%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS115+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:13:25 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KRS115+1 : TPTP v9.0.0. Released v3.1.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 19:15:34 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.42 % SZS status Unsatisfiable
% 0.20/0.42 % SZS output start Proof
% 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_4_type, type, (
% 0.20/0.42 tptp_fun_Y0_4: $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(i2003_11_14_17_21_30578_type, type, (
% 0.20/0.42 i2003_11_14_17_21_30578: $i)).
% 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(tptp_fun_Y_2_type, type, (
% 0.20/0.42 tptp_fun_Y_2: $i > $i)).
% 0.20/0.42 tff(rf1_type, type, (
% 0.20/0.42 rf1: ( $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(rr_type, type, (
% 0.20/0.42 rr: ( $i * $i ) > $o)).
% 0.20/0.42 tff(rf2_type, type, (
% 0.20/0.42 rf2: ( $i * $i ) > $o)).
% 0.20/0.42 tff(cp2_type, type, (
% 0.20/0.42 cp2: $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(cp2xcomp_type, type, (
% 0.20/0.42 cp2xcomp: $i > $o)).
% 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(1,assumption,(cowlNothing(i2003_11_14_17_21_30578) | (~cowlThing(i2003_11_14_17_21_30578))), 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: $i] : (~(cowlNothing(X) | (~cowlThing(X))))) | (~(cowlNothing(i2003_11_14_17_21_30578) | (~cowlThing(i2003_11_14_17_21_30578))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(13,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[12, 11, 1])).
% 0.20/0.42 tff(14,plain,(~(cowlNothing(i2003_11_14_17_21_30578) | (~cowlThing(i2003_11_14_17_21_30578)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(15,plain,
% 0.20/0.42 ((cowlNothing(i2003_11_14_17_21_30578) | (~cowlThing(i2003_11_14_17_21_30578))) | cowlThing(i2003_11_14_17_21_30578)),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(16,plain,
% 0.20/0.42 (cowlThing(i2003_11_14_17_21_30578)),
% 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) | (~rf1(X, Y0)) | (~rf1(X, Y1)))) <=> ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(X, Y0)) | (~rf1(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) | (~rf1(X, Y0)) | (~rf1(X, Y1)))) <=> ![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(X, Y0)) | (~rf1(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) | (~rf1(X, Y0)) | (~rf1(X, Y1)))) <=> ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(X, Y0)) | (~rf1(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) | (~rf1(X, Y0)) | (~rf1(X, Y1)))) <=> ![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(X, Y0)) | (~rf1(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) | (~rf1(X, Y0)) | (~rf1(X, Y1)))) <=> ![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(X, Y0)) | (~rf1(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] : ((~(rf1(X, Y0) & rf1(X, Y1))) | (Y0 = Y1))) <=> ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(X, Y0)) | (~rf1(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] : ((~(rf1(X, Y0) & rf1(X, Y1))) | (Y0 = Y1))) <=> ![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(X, Y0)) | (~rf1(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] : ((~(rf1(X, Y0) & rf1(X, Y1))) | (Y0 = Y1))) <=> ![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((~(rf1(X, Y0) & rf1(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(((rf1(X, Y0) & rf1(X, Y1)) => (Y0 = Y1)) <=> ((~(rf1(X, Y0) & rf1(X, Y1))) | (Y0 = Y1)))), (![Y0: $i, Y1: $i] : ((rf1(X, Y0) & rf1(X, Y1)) => (Y0 = Y1)) <=> ![Y0: $i, Y1: $i] : ((~(rf1(X, Y0) & rf1(X, Y1))) | (Y0 = Y1)))), ((cowlThing(X) => ![Y0: $i, Y1: $i] : ((rf1(X, Y0) & rf1(X, Y1)) => (Y0 = Y1))) <=> (cowlThing(X) => ![Y0: $i, Y1: $i] : ((~(rf1(X, Y0) & rf1(X, Y1))) | (Y0 = Y1))))), rewrite((cowlThing(X) => ![Y0: $i, Y1: $i] : ((~(rf1(X, Y0) & rf1(X, Y1))) | (Y0 = Y1))) <=> ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((~(rf1(X, Y0) & rf1(X, Y1))) | (Y0 = Y1)))), ((cowlThing(X) => ![Y0: $i, Y1: $i] : ((rf1(X, Y0) & rf1(X, Y1)) => (Y0 = Y1))) <=> ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((~(rf1(X, Y0) & rf1(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] : ((rf1(X, Y0) & rf1(X, Y1)) => (Y0 = Y1))) <=> ![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((~(rf1(X, Y0) & rf1(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] : ((rf1(X, Y0) & rf1(X, Y1)) => (Y0 = Y1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_6')).
% 0.20/0.42 tff(28,plain,
% 0.20/0.42 (![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((~(rf1(X, Y0) & rf1(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] : ((~(rf1(X, Y0) & rf1(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] : ((~(rf1(X, Y0) & rf1(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) | (~rf1(X, Y0)) | (~rf1(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) | (~rf1(X, Y0)) | (~rf1(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) | (~rf1(X, Y0)) | (~rf1(X, Y1))))) | ((~cowlThing(i2003_11_14_17_21_30578)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(i2003_11_14_17_21_30578, Y1)) | (~rf1(i2003_11_14_17_21_30578, Y0))))) <=> ((~![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(X, Y0)) | (~rf1(X, Y1))))) | (~cowlThing(i2003_11_14_17_21_30578)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(i2003_11_14_17_21_30578, Y1)) | (~rf1(i2003_11_14_17_21_30578, Y0))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(34,plain,
% 0.20/0.42 (((~cowlThing(i2003_11_14_17_21_30578)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(i2003_11_14_17_21_30578, Y0)) | (~rf1(i2003_11_14_17_21_30578, Y1)))) <=> ((~cowlThing(i2003_11_14_17_21_30578)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(i2003_11_14_17_21_30578, Y1)) | (~rf1(i2003_11_14_17_21_30578, 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) | (~rf1(X, Y0)) | (~rf1(X, Y1))))) | ((~cowlThing(i2003_11_14_17_21_30578)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(i2003_11_14_17_21_30578, Y0)) | (~rf1(i2003_11_14_17_21_30578, Y1))))) <=> ((~![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(X, Y0)) | (~rf1(X, Y1))))) | ((~cowlThing(i2003_11_14_17_21_30578)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(i2003_11_14_17_21_30578, Y1)) | (~rf1(i2003_11_14_17_21_30578, 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) | (~rf1(X, Y0)) | (~rf1(X, Y1))))) | ((~cowlThing(i2003_11_14_17_21_30578)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(i2003_11_14_17_21_30578, Y0)) | (~rf1(i2003_11_14_17_21_30578, Y1))))) <=> ((~![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(X, Y0)) | (~rf1(X, Y1))))) | (~cowlThing(i2003_11_14_17_21_30578)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(i2003_11_14_17_21_30578, Y1)) | (~rf1(i2003_11_14_17_21_30578, 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) | (~rf1(X, Y0)) | (~rf1(X, Y1))))) | ((~cowlThing(i2003_11_14_17_21_30578)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(i2003_11_14_17_21_30578, Y0)) | (~rf1(i2003_11_14_17_21_30578, 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) | (~rf1(X, Y0)) | (~rf1(X, Y1))))) | (~cowlThing(i2003_11_14_17_21_30578)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(i2003_11_14_17_21_30578, Y1)) | (~rf1(i2003_11_14_17_21_30578, Y0)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.20/0.42 tff(39,plain,
% 0.20/0.42 ((~cowlThing(i2003_11_14_17_21_30578)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(i2003_11_14_17_21_30578, Y1)) | (~rf1(i2003_11_14_17_21_30578, 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) | (~rf1(i2003_11_14_17_21_30578, Y1)) | (~rf1(i2003_11_14_17_21_30578, 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((~((~((~cUnsatisfiable(X)) | (~((~rf2(X, tptp_fun_Y_0(X))) | (~cp2(tptp_fun_Y_0(X))) | (~rf1(X, tptp_fun_Y_1(X))) | (~cp1(tptp_fun_Y_1(X))) | (~rr(X, tptp_fun_Y_2(X))) | (~cowlThing(tptp_fun_Y_2(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(X, Y))) | ![Y: $i] : ((~rf2(X, Y)) | (~cp2(Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(X, Y))))))) <=> (~((~((~cUnsatisfiable(X)) | (~((~rf2(X, tptp_fun_Y_0(X))) | (~cp2(tptp_fun_Y_0(X))) | (~rf1(X, tptp_fun_Y_1(X))) | (~cp1(tptp_fun_Y_1(X))) | (~rr(X, tptp_fun_Y_2(X))) | (~cowlThing(tptp_fun_Y_2(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(X, Y))) | ![Y: $i] : ((~rf2(X, Y)) | (~cp2(Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(X, Y))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(42,plain,
% 0.20/0.42 (![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~rf2(X, tptp_fun_Y_0(X))) | (~cp2(tptp_fun_Y_0(X))) | (~rf1(X, tptp_fun_Y_1(X))) | (~cp1(tptp_fun_Y_1(X))) | (~rr(X, tptp_fun_Y_2(X))) | (~cowlThing(tptp_fun_Y_2(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(X, Y))) | ![Y: $i] : ((~rf2(X, Y)) | (~cp2(Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(X, Y))))))) <=> ![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~rf2(X, tptp_fun_Y_0(X))) | (~cp2(tptp_fun_Y_0(X))) | (~rf1(X, tptp_fun_Y_1(X))) | (~cp1(tptp_fun_Y_1(X))) | (~rr(X, tptp_fun_Y_2(X))) | (~cowlThing(tptp_fun_Y_2(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(X, Y))) | ![Y: $i] : ((~rf2(X, Y)) | (~cp2(Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(X, 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((~((~((~cUnsatisfiable(X)) | (~((~rf2(X, tptp_fun_Y_0(X))) | (~cp2(tptp_fun_Y_0(X))) | (~rf1(X, tptp_fun_Y_1(X))) | (~cp1(tptp_fun_Y_1(X))) | (~rr(X, tptp_fun_Y_2(X))) | (~cowlThing(tptp_fun_Y_2(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(X, Y))) | ![Y: $i] : ((~rf2(X, Y)) | (~cp2(Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(X, Y))))))) <=> (~((~((~cUnsatisfiable(X)) | (~((~rf2(X, tptp_fun_Y_0(X))) | (~cp2(tptp_fun_Y_0(X))) | (~rf1(X, tptp_fun_Y_1(X))) | (~cp1(tptp_fun_Y_1(X))) | (~rr(X, tptp_fun_Y_2(X))) | (~cowlThing(tptp_fun_Y_2(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(X, Y))) | ![Y: $i] : ((~rf2(X, Y)) | (~cp2(Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(X, Y))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(44,plain,
% 0.20/0.42 (![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~rf2(X, tptp_fun_Y_0(X))) | (~cp2(tptp_fun_Y_0(X))) | (~rf1(X, tptp_fun_Y_1(X))) | (~cp1(tptp_fun_Y_1(X))) | (~rr(X, tptp_fun_Y_2(X))) | (~cowlThing(tptp_fun_Y_2(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(X, Y))) | ![Y: $i] : ((~rf2(X, Y)) | (~cp2(Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(X, Y))))))) <=> ![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~rf2(X, tptp_fun_Y_0(X))) | (~cp2(tptp_fun_Y_0(X))) | (~rf1(X, tptp_fun_Y_1(X))) | (~cp1(tptp_fun_Y_1(X))) | (~rr(X, tptp_fun_Y_2(X))) | (~cowlThing(tptp_fun_Y_2(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(X, Y))) | ![Y: $i] : ((~rf2(X, Y)) | (~cp2(Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(X, Y)))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[43])).
% 0.20/0.42 tff(45,plain,
% 0.20/0.42 (![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~rf2(X, tptp_fun_Y_0(X))) | (~cp2(tptp_fun_Y_0(X))) | (~rf1(X, tptp_fun_Y_1(X))) | (~cp1(tptp_fun_Y_1(X))) | (~rr(X, tptp_fun_Y_2(X))) | (~cowlThing(tptp_fun_Y_2(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(X, Y))) | ![Y: $i] : ((~rf2(X, Y)) | (~cp2(Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(X, Y))))))) <=> ![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~rf2(X, tptp_fun_Y_0(X))) | (~cp2(tptp_fun_Y_0(X))) | (~rf1(X, tptp_fun_Y_1(X))) | (~cp1(tptp_fun_Y_1(X))) | (~rr(X, tptp_fun_Y_2(X))) | (~cowlThing(tptp_fun_Y_2(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(X, Y))) | ![Y: $i] : ((~rf2(X, Y)) | (~cp2(Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(X, 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(((~cUnsatisfiable(X)) | (rf2(X, tptp_fun_Y_0(X)) & cp2(tptp_fun_Y_0(X)) & rf1(X, tptp_fun_Y_1(X)) & cp1(tptp_fun_Y_1(X)) & rr(X, tptp_fun_Y_2(X)) & cowlThing(tptp_fun_Y_2(X)))) <=> ((~cUnsatisfiable(X)) | (~((~rf2(X, tptp_fun_Y_0(X))) | (~cp2(tptp_fun_Y_0(X))) | (~rf1(X, tptp_fun_Y_1(X))) | (~cp1(tptp_fun_Y_1(X))) | (~rr(X, tptp_fun_Y_2(X))) | (~cowlThing(tptp_fun_Y_2(X))))))), trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(rewrite((rf2(X, Y) & cp2(Y)) <=> (~((~rf2(X, Y)) | (~cp2(Y))))), ((~(rf2(X, Y) & cp2(Y))) <=> (~(~((~rf2(X, Y)) | (~cp2(Y))))))), rewrite((~(~((~rf2(X, Y)) | (~cp2(Y))))) <=> ((~rf2(X, Y)) | (~cp2(Y)))), ((~(rf2(X, Y) & cp2(Y))) <=> ((~rf2(X, Y)) | (~cp2(Y)))))), (![Y: $i] : (~(rf2(X, Y) & cp2(Y))) <=> ![Y: $i] : ((~rf2(X, Y)) | (~cp2(Y))))), quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(rewrite((rf1(X, Y) & cp1(Y)) <=> (~((~cp1(Y)) | (~rf1(X, Y))))), ((~(rf1(X, Y) & cp1(Y))) <=> (~(~((~cp1(Y)) | (~rf1(X, Y))))))), rewrite((~(~((~cp1(Y)) | (~rf1(X, Y))))) <=> ((~cp1(Y)) | (~rf1(X, Y)))), ((~(rf1(X, Y) & cp1(Y))) <=> ((~cp1(Y)) | (~rf1(X, Y)))))), (![Y: $i] : (~(rf1(X, Y) & cp1(Y))) <=> ![Y: $i] : ((~cp1(Y)) | (~rf1(X, Y))))), quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(rewrite((rr(X, Y) & cowlThing(Y)) <=> (~((~cowlThing(Y)) | (~rr(X, Y))))), ((~(rr(X, Y) & cowlThing(Y))) <=> (~(~((~cowlThing(Y)) | (~rr(X, Y))))))), rewrite((~(~((~cowlThing(Y)) | (~rr(X, Y))))) <=> ((~cowlThing(Y)) | (~rr(X, Y)))), ((~(rr(X, Y) & cowlThing(Y))) <=> ((~cowlThing(Y)) | (~rr(X, Y)))))), (![Y: $i] : (~(rr(X, Y) & cowlThing(Y))) <=> ![Y: $i] : ((~cowlThing(Y)) | (~rr(X, Y))))), ((cUnsatisfiable(X) | ![Y: $i] : (~(rf2(X, Y) & cp2(Y))) | ![Y: $i] : (~(rf1(X, Y) & cp1(Y))) | ![Y: $i] : (~(rr(X, Y) & cowlThing(Y)))) <=> (cUnsatisfiable(X) | ![Y: $i] : ((~rf2(X, Y)) | (~cp2(Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(X, Y))) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(X, Y)))))), rewrite((cUnsatisfiable(X) | ![Y: $i] : ((~rf2(X, Y)) | (~cp2(Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(X, Y))) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(X, Y)))) <=> (cUnsatisfiable(X) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(X, Y))) | ![Y: $i] : ((~rf2(X, Y)) | (~cp2(Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(X, Y))))), ((cUnsatisfiable(X) | ![Y: $i] : (~(rf2(X, Y) & cp2(Y))) | ![Y: $i] : (~(rf1(X, Y) & cp1(Y))) | ![Y: $i] : (~(rr(X, Y) & cowlThing(Y)))) <=> (cUnsatisfiable(X) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(X, Y))) | ![Y: $i] : ((~rf2(X, Y)) | (~cp2(Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(X, Y)))))), ((((~cUnsatisfiable(X)) | (rf2(X, tptp_fun_Y_0(X)) & cp2(tptp_fun_Y_0(X)) & rf1(X, tptp_fun_Y_1(X)) & cp1(tptp_fun_Y_1(X)) & rr(X, tptp_fun_Y_2(X)) & cowlThing(tptp_fun_Y_2(X)))) & (cUnsatisfiable(X) | ![Y: $i] : (~(rf2(X, Y) & cp2(Y))) | ![Y: $i] : (~(rf1(X, Y) & cp1(Y))) | ![Y: $i] : (~(rr(X, Y) & cowlThing(Y))))) <=> (((~cUnsatisfiable(X)) | (~((~rf2(X, tptp_fun_Y_0(X))) | (~cp2(tptp_fun_Y_0(X))) | (~rf1(X, tptp_fun_Y_1(X))) | (~cp1(tptp_fun_Y_1(X))) | (~rr(X, tptp_fun_Y_2(X))) | (~cowlThing(tptp_fun_Y_2(X)))))) & (cUnsatisfiable(X) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(X, Y))) | ![Y: $i] : ((~rf2(X, Y)) | (~cp2(Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(X, Y))))))), rewrite((((~cUnsatisfiable(X)) | (~((~rf2(X, tptp_fun_Y_0(X))) | (~cp2(tptp_fun_Y_0(X))) | (~rf1(X, tptp_fun_Y_1(X))) | (~cp1(tptp_fun_Y_1(X))) | (~rr(X, tptp_fun_Y_2(X))) | (~cowlThing(tptp_fun_Y_2(X)))))) & (cUnsatisfiable(X) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(X, Y))) | ![Y: $i] : ((~rf2(X, Y)) | (~cp2(Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(X, Y))))) <=> (~((~((~cUnsatisfiable(X)) | (~((~rf2(X, tptp_fun_Y_0(X))) | (~cp2(tptp_fun_Y_0(X))) | (~rf1(X, tptp_fun_Y_1(X))) | (~cp1(tptp_fun_Y_1(X))) | (~rr(X, tptp_fun_Y_2(X))) | (~cowlThing(tptp_fun_Y_2(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(X, Y))) | ![Y: $i] : ((~rf2(X, Y)) | (~cp2(Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(X, Y)))))))), ((((~cUnsatisfiable(X)) | (rf2(X, tptp_fun_Y_0(X)) & cp2(tptp_fun_Y_0(X)) & rf1(X, tptp_fun_Y_1(X)) & cp1(tptp_fun_Y_1(X)) & rr(X, tptp_fun_Y_2(X)) & cowlThing(tptp_fun_Y_2(X)))) & (cUnsatisfiable(X) | ![Y: $i] : (~(rf2(X, Y) & cp2(Y))) | ![Y: $i] : (~(rf1(X, Y) & cp1(Y))) | ![Y: $i] : (~(rr(X, Y) & cowlThing(Y))))) <=> (~((~((~cUnsatisfiable(X)) | (~((~rf2(X, tptp_fun_Y_0(X))) | (~cp2(tptp_fun_Y_0(X))) | (~rf1(X, tptp_fun_Y_1(X))) | (~cp1(tptp_fun_Y_1(X))) | (~rr(X, tptp_fun_Y_2(X))) | (~cowlThing(tptp_fun_Y_2(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(X, Y))) | ![Y: $i] : ((~rf2(X, Y)) | (~cp2(Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(X, Y)))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(47,plain,
% 0.20/0.42 (![X: $i] : (((~cUnsatisfiable(X)) | (rf2(X, tptp_fun_Y_0(X)) & cp2(tptp_fun_Y_0(X)) & rf1(X, tptp_fun_Y_1(X)) & cp1(tptp_fun_Y_1(X)) & rr(X, tptp_fun_Y_2(X)) & cowlThing(tptp_fun_Y_2(X)))) & (cUnsatisfiable(X) | ![Y: $i] : (~(rf2(X, Y) & cp2(Y))) | ![Y: $i] : (~(rf1(X, Y) & cp1(Y))) | ![Y: $i] : (~(rr(X, Y) & cowlThing(Y))))) <=> ![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~rf2(X, tptp_fun_Y_0(X))) | (~cp2(tptp_fun_Y_0(X))) | (~rf1(X, tptp_fun_Y_1(X))) | (~cp1(tptp_fun_Y_1(X))) | (~rr(X, tptp_fun_Y_2(X))) | (~cowlThing(tptp_fun_Y_2(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(X, Y))) | ![Y: $i] : ((~rf2(X, Y)) | (~cp2(Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(X, Y)))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[46])).
% 0.20/0.42 tff(48,plain,
% 0.20/0.42 (^[X: $i] : rewrite((((~cUnsatisfiable(X)) | ((rf2(X, tptp_fun_Y_0(X)) & cp2(tptp_fun_Y_0(X))) & (rf1(X, tptp_fun_Y_1(X)) & cp1(tptp_fun_Y_1(X))) & (rr(X, tptp_fun_Y_2(X)) & cowlThing(tptp_fun_Y_2(X))))) & (cUnsatisfiable(X) | (![Y: $i] : (~(rf2(X, Y) & cp2(Y))) | ![Y: $i] : (~(rf1(X, Y) & cp1(Y))) | ![Y: $i] : (~(rr(X, Y) & cowlThing(Y)))))) <=> (((~cUnsatisfiable(X)) | (rf2(X, tptp_fun_Y_0(X)) & cp2(tptp_fun_Y_0(X)) & rf1(X, tptp_fun_Y_1(X)) & cp1(tptp_fun_Y_1(X)) & rr(X, tptp_fun_Y_2(X)) & cowlThing(tptp_fun_Y_2(X)))) & (cUnsatisfiable(X) | ![Y: $i] : (~(rf2(X, Y) & cp2(Y))) | ![Y: $i] : (~(rf1(X, Y) & cp1(Y))) | ![Y: $i] : (~(rr(X, Y) & cowlThing(Y))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(49,plain,
% 0.20/0.43 (![X: $i] : (((~cUnsatisfiable(X)) | ((rf2(X, tptp_fun_Y_0(X)) & cp2(tptp_fun_Y_0(X))) & (rf1(X, tptp_fun_Y_1(X)) & cp1(tptp_fun_Y_1(X))) & (rr(X, tptp_fun_Y_2(X)) & cowlThing(tptp_fun_Y_2(X))))) & (cUnsatisfiable(X) | (![Y: $i] : (~(rf2(X, Y) & cp2(Y))) | ![Y: $i] : (~(rf1(X, Y) & cp1(Y))) | ![Y: $i] : (~(rr(X, Y) & cowlThing(Y)))))) <=> ![X: $i] : (((~cUnsatisfiable(X)) | (rf2(X, tptp_fun_Y_0(X)) & cp2(tptp_fun_Y_0(X)) & rf1(X, tptp_fun_Y_1(X)) & cp1(tptp_fun_Y_1(X)) & rr(X, tptp_fun_Y_2(X)) & cowlThing(tptp_fun_Y_2(X)))) & (cUnsatisfiable(X) | ![Y: $i] : (~(rf2(X, Y) & cp2(Y))) | ![Y: $i] : (~(rf1(X, Y) & cp1(Y))) | ![Y: $i] : (~(rr(X, Y) & cowlThing(Y)))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[48])).
% 0.20/0.43 tff(50,plain,
% 0.20/0.43 (![X: $i] : (cUnsatisfiable(X) <=> (?[Y: $i] : (rf2(X, Y) & cp2(Y)) & ?[Y: $i] : (rf1(X, Y) & cp1(Y)) & ?[Y: $i] : (rr(X, Y) & cowlThing(Y)))) <=> ![X: $i] : (cUnsatisfiable(X) <=> (?[Y: $i] : (rf2(X, Y) & cp2(Y)) & ?[Y: $i] : (rf1(X, Y) & cp1(Y)) & ?[Y: $i] : (rr(X, Y) & cowlThing(Y))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(51,plain,
% 0.20/0.43 (^[X: $i] : rewrite((cUnsatisfiable(X) <=> ((?[Y: $i] : (rf2(X, Y) & cp2(Y)) & ?[Y: $i] : (rf1(X, Y) & cp1(Y))) & ?[Y: $i] : (rr(X, Y) & cowlThing(Y)))) <=> (cUnsatisfiable(X) <=> (?[Y: $i] : (rf2(X, Y) & cp2(Y)) & ?[Y: $i] : (rf1(X, Y) & cp1(Y)) & ?[Y: $i] : (rr(X, Y) & cowlThing(Y)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(52,plain,
% 0.20/0.43 (![X: $i] : (cUnsatisfiable(X) <=> ((?[Y: $i] : (rf2(X, Y) & cp2(Y)) & ?[Y: $i] : (rf1(X, Y) & cp1(Y))) & ?[Y: $i] : (rr(X, Y) & cowlThing(Y)))) <=> ![X: $i] : (cUnsatisfiable(X) <=> (?[Y: $i] : (rf2(X, Y) & cp2(Y)) & ?[Y: $i] : (rf1(X, Y) & cp1(Y)) & ?[Y: $i] : (rr(X, Y) & cowlThing(Y))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[51])).
% 0.20/0.43 tff(53,axiom,(![X: $i] : (cUnsatisfiable(X) <=> ((?[Y: $i] : (rf2(X, Y) & cp2(Y)) & ?[Y: $i] : (rf1(X, Y) & cp1(Y))) & ?[Y: $i] : (rr(X, Y) & cowlThing(Y))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_2')).
% 0.20/0.43 tff(54,plain,
% 0.20/0.43 (![X: $i] : (cUnsatisfiable(X) <=> (?[Y: $i] : (rf2(X, Y) & cp2(Y)) & ?[Y: $i] : (rf1(X, Y) & cp1(Y)) & ?[Y: $i] : (rr(X, Y) & cowlThing(Y))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.20/0.43 tff(55,plain,
% 0.20/0.43 (![X: $i] : (cUnsatisfiable(X) <=> (?[Y: $i] : (rf2(X, Y) & cp2(Y)) & ?[Y: $i] : (rf1(X, Y) & cp1(Y)) & ?[Y: $i] : (rr(X, Y) & cowlThing(Y))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.20/0.43 tff(56,plain,(
% 0.20/0.43 ![X: $i] : (((~cUnsatisfiable(X)) | ((rf2(X, tptp_fun_Y_0(X)) & cp2(tptp_fun_Y_0(X))) & (rf1(X, tptp_fun_Y_1(X)) & cp1(tptp_fun_Y_1(X))) & (rr(X, tptp_fun_Y_2(X)) & cowlThing(tptp_fun_Y_2(X))))) & (cUnsatisfiable(X) | (![Y: $i] : (~(rf2(X, Y) & cp2(Y))) | ![Y: $i] : (~(rf1(X, Y) & cp1(Y))) | ![Y: $i] : (~(rr(X, Y) & cowlThing(Y))))))),
% 0.20/0.43 inference(skolemize,[status(sab)],[55])).
% 0.20/0.43 tff(57,plain,
% 0.20/0.43 (![X: $i] : (((~cUnsatisfiable(X)) | (rf2(X, tptp_fun_Y_0(X)) & cp2(tptp_fun_Y_0(X)) & rf1(X, tptp_fun_Y_1(X)) & cp1(tptp_fun_Y_1(X)) & rr(X, tptp_fun_Y_2(X)) & cowlThing(tptp_fun_Y_2(X)))) & (cUnsatisfiable(X) | ![Y: $i] : (~(rf2(X, Y) & cp2(Y))) | ![Y: $i] : (~(rf1(X, Y) & cp1(Y))) | ![Y: $i] : (~(rr(X, Y) & cowlThing(Y)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[56, 49])).
% 0.20/0.43 tff(58,plain,
% 0.20/0.43 (![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~rf2(X, tptp_fun_Y_0(X))) | (~cp2(tptp_fun_Y_0(X))) | (~rf1(X, tptp_fun_Y_1(X))) | (~cp1(tptp_fun_Y_1(X))) | (~rr(X, tptp_fun_Y_2(X))) | (~cowlThing(tptp_fun_Y_2(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(X, Y))) | ![Y: $i] : ((~rf2(X, Y)) | (~cp2(Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(X, Y)))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[57, 47])).
% 0.20/0.43 tff(59,plain,
% 0.20/0.43 (![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~rf2(X, tptp_fun_Y_0(X))) | (~cp2(tptp_fun_Y_0(X))) | (~rf1(X, tptp_fun_Y_1(X))) | (~cp1(tptp_fun_Y_1(X))) | (~rr(X, tptp_fun_Y_2(X))) | (~cowlThing(tptp_fun_Y_2(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(X, Y))) | ![Y: $i] : ((~rf2(X, Y)) | (~cp2(Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(X, Y)))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[58, 45])).
% 0.20/0.43 tff(60,plain,
% 0.20/0.43 (((~![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~rf2(X, tptp_fun_Y_0(X))) | (~cp2(tptp_fun_Y_0(X))) | (~rf1(X, tptp_fun_Y_1(X))) | (~cp1(tptp_fun_Y_1(X))) | (~rr(X, tptp_fun_Y_2(X))) | (~cowlThing(tptp_fun_Y_2(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(X, Y))) | ![Y: $i] : ((~rf2(X, Y)) | (~cp2(Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(X, Y)))))))) | (~((~((~cUnsatisfiable(i2003_11_14_17_21_30578)) | (~((~cowlThing(tptp_fun_Y_2(i2003_11_14_17_21_30578))) | (~rr(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578))) | (~cp1(tptp_fun_Y_1(i2003_11_14_17_21_30578))) | (~rf1(i2003_11_14_17_21_30578, tptp_fun_Y_1(i2003_11_14_17_21_30578))) | (~cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))) | (~rf2(i2003_11_14_17_21_30578, tptp_fun_Y_0(i2003_11_14_17_21_30578))))))) | (~(cUnsatisfiable(i2003_11_14_17_21_30578) | ![Y: $i] : ((~cp1(Y)) | (~rf1(i2003_11_14_17_21_30578, Y))) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(i2003_11_14_17_21_30578, Y))) | ![Y: $i] : ((~cp2(Y)) | (~rf2(i2003_11_14_17_21_30578, Y)))))))) <=> ((~![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~rf2(X, tptp_fun_Y_0(X))) | (~cp2(tptp_fun_Y_0(X))) | (~rf1(X, tptp_fun_Y_1(X))) | (~cp1(tptp_fun_Y_1(X))) | (~rr(X, tptp_fun_Y_2(X))) | (~cowlThing(tptp_fun_Y_2(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(X, Y))) | ![Y: $i] : ((~rf2(X, Y)) | (~cp2(Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(X, Y)))))))) | (~((~((~cUnsatisfiable(i2003_11_14_17_21_30578)) | (~((~cowlThing(tptp_fun_Y_2(i2003_11_14_17_21_30578))) | (~rr(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578))) | (~cp1(tptp_fun_Y_1(i2003_11_14_17_21_30578))) | (~rf1(i2003_11_14_17_21_30578, tptp_fun_Y_1(i2003_11_14_17_21_30578))) | (~cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))) | (~rf2(i2003_11_14_17_21_30578, tptp_fun_Y_0(i2003_11_14_17_21_30578))))))) | (~(cUnsatisfiable(i2003_11_14_17_21_30578) | ![Y: $i] : ((~cp1(Y)) | (~rf1(i2003_11_14_17_21_30578, Y))) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(i2003_11_14_17_21_30578, Y))) | ![Y: $i] : ((~cp2(Y)) | (~rf2(i2003_11_14_17_21_30578, Y))))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(61,plain,
% 0.20/0.43 ((~((~((~cUnsatisfiable(i2003_11_14_17_21_30578)) | (~((~rf2(i2003_11_14_17_21_30578, tptp_fun_Y_0(i2003_11_14_17_21_30578))) | (~cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))) | (~rf1(i2003_11_14_17_21_30578, tptp_fun_Y_1(i2003_11_14_17_21_30578))) | (~cp1(tptp_fun_Y_1(i2003_11_14_17_21_30578))) | (~rr(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578))) | (~cowlThing(tptp_fun_Y_2(i2003_11_14_17_21_30578))))))) | (~(cUnsatisfiable(i2003_11_14_17_21_30578) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(i2003_11_14_17_21_30578, Y))) | ![Y: $i] : ((~rf2(i2003_11_14_17_21_30578, Y)) | (~cp2(Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(i2003_11_14_17_21_30578, Y))))))) <=> (~((~((~cUnsatisfiable(i2003_11_14_17_21_30578)) | (~((~cowlThing(tptp_fun_Y_2(i2003_11_14_17_21_30578))) | (~rr(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578))) | (~cp1(tptp_fun_Y_1(i2003_11_14_17_21_30578))) | (~rf1(i2003_11_14_17_21_30578, tptp_fun_Y_1(i2003_11_14_17_21_30578))) | (~cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))) | (~rf2(i2003_11_14_17_21_30578, tptp_fun_Y_0(i2003_11_14_17_21_30578))))))) | (~(cUnsatisfiable(i2003_11_14_17_21_30578) | ![Y: $i] : ((~cp1(Y)) | (~rf1(i2003_11_14_17_21_30578, Y))) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(i2003_11_14_17_21_30578, Y))) | ![Y: $i] : ((~cp2(Y)) | (~rf2(i2003_11_14_17_21_30578, Y)))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(62,plain,
% 0.20/0.43 (((~![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~rf2(X, tptp_fun_Y_0(X))) | (~cp2(tptp_fun_Y_0(X))) | (~rf1(X, tptp_fun_Y_1(X))) | (~cp1(tptp_fun_Y_1(X))) | (~rr(X, tptp_fun_Y_2(X))) | (~cowlThing(tptp_fun_Y_2(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(X, Y))) | ![Y: $i] : ((~rf2(X, Y)) | (~cp2(Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(X, Y)))))))) | (~((~((~cUnsatisfiable(i2003_11_14_17_21_30578)) | (~((~rf2(i2003_11_14_17_21_30578, tptp_fun_Y_0(i2003_11_14_17_21_30578))) | (~cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))) | (~rf1(i2003_11_14_17_21_30578, tptp_fun_Y_1(i2003_11_14_17_21_30578))) | (~cp1(tptp_fun_Y_1(i2003_11_14_17_21_30578))) | (~rr(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578))) | (~cowlThing(tptp_fun_Y_2(i2003_11_14_17_21_30578))))))) | (~(cUnsatisfiable(i2003_11_14_17_21_30578) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(i2003_11_14_17_21_30578, Y))) | ![Y: $i] : ((~rf2(i2003_11_14_17_21_30578, Y)) | (~cp2(Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(i2003_11_14_17_21_30578, Y)))))))) <=> ((~![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~rf2(X, tptp_fun_Y_0(X))) | (~cp2(tptp_fun_Y_0(X))) | (~rf1(X, tptp_fun_Y_1(X))) | (~cp1(tptp_fun_Y_1(X))) | (~rr(X, tptp_fun_Y_2(X))) | (~cowlThing(tptp_fun_Y_2(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(X, Y))) | ![Y: $i] : ((~rf2(X, Y)) | (~cp2(Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(X, Y)))))))) | (~((~((~cUnsatisfiable(i2003_11_14_17_21_30578)) | (~((~cowlThing(tptp_fun_Y_2(i2003_11_14_17_21_30578))) | (~rr(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578))) | (~cp1(tptp_fun_Y_1(i2003_11_14_17_21_30578))) | (~rf1(i2003_11_14_17_21_30578, tptp_fun_Y_1(i2003_11_14_17_21_30578))) | (~cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))) | (~rf2(i2003_11_14_17_21_30578, tptp_fun_Y_0(i2003_11_14_17_21_30578))))))) | (~(cUnsatisfiable(i2003_11_14_17_21_30578) | ![Y: $i] : ((~cp1(Y)) | (~rf1(i2003_11_14_17_21_30578, Y))) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(i2003_11_14_17_21_30578, Y))) | ![Y: $i] : ((~cp2(Y)) | (~rf2(i2003_11_14_17_21_30578, Y))))))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[61])).
% 0.20/0.43 tff(63,plain,
% 0.20/0.43 (((~![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~rf2(X, tptp_fun_Y_0(X))) | (~cp2(tptp_fun_Y_0(X))) | (~rf1(X, tptp_fun_Y_1(X))) | (~cp1(tptp_fun_Y_1(X))) | (~rr(X, tptp_fun_Y_2(X))) | (~cowlThing(tptp_fun_Y_2(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(X, Y))) | ![Y: $i] : ((~rf2(X, Y)) | (~cp2(Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(X, Y)))))))) | (~((~((~cUnsatisfiable(i2003_11_14_17_21_30578)) | (~((~rf2(i2003_11_14_17_21_30578, tptp_fun_Y_0(i2003_11_14_17_21_30578))) | (~cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))) | (~rf1(i2003_11_14_17_21_30578, tptp_fun_Y_1(i2003_11_14_17_21_30578))) | (~cp1(tptp_fun_Y_1(i2003_11_14_17_21_30578))) | (~rr(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578))) | (~cowlThing(tptp_fun_Y_2(i2003_11_14_17_21_30578))))))) | (~(cUnsatisfiable(i2003_11_14_17_21_30578) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(i2003_11_14_17_21_30578, Y))) | ![Y: $i] : ((~rf2(i2003_11_14_17_21_30578, Y)) | (~cp2(Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(i2003_11_14_17_21_30578, Y)))))))) <=> ((~![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~rf2(X, tptp_fun_Y_0(X))) | (~cp2(tptp_fun_Y_0(X))) | (~rf1(X, tptp_fun_Y_1(X))) | (~cp1(tptp_fun_Y_1(X))) | (~rr(X, tptp_fun_Y_2(X))) | (~cowlThing(tptp_fun_Y_2(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(X, Y))) | ![Y: $i] : ((~rf2(X, Y)) | (~cp2(Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(X, Y)))))))) | (~((~((~cUnsatisfiable(i2003_11_14_17_21_30578)) | (~((~cowlThing(tptp_fun_Y_2(i2003_11_14_17_21_30578))) | (~rr(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578))) | (~cp1(tptp_fun_Y_1(i2003_11_14_17_21_30578))) | (~rf1(i2003_11_14_17_21_30578, tptp_fun_Y_1(i2003_11_14_17_21_30578))) | (~cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))) | (~rf2(i2003_11_14_17_21_30578, tptp_fun_Y_0(i2003_11_14_17_21_30578))))))) | (~(cUnsatisfiable(i2003_11_14_17_21_30578) | ![Y: $i] : ((~cp1(Y)) | (~rf1(i2003_11_14_17_21_30578, Y))) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(i2003_11_14_17_21_30578, Y))) | ![Y: $i] : ((~cp2(Y)) | (~rf2(i2003_11_14_17_21_30578, Y))))))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[62, 60])).
% 0.20/0.43 tff(64,plain,
% 0.20/0.43 ((~![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~rf2(X, tptp_fun_Y_0(X))) | (~cp2(tptp_fun_Y_0(X))) | (~rf1(X, tptp_fun_Y_1(X))) | (~cp1(tptp_fun_Y_1(X))) | (~rr(X, tptp_fun_Y_2(X))) | (~cowlThing(tptp_fun_Y_2(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(X, Y))) | ![Y: $i] : ((~rf2(X, Y)) | (~cp2(Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(X, Y)))))))) | (~((~((~cUnsatisfiable(i2003_11_14_17_21_30578)) | (~((~rf2(i2003_11_14_17_21_30578, tptp_fun_Y_0(i2003_11_14_17_21_30578))) | (~cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))) | (~rf1(i2003_11_14_17_21_30578, tptp_fun_Y_1(i2003_11_14_17_21_30578))) | (~cp1(tptp_fun_Y_1(i2003_11_14_17_21_30578))) | (~rr(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578))) | (~cowlThing(tptp_fun_Y_2(i2003_11_14_17_21_30578))))))) | (~(cUnsatisfiable(i2003_11_14_17_21_30578) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(i2003_11_14_17_21_30578, Y))) | ![Y: $i] : ((~rf2(i2003_11_14_17_21_30578, Y)) | (~cp2(Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(i2003_11_14_17_21_30578, Y)))))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(65,plain,
% 0.20/0.43 ((~![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~rf2(X, tptp_fun_Y_0(X))) | (~cp2(tptp_fun_Y_0(X))) | (~rf1(X, tptp_fun_Y_1(X))) | (~cp1(tptp_fun_Y_1(X))) | (~rr(X, tptp_fun_Y_2(X))) | (~cowlThing(tptp_fun_Y_2(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(X, Y))) | ![Y: $i] : ((~rf2(X, Y)) | (~cp2(Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(X, Y)))))))) | (~((~((~cUnsatisfiable(i2003_11_14_17_21_30578)) | (~((~cowlThing(tptp_fun_Y_2(i2003_11_14_17_21_30578))) | (~rr(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578))) | (~cp1(tptp_fun_Y_1(i2003_11_14_17_21_30578))) | (~rf1(i2003_11_14_17_21_30578, tptp_fun_Y_1(i2003_11_14_17_21_30578))) | (~cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))) | (~rf2(i2003_11_14_17_21_30578, tptp_fun_Y_0(i2003_11_14_17_21_30578))))))) | (~(cUnsatisfiable(i2003_11_14_17_21_30578) | ![Y: $i] : ((~cp1(Y)) | (~rf1(i2003_11_14_17_21_30578, Y))) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(i2003_11_14_17_21_30578, Y))) | ![Y: $i] : ((~cp2(Y)) | (~rf2(i2003_11_14_17_21_30578, Y)))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.20/0.43 tff(66,plain,
% 0.20/0.43 (~((~((~cUnsatisfiable(i2003_11_14_17_21_30578)) | (~((~cowlThing(tptp_fun_Y_2(i2003_11_14_17_21_30578))) | (~rr(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578))) | (~cp1(tptp_fun_Y_1(i2003_11_14_17_21_30578))) | (~rf1(i2003_11_14_17_21_30578, tptp_fun_Y_1(i2003_11_14_17_21_30578))) | (~cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))) | (~rf2(i2003_11_14_17_21_30578, tptp_fun_Y_0(i2003_11_14_17_21_30578))))))) | (~(cUnsatisfiable(i2003_11_14_17_21_30578) | ![Y: $i] : ((~cp1(Y)) | (~rf1(i2003_11_14_17_21_30578, Y))) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(i2003_11_14_17_21_30578, Y))) | ![Y: $i] : ((~cp2(Y)) | (~rf2(i2003_11_14_17_21_30578, Y))))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[65, 59])).
% 0.20/0.43 tff(67,plain,
% 0.20/0.43 (((~((~cUnsatisfiable(i2003_11_14_17_21_30578)) | (~((~cowlThing(tptp_fun_Y_2(i2003_11_14_17_21_30578))) | (~rr(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578))) | (~cp1(tptp_fun_Y_1(i2003_11_14_17_21_30578))) | (~rf1(i2003_11_14_17_21_30578, tptp_fun_Y_1(i2003_11_14_17_21_30578))) | (~cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))) | (~rf2(i2003_11_14_17_21_30578, tptp_fun_Y_0(i2003_11_14_17_21_30578))))))) | (~(cUnsatisfiable(i2003_11_14_17_21_30578) | ![Y: $i] : ((~cp1(Y)) | (~rf1(i2003_11_14_17_21_30578, Y))) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(i2003_11_14_17_21_30578, Y))) | ![Y: $i] : ((~cp2(Y)) | (~rf2(i2003_11_14_17_21_30578, Y)))))) | ((~cUnsatisfiable(i2003_11_14_17_21_30578)) | (~((~cowlThing(tptp_fun_Y_2(i2003_11_14_17_21_30578))) | (~rr(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578))) | (~cp1(tptp_fun_Y_1(i2003_11_14_17_21_30578))) | (~rf1(i2003_11_14_17_21_30578, tptp_fun_Y_1(i2003_11_14_17_21_30578))) | (~cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))) | (~rf2(i2003_11_14_17_21_30578, tptp_fun_Y_0(i2003_11_14_17_21_30578))))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(68,plain,
% 0.20/0.43 ((~cUnsatisfiable(i2003_11_14_17_21_30578)) | (~((~cowlThing(tptp_fun_Y_2(i2003_11_14_17_21_30578))) | (~rr(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578))) | (~cp1(tptp_fun_Y_1(i2003_11_14_17_21_30578))) | (~rf1(i2003_11_14_17_21_30578, tptp_fun_Y_1(i2003_11_14_17_21_30578))) | (~cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))) | (~rf2(i2003_11_14_17_21_30578, tptp_fun_Y_0(i2003_11_14_17_21_30578)))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.20/0.43 tff(69,plain,
% 0.20/0.43 (cUnsatisfiable(i2003_11_14_17_21_30578) <=> cUnsatisfiable(i2003_11_14_17_21_30578)),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(70,axiom,(cUnsatisfiable(i2003_11_14_17_21_30578)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_8')).
% 0.20/0.43 tff(71,plain,
% 0.20/0.43 (cUnsatisfiable(i2003_11_14_17_21_30578)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.20/0.43 tff(72,plain,
% 0.20/0.43 ((~((~cUnsatisfiable(i2003_11_14_17_21_30578)) | (~((~cowlThing(tptp_fun_Y_2(i2003_11_14_17_21_30578))) | (~rr(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578))) | (~cp1(tptp_fun_Y_1(i2003_11_14_17_21_30578))) | (~rf1(i2003_11_14_17_21_30578, tptp_fun_Y_1(i2003_11_14_17_21_30578))) | (~cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))) | (~rf2(i2003_11_14_17_21_30578, tptp_fun_Y_0(i2003_11_14_17_21_30578))))))) | (~cUnsatisfiable(i2003_11_14_17_21_30578)) | (~((~cowlThing(tptp_fun_Y_2(i2003_11_14_17_21_30578))) | (~rr(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578))) | (~cp1(tptp_fun_Y_1(i2003_11_14_17_21_30578))) | (~rf1(i2003_11_14_17_21_30578, tptp_fun_Y_1(i2003_11_14_17_21_30578))) | (~cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))) | (~rf2(i2003_11_14_17_21_30578, tptp_fun_Y_0(i2003_11_14_17_21_30578)))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(73,plain,
% 0.20/0.43 ((~((~cUnsatisfiable(i2003_11_14_17_21_30578)) | (~((~cowlThing(tptp_fun_Y_2(i2003_11_14_17_21_30578))) | (~rr(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578))) | (~cp1(tptp_fun_Y_1(i2003_11_14_17_21_30578))) | (~rf1(i2003_11_14_17_21_30578, tptp_fun_Y_1(i2003_11_14_17_21_30578))) | (~cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))) | (~rf2(i2003_11_14_17_21_30578, tptp_fun_Y_0(i2003_11_14_17_21_30578))))))) | (~((~cowlThing(tptp_fun_Y_2(i2003_11_14_17_21_30578))) | (~rr(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578))) | (~cp1(tptp_fun_Y_1(i2003_11_14_17_21_30578))) | (~rf1(i2003_11_14_17_21_30578, tptp_fun_Y_1(i2003_11_14_17_21_30578))) | (~cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))) | (~rf2(i2003_11_14_17_21_30578, tptp_fun_Y_0(i2003_11_14_17_21_30578)))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.20/0.43 tff(74,plain,
% 0.20/0.43 (~((~cowlThing(tptp_fun_Y_2(i2003_11_14_17_21_30578))) | (~rr(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578))) | (~cp1(tptp_fun_Y_1(i2003_11_14_17_21_30578))) | (~rf1(i2003_11_14_17_21_30578, tptp_fun_Y_1(i2003_11_14_17_21_30578))) | (~cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))) | (~rf2(i2003_11_14_17_21_30578, tptp_fun_Y_0(i2003_11_14_17_21_30578))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[73, 68])).
% 0.20/0.43 tff(75,plain,
% 0.20/0.43 (((~cowlThing(tptp_fun_Y_2(i2003_11_14_17_21_30578))) | (~rr(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578))) | (~cp1(tptp_fun_Y_1(i2003_11_14_17_21_30578))) | (~rf1(i2003_11_14_17_21_30578, tptp_fun_Y_1(i2003_11_14_17_21_30578))) | (~cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))) | (~rf2(i2003_11_14_17_21_30578, tptp_fun_Y_0(i2003_11_14_17_21_30578)))) | rr(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(76,plain,
% 0.20/0.43 (rr(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.20/0.43 tff(77,plain,
% 0.20/0.43 (^[X: $i, Y: $i] : refl(((~rr(X, Y)) | rf1(X, Y)) <=> ((~rr(X, Y)) | rf1(X, Y)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(78,plain,
% 0.20/0.43 (![X: $i, Y: $i] : ((~rr(X, Y)) | rf1(X, Y)) <=> ![X: $i, Y: $i] : ((~rr(X, Y)) | rf1(X, Y))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[77])).
% 0.20/0.43 tff(79,plain,
% 0.20/0.43 (![X: $i, Y: $i] : ((~rr(X, Y)) | rf1(X, Y)) <=> ![X: $i, Y: $i] : ((~rr(X, Y)) | rf1(X, Y))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(80,plain,
% 0.20/0.44 (^[X: $i, Y: $i] : rewrite((rr(X, Y) => rf1(X, Y)) <=> ((~rr(X, Y)) | rf1(X, Y)))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(81,plain,
% 0.20/0.44 (![X: $i, Y: $i] : (rr(X, Y) => rf1(X, Y)) <=> ![X: $i, Y: $i] : ((~rr(X, Y)) | rf1(X, Y))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[80])).
% 0.20/0.44 tff(82,axiom,(![X: $i, Y: $i] : (rr(X, Y) => rf1(X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_10')).
% 0.20/0.44 tff(83,plain,
% 0.20/0.44 (![X: $i, Y: $i] : ((~rr(X, Y)) | rf1(X, Y))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.20/0.44 tff(84,plain,
% 0.20/0.44 (![X: $i, Y: $i] : ((~rr(X, Y)) | rf1(X, Y))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.20/0.44 tff(85,plain,(
% 0.20/0.44 ![X: $i, Y: $i] : ((~rr(X, Y)) | rf1(X, Y))),
% 0.20/0.44 inference(skolemize,[status(sab)],[84])).
% 0.20/0.44 tff(86,plain,
% 0.20/0.44 (![X: $i, Y: $i] : ((~rr(X, Y)) | rf1(X, Y))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.20/0.44 tff(87,plain,
% 0.20/0.44 (((~![X: $i, Y: $i] : ((~rr(X, Y)) | rf1(X, Y))) | ((~rr(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578))) | rf1(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578)))) <=> ((~![X: $i, Y: $i] : ((~rr(X, Y)) | rf1(X, Y))) | (~rr(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578))) | rf1(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(88,plain,
% 0.20/0.44 ((~![X: $i, Y: $i] : ((~rr(X, Y)) | rf1(X, Y))) | ((~rr(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578))) | rf1(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(89,plain,
% 0.20/0.44 ((~![X: $i, Y: $i] : ((~rr(X, Y)) | rf1(X, Y))) | (~rr(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578))) | rf1(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.20/0.44 tff(90,plain,
% 0.20/0.44 (rf1(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[89, 86, 76])).
% 0.20/0.44 tff(91,plain,
% 0.20/0.44 (((~cowlThing(tptp_fun_Y_2(i2003_11_14_17_21_30578))) | (~rr(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578))) | (~cp1(tptp_fun_Y_1(i2003_11_14_17_21_30578))) | (~rf1(i2003_11_14_17_21_30578, tptp_fun_Y_1(i2003_11_14_17_21_30578))) | (~cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))) | (~rf2(i2003_11_14_17_21_30578, tptp_fun_Y_0(i2003_11_14_17_21_30578)))) | rf1(i2003_11_14_17_21_30578, tptp_fun_Y_1(i2003_11_14_17_21_30578))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(92,plain,
% 0.20/0.44 (rf1(i2003_11_14_17_21_30578, tptp_fun_Y_1(i2003_11_14_17_21_30578))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[91, 74])).
% 0.20/0.44 tff(93,plain,
% 0.20/0.44 (((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(i2003_11_14_17_21_30578, Y1)) | (~rf1(i2003_11_14_17_21_30578, Y0)))) | ((~rf1(i2003_11_14_17_21_30578, tptp_fun_Y_1(i2003_11_14_17_21_30578))) | (tptp_fun_Y_1(i2003_11_14_17_21_30578) = tptp_fun_Y_2(i2003_11_14_17_21_30578)) | (~rf1(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578))))) <=> ((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(i2003_11_14_17_21_30578, Y1)) | (~rf1(i2003_11_14_17_21_30578, Y0)))) | (~rf1(i2003_11_14_17_21_30578, tptp_fun_Y_1(i2003_11_14_17_21_30578))) | (tptp_fun_Y_1(i2003_11_14_17_21_30578) = tptp_fun_Y_2(i2003_11_14_17_21_30578)) | (~rf1(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(94,plain,
% 0.20/0.44 (((tptp_fun_Y_1(i2003_11_14_17_21_30578) = tptp_fun_Y_2(i2003_11_14_17_21_30578)) | (~rf1(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578))) | (~rf1(i2003_11_14_17_21_30578, tptp_fun_Y_1(i2003_11_14_17_21_30578)))) <=> ((~rf1(i2003_11_14_17_21_30578, tptp_fun_Y_1(i2003_11_14_17_21_30578))) | (tptp_fun_Y_1(i2003_11_14_17_21_30578) = tptp_fun_Y_2(i2003_11_14_17_21_30578)) | (~rf1(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(95,plain,
% 0.20/0.44 (((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(i2003_11_14_17_21_30578, Y1)) | (~rf1(i2003_11_14_17_21_30578, Y0)))) | ((tptp_fun_Y_1(i2003_11_14_17_21_30578) = tptp_fun_Y_2(i2003_11_14_17_21_30578)) | (~rf1(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578))) | (~rf1(i2003_11_14_17_21_30578, tptp_fun_Y_1(i2003_11_14_17_21_30578))))) <=> ((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(i2003_11_14_17_21_30578, Y1)) | (~rf1(i2003_11_14_17_21_30578, Y0)))) | ((~rf1(i2003_11_14_17_21_30578, tptp_fun_Y_1(i2003_11_14_17_21_30578))) | (tptp_fun_Y_1(i2003_11_14_17_21_30578) = tptp_fun_Y_2(i2003_11_14_17_21_30578)) | (~rf1(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578)))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[94])).
% 0.20/0.44 tff(96,plain,
% 0.20/0.44 (((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(i2003_11_14_17_21_30578, Y1)) | (~rf1(i2003_11_14_17_21_30578, Y0)))) | ((tptp_fun_Y_1(i2003_11_14_17_21_30578) = tptp_fun_Y_2(i2003_11_14_17_21_30578)) | (~rf1(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578))) | (~rf1(i2003_11_14_17_21_30578, tptp_fun_Y_1(i2003_11_14_17_21_30578))))) <=> ((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(i2003_11_14_17_21_30578, Y1)) | (~rf1(i2003_11_14_17_21_30578, Y0)))) | (~rf1(i2003_11_14_17_21_30578, tptp_fun_Y_1(i2003_11_14_17_21_30578))) | (tptp_fun_Y_1(i2003_11_14_17_21_30578) = tptp_fun_Y_2(i2003_11_14_17_21_30578)) | (~rf1(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[95, 93])).
% 0.20/0.44 tff(97,plain,
% 0.20/0.44 ((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(i2003_11_14_17_21_30578, Y1)) | (~rf1(i2003_11_14_17_21_30578, Y0)))) | ((tptp_fun_Y_1(i2003_11_14_17_21_30578) = tptp_fun_Y_2(i2003_11_14_17_21_30578)) | (~rf1(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578))) | (~rf1(i2003_11_14_17_21_30578, tptp_fun_Y_1(i2003_11_14_17_21_30578))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(98,plain,
% 0.20/0.44 ((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(i2003_11_14_17_21_30578, Y1)) | (~rf1(i2003_11_14_17_21_30578, Y0)))) | (~rf1(i2003_11_14_17_21_30578, tptp_fun_Y_1(i2003_11_14_17_21_30578))) | (tptp_fun_Y_1(i2003_11_14_17_21_30578) = tptp_fun_Y_2(i2003_11_14_17_21_30578)) | (~rf1(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.20/0.44 tff(99,plain,
% 0.20/0.44 (tptp_fun_Y_1(i2003_11_14_17_21_30578) = tptp_fun_Y_2(i2003_11_14_17_21_30578)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[98, 92, 90, 40])).
% 0.20/0.44 tff(100,plain,
% 0.20/0.44 (tptp_fun_Y_2(i2003_11_14_17_21_30578) = tptp_fun_Y_1(i2003_11_14_17_21_30578)),
% 0.20/0.44 inference(symmetry,[status(thm)],[99])).
% 0.20/0.44 tff(101,plain,
% 0.20/0.44 (^[X: $i] : refl(((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(X, Y0)) | (~rf2(X, Y1)))) <=> ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(X, Y0)) | (~rf2(X, Y1)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(102,plain,
% 0.20/0.44 (![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(X, Y0)) | (~rf2(X, Y1)))) <=> ![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(X, Y0)) | (~rf2(X, Y1))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[101])).
% 0.20/0.44 tff(103,plain,
% 0.20/0.44 (^[X: $i] : rewrite(((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(X, Y0)) | (~rf2(X, Y1)))) <=> ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(X, Y0)) | (~rf2(X, Y1)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(104,plain,
% 0.20/0.44 (![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(X, Y0)) | (~rf2(X, Y1)))) <=> ![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(X, Y0)) | (~rf2(X, Y1))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[103])).
% 0.20/0.44 tff(105,plain,
% 0.20/0.44 (![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(X, Y0)) | (~rf2(X, Y1)))) <=> ![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(X, Y0)) | (~rf2(X, Y1))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[104, 102])).
% 0.20/0.44 tff(106,plain,
% 0.20/0.44 (^[X: $i] : rewrite(((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((~(rf2(X, Y0) & rf2(X, Y1))) | (Y0 = Y1))) <=> ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(X, Y0)) | (~rf2(X, Y1)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(107,plain,
% 0.20/0.44 (![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((~(rf2(X, Y0) & rf2(X, Y1))) | (Y0 = Y1))) <=> ![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(X, Y0)) | (~rf2(X, Y1))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[106])).
% 0.20/0.44 tff(108,plain,
% 0.20/0.44 (![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((~(rf2(X, Y0) & rf2(X, Y1))) | (Y0 = Y1))) <=> ![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((~(rf2(X, Y0) & rf2(X, Y1))) | (Y0 = Y1)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(109,plain,
% 0.20/0.44 (^[X: $i] : trans(monotonicity(quant_intro(proof_bind(^[Y0: $i, Y1: $i] : rewrite(((rf2(X, Y0) & rf2(X, Y1)) => (Y0 = Y1)) <=> ((~(rf2(X, Y0) & rf2(X, Y1))) | (Y0 = Y1)))), (![Y0: $i, Y1: $i] : ((rf2(X, Y0) & rf2(X, Y1)) => (Y0 = Y1)) <=> ![Y0: $i, Y1: $i] : ((~(rf2(X, Y0) & rf2(X, Y1))) | (Y0 = Y1)))), ((cowlThing(X) => ![Y0: $i, Y1: $i] : ((rf2(X, Y0) & rf2(X, Y1)) => (Y0 = Y1))) <=> (cowlThing(X) => ![Y0: $i, Y1: $i] : ((~(rf2(X, Y0) & rf2(X, Y1))) | (Y0 = Y1))))), rewrite((cowlThing(X) => ![Y0: $i, Y1: $i] : ((~(rf2(X, Y0) & rf2(X, Y1))) | (Y0 = Y1))) <=> ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((~(rf2(X, Y0) & rf2(X, Y1))) | (Y0 = Y1)))), ((cowlThing(X) => ![Y0: $i, Y1: $i] : ((rf2(X, Y0) & rf2(X, Y1)) => (Y0 = Y1))) <=> ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((~(rf2(X, Y0) & rf2(X, Y1))) | (Y0 = Y1)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(110,plain,
% 0.20/0.44 (![X: $i] : (cowlThing(X) => ![Y0: $i, Y1: $i] : ((rf2(X, Y0) & rf2(X, Y1)) => (Y0 = Y1))) <=> ![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((~(rf2(X, Y0) & rf2(X, Y1))) | (Y0 = Y1)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[109])).
% 0.20/0.44 tff(111,axiom,(![X: $i] : (cowlThing(X) => ![Y0: $i, Y1: $i] : ((rf2(X, Y0) & rf2(X, Y1)) => (Y0 = Y1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_7')).
% 0.20/0.44 tff(112,plain,
% 0.20/0.44 (![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((~(rf2(X, Y0) & rf2(X, Y1))) | (Y0 = Y1)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.20/0.44 tff(113,plain,
% 0.20/0.44 (![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((~(rf2(X, Y0) & rf2(X, Y1))) | (Y0 = Y1)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[112, 108])).
% 0.20/0.44 tff(114,plain,(
% 0.20/0.44 ![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((~(rf2(X, Y0) & rf2(X, Y1))) | (Y0 = Y1)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[113])).
% 0.20/0.44 tff(115,plain,
% 0.20/0.44 (![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(X, Y0)) | (~rf2(X, Y1))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[114, 107])).
% 0.20/0.44 tff(116,plain,
% 0.20/0.44 (![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(X, Y0)) | (~rf2(X, Y1))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[115, 105])).
% 0.20/0.44 tff(117,plain,
% 0.20/0.44 (((~![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(X, Y0)) | (~rf2(X, Y1))))) | ((~cowlThing(i2003_11_14_17_21_30578)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(i2003_11_14_17_21_30578, Y1)) | (~rf2(i2003_11_14_17_21_30578, Y0))))) <=> ((~![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(X, Y0)) | (~rf2(X, Y1))))) | (~cowlThing(i2003_11_14_17_21_30578)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(i2003_11_14_17_21_30578, Y1)) | (~rf2(i2003_11_14_17_21_30578, Y0))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(118,plain,
% 0.20/0.44 (((~cowlThing(i2003_11_14_17_21_30578)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(i2003_11_14_17_21_30578, Y0)) | (~rf2(i2003_11_14_17_21_30578, Y1)))) <=> ((~cowlThing(i2003_11_14_17_21_30578)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(i2003_11_14_17_21_30578, Y1)) | (~rf2(i2003_11_14_17_21_30578, Y0))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(119,plain,
% 0.20/0.44 (((~![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(X, Y0)) | (~rf2(X, Y1))))) | ((~cowlThing(i2003_11_14_17_21_30578)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(i2003_11_14_17_21_30578, Y0)) | (~rf2(i2003_11_14_17_21_30578, Y1))))) <=> ((~![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(X, Y0)) | (~rf2(X, Y1))))) | ((~cowlThing(i2003_11_14_17_21_30578)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(i2003_11_14_17_21_30578, Y1)) | (~rf2(i2003_11_14_17_21_30578, Y0)))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[118])).
% 0.20/0.44 tff(120,plain,
% 0.20/0.44 (((~![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(X, Y0)) | (~rf2(X, Y1))))) | ((~cowlThing(i2003_11_14_17_21_30578)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(i2003_11_14_17_21_30578, Y0)) | (~rf2(i2003_11_14_17_21_30578, Y1))))) <=> ((~![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(X, Y0)) | (~rf2(X, Y1))))) | (~cowlThing(i2003_11_14_17_21_30578)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(i2003_11_14_17_21_30578, Y1)) | (~rf2(i2003_11_14_17_21_30578, Y0))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[119, 117])).
% 0.20/0.44 tff(121,plain,
% 0.20/0.44 ((~![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(X, Y0)) | (~rf2(X, Y1))))) | ((~cowlThing(i2003_11_14_17_21_30578)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(i2003_11_14_17_21_30578, Y0)) | (~rf2(i2003_11_14_17_21_30578, Y1))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(122,plain,
% 0.20/0.44 ((~![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(X, Y0)) | (~rf2(X, Y1))))) | (~cowlThing(i2003_11_14_17_21_30578)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(i2003_11_14_17_21_30578, Y1)) | (~rf2(i2003_11_14_17_21_30578, Y0)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.20/0.44 tff(123,plain,
% 0.20/0.44 ((~cowlThing(i2003_11_14_17_21_30578)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(i2003_11_14_17_21_30578, Y1)) | (~rf2(i2003_11_14_17_21_30578, Y0)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[122, 116])).
% 0.20/0.44 tff(124,plain,
% 0.20/0.44 (![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(i2003_11_14_17_21_30578, Y1)) | (~rf2(i2003_11_14_17_21_30578, Y0)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[123, 16])).
% 0.20/0.44 tff(125,plain,
% 0.20/0.44 (^[X: $i, Y: $i] : refl(((~rr(X, Y)) | rf2(X, Y)) <=> ((~rr(X, Y)) | rf2(X, Y)))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(126,plain,
% 0.20/0.44 (![X: $i, Y: $i] : ((~rr(X, Y)) | rf2(X, Y)) <=> ![X: $i, Y: $i] : ((~rr(X, Y)) | rf2(X, Y))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[125])).
% 0.20/0.44 tff(127,plain,
% 0.20/0.44 (![X: $i, Y: $i] : ((~rr(X, Y)) | rf2(X, Y)) <=> ![X: $i, Y: $i] : ((~rr(X, Y)) | rf2(X, Y))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(128,plain,
% 0.20/0.44 (^[X: $i, Y: $i] : rewrite((rr(X, Y) => rf2(X, Y)) <=> ((~rr(X, Y)) | rf2(X, Y)))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(129,plain,
% 0.20/0.44 (![X: $i, Y: $i] : (rr(X, Y) => rf2(X, Y)) <=> ![X: $i, Y: $i] : ((~rr(X, Y)) | rf2(X, Y))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[128])).
% 0.20/0.44 tff(130,axiom,(![X: $i, Y: $i] : (rr(X, Y) => rf2(X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_9')).
% 0.20/0.44 tff(131,plain,
% 0.20/0.44 (![X: $i, Y: $i] : ((~rr(X, Y)) | rf2(X, Y))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.20/0.44 tff(132,plain,
% 0.20/0.44 (![X: $i, Y: $i] : ((~rr(X, Y)) | rf2(X, Y))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[131, 127])).
% 0.20/0.44 tff(133,plain,(
% 0.20/0.44 ![X: $i, Y: $i] : ((~rr(X, Y)) | rf2(X, Y))),
% 0.20/0.44 inference(skolemize,[status(sab)],[132])).
% 0.20/0.44 tff(134,plain,
% 0.20/0.44 (![X: $i, Y: $i] : ((~rr(X, Y)) | rf2(X, Y))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[133, 126])).
% 0.20/0.44 tff(135,plain,
% 0.20/0.44 (((~![X: $i, Y: $i] : ((~rr(X, Y)) | rf2(X, Y))) | ((~rr(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578))) | rf2(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578)))) <=> ((~![X: $i, Y: $i] : ((~rr(X, Y)) | rf2(X, Y))) | (~rr(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578))) | rf2(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(136,plain,
% 0.20/0.44 ((~![X: $i, Y: $i] : ((~rr(X, Y)) | rf2(X, Y))) | ((~rr(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578))) | rf2(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(137,plain,
% 0.20/0.44 ((~![X: $i, Y: $i] : ((~rr(X, Y)) | rf2(X, Y))) | (~rr(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578))) | rf2(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.20/0.44 tff(138,plain,
% 0.20/0.45 (rf2(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[137, 134, 76])).
% 0.20/0.45 tff(139,plain,
% 0.20/0.45 (((~cowlThing(tptp_fun_Y_2(i2003_11_14_17_21_30578))) | (~rr(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578))) | (~cp1(tptp_fun_Y_1(i2003_11_14_17_21_30578))) | (~rf1(i2003_11_14_17_21_30578, tptp_fun_Y_1(i2003_11_14_17_21_30578))) | (~cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))) | (~rf2(i2003_11_14_17_21_30578, tptp_fun_Y_0(i2003_11_14_17_21_30578)))) | rf2(i2003_11_14_17_21_30578, tptp_fun_Y_0(i2003_11_14_17_21_30578))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(140,plain,
% 0.20/0.45 (rf2(i2003_11_14_17_21_30578, tptp_fun_Y_0(i2003_11_14_17_21_30578))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[139, 74])).
% 0.20/0.45 tff(141,plain,
% 0.20/0.45 (((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(i2003_11_14_17_21_30578, Y1)) | (~rf2(i2003_11_14_17_21_30578, Y0)))) | ((~rf2(i2003_11_14_17_21_30578, tptp_fun_Y_0(i2003_11_14_17_21_30578))) | (tptp_fun_Y_0(i2003_11_14_17_21_30578) = tptp_fun_Y_2(i2003_11_14_17_21_30578)) | (~rf2(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578))))) <=> ((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(i2003_11_14_17_21_30578, Y1)) | (~rf2(i2003_11_14_17_21_30578, Y0)))) | (~rf2(i2003_11_14_17_21_30578, tptp_fun_Y_0(i2003_11_14_17_21_30578))) | (tptp_fun_Y_0(i2003_11_14_17_21_30578) = tptp_fun_Y_2(i2003_11_14_17_21_30578)) | (~rf2(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(142,plain,
% 0.20/0.45 (((tptp_fun_Y_0(i2003_11_14_17_21_30578) = tptp_fun_Y_2(i2003_11_14_17_21_30578)) | (~rf2(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578))) | (~rf2(i2003_11_14_17_21_30578, tptp_fun_Y_0(i2003_11_14_17_21_30578)))) <=> ((~rf2(i2003_11_14_17_21_30578, tptp_fun_Y_0(i2003_11_14_17_21_30578))) | (tptp_fun_Y_0(i2003_11_14_17_21_30578) = tptp_fun_Y_2(i2003_11_14_17_21_30578)) | (~rf2(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(143,plain,
% 0.20/0.45 (((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(i2003_11_14_17_21_30578, Y1)) | (~rf2(i2003_11_14_17_21_30578, Y0)))) | ((tptp_fun_Y_0(i2003_11_14_17_21_30578) = tptp_fun_Y_2(i2003_11_14_17_21_30578)) | (~rf2(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578))) | (~rf2(i2003_11_14_17_21_30578, tptp_fun_Y_0(i2003_11_14_17_21_30578))))) <=> ((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(i2003_11_14_17_21_30578, Y1)) | (~rf2(i2003_11_14_17_21_30578, Y0)))) | ((~rf2(i2003_11_14_17_21_30578, tptp_fun_Y_0(i2003_11_14_17_21_30578))) | (tptp_fun_Y_0(i2003_11_14_17_21_30578) = tptp_fun_Y_2(i2003_11_14_17_21_30578)) | (~rf2(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578)))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[142])).
% 0.20/0.45 tff(144,plain,
% 0.20/0.45 (((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(i2003_11_14_17_21_30578, Y1)) | (~rf2(i2003_11_14_17_21_30578, Y0)))) | ((tptp_fun_Y_0(i2003_11_14_17_21_30578) = tptp_fun_Y_2(i2003_11_14_17_21_30578)) | (~rf2(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578))) | (~rf2(i2003_11_14_17_21_30578, tptp_fun_Y_0(i2003_11_14_17_21_30578))))) <=> ((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(i2003_11_14_17_21_30578, Y1)) | (~rf2(i2003_11_14_17_21_30578, Y0)))) | (~rf2(i2003_11_14_17_21_30578, tptp_fun_Y_0(i2003_11_14_17_21_30578))) | (tptp_fun_Y_0(i2003_11_14_17_21_30578) = tptp_fun_Y_2(i2003_11_14_17_21_30578)) | (~rf2(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[143, 141])).
% 0.20/0.45 tff(145,plain,
% 0.20/0.45 ((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(i2003_11_14_17_21_30578, Y1)) | (~rf2(i2003_11_14_17_21_30578, Y0)))) | ((tptp_fun_Y_0(i2003_11_14_17_21_30578) = tptp_fun_Y_2(i2003_11_14_17_21_30578)) | (~rf2(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578))) | (~rf2(i2003_11_14_17_21_30578, tptp_fun_Y_0(i2003_11_14_17_21_30578))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(146,plain,
% 0.20/0.45 ((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(i2003_11_14_17_21_30578, Y1)) | (~rf2(i2003_11_14_17_21_30578, Y0)))) | (~rf2(i2003_11_14_17_21_30578, tptp_fun_Y_0(i2003_11_14_17_21_30578))) | (tptp_fun_Y_0(i2003_11_14_17_21_30578) = tptp_fun_Y_2(i2003_11_14_17_21_30578)) | (~rf2(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.20/0.45 tff(147,plain,
% 0.20/0.45 (tptp_fun_Y_0(i2003_11_14_17_21_30578) = tptp_fun_Y_2(i2003_11_14_17_21_30578)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[146, 140, 138, 124])).
% 0.20/0.45 tff(148,plain,
% 0.20/0.45 (tptp_fun_Y_0(i2003_11_14_17_21_30578) = tptp_fun_Y_1(i2003_11_14_17_21_30578)),
% 0.20/0.45 inference(transitivity,[status(thm)],[147, 100])).
% 0.20/0.45 tff(149,plain,
% 0.20/0.45 (ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_30578), tptp_fun_Y0_4(tptp_fun_Y_1(i2003_11_14_17_21_30578))) <=> ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_30578), tptp_fun_Y0_4(tptp_fun_Y_1(i2003_11_14_17_21_30578)))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[148])).
% 0.20/0.45 tff(150,plain,
% 0.20/0.45 (ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_30578), tptp_fun_Y0_4(tptp_fun_Y_1(i2003_11_14_17_21_30578))) <=> ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_30578), tptp_fun_Y0_4(tptp_fun_Y_1(i2003_11_14_17_21_30578)))),
% 0.20/0.45 inference(symmetry,[status(thm)],[149])).
% 0.20/0.45 tff(151,plain,
% 0.20/0.45 (^[X: $i] : refl((~((~((~cp2xcomp(X)) | ra_Px1(X, tptp_fun_Y0_4(X)))) | (~(cp2xcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))))) <=> (~((~((~cp2xcomp(X)) | ra_Px1(X, tptp_fun_Y0_4(X)))) | (~(cp2xcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(152,plain,
% 0.20/0.45 (![X: $i] : (~((~((~cp2xcomp(X)) | ra_Px1(X, tptp_fun_Y0_4(X)))) | (~(cp2xcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))))) <=> ![X: $i] : (~((~((~cp2xcomp(X)) | ra_Px1(X, tptp_fun_Y0_4(X)))) | (~(cp2xcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[151])).
% 0.20/0.45 tff(153,plain,
% 0.20/0.45 (^[X: $i] : rewrite((~((~((~cp2xcomp(X)) | ra_Px1(X, tptp_fun_Y0_4(X)))) | (~(cp2xcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))))) <=> (~((~((~cp2xcomp(X)) | ra_Px1(X, tptp_fun_Y0_4(X)))) | (~(cp2xcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(154,plain,
% 0.20/0.45 (![X: $i] : (~((~((~cp2xcomp(X)) | ra_Px1(X, tptp_fun_Y0_4(X)))) | (~(cp2xcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))))) <=> ![X: $i] : (~((~((~cp2xcomp(X)) | ra_Px1(X, tptp_fun_Y0_4(X)))) | (~(cp2xcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[153])).
% 0.20/0.45 tff(155,plain,
% 0.20/0.45 (![X: $i] : (~((~((~cp2xcomp(X)) | ra_Px1(X, tptp_fun_Y0_4(X)))) | (~(cp2xcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))))) <=> ![X: $i] : (~((~((~cp2xcomp(X)) | ra_Px1(X, tptp_fun_Y0_4(X)))) | (~(cp2xcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[154, 152])).
% 0.20/0.45 tff(156,plain,
% 0.20/0.45 (^[X: $i] : trans(monotonicity(rewrite((cp2xcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))) <=> (cp2xcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))), ((((~cp2xcomp(X)) | ra_Px1(X, tptp_fun_Y0_4(X))) & (cp2xcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))) <=> (((~cp2xcomp(X)) | ra_Px1(X, tptp_fun_Y0_4(X))) & (cp2xcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))))), rewrite((((~cp2xcomp(X)) | ra_Px1(X, tptp_fun_Y0_4(X))) & (cp2xcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))) <=> (~((~((~cp2xcomp(X)) | ra_Px1(X, tptp_fun_Y0_4(X)))) | (~(cp2xcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))), ((((~cp2xcomp(X)) | ra_Px1(X, tptp_fun_Y0_4(X))) & (cp2xcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))) <=> (~((~((~cp2xcomp(X)) | ra_Px1(X, tptp_fun_Y0_4(X)))) | (~(cp2xcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(157,plain,
% 0.20/0.45 (![X: $i] : (((~cp2xcomp(X)) | ra_Px1(X, tptp_fun_Y0_4(X))) & (cp2xcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))) <=> ![X: $i] : (~((~((~cp2xcomp(X)) | ra_Px1(X, tptp_fun_Y0_4(X)))) | (~(cp2xcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[156])).
% 0.20/0.45 tff(158,plain,
% 0.20/0.45 (![X: $i] : (cp2xcomp(X) <=> ?[Y0: $i] : ra_Px1(X, Y0)) <=> ![X: $i] : (cp2xcomp(X) <=> ?[Y0: $i] : ra_Px1(X, Y0))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(159,axiom,(![X: $i] : (cp2xcomp(X) <=> ?[Y0: $i] : ra_Px1(X, Y0))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_5')).
% 0.20/0.45 tff(160,plain,
% 0.20/0.45 (![X: $i] : (cp2xcomp(X) <=> ?[Y0: $i] : ra_Px1(X, Y0))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.20/0.45 tff(161,plain,(
% 0.20/0.45 ![X: $i] : (((~cp2xcomp(X)) | ra_Px1(X, tptp_fun_Y0_4(X))) & (cp2xcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))),
% 0.20/0.45 inference(skolemize,[status(sab)],[160])).
% 0.20/0.45 tff(162,plain,
% 0.20/0.45 (![X: $i] : (~((~((~cp2xcomp(X)) | ra_Px1(X, tptp_fun_Y0_4(X)))) | (~(cp2xcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[161, 157])).
% 0.20/0.45 tff(163,plain,
% 0.20/0.45 (![X: $i] : (~((~((~cp2xcomp(X)) | ra_Px1(X, tptp_fun_Y0_4(X)))) | (~(cp2xcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[162, 155])).
% 0.20/0.45 tff(164,plain,
% 0.20/0.45 ((~![X: $i] : (~((~((~cp2xcomp(X)) | ra_Px1(X, tptp_fun_Y0_4(X)))) | (~(cp2xcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))) | (~((~((~cp2xcomp(tptp_fun_Y_1(i2003_11_14_17_21_30578))) | ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_30578), tptp_fun_Y0_4(tptp_fun_Y_1(i2003_11_14_17_21_30578))))) | (~(cp2xcomp(tptp_fun_Y_1(i2003_11_14_17_21_30578)) | ![Y0: $i] : (~ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_30578), Y0))))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(165,plain,
% 0.20/0.45 (~((~((~cp2xcomp(tptp_fun_Y_1(i2003_11_14_17_21_30578))) | ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_30578), tptp_fun_Y0_4(tptp_fun_Y_1(i2003_11_14_17_21_30578))))) | (~(cp2xcomp(tptp_fun_Y_1(i2003_11_14_17_21_30578)) | ![Y0: $i] : (~ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_30578), Y0)))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[164, 163])).
% 0.20/0.45 tff(166,plain,
% 0.20/0.45 (((~((~cp2xcomp(tptp_fun_Y_1(i2003_11_14_17_21_30578))) | ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_30578), tptp_fun_Y0_4(tptp_fun_Y_1(i2003_11_14_17_21_30578))))) | (~(cp2xcomp(tptp_fun_Y_1(i2003_11_14_17_21_30578)) | ![Y0: $i] : (~ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_30578), Y0))))) | ((~cp2xcomp(tptp_fun_Y_1(i2003_11_14_17_21_30578))) | ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_30578), tptp_fun_Y0_4(tptp_fun_Y_1(i2003_11_14_17_21_30578))))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(167,plain,
% 0.20/0.45 ((~cp2xcomp(tptp_fun_Y_1(i2003_11_14_17_21_30578))) | ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_30578), tptp_fun_Y0_4(tptp_fun_Y_1(i2003_11_14_17_21_30578)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[166, 165])).
% 0.20/0.45 tff(168,plain,
% 0.20/0.45 (((~cowlThing(tptp_fun_Y_2(i2003_11_14_17_21_30578))) | (~rr(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578))) | (~cp1(tptp_fun_Y_1(i2003_11_14_17_21_30578))) | (~rf1(i2003_11_14_17_21_30578, tptp_fun_Y_1(i2003_11_14_17_21_30578))) | (~cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))) | (~rf2(i2003_11_14_17_21_30578, tptp_fun_Y_0(i2003_11_14_17_21_30578)))) | cp1(tptp_fun_Y_1(i2003_11_14_17_21_30578))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(169,plain,
% 0.20/0.45 (cp1(tptp_fun_Y_1(i2003_11_14_17_21_30578))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[168, 74])).
% 0.20/0.45 tff(170,plain,
% 0.20/0.45 (^[X: $i] : refl((cp2xcomp(X) | (~cp1(X))) <=> (cp2xcomp(X) | (~cp1(X))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(171,plain,
% 0.20/0.45 (![X: $i] : (cp2xcomp(X) | (~cp1(X))) <=> ![X: $i] : (cp2xcomp(X) | (~cp1(X)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[170])).
% 0.20/0.45 tff(172,plain,
% 0.20/0.45 (![X: $i] : (cp2xcomp(X) | (~cp1(X))) <=> ![X: $i] : (cp2xcomp(X) | (~cp1(X)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(173,plain,
% 0.20/0.45 (^[X: $i] : rewrite((cp1(X) => cp2xcomp(X)) <=> (cp2xcomp(X) | (~cp1(X))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(174,plain,
% 0.20/0.45 (![X: $i] : (cp1(X) => cp2xcomp(X)) <=> ![X: $i] : (cp2xcomp(X) | (~cp1(X)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[173])).
% 0.20/0.45 tff(175,axiom,(![X: $i] : (cp1(X) => cp2xcomp(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_3')).
% 0.20/0.45 tff(176,plain,
% 0.20/0.45 (![X: $i] : (cp2xcomp(X) | (~cp1(X)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.20/0.45 tff(177,plain,
% 0.20/0.45 (![X: $i] : (cp2xcomp(X) | (~cp1(X)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[176, 172])).
% 0.20/0.45 tff(178,plain,(
% 0.20/0.45 ![X: $i] : (cp2xcomp(X) | (~cp1(X)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[177])).
% 0.20/0.45 tff(179,plain,
% 0.20/0.45 (![X: $i] : (cp2xcomp(X) | (~cp1(X)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[178, 171])).
% 0.20/0.45 tff(180,plain,
% 0.20/0.45 (((~![X: $i] : (cp2xcomp(X) | (~cp1(X)))) | (cp2xcomp(tptp_fun_Y_1(i2003_11_14_17_21_30578)) | (~cp1(tptp_fun_Y_1(i2003_11_14_17_21_30578))))) <=> ((~![X: $i] : (cp2xcomp(X) | (~cp1(X)))) | cp2xcomp(tptp_fun_Y_1(i2003_11_14_17_21_30578)) | (~cp1(tptp_fun_Y_1(i2003_11_14_17_21_30578))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(181,plain,
% 0.20/0.45 ((~![X: $i] : (cp2xcomp(X) | (~cp1(X)))) | (cp2xcomp(tptp_fun_Y_1(i2003_11_14_17_21_30578)) | (~cp1(tptp_fun_Y_1(i2003_11_14_17_21_30578))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(182,plain,
% 0.20/0.45 ((~![X: $i] : (cp2xcomp(X) | (~cp1(X)))) | cp2xcomp(tptp_fun_Y_1(i2003_11_14_17_21_30578)) | (~cp1(tptp_fun_Y_1(i2003_11_14_17_21_30578)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.20/0.45 tff(183,plain,
% 0.20/0.45 (cp2xcomp(tptp_fun_Y_1(i2003_11_14_17_21_30578))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[182, 179, 169])).
% 0.20/0.45 tff(184,plain,
% 0.20/0.45 ((~((~cp2xcomp(tptp_fun_Y_1(i2003_11_14_17_21_30578))) | ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_30578), tptp_fun_Y0_4(tptp_fun_Y_1(i2003_11_14_17_21_30578))))) | (~cp2xcomp(tptp_fun_Y_1(i2003_11_14_17_21_30578))) | ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_30578), tptp_fun_Y0_4(tptp_fun_Y_1(i2003_11_14_17_21_30578)))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(185,plain,
% 0.20/0.45 ((~((~cp2xcomp(tptp_fun_Y_1(i2003_11_14_17_21_30578))) | ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_30578), tptp_fun_Y0_4(tptp_fun_Y_1(i2003_11_14_17_21_30578))))) | ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_30578), tptp_fun_Y0_4(tptp_fun_Y_1(i2003_11_14_17_21_30578)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[184, 183])).
% 0.20/0.45 tff(186,plain,
% 0.20/0.45 (ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_30578), tptp_fun_Y0_4(tptp_fun_Y_1(i2003_11_14_17_21_30578)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[185, 167])).
% 0.20/0.45 tff(187,plain,
% 0.20/0.45 (ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_30578), tptp_fun_Y0_4(tptp_fun_Y_1(i2003_11_14_17_21_30578)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[186, 150])).
% 0.20/0.45 tff(188,plain,
% 0.20/0.45 (^[X: $i] : rewrite((~((~(cp2(X) | ra_Px1(X, tptp_fun_Y_3(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~cp2(X)))))) <=> (~((~(cp2(X) | ra_Px1(X, tptp_fun_Y_3(X)))) | (~((~cp2(X)) | ![Y: $i] : (~ra_Px1(X, Y)))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(189,plain,
% 0.20/0.45 (![X: $i] : (~((~(cp2(X) | ra_Px1(X, tptp_fun_Y_3(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~cp2(X)))))) <=> ![X: $i] : (~((~(cp2(X) | ra_Px1(X, tptp_fun_Y_3(X)))) | (~((~cp2(X)) | ![Y: $i] : (~ra_Px1(X, Y))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[188])).
% 0.20/0.45 tff(190,plain,
% 0.20/0.45 (^[X: $i] : refl((~((~(cp2(X) | ra_Px1(X, tptp_fun_Y_3(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~cp2(X)))))) <=> (~((~(cp2(X) | ra_Px1(X, tptp_fun_Y_3(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~cp2(X)))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(191,plain,
% 0.20/0.45 (![X: $i] : (~((~(cp2(X) | ra_Px1(X, tptp_fun_Y_3(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~cp2(X)))))) <=> ![X: $i] : (~((~(cp2(X) | ra_Px1(X, tptp_fun_Y_3(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~cp2(X))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[190])).
% 0.20/0.45 tff(192,plain,
% 0.20/0.45 (^[X: $i] : rewrite((~((~(cp2(X) | ra_Px1(X, tptp_fun_Y_3(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~cp2(X)))))) <=> (~((~(cp2(X) | ra_Px1(X, tptp_fun_Y_3(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~cp2(X)))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(193,plain,
% 0.20/0.45 (![X: $i] : (~((~(cp2(X) | ra_Px1(X, tptp_fun_Y_3(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~cp2(X)))))) <=> ![X: $i] : (~((~(cp2(X) | ra_Px1(X, tptp_fun_Y_3(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~cp2(X))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[192])).
% 0.20/0.45 tff(194,plain,
% 0.20/0.45 (![X: $i] : (~((~(cp2(X) | ra_Px1(X, tptp_fun_Y_3(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~cp2(X)))))) <=> ![X: $i] : (~((~(cp2(X) | ra_Px1(X, tptp_fun_Y_3(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~cp2(X))))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[193, 191])).
% 0.20/0.45 tff(195,plain,
% 0.20/0.45 (^[X: $i] : trans(monotonicity(rewrite((![Y: $i] : (~ra_Px1(X, Y)) | (~cp2(X))) <=> (![Y: $i] : (~ra_Px1(X, Y)) | (~cp2(X)))), (((cp2(X) | ra_Px1(X, tptp_fun_Y_3(X))) & (![Y: $i] : (~ra_Px1(X, Y)) | (~cp2(X)))) <=> ((cp2(X) | ra_Px1(X, tptp_fun_Y_3(X))) & (![Y: $i] : (~ra_Px1(X, Y)) | (~cp2(X)))))), rewrite(((cp2(X) | ra_Px1(X, tptp_fun_Y_3(X))) & (![Y: $i] : (~ra_Px1(X, Y)) | (~cp2(X)))) <=> (~((~(cp2(X) | ra_Px1(X, tptp_fun_Y_3(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~cp2(X))))))), (((cp2(X) | ra_Px1(X, tptp_fun_Y_3(X))) & (![Y: $i] : (~ra_Px1(X, Y)) | (~cp2(X)))) <=> (~((~(cp2(X) | ra_Px1(X, tptp_fun_Y_3(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~cp2(X))))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(196,plain,
% 0.20/0.45 (![X: $i] : ((cp2(X) | ra_Px1(X, tptp_fun_Y_3(X))) & (![Y: $i] : (~ra_Px1(X, Y)) | (~cp2(X)))) <=> ![X: $i] : (~((~(cp2(X) | ra_Px1(X, tptp_fun_Y_3(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~cp2(X))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[195])).
% 0.20/0.45 tff(197,plain,
% 0.20/0.45 (^[X: $i] : rewrite(((ra_Px1(X, tptp_fun_Y_3(X)) | cp2(X)) & (![Y: $i] : (~ra_Px1(X, Y)) | (~cp2(X)))) <=> ((cp2(X) | ra_Px1(X, tptp_fun_Y_3(X))) & (![Y: $i] : (~ra_Px1(X, Y)) | (~cp2(X)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(198,plain,
% 0.20/0.45 (![X: $i] : ((ra_Px1(X, tptp_fun_Y_3(X)) | cp2(X)) & (![Y: $i] : (~ra_Px1(X, Y)) | (~cp2(X)))) <=> ![X: $i] : ((cp2(X) | ra_Px1(X, tptp_fun_Y_3(X))) & (![Y: $i] : (~ra_Px1(X, Y)) | (~cp2(X))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[197])).
% 0.20/0.45 tff(199,plain,
% 0.20/0.45 (![X: $i] : (~(?[Y: $i] : ra_Px1(X, Y) <=> cp2(X))) <=> ![X: $i] : (~(?[Y: $i] : ra_Px1(X, Y) <=> cp2(X)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(200,plain,
% 0.20/0.45 (^[X: $i] : trans(trans(monotonicity(rewrite((~?[Y: $i] : ra_Px1(X, Y)) <=> (~?[Y: $i] : ra_Px1(X, Y))), ((cp2(X) <=> (~?[Y: $i] : ra_Px1(X, Y))) <=> (cp2(X) <=> (~?[Y: $i] : ra_Px1(X, Y))))), rewrite((cp2(X) <=> (~?[Y: $i] : ra_Px1(X, Y))) <=> (~(?[Y: $i] : ra_Px1(X, Y) <=> cp2(X)))), ((cp2(X) <=> (~?[Y: $i] : ra_Px1(X, Y))) <=> (~(?[Y: $i] : ra_Px1(X, Y) <=> cp2(X))))), rewrite((~(?[Y: $i] : ra_Px1(X, Y) <=> cp2(X))) <=> (~(?[Y: $i] : ra_Px1(X, Y) <=> cp2(X)))), ((cp2(X) <=> (~?[Y: $i] : ra_Px1(X, Y))) <=> (~(?[Y: $i] : ra_Px1(X, Y) <=> cp2(X)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(201,plain,
% 0.20/0.45 (![X: $i] : (cp2(X) <=> (~?[Y: $i] : ra_Px1(X, Y))) <=> ![X: $i] : (~(?[Y: $i] : ra_Px1(X, Y) <=> cp2(X)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[200])).
% 0.20/0.45 tff(202,axiom,(![X: $i] : (cp2(X) <=> (~?[Y: $i] : ra_Px1(X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_4')).
% 0.20/0.45 tff(203,plain,
% 0.20/0.45 (![X: $i] : (~(?[Y: $i] : ra_Px1(X, Y) <=> cp2(X)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.20/0.45 tff(204,plain,
% 0.20/0.45 (![X: $i] : (~(?[Y: $i] : ra_Px1(X, Y) <=> cp2(X)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[203, 199])).
% 0.20/0.45 tff(205,plain,(
% 0.20/0.45 ![X: $i] : ((ra_Px1(X, tptp_fun_Y_3(X)) | cp2(X)) & (![Y: $i] : (~ra_Px1(X, Y)) | (~cp2(X))))),
% 0.20/0.45 inference(skolemize,[status(sab)],[204])).
% 0.20/0.45 tff(206,plain,
% 0.20/0.45 (![X: $i] : ((cp2(X) | ra_Px1(X, tptp_fun_Y_3(X))) & (![Y: $i] : (~ra_Px1(X, Y)) | (~cp2(X))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[205, 198])).
% 0.20/0.45 tff(207,plain,
% 0.20/0.45 (![X: $i] : (~((~(cp2(X) | ra_Px1(X, tptp_fun_Y_3(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~cp2(X))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[206, 196])).
% 0.20/0.45 tff(208,plain,
% 0.20/0.45 (![X: $i] : (~((~(cp2(X) | ra_Px1(X, tptp_fun_Y_3(X)))) | (~(![Y: $i] : (~ra_Px1(X, Y)) | (~cp2(X))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[207, 194])).
% 0.20/0.45 tff(209,plain,
% 0.20/0.45 (![X: $i] : (~((~(cp2(X) | ra_Px1(X, tptp_fun_Y_3(X)))) | (~((~cp2(X)) | ![Y: $i] : (~ra_Px1(X, Y))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[208, 189])).
% 0.20/0.45 tff(210,plain,
% 0.20/0.45 ((~![X: $i] : (~((~(cp2(X) | ra_Px1(X, tptp_fun_Y_3(X)))) | (~((~cp2(X)) | ![Y: $i] : (~ra_Px1(X, Y))))))) | (~((~(cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578)) | ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_30578), tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_30578))))) | (~((~cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))) | ![Y: $i] : (~ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_30578), Y))))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(211,plain,
% 0.20/0.45 (~((~(cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578)) | ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_30578), tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_30578))))) | (~((~cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))) | ![Y: $i] : (~ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_30578), Y)))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[210, 209])).
% 0.20/0.45 tff(212,plain,
% 0.20/0.45 (((~(cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578)) | ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_30578), tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_30578))))) | (~((~cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))) | ![Y: $i] : (~ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_30578), Y))))) | ((~cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))) | ![Y: $i] : (~ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_30578), Y)))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(213,plain,
% 0.20/0.45 ((~cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))) | ![Y: $i] : (~ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_30578), Y))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[212, 211])).
% 0.20/0.45 tff(214,plain,
% 0.20/0.45 (((~cowlThing(tptp_fun_Y_2(i2003_11_14_17_21_30578))) | (~rr(i2003_11_14_17_21_30578, tptp_fun_Y_2(i2003_11_14_17_21_30578))) | (~cp1(tptp_fun_Y_1(i2003_11_14_17_21_30578))) | (~rf1(i2003_11_14_17_21_30578, tptp_fun_Y_1(i2003_11_14_17_21_30578))) | (~cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))) | (~rf2(i2003_11_14_17_21_30578, tptp_fun_Y_0(i2003_11_14_17_21_30578)))) | cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(215,plain,
% 0.20/0.45 (cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[214, 74])).
% 0.20/0.45 tff(216,plain,
% 0.20/0.45 ((~((~cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))) | ![Y: $i] : (~ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_30578), Y)))) | (~cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))) | ![Y: $i] : (~ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_30578), Y))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(217,plain,
% 0.20/0.45 ((~((~cp2(tptp_fun_Y_0(i2003_11_14_17_21_30578))) | ![Y: $i] : (~ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_30578), Y)))) | ![Y: $i] : (~ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_30578), Y))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[216, 215])).
% 0.20/0.45 tff(218,plain,
% 0.20/0.45 (![Y: $i] : (~ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_30578), Y))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[217, 213])).
% 0.20/0.45 tff(219,plain,
% 0.20/0.45 ((~![Y: $i] : (~ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_30578), Y))) | (~ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_30578), tptp_fun_Y0_4(tptp_fun_Y_1(i2003_11_14_17_21_30578))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(220,plain,
% 0.20/0.45 (~ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_30578), tptp_fun_Y0_4(tptp_fun_Y_1(i2003_11_14_17_21_30578)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[219, 218])).
% 0.20/0.45 tff(221,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[220, 187])).
% 0.20/0.45 % SZS output end Proof
% 0.20/0.46 % E exiting
%------------------------------------------------------------------------------