%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS079+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:13:19 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : KRS079+1 : TPTP v9.0.0. Released v3.1.0.
% 0.12/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n007.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 19:12:04 EDT 2025
% 0.19/0.34 % CPUTime :
% 0.19/0.41 % SZS status Unsatisfiable
% 0.19/0.41 % SZS output start Proof
% 0.19/0.41 tff(cp2_type, type, (
% 0.19/0.41 cp2: $i > $o)).
% 0.19/0.41 tff(tptp_fun_Y_0_type, type, (
% 0.19/0.41 tptp_fun_Y_0: $i > $i)).
% 0.19/0.41 tff(i2003_11_14_17_19_17492_type, type, (
% 0.19/0.41 i2003_11_14_17_19_17492: $i)).
% 0.19/0.41 tff(tptp_fun_Y_1_type, type, (
% 0.19/0.41 tptp_fun_Y_1: $i > $i)).
% 0.19/0.41 tff(rf2_type, type, (
% 0.19/0.41 rf2: ( $i * $i ) > $o)).
% 0.19/0.41 tff(tptp_fun_Y_2_type, type, (
% 0.19/0.41 tptp_fun_Y_2: $i > $i)).
% 0.19/0.41 tff(rf1_type, type, (
% 0.19/0.41 rf1: ( $i * $i ) > $o)).
% 0.19/0.41 tff(cowlThing_type, type, (
% 0.19/0.41 cowlThing: $i > $o)).
% 0.19/0.41 tff(cowlNothing_type, type, (
% 0.19/0.41 cowlNothing: $i > $o)).
% 0.19/0.41 tff(rr_type, type, (
% 0.19/0.41 rr: ( $i * $i ) > $o)).
% 0.19/0.41 tff(cp1_type, type, (
% 0.19/0.41 cp1: $i > $o)).
% 0.19/0.41 tff(cUnsatisfiable_type, type, (
% 0.19/0.41 cUnsatisfiable: $i > $o)).
% 0.19/0.41 tff(1,assumption,(cowlNothing(i2003_11_14_17_19_17492) | (~cowlThing(i2003_11_14_17_19_17492))), introduced(assumption)).
% 0.19/0.41 tff(2,plain,
% 0.19/0.41 (^[X: $i] : refl((~(cowlNothing(X) | (~cowlThing(X)))) <=> (~(cowlNothing(X) | (~cowlThing(X)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(3,plain,
% 0.19/0.41 (![X: $i] : (~(cowlNothing(X) | (~cowlThing(X)))) <=> ![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.41 tff(4,plain,
% 0.19/0.41 (^[X: $i] : rewrite((cowlThing(X) & (~cowlNothing(X))) <=> (~(cowlNothing(X) | (~cowlThing(X)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(5,plain,
% 0.19/0.41 (![X: $i] : (cowlThing(X) & (~cowlNothing(X))) <=> ![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[4])).
% 0.19/0.41 tff(6,plain,
% 0.19/0.41 (![X: $i] : (cowlThing(X) & (~cowlNothing(X))) <=> ![X: $i] : (cowlThing(X) & (~cowlNothing(X)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(7,axiom,(![X: $i] : (cowlThing(X) & (~cowlNothing(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_0')).
% 0.19/0.41 tff(8,plain,
% 0.19/0.41 (![X: $i] : (cowlThing(X) & (~cowlNothing(X)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.19/0.41 tff(9,plain,(
% 0.19/0.41 ![X: $i] : (cowlThing(X) & (~cowlNothing(X)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[8])).
% 0.19/0.41 tff(10,plain,
% 0.19/0.41 (![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.19/0.41 tff(11,plain,
% 0.19/0.41 (![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.19/0.41 tff(12,plain,
% 0.19/0.41 ((~![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))) | (~(cowlNothing(i2003_11_14_17_19_17492) | (~cowlThing(i2003_11_14_17_19_17492))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(13,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[12, 11, 1])).
% 0.19/0.41 tff(14,plain,(~(cowlNothing(i2003_11_14_17_19_17492) | (~cowlThing(i2003_11_14_17_19_17492)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(15,plain,
% 0.19/0.41 ((cowlNothing(i2003_11_14_17_19_17492) | (~cowlThing(i2003_11_14_17_19_17492))) | cowlThing(i2003_11_14_17_19_17492)),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(16,plain,
% 0.19/0.41 (cowlThing(i2003_11_14_17_19_17492)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[15, 14])).
% 0.19/0.41 tff(17,plain,
% 0.19/0.41 (^[X: $i] : refl(((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(X, Y1)) | (~rf1(X, Y0)))) <=> ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(X, Y1)) | (~rf1(X, Y0)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(18,plain,
% 0.19/0.41 (![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(X, Y1)) | (~rf1(X, Y0)))) <=> ![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(X, Y1)) | (~rf1(X, Y0))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[17])).
% 0.19/0.41 tff(19,plain,
% 0.19/0.41 (^[X: $i] : rewrite(((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(X, Y1)) | (~rf1(X, Y0)))) <=> ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(X, Y1)) | (~rf1(X, Y0)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(20,plain,
% 0.19/0.41 (![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(X, Y1)) | (~rf1(X, Y0)))) <=> ![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(X, Y1)) | (~rf1(X, Y0))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[19])).
% 0.19/0.41 tff(21,plain,
% 0.19/0.41 (![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(X, Y1)) | (~rf1(X, Y0)))) <=> ![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(X, Y1)) | (~rf1(X, Y0))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[20, 18])).
% 0.19/0.42 tff(22,plain,
% 0.19/0.42 (^[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, Y1)) | (~rf1(X, Y0)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(23,plain,
% 0.19/0.42 (![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, Y1)) | (~rf1(X, Y0))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[22])).
% 0.19/0.42 tff(24,plain,
% 0.19/0.42 (![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)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(25,plain,
% 0.19/0.42 (^[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)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(26,plain,
% 0.19/0.42 (![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)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[25])).
% 0.19/0.42 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_4')).
% 0.19/0.42 tff(28,plain,
% 0.19/0.42 (![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((~(rf1(X, Y0) & rf1(X, Y1))) | (Y0 = Y1)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.19/0.42 tff(29,plain,
% 0.19/0.42 (![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((~(rf1(X, Y0) & rf1(X, Y1))) | (Y0 = Y1)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.19/0.42 tff(30,plain,(
% 0.19/0.42 ![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((~(rf1(X, Y0) & rf1(X, Y1))) | (Y0 = Y1)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[29])).
% 0.19/0.42 tff(31,plain,
% 0.19/0.42 (![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(X, Y1)) | (~rf1(X, Y0))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.19/0.42 tff(32,plain,
% 0.19/0.42 (![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(X, Y1)) | (~rf1(X, Y0))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[31, 21])).
% 0.19/0.42 tff(33,plain,
% 0.19/0.42 (((~![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(X, Y1)) | (~rf1(X, Y0))))) | ((~cowlThing(i2003_11_14_17_19_17492)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(i2003_11_14_17_19_17492, Y1)) | (~rf1(i2003_11_14_17_19_17492, Y0))))) <=> ((~![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(X, Y1)) | (~rf1(X, Y0))))) | (~cowlThing(i2003_11_14_17_19_17492)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(i2003_11_14_17_19_17492, Y1)) | (~rf1(i2003_11_14_17_19_17492, Y0))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(34,plain,
% 0.19/0.42 ((~![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(X, Y1)) | (~rf1(X, Y0))))) | ((~cowlThing(i2003_11_14_17_19_17492)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(i2003_11_14_17_19_17492, Y1)) | (~rf1(i2003_11_14_17_19_17492, Y0))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(35,plain,
% 0.19/0.42 ((~![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(X, Y1)) | (~rf1(X, Y0))))) | (~cowlThing(i2003_11_14_17_19_17492)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(i2003_11_14_17_19_17492, Y1)) | (~rf1(i2003_11_14_17_19_17492, Y0)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.19/0.42 tff(36,plain,
% 0.19/0.42 ((~cowlThing(i2003_11_14_17_19_17492)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(i2003_11_14_17_19_17492, Y1)) | (~rf1(i2003_11_14_17_19_17492, Y0)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[35, 32])).
% 0.19/0.42 tff(37,plain,
% 0.19/0.42 (![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(i2003_11_14_17_19_17492, Y1)) | (~rf1(i2003_11_14_17_19_17492, Y0)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[36, 16])).
% 0.19/0.42 tff(38,plain,
% 0.19/0.42 (^[X: $i] : refl((~((~((~cUnsatisfiable(X)) | (~((~rf1(X, tptp_fun_Y_1(X))) | (~cp2(tptp_fun_Y_0(X))) | (~rf2(X, tptp_fun_Y_0(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] : ((~cp2(Y)) | (~rf2(X, Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(X, Y))))))) <=> (~((~((~cUnsatisfiable(X)) | (~((~rf1(X, tptp_fun_Y_1(X))) | (~cp2(tptp_fun_Y_0(X))) | (~rf2(X, tptp_fun_Y_0(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] : ((~cp2(Y)) | (~rf2(X, Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(X, Y))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(39,plain,
% 0.19/0.42 (![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~rf1(X, tptp_fun_Y_1(X))) | (~cp2(tptp_fun_Y_0(X))) | (~rf2(X, tptp_fun_Y_0(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] : ((~cp2(Y)) | (~rf2(X, Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(X, Y))))))) <=> ![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~rf1(X, tptp_fun_Y_1(X))) | (~cp2(tptp_fun_Y_0(X))) | (~rf2(X, tptp_fun_Y_0(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] : ((~cp2(Y)) | (~rf2(X, Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(X, Y)))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[38])).
% 0.19/0.42 tff(40,plain,
% 0.19/0.42 (^[X: $i] : rewrite((~((~((~cUnsatisfiable(X)) | (~((~rf1(X, tptp_fun_Y_1(X))) | (~cp2(tptp_fun_Y_0(X))) | (~rf2(X, tptp_fun_Y_0(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] : ((~cp2(Y)) | (~rf2(X, Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(X, Y))))))) <=> (~((~((~cUnsatisfiable(X)) | (~((~rf1(X, tptp_fun_Y_1(X))) | (~cp2(tptp_fun_Y_0(X))) | (~rf2(X, tptp_fun_Y_0(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] : ((~cp2(Y)) | (~rf2(X, Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(X, Y))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(41,plain,
% 0.19/0.42 (![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~rf1(X, tptp_fun_Y_1(X))) | (~cp2(tptp_fun_Y_0(X))) | (~rf2(X, tptp_fun_Y_0(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] : ((~cp2(Y)) | (~rf2(X, Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(X, Y))))))) <=> ![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~rf1(X, tptp_fun_Y_1(X))) | (~cp2(tptp_fun_Y_0(X))) | (~rf2(X, tptp_fun_Y_0(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] : ((~cp2(Y)) | (~rf2(X, Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(X, Y)))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[40])).
% 0.19/0.42 tff(42,plain,
% 0.19/0.42 (![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~rf1(X, tptp_fun_Y_1(X))) | (~cp2(tptp_fun_Y_0(X))) | (~rf2(X, tptp_fun_Y_0(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] : ((~cp2(Y)) | (~rf2(X, Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(X, Y))))))) <=> ![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~rf1(X, tptp_fun_Y_1(X))) | (~cp2(tptp_fun_Y_0(X))) | (~rf2(X, tptp_fun_Y_0(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] : ((~cp2(Y)) | (~rf2(X, Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(X, Y)))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[41, 39])).
% 0.19/0.42 tff(43,plain,
% 0.19/0.42 (^[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)) | (~((~rf1(X, tptp_fun_Y_1(X))) | (~cp2(tptp_fun_Y_0(X))) | (~rf2(X, tptp_fun_Y_0(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)) <=> (~((~cp2(Y)) | (~rf2(X, Y))))), ((~(rf2(X, Y) & cp2(Y))) <=> (~(~((~cp2(Y)) | (~rf2(X, Y))))))), rewrite((~(~((~cp2(Y)) | (~rf2(X, Y))))) <=> ((~cp2(Y)) | (~rf2(X, Y)))), ((~(rf2(X, Y) & cp2(Y))) <=> ((~cp2(Y)) | (~rf2(X, Y)))))), (![Y: $i] : (~(rf2(X, Y) & cp2(Y))) <=> ![Y: $i] : ((~cp2(Y)) | (~rf2(X, 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] : ((~cp2(Y)) | (~rf2(X, Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(X, Y))) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(X, Y)))))), rewrite((cUnsatisfiable(X) | ![Y: $i] : ((~cp2(Y)) | (~rf2(X, 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] : ((~cp2(Y)) | (~rf2(X, 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] : ((~cp2(Y)) | (~rf2(X, 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)) | (~((~rf1(X, tptp_fun_Y_1(X))) | (~cp2(tptp_fun_Y_0(X))) | (~rf2(X, tptp_fun_Y_0(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] : ((~cp2(Y)) | (~rf2(X, Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(X, Y))))))), rewrite((((~cUnsatisfiable(X)) | (~((~rf1(X, tptp_fun_Y_1(X))) | (~cp2(tptp_fun_Y_0(X))) | (~rf2(X, tptp_fun_Y_0(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] : ((~cp2(Y)) | (~rf2(X, Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(X, Y))))) <=> (~((~((~cUnsatisfiable(X)) | (~((~rf1(X, tptp_fun_Y_1(X))) | (~cp2(tptp_fun_Y_0(X))) | (~rf2(X, tptp_fun_Y_0(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] : ((~cp2(Y)) | (~rf2(X, 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)) | (~((~rf1(X, tptp_fun_Y_1(X))) | (~cp2(tptp_fun_Y_0(X))) | (~rf2(X, tptp_fun_Y_0(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] : ((~cp2(Y)) | (~rf2(X, Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(X, Y)))))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(44,plain,
% 0.19/0.42 (![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)) | (~((~rf1(X, tptp_fun_Y_1(X))) | (~cp2(tptp_fun_Y_0(X))) | (~rf2(X, tptp_fun_Y_0(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] : ((~cp2(Y)) | (~rf2(X, Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(X, Y)))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[43])).
% 0.19/0.42 tff(45,plain,
% 0.19/0.42 (^[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))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(46,plain,
% 0.19/0.42 (![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] : (~(rf2(X, Y) & cp2(Y))) | ![Y: $i] : (~(rf1(X, Y) & cp1(Y))) | ![Y: $i] : (~(rr(X, Y) & cowlThing(Y)))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[45])).
% 0.19/0.42 tff(47,plain,
% 0.19/0.42 (![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))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(48,plain,
% 0.19/0.42 (^[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)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(49,plain,
% 0.19/0.42 (![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)],[48])).
% 0.20/0.43 tff(50,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(51,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)],[50, 49])).
% 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))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.20/0.43 tff(53,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)],[52])).
% 0.20/0.43 tff(54,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)],[53, 46])).
% 0.20/0.43 tff(55,plain,
% 0.20/0.43 (![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~rf1(X, tptp_fun_Y_1(X))) | (~cp2(tptp_fun_Y_0(X))) | (~rf2(X, tptp_fun_Y_0(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] : ((~cp2(Y)) | (~rf2(X, Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(X, Y)))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[54, 44])).
% 0.20/0.43 tff(56,plain,
% 0.20/0.43 (![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~rf1(X, tptp_fun_Y_1(X))) | (~cp2(tptp_fun_Y_0(X))) | (~rf2(X, tptp_fun_Y_0(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] : ((~cp2(Y)) | (~rf2(X, Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(X, Y)))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[55, 42])).
% 0.20/0.43 tff(57,plain,
% 0.20/0.43 (((~![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~rf1(X, tptp_fun_Y_1(X))) | (~cp2(tptp_fun_Y_0(X))) | (~rf2(X, tptp_fun_Y_0(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] : ((~cp2(Y)) | (~rf2(X, Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(X, Y)))))))) | (~((~((~cUnsatisfiable(i2003_11_14_17_19_17492)) | (~((~cowlThing(tptp_fun_Y_2(i2003_11_14_17_19_17492))) | (~rr(i2003_11_14_17_19_17492, tptp_fun_Y_2(i2003_11_14_17_19_17492))) | (~cp1(tptp_fun_Y_1(i2003_11_14_17_19_17492))) | (~rf2(i2003_11_14_17_19_17492, tptp_fun_Y_0(i2003_11_14_17_19_17492))) | (~cp2(tptp_fun_Y_0(i2003_11_14_17_19_17492))) | (~rf1(i2003_11_14_17_19_17492, tptp_fun_Y_1(i2003_11_14_17_19_17492))))))) | (~(cUnsatisfiable(i2003_11_14_17_19_17492) | ![Y: $i] : ((~cp1(Y)) | (~rf1(i2003_11_14_17_19_17492, Y))) | ![Y: $i] : ((~cp2(Y)) | (~rf2(i2003_11_14_17_19_17492, Y))) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(i2003_11_14_17_19_17492, Y)))))))) <=> ((~![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~rf1(X, tptp_fun_Y_1(X))) | (~cp2(tptp_fun_Y_0(X))) | (~rf2(X, tptp_fun_Y_0(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] : ((~cp2(Y)) | (~rf2(X, Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(X, Y)))))))) | (~((~((~cUnsatisfiable(i2003_11_14_17_19_17492)) | (~((~cowlThing(tptp_fun_Y_2(i2003_11_14_17_19_17492))) | (~rr(i2003_11_14_17_19_17492, tptp_fun_Y_2(i2003_11_14_17_19_17492))) | (~cp1(tptp_fun_Y_1(i2003_11_14_17_19_17492))) | (~rf2(i2003_11_14_17_19_17492, tptp_fun_Y_0(i2003_11_14_17_19_17492))) | (~cp2(tptp_fun_Y_0(i2003_11_14_17_19_17492))) | (~rf1(i2003_11_14_17_19_17492, tptp_fun_Y_1(i2003_11_14_17_19_17492))))))) | (~(cUnsatisfiable(i2003_11_14_17_19_17492) | ![Y: $i] : ((~cp1(Y)) | (~rf1(i2003_11_14_17_19_17492, Y))) | ![Y: $i] : ((~cp2(Y)) | (~rf2(i2003_11_14_17_19_17492, Y))) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(i2003_11_14_17_19_17492, Y))))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(58,plain,
% 0.20/0.43 ((~((~((~cUnsatisfiable(i2003_11_14_17_19_17492)) | (~((~rf1(i2003_11_14_17_19_17492, tptp_fun_Y_1(i2003_11_14_17_19_17492))) | (~cp2(tptp_fun_Y_0(i2003_11_14_17_19_17492))) | (~rf2(i2003_11_14_17_19_17492, tptp_fun_Y_0(i2003_11_14_17_19_17492))) | (~cp1(tptp_fun_Y_1(i2003_11_14_17_19_17492))) | (~rr(i2003_11_14_17_19_17492, tptp_fun_Y_2(i2003_11_14_17_19_17492))) | (~cowlThing(tptp_fun_Y_2(i2003_11_14_17_19_17492))))))) | (~(cUnsatisfiable(i2003_11_14_17_19_17492) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(i2003_11_14_17_19_17492, Y))) | ![Y: $i] : ((~cp2(Y)) | (~rf2(i2003_11_14_17_19_17492, Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(i2003_11_14_17_19_17492, Y))))))) <=> (~((~((~cUnsatisfiable(i2003_11_14_17_19_17492)) | (~((~cowlThing(tptp_fun_Y_2(i2003_11_14_17_19_17492))) | (~rr(i2003_11_14_17_19_17492, tptp_fun_Y_2(i2003_11_14_17_19_17492))) | (~cp1(tptp_fun_Y_1(i2003_11_14_17_19_17492))) | (~rf2(i2003_11_14_17_19_17492, tptp_fun_Y_0(i2003_11_14_17_19_17492))) | (~cp2(tptp_fun_Y_0(i2003_11_14_17_19_17492))) | (~rf1(i2003_11_14_17_19_17492, tptp_fun_Y_1(i2003_11_14_17_19_17492))))))) | (~(cUnsatisfiable(i2003_11_14_17_19_17492) | ![Y: $i] : ((~cp1(Y)) | (~rf1(i2003_11_14_17_19_17492, Y))) | ![Y: $i] : ((~cp2(Y)) | (~rf2(i2003_11_14_17_19_17492, Y))) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(i2003_11_14_17_19_17492, Y)))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(59,plain,
% 0.20/0.43 (((~![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~rf1(X, tptp_fun_Y_1(X))) | (~cp2(tptp_fun_Y_0(X))) | (~rf2(X, tptp_fun_Y_0(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] : ((~cp2(Y)) | (~rf2(X, Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(X, Y)))))))) | (~((~((~cUnsatisfiable(i2003_11_14_17_19_17492)) | (~((~rf1(i2003_11_14_17_19_17492, tptp_fun_Y_1(i2003_11_14_17_19_17492))) | (~cp2(tptp_fun_Y_0(i2003_11_14_17_19_17492))) | (~rf2(i2003_11_14_17_19_17492, tptp_fun_Y_0(i2003_11_14_17_19_17492))) | (~cp1(tptp_fun_Y_1(i2003_11_14_17_19_17492))) | (~rr(i2003_11_14_17_19_17492, tptp_fun_Y_2(i2003_11_14_17_19_17492))) | (~cowlThing(tptp_fun_Y_2(i2003_11_14_17_19_17492))))))) | (~(cUnsatisfiable(i2003_11_14_17_19_17492) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(i2003_11_14_17_19_17492, Y))) | ![Y: $i] : ((~cp2(Y)) | (~rf2(i2003_11_14_17_19_17492, Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(i2003_11_14_17_19_17492, Y)))))))) <=> ((~![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~rf1(X, tptp_fun_Y_1(X))) | (~cp2(tptp_fun_Y_0(X))) | (~rf2(X, tptp_fun_Y_0(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] : ((~cp2(Y)) | (~rf2(X, Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(X, Y)))))))) | (~((~((~cUnsatisfiable(i2003_11_14_17_19_17492)) | (~((~cowlThing(tptp_fun_Y_2(i2003_11_14_17_19_17492))) | (~rr(i2003_11_14_17_19_17492, tptp_fun_Y_2(i2003_11_14_17_19_17492))) | (~cp1(tptp_fun_Y_1(i2003_11_14_17_19_17492))) | (~rf2(i2003_11_14_17_19_17492, tptp_fun_Y_0(i2003_11_14_17_19_17492))) | (~cp2(tptp_fun_Y_0(i2003_11_14_17_19_17492))) | (~rf1(i2003_11_14_17_19_17492, tptp_fun_Y_1(i2003_11_14_17_19_17492))))))) | (~(cUnsatisfiable(i2003_11_14_17_19_17492) | ![Y: $i] : ((~cp1(Y)) | (~rf1(i2003_11_14_17_19_17492, Y))) | ![Y: $i] : ((~cp2(Y)) | (~rf2(i2003_11_14_17_19_17492, Y))) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(i2003_11_14_17_19_17492, Y))))))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[58])).
% 0.20/0.43 tff(60,plain,
% 0.20/0.43 (((~![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~rf1(X, tptp_fun_Y_1(X))) | (~cp2(tptp_fun_Y_0(X))) | (~rf2(X, tptp_fun_Y_0(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] : ((~cp2(Y)) | (~rf2(X, Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(X, Y)))))))) | (~((~((~cUnsatisfiable(i2003_11_14_17_19_17492)) | (~((~rf1(i2003_11_14_17_19_17492, tptp_fun_Y_1(i2003_11_14_17_19_17492))) | (~cp2(tptp_fun_Y_0(i2003_11_14_17_19_17492))) | (~rf2(i2003_11_14_17_19_17492, tptp_fun_Y_0(i2003_11_14_17_19_17492))) | (~cp1(tptp_fun_Y_1(i2003_11_14_17_19_17492))) | (~rr(i2003_11_14_17_19_17492, tptp_fun_Y_2(i2003_11_14_17_19_17492))) | (~cowlThing(tptp_fun_Y_2(i2003_11_14_17_19_17492))))))) | (~(cUnsatisfiable(i2003_11_14_17_19_17492) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(i2003_11_14_17_19_17492, Y))) | ![Y: $i] : ((~cp2(Y)) | (~rf2(i2003_11_14_17_19_17492, Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(i2003_11_14_17_19_17492, Y)))))))) <=> ((~![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~rf1(X, tptp_fun_Y_1(X))) | (~cp2(tptp_fun_Y_0(X))) | (~rf2(X, tptp_fun_Y_0(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] : ((~cp2(Y)) | (~rf2(X, Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(X, Y)))))))) | (~((~((~cUnsatisfiable(i2003_11_14_17_19_17492)) | (~((~cowlThing(tptp_fun_Y_2(i2003_11_14_17_19_17492))) | (~rr(i2003_11_14_17_19_17492, tptp_fun_Y_2(i2003_11_14_17_19_17492))) | (~cp1(tptp_fun_Y_1(i2003_11_14_17_19_17492))) | (~rf2(i2003_11_14_17_19_17492, tptp_fun_Y_0(i2003_11_14_17_19_17492))) | (~cp2(tptp_fun_Y_0(i2003_11_14_17_19_17492))) | (~rf1(i2003_11_14_17_19_17492, tptp_fun_Y_1(i2003_11_14_17_19_17492))))))) | (~(cUnsatisfiable(i2003_11_14_17_19_17492) | ![Y: $i] : ((~cp1(Y)) | (~rf1(i2003_11_14_17_19_17492, Y))) | ![Y: $i] : ((~cp2(Y)) | (~rf2(i2003_11_14_17_19_17492, Y))) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(i2003_11_14_17_19_17492, Y))))))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[59, 57])).
% 0.20/0.43 tff(61,plain,
% 0.20/0.43 ((~![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~rf1(X, tptp_fun_Y_1(X))) | (~cp2(tptp_fun_Y_0(X))) | (~rf2(X, tptp_fun_Y_0(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] : ((~cp2(Y)) | (~rf2(X, Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(X, Y)))))))) | (~((~((~cUnsatisfiable(i2003_11_14_17_19_17492)) | (~((~rf1(i2003_11_14_17_19_17492, tptp_fun_Y_1(i2003_11_14_17_19_17492))) | (~cp2(tptp_fun_Y_0(i2003_11_14_17_19_17492))) | (~rf2(i2003_11_14_17_19_17492, tptp_fun_Y_0(i2003_11_14_17_19_17492))) | (~cp1(tptp_fun_Y_1(i2003_11_14_17_19_17492))) | (~rr(i2003_11_14_17_19_17492, tptp_fun_Y_2(i2003_11_14_17_19_17492))) | (~cowlThing(tptp_fun_Y_2(i2003_11_14_17_19_17492))))))) | (~(cUnsatisfiable(i2003_11_14_17_19_17492) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(i2003_11_14_17_19_17492, Y))) | ![Y: $i] : ((~cp2(Y)) | (~rf2(i2003_11_14_17_19_17492, Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(i2003_11_14_17_19_17492, Y)))))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(62,plain,
% 0.20/0.43 ((~![X: $i] : (~((~((~cUnsatisfiable(X)) | (~((~rf1(X, tptp_fun_Y_1(X))) | (~cp2(tptp_fun_Y_0(X))) | (~rf2(X, tptp_fun_Y_0(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] : ((~cp2(Y)) | (~rf2(X, Y))) | ![Y: $i] : ((~cp1(Y)) | (~rf1(X, Y)))))))) | (~((~((~cUnsatisfiable(i2003_11_14_17_19_17492)) | (~((~cowlThing(tptp_fun_Y_2(i2003_11_14_17_19_17492))) | (~rr(i2003_11_14_17_19_17492, tptp_fun_Y_2(i2003_11_14_17_19_17492))) | (~cp1(tptp_fun_Y_1(i2003_11_14_17_19_17492))) | (~rf2(i2003_11_14_17_19_17492, tptp_fun_Y_0(i2003_11_14_17_19_17492))) | (~cp2(tptp_fun_Y_0(i2003_11_14_17_19_17492))) | (~rf1(i2003_11_14_17_19_17492, tptp_fun_Y_1(i2003_11_14_17_19_17492))))))) | (~(cUnsatisfiable(i2003_11_14_17_19_17492) | ![Y: $i] : ((~cp1(Y)) | (~rf1(i2003_11_14_17_19_17492, Y))) | ![Y: $i] : ((~cp2(Y)) | (~rf2(i2003_11_14_17_19_17492, Y))) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(i2003_11_14_17_19_17492, Y)))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.20/0.43 tff(63,plain,
% 0.20/0.43 (~((~((~cUnsatisfiable(i2003_11_14_17_19_17492)) | (~((~cowlThing(tptp_fun_Y_2(i2003_11_14_17_19_17492))) | (~rr(i2003_11_14_17_19_17492, tptp_fun_Y_2(i2003_11_14_17_19_17492))) | (~cp1(tptp_fun_Y_1(i2003_11_14_17_19_17492))) | (~rf2(i2003_11_14_17_19_17492, tptp_fun_Y_0(i2003_11_14_17_19_17492))) | (~cp2(tptp_fun_Y_0(i2003_11_14_17_19_17492))) | (~rf1(i2003_11_14_17_19_17492, tptp_fun_Y_1(i2003_11_14_17_19_17492))))))) | (~(cUnsatisfiable(i2003_11_14_17_19_17492) | ![Y: $i] : ((~cp1(Y)) | (~rf1(i2003_11_14_17_19_17492, Y))) | ![Y: $i] : ((~cp2(Y)) | (~rf2(i2003_11_14_17_19_17492, Y))) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(i2003_11_14_17_19_17492, Y))))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[62, 56])).
% 0.20/0.43 tff(64,plain,
% 0.20/0.43 (((~((~cUnsatisfiable(i2003_11_14_17_19_17492)) | (~((~cowlThing(tptp_fun_Y_2(i2003_11_14_17_19_17492))) | (~rr(i2003_11_14_17_19_17492, tptp_fun_Y_2(i2003_11_14_17_19_17492))) | (~cp1(tptp_fun_Y_1(i2003_11_14_17_19_17492))) | (~rf2(i2003_11_14_17_19_17492, tptp_fun_Y_0(i2003_11_14_17_19_17492))) | (~cp2(tptp_fun_Y_0(i2003_11_14_17_19_17492))) | (~rf1(i2003_11_14_17_19_17492, tptp_fun_Y_1(i2003_11_14_17_19_17492))))))) | (~(cUnsatisfiable(i2003_11_14_17_19_17492) | ![Y: $i] : ((~cp1(Y)) | (~rf1(i2003_11_14_17_19_17492, Y))) | ![Y: $i] : ((~cp2(Y)) | (~rf2(i2003_11_14_17_19_17492, Y))) | ![Y: $i] : ((~cowlThing(Y)) | (~rr(i2003_11_14_17_19_17492, Y)))))) | ((~cUnsatisfiable(i2003_11_14_17_19_17492)) | (~((~cowlThing(tptp_fun_Y_2(i2003_11_14_17_19_17492))) | (~rr(i2003_11_14_17_19_17492, tptp_fun_Y_2(i2003_11_14_17_19_17492))) | (~cp1(tptp_fun_Y_1(i2003_11_14_17_19_17492))) | (~rf2(i2003_11_14_17_19_17492, tptp_fun_Y_0(i2003_11_14_17_19_17492))) | (~cp2(tptp_fun_Y_0(i2003_11_14_17_19_17492))) | (~rf1(i2003_11_14_17_19_17492, tptp_fun_Y_1(i2003_11_14_17_19_17492))))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(65,plain,
% 0.20/0.43 ((~cUnsatisfiable(i2003_11_14_17_19_17492)) | (~((~cowlThing(tptp_fun_Y_2(i2003_11_14_17_19_17492))) | (~rr(i2003_11_14_17_19_17492, tptp_fun_Y_2(i2003_11_14_17_19_17492))) | (~cp1(tptp_fun_Y_1(i2003_11_14_17_19_17492))) | (~rf2(i2003_11_14_17_19_17492, tptp_fun_Y_0(i2003_11_14_17_19_17492))) | (~cp2(tptp_fun_Y_0(i2003_11_14_17_19_17492))) | (~rf1(i2003_11_14_17_19_17492, tptp_fun_Y_1(i2003_11_14_17_19_17492)))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.20/0.43 tff(66,plain,
% 0.20/0.43 (cUnsatisfiable(i2003_11_14_17_19_17492) <=> cUnsatisfiable(i2003_11_14_17_19_17492)),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(67,axiom,(cUnsatisfiable(i2003_11_14_17_19_17492)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_6')).
% 0.20/0.43 tff(68,plain,
% 0.20/0.43 (cUnsatisfiable(i2003_11_14_17_19_17492)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.20/0.43 tff(69,plain,
% 0.20/0.43 ((~((~cUnsatisfiable(i2003_11_14_17_19_17492)) | (~((~cowlThing(tptp_fun_Y_2(i2003_11_14_17_19_17492))) | (~rr(i2003_11_14_17_19_17492, tptp_fun_Y_2(i2003_11_14_17_19_17492))) | (~cp1(tptp_fun_Y_1(i2003_11_14_17_19_17492))) | (~rf2(i2003_11_14_17_19_17492, tptp_fun_Y_0(i2003_11_14_17_19_17492))) | (~cp2(tptp_fun_Y_0(i2003_11_14_17_19_17492))) | (~rf1(i2003_11_14_17_19_17492, tptp_fun_Y_1(i2003_11_14_17_19_17492))))))) | (~cUnsatisfiable(i2003_11_14_17_19_17492)) | (~((~cowlThing(tptp_fun_Y_2(i2003_11_14_17_19_17492))) | (~rr(i2003_11_14_17_19_17492, tptp_fun_Y_2(i2003_11_14_17_19_17492))) | (~cp1(tptp_fun_Y_1(i2003_11_14_17_19_17492))) | (~rf2(i2003_11_14_17_19_17492, tptp_fun_Y_0(i2003_11_14_17_19_17492))) | (~cp2(tptp_fun_Y_0(i2003_11_14_17_19_17492))) | (~rf1(i2003_11_14_17_19_17492, tptp_fun_Y_1(i2003_11_14_17_19_17492)))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(70,plain,
% 0.20/0.43 ((~((~cUnsatisfiable(i2003_11_14_17_19_17492)) | (~((~cowlThing(tptp_fun_Y_2(i2003_11_14_17_19_17492))) | (~rr(i2003_11_14_17_19_17492, tptp_fun_Y_2(i2003_11_14_17_19_17492))) | (~cp1(tptp_fun_Y_1(i2003_11_14_17_19_17492))) | (~rf2(i2003_11_14_17_19_17492, tptp_fun_Y_0(i2003_11_14_17_19_17492))) | (~cp2(tptp_fun_Y_0(i2003_11_14_17_19_17492))) | (~rf1(i2003_11_14_17_19_17492, tptp_fun_Y_1(i2003_11_14_17_19_17492))))))) | (~((~cowlThing(tptp_fun_Y_2(i2003_11_14_17_19_17492))) | (~rr(i2003_11_14_17_19_17492, tptp_fun_Y_2(i2003_11_14_17_19_17492))) | (~cp1(tptp_fun_Y_1(i2003_11_14_17_19_17492))) | (~rf2(i2003_11_14_17_19_17492, tptp_fun_Y_0(i2003_11_14_17_19_17492))) | (~cp2(tptp_fun_Y_0(i2003_11_14_17_19_17492))) | (~rf1(i2003_11_14_17_19_17492, tptp_fun_Y_1(i2003_11_14_17_19_17492)))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.20/0.43 tff(71,plain,
% 0.20/0.43 (~((~cowlThing(tptp_fun_Y_2(i2003_11_14_17_19_17492))) | (~rr(i2003_11_14_17_19_17492, tptp_fun_Y_2(i2003_11_14_17_19_17492))) | (~cp1(tptp_fun_Y_1(i2003_11_14_17_19_17492))) | (~rf2(i2003_11_14_17_19_17492, tptp_fun_Y_0(i2003_11_14_17_19_17492))) | (~cp2(tptp_fun_Y_0(i2003_11_14_17_19_17492))) | (~rf1(i2003_11_14_17_19_17492, tptp_fun_Y_1(i2003_11_14_17_19_17492))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[70, 65])).
% 0.20/0.43 tff(72,plain,
% 0.20/0.43 (((~cowlThing(tptp_fun_Y_2(i2003_11_14_17_19_17492))) | (~rr(i2003_11_14_17_19_17492, tptp_fun_Y_2(i2003_11_14_17_19_17492))) | (~cp1(tptp_fun_Y_1(i2003_11_14_17_19_17492))) | (~rf2(i2003_11_14_17_19_17492, tptp_fun_Y_0(i2003_11_14_17_19_17492))) | (~cp2(tptp_fun_Y_0(i2003_11_14_17_19_17492))) | (~rf1(i2003_11_14_17_19_17492, tptp_fun_Y_1(i2003_11_14_17_19_17492)))) | rr(i2003_11_14_17_19_17492, tptp_fun_Y_2(i2003_11_14_17_19_17492))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(73,plain,
% 0.20/0.43 (rr(i2003_11_14_17_19_17492, tptp_fun_Y_2(i2003_11_14_17_19_17492))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.20/0.43 tff(74,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(75,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)],[74])).
% 0.20/0.43 tff(76,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(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(77,plain,
% 0.20/0.43 (^[X: $i, Y: $i] : rewrite((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,axiom,(![X: $i, Y: $i] : (rr(X, Y) => rf1(X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_7')).
% 0.20/0.43 tff(80,plain,
% 0.20/0.43 (![X: $i, Y: $i] : ((~rr(X, Y)) | rf1(X, Y))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.20/0.43 tff(81,plain,
% 0.20/0.43 (![X: $i, Y: $i] : ((~rr(X, Y)) | rf1(X, Y))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.20/0.43 tff(82,plain,(
% 0.20/0.43 ![X: $i, Y: $i] : ((~rr(X, Y)) | rf1(X, Y))),
% 0.20/0.43 inference(skolemize,[status(sab)],[81])).
% 0.20/0.43 tff(83,plain,
% 0.20/0.43 (![X: $i, Y: $i] : ((~rr(X, Y)) | rf1(X, Y))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[82, 75])).
% 0.20/0.43 tff(84,plain,
% 0.20/0.43 (((~![X: $i, Y: $i] : ((~rr(X, Y)) | rf1(X, Y))) | ((~rr(i2003_11_14_17_19_17492, tptp_fun_Y_2(i2003_11_14_17_19_17492))) | rf1(i2003_11_14_17_19_17492, tptp_fun_Y_2(i2003_11_14_17_19_17492)))) <=> ((~![X: $i, Y: $i] : ((~rr(X, Y)) | rf1(X, Y))) | (~rr(i2003_11_14_17_19_17492, tptp_fun_Y_2(i2003_11_14_17_19_17492))) | rf1(i2003_11_14_17_19_17492, tptp_fun_Y_2(i2003_11_14_17_19_17492)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(85,plain,
% 0.20/0.43 ((~![X: $i, Y: $i] : ((~rr(X, Y)) | rf1(X, Y))) | ((~rr(i2003_11_14_17_19_17492, tptp_fun_Y_2(i2003_11_14_17_19_17492))) | rf1(i2003_11_14_17_19_17492, tptp_fun_Y_2(i2003_11_14_17_19_17492)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(86,plain,
% 0.20/0.43 ((~![X: $i, Y: $i] : ((~rr(X, Y)) | rf1(X, Y))) | (~rr(i2003_11_14_17_19_17492, tptp_fun_Y_2(i2003_11_14_17_19_17492))) | rf1(i2003_11_14_17_19_17492, tptp_fun_Y_2(i2003_11_14_17_19_17492))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.20/0.44 tff(87,plain,
% 0.20/0.44 (rf1(i2003_11_14_17_19_17492, tptp_fun_Y_2(i2003_11_14_17_19_17492))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[86, 83, 73])).
% 0.20/0.44 tff(88,plain,
% 0.20/0.44 (((~cowlThing(tptp_fun_Y_2(i2003_11_14_17_19_17492))) | (~rr(i2003_11_14_17_19_17492, tptp_fun_Y_2(i2003_11_14_17_19_17492))) | (~cp1(tptp_fun_Y_1(i2003_11_14_17_19_17492))) | (~rf2(i2003_11_14_17_19_17492, tptp_fun_Y_0(i2003_11_14_17_19_17492))) | (~cp2(tptp_fun_Y_0(i2003_11_14_17_19_17492))) | (~rf1(i2003_11_14_17_19_17492, tptp_fun_Y_1(i2003_11_14_17_19_17492)))) | rf1(i2003_11_14_17_19_17492, tptp_fun_Y_1(i2003_11_14_17_19_17492))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(89,plain,
% 0.20/0.44 (rf1(i2003_11_14_17_19_17492, tptp_fun_Y_1(i2003_11_14_17_19_17492))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[88, 71])).
% 0.20/0.44 tff(90,plain,
% 0.20/0.44 (((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(i2003_11_14_17_19_17492, Y1)) | (~rf1(i2003_11_14_17_19_17492, Y0)))) | ((~rf1(i2003_11_14_17_19_17492, tptp_fun_Y_1(i2003_11_14_17_19_17492))) | (tptp_fun_Y_2(i2003_11_14_17_19_17492) = tptp_fun_Y_1(i2003_11_14_17_19_17492)) | (~rf1(i2003_11_14_17_19_17492, tptp_fun_Y_2(i2003_11_14_17_19_17492))))) <=> ((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(i2003_11_14_17_19_17492, Y1)) | (~rf1(i2003_11_14_17_19_17492, Y0)))) | (~rf1(i2003_11_14_17_19_17492, tptp_fun_Y_1(i2003_11_14_17_19_17492))) | (tptp_fun_Y_2(i2003_11_14_17_19_17492) = tptp_fun_Y_1(i2003_11_14_17_19_17492)) | (~rf1(i2003_11_14_17_19_17492, tptp_fun_Y_2(i2003_11_14_17_19_17492))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(91,plain,
% 0.20/0.44 (((tptp_fun_Y_2(i2003_11_14_17_19_17492) = tptp_fun_Y_1(i2003_11_14_17_19_17492)) | (~rf1(i2003_11_14_17_19_17492, tptp_fun_Y_1(i2003_11_14_17_19_17492))) | (~rf1(i2003_11_14_17_19_17492, tptp_fun_Y_2(i2003_11_14_17_19_17492)))) <=> ((~rf1(i2003_11_14_17_19_17492, tptp_fun_Y_1(i2003_11_14_17_19_17492))) | (tptp_fun_Y_2(i2003_11_14_17_19_17492) = tptp_fun_Y_1(i2003_11_14_17_19_17492)) | (~rf1(i2003_11_14_17_19_17492, tptp_fun_Y_2(i2003_11_14_17_19_17492))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(92,plain,
% 0.20/0.44 (((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(i2003_11_14_17_19_17492, Y1)) | (~rf1(i2003_11_14_17_19_17492, Y0)))) | ((tptp_fun_Y_2(i2003_11_14_17_19_17492) = tptp_fun_Y_1(i2003_11_14_17_19_17492)) | (~rf1(i2003_11_14_17_19_17492, tptp_fun_Y_1(i2003_11_14_17_19_17492))) | (~rf1(i2003_11_14_17_19_17492, tptp_fun_Y_2(i2003_11_14_17_19_17492))))) <=> ((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(i2003_11_14_17_19_17492, Y1)) | (~rf1(i2003_11_14_17_19_17492, Y0)))) | ((~rf1(i2003_11_14_17_19_17492, tptp_fun_Y_1(i2003_11_14_17_19_17492))) | (tptp_fun_Y_2(i2003_11_14_17_19_17492) = tptp_fun_Y_1(i2003_11_14_17_19_17492)) | (~rf1(i2003_11_14_17_19_17492, tptp_fun_Y_2(i2003_11_14_17_19_17492)))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[91])).
% 0.20/0.44 tff(93,plain,
% 0.20/0.44 (((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(i2003_11_14_17_19_17492, Y1)) | (~rf1(i2003_11_14_17_19_17492, Y0)))) | ((tptp_fun_Y_2(i2003_11_14_17_19_17492) = tptp_fun_Y_1(i2003_11_14_17_19_17492)) | (~rf1(i2003_11_14_17_19_17492, tptp_fun_Y_1(i2003_11_14_17_19_17492))) | (~rf1(i2003_11_14_17_19_17492, tptp_fun_Y_2(i2003_11_14_17_19_17492))))) <=> ((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(i2003_11_14_17_19_17492, Y1)) | (~rf1(i2003_11_14_17_19_17492, Y0)))) | (~rf1(i2003_11_14_17_19_17492, tptp_fun_Y_1(i2003_11_14_17_19_17492))) | (tptp_fun_Y_2(i2003_11_14_17_19_17492) = tptp_fun_Y_1(i2003_11_14_17_19_17492)) | (~rf1(i2003_11_14_17_19_17492, tptp_fun_Y_2(i2003_11_14_17_19_17492))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[92, 90])).
% 0.20/0.44 tff(94,plain,
% 0.20/0.44 ((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(i2003_11_14_17_19_17492, Y1)) | (~rf1(i2003_11_14_17_19_17492, Y0)))) | ((tptp_fun_Y_2(i2003_11_14_17_19_17492) = tptp_fun_Y_1(i2003_11_14_17_19_17492)) | (~rf1(i2003_11_14_17_19_17492, tptp_fun_Y_1(i2003_11_14_17_19_17492))) | (~rf1(i2003_11_14_17_19_17492, tptp_fun_Y_2(i2003_11_14_17_19_17492))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(95,plain,
% 0.20/0.44 ((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf1(i2003_11_14_17_19_17492, Y1)) | (~rf1(i2003_11_14_17_19_17492, Y0)))) | (~rf1(i2003_11_14_17_19_17492, tptp_fun_Y_1(i2003_11_14_17_19_17492))) | (tptp_fun_Y_2(i2003_11_14_17_19_17492) = tptp_fun_Y_1(i2003_11_14_17_19_17492)) | (~rf1(i2003_11_14_17_19_17492, tptp_fun_Y_2(i2003_11_14_17_19_17492)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.20/0.44 tff(96,plain,
% 0.20/0.44 (tptp_fun_Y_2(i2003_11_14_17_19_17492) = tptp_fun_Y_1(i2003_11_14_17_19_17492)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[95, 89, 87, 37])).
% 0.20/0.44 tff(97,plain,
% 0.20/0.44 (tptp_fun_Y_1(i2003_11_14_17_19_17492) = tptp_fun_Y_2(i2003_11_14_17_19_17492)),
% 0.20/0.44 inference(symmetry,[status(thm)],[96])).
% 0.20/0.44 tff(98,plain,
% 0.20/0.44 (rf2(i2003_11_14_17_19_17492, tptp_fun_Y_1(i2003_11_14_17_19_17492)) <=> rf2(i2003_11_14_17_19_17492, tptp_fun_Y_2(i2003_11_14_17_19_17492))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[97])).
% 0.20/0.44 tff(99,plain,
% 0.20/0.44 (rf2(i2003_11_14_17_19_17492, tptp_fun_Y_2(i2003_11_14_17_19_17492)) <=> rf2(i2003_11_14_17_19_17492, tptp_fun_Y_1(i2003_11_14_17_19_17492))),
% 0.20/0.44 inference(symmetry,[status(thm)],[98])).
% 0.20/0.44 tff(100,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(101,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)],[100])).
% 0.20/0.44 tff(102,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(103,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(104,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)],[103])).
% 0.20/0.44 tff(105,axiom,(![X: $i, Y: $i] : (rr(X, Y) => rf2(X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_8')).
% 0.20/0.44 tff(106,plain,
% 0.20/0.44 (![X: $i, Y: $i] : ((~rr(X, Y)) | rf2(X, Y))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.20/0.44 tff(107,plain,
% 0.20/0.44 (![X: $i, Y: $i] : ((~rr(X, Y)) | rf2(X, Y))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[106, 102])).
% 0.20/0.44 tff(108,plain,(
% 0.20/0.44 ![X: $i, Y: $i] : ((~rr(X, Y)) | rf2(X, Y))),
% 0.20/0.44 inference(skolemize,[status(sab)],[107])).
% 0.20/0.44 tff(109,plain,
% 0.20/0.44 (![X: $i, Y: $i] : ((~rr(X, Y)) | rf2(X, Y))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[108, 101])).
% 0.20/0.44 tff(110,plain,
% 0.20/0.44 (((~![X: $i, Y: $i] : ((~rr(X, Y)) | rf2(X, Y))) | ((~rr(i2003_11_14_17_19_17492, tptp_fun_Y_2(i2003_11_14_17_19_17492))) | rf2(i2003_11_14_17_19_17492, tptp_fun_Y_2(i2003_11_14_17_19_17492)))) <=> ((~![X: $i, Y: $i] : ((~rr(X, Y)) | rf2(X, Y))) | (~rr(i2003_11_14_17_19_17492, tptp_fun_Y_2(i2003_11_14_17_19_17492))) | rf2(i2003_11_14_17_19_17492, tptp_fun_Y_2(i2003_11_14_17_19_17492)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(111,plain,
% 0.20/0.44 ((~![X: $i, Y: $i] : ((~rr(X, Y)) | rf2(X, Y))) | ((~rr(i2003_11_14_17_19_17492, tptp_fun_Y_2(i2003_11_14_17_19_17492))) | rf2(i2003_11_14_17_19_17492, tptp_fun_Y_2(i2003_11_14_17_19_17492)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(112,plain,
% 0.20/0.44 ((~![X: $i, Y: $i] : ((~rr(X, Y)) | rf2(X, Y))) | (~rr(i2003_11_14_17_19_17492, tptp_fun_Y_2(i2003_11_14_17_19_17492))) | rf2(i2003_11_14_17_19_17492, tptp_fun_Y_2(i2003_11_14_17_19_17492))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.20/0.44 tff(113,plain,
% 0.20/0.44 (rf2(i2003_11_14_17_19_17492, tptp_fun_Y_2(i2003_11_14_17_19_17492))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[112, 109, 73])).
% 0.20/0.44 tff(114,plain,
% 0.20/0.44 (rf2(i2003_11_14_17_19_17492, tptp_fun_Y_1(i2003_11_14_17_19_17492))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[113, 99])).
% 0.20/0.44 tff(115,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(116,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)],[115])).
% 0.20/0.44 tff(117,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(118,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)],[117])).
% 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)))) <=> ![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(X, Y0)) | (~rf2(X, Y1))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[118, 116])).
% 0.20/0.44 tff(120,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(121,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)],[120])).
% 0.20/0.44 tff(122,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(123,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(124,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)],[123])).
% 0.20/0.44 tff(125,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_5')).
% 0.20/0.44 tff(126,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)],[125, 124])).
% 0.20/0.44 tff(127,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)],[126, 122])).
% 0.20/0.44 tff(128,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)],[127])).
% 0.20/0.44 tff(129,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)],[128, 121])).
% 0.20/0.44 tff(130,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)],[129, 119])).
% 0.20/0.44 tff(131,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_19_17492)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(i2003_11_14_17_19_17492, Y1)) | (~rf2(i2003_11_14_17_19_17492, Y0))))) <=> ((~![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(X, Y0)) | (~rf2(X, Y1))))) | (~cowlThing(i2003_11_14_17_19_17492)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(i2003_11_14_17_19_17492, Y1)) | (~rf2(i2003_11_14_17_19_17492, Y0))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(132,plain,
% 0.20/0.44 (((~cowlThing(i2003_11_14_17_19_17492)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(i2003_11_14_17_19_17492, Y0)) | (~rf2(i2003_11_14_17_19_17492, Y1)))) <=> ((~cowlThing(i2003_11_14_17_19_17492)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(i2003_11_14_17_19_17492, Y1)) | (~rf2(i2003_11_14_17_19_17492, Y0))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(133,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_19_17492)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(i2003_11_14_17_19_17492, Y0)) | (~rf2(i2003_11_14_17_19_17492, Y1))))) <=> ((~![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(X, Y0)) | (~rf2(X, Y1))))) | ((~cowlThing(i2003_11_14_17_19_17492)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(i2003_11_14_17_19_17492, Y1)) | (~rf2(i2003_11_14_17_19_17492, Y0)))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[132])).
% 0.20/0.44 tff(134,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_19_17492)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(i2003_11_14_17_19_17492, Y0)) | (~rf2(i2003_11_14_17_19_17492, Y1))))) <=> ((~![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(X, Y0)) | (~rf2(X, Y1))))) | (~cowlThing(i2003_11_14_17_19_17492)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(i2003_11_14_17_19_17492, Y1)) | (~rf2(i2003_11_14_17_19_17492, Y0))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[133, 131])).
% 0.20/0.44 tff(135,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_19_17492)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(i2003_11_14_17_19_17492, Y0)) | (~rf2(i2003_11_14_17_19_17492, Y1))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(136,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_19_17492)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(i2003_11_14_17_19_17492, Y1)) | (~rf2(i2003_11_14_17_19_17492, Y0)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.20/0.44 tff(137,plain,
% 0.20/0.44 (![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(i2003_11_14_17_19_17492, Y1)) | (~rf2(i2003_11_14_17_19_17492, Y0)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[136, 130, 16])).
% 0.20/0.44 tff(138,plain,
% 0.20/0.44 (((~cowlThing(tptp_fun_Y_2(i2003_11_14_17_19_17492))) | (~rr(i2003_11_14_17_19_17492, tptp_fun_Y_2(i2003_11_14_17_19_17492))) | (~cp1(tptp_fun_Y_1(i2003_11_14_17_19_17492))) | (~rf2(i2003_11_14_17_19_17492, tptp_fun_Y_0(i2003_11_14_17_19_17492))) | (~cp2(tptp_fun_Y_0(i2003_11_14_17_19_17492))) | (~rf1(i2003_11_14_17_19_17492, tptp_fun_Y_1(i2003_11_14_17_19_17492)))) | rf2(i2003_11_14_17_19_17492, tptp_fun_Y_0(i2003_11_14_17_19_17492))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(139,plain,
% 0.20/0.44 (rf2(i2003_11_14_17_19_17492, tptp_fun_Y_0(i2003_11_14_17_19_17492))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[138, 71])).
% 0.20/0.44 tff(140,plain,
% 0.20/0.44 (((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(i2003_11_14_17_19_17492, Y1)) | (~rf2(i2003_11_14_17_19_17492, Y0)))) | ((~rf2(i2003_11_14_17_19_17492, tptp_fun_Y_0(i2003_11_14_17_19_17492))) | (tptp_fun_Y_0(i2003_11_14_17_19_17492) = tptp_fun_Y_1(i2003_11_14_17_19_17492)) | (~rf2(i2003_11_14_17_19_17492, tptp_fun_Y_1(i2003_11_14_17_19_17492))))) <=> ((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(i2003_11_14_17_19_17492, Y1)) | (~rf2(i2003_11_14_17_19_17492, Y0)))) | (~rf2(i2003_11_14_17_19_17492, tptp_fun_Y_0(i2003_11_14_17_19_17492))) | (tptp_fun_Y_0(i2003_11_14_17_19_17492) = tptp_fun_Y_1(i2003_11_14_17_19_17492)) | (~rf2(i2003_11_14_17_19_17492, tptp_fun_Y_1(i2003_11_14_17_19_17492))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(141,plain,
% 0.20/0.44 (((tptp_fun_Y_0(i2003_11_14_17_19_17492) = tptp_fun_Y_1(i2003_11_14_17_19_17492)) | (~rf2(i2003_11_14_17_19_17492, tptp_fun_Y_1(i2003_11_14_17_19_17492))) | (~rf2(i2003_11_14_17_19_17492, tptp_fun_Y_0(i2003_11_14_17_19_17492)))) <=> ((~rf2(i2003_11_14_17_19_17492, tptp_fun_Y_0(i2003_11_14_17_19_17492))) | (tptp_fun_Y_0(i2003_11_14_17_19_17492) = tptp_fun_Y_1(i2003_11_14_17_19_17492)) | (~rf2(i2003_11_14_17_19_17492, tptp_fun_Y_1(i2003_11_14_17_19_17492))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(142,plain,
% 0.20/0.44 (((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(i2003_11_14_17_19_17492, Y1)) | (~rf2(i2003_11_14_17_19_17492, Y0)))) | ((tptp_fun_Y_0(i2003_11_14_17_19_17492) = tptp_fun_Y_1(i2003_11_14_17_19_17492)) | (~rf2(i2003_11_14_17_19_17492, tptp_fun_Y_1(i2003_11_14_17_19_17492))) | (~rf2(i2003_11_14_17_19_17492, tptp_fun_Y_0(i2003_11_14_17_19_17492))))) <=> ((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(i2003_11_14_17_19_17492, Y1)) | (~rf2(i2003_11_14_17_19_17492, Y0)))) | ((~rf2(i2003_11_14_17_19_17492, tptp_fun_Y_0(i2003_11_14_17_19_17492))) | (tptp_fun_Y_0(i2003_11_14_17_19_17492) = tptp_fun_Y_1(i2003_11_14_17_19_17492)) | (~rf2(i2003_11_14_17_19_17492, tptp_fun_Y_1(i2003_11_14_17_19_17492)))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[141])).
% 0.20/0.44 tff(143,plain,
% 0.20/0.44 (((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(i2003_11_14_17_19_17492, Y1)) | (~rf2(i2003_11_14_17_19_17492, Y0)))) | ((tptp_fun_Y_0(i2003_11_14_17_19_17492) = tptp_fun_Y_1(i2003_11_14_17_19_17492)) | (~rf2(i2003_11_14_17_19_17492, tptp_fun_Y_1(i2003_11_14_17_19_17492))) | (~rf2(i2003_11_14_17_19_17492, tptp_fun_Y_0(i2003_11_14_17_19_17492))))) <=> ((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(i2003_11_14_17_19_17492, Y1)) | (~rf2(i2003_11_14_17_19_17492, Y0)))) | (~rf2(i2003_11_14_17_19_17492, tptp_fun_Y_0(i2003_11_14_17_19_17492))) | (tptp_fun_Y_0(i2003_11_14_17_19_17492) = tptp_fun_Y_1(i2003_11_14_17_19_17492)) | (~rf2(i2003_11_14_17_19_17492, tptp_fun_Y_1(i2003_11_14_17_19_17492))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[142, 140])).
% 0.20/0.44 tff(144,plain,
% 0.20/0.44 ((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(i2003_11_14_17_19_17492, Y1)) | (~rf2(i2003_11_14_17_19_17492, Y0)))) | ((tptp_fun_Y_0(i2003_11_14_17_19_17492) = tptp_fun_Y_1(i2003_11_14_17_19_17492)) | (~rf2(i2003_11_14_17_19_17492, tptp_fun_Y_1(i2003_11_14_17_19_17492))) | (~rf2(i2003_11_14_17_19_17492, tptp_fun_Y_0(i2003_11_14_17_19_17492))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(145,plain,
% 0.20/0.44 ((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf2(i2003_11_14_17_19_17492, Y1)) | (~rf2(i2003_11_14_17_19_17492, Y0)))) | (~rf2(i2003_11_14_17_19_17492, tptp_fun_Y_0(i2003_11_14_17_19_17492))) | (tptp_fun_Y_0(i2003_11_14_17_19_17492) = tptp_fun_Y_1(i2003_11_14_17_19_17492)) | (~rf2(i2003_11_14_17_19_17492, tptp_fun_Y_1(i2003_11_14_17_19_17492)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.20/0.44 tff(146,plain,
% 0.20/0.44 ((tptp_fun_Y_0(i2003_11_14_17_19_17492) = tptp_fun_Y_1(i2003_11_14_17_19_17492)) | (~rf2(i2003_11_14_17_19_17492, tptp_fun_Y_1(i2003_11_14_17_19_17492)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[145, 139, 137])).
% 0.20/0.44 tff(147,plain,
% 0.20/0.44 (tptp_fun_Y_0(i2003_11_14_17_19_17492) = tptp_fun_Y_1(i2003_11_14_17_19_17492)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[146, 114])).
% 0.20/0.44 tff(148,plain,
% 0.20/0.44 (cp2(tptp_fun_Y_0(i2003_11_14_17_19_17492)) <=> cp2(tptp_fun_Y_1(i2003_11_14_17_19_17492))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[147])).
% 0.20/0.44 tff(149,plain,
% 0.20/0.44 (cp2(tptp_fun_Y_1(i2003_11_14_17_19_17492)) <=> cp2(tptp_fun_Y_0(i2003_11_14_17_19_17492))),
% 0.20/0.44 inference(symmetry,[status(thm)],[148])).
% 0.20/0.44 tff(150,plain,
% 0.20/0.44 ((~cp2(tptp_fun_Y_1(i2003_11_14_17_19_17492))) <=> (~cp2(tptp_fun_Y_0(i2003_11_14_17_19_17492)))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[149])).
% 0.20/0.44 tff(151,plain,
% 0.20/0.44 (((~cowlThing(tptp_fun_Y_2(i2003_11_14_17_19_17492))) | (~rr(i2003_11_14_17_19_17492, tptp_fun_Y_2(i2003_11_14_17_19_17492))) | (~cp1(tptp_fun_Y_1(i2003_11_14_17_19_17492))) | (~rf2(i2003_11_14_17_19_17492, tptp_fun_Y_0(i2003_11_14_17_19_17492))) | (~cp2(tptp_fun_Y_0(i2003_11_14_17_19_17492))) | (~rf1(i2003_11_14_17_19_17492, tptp_fun_Y_1(i2003_11_14_17_19_17492)))) | cp1(tptp_fun_Y_1(i2003_11_14_17_19_17492))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(152,plain,
% 0.20/0.45 (cp1(tptp_fun_Y_1(i2003_11_14_17_19_17492))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[151, 71])).
% 0.20/0.45 tff(153,plain,
% 0.20/0.45 (^[X: $i] : refl(((~cp1(X)) | (~cp2(X))) <=> ((~cp1(X)) | (~cp2(X))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(154,plain,
% 0.20/0.45 (![X: $i] : ((~cp1(X)) | (~cp2(X))) <=> ![X: $i] : ((~cp1(X)) | (~cp2(X)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[153])).
% 0.20/0.45 tff(155,plain,
% 0.20/0.45 (![X: $i] : ((~cp1(X)) | (~cp2(X))) <=> ![X: $i] : ((~cp1(X)) | (~cp2(X)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(156,plain,
% 0.20/0.45 (^[X: $i] : rewrite((cp1(X) => (~cp2(X))) <=> ((~cp1(X)) | (~cp2(X))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(157,plain,
% 0.20/0.45 (![X: $i] : (cp1(X) => (~cp2(X))) <=> ![X: $i] : ((~cp1(X)) | (~cp2(X)))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[156])).
% 0.20/0.45 tff(158,axiom,(![X: $i] : (cp1(X) => (~cp2(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_3')).
% 0.20/0.45 tff(159,plain,
% 0.20/0.45 (![X: $i] : ((~cp1(X)) | (~cp2(X)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.20/0.45 tff(160,plain,
% 0.20/0.45 (![X: $i] : ((~cp1(X)) | (~cp2(X)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[159, 155])).
% 0.20/0.45 tff(161,plain,(
% 0.20/0.45 ![X: $i] : ((~cp1(X)) | (~cp2(X)))),
% 0.20/0.45 inference(skolemize,[status(sab)],[160])).
% 0.20/0.45 tff(162,plain,
% 0.20/0.45 (![X: $i] : ((~cp1(X)) | (~cp2(X)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[161, 154])).
% 0.20/0.45 tff(163,plain,
% 0.20/0.45 (((~![X: $i] : ((~cp1(X)) | (~cp2(X)))) | ((~cp1(tptp_fun_Y_1(i2003_11_14_17_19_17492))) | (~cp2(tptp_fun_Y_1(i2003_11_14_17_19_17492))))) <=> ((~![X: $i] : ((~cp1(X)) | (~cp2(X)))) | (~cp1(tptp_fun_Y_1(i2003_11_14_17_19_17492))) | (~cp2(tptp_fun_Y_1(i2003_11_14_17_19_17492))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(164,plain,
% 0.20/0.45 ((~![X: $i] : ((~cp1(X)) | (~cp2(X)))) | ((~cp1(tptp_fun_Y_1(i2003_11_14_17_19_17492))) | (~cp2(tptp_fun_Y_1(i2003_11_14_17_19_17492))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(165,plain,
% 0.20/0.45 ((~![X: $i] : ((~cp1(X)) | (~cp2(X)))) | (~cp1(tptp_fun_Y_1(i2003_11_14_17_19_17492))) | (~cp2(tptp_fun_Y_1(i2003_11_14_17_19_17492)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.20/0.45 tff(166,plain,
% 0.20/0.45 (~cp2(tptp_fun_Y_1(i2003_11_14_17_19_17492))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[165, 162, 152])).
% 0.20/0.45 tff(167,plain,
% 0.20/0.45 (~cp2(tptp_fun_Y_0(i2003_11_14_17_19_17492))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[166, 150])).
% 0.20/0.45 tff(168,plain,
% 0.20/0.45 (((~cowlThing(tptp_fun_Y_2(i2003_11_14_17_19_17492))) | (~rr(i2003_11_14_17_19_17492, tptp_fun_Y_2(i2003_11_14_17_19_17492))) | (~cp1(tptp_fun_Y_1(i2003_11_14_17_19_17492))) | (~rf2(i2003_11_14_17_19_17492, tptp_fun_Y_0(i2003_11_14_17_19_17492))) | (~cp2(tptp_fun_Y_0(i2003_11_14_17_19_17492))) | (~rf1(i2003_11_14_17_19_17492, tptp_fun_Y_1(i2003_11_14_17_19_17492)))) | cp2(tptp_fun_Y_0(i2003_11_14_17_19_17492))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(169,plain,
% 0.20/0.45 (cp2(tptp_fun_Y_0(i2003_11_14_17_19_17492))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[168, 71])).
% 0.20/0.45 tff(170,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[169, 167])).
% 0.20/0.45 % SZS output end Proof
% 0.20/0.45 % E exiting
%------------------------------------------------------------------------------