/0.38 (![X: $i] : (~((~((~caxcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(caxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))))) <=> ![X: $i] : (~((~((~caxcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(caxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.38 tff(6,plain,
% 0.20/0.38 (![X: $i] : (~((~((~caxcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(caxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))))) <=> ![X: $i] : (~((~((~caxcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(caxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))),
% 0.20/0.38 inference(transitivity,[status(thm)],[5, 3])).
% 0.20/0.38 tff(7,plain,
% 0.20/0.38 (^[X: $i] : trans(monotonicity(rewrite((caxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))) <=> (caxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))), ((((~caxcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X))) & (caxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))) <=> (((~caxcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X))) & (caxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))))), rewrite((((~caxcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X))) & (caxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))) <=> (~((~((~caxcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(caxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))), ((((~caxcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X))) & (caxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))) <=> (~((~((~caxcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(caxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(8,plain,
% 0.20/0.38 (![X: $i] : (((~caxcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X))) & (caxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))) <=> ![X: $i] : (~((~((~caxcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(caxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[7])).
% 0.20/0.38 tff(9,plain,
% 0.20/0.38 (![X: $i] : (caxcomp(X) <=> ?[Y0: $i] : ra_Px1(X, Y0)) <=> ![X: $i] : (caxcomp(X) <=> ?[Y0: $i] : ra_Px1(X, Y0))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(10,axiom,(![X: $i] : (caxcomp(X) <=> ?[Y0: $i] : ra_Px1(X, Y0))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_5')).
% 0.20/0.38 tff(11,plain,
% 0.20/0.38 (![X: $i] : (caxcomp(X) <=> ?[Y0: $i] : ra_Px1(X, Y0))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.20/0.38 tff(12,plain,(
% 0.20/0.38 ![X: $i] : (((~caxcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X))) & (caxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))),
% 0.20/0.38 inference(skolemize,[status(sab)],[11])).
% 0.20/0.38 tff(13,plain,
% 0.20/0.38 (![X: $i] : (~((~((~caxcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(caxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.20/0.38 tff(14,plain,
% 0.20/0.38 (![X: $i] : (~((~((~caxcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(caxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[13, 6])).
% 0.20/0.38 tff(15,plain,
% 0.20/0.38 ((~![X: $i] : (~((~((~caxcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(caxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))) | (~((~((~caxcomp(i2003_11_14_17_21_33997)) | ra_Px1(i2003_11_14_17_21_33997, tptp_fun_Y0_2(i2003_11_14_17_21_33997)))) | (~(caxcomp(i2003_11_14_17_21_33997) | ![Y0: $i] : (~ra_Px1(i2003_11_14_17_21_33997, Y0))))))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(16,plain,
% 0.20/0.38 ($false),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[15, 14, 1])).
% 0.20/0.38 tff(17,plain,(~((~((~caxcomp(i2003_11_14_17_21_33997)) | ra_Px1(i2003_11_14_17_21_33997, tptp_fun_Y0_2(i2003_11_14_17_21_33997)))) | (~(caxcomp(i2003_11_14_17_21_33997) | ![Y0: $i] : (~ra_Px1(i2003_11_14_17_21_33997, Y0)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.38 tff(18,plain,
% 0.20/0.38 (((~((~caxcomp(i2003_11_14_17_21_33997)) | ra_Px1(i2003_11_14_17_21_33997, tptp_fun_Y0_2(i2003_11_14_17_21_33997)))) | (~(caxcomp(i2003_11_14_17_21_33997) | ![Y0: $i] : (~ra_Px1(i2003_11_14_17_21_33997, Y0))))) | ((~caxcomp(i2003_11_14_17_21_33997)) | ra_Px1(i2003_11_14_17_21_33997, tptp_fun_Y0_2(i2003_11_14_17_21_33997)))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(19,plain,
% 0.20/0.38 ((~caxcomp(i2003_11_14_17_21_33997)) | ra_Px1(i2003_11_14_17_21_33997, tptp_fun_Y0_2(i2003_11_14_17_21_33997))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.20/0.38 tff(20,assumption,(ra_Px1(i2003_11_14_17_21_33997, tptp_fun_Y0_2(i2003_11_14_17_21_33997))), introduced(assumption)).
% 0.20/0.38 tff(21,plain,
% 0.20/0.38 (^[X: $i] : rewrite((~((~(ca(X) | ra_Px1(X, tptp_fun_Y_1(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~ca(X)))))) <=> (~((~(ca(X) | ra_Px1(X, tptp_fun_Y_1(X)))) | (~((~ca(X)) | ![Y: $i] : (~ra_Px1(X, Y)))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(22,plain,
% 0.20/0.38 (![X: $i] : (~((~(ca(X) | ra_Px1(X, tptp_fun_Y_1(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~ca(X)))))) <=> ![X: $i] : (~((~(ca(X) | ra_Px1(X, tptp_fun_Y_1(X)))) | (~((~ca(X)) | ![Y: $i] : (~ra_Px1(X, Y))))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[21])).
% 0.20/0.38 tff(23,plain,
% 0.20/0.38 (^[X: $i] : refl((~((~(ca(X) | ra_Px1(X, tptp_fun_Y_1(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~ca(X)))))) <=> (~((~(ca(X) | ra_Px1(X, tptp_fun_Y_1(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~ca(X)))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(24,plain,
% 0.20/0.38 (![X: $i] : (~((~(ca(X) | ra_Px1(X, tptp_fun_Y_1(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~ca(X)))))) <=> ![X: $i] : (~((~(ca(X) | ra_Px1(X, tptp_fun_Y_1(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~ca(X))))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[23])).
% 0.20/0.38 tff(25,plain,
% 0.20/0.38 (^[X: $i] : rewrite((~((~(ca(X) | ra_Px1(X, tptp_fun_Y_1(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~ca(X)))))) <=> (~((~(ca(X) | ra_Px1(X, tptp_fun_Y_1(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~ca(X)))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(26,plain,
% 0.20/0.38 (![X: $i] : (~((~(ca(X) | ra_Px1(X, tptp_fun_Y_1(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~ca(X)))))) <=> ![X: $i] : (~((~(ca(X) | ra_Px1(X, tptp_fun_Y_1(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~ca(X))))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[25])).
% 0.20/0.38 tff(27,plain,
% 0.20/0.38 (![X: $i] : (~((~(ca(X) | ra_Px1(X, tptp_fun_Y_1(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~ca(X)))))) <=> ![X: $i] : (~((~(ca(X) | ra_Px1(X, tptp_fun_Y_1(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~ca(X))))))),
% 0.20/0.38 inference(transitivity,[status(thm)],[26, 24])).
% 0.20/0.38 tff(28,plain,
% 0.20/0.38 (^[X: $i] : trans(monotonicity(rewrite((![Y: $i] : (~ra_Px1(X, Y)) | (~ca(X))) <=> (![Y: $i] : (~ra_Px1(X, Y)) | (~ca(X)))), (((ca(X) | ra_Px1(X, tptp_fun_Y_1(X))) & (![Y: $i] : (~ra_Px1(X, Y)) | (~ca(X)))) <=> ((ca(X) | ra_Px1(X, tptp_fun_Y_1(X))) & (![Y: $i] : (~ra_Px1(X, Y)) | (~ca(X)))))), rewrite(((ca(X) | ra_Px1(X, tptp_fun_Y_1(X))) & (![Y: $i] : (~ra_Px1(X, Y)) | (~ca(X)))) <=> (~((~(ca(X) | ra_Px1(X, tptp_fun_Y_1(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~ca(X))))))), (((ca(X) | ra_Px1(X, tptp_fun_Y_1(X))) & (![Y: $i] : (~ra_Px1(X, Y)) | (~ca(X)))) <=> (~((~(ca(X) | ra_Px1(X, tptp_fun_Y_1(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~ca(X))))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(29,plain,
% 0.20/0.38 (![X: $i] : ((ca(X) | ra_Px1(X, tptp_fun_Y_1(X))) & (![Y: $i] : (~ra_Px1(X, Y)) | (~ca(X)))) <=> ![X: $i] : (~((~(ca(X) | ra_Px1(X, tptp_fun_Y_1(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~ca(X))))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[28])).
% 0.20/0.38 tff(30,plain,
% 0.20/0.38 (^[X: $i] : rewrite(((ra_Px1(X, tptp_fun_Y_1(X)) | ca(X)) & (![Y: $i] : (~ra_Px1(X, Y)) | (~ca(X)))) <=> ((ca(X) | ra_Px1(X, tptp_fun_Y_1(X))) & (![Y: $i] : (~ra_Px1(X, Y)) | (~ca(X)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(31,plain,
% 0.20/0.38 (![X: $i] : ((ra_Px1(X, tptp_fun_Y_1(X)) | ca(X)) & (![Y: $i] : (~ra_Px1(X, Y)) | (~ca(X)))) <=> ![X: $i] : ((ca(X) | ra_Px1(X, tptp_fun_Y_1(X))) & (![Y: $i] : (~ra_Px1(X, Y)) | (~ca(X))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[30])).
% 0.20/0.38 tff(32,plain,
% 0.20/0.38 (![X: $i] : (~(?[Y: $i] : ra_Px1(X, Y) <=> ca(X))) <=> ![X: $i] : (~(?[Y: $i] : ra_Px1(X, Y) <=> ca(X)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(33,plain,
% 0.20/0.38 (^[X: $i] : trans(trans(monotonicity(rewrite((~?[Y: $i] : ra_Px1(X, Y)) <=> (~?[Y: $i] : ra_Px1(X, Y))), ((ca(X) <=> (~?[Y: $i] : ra_Px1(X, Y))) <=> (ca(X) <=> (~?[Y: $i] : ra_Px1(X, Y))))), rewrite((ca(X) <=> (~?[Y: $i] : ra_Px1(X, Y))) <=> (~(?[Y: $i] : ra_Px1(X, Y) <=> ca(X)))), ((ca(X) <=> (~?[Y: $i] : ra_Px1(X, Y))) <=> (~(?[Y: $i] : ra_Px1(X, Y) <=> ca(X))))), rewrite((~(?[Y: $i] : ra_Px1(X, Y) <=> ca(X))) <=> (~(?[Y: $i] : ra_Px1(X, Y) <=> ca(X)))), ((ca(X) <=> (~?[Y: $i] : ra_Px1(X, Y))) <=> (~(?[Y: $i] : ra_Px1(X, Y) <=> ca(X)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(34,plain,
% 0.20/0.38 (![X: $i] : (ca(X) <=> (~?[Y: $i] : ra_Px1(X, Y))) <=> ![X: $i] : (~(?[Y: $i] : ra_Px1(X, Y) <=> ca(X)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[33])).
% 0.20/0.38 tff(35,axiom,(![X: $i] : (ca(X) <=> (~?[Y: $i] : ra_Px1(X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_4')).
% 0.20/0.38 tff(36,plain,
% 0.20/0.38 (![X: $i] : (~(?[Y: $i] : ra_Px1(X, Y) <=> ca(X)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.20/0.38 tff(37,plain,
% 0.20/0.38 (![X: $i] : (~(?[Y: $i] : ra_Px1(X, Y) <=> ca(X)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.20/0.38 tff(38,plain,(
% 0.20/0.38 ![X: $i] : ((ra_Px1(X, tptp_fun_Y_1(X)) | ca(X)) & (![Y: $i] : (~ra_Px1(X, Y)) | (~ca(X))))),
% 0.20/0.38 inference(skolemize,[status(sab)],[37])).
% 0.20/0.38 tff(39,plain,
% 0.20/0.38 (![X: $i] : ((ca(X) | ra_Px1(X, tptp_fun_Y_1(X))) & (![Y: $i] : (~ra_Px1(X, Y)) | (~ca(X))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.20/0.38 tff(40,plain,
% 0.20/0.38 (![X: $i] : (~((~(ca(X) | ra_Px1(X, tptp_fun_Y_1(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~ca(X))))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[39, 29])).
% 0.20/0.38 tff(41,plain,
% 0.20/0.38 (![X: $i] : (~((~(ca(X) | ra_Px1(X, tptp_fun_Y_1(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~ca(X))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[40, 27])).
% 0.20/0.39 tff(42,plain,
% 0.20/0.39 (![X: $i] : (~((~(ca(X) | ra_Px1(X, tptp_fun_Y_1(X)))) | (~((~ca(X)) | ![Y: $i] : (~ra_Px1(X, Y))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[41, 22])).
% 0.20/0.39 tff(43,plain,
% 0.20/0.39 ((~![X: $i] : (~((~(ca(X) | ra_Px1(X, tptp_fun_Y_1(X)))) | (~((~ca(X)) | ![Y: $i] : (~ra_Px1(X, Y))))))) | (~((~(ca(i2003_11_14_17_21_33997) | ra_Px1(i2003_11_14_17_21_33997, tptp_fun_Y_1(i2003_11_14_17_21_33997)))) | (~((~ca(i2003_11_14_17_21_33997)) | ![Y: $i] : (~ra_Px1(i2003_11_14_17_21_33997, Y))))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(44,plain,
% 0.20/0.39 (~((~(ca(i2003_11_14_17_21_33997) | ra_Px1(i2003_11_14_17_21_33997, tptp_fun_Y_1(i2003_11_14_17_21_33997)))) | (~((~ca(i2003_11_14_17_21_33997)) | ![Y: $i] : (~ra_Px1(i2003_11_14_17_21_33997, Y)))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.20/0.39 tff(45,plain,
% 0.20/0.39 (((~(ca(i2003_11_14_17_21_33997) | ra_Px1(i2003_11_14_17_21_33997, tptp_fun_Y_1(i2003_11_14_17_21_33997)))) | (~((~ca(i2003_11_14_17_21_33997)) | ![Y: $i] : (~ra_Px1(i2003_11_14_17_21_33997, Y))))) | ((~ca(i2003_11_14_17_21_33997)) | ![Y: $i] : (~ra_Px1(i2003_11_14_17_21_33997, Y)))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(46,plain,
% 0.20/0.39 ((~ca(i2003_11_14_17_21_33997)) | ![Y: $i] : (~ra_Px1(i2003_11_14_17_21_33997, Y))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.20/0.39 tff(47,plain,
% 0.20/0.39 (cUnsatisfiable(i2003_11_14_17_21_33997) <=> cUnsatisfiable(i2003_11_14_17_21_33997)),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(48,axiom,(cUnsatisfiable(i2003_11_14_17_21_33997)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_17')).
% 0.20/0.39 tff(49,plain,
% 0.20/0.39 (cUnsatisfiable(i2003_11_14_17_21_33997)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.20/0.39 tff(50,plain,
% 0.20/0.39 (^[X: $i] : refl((ca(X) | (~cUnsatisfiable(X))) <=> (ca(X) | (~cUnsatisfiable(X))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(51,plain,
% 0.20/0.39 (![X: $i] : (ca(X) | (~cUnsatisfiable(X))) <=> ![X: $i] : (ca(X) | (~cUnsatisfiable(X)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[50])).
% 0.20/0.39 tff(52,plain,
% 0.20/0.39 (![X: $i] : (ca(X) | (~cUnsatisfiable(X))) <=> ![X: $i] : (ca(X) | (~cUnsatisfiable(X)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(53,plain,
% 0.20/0.39 (^[X: $i] : rewrite((cUnsatisfiable(X) => ca(X)) <=> (ca(X) | (~cUnsatisfiable(X))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(54,plain,
% 0.20/0.39 (![X: $i] : (cUnsatisfiable(X) => ca(X)) <=> ![X: $i] : (ca(X) | (~cUnsatisfiable(X)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[53])).
% 0.20/0.39 tff(55,axiom,(![X: $i] : (cUnsatisfiable(X) => ca(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_2')).
% 0.20/0.39 tff(56,plain,
% 0.20/0.39 (![X: $i] : (ca(X) | (~cUnsatisfiable(X)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.20/0.39 tff(57,plain,
% 0.20/0.39 (![X: $i] : (ca(X) | (~cUnsatisfiable(X)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.20/0.39 tff(58,plain,(
% 0.20/0.39 ![X: $i] : (ca(X) | (~cUnsatisfiable(X)))),
% 0.20/0.39 inference(skolemize,[status(sab)],[57])).
% 0.20/0.39 tff(59,plain,
% 0.20/0.39 (![X: $i] : (ca(X) | (~cUnsatisfiable(X)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.20/0.39 tff(60,plain,
% 0.20/0.39 (((~![X: $i] : (ca(X) | (~cUnsatisfiable(X)))) | (ca(i2003_11_14_17_21_33997) | (~cUnsatisfiable(i2003_11_14_17_21_33997)))) <=> ((~![X: $i] : (ca(X) | (~cUnsatisfiable(X)))) | ca(i2003_11_14_17_21_33997) | (~cUnsatisfiable(i2003_11_14_17_21_33997)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(61,plain,
% 0.20/0.39 ((~![X: $i] : (ca(X) | (~cUnsatisfiable(X)))) | (ca(i2003_11_14_17_21_33997) | (~cUnsatisfiable(i2003_11_14_17_21_33997)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(62,plain,
% 0.20/0.39 ((~![X: $i] : (ca(X) | (~cUnsatisfiable(X)))) | ca(i2003_11_14_17_21_33997) | (~cUnsatisfiable(i2003_11_14_17_21_33997))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.20/0.39 tff(63,plain,
% 0.20/0.39 (ca(i2003_11_14_17_21_33997)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[62, 59, 49])).
% 0.20/0.39 tff(64,plain,
% 0.20/0.39 ((~((~ca(i2003_11_14_17_21_33997)) | ![Y: $i] : (~ra_Px1(i2003_11_14_17_21_33997, Y)))) | (~ca(i2003_11_14_17_21_33997)) | ![Y: $i] : (~ra_Px1(i2003_11_14_17_21_33997, Y))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(65,plain,
% 0.20/0.39 ((~((~ca(i2003_11_14_17_21_33997)) | ![Y: $i] : (~ra_Px1(i2003_11_14_17_21_33997, Y)))) | ![Y: $i] : (~ra_Px1(i2003_11_14_17_21_33997, Y))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.20/0.39 tff(66,plain,
% 0.20/0.39 (![Y: $i] : (~ra_Px1(i2003_11_14_17_21_33997, Y))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[65, 46])).
% 0.20/0.39 tff(67,plain,
% 0.20/0.39 ((~![Y: $i] : (~ra_Px1(i2003_11_14_17_21_33997, Y))) | (~ra_Px1(i2003_11_14_17_21_33997, tptp_fun_Y0_2(i2003_11_14_17_21_33997)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(68,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[67, 66, 20])).
% 0.20/0.39 tff(69,plain,(~ra_Px1(i2003_11_14_17_21_33997, tptp_fun_Y0_2(i2003_11_14_17_21_33997))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(70,plain,
% 0.20/0.39 ((~((~caxcomp(i2003_11_14_17_21_33997)) | ra_Px1(i2003_11_14_17_21_33997, tptp_fun_Y0_2(i2003_11_14_17_21_33997)))) | (~caxcomp(i2003_11_14_17_21_33997)) | ra_Px1(i2003_11_14_17_21_33997, tptp_fun_Y0_2(i2003_11_14_17_21_33997))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(71,plain,
% 0.20/0.39 ((~((~caxcomp(i2003_11_14_17_21_33997)) | ra_Px1(i2003_11_14_17_21_33997, tptp_fun_Y0_2(i2003_11_14_17_21_33997)))) | (~caxcomp(i2003_11_14_17_21_33997))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.20/0.39 tff(72,plain,
% 0.20/0.39 (~caxcomp(i2003_11_14_17_21_33997)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[71, 19])).
% 0.20/0.39 tff(73,plain,
% 0.20/0.39 (^[X: $i] : refl((~((~((~ca_Vx6(X)) | ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y))))) | (~(ca_Vx6(X) | (~(caxcomp(tptp_fun_Y_10(X)) | (~rinvS(X, tptp_fun_Y_10(X))))))))) <=> (~((~((~ca_Vx6(X)) | ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y))))) | (~(ca_Vx6(X) | (~(caxcomp(tptp_fun_Y_10(X)) | (~rinvS(X, tptp_fun_Y_10(X))))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(74,plain,
% 0.20/0.39 (![X: $i] : (~((~((~ca_Vx6(X)) | ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y))))) | (~(ca_Vx6(X) | (~(caxcomp(tptp_fun_Y_10(X)) | (~rinvS(X, tptp_fun_Y_10(X))))))))) <=> ![X: $i] : (~((~((~ca_Vx6(X)) | ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y))))) | (~(ca_Vx6(X) | (~(caxcomp(tptp_fun_Y_10(X)) | (~rinvS(X, tptp_fun_Y_10(X)))))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[73])).
% 0.20/0.39 tff(75,plain,
% 0.20/0.39 (^[X: $i] : rewrite((~((~((~ca_Vx6(X)) | ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y))))) | (~(ca_Vx6(X) | (~(caxcomp(tptp_fun_Y_10(X)) | (~rinvS(X, tptp_fun_Y_10(X))))))))) <=> (~((~((~ca_Vx6(X)) | ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y))))) | (~(ca_Vx6(X) | (~(caxcomp(tptp_fun_Y_10(X)) | (~rinvS(X, tptp_fun_Y_10(X))))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(76,plain,
% 0.20/0.39 (![X: $i] : (~((~((~ca_Vx6(X)) | ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y))))) | (~(ca_Vx6(X) | (~(caxcomp(tptp_fun_Y_10(X)) | (~rinvS(X, tptp_fun_Y_10(X))))))))) <=> ![X: $i] : (~((~((~ca_Vx6(X)) | ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y))))) | (~(ca_Vx6(X) | (~(caxcomp(tptp_fun_Y_10(X)) | (~rinvS(X, tptp_fun_Y_10(X)))))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[75])).
% 0.20/0.39 tff(77,plain,
% 0.20/0.39 (![X: $i] : (~((~((~ca_Vx6(X)) | ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y))))) | (~(ca_Vx6(X) | (~(caxcomp(tptp_fun_Y_10(X)) | (~rinvS(X, tptp_fun_Y_10(X))))))))) <=> ![X: $i] : (~((~((~ca_Vx6(X)) | ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y))))) | (~(ca_Vx6(X) | (~(caxcomp(tptp_fun_Y_10(X)) | (~rinvS(X, tptp_fun_Y_10(X)))))))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[76, 74])).
% 0.20/0.39 tff(78,plain,
% 0.20/0.39 (^[X: $i] : trans(monotonicity(rewrite(((~ca_Vx6(X)) | ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y)))) <=> ((~ca_Vx6(X)) | ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y))))), ((((~ca_Vx6(X)) | ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y)))) & (ca_Vx6(X) | (~(caxcomp(tptp_fun_Y_10(X)) | (~rinvS(X, tptp_fun_Y_10(X))))))) <=> (((~ca_Vx6(X)) | ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y)))) & (ca_Vx6(X) | (~(caxcomp(tptp_fun_Y_10(X)) | (~rinvS(X, tptp_fun_Y_10(X))))))))), rewrite((((~ca_Vx6(X)) | ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y)))) & (ca_Vx6(X) | (~(caxcomp(tptp_fun_Y_10(X)) | (~rinvS(X, tptp_fun_Y_10(X))))))) <=> (~((~((~ca_Vx6(X)) | ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y))))) | (~(ca_Vx6(X) | (~(caxcomp(tptp_fun_Y_10(X)) | (~rinvS(X, tptp_fun_Y_10(X)))))))))), ((((~ca_Vx6(X)) | ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y)))) & (ca_Vx6(X) | (~(caxcomp(tptp_fun_Y_10(X)) | (~rinvS(X, tptp_fun_Y_10(X))))))) <=> (~((~((~ca_Vx6(X)) | ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y))))) | (~(ca_Vx6(X) | (~(caxcomp(tptp_fun_Y_10(X)) | (~rinvS(X, tptp_fun_Y_10(X)))))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(79,plain,
% 0.20/0.39 (![X: $i] : (((~ca_Vx6(X)) | ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y)))) & (ca_Vx6(X) | (~(caxcomp(tptp_fun_Y_10(X)) | (~rinvS(X, tptp_fun_Y_10(X))))))) <=> ![X: $i] : (~((~((~ca_Vx6(X)) | ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y))))) | (~(ca_Vx6(X) | (~(caxcomp(tptp_fun_Y_10(X)) | (~rinvS(X, tptp_fun_Y_10(X)))))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[78])).
% 0.20/0.39 tff(80,plain,
% 0.20/0.39 (![X: $i] : (ca_Vx6(X) <=> ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y)))) <=> ![X: $i] : (ca_Vx6(X) <=> ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(81,plain,
% 0.20/0.39 (^[X: $i] : rewrite((ca_Vx6(X) <=> ![Y: $i] : (rinvS(X, Y) => caxcomp(Y))) <=> (ca_Vx6(X) <=> ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(82,plain,
% 0.20/0.39 (![X: $i] : (ca_Vx6(X) <=> ![Y: $i] : (rinvS(X, Y) => caxcomp(Y))) <=> ![X: $i] : (ca_Vx6(X) <=> ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[81])).
% 0.20/0.39 tff(83,axiom,(![X: $i] : (ca_Vx6(X) <=> ![Y: $i] : (rinvS(X, Y) => caxcomp(Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_11')).
% 0.20/0.39 tff(84,plain,
% 0.20/0.39 (![X: $i] : (ca_Vx6(X) <=> ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.20/0.39 tff(85,plain,
% 0.20/0.39 (![X: $i] : (ca_Vx6(X) <=> ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.20/0.39 tff(86,plain,(
% 0.20/0.39 ![X: $i] : (((~ca_Vx6(X)) | ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y)))) & (ca_Vx6(X) | (~(caxcomp(tptp_fun_Y_10(X)) | (~rinvS(X, tptp_fun_Y_10(X)))))))),
% 0.20/0.39 inference(skolemize,[status(sab)],[85])).
% 0.20/0.39 tff(87,plain,
% 0.20/0.39 (![X: $i] : (~((~((~ca_Vx6(X)) | ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y))))) | (~(ca_Vx6(X) | (~(caxcomp(tptp_fun_Y_10(X)) | (~rinvS(X, tptp_fun_Y_10(X)))))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[86, 79])).
% 0.20/0.39 tff(88,plain,
% 0.20/0.39 (![X: $i] : (~((~((~ca_Vx6(X)) | ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y))))) | (~(ca_Vx6(X) | (~(caxcomp(tptp_fun_Y_10(X)) | (~rinvS(X, tptp_fun_Y_10(X)))))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[87, 77])).
% 0.20/0.39 tff(89,plain,
% 0.20/0.39 ((~![X: $i] : (~((~((~ca_Vx6(X)) | ![Y: $i] : (caxcomp(Y) | (~rinvS(X, Y))))) | (~(ca_Vx6(X) | (~(caxcomp(tptp_fun_Y_10(X)) | (~rinvS(X, tptp_fun_Y_10(X)))))))))) | (~((~((~ca_Vx6(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | ![Y: $i] : (caxcomp(Y) | (~rinvS(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))))) | (~(ca_Vx6(tptp_fun_Y_0(i2003_11_14_17_21_33997)) | (~(caxcomp(tptp_fun_Y_10(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rinvS(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_10(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(90,plain,
% 0.20/0.39 (~((~((~ca_Vx6(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | ![Y: $i] : (caxcomp(Y) | (~rinvS(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))))) | (~(ca_Vx6(tptp_fun_Y_0(i2003_11_14_17_21_33997)) | (~(caxcomp(tptp_fun_Y_10(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rinvS(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_10(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.20/0.39 tff(91,plain,
% 0.20/0.39 (((~((~ca_Vx6(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | ![Y: $i] : (caxcomp(Y) | (~rinvS(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))))) | (~(ca_Vx6(tptp_fun_Y_0(i2003_11_14_17_21_33997)) | (~(caxcomp(tptp_fun_Y_10(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rinvS(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_10(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))))) | ((~ca_Vx6(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | ![Y: $i] : (caxcomp(Y) | (~rinvS(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(92,plain,
% 0.20/0.39 ((~ca_Vx6(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | ![Y: $i] : (caxcomp(Y) | (~rinvS(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.20/0.39 tff(93,plain,
% 0.20/0.39 (^[X: $i] : refl((~((~((~ca_Vx7(X)) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y))))) | (~(ca_Vx7(X) | (~(ca_Vx6(tptp_fun_Y_11(X)) | (~rinvP(X, tptp_fun_Y_11(X))))))))) <=> (~((~((~ca_Vx7(X)) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y))))) | (~(ca_Vx7(X) | (~(ca_Vx6(tptp_fun_Y_11(X)) | (~rinvP(X, tptp_fun_Y_11(X))))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(94,plain,
% 0.20/0.39 (![X: $i] : (~((~((~ca_Vx7(X)) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y))))) | (~(ca_Vx7(X) | (~(ca_Vx6(tptp_fun_Y_11(X)) | (~rinvP(X, tptp_fun_Y_11(X))))))))) <=> ![X: $i] : (~((~((~ca_Vx7(X)) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y))))) | (~(ca_Vx7(X) | (~(ca_Vx6(tptp_fun_Y_11(X)) | (~rinvP(X, tptp_fun_Y_11(X)))))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[93])).
% 0.20/0.39 tff(95,plain,
% 0.20/0.39 (^[X: $i] : rewrite((~((~((~ca_Vx7(X)) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y))))) | (~(ca_Vx7(X) | (~(ca_Vx6(tptp_fun_Y_11(X)) | (~rinvP(X, tptp_fun_Y_11(X))))))))) <=> (~((~((~ca_Vx7(X)) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y))))) | (~(ca_Vx7(X) | (~(ca_Vx6(tptp_fun_Y_11(X)) | (~rinvP(X, tptp_fun_Y_11(X))))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(96,plain,
% 0.20/0.39 (![X: $i] : (~((~((~ca_Vx7(X)) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y))))) | (~(ca_Vx7(X) | (~(ca_Vx6(tptp_fun_Y_11(X)) | (~rinvP(X, tptp_fun_Y_11(X))))))))) <=> ![X: $i] : (~((~((~ca_Vx7(X)) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y))))) | (~(ca_Vx7(X) | (~(ca_Vx6(tptp_fun_Y_11(X)) | (~rinvP(X, tptp_fun_Y_11(X)))))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[95])).
% 0.20/0.39 tff(97,plain,
% 0.20/0.39 (![X: $i] : (~((~((~ca_Vx7(X)) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y))))) | (~(ca_Vx7(X) | (~(ca_Vx6(tptp_fun_Y_11(X)) | (~rinvP(X, tptp_fun_Y_11(X))))))))) <=> ![X: $i] : (~((~((~ca_Vx7(X)) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y))))) | (~(ca_Vx7(X) | (~(ca_Vx6(tptp_fun_Y_11(X)) | (~rinvP(X, tptp_fun_Y_11(X)))))))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[96, 94])).
% 0.20/0.39 tff(98,plain,
% 0.20/0.39 (^[X: $i] : trans(monotonicity(rewrite(((~ca_Vx7(X)) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y)))) <=> ((~ca_Vx7(X)) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y))))), ((((~ca_Vx7(X)) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y)))) & (ca_Vx7(X) | (~(ca_Vx6(tptp_fun_Y_11(X)) | (~rinvP(X, tptp_fun_Y_11(X))))))) <=> (((~ca_Vx7(X)) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y)))) & (ca_Vx7(X) | (~(ca_Vx6(tptp_fun_Y_11(X)) | (~rinvP(X, tptp_fun_Y_11(X))))))))), rewrite((((~ca_Vx7(X)) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y)))) & (ca_Vx7(X) | (~(ca_Vx6(tptp_fun_Y_11(X)) | (~rinvP(X, tptp_fun_Y_11(X))))))) <=> (~((~((~ca_Vx7(X)) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y))))) | (~(ca_Vx7(X) | (~(ca_Vx6(tptp_fun_Y_11(X)) | (~rinvP(X, tptp_fun_Y_11(X)))))))))), ((((~ca_Vx7(X)) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y)))) & (ca_Vx7(X) | (~(ca_Vx6(tptp_fun_Y_11(X)) | (~rinvP(X, tptp_fun_Y_11(X))))))) <=> (~((~((~ca_Vx7(X)) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y))))) | (~(ca_Vx7(X) | (~(ca_Vx6(tptp_fun_Y_11(X)) | (~rinvP(X, tptp_fun_Y_11(X)))))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(99,plain,
% 0.20/0.39 (![X: $i] : (((~ca_Vx7(X)) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y)))) & (ca_Vx7(X) | (~(ca_Vx6(tptp_fun_Y_11(X)) | (~rinvP(X, tptp_fun_Y_11(X))))))) <=> ![X: $i] : (~((~((~ca_Vx7(X)) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y))))) | (~(ca_Vx7(X) | (~(ca_Vx6(tptp_fun_Y_11(X)) | (~rinvP(X, tptp_fun_Y_11(X)))))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[98])).
% 0.20/0.39 tff(100,plain,
% 0.20/0.39 (![X: $i] : (ca_Vx7(X) <=> ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y)))) <=> ![X: $i] : (ca_Vx7(X) <=> ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(101,plain,
% 0.20/0.39 (^[X: $i] : rewrite((ca_Vx7(X) <=> ![Y: $i] : (rinvP(X, Y) => ca_Vx6(Y))) <=> (ca_Vx7(X) <=> ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(102,plain,
% 0.20/0.39 (![X: $i] : (ca_Vx7(X) <=> ![Y: $i] : (rinvP(X, Y) => ca_Vx6(Y))) <=> ![X: $i] : (ca_Vx7(X) <=> ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[101])).
% 0.20/0.39 tff(103,axiom,(![X: $i] : (ca_Vx7(X) <=> ![Y: $i] : (rinvP(X, Y) => ca_Vx6(Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_12')).
% 0.20/0.39 tff(104,plain,
% 0.20/0.39 (![X: $i] : (ca_Vx7(X) <=> ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.20/0.39 tff(105,plain,
% 0.20/0.39 (![X: $i] : (ca_Vx7(X) <=> ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[104, 100])).
% 0.20/0.39 tff(106,plain,(
% 0.20/0.39 ![X: $i] : (((~ca_Vx7(X)) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y)))) & (ca_Vx7(X) | (~(ca_Vx6(tptp_fun_Y_11(X)) | (~rinvP(X, tptp_fun_Y_11(X)))))))),
% 0.20/0.39 inference(skolemize,[status(sab)],[105])).
% 0.20/0.39 tff(107,plain,
% 0.20/0.39 (![X: $i] : (~((~((~ca_Vx7(X)) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y))))) | (~(ca_Vx7(X) | (~(ca_Vx6(tptp_fun_Y_11(X)) | (~rinvP(X, tptp_fun_Y_11(X)))))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[106, 99])).
% 0.20/0.39 tff(108,plain,
% 0.20/0.39 (![X: $i] : (~((~((~ca_Vx7(X)) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y))))) | (~(ca_Vx7(X) | (~(ca_Vx6(tptp_fun_Y_11(X)) | (~rinvP(X, tptp_fun_Y_11(X)))))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[107, 97])).
% 0.20/0.39 tff(109,plain,
% 0.20/0.39 ((~![X: $i] : (~((~((~ca_Vx7(X)) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(X, Y))))) | (~(ca_Vx7(X) | (~(ca_Vx6(tptp_fun_Y_11(X)) | (~rinvP(X, tptp_fun_Y_11(X)))))))))) | (~((~((~ca_Vx7(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y))))) | (~(ca_Vx7(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~(ca_Vx6(tptp_fun_Y_11(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rinvP(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_11(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))))))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(110,plain,
% 0.20/0.39 (~((~((~ca_Vx7(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y))))) | (~(ca_Vx7(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~(ca_Vx6(tptp_fun_Y_11(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rinvP(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_11(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[109, 108])).
% 0.20/0.39 tff(111,plain,
% 0.20/0.39 (((~((~ca_Vx7(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y))))) | (~(ca_Vx7(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~(ca_Vx6(tptp_fun_Y_11(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rinvP(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_11(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))))))) | ((~ca_Vx7(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y))))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(112,plain,
% 0.20/0.39 ((~ca_Vx7(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y)))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.20/0.39 tff(113,plain,
% 0.20/0.39 (^[X: $i] : refl((~((~((~cc(X)) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y))))) | (~(cc(X) | (~(ca_Vx7(tptp_fun_Y_3(X)) | (~rinvR(X, tptp_fun_Y_3(X))))))))) <=> (~((~((~cc(X)) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y))))) | (~(cc(X) | (~(ca_Vx7(tptp_fun_Y_3(X)) | (~rinvR(X, tptp_fun_Y_3(X))))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(114,plain,
% 0.20/0.39 (![X: $i] : (~((~((~cc(X)) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y))))) | (~(cc(X) | (~(ca_Vx7(tptp_fun_Y_3(X)) | (~rinvR(X, tptp_fun_Y_3(X))))))))) <=> ![X: $i] : (~((~((~cc(X)) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y))))) | (~(cc(X) | (~(ca_Vx7(tptp_fun_Y_3(X)) | (~rinvR(X, tptp_fun_Y_3(X)))))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[113])).
% 0.20/0.39 tff(115,plain,
% 0.20/0.39 (^[X: $i] : rewrite((~((~((~cc(X)) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y))))) | (~(cc(X) | (~(ca_Vx7(tptp_fun_Y_3(X)) | (~rinvR(X, tptp_fun_Y_3(X))))))))) <=> (~((~((~cc(X)) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y))))) | (~(cc(X) | (~(ca_Vx7(tptp_fun_Y_3(X)) | (~rinvR(X, tptp_fun_Y_3(X))))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(116,plain,
% 0.20/0.39 (![X: $i] : (~((~((~cc(X)) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y))))) | (~(cc(X) | (~(ca_Vx7(tptp_fun_Y_3(X)) | (~rinvR(X, tptp_fun_Y_3(X))))))))) <=> ![X: $i] : (~((~((~cc(X)) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y))))) | (~(cc(X) | (~(ca_Vx7(tptp_fun_Y_3(X)) | (~rinvR(X, tptp_fun_Y_3(X)))))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[115])).
% 0.20/0.39 tff(117,plain,
% 0.20/0.39 (![X: $i] : (~((~((~cc(X)) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y))))) | (~(cc(X) | (~(ca_Vx7(tptp_fun_Y_3(X)) | (~rinvR(X, tptp_fun_Y_3(X))))))))) <=> ![X: $i] : (~((~((~cc(X)) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y))))) | (~(cc(X) | (~(ca_Vx7(tptp_fun_Y_3(X)) | (~rinvR(X, tptp_fun_Y_3(X)))))))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[116, 114])).
% 0.20/0.39 tff(118,plain,
% 0.20/0.39 (^[X: $i] : trans(monotonicity(rewrite(((~cc(X)) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y)))) <=> ((~cc(X)) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y))))), ((((~cc(X)) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y)))) & (cc(X) | (~(ca_Vx7(tptp_fun_Y_3(X)) | (~rinvR(X, tptp_fun_Y_3(X))))))) <=> (((~cc(X)) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y)))) & (cc(X) | (~(ca_Vx7(tptp_fun_Y_3(X)) | (~rinvR(X, tptp_fun_Y_3(X))))))))), rewrite((((~cc(X)) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y)))) & (cc(X) | (~(ca_Vx7(tptp_fun_Y_3(X)) | (~rinvR(X, tptp_fun_Y_3(X))))))) <=> (~((~((~cc(X)) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y))))) | (~(cc(X) | (~(ca_Vx7(tptp_fun_Y_3(X)) | (~rinvR(X, tptp_fun_Y_3(X)))))))))), ((((~cc(X)) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y)))) & (cc(X) | (~(ca_Vx7(tptp_fun_Y_3(X)) | (~rinvR(X, tptp_fun_Y_3(X))))))) <=> (~((~((~cc(X)) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y))))) | (~(cc(X) | (~(ca_Vx7(tptp_fun_Y_3(X)) | (~rinvR(X, tptp_fun_Y_3(X)))))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(119,plain,
% 0.20/0.39 (![X: $i] : (((~cc(X)) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y)))) & (cc(X) | (~(ca_Vx7(tptp_fun_Y_3(X)) | (~rinvR(X, tptp_fun_Y_3(X))))))) <=> ![X: $i] : (~((~((~cc(X)) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y))))) | (~(cc(X) | (~(ca_Vx7(tptp_fun_Y_3(X)) | (~rinvR(X, tptp_fun_Y_3(X)))))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[118])).
% 0.20/0.39 tff(120,plain,
% 0.20/0.39 (![X: $i] : (cc(X) <=> ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y)))) <=> ![X: $i] : (cc(X) <=> ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(121,plain,
% 0.20/0.39 (^[X: $i] : rewrite((cc(X) <=> ![Y: $i] : (rinvR(X, Y) => ca_Vx7(Y))) <=> (cc(X) <=> ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(122,plain,
% 0.20/0.39 (![X: $i] : (cc(X) <=> ![Y: $i] : (rinvR(X, Y) => ca_Vx7(Y))) <=> ![X: $i] : (cc(X) <=> ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[121])).
% 0.20/0.39 tff(123,axiom,(![X: $i] : (cc(X) <=> ![Y: $i] : (rinvR(X, Y) => ca_Vx7(Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_6')).
% 0.20/0.39 tff(124,plain,
% 0.20/0.39 (![X: $i] : (cc(X) <=> ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.20/0.39 tff(125,plain,
% 0.20/0.39 (![X: $i] : (cc(X) <=> ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[124, 120])).
% 0.20/0.39 tff(126,plain,(
% 0.20/0.39 ![X: $i] : (((~cc(X)) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y)))) & (cc(X) | (~(ca_Vx7(tptp_fun_Y_3(X)) | (~rinvR(X, tptp_fun_Y_3(X)))))))),
% 0.20/0.39 inference(skolemize,[status(sab)],[125])).
% 0.20/0.39 tff(127,plain,
% 0.20/0.39 (![X: $i] : (~((~((~cc(X)) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y))))) | (~(cc(X) | (~(ca_Vx7(tptp_fun_Y_3(X)) | (~rinvR(X, tptp_fun_Y_3(X)))))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[126, 119])).
% 0.20/0.39 tff(128,plain,
% 0.20/0.39 (![X: $i] : (~((~((~cc(X)) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y))))) | (~(cc(X) | (~(ca_Vx7(tptp_fun_Y_3(X)) | (~rinvR(X, tptp_fun_Y_3(X)))))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[127, 117])).
% 0.20/0.39 tff(129,plain,
% 0.20/0.39 ((~![X: $i] : (~((~((~cc(X)) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(X, Y))))) | (~(cc(X) | (~(ca_Vx7(tptp_fun_Y_3(X)) | (~rinvR(X, tptp_fun_Y_3(X)))))))))) | (~((~((~cc(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))), Y))))) | (~(cc(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~(ca_Vx7(tptp_fun_Y_3(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | (~rinvR(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))), tptp_fun_Y_3(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))))))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(130,plain,
% 0.20/0.40 (~((~((~cc(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))), Y))))) | (~(cc(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~(ca_Vx7(tptp_fun_Y_3(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | (~rinvR(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))), tptp_fun_Y_3(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))))))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[129, 128])).
% 0.20/0.40 tff(131,plain,
% 0.20/0.40 (((~((~cc(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))), Y))))) | (~(cc(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~(ca_Vx7(tptp_fun_Y_3(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | (~rinvR(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))), tptp_fun_Y_3(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))))))) | ((~cc(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))), Y))))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(132,plain,
% 0.20/0.40 ((~cc(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))), Y)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[131, 130])).
% 0.20/0.40 tff(133,plain,
% 0.20/0.40 (^[X: $i] : refl((~((~((~ca_Vx5(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))) | (~(ca_Vx5(X) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))))))) <=> (~((~((~ca_Vx5(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))) | (~(ca_Vx5(X) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(134,plain,
% 0.20/0.40 (![X: $i] : (~((~((~ca_Vx5(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))) | (~(ca_Vx5(X) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))))))) <=> ![X: $i] : (~((~((~ca_Vx5(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))) | (~(ca_Vx5(X) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X)))))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[133])).
% 0.20/0.40 tff(135,plain,
% 0.20/0.40 (^[X: $i] : rewrite((~((~((~ca_Vx5(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))) | (~(ca_Vx5(X) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))))))) <=> (~((~((~ca_Vx5(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))) | (~(ca_Vx5(X) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(136,plain,
% 0.20/0.40 (![X: $i] : (~((~((~ca_Vx5(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))) | (~(ca_Vx5(X) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))))))) <=> ![X: $i] : (~((~((~ca_Vx5(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))) | (~(ca_Vx5(X) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X)))))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[135])).
% 0.20/0.40 tff(137,plain,
% 0.20/0.40 (![X: $i] : (~((~((~ca_Vx5(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))) | (~(ca_Vx5(X) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))))))) <=> ![X: $i] : (~((~((~ca_Vx5(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))) | (~(ca_Vx5(X) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X)))))))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[136, 134])).
% 0.20/0.40 tff(138,plain,
% 0.20/0.40 (^[X: $i] : trans(monotonicity(rewrite(((~ca_Vx5(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y)))) <=> ((~ca_Vx5(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))), ((((~ca_Vx5(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y)))) & (ca_Vx5(X) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))))) <=> (((~ca_Vx5(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y)))) & (ca_Vx5(X) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))))))), rewrite((((~ca_Vx5(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y)))) & (ca_Vx5(X) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))))) <=> (~((~((~ca_Vx5(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))) | (~(ca_Vx5(X) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X)))))))))), ((((~ca_Vx5(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y)))) & (ca_Vx5(X) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))))) <=> (~((~((~ca_Vx5(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))) | (~(ca_Vx5(X) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X)))))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(139,plain,
% 0.20/0.40 (![X: $i] : (((~ca_Vx5(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y)))) & (ca_Vx5(X) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))))) <=> ![X: $i] : (~((~((~ca_Vx5(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))) | (~(ca_Vx5(X) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X)))))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[138])).
% 0.20/0.40 tff(140,plain,
% 0.20/0.40 (![X: $i] : (ca_Vx5(X) <=> ![Y: $i] : (cc(Y) | (~rr(X, Y)))) <=> ![X: $i] : (ca_Vx5(X) <=> ![Y: $i] : (cc(Y) | (~rr(X, Y))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(141,plain,
% 0.20/0.40 (^[X: $i] : rewrite((ca_Vx5(X) <=> ![Y: $i] : (rr(X, Y) => cc(Y))) <=> (ca_Vx5(X) <=> ![Y: $i] : (cc(Y) | (~rr(X, Y)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(142,plain,
% 0.20/0.40 (![X: $i] : (ca_Vx5(X) <=> ![Y: $i] : (rr(X, Y) => cc(Y))) <=> ![X: $i] : (ca_Vx5(X) <=> ![Y: $i] : (cc(Y) | (~rr(X, Y))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[141])).
% 0.20/0.40 tff(143,axiom,(![X: $i] : (ca_Vx5(X) <=> ![Y: $i] : (rr(X, Y) => cc(Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_10')).
% 0.20/0.40 tff(144,plain,
% 0.20/0.40 (![X: $i] : (ca_Vx5(X) <=> ![Y: $i] : (cc(Y) | (~rr(X, Y))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.20/0.40 tff(145,plain,
% 0.20/0.40 (![X: $i] : (ca_Vx5(X) <=> ![Y: $i] : (cc(Y) | (~rr(X, Y))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[144, 140])).
% 0.20/0.40 tff(146,plain,(
% 0.20/0.40 ![X: $i] : (((~ca_Vx5(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y)))) & (ca_Vx5(X) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X)))))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[145])).
% 0.20/0.40 tff(147,plain,
% 0.20/0.40 (![X: $i] : (~((~((~ca_Vx5(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))) | (~(ca_Vx5(X) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X)))))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[146, 139])).
% 0.20/0.40 tff(148,plain,
% 0.20/0.40 (![X: $i] : (~((~((~ca_Vx5(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))) | (~(ca_Vx5(X) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X)))))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[147, 137])).
% 0.20/0.40 tff(149,plain,
% 0.20/0.40 ((~![X: $i] : (~((~((~ca_Vx5(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))) | (~(ca_Vx5(X) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X)))))))))) | (~((~((~ca_Vx5(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | ![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y))))) | (~(ca_Vx5(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~(cc(tptp_fun_Y_8(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_8(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))))))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(150,plain,
% 0.20/0.40 (~((~((~ca_Vx5(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | ![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y))))) | (~(ca_Vx5(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~(cc(tptp_fun_Y_8(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_8(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[149, 148])).
% 0.20/0.40 tff(151,plain,
% 0.20/0.40 (((~((~ca_Vx5(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | ![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y))))) | (~(ca_Vx5(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~(cc(tptp_fun_Y_8(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_8(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))))))) | ((~ca_Vx5(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | ![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y))))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(152,plain,
% 0.20/0.40 ((~ca_Vx5(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | ![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[151, 150])).
% 0.20/0.40 tff(153,plain,
% 0.20/0.40 (^[X: $i] : rewrite((~((~((~ca_Ax2(X)) | (~((~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y)))) | (~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))))))) | (~(ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y))))))) <=> (~((~(ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y))))) | (~((~ca_Ax2(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y)))))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(154,plain,
% 0.20/0.40 (![X: $i] : (~((~((~ca_Ax2(X)) | (~((~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y)))) | (~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))))))) | (~(ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y))))))) <=> ![X: $i] : (~((~(ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y))))) | (~((~ca_Ax2(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y))))))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[153])).
% 0.20/0.40 tff(155,plain,
% 0.20/0.40 (^[X: $i] : refl((~((~((~ca_Ax2(X)) | (~((~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y)))) | (~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))))))) | (~(ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y))))))) <=> (~((~((~ca_Ax2(X)) | (~((~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y)))) | (~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))))))) | (~(ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(156,plain,
% 0.20/0.40 (![X: $i] : (~((~((~ca_Ax2(X)) | (~((~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y)))) | (~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))))))) | (~(ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y))))))) <=> ![X: $i] : (~((~((~ca_Ax2(X)) | (~((~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y)))) | (~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))))))) | (~(ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y)))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[155])).
% 0.20/0.40 tff(157,plain,
% 0.20/0.40 (^[X: $i] : rewrite((~((~((~ca_Ax2(X)) | (~((~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y)))) | (~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))))))) | (~(ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y))))))) <=> (~((~((~ca_Ax2(X)) | (~((~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y)))) | (~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))))))) | (~(ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(158,plain,
% 0.20/0.40 (![X: $i] : (~((~((~ca_Ax2(X)) | (~((~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y)))) | (~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))))))) | (~(ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y))))))) <=> ![X: $i] : (~((~((~ca_Ax2(X)) | (~((~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y)))) | (~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))))))) | (~(ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y)))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[157])).
% 0.20/0.40 tff(159,plain,
% 0.20/0.40 (![X: $i] : (~((~((~ca_Ax2(X)) | (~((~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y)))) | (~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))))))) | (~(ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y))))))) <=> ![X: $i] : (~((~((~ca_Ax2(X)) | (~((~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y)))) | (~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))))))) | (~(ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y)))))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[158, 156])).
% 0.20/0.40 tff(160,plain,
% 0.20/0.40 (^[X: $i] : trans(monotonicity(rewrite(((~ca_Ax2(X)) | (![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y))) & ![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y))) & ![Y: $i] : (cc(Y) | (~rr(X, Y))) & rr(X, tptp_fun_Y_4(X)) & cowlThing(tptp_fun_Y_4(X)) & rp(X, tptp_fun_Y_5(X)) & cowlThing(tptp_fun_Y_5(X)) & ![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y))))) <=> ((~ca_Ax2(X)) | (~((~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y)))) | (~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))))))), trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(rewrite((rr(X, Y) & cowlThing(Y)) <=> (~((~rr(X, Y)) | (~cowlThing(Y))))), ((~(rr(X, Y) & cowlThing(Y))) <=> (~(~((~rr(X, Y)) | (~cowlThing(Y))))))), rewrite((~(~((~rr(X, Y)) | (~cowlThing(Y))))) <=> ((~rr(X, Y)) | (~cowlThing(Y)))), ((~(rr(X, Y) & cowlThing(Y))) <=> ((~rr(X, Y)) | (~cowlThing(Y)))))), (![Y: $i] : (~(rr(X, Y) & cowlThing(Y))) <=> ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))))), quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(rewrite((rp(X, Y) & cowlThing(Y)) <=> (~((~rp(X, Y)) | (~cowlThing(Y))))), ((~(rp(X, Y) & cowlThing(Y))) <=> (~(~((~rp(X, Y)) | (~cowlThing(Y))))))), rewrite((~(~((~rp(X, Y)) | (~cowlThing(Y))))) <=> ((~rp(X, Y)) | (~cowlThing(Y)))), ((~(rp(X, Y) & cowlThing(Y))) <=> ((~rp(X, Y)) | (~cowlThing(Y)))))), (![Y: $i] : (~(rp(X, Y) & cowlThing(Y))) <=> ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y))))), ((ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | ![Y: $i] : (~(rr(X, Y) & cowlThing(Y))) | ![Y: $i] : (~(rp(X, Y) & cowlThing(Y))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X)))))) <=> (ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X)))))))), rewrite((ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X)))))) <=> (ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y))))), ((ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | ![Y: $i] : (~(rr(X, Y) & cowlThing(Y))) | ![Y: $i] : (~(rp(X, Y) & cowlThing(Y))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X)))))) <=> (ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y)))))), ((((~ca_Ax2(X)) | (![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y))) & ![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y))) & ![Y: $i] : (cc(Y) | (~rr(X, Y))) & rr(X, tptp_fun_Y_4(X)) & cowlThing(tptp_fun_Y_4(X)) & rp(X, tptp_fun_Y_5(X)) & cowlThing(tptp_fun_Y_5(X)) & ![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y))))) & (ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | ![Y: $i] : (~(rr(X, Y) & cowlThing(Y))) | ![Y: $i] : (~(rp(X, Y) & cowlThing(Y))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))))) <=> (((~ca_Ax2(X)) | (~((~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y)))) | (~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X)))))) & (ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y))))))), rewrite((((~ca_Ax2(X)) | (~((~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y)))) | (~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X)))))) & (ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y))))) <=> (~((~((~ca_Ax2(X)) | (~((~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y)))) | (~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))))))) | (~(ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y)))))))), ((((~ca_Ax2(X)) | (![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y))) & ![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y))) & ![Y: $i] : (cc(Y) | (~rr(X, Y))) & rr(X, tptp_fun_Y_4(X)) & cowlThing(tptp_fun_Y_4(X)) & rp(X, tptp_fun_Y_5(X)) & cowlThing(tptp_fun_Y_5(X)) & ![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y))))) & (ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | ![Y: $i] : (~(rr(X, Y) & cowlThing(Y))) | ![Y: $i] : (~(rp(X, Y) & cowlThing(Y))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))))) <=> (~((~((~ca_Ax2(X)) | (~((~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y)))) | (~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))))))) | (~(ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y)))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(161,plain,
% 0.20/0.41 (![X: $i] : (((~ca_Ax2(X)) | (![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y))) & ![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y))) & ![Y: $i] : (cc(Y) | (~rr(X, Y))) & rr(X, tptp_fun_Y_4(X)) & cowlThing(tptp_fun_Y_4(X)) & rp(X, tptp_fun_Y_5(X)) & cowlThing(tptp_fun_Y_5(X)) & ![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y))))) & (ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | ![Y: $i] : (~(rr(X, Y) & cowlThing(Y))) | ![Y: $i] : (~(rp(X, Y) & cowlThing(Y))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))))) <=> ![X: $i] : (~((~((~ca_Ax2(X)) | (~((~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y)))) | (~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))))))) | (~(ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y)))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[160])).
% 0.20/0.41 tff(162,plain,
% 0.20/0.41 (^[X: $i] : rewrite((((~ca_Ax2(X)) | (![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y))) & ![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y))) & ![Y: $i] : (cc(Y) | (~rr(X, Y))) & (rr(X, tptp_fun_Y_4(X)) & cowlThing(tptp_fun_Y_4(X))) & (rp(X, tptp_fun_Y_5(X)) & cowlThing(tptp_fun_Y_5(X))) & ![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y))))) & (ca_Ax2(X) | ((~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | ![Y: $i] : (~(rr(X, Y) & cowlThing(Y))) | ![Y: $i] : (~(rp(X, Y) & cowlThing(Y))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X)))))))) <=> (((~ca_Ax2(X)) | (![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y))) & ![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y))) & ![Y: $i] : (cc(Y) | (~rr(X, Y))) & rr(X, tptp_fun_Y_4(X)) & cowlThing(tptp_fun_Y_4(X)) & rp(X, tptp_fun_Y_5(X)) & cowlThing(tptp_fun_Y_5(X)) & ![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y))))) & (ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | ![Y: $i] : (~(rr(X, Y) & cowlThing(Y))) | ![Y: $i] : (~(rp(X, Y) & cowlThing(Y))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(163,plain,
% 0.20/0.41 (![X: $i] : (((~ca_Ax2(X)) | (![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y))) & ![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y))) & ![Y: $i] : (cc(Y) | (~rr(X, Y))) & (rr(X, tptp_fun_Y_4(X)) & cowlThing(tptp_fun_Y_4(X))) & (rp(X, tptp_fun_Y_5(X)) & cowlThing(tptp_fun_Y_5(X))) & ![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y))))) & (ca_Ax2(X) | ((~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | ![Y: $i] : (~(rr(X, Y) & cowlThing(Y))) | ![Y: $i] : (~(rp(X, Y) & cowlThing(Y))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X)))))))) <=> ![X: $i] : (((~ca_Ax2(X)) | (![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y))) & ![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y))) & ![Y: $i] : (cc(Y) | (~rr(X, Y))) & rr(X, tptp_fun_Y_4(X)) & cowlThing(tptp_fun_Y_4(X)) & rp(X, tptp_fun_Y_5(X)) & cowlThing(tptp_fun_Y_5(X)) & ![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y))))) & (ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | ![Y: $i] : (~(rr(X, Y) & cowlThing(Y))) | ![Y: $i] : (~(rp(X, Y) & cowlThing(Y))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X)))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[162])).
% 0.20/0.41 tff(164,plain,
% 0.20/0.41 (![X: $i] : (ca_Ax2(X) <=> (![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y))) & ![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y))) & ![Y: $i] : (cc(Y) | (~rr(X, Y))) & ?[Y: $i] : (rr(X, Y) & cowlThing(Y)) & ?[Y: $i] : (rp(X, Y) & cowlThing(Y)) & ![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y))))) <=> ![X: $i] : (ca_Ax2(X) <=> (![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y))) & ![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y))) & ![Y: $i] : (cc(Y) | (~rr(X, Y))) & ?[Y: $i] : (rr(X, Y) & cowlThing(Y)) & ?[Y: $i] : (rp(X, Y) & cowlThing(Y)) & ![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y)))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(165,plain,
% 0.20/0.41 (^[X: $i] : rewrite((ca_Ax2(X) <=> (((((![Y: $i] : (rp(X, Y) => ca_Vx3(Y)) & ![Y: $i] : (rp(X, Y) => ca_Vx5(Y))) & ![Y: $i] : (rr(X, Y) => cc(Y))) & ?[Y: $i] : (rr(X, Y) & cowlThing(Y))) & ?[Y: $i] : (rp(X, Y) & cowlThing(Y))) & ![Y: $i] : (rp(X, Y) => ca_Vx4(Y)))) <=> (ca_Ax2(X) <=> (![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y))) & ![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y))) & ![Y: $i] : (cc(Y) | (~rr(X, Y))) & ?[Y: $i] : (rr(X, Y) & cowlThing(Y)) & ?[Y: $i] : (rp(X, Y) & cowlThing(Y)) & ![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(166,plain,
% 0.20/0.41 (![X: $i] : (ca_Ax2(X) <=> (((((![Y: $i] : (rp(X, Y) => ca_Vx3(Y)) & ![Y: $i] : (rp(X, Y) => ca_Vx5(Y))) & ![Y: $i] : (rr(X, Y) => cc(Y))) & ?[Y: $i] : (rr(X, Y) & cowlThing(Y))) & ?[Y: $i] : (rp(X, Y) & cowlThing(Y))) & ![Y: $i] : (rp(X, Y) => ca_Vx4(Y)))) <=> ![X: $i] : (ca_Ax2(X) <=> (![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y))) & ![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y))) & ![Y: $i] : (cc(Y) | (~rr(X, Y))) & ?[Y: $i] : (rr(X, Y) & cowlThing(Y)) & ?[Y: $i] : (rp(X, Y) & cowlThing(Y)) & ![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y)))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[165])).
% 0.20/0.41 tff(167,axiom,(![X: $i] : (ca_Ax2(X) <=> (((((![Y: $i] : (rp(X, Y) => ca_Vx3(Y)) & ![Y: $i] : (rp(X, Y) => ca_Vx5(Y))) & ![Y: $i] : (rr(X, Y) => cc(Y))) & ?[Y: $i] : (rr(X, Y) & cowlThing(Y))) & ?[Y: $i] : (rp(X, Y) & cowlThing(Y))) & ![Y: $i] : (rp(X, Y) => ca_Vx4(Y))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_7')).
% 0.20/0.41 tff(168,plain,
% 0.20/0.41 (![X: $i] : (ca_Ax2(X) <=> (![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y))) & ![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y))) & ![Y: $i] : (cc(Y) | (~rr(X, Y))) & ?[Y: $i] : (rr(X, Y) & cowlThing(Y)) & ?[Y: $i] : (rp(X, Y) & cowlThing(Y)) & ![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.20/0.41 tff(169,plain,
% 0.20/0.41 (![X: $i] : (ca_Ax2(X) <=> (![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y))) & ![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y))) & ![Y: $i] : (cc(Y) | (~rr(X, Y))) & ?[Y: $i] : (rr(X, Y) & cowlThing(Y)) & ?[Y: $i] : (rp(X, Y) & cowlThing(Y)) & ![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[168, 164])).
% 0.20/0.41 tff(170,plain,(
% 0.20/0.41 ![X: $i] : (((~ca_Ax2(X)) | (![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y))) & ![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y))) & ![Y: $i] : (cc(Y) | (~rr(X, Y))) & (rr(X, tptp_fun_Y_4(X)) & cowlThing(tptp_fun_Y_4(X))) & (rp(X, tptp_fun_Y_5(X)) & cowlThing(tptp_fun_Y_5(X))) & ![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y))))) & (ca_Ax2(X) | ((~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | ![Y: $i] : (~(rr(X, Y) & cowlThing(Y))) | ![Y: $i] : (~(rp(X, Y) & cowlThing(Y))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[169])).
% 0.20/0.41 tff(171,plain,
% 0.20/0.41 (![X: $i] : (((~ca_Ax2(X)) | (![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y))) & ![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y))) & ![Y: $i] : (cc(Y) | (~rr(X, Y))) & rr(X, tptp_fun_Y_4(X)) & cowlThing(tptp_fun_Y_4(X)) & rp(X, tptp_fun_Y_5(X)) & cowlThing(tptp_fun_Y_5(X)) & ![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y))))) & (ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | ![Y: $i] : (~(rr(X, Y) & cowlThing(Y))) | ![Y: $i] : (~(rp(X, Y) & cowlThing(Y))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X)))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[170, 163])).
% 0.20/0.41 tff(172,plain,
% 0.20/0.41 (![X: $i] : (~((~((~ca_Ax2(X)) | (~((~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y)))) | (~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))))))) | (~(ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y)))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[171, 161])).
% 0.20/0.41 tff(173,plain,
% 0.20/0.41 (![X: $i] : (~((~((~ca_Ax2(X)) | (~((~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y)))) | (~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))))))) | (~(ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y)))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[172, 159])).
% 0.20/0.41 tff(174,plain,
% 0.20/0.41 (![X: $i] : (~((~(ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y))))) | (~((~ca_Ax2(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y))))))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[173, 154])).
% 0.20/0.41 tff(175,plain,
% 0.20/0.41 (((~![X: $i] : (~((~(ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y))))) | (~((~ca_Ax2(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y))))))))))) | (~((~(ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997)) | (~(ca_Vx4(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(cc(tptp_fun_Y_8(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_8(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(ca_Vx5(tptp_fun_Y_7(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_7(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(ca_Vx3(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))) | ![Y: $i] : ((~cowlThing(Y)) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))))) | (~((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~((~![Y: $i] : (ca_Vx4(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~cowlThing(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))))))) <=> ((~![X: $i] : (~((~(ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y))))) | (~((~ca_Ax2(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y))))))))))) | (~((~(ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997)) | (~(ca_Vx4(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(cc(tptp_fun_Y_8(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_8(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(ca_Vx5(tptp_fun_Y_7(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_7(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(ca_Vx3(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))) | ![Y: $i] : ((~cowlThing(Y)) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))))) | (~((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~((~![Y: $i] : (ca_Vx4(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~cowlThing(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(176,plain,
% 0.20/0.42 ((~((~(ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997)) | (~(ca_Vx3(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(ca_Vx5(tptp_fun_Y_7(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_7(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(cc(tptp_fun_Y_8(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_8(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(ca_Vx4(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | ![Y: $i] : ((~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)) | (~cowlThing(Y))))) | (~((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~((~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))))))))) <=> (~((~(ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997)) | (~(ca_Vx4(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(cc(tptp_fun_Y_8(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_8(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(ca_Vx5(tptp_fun_Y_7(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_7(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(ca_Vx3(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))) | ![Y: $i] : ((~cowlThing(Y)) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))))) | (~((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~((~![Y: $i] : (ca_Vx4(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~cowlThing(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(177,plain,
% 0.20/0.42 (((~![X: $i] : (~((~(ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y))))) | (~((~ca_Ax2(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y))))))))))) | (~((~(ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997)) | (~(ca_Vx3(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(ca_Vx5(tptp_fun_Y_7(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_7(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(cc(tptp_fun_Y_8(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_8(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(ca_Vx4(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | ![Y: $i] : ((~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)) | (~cowlThing(Y))))) | (~((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~((~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))))))))))) <=> ((~![X: $i] : (~((~(ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y))))) | (~((~ca_Ax2(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y))))))))))) | (~((~(ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997)) | (~(ca_Vx4(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(cc(tptp_fun_Y_8(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_8(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(ca_Vx5(tptp_fun_Y_7(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_7(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(ca_Vx3(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))) | ![Y: $i] : ((~cowlThing(Y)) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))))) | (~((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~((~![Y: $i] : (ca_Vx4(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~cowlThing(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))))))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[176])).
% 0.20/0.42 tff(178,plain,
% 0.20/0.42 (((~![X: $i] : (~((~(ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y))))) | (~((~ca_Ax2(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y))))))))))) | (~((~(ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997)) | (~(ca_Vx3(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(ca_Vx5(tptp_fun_Y_7(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_7(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(cc(tptp_fun_Y_8(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_8(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(ca_Vx4(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | ![Y: $i] : ((~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)) | (~cowlThing(Y))))) | (~((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~((~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))))))))))) <=> ((~![X: $i] : (~((~(ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y))))) | (~((~ca_Ax2(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y))))))))))) | (~((~(ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997)) | (~(ca_Vx4(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(cc(tptp_fun_Y_8(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_8(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(ca_Vx5(tptp_fun_Y_7(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_7(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(ca_Vx3(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))) | ![Y: $i] : ((~cowlThing(Y)) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))))) | (~((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~((~![Y: $i] : (ca_Vx4(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~cowlThing(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[177, 175])).
% 0.20/0.42 tff(179,plain,
% 0.20/0.42 ((~![X: $i] : (~((~(ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y))))) | (~((~ca_Ax2(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y))))))))))) | (~((~(ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997)) | (~(ca_Vx3(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(ca_Vx5(tptp_fun_Y_7(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_7(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(cc(tptp_fun_Y_8(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_8(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(ca_Vx4(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | ![Y: $i] : ((~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)) | (~cowlThing(Y))))) | (~((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~((~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))))))))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(180,plain,
% 0.20/0.42 ((~![X: $i] : (~((~(ca_Ax2(X) | (~(ca_Vx3(tptp_fun_Y_6(X)) | (~rp(X, tptp_fun_Y_6(X))))) | (~(ca_Vx5(tptp_fun_Y_7(X)) | (~rp(X, tptp_fun_Y_7(X))))) | (~(cc(tptp_fun_Y_8(X)) | (~rr(X, tptp_fun_Y_8(X))))) | (~(ca_Vx4(tptp_fun_Y_9(X)) | (~rp(X, tptp_fun_Y_9(X))))) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))) | ![Y: $i] : ((~rp(X, Y)) | (~cowlThing(Y))))) | (~((~ca_Ax2(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))) | (~rp(X, tptp_fun_Y_5(X))) | (~cowlThing(tptp_fun_Y_5(X))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(X, Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(X, Y)))) | (~![Y: $i] : (cc(Y) | (~rr(X, Y)))) | (~![Y: $i] : (ca_Vx4(Y) | (~rp(X, Y))))))))))) | (~((~(ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997)) | (~(ca_Vx4(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(cc(tptp_fun_Y_8(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_8(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(ca_Vx5(tptp_fun_Y_7(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_7(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(ca_Vx3(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))) | ![Y: $i] : ((~cowlThing(Y)) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))))) | (~((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~((~![Y: $i] : (ca_Vx4(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~cowlThing(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[179, 178])).
% 0.20/0.42 tff(181,plain,
% 0.20/0.42 (~((~(ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997)) | (~(ca_Vx4(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(cc(tptp_fun_Y_8(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_8(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(ca_Vx5(tptp_fun_Y_7(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_7(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(ca_Vx3(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))) | ![Y: $i] : ((~cowlThing(Y)) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))))) | (~((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~((~![Y: $i] : (ca_Vx4(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~cowlThing(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[180, 174])).
% 0.20/0.42 tff(182,plain,
% 0.20/0.42 (((~(ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997)) | (~(ca_Vx4(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(cc(tptp_fun_Y_8(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_8(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(ca_Vx5(tptp_fun_Y_7(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_7(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | (~(ca_Vx3(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))) | ![Y: $i] : ((~cowlThing(Y)) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))))) | (~((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~((~![Y: $i] : (ca_Vx4(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~cowlThing(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))))) | ((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~((~![Y: $i] : (ca_Vx4(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~cowlThing(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(183,plain,
% 0.20/0.43 ((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~((~![Y: $i] : (ca_Vx4(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~cowlThing(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[182, 181])).
% 0.20/0.43 tff(184,plain,
% 0.20/0.43 (^[X: $i] : refl(((~cUnsatisfiable(X)) | (~((~rs(X, tptp_fun_Y_0(X))) | (~ca_Ax2(tptp_fun_Y_0(X)))))) <=> ((~cUnsatisfiable(X)) | (~((~rs(X, tptp_fun_Y_0(X))) | (~ca_Ax2(tptp_fun_Y_0(X)))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(185,plain,
% 0.20/0.43 (![X: $i] : ((~cUnsatisfiable(X)) | (~((~rs(X, tptp_fun_Y_0(X))) | (~ca_Ax2(tptp_fun_Y_0(X)))))) <=> ![X: $i] : ((~cUnsatisfiable(X)) | (~((~rs(X, tptp_fun_Y_0(X))) | (~ca_Ax2(tptp_fun_Y_0(X))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[184])).
% 0.20/0.43 tff(186,plain,
% 0.20/0.43 (^[X: $i] : rewrite(((~cUnsatisfiable(X)) | (rs(X, tptp_fun_Y_0(X)) & ca_Ax2(tptp_fun_Y_0(X)))) <=> ((~cUnsatisfiable(X)) | (~((~rs(X, tptp_fun_Y_0(X))) | (~ca_Ax2(tptp_fun_Y_0(X)))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(187,plain,
% 0.20/0.43 (![X: $i] : ((~cUnsatisfiable(X)) | (rs(X, tptp_fun_Y_0(X)) & ca_Ax2(tptp_fun_Y_0(X)))) <=> ![X: $i] : ((~cUnsatisfiable(X)) | (~((~rs(X, tptp_fun_Y_0(X))) | (~ca_Ax2(tptp_fun_Y_0(X))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[186])).
% 0.20/0.43 tff(188,plain,
% 0.20/0.43 (![X: $i] : ((~cUnsatisfiable(X)) | ?[Y: $i] : (rs(X, Y) & ca_Ax2(Y))) <=> ![X: $i] : ((~cUnsatisfiable(X)) | ?[Y: $i] : (rs(X, Y) & ca_Ax2(Y)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(189,plain,
% 0.20/0.43 (^[X: $i] : rewrite((cUnsatisfiable(X) => ?[Y: $i] : (rs(X, Y) & ca_Ax2(Y))) <=> ((~cUnsatisfiable(X)) | ?[Y: $i] : (rs(X, Y) & ca_Ax2(Y))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(190,plain,
% 0.20/0.43 (![X: $i] : (cUnsatisfiable(X) => ?[Y: $i] : (rs(X, Y) & ca_Ax2(Y))) <=> ![X: $i] : ((~cUnsatisfiable(X)) | ?[Y: $i] : (rs(X, Y) & ca_Ax2(Y)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[189])).
% 0.20/0.43 tff(191,axiom,(![X: $i] : (cUnsatisfiable(X) => ?[Y: $i] : (rs(X, Y) & ca_Ax2(Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_3')).
% 0.20/0.43 tff(192,plain,
% 0.20/0.43 (![X: $i] : ((~cUnsatisfiable(X)) | ?[Y: $i] : (rs(X, Y) & ca_Ax2(Y)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.20/0.43 tff(193,plain,
% 0.20/0.43 (![X: $i] : ((~cUnsatisfiable(X)) | ?[Y: $i] : (rs(X, Y) & ca_Ax2(Y)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[192, 188])).
% 0.20/0.43 tff(194,plain,(
% 0.20/0.43 ![X: $i] : ((~cUnsatisfiable(X)) | (rs(X, tptp_fun_Y_0(X)) & ca_Ax2(tptp_fun_Y_0(X))))),
% 0.20/0.43 inference(skolemize,[status(sab)],[193])).
% 0.20/0.43 tff(195,plain,
% 0.20/0.43 (![X: $i] : ((~cUnsatisfiable(X)) | (~((~rs(X, tptp_fun_Y_0(X))) | (~ca_Ax2(tptp_fun_Y_0(X))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[194, 187])).
% 0.20/0.43 tff(196,plain,
% 0.20/0.43 (![X: $i] : ((~cUnsatisfiable(X)) | (~((~rs(X, tptp_fun_Y_0(X))) | (~ca_Ax2(tptp_fun_Y_0(X))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[195, 185])).
% 0.20/0.43 tff(197,plain,
% 0.20/0.43 (((~![X: $i] : ((~cUnsatisfiable(X)) | (~((~rs(X, tptp_fun_Y_0(X))) | (~ca_Ax2(tptp_fun_Y_0(X))))))) | ((~cUnsatisfiable(i2003_11_14_17_21_33997)) | (~((~rs(i2003_11_14_17_21_33997, tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))) <=> ((~![X: $i] : ((~cUnsatisfiable(X)) | (~((~rs(X, tptp_fun_Y_0(X))) | (~ca_Ax2(tptp_fun_Y_0(X))))))) | (~cUnsatisfiable(i2003_11_14_17_21_33997)) | (~((~rs(i2003_11_14_17_21_33997, tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(198,plain,
% 0.20/0.43 ((~![X: $i] : ((~cUnsatisfiable(X)) | (~((~rs(X, tptp_fun_Y_0(X))) | (~ca_Ax2(tptp_fun_Y_0(X))))))) | ((~cUnsatisfiable(i2003_11_14_17_21_33997)) | (~((~rs(i2003_11_14_17_21_33997, tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(199,plain,
% 0.20/0.43 ((~![X: $i] : ((~cUnsatisfiable(X)) | (~((~rs(X, tptp_fun_Y_0(X))) | (~ca_Ax2(tptp_fun_Y_0(X))))))) | (~cUnsatisfiable(i2003_11_14_17_21_33997)) | (~((~rs(i2003_11_14_17_21_33997, tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.20/0.43 tff(200,plain,
% 0.20/0.43 (~((~rs(i2003_11_14_17_21_33997, tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[199, 196, 49])).
% 0.20/0.43 tff(201,plain,
% 0.20/0.43 (((~rs(i2003_11_14_17_21_33997, tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(202,plain,
% 0.20/0.43 (ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[201, 200])).
% 0.20/0.43 tff(203,plain,
% 0.20/0.43 ((~((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~((~![Y: $i] : (ca_Vx4(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~cowlThing(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))))) | (~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~((~![Y: $i] : (ca_Vx4(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~cowlThing(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(204,plain,
% 0.20/0.43 ((~((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~((~![Y: $i] : (ca_Vx4(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~cowlThing(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))))) | (~((~![Y: $i] : (ca_Vx4(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~cowlThing(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[203, 202])).
% 0.20/0.43 tff(205,plain,
% 0.20/0.43 (~((~![Y: $i] : (ca_Vx4(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~cowlThing(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[204, 183])).
% 0.20/0.43 tff(206,plain,
% 0.20/0.43 (((~![Y: $i] : (ca_Vx4(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~cowlThing(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(207,plain,
% 0.20/0.43 (rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[206, 205])).
% 0.20/0.43 tff(208,plain,
% 0.20/0.43 (((~![Y: $i] : (ca_Vx4(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~cowlThing(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | ![Y: $i] : (ca_Vx5(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(209,plain,
% 0.20/0.43 (![Y: $i] : (ca_Vx5(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[208, 205])).
% 0.20/0.43 tff(210,plain,
% 0.20/0.43 (((~![Y: $i] : (ca_Vx5(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (ca_Vx5(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) <=> ((~![Y: $i] : (ca_Vx5(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | ca_Vx5(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(211,plain,
% 0.20/0.43 ((~![Y: $i] : (ca_Vx5(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (ca_Vx5(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(212,plain,
% 0.20/0.43 ((~![Y: $i] : (ca_Vx5(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | ca_Vx5(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[211, 210])).
% 0.20/0.43 tff(213,plain,
% 0.20/0.43 (ca_Vx5(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[212, 209, 207])).
% 0.20/0.43 tff(214,plain,
% 0.20/0.43 ((~((~ca_Vx5(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | ![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y))))) | (~ca_Vx5(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | ![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y)))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(215,plain,
% 0.20/0.43 ((~((~ca_Vx5(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | ![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y))))) | ![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[214, 213])).
% 0.20/0.43 tff(216,plain,
% 0.20/0.43 (![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[215, 152])).
% 0.20/0.43 tff(217,plain,
% 0.20/0.43 (^[X: $i] : refl((~((~((~ca_Vx3(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))))))) <=> (~((~((~ca_Vx3(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(218,plain,
% 0.20/0.43 (![X: $i] : (~((~((~ca_Vx3(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))))))) <=> ![X: $i] : (~((~((~ca_Vx3(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y)))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[217])).
% 0.20/0.43 tff(219,plain,
% 0.20/0.43 (^[X: $i] : rewrite((~((~((~ca_Vx3(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))))))) <=> (~((~((~ca_Vx3(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(220,plain,
% 0.20/0.43 (![X: $i] : (~((~((~ca_Vx3(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))))))) <=> ![X: $i] : (~((~((~ca_Vx3(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y)))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[219])).
% 0.20/0.43 tff(221,plain,
% 0.20/0.43 (![X: $i] : (~((~((~ca_Vx3(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))))))) <=> ![X: $i] : (~((~((~ca_Vx3(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y)))))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[220, 218])).
% 0.20/0.43 tff(222,plain,
% 0.20/0.43 (^[X: $i] : trans(monotonicity(rewrite(((~ca_Vx3(X)) | (rr(X, tptp_fun_Y_4(X)) & cowlThing(tptp_fun_Y_4(X)))) <=> ((~ca_Vx3(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))))))), rewrite((ca_Vx3(X) | ![Y: $i] : (~(rr(X, Y) & cowlThing(Y)))) <=> (ca_Vx3(X) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))))), ((((~ca_Vx3(X)) | (rr(X, tptp_fun_Y_4(X)) & cowlThing(tptp_fun_Y_4(X)))) & (ca_Vx3(X) | ![Y: $i] : (~(rr(X, Y) & cowlThing(Y))))) <=> (((~ca_Vx3(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X)))))) & (ca_Vx3(X) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))))))), rewrite((((~ca_Vx3(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X)))))) & (ca_Vx3(X) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y))))) <=> (~((~((~ca_Vx3(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y)))))))), ((((~ca_Vx3(X)) | (rr(X, tptp_fun_Y_4(X)) & cowlThing(tptp_fun_Y_4(X)))) & (ca_Vx3(X) | ![Y: $i] : (~(rr(X, Y) & cowlThing(Y))))) <=> (~((~((~ca_Vx3(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y)))))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(223,plain,
% 0.20/0.43 (![X: $i] : (((~ca_Vx3(X)) | (rr(X, tptp_fun_Y_4(X)) & cowlThing(tptp_fun_Y_4(X)))) & (ca_Vx3(X) | ![Y: $i] : (~(rr(X, Y) & cowlThing(Y))))) <=> ![X: $i] : (~((~((~ca_Vx3(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y)))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[222])).
% 0.20/0.43 tff(224,plain,
% 0.20/0.43 (![X: $i] : (ca_Vx3(X) <=> ?[Y: $i] : (rr(X, Y) & cowlThing(Y))) <=> ![X: $i] : (ca_Vx3(X) <=> ?[Y: $i] : (rr(X, Y) & cowlThing(Y)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(225,axiom,(![X: $i] : (ca_Vx3(X) <=> ?[Y: $i] : (rr(X, Y) & cowlThing(Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_8')).
% 0.20/0.43 tff(226,plain,
% 0.20/0.43 (![X: $i] : (ca_Vx3(X) <=> ?[Y: $i] : (rr(X, Y) & cowlThing(Y)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.20/0.43 tff(227,plain,(
% 0.20/0.43 ![X: $i] : (((~ca_Vx3(X)) | (rr(X, tptp_fun_Y_4(X)) & cowlThing(tptp_fun_Y_4(X)))) & (ca_Vx3(X) | ![Y: $i] : (~(rr(X, Y) & cowlThing(Y)))))),
% 0.20/0.43 inference(skolemize,[status(sab)],[226])).
% 0.20/0.43 tff(228,plain,
% 0.20/0.43 (![X: $i] : (~((~((~ca_Vx3(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y)))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[227, 223])).
% 0.20/0.43 tff(229,plain,
% 0.20/0.43 (![X: $i] : (~((~((~ca_Vx3(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y)))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[228, 221])).
% 0.20/0.43 tff(230,plain,
% 0.20/0.43 (((~![X: $i] : (~((~((~ca_Vx3(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y)))))))) | (~((~((~ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~((~cowlThing(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))))) | (~(ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y)))))))) <=> ((~![X: $i] : (~((~((~ca_Vx3(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y)))))))) | (~((~((~ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~((~cowlThing(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))))) | (~(ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y))))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(231,plain,
% 0.20/0.43 ((~((~((~ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~((~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))))) | (~(ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | ![Y: $i] : ((~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y)) | (~cowlThing(Y))))))) <=> (~((~((~ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~((~cowlThing(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))))) | (~(ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y)))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(232,plain,
% 0.20/0.43 (((~![X: $i] : (~((~((~ca_Vx3(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y)))))))) | (~((~((~ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~((~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))))) | (~(ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | ![Y: $i] : ((~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y)) | (~cowlThing(Y)))))))) <=> ((~![X: $i] : (~((~((~ca_Vx3(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y)))))))) | (~((~((~ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~((~cowlThing(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))))) | (~(ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y))))))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[231])).
% 0.20/0.43 tff(233,plain,
% 0.20/0.43 (((~![X: $i] : (~((~((~ca_Vx3(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y)))))))) | (~((~((~ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~((~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))))) | (~(ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | ![Y: $i] : ((~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y)) | (~cowlThing(Y)))))))) <=> ((~![X: $i] : (~((~((~ca_Vx3(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y)))))))) | (~((~((~ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~((~cowlThing(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))))) | (~(ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y))))))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[232, 230])).
% 0.20/0.43 tff(234,plain,
% 0.20/0.43 ((~![X: $i] : (~((~((~ca_Vx3(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y)))))))) | (~((~((~ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~((~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))))) | (~(ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | ![Y: $i] : ((~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y)) | (~cowlThing(Y)))))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(235,plain,
% 0.20/0.43 ((~![X: $i] : (~((~((~ca_Vx3(X)) | (~((~rr(X, tptp_fun_Y_4(X))) | (~cowlThing(tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rr(X, Y)) | (~cowlThing(Y)))))))) | (~((~((~ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~((~cowlThing(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))))) | (~(ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y)))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[234, 233])).
% 0.20/0.44 tff(236,plain,
% 0.20/0.44 (~((~((~ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~((~cowlThing(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))))) | (~(ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y))))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[235, 229])).
% 0.20/0.44 tff(237,plain,
% 0.20/0.44 (((~((~ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~((~cowlThing(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))))) | (~(ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y)))))) | ((~ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~((~cowlThing(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(238,plain,
% 0.20/0.44 ((~ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~((~cowlThing(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[237, 236])).
% 0.20/0.44 tff(239,plain,
% 0.20/0.44 (((~![Y: $i] : (ca_Vx4(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx5(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~![Y: $i] : (ca_Vx3(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (~cowlThing(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~cowlThing(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rr(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | ![Y: $i] : (ca_Vx3(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(240,plain,
% 0.20/0.44 (![Y: $i] : (ca_Vx3(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[239, 205])).
% 0.20/0.44 tff(241,plain,
% 0.20/0.44 (((~![Y: $i] : (ca_Vx3(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) <=> ((~![Y: $i] : (ca_Vx3(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(242,plain,
% 0.20/0.44 ((~![Y: $i] : (ca_Vx3(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(243,plain,
% 0.20/0.44 ((~![Y: $i] : (ca_Vx3(Y) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[242, 241])).
% 0.20/0.44 tff(244,plain,
% 0.20/0.44 (ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[243, 240, 207])).
% 0.20/0.44 tff(245,plain,
% 0.20/0.44 ((~((~ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~((~cowlThing(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))))) | (~ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~((~cowlThing(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(246,plain,
% 0.20/0.44 ((~((~ca_Vx3(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~((~cowlThing(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))))) | (~((~cowlThing(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[245, 244])).
% 0.20/0.44 tff(247,plain,
% 0.20/0.44 (~((~cowlThing(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[246, 238])).
% 0.20/0.44 tff(248,plain,
% 0.20/0.44 (((~cowlThing(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(249,plain,
% 0.20/0.44 (rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[248, 247])).
% 0.20/0.44 tff(250,plain,
% 0.20/0.44 (((~![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y)))) | (cc(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))) <=> ((~![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y)))) | cc(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(251,plain,
% 0.20/0.44 ((~![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y)))) | (cc(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(252,plain,
% 0.20/0.44 ((~![Y: $i] : (cc(Y) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y)))) | cc(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.20/0.44 tff(253,plain,
% 0.20/0.44 (cc(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[252, 249, 216])).
% 0.20/0.44 tff(254,plain,
% 0.20/0.44 ((~((~cc(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))), Y))))) | (~cc(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))), Y)))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(255,plain,
% 0.20/0.44 ((~((~cc(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))), Y))))) | ![Y: $i] : (ca_Vx7(Y) | (~rinvR(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))), Y)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[254, 253])).
% 0.20/0.44 tff(256,plain,
% 0.20/0.44 (![Y: $i] : (ca_Vx7(Y) | (~rinvR(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))), Y)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[255, 132])).
% 0.20/0.44 tff(257,plain,
% 0.20/0.44 (^[X: $i, Y: $i] : refl((rinvR(X, Y) <=> rr(Y, X)) <=> (rinvR(X, Y) <=> rr(Y, X)))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(258,plain,
% 0.20/0.44 (![X: $i, Y: $i] : (rinvR(X, Y) <=> rr(Y, X)) <=> ![X: $i, Y: $i] : (rinvR(X, Y) <=> rr(Y, X))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[257])).
% 0.20/0.44 tff(259,plain,
% 0.20/0.44 (![X: $i, Y: $i] : (rinvR(X, Y) <=> rr(Y, X)) <=> ![X: $i, Y: $i] : (rinvR(X, Y) <=> rr(Y, X))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(260,axiom,(![X: $i, Y: $i] : (rinvR(X, Y) <=> rr(Y, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_14')).
% 0.20/0.44 tff(261,plain,
% 0.20/0.44 (![X: $i, Y: $i] : (rinvR(X, Y) <=> rr(Y, X))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[260, 259])).
% 0.20/0.44 tff(262,plain,(
% 0.20/0.44 ![X: $i, Y: $i] : (rinvR(X, Y) <=> rr(Y, X))),
% 0.20/0.44 inference(skolemize,[status(sab)],[261])).
% 0.20/0.44 tff(263,plain,
% 0.20/0.44 (![X: $i, Y: $i] : (rinvR(X, Y) <=> rr(Y, X))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[262, 258])).
% 0.20/0.44 tff(264,plain,
% 0.20/0.44 ((~![X: $i, Y: $i] : (rinvR(X, Y) <=> rr(Y, X))) | (rinvR(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) <=> rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(265,plain,
% 0.20/0.44 (rinvR(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) <=> rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[264, 263])).
% 0.20/0.44 tff(266,plain,
% 0.20/0.44 ((~(rinvR(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) <=> rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | rinvR(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(267,plain,
% 0.20/0.44 ((~(rinvR(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) <=> rr(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) | rinvR(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[266, 249])).
% 0.20/0.44 tff(268,plain,
% 0.20/0.44 (rinvR(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[267, 265])).
% 0.20/0.44 tff(269,plain,
% 0.20/0.44 (((~![Y: $i] : (ca_Vx7(Y) | (~rinvR(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))), Y)))) | (ca_Vx7(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rinvR(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))) <=> ((~![Y: $i] : (ca_Vx7(Y) | (~rinvR(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))), Y)))) | ca_Vx7(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rinvR(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(270,plain,
% 0.20/0.44 ((~![Y: $i] : (ca_Vx7(Y) | (~rinvR(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))), Y)))) | (ca_Vx7(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rinvR(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(271,plain,
% 0.20/0.44 ((~![Y: $i] : (ca_Vx7(Y) | (~rinvR(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))), Y)))) | ca_Vx7(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~rinvR(tptp_fun_Y_4(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[270, 269])).
% 0.20/0.44 tff(272,plain,
% 0.20/0.44 (ca_Vx7(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[271, 268, 256])).
% 0.20/0.44 tff(273,plain,
% 0.20/0.44 ((~((~ca_Vx7(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y))))) | (~ca_Vx7(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y)))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(274,plain,
% 0.20/0.44 ((~((~ca_Vx7(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y))))) | ![Y: $i] : (ca_Vx6(Y) | (~rinvP(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[273, 272])).
% 0.20/0.44 tff(275,plain,
% 0.20/0.44 (![Y: $i] : (ca_Vx6(Y) | (~rinvP(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[274, 112])).
% 0.20/0.44 tff(276,plain,
% 0.20/0.44 (^[X: $i, Y: $i] : refl((rinvP(X, Y) <=> rp(Y, X)) <=> (rinvP(X, Y) <=> rp(Y, X)))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(277,plain,
% 0.20/0.44 (![X: $i, Y: $i] : (rinvP(X, Y) <=> rp(Y, X)) <=> ![X: $i, Y: $i] : (rinvP(X, Y) <=> rp(Y, X))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[276])).
% 0.20/0.44 tff(278,plain,
% 0.20/0.44 (![X: $i, Y: $i] : (rinvP(X, Y) <=> rp(Y, X)) <=> ![X: $i, Y: $i] : (rinvP(X, Y) <=> rp(Y, X))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(279,axiom,(![X: $i, Y: $i] : (rinvP(X, Y) <=> rp(Y, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_13')).
% 0.20/0.44 tff(280,plain,
% 0.20/0.44 (![X: $i, Y: $i] : (rinvP(X, Y) <=> rp(Y, X))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[279, 278])).
% 0.20/0.44 tff(281,plain,(
% 0.20/0.44 ![X: $i, Y: $i] : (rinvP(X, Y) <=> rp(Y, X))),
% 0.20/0.44 inference(skolemize,[status(sab)],[280])).
% 0.20/0.44 tff(282,plain,
% 0.20/0.44 (![X: $i, Y: $i] : (rinvP(X, Y) <=> rp(Y, X))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[281, 277])).
% 0.20/0.44 tff(283,plain,
% 0.20/0.44 ((~![X: $i, Y: $i] : (rinvP(X, Y) <=> rp(Y, X))) | (rinvP(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_0(i2003_11_14_17_21_33997)) <=> rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(284,plain,
% 0.20/0.44 (rinvP(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_0(i2003_11_14_17_21_33997)) <=> rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[283, 282])).
% 0.20/0.44 tff(285,plain,
% 0.20/0.44 ((~(rinvP(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_0(i2003_11_14_17_21_33997)) <=> rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | rinvP(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_0(i2003_11_14_17_21_33997)) | (~rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(286,plain,
% 0.20/0.44 ((~(rinvP(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_0(i2003_11_14_17_21_33997)) <=> rp(tptp_fun_Y_0(i2003_11_14_17_21_33997), tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997))))) | rinvP(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_0(i2003_11_14_17_21_33997))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[285, 207])).
% 0.20/0.44 tff(287,plain,
% 0.20/0.44 (rinvP(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_0(i2003_11_14_17_21_33997))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[286, 284])).
% 0.20/0.44 tff(288,plain,
% 0.20/0.44 (((~![Y: $i] : (ca_Vx6(Y) | (~rinvP(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y)))) | (ca_Vx6(tptp_fun_Y_0(i2003_11_14_17_21_33997)) | (~rinvP(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_0(i2003_11_14_17_21_33997))))) <=> ((~![Y: $i] : (ca_Vx6(Y) | (~rinvP(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y)))) | ca_Vx6(tptp_fun_Y_0(i2003_11_14_17_21_33997)) | (~rinvP(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_0(i2003_11_14_17_21_33997))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(289,plain,
% 0.20/0.44 ((~![Y: $i] : (ca_Vx6(Y) | (~rinvP(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y)))) | (ca_Vx6(tptp_fun_Y_0(i2003_11_14_17_21_33997)) | (~rinvP(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_0(i2003_11_14_17_21_33997))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(290,plain,
% 0.20/0.44 ((~![Y: $i] : (ca_Vx6(Y) | (~rinvP(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), Y)))) | ca_Vx6(tptp_fun_Y_0(i2003_11_14_17_21_33997)) | (~rinvP(tptp_fun_Y_5(tptp_fun_Y_0(i2003_11_14_17_21_33997)), tptp_fun_Y_0(i2003_11_14_17_21_33997)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[289, 288])).
% 0.20/0.44 tff(291,plain,
% 0.20/0.44 (ca_Vx6(tptp_fun_Y_0(i2003_11_14_17_21_33997))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[290, 287, 275])).
% 0.20/0.44 tff(292,plain,
% 0.20/0.44 ((~((~ca_Vx6(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | ![Y: $i] : (caxcomp(Y) | (~rinvS(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))))) | (~ca_Vx6(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | ![Y: $i] : (caxcomp(Y) | (~rinvS(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(293,plain,
% 0.20/0.44 ((~((~ca_Vx6(tptp_fun_Y_0(i2003_11_14_17_21_33997))) | ![Y: $i] : (caxcomp(Y) | (~rinvS(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y))))) | ![Y: $i] : (caxcomp(Y) | (~rinvS(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[292, 291])).
% 0.20/0.44 tff(294,plain,
% 0.20/0.44 (![Y: $i] : (caxcomp(Y) | (~rinvS(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[293, 92])).
% 0.20/0.44 tff(295,plain,
% 0.20/0.44 (^[X: $i, Y: $i] : refl((rinvS(X, Y) <=> rs(Y, X)) <=> (rinvS(X, Y) <=> rs(Y, X)))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(296,plain,
% 0.20/0.44 (![X: $i, Y: $i] : (rinvS(X, Y) <=> rs(Y, X)) <=> ![X: $i, Y: $i] : (rinvS(X, Y) <=> rs(Y, X))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[295])).
% 0.20/0.44 tff(297,plain,
% 0.20/0.44 (![X: $i, Y: $i] : (rinvS(X, Y) <=> rs(Y, X)) <=> ![X: $i, Y: $i] : (rinvS(X, Y) <=> rs(Y, X))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(298,axiom,(![X: $i, Y: $i] : (rinvS(X, Y) <=> rs(Y, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_15')).
% 0.20/0.44 tff(299,plain,
% 0.20/0.44 (![X: $i, Y: $i] : (rinvS(X, Y) <=> rs(Y, X))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[298, 297])).
% 0.20/0.44 tff(300,plain,(
% 0.20/0.44 ![X: $i, Y: $i] : (rinvS(X, Y) <=> rs(Y, X))),
% 0.20/0.44 inference(skolemize,[status(sab)],[299])).
% 0.20/0.44 tff(301,plain,
% 0.20/0.44 (![X: $i, Y: $i] : (rinvS(X, Y) <=> rs(Y, X))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[300, 296])).
% 0.20/0.44 tff(302,plain,
% 0.20/0.44 ((~![X: $i, Y: $i] : (rinvS(X, Y) <=> rs(Y, X))) | (rinvS(tptp_fun_Y_0(i2003_11_14_17_21_33997), i2003_11_14_17_21_33997) <=> rs(i2003_11_14_17_21_33997, tptp_fun_Y_0(i2003_11_14_17_21_33997)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(303,plain,
% 0.20/0.44 (rinvS(tptp_fun_Y_0(i2003_11_14_17_21_33997), i2003_11_14_17_21_33997) <=> rs(i2003_11_14_17_21_33997, tptp_fun_Y_0(i2003_11_14_17_21_33997))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[302, 301])).
% 0.20/0.44 tff(304,plain,
% 0.20/0.44 (((~rs(i2003_11_14_17_21_33997, tptp_fun_Y_0(i2003_11_14_17_21_33997))) | (~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | rs(i2003_11_14_17_21_33997, tptp_fun_Y_0(i2003_11_14_17_21_33997))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(305,plain,
% 0.20/0.45 (rs(i2003_11_14_17_21_33997, tptp_fun_Y_0(i2003_11_14_17_21_33997))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[304, 200])).
% 0.20/0.45 tff(306,plain,
% 0.20/0.45 ((~(rinvS(tptp_fun_Y_0(i2003_11_14_17_21_33997), i2003_11_14_17_21_33997) <=> rs(i2003_11_14_17_21_33997, tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | rinvS(tptp_fun_Y_0(i2003_11_14_17_21_33997), i2003_11_14_17_21_33997) | (~rs(i2003_11_14_17_21_33997, tptp_fun_Y_0(i2003_11_14_17_21_33997)))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(307,plain,
% 0.20/0.45 ((~(rinvS(tptp_fun_Y_0(i2003_11_14_17_21_33997), i2003_11_14_17_21_33997) <=> rs(i2003_11_14_17_21_33997, tptp_fun_Y_0(i2003_11_14_17_21_33997)))) | rinvS(tptp_fun_Y_0(i2003_11_14_17_21_33997), i2003_11_14_17_21_33997)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[306, 305])).
% 0.20/0.45 tff(308,plain,
% 0.20/0.45 (rinvS(tptp_fun_Y_0(i2003_11_14_17_21_33997), i2003_11_14_17_21_33997)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[307, 303])).
% 0.20/0.45 tff(309,plain,
% 0.20/0.45 (((~![Y: $i] : (caxcomp(Y) | (~rinvS(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (caxcomp(i2003_11_14_17_21_33997) | (~rinvS(tptp_fun_Y_0(i2003_11_14_17_21_33997), i2003_11_14_17_21_33997)))) <=> ((~![Y: $i] : (caxcomp(Y) | (~rinvS(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | caxcomp(i2003_11_14_17_21_33997) | (~rinvS(tptp_fun_Y_0(i2003_11_14_17_21_33997), i2003_11_14_17_21_33997)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(310,plain,
% 0.20/0.45 ((~![Y: $i] : (caxcomp(Y) | (~rinvS(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | (caxcomp(i2003_11_14_17_21_33997) | (~rinvS(tptp_fun_Y_0(i2003_11_14_17_21_33997), i2003_11_14_17_21_33997)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(311,plain,
% 0.20/0.45 ((~![Y: $i] : (caxcomp(Y) | (~rinvS(tptp_fun_Y_0(i2003_11_14_17_21_33997), Y)))) | caxcomp(i2003_11_14_17_21_33997) | (~rinvS(tptp_fun_Y_0(i2003_11_14_17_21_33997), i2003_11_14_17_21_33997))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[310, 309])).
% 0.20/0.45 tff(312,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[311, 308, 294, 72])).
% 0.20/0.45 % SZS output end Proof
% 0.20/0.45 % E exiting
%------------------------------------------------------------------------------