%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS120+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:13:26 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KRS120+1 : TPTP v9.0.0. Released v3.1.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 19:11:41 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.42 % SZS status Unsatisfiable
% 0.20/0.42 % SZS output start Proof
% 0.20/0.42 tff(ca_Ax2_type, type, (
% 0.20/0.42 ca_Ax2: $i > $o)).
% 0.20/0.42 tff(tptp_fun_Y_0_type, type, (
% 0.20/0.42 tptp_fun_Y_0: $i > $i)).
% 0.20/0.42 tff(i2003_11_14_17_21_48796_type, type, (
% 0.20/0.42 i2003_11_14_17_21_48796: $i)).
% 0.20/0.42 tff(tptp_fun_Y_4_type, type, (
% 0.20/0.42 tptp_fun_Y_4: $i > $i)).
% 0.20/0.42 tff(tptp_fun_Y_3_type, type, (
% 0.20/0.42 tptp_fun_Y_3: $i > $i)).
% 0.20/0.42 tff(rf_type, type, (
% 0.20/0.42 rf: ( $i * $i ) > $o)).
% 0.20/0.42 tff(cowlThing_type, type, (
% 0.20/0.42 cowlThing: $i > $o)).
% 0.20/0.42 tff(cowlNothing_type, type, (
% 0.20/0.42 cowlNothing: $i > $o)).
% 0.20/0.42 tff(cp1xcomp_type, type, (
% 0.20/0.42 cp1xcomp: $i > $o)).
% 0.20/0.42 tff(ca_Vx3_type, type, (
% 0.20/0.42 ca_Vx3: $i > $o)).
% 0.20/0.42 tff(rinvF_type, type, (
% 0.20/0.42 rinvF: ( $i * $i ) > $o)).
% 0.20/0.42 tff(cp1_type, type, (
% 0.20/0.42 cp1: $i > $o)).
% 0.20/0.42 tff(cUnsatisfiable_type, type, (
% 0.20/0.42 cUnsatisfiable: $i > $o)).
% 0.20/0.42 tff(ra_Px1_type, type, (
% 0.20/0.42 ra_Px1: ( $i * $i ) > $o)).
% 0.20/0.42 tff(tptp_fun_Y0_2_type, type, (
% 0.20/0.42 tptp_fun_Y0_2: $i > $i)).
% 0.20/0.42 tff(tptp_fun_Y_1_type, type, (
% 0.20/0.42 tptp_fun_Y_1: $i > $i)).
% 0.20/0.42 tff(1,assumption,(cowlNothing(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~cowlThing(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))), introduced(assumption)).
% 0.20/0.42 tff(2,plain,
% 0.20/0.42 (^[X: $i] : refl((~(cowlNothing(X) | (~cowlThing(X)))) <=> (~(cowlNothing(X) | (~cowlThing(X)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(3,plain,
% 0.20/0.42 (![X: $i] : (~(cowlNothing(X) | (~cowlThing(X)))) <=> ![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.42 tff(4,plain,
% 0.20/0.42 (^[X: $i] : rewrite((cowlThing(X) & (~cowlNothing(X))) <=> (~(cowlNothing(X) | (~cowlThing(X)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(5,plain,
% 0.20/0.42 (![X: $i] : (cowlThing(X) & (~cowlNothing(X))) <=> ![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.42 tff(6,plain,
% 0.20/0.42 (![X: $i] : (cowlThing(X) & (~cowlNothing(X))) <=> ![X: $i] : (cowlThing(X) & (~cowlNothing(X)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(7,axiom,(![X: $i] : (cowlThing(X) & (~cowlNothing(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_0')).
% 0.20/0.42 tff(8,plain,
% 0.20/0.42 (![X: $i] : (cowlThing(X) & (~cowlNothing(X)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.20/0.42 tff(9,plain,(
% 0.20/0.42 ![X: $i] : (cowlThing(X) & (~cowlNothing(X)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[8])).
% 0.20/0.42 tff(10,plain,
% 0.20/0.42 (![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.20/0.42 tff(11,plain,
% 0.20/0.42 (![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.20/0.42 tff(12,plain,
% 0.20/0.42 ((~![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))) | (~(cowlNothing(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~cowlThing(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(13,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[12, 11, 1])).
% 0.20/0.42 tff(14,plain,(~(cowlNothing(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~cowlThing(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(15,plain,
% 0.20/0.42 ((cowlNothing(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~cowlThing(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | cowlThing(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(16,plain,
% 0.20/0.42 (cowlThing(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[15, 14])).
% 0.20/0.42 tff(17,plain,
% 0.20/0.42 (^[X: $i] : refl(((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(X, Y0)) | (~rf(X, Y1)))) <=> ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(X, Y0)) | (~rf(X, Y1)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(18,plain,
% 0.20/0.42 (![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(X, Y0)) | (~rf(X, Y1)))) <=> ![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(X, Y0)) | (~rf(X, Y1))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[17])).
% 0.20/0.42 tff(19,plain,
% 0.20/0.42 (^[X: $i] : rewrite(((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(X, Y0)) | (~rf(X, Y1)))) <=> ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(X, Y0)) | (~rf(X, Y1)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(20,plain,
% 0.20/0.42 (![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(X, Y0)) | (~rf(X, Y1)))) <=> ![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(X, Y0)) | (~rf(X, Y1))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[19])).
% 0.20/0.42 tff(21,plain,
% 0.20/0.42 (![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(X, Y0)) | (~rf(X, Y1)))) <=> ![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(X, Y0)) | (~rf(X, Y1))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[20, 18])).
% 0.20/0.42 tff(22,plain,
% 0.20/0.42 (^[X: $i] : rewrite(((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((~(rf(X, Y0) & rf(X, Y1))) | (Y0 = Y1))) <=> ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(X, Y0)) | (~rf(X, Y1)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(23,plain,
% 0.20/0.42 (![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((~(rf(X, Y0) & rf(X, Y1))) | (Y0 = Y1))) <=> ![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(X, Y0)) | (~rf(X, Y1))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[22])).
% 0.20/0.42 tff(24,plain,
% 0.20/0.42 (![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((~(rf(X, Y0) & rf(X, Y1))) | (Y0 = Y1))) <=> ![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((~(rf(X, Y0) & rf(X, Y1))) | (Y0 = Y1)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(25,plain,
% 0.20/0.42 (^[X: $i] : trans(monotonicity(quant_intro(proof_bind(^[Y0: $i, Y1: $i] : rewrite(((rf(X, Y0) & rf(X, Y1)) => (Y0 = Y1)) <=> ((~(rf(X, Y0) & rf(X, Y1))) | (Y0 = Y1)))), (![Y0: $i, Y1: $i] : ((rf(X, Y0) & rf(X, Y1)) => (Y0 = Y1)) <=> ![Y0: $i, Y1: $i] : ((~(rf(X, Y0) & rf(X, Y1))) | (Y0 = Y1)))), ((cowlThing(X) => ![Y0: $i, Y1: $i] : ((rf(X, Y0) & rf(X, Y1)) => (Y0 = Y1))) <=> (cowlThing(X) => ![Y0: $i, Y1: $i] : ((~(rf(X, Y0) & rf(X, Y1))) | (Y0 = Y1))))), rewrite((cowlThing(X) => ![Y0: $i, Y1: $i] : ((~(rf(X, Y0) & rf(X, Y1))) | (Y0 = Y1))) <=> ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((~(rf(X, Y0) & rf(X, Y1))) | (Y0 = Y1)))), ((cowlThing(X) => ![Y0: $i, Y1: $i] : ((rf(X, Y0) & rf(X, Y1)) => (Y0 = Y1))) <=> ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((~(rf(X, Y0) & rf(X, Y1))) | (Y0 = Y1)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(26,plain,
% 0.20/0.42 (![X: $i] : (cowlThing(X) => ![Y0: $i, Y1: $i] : ((rf(X, Y0) & rf(X, Y1)) => (Y0 = Y1))) <=> ![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((~(rf(X, Y0) & rf(X, Y1))) | (Y0 = Y1)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[25])).
% 0.20/0.42 tff(27,axiom,(![X: $i] : (cowlThing(X) => ![Y0: $i, Y1: $i] : ((rf(X, Y0) & rf(X, Y1)) => (Y0 = Y1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_7')).
% 0.20/0.42 tff(28,plain,
% 0.20/0.42 (![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((~(rf(X, Y0) & rf(X, Y1))) | (Y0 = Y1)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.20/0.42 tff(29,plain,
% 0.20/0.42 (![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((~(rf(X, Y0) & rf(X, Y1))) | (Y0 = Y1)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.20/0.42 tff(30,plain,(
% 0.20/0.42 ![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((~(rf(X, Y0) & rf(X, Y1))) | (Y0 = Y1)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[29])).
% 0.20/0.42 tff(31,plain,
% 0.20/0.42 (![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(X, Y0)) | (~rf(X, Y1))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.20/0.42 tff(32,plain,
% 0.20/0.42 (![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(X, Y0)) | (~rf(X, Y1))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[31, 21])).
% 0.20/0.42 tff(33,plain,
% 0.20/0.42 (((~![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(X, Y0)) | (~rf(X, Y1))))) | ((~cowlThing(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), Y1)) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), Y0))))) <=> ((~![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(X, Y0)) | (~rf(X, Y1))))) | (~cowlThing(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), Y1)) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), Y0))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(34,plain,
% 0.20/0.42 (((~cowlThing(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), Y0)) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), Y1)))) <=> ((~cowlThing(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), Y1)) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), Y0))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(35,plain,
% 0.20/0.42 (((~![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(X, Y0)) | (~rf(X, Y1))))) | ((~cowlThing(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), Y0)) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), Y1))))) <=> ((~![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(X, Y0)) | (~rf(X, Y1))))) | ((~cowlThing(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), Y1)) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), Y0)))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[34])).
% 0.20/0.42 tff(36,plain,
% 0.20/0.42 (((~![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(X, Y0)) | (~rf(X, Y1))))) | ((~cowlThing(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), Y0)) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), Y1))))) <=> ((~![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(X, Y0)) | (~rf(X, Y1))))) | (~cowlThing(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), Y1)) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), Y0))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[35, 33])).
% 0.20/0.42 tff(37,plain,
% 0.20/0.42 ((~![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(X, Y0)) | (~rf(X, Y1))))) | ((~cowlThing(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), Y0)) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), Y1))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(38,plain,
% 0.20/0.42 ((~![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(X, Y0)) | (~rf(X, Y1))))) | (~cowlThing(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), Y1)) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), Y0)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.20/0.42 tff(39,plain,
% 0.20/0.42 ((~cowlThing(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), Y1)) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), Y0)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[38, 32])).
% 0.20/0.42 tff(40,plain,
% 0.20/0.42 (![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), Y1)) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), Y0)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[39, 16])).
% 0.20/0.42 tff(41,plain,
% 0.20/0.42 (^[X: $i] : refl((~((~((~ca_Vx3(X)) | (~((~cp1xcomp(tptp_fun_Y_4(X))) | (~rf(X, tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rf(X, Y)) | (~cp1xcomp(Y))))))) <=> (~((~((~ca_Vx3(X)) | (~((~cp1xcomp(tptp_fun_Y_4(X))) | (~rf(X, tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rf(X, Y)) | (~cp1xcomp(Y))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(42,plain,
% 0.20/0.42 (![X: $i] : (~((~((~ca_Vx3(X)) | (~((~cp1xcomp(tptp_fun_Y_4(X))) | (~rf(X, tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rf(X, Y)) | (~cp1xcomp(Y))))))) <=> ![X: $i] : (~((~((~ca_Vx3(X)) | (~((~cp1xcomp(tptp_fun_Y_4(X))) | (~rf(X, tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rf(X, Y)) | (~cp1xcomp(Y)))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[41])).
% 0.20/0.42 tff(43,plain,
% 0.20/0.42 (^[X: $i] : rewrite((~((~((~ca_Vx3(X)) | (~((~cp1xcomp(tptp_fun_Y_4(X))) | (~rf(X, tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rf(X, Y)) | (~cp1xcomp(Y))))))) <=> (~((~((~ca_Vx3(X)) | (~((~cp1xcomp(tptp_fun_Y_4(X))) | (~rf(X, tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rf(X, Y)) | (~cp1xcomp(Y))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(44,plain,
% 0.20/0.42 (![X: $i] : (~((~((~ca_Vx3(X)) | (~((~cp1xcomp(tptp_fun_Y_4(X))) | (~rf(X, tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rf(X, Y)) | (~cp1xcomp(Y))))))) <=> ![X: $i] : (~((~((~ca_Vx3(X)) | (~((~cp1xcomp(tptp_fun_Y_4(X))) | (~rf(X, tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rf(X, Y)) | (~cp1xcomp(Y)))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[43])).
% 0.20/0.42 tff(45,plain,
% 0.20/0.42 (![X: $i] : (~((~((~ca_Vx3(X)) | (~((~cp1xcomp(tptp_fun_Y_4(X))) | (~rf(X, tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rf(X, Y)) | (~cp1xcomp(Y))))))) <=> ![X: $i] : (~((~((~ca_Vx3(X)) | (~((~cp1xcomp(tptp_fun_Y_4(X))) | (~rf(X, tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rf(X, Y)) | (~cp1xcomp(Y)))))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[44, 42])).
% 0.20/0.42 tff(46,plain,
% 0.20/0.42 (^[X: $i] : trans(monotonicity(rewrite(((~ca_Vx3(X)) | (rf(X, tptp_fun_Y_4(X)) & cp1xcomp(tptp_fun_Y_4(X)))) <=> ((~ca_Vx3(X)) | (~((~cp1xcomp(tptp_fun_Y_4(X))) | (~rf(X, tptp_fun_Y_4(X))))))), rewrite((ca_Vx3(X) | ![Y: $i] : (~(rf(X, Y) & cp1xcomp(Y)))) <=> (ca_Vx3(X) | ![Y: $i] : ((~rf(X, Y)) | (~cp1xcomp(Y))))), ((((~ca_Vx3(X)) | (rf(X, tptp_fun_Y_4(X)) & cp1xcomp(tptp_fun_Y_4(X)))) & (ca_Vx3(X) | ![Y: $i] : (~(rf(X, Y) & cp1xcomp(Y))))) <=> (((~ca_Vx3(X)) | (~((~cp1xcomp(tptp_fun_Y_4(X))) | (~rf(X, tptp_fun_Y_4(X)))))) & (ca_Vx3(X) | ![Y: $i] : ((~rf(X, Y)) | (~cp1xcomp(Y))))))), rewrite((((~ca_Vx3(X)) | (~((~cp1xcomp(tptp_fun_Y_4(X))) | (~rf(X, tptp_fun_Y_4(X)))))) & (ca_Vx3(X) | ![Y: $i] : ((~rf(X, Y)) | (~cp1xcomp(Y))))) <=> (~((~((~ca_Vx3(X)) | (~((~cp1xcomp(tptp_fun_Y_4(X))) | (~rf(X, tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rf(X, Y)) | (~cp1xcomp(Y)))))))), ((((~ca_Vx3(X)) | (rf(X, tptp_fun_Y_4(X)) & cp1xcomp(tptp_fun_Y_4(X)))) & (ca_Vx3(X) | ![Y: $i] : (~(rf(X, Y) & cp1xcomp(Y))))) <=> (~((~((~ca_Vx3(X)) | (~((~cp1xcomp(tptp_fun_Y_4(X))) | (~rf(X, tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rf(X, Y)) | (~cp1xcomp(Y)))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(47,plain,
% 0.20/0.42 (![X: $i] : (((~ca_Vx3(X)) | (rf(X, tptp_fun_Y_4(X)) & cp1xcomp(tptp_fun_Y_4(X)))) & (ca_Vx3(X) | ![Y: $i] : (~(rf(X, Y) & cp1xcomp(Y))))) <=> ![X: $i] : (~((~((~ca_Vx3(X)) | (~((~cp1xcomp(tptp_fun_Y_4(X))) | (~rf(X, tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rf(X, Y)) | (~cp1xcomp(Y)))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[46])).
% 0.20/0.42 tff(48,plain,
% 0.20/0.42 (![X: $i] : (ca_Vx3(X) <=> ?[Y: $i] : (rf(X, Y) & cp1xcomp(Y))) <=> ![X: $i] : (ca_Vx3(X) <=> ?[Y: $i] : (rf(X, Y) & cp1xcomp(Y)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(49,axiom,(![X: $i] : (ca_Vx3(X) <=> ?[Y: $i] : (rf(X, Y) & cp1xcomp(Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_6')).
% 0.20/0.42 tff(50,plain,
% 0.20/0.42 (![X: $i] : (ca_Vx3(X) <=> ?[Y: $i] : (rf(X, Y) & cp1xcomp(Y)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.20/0.42 tff(51,plain,(
% 0.20/0.42 ![X: $i] : (((~ca_Vx3(X)) | (rf(X, tptp_fun_Y_4(X)) & cp1xcomp(tptp_fun_Y_4(X)))) & (ca_Vx3(X) | ![Y: $i] : (~(rf(X, Y) & cp1xcomp(Y)))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[50])).
% 0.20/0.42 tff(52,plain,
% 0.20/0.42 (![X: $i] : (~((~((~ca_Vx3(X)) | (~((~cp1xcomp(tptp_fun_Y_4(X))) | (~rf(X, tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rf(X, Y)) | (~cp1xcomp(Y)))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.20/0.42 tff(53,plain,
% 0.20/0.42 (![X: $i] : (~((~((~ca_Vx3(X)) | (~((~cp1xcomp(tptp_fun_Y_4(X))) | (~rf(X, tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rf(X, Y)) | (~cp1xcomp(Y)))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.20/0.42 tff(54,plain,
% 0.20/0.43 (((~![X: $i] : (~((~((~ca_Vx3(X)) | (~((~cp1xcomp(tptp_fun_Y_4(X))) | (~rf(X, tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rf(X, Y)) | (~cp1xcomp(Y)))))))) | (~((~((~ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~((~cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))))))) | (~(ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | ![Y: $i] : ((~cp1xcomp(Y)) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), Y)))))))) <=> ((~![X: $i] : (~((~((~ca_Vx3(X)) | (~((~cp1xcomp(tptp_fun_Y_4(X))) | (~rf(X, tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rf(X, Y)) | (~cp1xcomp(Y)))))))) | (~((~((~ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~((~cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))))))) | (~(ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | ![Y: $i] : ((~cp1xcomp(Y)) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), Y))))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(55,plain,
% 0.20/0.43 ((~((~((~ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~((~cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))))))) | (~(ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | ![Y: $i] : ((~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), Y)) | (~cp1xcomp(Y))))))) <=> (~((~((~ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~((~cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))))))) | (~(ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | ![Y: $i] : ((~cp1xcomp(Y)) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), Y)))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(56,plain,
% 0.20/0.43 (((~![X: $i] : (~((~((~ca_Vx3(X)) | (~((~cp1xcomp(tptp_fun_Y_4(X))) | (~rf(X, tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rf(X, Y)) | (~cp1xcomp(Y)))))))) | (~((~((~ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~((~cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))))))) | (~(ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | ![Y: $i] : ((~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), Y)) | (~cp1xcomp(Y)))))))) <=> ((~![X: $i] : (~((~((~ca_Vx3(X)) | (~((~cp1xcomp(tptp_fun_Y_4(X))) | (~rf(X, tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rf(X, Y)) | (~cp1xcomp(Y)))))))) | (~((~((~ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~((~cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))))))) | (~(ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | ![Y: $i] : ((~cp1xcomp(Y)) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), Y))))))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[55])).
% 0.20/0.43 tff(57,plain,
% 0.20/0.43 (((~![X: $i] : (~((~((~ca_Vx3(X)) | (~((~cp1xcomp(tptp_fun_Y_4(X))) | (~rf(X, tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rf(X, Y)) | (~cp1xcomp(Y)))))))) | (~((~((~ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~((~cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))))))) | (~(ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | ![Y: $i] : ((~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), Y)) | (~cp1xcomp(Y)))))))) <=> ((~![X: $i] : (~((~((~ca_Vx3(X)) | (~((~cp1xcomp(tptp_fun_Y_4(X))) | (~rf(X, tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rf(X, Y)) | (~cp1xcomp(Y)))))))) | (~((~((~ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~((~cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))))))) | (~(ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | ![Y: $i] : ((~cp1xcomp(Y)) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), Y))))))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[56, 54])).
% 0.20/0.43 tff(58,plain,
% 0.20/0.43 ((~![X: $i] : (~((~((~ca_Vx3(X)) | (~((~cp1xcomp(tptp_fun_Y_4(X))) | (~rf(X, tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rf(X, Y)) | (~cp1xcomp(Y)))))))) | (~((~((~ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~((~cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))))))) | (~(ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | ![Y: $i] : ((~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), Y)) | (~cp1xcomp(Y)))))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(59,plain,
% 0.20/0.43 ((~![X: $i] : (~((~((~ca_Vx3(X)) | (~((~cp1xcomp(tptp_fun_Y_4(X))) | (~rf(X, tptp_fun_Y_4(X))))))) | (~(ca_Vx3(X) | ![Y: $i] : ((~rf(X, Y)) | (~cp1xcomp(Y)))))))) | (~((~((~ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~((~cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))))))) | (~(ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | ![Y: $i] : ((~cp1xcomp(Y)) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), Y)))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.20/0.43 tff(60,plain,
% 0.20/0.43 (~((~((~ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~((~cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))))))) | (~(ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | ![Y: $i] : ((~cp1xcomp(Y)) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), Y))))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[59, 53])).
% 0.20/0.43 tff(61,plain,
% 0.20/0.43 (((~((~ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~((~cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))))))) | (~(ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | ![Y: $i] : ((~cp1xcomp(Y)) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), Y)))))) | ((~ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~((~cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(62,plain,
% 0.20/0.43 ((~ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~((~cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[61, 60])).
% 0.20/0.43 tff(63,plain,
% 0.20/0.43 (^[X: $i] : refl((~((~(ca_Ax2(X) | (~cp1(X)) | ![Y: $i] : ((~rinvF(X, Y)) | (~ca_Vx3(Y))))) | (~((~ca_Ax2(X)) | (~((~rinvF(X, tptp_fun_Y_3(X))) | (~ca_Vx3(tptp_fun_Y_3(X))) | (~cp1(X)))))))) <=> (~((~(ca_Ax2(X) | (~cp1(X)) | ![Y: $i] : ((~rinvF(X, Y)) | (~ca_Vx3(Y))))) | (~((~ca_Ax2(X)) | (~((~rinvF(X, tptp_fun_Y_3(X))) | (~ca_Vx3(tptp_fun_Y_3(X))) | (~cp1(X)))))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(64,plain,
% 0.20/0.43 (![X: $i] : (~((~(ca_Ax2(X) | (~cp1(X)) | ![Y: $i] : ((~rinvF(X, Y)) | (~ca_Vx3(Y))))) | (~((~ca_Ax2(X)) | (~((~rinvF(X, tptp_fun_Y_3(X))) | (~ca_Vx3(tptp_fun_Y_3(X))) | (~cp1(X)))))))) <=> ![X: $i] : (~((~(ca_Ax2(X) | (~cp1(X)) | ![Y: $i] : ((~rinvF(X, Y)) | (~ca_Vx3(Y))))) | (~((~ca_Ax2(X)) | (~((~rinvF(X, tptp_fun_Y_3(X))) | (~ca_Vx3(tptp_fun_Y_3(X))) | (~cp1(X))))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[63])).
% 0.20/0.43 tff(65,plain,
% 0.20/0.43 (^[X: $i] : rewrite((~((~(ca_Ax2(X) | (~cp1(X)) | ![Y: $i] : ((~rinvF(X, Y)) | (~ca_Vx3(Y))))) | (~((~ca_Ax2(X)) | (~((~rinvF(X, tptp_fun_Y_3(X))) | (~ca_Vx3(tptp_fun_Y_3(X))) | (~cp1(X)))))))) <=> (~((~(ca_Ax2(X) | (~cp1(X)) | ![Y: $i] : ((~rinvF(X, Y)) | (~ca_Vx3(Y))))) | (~((~ca_Ax2(X)) | (~((~rinvF(X, tptp_fun_Y_3(X))) | (~ca_Vx3(tptp_fun_Y_3(X))) | (~cp1(X)))))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(66,plain,
% 0.20/0.43 (![X: $i] : (~((~(ca_Ax2(X) | (~cp1(X)) | ![Y: $i] : ((~rinvF(X, Y)) | (~ca_Vx3(Y))))) | (~((~ca_Ax2(X)) | (~((~rinvF(X, tptp_fun_Y_3(X))) | (~ca_Vx3(tptp_fun_Y_3(X))) | (~cp1(X)))))))) <=> ![X: $i] : (~((~(ca_Ax2(X) | (~cp1(X)) | ![Y: $i] : ((~rinvF(X, Y)) | (~ca_Vx3(Y))))) | (~((~ca_Ax2(X)) | (~((~rinvF(X, tptp_fun_Y_3(X))) | (~ca_Vx3(tptp_fun_Y_3(X))) | (~cp1(X))))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[65])).
% 0.20/0.43 tff(67,plain,
% 0.20/0.43 (![X: $i] : (~((~(ca_Ax2(X) | (~cp1(X)) | ![Y: $i] : ((~rinvF(X, Y)) | (~ca_Vx3(Y))))) | (~((~ca_Ax2(X)) | (~((~rinvF(X, tptp_fun_Y_3(X))) | (~ca_Vx3(tptp_fun_Y_3(X))) | (~cp1(X)))))))) <=> ![X: $i] : (~((~(ca_Ax2(X) | (~cp1(X)) | ![Y: $i] : ((~rinvF(X, Y)) | (~ca_Vx3(Y))))) | (~((~ca_Ax2(X)) | (~((~rinvF(X, tptp_fun_Y_3(X))) | (~ca_Vx3(tptp_fun_Y_3(X))) | (~cp1(X))))))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[66, 64])).
% 0.20/0.43 tff(68,plain,
% 0.20/0.43 (^[X: $i] : trans(monotonicity(rewrite(((~ca_Ax2(X)) | (rinvF(X, tptp_fun_Y_3(X)) & ca_Vx3(tptp_fun_Y_3(X)) & cp1(X))) <=> ((~ca_Ax2(X)) | (~((~rinvF(X, tptp_fun_Y_3(X))) | (~ca_Vx3(tptp_fun_Y_3(X))) | (~cp1(X)))))), rewrite((ca_Ax2(X) | (~cp1(X)) | ![Y: $i] : (~(rinvF(X, Y) & ca_Vx3(Y)))) <=> (ca_Ax2(X) | (~cp1(X)) | ![Y: $i] : ((~rinvF(X, Y)) | (~ca_Vx3(Y))))), ((((~ca_Ax2(X)) | (rinvF(X, tptp_fun_Y_3(X)) & ca_Vx3(tptp_fun_Y_3(X)) & cp1(X))) & (ca_Ax2(X) | (~cp1(X)) | ![Y: $i] : (~(rinvF(X, Y) & ca_Vx3(Y))))) <=> (((~ca_Ax2(X)) | (~((~rinvF(X, tptp_fun_Y_3(X))) | (~ca_Vx3(tptp_fun_Y_3(X))) | (~cp1(X))))) & (ca_Ax2(X) | (~cp1(X)) | ![Y: $i] : ((~rinvF(X, Y)) | (~ca_Vx3(Y))))))), rewrite((((~ca_Ax2(X)) | (~((~rinvF(X, tptp_fun_Y_3(X))) | (~ca_Vx3(tptp_fun_Y_3(X))) | (~cp1(X))))) & (ca_Ax2(X) | (~cp1(X)) | ![Y: $i] : ((~rinvF(X, Y)) | (~ca_Vx3(Y))))) <=> (~((~(ca_Ax2(X) | (~cp1(X)) | ![Y: $i] : ((~rinvF(X, Y)) | (~ca_Vx3(Y))))) | (~((~ca_Ax2(X)) | (~((~rinvF(X, tptp_fun_Y_3(X))) | (~ca_Vx3(tptp_fun_Y_3(X))) | (~cp1(X))))))))), ((((~ca_Ax2(X)) | (rinvF(X, tptp_fun_Y_3(X)) & ca_Vx3(tptp_fun_Y_3(X)) & cp1(X))) & (ca_Ax2(X) | (~cp1(X)) | ![Y: $i] : (~(rinvF(X, Y) & ca_Vx3(Y))))) <=> (~((~(ca_Ax2(X) | (~cp1(X)) | ![Y: $i] : ((~rinvF(X, Y)) | (~ca_Vx3(Y))))) | (~((~ca_Ax2(X)) | (~((~rinvF(X, tptp_fun_Y_3(X))) | (~ca_Vx3(tptp_fun_Y_3(X))) | (~cp1(X))))))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(69,plain,
% 0.20/0.43 (![X: $i] : (((~ca_Ax2(X)) | (rinvF(X, tptp_fun_Y_3(X)) & ca_Vx3(tptp_fun_Y_3(X)) & cp1(X))) & (ca_Ax2(X) | (~cp1(X)) | ![Y: $i] : (~(rinvF(X, Y) & ca_Vx3(Y))))) <=> ![X: $i] : (~((~(ca_Ax2(X) | (~cp1(X)) | ![Y: $i] : ((~rinvF(X, Y)) | (~ca_Vx3(Y))))) | (~((~ca_Ax2(X)) | (~((~rinvF(X, tptp_fun_Y_3(X))) | (~ca_Vx3(tptp_fun_Y_3(X))) | (~cp1(X))))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[68])).
% 0.20/0.43 tff(70,plain,
% 0.20/0.43 (^[X: $i] : rewrite((((~ca_Ax2(X)) | ((rinvF(X, tptp_fun_Y_3(X)) & ca_Vx3(tptp_fun_Y_3(X))) & cp1(X))) & (ca_Ax2(X) | (![Y: $i] : (~(rinvF(X, Y) & ca_Vx3(Y))) | (~cp1(X))))) <=> (((~ca_Ax2(X)) | (rinvF(X, tptp_fun_Y_3(X)) & ca_Vx3(tptp_fun_Y_3(X)) & cp1(X))) & (ca_Ax2(X) | (~cp1(X)) | ![Y: $i] : (~(rinvF(X, Y) & ca_Vx3(Y))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(71,plain,
% 0.20/0.43 (![X: $i] : (((~ca_Ax2(X)) | ((rinvF(X, tptp_fun_Y_3(X)) & ca_Vx3(tptp_fun_Y_3(X))) & cp1(X))) & (ca_Ax2(X) | (![Y: $i] : (~(rinvF(X, Y) & ca_Vx3(Y))) | (~cp1(X))))) <=> ![X: $i] : (((~ca_Ax2(X)) | (rinvF(X, tptp_fun_Y_3(X)) & ca_Vx3(tptp_fun_Y_3(X)) & cp1(X))) & (ca_Ax2(X) | (~cp1(X)) | ![Y: $i] : (~(rinvF(X, Y) & ca_Vx3(Y)))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[70])).
% 0.20/0.43 tff(72,plain,
% 0.20/0.43 (![X: $i] : (ca_Ax2(X) <=> (?[Y: $i] : (rinvF(X, Y) & ca_Vx3(Y)) & cp1(X))) <=> ![X: $i] : (ca_Ax2(X) <=> (?[Y: $i] : (rinvF(X, Y) & ca_Vx3(Y)) & cp1(X)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(73,axiom,(![X: $i] : (ca_Ax2(X) <=> (?[Y: $i] : (rinvF(X, Y) & ca_Vx3(Y)) & cp1(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_5')).
% 0.20/0.43 tff(74,plain,
% 0.20/0.43 (![X: $i] : (ca_Ax2(X) <=> (?[Y: $i] : (rinvF(X, Y) & ca_Vx3(Y)) & cp1(X)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.20/0.43 tff(75,plain,(
% 0.20/0.43 ![X: $i] : (((~ca_Ax2(X)) | ((rinvF(X, tptp_fun_Y_3(X)) & ca_Vx3(tptp_fun_Y_3(X))) & cp1(X))) & (ca_Ax2(X) | (![Y: $i] : (~(rinvF(X, Y) & ca_Vx3(Y))) | (~cp1(X)))))),
% 0.20/0.43 inference(skolemize,[status(sab)],[74])).
% 0.20/0.43 tff(76,plain,
% 0.20/0.43 (![X: $i] : (((~ca_Ax2(X)) | (rinvF(X, tptp_fun_Y_3(X)) & ca_Vx3(tptp_fun_Y_3(X)) & cp1(X))) & (ca_Ax2(X) | (~cp1(X)) | ![Y: $i] : (~(rinvF(X, Y) & ca_Vx3(Y)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[75, 71])).
% 0.20/0.43 tff(77,plain,
% 0.20/0.43 (![X: $i] : (~((~(ca_Ax2(X) | (~cp1(X)) | ![Y: $i] : ((~rinvF(X, Y)) | (~ca_Vx3(Y))))) | (~((~ca_Ax2(X)) | (~((~rinvF(X, tptp_fun_Y_3(X))) | (~ca_Vx3(tptp_fun_Y_3(X))) | (~cp1(X))))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[76, 69])).
% 0.20/0.43 tff(78,plain,
% 0.20/0.43 (![X: $i] : (~((~(ca_Ax2(X) | (~cp1(X)) | ![Y: $i] : ((~rinvF(X, Y)) | (~ca_Vx3(Y))))) | (~((~ca_Ax2(X)) | (~((~rinvF(X, tptp_fun_Y_3(X))) | (~ca_Vx3(tptp_fun_Y_3(X))) | (~cp1(X))))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[77, 67])).
% 0.20/0.43 tff(79,plain,
% 0.20/0.43 (((~![X: $i] : (~((~(ca_Ax2(X) | (~cp1(X)) | ![Y: $i] : ((~rinvF(X, Y)) | (~ca_Vx3(Y))))) | (~((~ca_Ax2(X)) | (~((~rinvF(X, tptp_fun_Y_3(X))) | (~ca_Vx3(tptp_fun_Y_3(X))) | (~cp1(X))))))))) | (~((~(ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796)) | (~cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | ![Y: $i] : ((~ca_Vx3(Y)) | (~rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796), Y))))) | (~((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~((~cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796), tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))))))))) <=> ((~![X: $i] : (~((~(ca_Ax2(X) | (~cp1(X)) | ![Y: $i] : ((~rinvF(X, Y)) | (~ca_Vx3(Y))))) | (~((~ca_Ax2(X)) | (~((~rinvF(X, tptp_fun_Y_3(X))) | (~ca_Vx3(tptp_fun_Y_3(X))) | (~cp1(X))))))))) | (~((~(ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796)) | (~cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | ![Y: $i] : ((~ca_Vx3(Y)) | (~rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796), Y))))) | (~((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~((~cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796), tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(80,plain,
% 0.20/0.43 ((~((~(ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796)) | (~cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | ![Y: $i] : ((~rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796), Y)) | (~ca_Vx3(Y))))) | (~((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~((~rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796), tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796))))))))) <=> (~((~(ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796)) | (~cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | ![Y: $i] : ((~ca_Vx3(Y)) | (~rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796), Y))))) | (~((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~((~cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796), tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(81,plain,
% 0.20/0.43 (((~![X: $i] : (~((~(ca_Ax2(X) | (~cp1(X)) | ![Y: $i] : ((~rinvF(X, Y)) | (~ca_Vx3(Y))))) | (~((~ca_Ax2(X)) | (~((~rinvF(X, tptp_fun_Y_3(X))) | (~ca_Vx3(tptp_fun_Y_3(X))) | (~cp1(X))))))))) | (~((~(ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796)) | (~cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | ![Y: $i] : ((~rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796), Y)) | (~ca_Vx3(Y))))) | (~((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~((~rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796), tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))))))) <=> ((~![X: $i] : (~((~(ca_Ax2(X) | (~cp1(X)) | ![Y: $i] : ((~rinvF(X, Y)) | (~ca_Vx3(Y))))) | (~((~ca_Ax2(X)) | (~((~rinvF(X, tptp_fun_Y_3(X))) | (~ca_Vx3(tptp_fun_Y_3(X))) | (~cp1(X))))))))) | (~((~(ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796)) | (~cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | ![Y: $i] : ((~ca_Vx3(Y)) | (~rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796), Y))))) | (~((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~((~cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796), tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))))))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[80])).
% 0.20/0.43 tff(82,plain,
% 0.20/0.43 (((~![X: $i] : (~((~(ca_Ax2(X) | (~cp1(X)) | ![Y: $i] : ((~rinvF(X, Y)) | (~ca_Vx3(Y))))) | (~((~ca_Ax2(X)) | (~((~rinvF(X, tptp_fun_Y_3(X))) | (~ca_Vx3(tptp_fun_Y_3(X))) | (~cp1(X))))))))) | (~((~(ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796)) | (~cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | ![Y: $i] : ((~rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796), Y)) | (~ca_Vx3(Y))))) | (~((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~((~rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796), tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))))))) <=> ((~![X: $i] : (~((~(ca_Ax2(X) | (~cp1(X)) | ![Y: $i] : ((~rinvF(X, Y)) | (~ca_Vx3(Y))))) | (~((~ca_Ax2(X)) | (~((~rinvF(X, tptp_fun_Y_3(X))) | (~ca_Vx3(tptp_fun_Y_3(X))) | (~cp1(X))))))))) | (~((~(ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796)) | (~cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | ![Y: $i] : ((~ca_Vx3(Y)) | (~rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796), Y))))) | (~((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~((~cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796), tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))))))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[81, 79])).
% 0.20/0.43 tff(83,plain,
% 0.20/0.43 ((~![X: $i] : (~((~(ca_Ax2(X) | (~cp1(X)) | ![Y: $i] : ((~rinvF(X, Y)) | (~ca_Vx3(Y))))) | (~((~ca_Ax2(X)) | (~((~rinvF(X, tptp_fun_Y_3(X))) | (~ca_Vx3(tptp_fun_Y_3(X))) | (~cp1(X))))))))) | (~((~(ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796)) | (~cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | ![Y: $i] : ((~rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796), Y)) | (~ca_Vx3(Y))))) | (~((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~((~rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796), tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(84,plain,
% 0.20/0.43 ((~![X: $i] : (~((~(ca_Ax2(X) | (~cp1(X)) | ![Y: $i] : ((~rinvF(X, Y)) | (~ca_Vx3(Y))))) | (~((~ca_Ax2(X)) | (~((~rinvF(X, tptp_fun_Y_3(X))) | (~ca_Vx3(tptp_fun_Y_3(X))) | (~cp1(X))))))))) | (~((~(ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796)) | (~cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | ![Y: $i] : ((~ca_Vx3(Y)) | (~rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796), Y))))) | (~((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~((~cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796), tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.20/0.43 tff(85,plain,
% 0.20/0.43 (~((~(ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796)) | (~cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | ![Y: $i] : ((~ca_Vx3(Y)) | (~rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796), Y))))) | (~((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~((~cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796), tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[84, 78])).
% 0.20/0.43 tff(86,plain,
% 0.20/0.43 (((~(ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796)) | (~cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | ![Y: $i] : ((~ca_Vx3(Y)) | (~rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796), Y))))) | (~((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~((~cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796), tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))))))) | ((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~((~cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796), tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(87,plain,
% 0.20/0.43 ((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~((~cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796), tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.20/0.43 tff(88,plain,
% 0.20/0.43 (^[X: $i] : refl((~((~((~cUnsatisfiable(X)) | (~((~rf(X, tptp_fun_Y_0(X))) | (~ca_Ax2(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~rf(X, Y)) | (~ca_Ax2(Y))))))) <=> (~((~((~cUnsatisfiable(X)) | (~((~rf(X, tptp_fun_Y_0(X))) | (~ca_Ax2(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~rf(X, Y)) | (~ca_Ax2(Y))))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(89,plain,
% 0.20/0.43 (![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~rf(X, tptp_fun_Y_0(X))) | (~ca_Ax2(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~rf(X, Y)) | (~ca_Ax2(Y))))))) <=> ![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~rf(X, tptp_fun_Y_0(X))) | (~ca_Ax2(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~rf(X, Y)) | (~ca_Ax2(Y)))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[88])).
% 0.20/0.43 tff(90,plain,
% 0.20/0.43 (^[X: $i] : rewrite((~((~((~cUnsatisfiable(X)) | (~((~rf(X, tptp_fun_Y_0(X))) | (~ca_Ax2(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~rf(X, Y)) | (~ca_Ax2(Y))))))) <=> (~((~((~cUnsatisfiable(X)) | (~((~rf(X, tptp_fun_Y_0(X))) | (~ca_Ax2(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~rf(X, Y)) | (~ca_Ax2(Y))))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(91,plain,
% 0.20/0.43 (![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~rf(X, tptp_fun_Y_0(X))) | (~ca_Ax2(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~rf(X, Y)) | (~ca_Ax2(Y))))))) <=> ![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~rf(X, tptp_fun_Y_0(X))) | (~ca_Ax2(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~rf(X, Y)) | (~ca_Ax2(Y)))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[90])).
% 0.20/0.43 tff(92,plain,
% 0.20/0.43 (![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~rf(X, tptp_fun_Y_0(X))) | (~ca_Ax2(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~rf(X, Y)) | (~ca_Ax2(Y))))))) <=> ![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~rf(X, tptp_fun_Y_0(X))) | (~ca_Ax2(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~rf(X, Y)) | (~ca_Ax2(Y)))))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[91, 89])).
% 0.20/0.43 tff(93,plain,
% 0.20/0.43 (^[X: $i] : trans(monotonicity(rewrite(((~cUnsatisfiable(X)) | (rf(X, tptp_fun_Y_0(X)) & ca_Ax2(tptp_fun_Y_0(X)))) <=> ((~cUnsatisfiable(X)) | (~((~rf(X, tptp_fun_Y_0(X))) | (~ca_Ax2(tptp_fun_Y_0(X))))))), rewrite((cUnsatisfiable(X) | ![Y: $i] : (~(rf(X, Y) & ca_Ax2(Y)))) <=> (cUnsatisfiable(X) | ![Y: $i] : ((~rf(X, Y)) | (~ca_Ax2(Y))))), ((((~cUnsatisfiable(X)) | (rf(X, tptp_fun_Y_0(X)) & ca_Ax2(tptp_fun_Y_0(X)))) & (cUnsatisfiable(X) | ![Y: $i] : (~(rf(X, Y) & ca_Ax2(Y))))) <=> (((~cUnsatisfiable(X)) | (~((~rf(X, tptp_fun_Y_0(X))) | (~ca_Ax2(tptp_fun_Y_0(X)))))) & (cUnsatisfiable(X) | ![Y: $i] : ((~rf(X, Y)) | (~ca_Ax2(Y))))))), rewrite((((~cUnsatisfiable(X)) | (~((~rf(X, tptp_fun_Y_0(X))) | (~ca_Ax2(tptp_fun_Y_0(X)))))) & (cUnsatisfiable(X) | ![Y: $i] : ((~rf(X, Y)) | (~ca_Ax2(Y))))) <=> (~((~((~cUnsatisfiable(X)) | (~((~rf(X, tptp_fun_Y_0(X))) | (~ca_Ax2(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~rf(X, Y)) | (~ca_Ax2(Y)))))))), ((((~cUnsatisfiable(X)) | (rf(X, tptp_fun_Y_0(X)) & ca_Ax2(tptp_fun_Y_0(X)))) & (cUnsatisfiable(X) | ![Y: $i] : (~(rf(X, Y) & ca_Ax2(Y))))) <=> (~((~((~cUnsatisfiable(X)) | (~((~rf(X, tptp_fun_Y_0(X))) | (~ca_Ax2(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~rf(X, Y)) | (~ca_Ax2(Y)))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(94,plain,
% 0.20/0.44 (![X: $i] : (((~cUnsatisfiable(X)) | (rf(X, tptp_fun_Y_0(X)) & ca_Ax2(tptp_fun_Y_0(X)))) & (cUnsatisfiable(X) | ![Y: $i] : (~(rf(X, Y) & ca_Ax2(Y))))) <=> ![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~rf(X, tptp_fun_Y_0(X))) | (~ca_Ax2(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~rf(X, Y)) | (~ca_Ax2(Y)))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[93])).
% 0.20/0.44 tff(95,plain,
% 0.20/0.44 (![X: $i] : (cUnsatisfiable(X) <=> ?[Y: $i] : (rf(X, Y) & ca_Ax2(Y))) <=> ![X: $i] : (cUnsatisfiable(X) <=> ?[Y: $i] : (rf(X, Y) & ca_Ax2(Y)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(96,axiom,(![X: $i] : (cUnsatisfiable(X) <=> ?[Y: $i] : (rf(X, Y) & ca_Ax2(Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_2')).
% 0.20/0.44 tff(97,plain,
% 0.20/0.44 (![X: $i] : (cUnsatisfiable(X) <=> ?[Y: $i] : (rf(X, Y) & ca_Ax2(Y)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.20/0.44 tff(98,plain,(
% 0.20/0.44 ![X: $i] : (((~cUnsatisfiable(X)) | (rf(X, tptp_fun_Y_0(X)) & ca_Ax2(tptp_fun_Y_0(X)))) & (cUnsatisfiable(X) | ![Y: $i] : (~(rf(X, Y) & ca_Ax2(Y)))))),
% 0.20/0.44 inference(skolemize,[status(sab)],[97])).
% 0.20/0.44 tff(99,plain,
% 0.20/0.44 (![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~rf(X, tptp_fun_Y_0(X))) | (~ca_Ax2(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~rf(X, Y)) | (~ca_Ax2(Y)))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[98, 94])).
% 0.20/0.44 tff(100,plain,
% 0.20/0.44 (![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~rf(X, tptp_fun_Y_0(X))) | (~ca_Ax2(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~rf(X, Y)) | (~ca_Ax2(Y)))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[99, 92])).
% 0.20/0.44 tff(101,plain,
% 0.20/0.44 (((~![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~rf(X, tptp_fun_Y_0(X))) | (~ca_Ax2(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~rf(X, Y)) | (~ca_Ax2(Y)))))))) | (~((~((~cUnsatisfiable(i2003_11_14_17_21_48796)) | (~((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~rf(i2003_11_14_17_21_48796, tptp_fun_Y_0(i2003_11_14_17_21_48796))))))) | (~(cUnsatisfiable(i2003_11_14_17_21_48796) | ![Y: $i] : ((~ca_Ax2(Y)) | (~rf(i2003_11_14_17_21_48796, Y)))))))) <=> ((~![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~rf(X, tptp_fun_Y_0(X))) | (~ca_Ax2(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~rf(X, Y)) | (~ca_Ax2(Y)))))))) | (~((~((~cUnsatisfiable(i2003_11_14_17_21_48796)) | (~((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~rf(i2003_11_14_17_21_48796, tptp_fun_Y_0(i2003_11_14_17_21_48796))))))) | (~(cUnsatisfiable(i2003_11_14_17_21_48796) | ![Y: $i] : ((~ca_Ax2(Y)) | (~rf(i2003_11_14_17_21_48796, Y))))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(102,plain,
% 0.20/0.44 ((~((~((~cUnsatisfiable(i2003_11_14_17_21_48796)) | (~((~rf(i2003_11_14_17_21_48796, tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796))))))) | (~(cUnsatisfiable(i2003_11_14_17_21_48796) | ![Y: $i] : ((~rf(i2003_11_14_17_21_48796, Y)) | (~ca_Ax2(Y))))))) <=> (~((~((~cUnsatisfiable(i2003_11_14_17_21_48796)) | (~((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~rf(i2003_11_14_17_21_48796, tptp_fun_Y_0(i2003_11_14_17_21_48796))))))) | (~(cUnsatisfiable(i2003_11_14_17_21_48796) | ![Y: $i] : ((~ca_Ax2(Y)) | (~rf(i2003_11_14_17_21_48796, Y)))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(103,plain,
% 0.20/0.44 (((~![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~rf(X, tptp_fun_Y_0(X))) | (~ca_Ax2(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~rf(X, Y)) | (~ca_Ax2(Y)))))))) | (~((~((~cUnsatisfiable(i2003_11_14_17_21_48796)) | (~((~rf(i2003_11_14_17_21_48796, tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796))))))) | (~(cUnsatisfiable(i2003_11_14_17_21_48796) | ![Y: $i] : ((~rf(i2003_11_14_17_21_48796, Y)) | (~ca_Ax2(Y)))))))) <=> ((~![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~rf(X, tptp_fun_Y_0(X))) | (~ca_Ax2(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~rf(X, Y)) | (~ca_Ax2(Y)))))))) | (~((~((~cUnsatisfiable(i2003_11_14_17_21_48796)) | (~((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~rf(i2003_11_14_17_21_48796, tptp_fun_Y_0(i2003_11_14_17_21_48796))))))) | (~(cUnsatisfiable(i2003_11_14_17_21_48796) | ![Y: $i] : ((~ca_Ax2(Y)) | (~rf(i2003_11_14_17_21_48796, Y))))))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[102])).
% 0.20/0.44 tff(104,plain,
% 0.20/0.44 (((~![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~rf(X, tptp_fun_Y_0(X))) | (~ca_Ax2(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~rf(X, Y)) | (~ca_Ax2(Y)))))))) | (~((~((~cUnsatisfiable(i2003_11_14_17_21_48796)) | (~((~rf(i2003_11_14_17_21_48796, tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796))))))) | (~(cUnsatisfiable(i2003_11_14_17_21_48796) | ![Y: $i] : ((~rf(i2003_11_14_17_21_48796, Y)) | (~ca_Ax2(Y)))))))) <=> ((~![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~rf(X, tptp_fun_Y_0(X))) | (~ca_Ax2(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~rf(X, Y)) | (~ca_Ax2(Y)))))))) | (~((~((~cUnsatisfiable(i2003_11_14_17_21_48796)) | (~((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~rf(i2003_11_14_17_21_48796, tptp_fun_Y_0(i2003_11_14_17_21_48796))))))) | (~(cUnsatisfiable(i2003_11_14_17_21_48796) | ![Y: $i] : ((~ca_Ax2(Y)) | (~rf(i2003_11_14_17_21_48796, Y))))))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[103, 101])).
% 0.20/0.44 tff(105,plain,
% 0.20/0.44 ((~![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~rf(X, tptp_fun_Y_0(X))) | (~ca_Ax2(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~rf(X, Y)) | (~ca_Ax2(Y)))))))) | (~((~((~cUnsatisfiable(i2003_11_14_17_21_48796)) | (~((~rf(i2003_11_14_17_21_48796, tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796))))))) | (~(cUnsatisfiable(i2003_11_14_17_21_48796) | ![Y: $i] : ((~rf(i2003_11_14_17_21_48796, Y)) | (~ca_Ax2(Y)))))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(106,plain,
% 0.20/0.44 ((~![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~rf(X, tptp_fun_Y_0(X))) | (~ca_Ax2(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~rf(X, Y)) | (~ca_Ax2(Y)))))))) | (~((~((~cUnsatisfiable(i2003_11_14_17_21_48796)) | (~((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~rf(i2003_11_14_17_21_48796, tptp_fun_Y_0(i2003_11_14_17_21_48796))))))) | (~(cUnsatisfiable(i2003_11_14_17_21_48796) | ![Y: $i] : ((~ca_Ax2(Y)) | (~rf(i2003_11_14_17_21_48796, Y)))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.20/0.44 tff(107,plain,
% 0.20/0.44 (~((~((~cUnsatisfiable(i2003_11_14_17_21_48796)) | (~((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~rf(i2003_11_14_17_21_48796, tptp_fun_Y_0(i2003_11_14_17_21_48796))))))) | (~(cUnsatisfiable(i2003_11_14_17_21_48796) | ![Y: $i] : ((~ca_Ax2(Y)) | (~rf(i2003_11_14_17_21_48796, Y))))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[106, 100])).
% 0.20/0.44 tff(108,plain,
% 0.20/0.44 (((~((~cUnsatisfiable(i2003_11_14_17_21_48796)) | (~((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~rf(i2003_11_14_17_21_48796, tptp_fun_Y_0(i2003_11_14_17_21_48796))))))) | (~(cUnsatisfiable(i2003_11_14_17_21_48796) | ![Y: $i] : ((~ca_Ax2(Y)) | (~rf(i2003_11_14_17_21_48796, Y)))))) | ((~cUnsatisfiable(i2003_11_14_17_21_48796)) | (~((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~rf(i2003_11_14_17_21_48796, tptp_fun_Y_0(i2003_11_14_17_21_48796))))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(109,plain,
% 0.20/0.44 ((~cUnsatisfiable(i2003_11_14_17_21_48796)) | (~((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~rf(i2003_11_14_17_21_48796, tptp_fun_Y_0(i2003_11_14_17_21_48796)))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[108, 107])).
% 0.20/0.44 tff(110,plain,
% 0.20/0.44 (cUnsatisfiable(i2003_11_14_17_21_48796) <=> cUnsatisfiable(i2003_11_14_17_21_48796)),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(111,axiom,(cUnsatisfiable(i2003_11_14_17_21_48796)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_11')).
% 0.20/0.44 tff(112,plain,
% 0.20/0.44 (cUnsatisfiable(i2003_11_14_17_21_48796)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.20/0.44 tff(113,plain,
% 0.20/0.44 ((~((~cUnsatisfiable(i2003_11_14_17_21_48796)) | (~((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~rf(i2003_11_14_17_21_48796, tptp_fun_Y_0(i2003_11_14_17_21_48796))))))) | (~cUnsatisfiable(i2003_11_14_17_21_48796)) | (~((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~rf(i2003_11_14_17_21_48796, tptp_fun_Y_0(i2003_11_14_17_21_48796)))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(114,plain,
% 0.20/0.44 ((~((~cUnsatisfiable(i2003_11_14_17_21_48796)) | (~((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~rf(i2003_11_14_17_21_48796, tptp_fun_Y_0(i2003_11_14_17_21_48796))))))) | (~((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~rf(i2003_11_14_17_21_48796, tptp_fun_Y_0(i2003_11_14_17_21_48796)))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[113, 112])).
% 0.20/0.44 tff(115,plain,
% 0.20/0.44 (~((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~rf(i2003_11_14_17_21_48796, tptp_fun_Y_0(i2003_11_14_17_21_48796))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[114, 109])).
% 0.20/0.44 tff(116,plain,
% 0.20/0.44 (((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~rf(i2003_11_14_17_21_48796, tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(117,plain,
% 0.20/0.44 (ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[116, 115])).
% 0.20/0.44 tff(118,plain,
% 0.20/0.44 ((~((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~((~cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796), tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))))) | (~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~((~cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796), tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(119,plain,
% 0.20/0.44 ((~((~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~((~cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796), tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))))) | (~((~cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796), tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[118, 117])).
% 0.20/0.44 tff(120,plain,
% 0.20/0.44 (~((~cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796), tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[119, 87])).
% 0.20/0.44 tff(121,plain,
% 0.20/0.44 (((~cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796), tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(122,plain,
% 0.20/0.44 (ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[121, 120])).
% 0.20/0.44 tff(123,plain,
% 0.20/0.44 ((~((~ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~((~cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))))))) | (~ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~((~cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(124,plain,
% 0.20/0.44 ((~((~ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~((~cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))))))) | (~((~cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[123, 122])).
% 0.20/0.44 tff(125,plain,
% 0.20/0.44 (~((~cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[124, 62])).
% 0.20/0.44 tff(126,plain,
% 0.20/0.44 (((~cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))) | rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(127,plain,
% 0.20/0.44 (rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[126, 125])).
% 0.20/0.44 tff(128,plain,
% 0.20/0.44 (^[X: $i, Y: $i] : refl((rinvF(X, Y) <=> rf(Y, X)) <=> (rinvF(X, Y) <=> rf(Y, X)))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(129,plain,
% 0.20/0.44 (![X: $i, Y: $i] : (rinvF(X, Y) <=> rf(Y, X)) <=> ![X: $i, Y: $i] : (rinvF(X, Y) <=> rf(Y, X))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[128])).
% 0.20/0.44 tff(130,plain,
% 0.20/0.44 (![X: $i, Y: $i] : (rinvF(X, Y) <=> rf(Y, X)) <=> ![X: $i, Y: $i] : (rinvF(X, Y) <=> rf(Y, X))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(131,axiom,(![X: $i, Y: $i] : (rinvF(X, Y) <=> rf(Y, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_8')).
% 0.20/0.44 tff(132,plain,
% 0.20/0.44 (![X: $i, Y: $i] : (rinvF(X, Y) <=> rf(Y, X))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.20/0.44 tff(133,plain,(
% 0.20/0.44 ![X: $i, Y: $i] : (rinvF(X, Y) <=> rf(Y, X))),
% 0.20/0.44 inference(skolemize,[status(sab)],[132])).
% 0.20/0.44 tff(134,plain,
% 0.20/0.44 (![X: $i, Y: $i] : (rinvF(X, Y) <=> rf(Y, X))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[133, 129])).
% 0.20/0.44 tff(135,plain,
% 0.20/0.44 ((~![X: $i, Y: $i] : (rinvF(X, Y) <=> rf(Y, X))) | (rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796), tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))) <=> rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), tptp_fun_Y_0(i2003_11_14_17_21_48796)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(136,plain,
% 0.20/0.44 (rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796), tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))) <=> rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), tptp_fun_Y_0(i2003_11_14_17_21_48796))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[135, 134])).
% 0.20/0.44 tff(137,plain,
% 0.20/0.44 (((~cp1(tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796), tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796), tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(138,plain,
% 0.20/0.44 (rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796), tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[137, 120])).
% 0.20/0.44 tff(139,plain,
% 0.20/0.44 ((~(rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796), tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))) <=> rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796), tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), tptp_fun_Y_0(i2003_11_14_17_21_48796))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(140,plain,
% 0.20/0.44 ((~(rinvF(tptp_fun_Y_0(i2003_11_14_17_21_48796), tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))) <=> rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), tptp_fun_Y_0(i2003_11_14_17_21_48796))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[139, 138])).
% 0.20/0.44 tff(141,plain,
% 0.20/0.44 (rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), tptp_fun_Y_0(i2003_11_14_17_21_48796))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[140, 136])).
% 0.20/0.44 tff(142,plain,
% 0.20/0.44 (((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), Y1)) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), Y0)))) | ((~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (tptp_fun_Y_0(i2003_11_14_17_21_48796) = tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))) <=> ((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), Y1)) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), Y0)))) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (tptp_fun_Y_0(i2003_11_14_17_21_48796) = tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(143,plain,
% 0.20/0.44 (((tptp_fun_Y_0(i2003_11_14_17_21_48796) = tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), tptp_fun_Y_0(i2003_11_14_17_21_48796)))) <=> ((~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (tptp_fun_Y_0(i2003_11_14_17_21_48796) = tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(144,plain,
% 0.20/0.44 (((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), Y1)) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), Y0)))) | ((tptp_fun_Y_0(i2003_11_14_17_21_48796) = tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), tptp_fun_Y_0(i2003_11_14_17_21_48796))))) <=> ((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), Y1)) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), Y0)))) | ((~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (tptp_fun_Y_0(i2003_11_14_17_21_48796) = tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[143])).
% 0.20/0.44 tff(145,plain,
% 0.20/0.44 (((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), Y1)) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), Y0)))) | ((tptp_fun_Y_0(i2003_11_14_17_21_48796) = tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), tptp_fun_Y_0(i2003_11_14_17_21_48796))))) <=> ((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), Y1)) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), Y0)))) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (tptp_fun_Y_0(i2003_11_14_17_21_48796) = tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[144, 142])).
% 0.20/0.44 tff(146,plain,
% 0.20/0.44 ((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), Y1)) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), Y0)))) | ((tptp_fun_Y_0(i2003_11_14_17_21_48796) = tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), tptp_fun_Y_0(i2003_11_14_17_21_48796))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(147,plain,
% 0.20/0.44 ((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), Y1)) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), Y0)))) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), tptp_fun_Y_0(i2003_11_14_17_21_48796))) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (tptp_fun_Y_0(i2003_11_14_17_21_48796) = tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.20/0.44 tff(148,plain,
% 0.20/0.44 (tptp_fun_Y_0(i2003_11_14_17_21_48796) = tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[147, 141, 127, 40])).
% 0.20/0.44 tff(149,plain,
% 0.20/0.44 (ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796)) <=> ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[148])).
% 0.20/0.44 tff(150,plain,
% 0.20/0.44 (ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) <=> ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796))),
% 0.20/0.44 inference(symmetry,[status(thm)],[149])).
% 0.20/0.44 tff(151,plain,
% 0.20/0.44 ((~ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) <=> (~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796)))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[150])).
% 0.20/0.44 tff(152,plain,
% 0.20/0.44 (((~![X: $i] : (~((~(ca_Ax2(X) | (~cp1(X)) | ![Y: $i] : ((~rinvF(X, Y)) | (~ca_Vx3(Y))))) | (~((~ca_Ax2(X)) | (~((~rinvF(X, tptp_fun_Y_3(X))) | (~ca_Vx3(tptp_fun_Y_3(X))) | (~cp1(X))))))))) | (~((~(ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~cp1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | ![Y: $i] : ((~ca_Vx3(Y)) | (~rinvF(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), Y))))) | (~((~ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (~((~cp1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (~ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))) | (~rinvF(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), tptp_fun_Y_3(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))))))))))) <=> ((~![X: $i] : (~((~(ca_Ax2(X) | (~cp1(X)) | ![Y: $i] : ((~rinvF(X, Y)) | (~ca_Vx3(Y))))) | (~((~ca_Ax2(X)) | (~((~rinvF(X, tptp_fun_Y_3(X))) | (~ca_Vx3(tptp_fun_Y_3(X))) | (~cp1(X))))))))) | (~((~(ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~cp1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | ![Y: $i] : ((~ca_Vx3(Y)) | (~rinvF(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), Y))))) | (~((~ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (~((~cp1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (~ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))) | (~rinvF(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), tptp_fun_Y_3(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))))))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(153,plain,
% 0.20/0.45 ((~((~(ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~cp1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | ![Y: $i] : ((~rinvF(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), Y)) | (~ca_Vx3(Y))))) | (~((~ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (~((~rinvF(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), tptp_fun_Y_3(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))) | (~ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))) | (~cp1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))))))))) <=> (~((~(ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~cp1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | ![Y: $i] : ((~ca_Vx3(Y)) | (~rinvF(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), Y))))) | (~((~ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (~((~cp1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (~ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))) | (~rinvF(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), tptp_fun_Y_3(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))))))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(154,plain,
% 0.20/0.45 (((~![X: $i] : (~((~(ca_Ax2(X) | (~cp1(X)) | ![Y: $i] : ((~rinvF(X, Y)) | (~ca_Vx3(Y))))) | (~((~ca_Ax2(X)) | (~((~rinvF(X, tptp_fun_Y_3(X))) | (~ca_Vx3(tptp_fun_Y_3(X))) | (~cp1(X))))))))) | (~((~(ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~cp1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | ![Y: $i] : ((~rinvF(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), Y)) | (~ca_Vx3(Y))))) | (~((~ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (~((~rinvF(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), tptp_fun_Y_3(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))) | (~ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))) | (~cp1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))))))))) <=> ((~![X: $i] : (~((~(ca_Ax2(X) | (~cp1(X)) | ![Y: $i] : ((~rinvF(X, Y)) | (~ca_Vx3(Y))))) | (~((~ca_Ax2(X)) | (~((~rinvF(X, tptp_fun_Y_3(X))) | (~ca_Vx3(tptp_fun_Y_3(X))) | (~cp1(X))))))))) | (~((~(ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~cp1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | ![Y: $i] : ((~ca_Vx3(Y)) | (~rinvF(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), Y))))) | (~((~ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (~((~cp1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (~ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))) | (~rinvF(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), tptp_fun_Y_3(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))))))))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[153])).
% 0.20/0.45 tff(155,plain,
% 0.20/0.45 (((~![X: $i] : (~((~(ca_Ax2(X) | (~cp1(X)) | ![Y: $i] : ((~rinvF(X, Y)) | (~ca_Vx3(Y))))) | (~((~ca_Ax2(X)) | (~((~rinvF(X, tptp_fun_Y_3(X))) | (~ca_Vx3(tptp_fun_Y_3(X))) | (~cp1(X))))))))) | (~((~(ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~cp1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | ![Y: $i] : ((~rinvF(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), Y)) | (~ca_Vx3(Y))))) | (~((~ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (~((~rinvF(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), tptp_fun_Y_3(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))) | (~ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))) | (~cp1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))))))))) <=> ((~![X: $i] : (~((~(ca_Ax2(X) | (~cp1(X)) | ![Y: $i] : ((~rinvF(X, Y)) | (~ca_Vx3(Y))))) | (~((~ca_Ax2(X)) | (~((~rinvF(X, tptp_fun_Y_3(X))) | (~ca_Vx3(tptp_fun_Y_3(X))) | (~cp1(X))))))))) | (~((~(ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~cp1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | ![Y: $i] : ((~ca_Vx3(Y)) | (~rinvF(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), Y))))) | (~((~ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (~((~cp1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (~ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))) | (~rinvF(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), tptp_fun_Y_3(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))))))))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[154, 152])).
% 0.20/0.45 tff(156,plain,
% 0.20/0.45 ((~![X: $i] : (~((~(ca_Ax2(X) | (~cp1(X)) | ![Y: $i] : ((~rinvF(X, Y)) | (~ca_Vx3(Y))))) | (~((~ca_Ax2(X)) | (~((~rinvF(X, tptp_fun_Y_3(X))) | (~ca_Vx3(tptp_fun_Y_3(X))) | (~cp1(X))))))))) | (~((~(ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~cp1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | ![Y: $i] : ((~rinvF(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), Y)) | (~ca_Vx3(Y))))) | (~((~ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (~((~rinvF(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), tptp_fun_Y_3(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))) | (~ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))) | (~cp1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))))))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(157,plain,
% 0.20/0.45 ((~![X: $i] : (~((~(ca_Ax2(X) | (~cp1(X)) | ![Y: $i] : ((~rinvF(X, Y)) | (~ca_Vx3(Y))))) | (~((~ca_Ax2(X)) | (~((~rinvF(X, tptp_fun_Y_3(X))) | (~ca_Vx3(tptp_fun_Y_3(X))) | (~cp1(X))))))))) | (~((~(ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~cp1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | ![Y: $i] : ((~ca_Vx3(Y)) | (~rinvF(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), Y))))) | (~((~ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (~((~cp1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (~ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))) | (~rinvF(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), tptp_fun_Y_3(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))))))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.20/0.45 tff(158,plain,
% 0.20/0.45 (~((~(ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~cp1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | ![Y: $i] : ((~ca_Vx3(Y)) | (~rinvF(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), Y))))) | (~((~ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (~((~cp1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (~ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))) | (~rinvF(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), tptp_fun_Y_3(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))))))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[157, 78])).
% 0.20/0.45 tff(159,plain,
% 0.20/0.45 (((~(ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | (~cp1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | ![Y: $i] : ((~ca_Vx3(Y)) | (~rinvF(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), Y))))) | (~((~ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (~((~cp1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (~ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))) | (~rinvF(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), tptp_fun_Y_3(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))))))))) | ((~ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (~((~cp1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (~ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))) | (~rinvF(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), tptp_fun_Y_3(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))))))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(160,plain,
% 0.20/0.45 ((~ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (~((~cp1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (~ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))) | (~rinvF(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), tptp_fun_Y_3(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[159, 158])).
% 0.20/0.45 tff(161,assumption,(![Y: $i] : (~ra_Px1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), Y))), introduced(assumption)).
% 0.20/0.45 tff(162,plain,
% 0.20/0.45 (^[X: $i] : refl((~((~((~cp1xcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(cp1xcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))))) <=> (~((~((~cp1xcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(cp1xcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(163,plain,
% 0.20/0.45 (![X: $i] : (~((~((~cp1xcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(cp1xcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))))) <=> ![X: $i] : (~((~((~cp1xcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(cp1xcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[162])).
% 0.20/0.45 tff(164,plain,
% 0.20/0.45 (^[X: $i] : rewrite((~((~((~cp1xcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(cp1xcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))))) <=> (~((~((~cp1xcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(cp1xcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(165,plain,
% 0.20/0.45 (![X: $i] : (~((~((~cp1xcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(cp1xcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))))) <=> ![X: $i] : (~((~((~cp1xcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(cp1xcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[164])).
% 0.20/0.45 tff(166,plain,
% 0.20/0.45 (![X: $i] : (~((~((~cp1xcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(cp1xcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))))) <=> ![X: $i] : (~((~((~cp1xcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(cp1xcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[165, 163])).
% 0.20/0.45 tff(167,plain,
% 0.20/0.45 (^[X: $i] : trans(monotonicity(rewrite((cp1xcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))) <=> (cp1xcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))), ((((~cp1xcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X))) & (cp1xcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))) <=> (((~cp1xcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X))) & (cp1xcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))))), rewrite((((~cp1xcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X))) & (cp1xcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))) <=> (~((~((~cp1xcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(cp1xcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))), ((((~cp1xcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X))) & (cp1xcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))) <=> (~((~((~cp1xcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(cp1xcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(168,plain,
% 0.20/0.45 (![X: $i] : (((~cp1xcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X))) & (cp1xcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))) <=> ![X: $i] : (~((~((~cp1xcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(cp1xcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[167])).
% 0.20/0.45 tff(169,plain,
% 0.20/0.45 (![X: $i] : (cp1xcomp(X) <=> ?[Y0: $i] : ra_Px1(X, Y0)) <=> ![X: $i] : (cp1xcomp(X) <=> ?[Y0: $i] : ra_Px1(X, Y0))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(170,axiom,(![X: $i] : (cp1xcomp(X) <=> ?[Y0: $i] : ra_Px1(X, Y0))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_4')).
% 0.20/0.45 tff(171,plain,
% 0.20/0.45 (![X: $i] : (cp1xcomp(X) <=> ?[Y0: $i] : ra_Px1(X, Y0))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.20/0.45 tff(172,plain,(
% 0.20/0.45 ![X: $i] : (((~cp1xcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X))) & (cp1xcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))),
% 0.20/0.45 inference(skolemize,[status(sab)],[171])).
% 0.20/0.45 tff(173,plain,
% 0.20/0.45 (![X: $i] : (~((~((~cp1xcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(cp1xcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[172, 168])).
% 0.20/0.45 tff(174,plain,
% 0.20/0.45 (![X: $i] : (~((~((~cp1xcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(cp1xcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[173, 166])).
% 0.20/0.45 tff(175,plain,
% 0.20/0.45 ((~![X: $i] : (~((~((~cp1xcomp(X)) | ra_Px1(X, tptp_fun_Y0_2(X)))) | (~(cp1xcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))) | (~((~((~cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | ra_Px1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), tptp_fun_Y0_2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))))) | (~(cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | ![Y0: $i] : (~ra_Px1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), Y0))))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(176,plain,
% 0.20/0.45 (~((~((~cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | ra_Px1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), tptp_fun_Y0_2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))))) | (~(cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | ![Y0: $i] : (~ra_Px1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), Y0)))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[175, 174])).
% 0.20/0.45 tff(177,plain,
% 0.20/0.45 (((~((~cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | ra_Px1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), tptp_fun_Y0_2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))))) | (~(cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | ![Y0: $i] : (~ra_Px1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), Y0))))) | ((~cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | ra_Px1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), tptp_fun_Y0_2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(178,plain,
% 0.20/0.45 ((~cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | ra_Px1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), tptp_fun_Y0_2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[177, 176])).
% 0.20/0.45 tff(179,plain,
% 0.20/0.45 (((~cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (~rf(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)), tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))) | cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(180,plain,
% 0.20/0.45 (cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[179, 125])).
% 0.20/0.45 tff(181,plain,
% 0.20/0.45 ((~((~cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | ra_Px1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), tptp_fun_Y0_2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))))) | (~cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | ra_Px1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), tptp_fun_Y0_2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(182,plain,
% 0.20/0.45 ((~((~cp1xcomp(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | ra_Px1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), tptp_fun_Y0_2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))))) | ra_Px1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), tptp_fun_Y0_2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[181, 180])).
% 0.20/0.45 tff(183,plain,
% 0.20/0.45 (ra_Px1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), tptp_fun_Y0_2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[182, 178])).
% 0.20/0.45 tff(184,plain,
% 0.20/0.45 ((~![Y: $i] : (~ra_Px1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), Y))) | (~ra_Px1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), tptp_fun_Y0_2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(185,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[184, 183, 161])).
% 0.20/0.45 tff(186,plain,(~![Y: $i] : (~ra_Px1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), Y))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(187,plain,
% 0.20/0.45 (^[X: $i] : rewrite((~((~(cp1(X) | ra_Px1(X, tptp_fun_Y_1(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~cp1(X)))))) <=> (~((~(cp1(X) | ra_Px1(X, tptp_fun_Y_1(X)))) | (~((~cp1(X)) | ![Y: $i] : (~ra_Px1(X, Y)))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(188,plain,
% 0.20/0.45 (![X: $i] : (~((~(cp1(X) | ra_Px1(X, tptp_fun_Y_1(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~cp1(X)))))) <=> ![X: $i] : (~((~(cp1(X) | ra_Px1(X, tptp_fun_Y_1(X)))) | (~((~cp1(X)) | ![Y: $i] : (~ra_Px1(X, Y))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[187])).
% 0.20/0.45 tff(189,plain,
% 0.20/0.45 (^[X: $i] : refl((~((~(cp1(X) | ra_Px1(X, tptp_fun_Y_1(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~cp1(X)))))) <=> (~((~(cp1(X) | ra_Px1(X, tptp_fun_Y_1(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~cp1(X)))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(190,plain,
% 0.20/0.45 (![X: $i] : (~((~(cp1(X) | ra_Px1(X, tptp_fun_Y_1(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~cp1(X)))))) <=> ![X: $i] : (~((~(cp1(X) | ra_Px1(X, tptp_fun_Y_1(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~cp1(X))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[189])).
% 0.20/0.45 tff(191,plain,
% 0.20/0.45 (^[X: $i] : rewrite((~((~(cp1(X) | ra_Px1(X, tptp_fun_Y_1(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~cp1(X)))))) <=> (~((~(cp1(X) | ra_Px1(X, tptp_fun_Y_1(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~cp1(X)))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(192,plain,
% 0.20/0.45 (![X: $i] : (~((~(cp1(X) | ra_Px1(X, tptp_fun_Y_1(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~cp1(X)))))) <=> ![X: $i] : (~((~(cp1(X) | ra_Px1(X, tptp_fun_Y_1(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~cp1(X))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[191])).
% 0.20/0.45 tff(193,plain,
% 0.20/0.45 (![X: $i] : (~((~(cp1(X) | ra_Px1(X, tptp_fun_Y_1(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~cp1(X)))))) <=> ![X: $i] : (~((~(cp1(X) | ra_Px1(X, tptp_fun_Y_1(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~cp1(X))))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[192, 190])).
% 0.20/0.45 tff(194,plain,
% 0.20/0.45 (^[X: $i] : trans(monotonicity(rewrite((![Y: $i] : (~ra_Px1(X, Y)) | (~cp1(X))) <=> (![Y: $i] : (~ra_Px1(X, Y)) | (~cp1(X)))), (((cp1(X) | ra_Px1(X, tptp_fun_Y_1(X))) & (![Y: $i] : (~ra_Px1(X, Y)) | (~cp1(X)))) <=> ((cp1(X) | ra_Px1(X, tptp_fun_Y_1(X))) & (![Y: $i] : (~ra_Px1(X, Y)) | (~cp1(X)))))), rewrite(((cp1(X) | ra_Px1(X, tptp_fun_Y_1(X))) & (![Y: $i] : (~ra_Px1(X, Y)) | (~cp1(X)))) <=> (~((~(cp1(X) | ra_Px1(X, tptp_fun_Y_1(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~cp1(X))))))), (((cp1(X) | ra_Px1(X, tptp_fun_Y_1(X))) & (![Y: $i] : (~ra_Px1(X, Y)) | (~cp1(X)))) <=> (~((~(cp1(X) | ra_Px1(X, tptp_fun_Y_1(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~cp1(X))))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(195,plain,
% 0.20/0.45 (![X: $i] : ((cp1(X) | ra_Px1(X, tptp_fun_Y_1(X))) & (![Y: $i] : (~ra_Px1(X, Y)) | (~cp1(X)))) <=> ![X: $i] : (~((~(cp1(X) | ra_Px1(X, tptp_fun_Y_1(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~cp1(X))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[194])).
% 0.20/0.45 tff(196,plain,
% 0.20/0.45 (^[X: $i] : rewrite(((ra_Px1(X, tptp_fun_Y_1(X)) | cp1(X)) & (![Y: $i] : (~ra_Px1(X, Y)) | (~cp1(X)))) <=> ((cp1(X) | ra_Px1(X, tptp_fun_Y_1(X))) & (![Y: $i] : (~ra_Px1(X, Y)) | (~cp1(X)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(197,plain,
% 0.20/0.45 (![X: $i] : ((ra_Px1(X, tptp_fun_Y_1(X)) | cp1(X)) & (![Y: $i] : (~ra_Px1(X, Y)) | (~cp1(X)))) <=> ![X: $i] : ((cp1(X) | ra_Px1(X, tptp_fun_Y_1(X))) & (![Y: $i] : (~ra_Px1(X, Y)) | (~cp1(X))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[196])).
% 0.20/0.45 tff(198,plain,
% 0.20/0.45 (![X: $i] : (~(?[Y: $i] : ra_Px1(X, Y) <=> cp1(X))) <=> ![X: $i] : (~(?[Y: $i] : ra_Px1(X, Y) <=> cp1(X)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(199,plain,
% 0.20/0.45 (^[X: $i] : trans(trans(monotonicity(rewrite((~?[Y: $i] : ra_Px1(X, Y)) <=> (~?[Y: $i] : ra_Px1(X, Y))), ((cp1(X) <=> (~?[Y: $i] : ra_Px1(X, Y))) <=> (cp1(X) <=> (~?[Y: $i] : ra_Px1(X, Y))))), rewrite((cp1(X) <=> (~?[Y: $i] : ra_Px1(X, Y))) <=> (~(?[Y: $i] : ra_Px1(X, Y) <=> cp1(X)))), ((cp1(X) <=> (~?[Y: $i] : ra_Px1(X, Y))) <=> (~(?[Y: $i] : ra_Px1(X, Y) <=> cp1(X))))), rewrite((~(?[Y: $i] : ra_Px1(X, Y) <=> cp1(X))) <=> (~(?[Y: $i] : ra_Px1(X, Y) <=> cp1(X)))), ((cp1(X) <=> (~?[Y: $i] : ra_Px1(X, Y))) <=> (~(?[Y: $i] : ra_Px1(X, Y) <=> cp1(X)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(200,plain,
% 0.20/0.45 (![X: $i] : (cp1(X) <=> (~?[Y: $i] : ra_Px1(X, Y))) <=> ![X: $i] : (~(?[Y: $i] : ra_Px1(X, Y) <=> cp1(X)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[199])).
% 0.20/0.45 tff(201,axiom,(![X: $i] : (cp1(X) <=> (~?[Y: $i] : ra_Px1(X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_3')).
% 0.20/0.45 tff(202,plain,
% 0.20/0.45 (![X: $i] : (~(?[Y: $i] : ra_Px1(X, Y) <=> cp1(X)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.20/0.45 tff(203,plain,
% 0.20/0.45 (![X: $i] : (~(?[Y: $i] : ra_Px1(X, Y) <=> cp1(X)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[202, 198])).
% 0.20/0.45 tff(204,plain,(
% 0.20/0.45 ![X: $i] : ((ra_Px1(X, tptp_fun_Y_1(X)) | cp1(X)) & (![Y: $i] : (~ra_Px1(X, Y)) | (~cp1(X))))),
% 0.20/0.45 inference(skolemize,[status(sab)],[203])).
% 0.20/0.45 tff(205,plain,
% 0.20/0.45 (![X: $i] : ((cp1(X) | ra_Px1(X, tptp_fun_Y_1(X))) & (![Y: $i] : (~ra_Px1(X, Y)) | (~cp1(X))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[204, 197])).
% 0.20/0.45 tff(206,plain,
% 0.20/0.45 (![X: $i] : (~((~(cp1(X) | ra_Px1(X, tptp_fun_Y_1(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~cp1(X))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[205, 195])).
% 0.20/0.45 tff(207,plain,
% 0.20/0.45 (![X: $i] : (~((~(cp1(X) | ra_Px1(X, tptp_fun_Y_1(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~cp1(X))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[206, 193])).
% 0.20/0.45 tff(208,plain,
% 0.20/0.45 (![X: $i] : (~((~(cp1(X) | ra_Px1(X, tptp_fun_Y_1(X)))) | (~((~cp1(X)) | ![Y: $i] : (~ra_Px1(X, Y))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[207, 188])).
% 0.20/0.45 tff(209,plain,
% 0.20/0.45 ((~![X: $i] : (~((~(cp1(X) | ra_Px1(X, tptp_fun_Y_1(X)))) | (~((~cp1(X)) | ![Y: $i] : (~ra_Px1(X, Y))))))) | (~((~(cp1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | ra_Px1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), tptp_fun_Y_1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))))) | (~((~cp1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | ![Y: $i] : (~ra_Px1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), Y))))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(210,plain,
% 0.20/0.46 (~((~(cp1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | ra_Px1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), tptp_fun_Y_1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))))) | (~((~cp1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | ![Y: $i] : (~ra_Px1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), Y)))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[209, 208])).
% 0.20/0.46 tff(211,plain,
% 0.20/0.46 (((~(cp1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))) | ra_Px1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), tptp_fun_Y_1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))))) | (~((~cp1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | ![Y: $i] : (~ra_Px1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), Y))))) | ((~cp1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | ![Y: $i] : (~ra_Px1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), Y)))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(212,plain,
% 0.20/0.46 ((~cp1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | ![Y: $i] : (~ra_Px1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), Y))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[211, 210])).
% 0.20/0.46 tff(213,plain,
% 0.20/0.46 ((~((~cp1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | ![Y: $i] : (~ra_Px1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), Y)))) | (~cp1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | ![Y: $i] : (~ra_Px1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), Y))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(214,plain,
% 0.20/0.46 ((~cp1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | ![Y: $i] : (~ra_Px1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), Y))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[213, 212])).
% 0.20/0.46 tff(215,plain,
% 0.20/0.46 (~cp1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[214, 186])).
% 0.20/0.46 tff(216,plain,
% 0.20/0.46 (((~cp1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (~ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))) | (~rinvF(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), tptp_fun_Y_3(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))))) | cp1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(217,plain,
% 0.20/0.46 ((~cp1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (~ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))) | (~rinvF(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), tptp_fun_Y_3(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[216, 215])).
% 0.20/0.46 tff(218,plain,
% 0.20/0.46 ((~((~ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (~((~cp1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (~ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))) | (~rinvF(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), tptp_fun_Y_3(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))))))) | (~ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (~((~cp1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (~ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))) | (~rinvF(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), tptp_fun_Y_3(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))))))),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(219,plain,
% 0.20/0.46 ((~((~ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (~((~cp1(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))) | (~ca_Vx3(tptp_fun_Y_3(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))) | (~rinvF(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))), tptp_fun_Y_3(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))))))) | (~ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796)))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[218, 217])).
% 0.20/0.46 tff(220,plain,
% 0.20/0.46 (~ca_Ax2(tptp_fun_Y_4(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_48796))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[219, 160])).
% 0.20/0.46 tff(221,plain,
% 0.20/0.46 (~ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_48796))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[220, 151])).
% 0.20/0.46 tff(222,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[117, 221])).
% 0.20/0.46 % SZS output end Proof
% 0.20/0.46 % E exiting
%------------------------------------------------------------------------------