%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS086+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:13:21 AM UTC 2025
% Result : Unsatisfiable 0.11s 0.38s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : KRS086+1 : TPTP v9.0.0. Released v3.1.0.
% 0.11/0.11 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n011.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 19:11:12 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.38 % SZS status Unsatisfiable
% 0.11/0.38 % SZS output start Proof
% 0.11/0.38 tff(cp1_type, type, (
% 0.11/0.38 cp1: $i > $o)).
% 0.11/0.38 tff(tptp_fun_W_2_type, type, (
% 0.11/0.38 tptp_fun_W_2: $i > $i)).
% 0.11/0.38 tff(i2003_11_14_17_19_42328_type, type, (
% 0.11/0.38 i2003_11_14_17_19_42328: $i)).
% 0.11/0.38 tff(tptp_fun_Y_0_type, type, (
% 0.11/0.38 tptp_fun_Y_0: $i > $i)).
% 0.11/0.38 tff(rf_type, type, (
% 0.11/0.38 rf: ( $i * $i ) > $o)).
% 0.11/0.38 tff(tptp_fun_Z_1_type, type, (
% 0.11/0.38 tptp_fun_Z_1: $i > $i)).
% 0.11/0.38 tff(cowlThing_type, type, (
% 0.11/0.38 cowlThing: $i > $o)).
% 0.11/0.38 tff(cowlNothing_type, type, (
% 0.11/0.38 cowlNothing: $i > $o)).
% 0.11/0.38 tff(rinvF_type, type, (
% 0.11/0.38 rinvF: ( $i * $i ) > $o)).
% 0.11/0.38 tff(cUnsatisfiable_type, type, (
% 0.11/0.38 cUnsatisfiable: $i > $o)).
% 0.11/0.38 tff(1,assumption,(cowlNothing(tptp_fun_Z_1(i2003_11_14_17_19_42328)) | (~cowlThing(tptp_fun_Z_1(i2003_11_14_17_19_42328)))), introduced(assumption)).
% 0.11/0.38 tff(2,plain,
% 0.11/0.38 (^[X: $i] : refl((~(cowlNothing(X) | (~cowlThing(X)))) <=> (~(cowlNothing(X) | (~cowlThing(X)))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(3,plain,
% 0.11/0.38 (![X: $i] : (~(cowlNothing(X) | (~cowlThing(X)))) <=> ![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.11/0.38 tff(4,plain,
% 0.11/0.38 (^[X: $i] : rewrite((cowlThing(X) & (~cowlNothing(X))) <=> (~(cowlNothing(X) | (~cowlThing(X)))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(5,plain,
% 0.11/0.38 (![X: $i] : (cowlThing(X) & (~cowlNothing(X))) <=> ![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[4])).
% 0.11/0.38 tff(6,plain,
% 0.11/0.38 (![X: $i] : (cowlThing(X) & (~cowlNothing(X))) <=> ![X: $i] : (cowlThing(X) & (~cowlNothing(X)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(7,axiom,(![X: $i] : (cowlThing(X) & (~cowlNothing(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_0')).
% 0.11/0.38 tff(8,plain,
% 0.11/0.38 (![X: $i] : (cowlThing(X) & (~cowlNothing(X)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.11/0.38 tff(9,plain,(
% 0.11/0.38 ![X: $i] : (cowlThing(X) & (~cowlNothing(X)))),
% 0.11/0.38 inference(skolemize,[status(sab)],[8])).
% 0.11/0.38 tff(10,plain,
% 0.11/0.38 (![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.11/0.38 tff(11,plain,
% 0.11/0.38 (![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.11/0.38 tff(12,plain,
% 0.11/0.38 ((~![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))) | (~(cowlNothing(tptp_fun_Z_1(i2003_11_14_17_19_42328)) | (~cowlThing(tptp_fun_Z_1(i2003_11_14_17_19_42328)))))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(13,plain,
% 0.11/0.38 ($false),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[12, 11, 1])).
% 0.11/0.38 tff(14,plain,(~(cowlNothing(tptp_fun_Z_1(i2003_11_14_17_19_42328)) | (~cowlThing(tptp_fun_Z_1(i2003_11_14_17_19_42328))))), inference(lemma,lemma(discharge,[]))).
% 0.11/0.38 tff(15,plain,
% 0.11/0.38 ((cowlNothing(tptp_fun_Z_1(i2003_11_14_17_19_42328)) | (~cowlThing(tptp_fun_Z_1(i2003_11_14_17_19_42328)))) | cowlThing(tptp_fun_Z_1(i2003_11_14_17_19_42328))),
% 0.11/0.38 inference(tautology,[status(thm)],[])).
% 0.11/0.38 tff(16,plain,
% 0.11/0.38 (cowlThing(tptp_fun_Z_1(i2003_11_14_17_19_42328))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[15, 14])).
% 0.11/0.38 tff(17,plain,
% 0.11/0.38 (^[X: $i] : refl(((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(X, Y0)) | (~rf(X, Y1)))) <=> ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(X, Y0)) | (~rf(X, Y1)))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(18,plain,
% 0.11/0.38 (![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(X, Y0)) | (~rf(X, Y1)))) <=> ![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(X, Y0)) | (~rf(X, Y1))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[17])).
% 0.11/0.38 tff(19,plain,
% 0.11/0.38 (^[X: $i] : rewrite(((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(X, Y0)) | (~rf(X, Y1)))) <=> ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(X, Y0)) | (~rf(X, Y1)))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(20,plain,
% 0.11/0.38 (![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(X, Y0)) | (~rf(X, Y1)))) <=> ![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(X, Y0)) | (~rf(X, Y1))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[19])).
% 0.11/0.38 tff(21,plain,
% 0.11/0.38 (![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(X, Y0)) | (~rf(X, Y1)))) <=> ![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(X, Y0)) | (~rf(X, Y1))))),
% 0.11/0.38 inference(transitivity,[status(thm)],[20, 18])).
% 0.11/0.38 tff(22,plain,
% 0.11/0.38 (^[X: $i] : rewrite(((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((~(rf(X, Y0) & rf(X, Y1))) | (Y0 = Y1))) <=> ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(X, Y0)) | (~rf(X, Y1)))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(23,plain,
% 0.11/0.38 (![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((~(rf(X, Y0) & rf(X, Y1))) | (Y0 = Y1))) <=> ![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(X, Y0)) | (~rf(X, Y1))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[22])).
% 0.11/0.38 tff(24,plain,
% 0.11/0.38 (![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((~(rf(X, Y0) & rf(X, Y1))) | (Y0 = Y1))) <=> ![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((~(rf(X, Y0) & rf(X, Y1))) | (Y0 = Y1)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(25,plain,
% 0.11/0.38 (^[X: $i] : trans(monotonicity(quant_intro(proof_bind(^[Y0: $i, Y1: $i] : rewrite(((rf(X, Y0) & rf(X, Y1)) => (Y0 = Y1)) <=> ((~(rf(X, Y0) & rf(X, Y1))) | (Y0 = Y1)))), (![Y0: $i, Y1: $i] : ((rf(X, Y0) & rf(X, Y1)) => (Y0 = Y1)) <=> ![Y0: $i, Y1: $i] : ((~(rf(X, Y0) & rf(X, Y1))) | (Y0 = Y1)))), ((cowlThing(X) => ![Y0: $i, Y1: $i] : ((rf(X, Y0) & rf(X, Y1)) => (Y0 = Y1))) <=> (cowlThing(X) => ![Y0: $i, Y1: $i] : ((~(rf(X, Y0) & rf(X, Y1))) | (Y0 = Y1))))), rewrite((cowlThing(X) => ![Y0: $i, Y1: $i] : ((~(rf(X, Y0) & rf(X, Y1))) | (Y0 = Y1))) <=> ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((~(rf(X, Y0) & rf(X, Y1))) | (Y0 = Y1)))), ((cowlThing(X) => ![Y0: $i, Y1: $i] : ((rf(X, Y0) & rf(X, Y1)) => (Y0 = Y1))) <=> ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((~(rf(X, Y0) & rf(X, Y1))) | (Y0 = Y1)))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(26,plain,
% 0.11/0.38 (![X: $i] : (cowlThing(X) => ![Y0: $i, Y1: $i] : ((rf(X, Y0) & rf(X, Y1)) => (Y0 = Y1))) <=> ![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((~(rf(X, Y0) & rf(X, Y1))) | (Y0 = Y1)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[25])).
% 0.11/0.38 tff(27,axiom,(![X: $i] : (cowlThing(X) => ![Y0: $i, Y1: $i] : ((rf(X, Y0) & rf(X, Y1)) => (Y0 = Y1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_3')).
% 0.11/0.38 tff(28,plain,
% 0.11/0.38 (![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((~(rf(X, Y0) & rf(X, Y1))) | (Y0 = Y1)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.11/0.38 tff(29,plain,
% 0.11/0.38 (![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((~(rf(X, Y0) & rf(X, Y1))) | (Y0 = Y1)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.11/0.38 tff(30,plain,(
% 0.11/0.38 ![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((~(rf(X, Y0) & rf(X, Y1))) | (Y0 = Y1)))),
% 0.11/0.38 inference(skolemize,[status(sab)],[29])).
% 0.11/0.38 tff(31,plain,
% 0.11/0.38 (![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(X, Y0)) | (~rf(X, Y1))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.11/0.38 tff(32,plain,
% 0.11/0.38 (![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(X, Y0)) | (~rf(X, Y1))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[31, 21])).
% 0.11/0.38 tff(33,plain,
% 0.11/0.38 (((~![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(X, Y0)) | (~rf(X, Y1))))) | ((~cowlThing(tptp_fun_Z_1(i2003_11_14_17_19_42328))) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), Y0)) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), Y1))))) <=> ((~![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(X, Y0)) | (~rf(X, Y1))))) | (~cowlThing(tptp_fun_Z_1(i2003_11_14_17_19_42328))) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), Y0)) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), Y1))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(34,plain,
% 0.11/0.38 ((~![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(X, Y0)) | (~rf(X, Y1))))) | ((~cowlThing(tptp_fun_Z_1(i2003_11_14_17_19_42328))) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), Y0)) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), Y1))))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(35,plain,
% 0.11/0.38 ((~![X: $i] : ((~cowlThing(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(X, Y0)) | (~rf(X, Y1))))) | (~cowlThing(tptp_fun_Z_1(i2003_11_14_17_19_42328))) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), Y0)) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), Y1)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.11/0.39 tff(36,plain,
% 0.11/0.39 ((~cowlThing(tptp_fun_Z_1(i2003_11_14_17_19_42328))) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), Y0)) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), Y1)))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[35, 32])).
% 0.11/0.39 tff(37,plain,
% 0.11/0.39 (![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), Y0)) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), Y1)))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[36, 16])).
% 0.11/0.39 tff(38,plain,
% 0.11/0.39 (^[X: $i, Y: $i] : refl((rinvF(X, Y) <=> rf(Y, X)) <=> (rinvF(X, Y) <=> rf(Y, X)))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(39,plain,
% 0.11/0.39 (![X: $i, Y: $i] : (rinvF(X, Y) <=> rf(Y, X)) <=> ![X: $i, Y: $i] : (rinvF(X, Y) <=> rf(Y, X))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[38])).
% 0.11/0.39 tff(40,plain,
% 0.11/0.39 (![X: $i, Y: $i] : (rinvF(X, Y) <=> rf(Y, X)) <=> ![X: $i, Y: $i] : (rinvF(X, Y) <=> rf(Y, X))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(41,axiom,(![X: $i, Y: $i] : (rinvF(X, Y) <=> rf(Y, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_4')).
% 0.11/0.39 tff(42,plain,
% 0.11/0.39 (![X: $i, Y: $i] : (rinvF(X, Y) <=> rf(Y, X))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.11/0.39 tff(43,plain,(
% 0.11/0.39 ![X: $i, Y: $i] : (rinvF(X, Y) <=> rf(Y, X))),
% 0.11/0.39 inference(skolemize,[status(sab)],[42])).
% 0.11/0.39 tff(44,plain,
% 0.11/0.39 (![X: $i, Y: $i] : (rinvF(X, Y) <=> rf(Y, X))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.11/0.39 tff(45,plain,
% 0.11/0.39 ((~![X: $i, Y: $i] : (rinvF(X, Y) <=> rf(Y, X))) | (rinvF(tptp_fun_Y_0(i2003_11_14_17_19_42328), tptp_fun_Z_1(i2003_11_14_17_19_42328)) <=> rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), tptp_fun_Y_0(i2003_11_14_17_19_42328)))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(46,plain,
% 0.11/0.39 (rinvF(tptp_fun_Y_0(i2003_11_14_17_19_42328), tptp_fun_Z_1(i2003_11_14_17_19_42328)) <=> rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), tptp_fun_Y_0(i2003_11_14_17_19_42328))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.11/0.39 tff(47,plain,
% 0.11/0.39 (^[X: $i] : refl((~((~((~cUnsatisfiable(X)) | (~(cp1(tptp_fun_W_2(X)) | (~rf(X, tptp_fun_Y_0(X))) | (~rinvF(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | (~rf(tptp_fun_Z_1(X), tptp_fun_W_2(X))) | (~cp1(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~cp1(Y)) | (~rf(X, Y)) | ![Z: $i] : ((~rinvF(Y, Z)) | ![W: $i] : (cp1(W) | (~rf(Z, W))))))))) <=> (~((~((~cUnsatisfiable(X)) | (~(cp1(tptp_fun_W_2(X)) | (~rf(X, tptp_fun_Y_0(X))) | (~rinvF(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | (~rf(tptp_fun_Z_1(X), tptp_fun_W_2(X))) | (~cp1(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~cp1(Y)) | (~rf(X, Y)) | ![Z: $i] : ((~rinvF(Y, Z)) | ![W: $i] : (cp1(W) | (~rf(Z, W))))))))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(48,plain,
% 0.11/0.39 (![X: $i] : (~((~((~cUnsatisfiable(X)) | (~(cp1(tptp_fun_W_2(X)) | (~rf(X, tptp_fun_Y_0(X))) | (~rinvF(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | (~rf(tptp_fun_Z_1(X), tptp_fun_W_2(X))) | (~cp1(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~cp1(Y)) | (~rf(X, Y)) | ![Z: $i] : ((~rinvF(Y, Z)) | ![W: $i] : (cp1(W) | (~rf(Z, W))))))))) <=> ![X: $i] : (~((~((~cUnsatisfiable(X)) | (~(cp1(tptp_fun_W_2(X)) | (~rf(X, tptp_fun_Y_0(X))) | (~rinvF(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | (~rf(tptp_fun_Z_1(X), tptp_fun_W_2(X))) | (~cp1(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~cp1(Y)) | (~rf(X, Y)) | ![Z: $i] : ((~rinvF(Y, Z)) | ![W: $i] : (cp1(W) | (~rf(Z, W)))))))))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[47])).
% 0.11/0.39 tff(49,plain,
% 0.11/0.39 (^[X: $i] : rewrite((~((~((~cUnsatisfiable(X)) | (~(cp1(tptp_fun_W_2(X)) | (~rf(X, tptp_fun_Y_0(X))) | (~rinvF(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | (~rf(tptp_fun_Z_1(X), tptp_fun_W_2(X))) | (~cp1(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~cp1(Y)) | (~rf(X, Y)) | ![Z: $i] : ((~rinvF(Y, Z)) | ![W: $i] : (cp1(W) | (~rf(Z, W))))))))) <=> (~((~((~cUnsatisfiable(X)) | (~(cp1(tptp_fun_W_2(X)) | (~rf(X, tptp_fun_Y_0(X))) | (~rinvF(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | (~rf(tptp_fun_Z_1(X), tptp_fun_W_2(X))) | (~cp1(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~cp1(Y)) | (~rf(X, Y)) | ![Z: $i] : ((~rinvF(Y, Z)) | ![W: $i] : (cp1(W) | (~rf(Z, W))))))))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(50,plain,
% 0.11/0.39 (![X: $i] : (~((~((~cUnsatisfiable(X)) | (~(cp1(tptp_fun_W_2(X)) | (~rf(X, tptp_fun_Y_0(X))) | (~rinvF(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | (~rf(tptp_fun_Z_1(X), tptp_fun_W_2(X))) | (~cp1(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~cp1(Y)) | (~rf(X, Y)) | ![Z: $i] : ((~rinvF(Y, Z)) | ![W: $i] : (cp1(W) | (~rf(Z, W))))))))) <=> ![X: $i] : (~((~((~cUnsatisfiable(X)) | (~(cp1(tptp_fun_W_2(X)) | (~rf(X, tptp_fun_Y_0(X))) | (~rinvF(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | (~rf(tptp_fun_Z_1(X), tptp_fun_W_2(X))) | (~cp1(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~cp1(Y)) | (~rf(X, Y)) | ![Z: $i] : ((~rinvF(Y, Z)) | ![W: $i] : (cp1(W) | (~rf(Z, W)))))))))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[49])).
% 0.11/0.39 tff(51,plain,
% 0.11/0.39 (![X: $i] : (~((~((~cUnsatisfiable(X)) | (~(cp1(tptp_fun_W_2(X)) | (~rf(X, tptp_fun_Y_0(X))) | (~rinvF(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | (~rf(tptp_fun_Z_1(X), tptp_fun_W_2(X))) | (~cp1(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~cp1(Y)) | (~rf(X, Y)) | ![Z: $i] : ((~rinvF(Y, Z)) | ![W: $i] : (cp1(W) | (~rf(Z, W))))))))) <=> ![X: $i] : (~((~((~cUnsatisfiable(X)) | (~(cp1(tptp_fun_W_2(X)) | (~rf(X, tptp_fun_Y_0(X))) | (~rinvF(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | (~rf(tptp_fun_Z_1(X), tptp_fun_W_2(X))) | (~cp1(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~cp1(Y)) | (~rf(X, Y)) | ![Z: $i] : ((~rinvF(Y, Z)) | ![W: $i] : (cp1(W) | (~rf(Z, W)))))))))),
% 0.11/0.39 inference(transitivity,[status(thm)],[50, 48])).
% 0.11/0.39 tff(52,plain,
% 0.11/0.39 (^[X: $i] : trans(monotonicity(rewrite(((~cUnsatisfiable(X)) | (rf(X, tptp_fun_Y_0(X)) & rinvF(tptp_fun_Y_0(X), tptp_fun_Z_1(X)) & rf(tptp_fun_Z_1(X), tptp_fun_W_2(X)) & (~cp1(tptp_fun_W_2(X))) & cp1(tptp_fun_Y_0(X)))) <=> ((~cUnsatisfiable(X)) | (~(cp1(tptp_fun_W_2(X)) | (~rf(X, tptp_fun_Y_0(X))) | (~rinvF(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | (~rf(tptp_fun_Z_1(X), tptp_fun_W_2(X))) | (~cp1(tptp_fun_Y_0(X))))))), rewrite((cUnsatisfiable(X) | ![Y: $i] : ((~cp1(Y)) | (~rf(X, Y)) | ![Z: $i] : ((~rinvF(Y, Z)) | ![W: $i] : (~(rf(Z, W) & (~cp1(W))))))) <=> (cUnsatisfiable(X) | ![Y: $i] : ((~cp1(Y)) | (~rf(X, Y)) | ![Z: $i] : ((~rinvF(Y, Z)) | ![W: $i] : (cp1(W) | (~rf(Z, W))))))), ((((~cUnsatisfiable(X)) | (rf(X, tptp_fun_Y_0(X)) & rinvF(tptp_fun_Y_0(X), tptp_fun_Z_1(X)) & rf(tptp_fun_Z_1(X), tptp_fun_W_2(X)) & (~cp1(tptp_fun_W_2(X))) & cp1(tptp_fun_Y_0(X)))) & (cUnsatisfiable(X) | ![Y: $i] : ((~cp1(Y)) | (~rf(X, Y)) | ![Z: $i] : ((~rinvF(Y, Z)) | ![W: $i] : (~(rf(Z, W) & (~cp1(W)))))))) <=> (((~cUnsatisfiable(X)) | (~(cp1(tptp_fun_W_2(X)) | (~rf(X, tptp_fun_Y_0(X))) | (~rinvF(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | (~rf(tptp_fun_Z_1(X), tptp_fun_W_2(X))) | (~cp1(tptp_fun_Y_0(X)))))) & (cUnsatisfiable(X) | ![Y: $i] : ((~cp1(Y)) | (~rf(X, Y)) | ![Z: $i] : ((~rinvF(Y, Z)) | ![W: $i] : (cp1(W) | (~rf(Z, W))))))))), rewrite((((~cUnsatisfiable(X)) | (~(cp1(tptp_fun_W_2(X)) | (~rf(X, tptp_fun_Y_0(X))) | (~rinvF(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | (~rf(tptp_fun_Z_1(X), tptp_fun_W_2(X))) | (~cp1(tptp_fun_Y_0(X)))))) & (cUnsatisfiable(X) | ![Y: $i] : ((~cp1(Y)) | (~rf(X, Y)) | ![Z: $i] : ((~rinvF(Y, Z)) | ![W: $i] : (cp1(W) | (~rf(Z, W))))))) <=> (~((~((~cUnsatisfiable(X)) | (~(cp1(tptp_fun_W_2(X)) | (~rf(X, tptp_fun_Y_0(X))) | (~rinvF(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | (~rf(tptp_fun_Z_1(X), tptp_fun_W_2(X))) | (~cp1(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~cp1(Y)) | (~rf(X, Y)) | ![Z: $i] : ((~rinvF(Y, Z)) | ![W: $i] : (cp1(W) | (~rf(Z, W)))))))))), ((((~cUnsatisfiable(X)) | (rf(X, tptp_fun_Y_0(X)) & rinvF(tptp_fun_Y_0(X), tptp_fun_Z_1(X)) & rf(tptp_fun_Z_1(X), tptp_fun_W_2(X)) & (~cp1(tptp_fun_W_2(X))) & cp1(tptp_fun_Y_0(X)))) & (cUnsatisfiable(X) | ![Y: $i] : ((~cp1(Y)) | (~rf(X, Y)) | ![Z: $i] : ((~rinvF(Y, Z)) | ![W: $i] : (~(rf(Z, W) & (~cp1(W)))))))) <=> (~((~((~cUnsatisfiable(X)) | (~(cp1(tptp_fun_W_2(X)) | (~rf(X, tptp_fun_Y_0(X))) | (~rinvF(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | (~rf(tptp_fun_Z_1(X), tptp_fun_W_2(X))) | (~cp1(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~cp1(Y)) | (~rf(X, Y)) | ![Z: $i] : ((~rinvF(Y, Z)) | ![W: $i] : (cp1(W) | (~rf(Z, W)))))))))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(53,plain,
% 0.11/0.39 (![X: $i] : (((~cUnsatisfiable(X)) | (rf(X, tptp_fun_Y_0(X)) & rinvF(tptp_fun_Y_0(X), tptp_fun_Z_1(X)) & rf(tptp_fun_Z_1(X), tptp_fun_W_2(X)) & (~cp1(tptp_fun_W_2(X))) & cp1(tptp_fun_Y_0(X)))) & (cUnsatisfiable(X) | ![Y: $i] : ((~cp1(Y)) | (~rf(X, Y)) | ![Z: $i] : ((~rinvF(Y, Z)) | ![W: $i] : (~(rf(Z, W) & (~cp1(W)))))))) <=> ![X: $i] : (~((~((~cUnsatisfiable(X)) | (~(cp1(tptp_fun_W_2(X)) | (~rf(X, tptp_fun_Y_0(X))) | (~rinvF(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | (~rf(tptp_fun_Z_1(X), tptp_fun_W_2(X))) | (~cp1(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~cp1(Y)) | (~rf(X, Y)) | ![Z: $i] : ((~rinvF(Y, Z)) | ![W: $i] : (cp1(W) | (~rf(Z, W)))))))))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[52])).
% 0.11/0.39 tff(54,plain,
% 0.11/0.39 (^[X: $i] : rewrite((((~cUnsatisfiable(X)) | (rf(X, tptp_fun_Y_0(X)) & (rinvF(tptp_fun_Y_0(X), tptp_fun_Z_1(X)) & (rf(tptp_fun_Z_1(X), tptp_fun_W_2(X)) & (~cp1(tptp_fun_W_2(X))))) & cp1(tptp_fun_Y_0(X)))) & (cUnsatisfiable(X) | ![Y: $i] : ((~rf(X, Y)) | ![Z: $i] : ((~rinvF(Y, Z)) | ![W: $i] : (~(rf(Z, W) & (~cp1(W))))) | (~cp1(Y))))) <=> (((~cUnsatisfiable(X)) | (rf(X, tptp_fun_Y_0(X)) & rinvF(tptp_fun_Y_0(X), tptp_fun_Z_1(X)) & rf(tptp_fun_Z_1(X), tptp_fun_W_2(X)) & (~cp1(tptp_fun_W_2(X))) & cp1(tptp_fun_Y_0(X)))) & (cUnsatisfiable(X) | ![Y: $i] : ((~cp1(Y)) | (~rf(X, Y)) | ![Z: $i] : ((~rinvF(Y, Z)) | ![W: $i] : (~(rf(Z, W) & (~cp1(W)))))))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(55,plain,
% 0.11/0.39 (![X: $i] : (((~cUnsatisfiable(X)) | (rf(X, tptp_fun_Y_0(X)) & (rinvF(tptp_fun_Y_0(X), tptp_fun_Z_1(X)) & (rf(tptp_fun_Z_1(X), tptp_fun_W_2(X)) & (~cp1(tptp_fun_W_2(X))))) & cp1(tptp_fun_Y_0(X)))) & (cUnsatisfiable(X) | ![Y: $i] : ((~rf(X, Y)) | ![Z: $i] : ((~rinvF(Y, Z)) | ![W: $i] : (~(rf(Z, W) & (~cp1(W))))) | (~cp1(Y))))) <=> ![X: $i] : (((~cUnsatisfiable(X)) | (rf(X, tptp_fun_Y_0(X)) & rinvF(tptp_fun_Y_0(X), tptp_fun_Z_1(X)) & rf(tptp_fun_Z_1(X), tptp_fun_W_2(X)) & (~cp1(tptp_fun_W_2(X))) & cp1(tptp_fun_Y_0(X)))) & (cUnsatisfiable(X) | ![Y: $i] : ((~cp1(Y)) | (~rf(X, Y)) | ![Z: $i] : ((~rinvF(Y, Z)) | ![W: $i] : (~(rf(Z, W) & (~cp1(W))))))))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[54])).
% 0.11/0.39 tff(56,plain,
% 0.11/0.39 (![X: $i] : (cUnsatisfiable(X) <=> ?[Y: $i] : (rf(X, Y) & ?[Z: $i] : (rinvF(Y, Z) & ?[W: $i] : (rf(Z, W) & (~cp1(W)))) & cp1(Y))) <=> ![X: $i] : (cUnsatisfiable(X) <=> ?[Y: $i] : (rf(X, Y) & ?[Z: $i] : (rinvF(Y, Z) & ?[W: $i] : (rf(Z, W) & (~cp1(W)))) & cp1(Y)))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(57,plain,
% 0.11/0.39 (^[X: $i] : rewrite((cUnsatisfiable(X) <=> ?[Y: $i] : ((rf(X, Y) & ?[Z: $i] : (rinvF(Y, Z) & ?[W: $i] : (rf(Z, W) & (~cp1(W))))) & cp1(Y))) <=> (cUnsatisfiable(X) <=> ?[Y: $i] : (rf(X, Y) & ?[Z: $i] : (rinvF(Y, Z) & ?[W: $i] : (rf(Z, W) & (~cp1(W)))) & cp1(Y))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(58,plain,
% 0.11/0.39 (![X: $i] : (cUnsatisfiable(X) <=> ?[Y: $i] : ((rf(X, Y) & ?[Z: $i] : (rinvF(Y, Z) & ?[W: $i] : (rf(Z, W) & (~cp1(W))))) & cp1(Y))) <=> ![X: $i] : (cUnsatisfiable(X) <=> ?[Y: $i] : (rf(X, Y) & ?[Z: $i] : (rinvF(Y, Z) & ?[W: $i] : (rf(Z, W) & (~cp1(W)))) & cp1(Y)))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[57])).
% 0.11/0.39 tff(59,axiom,(![X: $i] : (cUnsatisfiable(X) <=> ?[Y: $i] : ((rf(X, Y) & ?[Z: $i] : (rinvF(Y, Z) & ?[W: $i] : (rf(Z, W) & (~cp1(W))))) & cp1(Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_2')).
% 0.11/0.39 tff(60,plain,
% 0.11/0.39 (![X: $i] : (cUnsatisfiable(X) <=> ?[Y: $i] : (rf(X, Y) & ?[Z: $i] : (rinvF(Y, Z) & ?[W: $i] : (rf(Z, W) & (~cp1(W)))) & cp1(Y)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.11/0.39 tff(61,plain,
% 0.11/0.39 (![X: $i] : (cUnsatisfiable(X) <=> ?[Y: $i] : (rf(X, Y) & ?[Z: $i] : (rinvF(Y, Z) & ?[W: $i] : (rf(Z, W) & (~cp1(W)))) & cp1(Y)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.11/0.39 tff(62,plain,(
% 0.11/0.39 ![X: $i] : (((~cUnsatisfiable(X)) | (rf(X, tptp_fun_Y_0(X)) & (rinvF(tptp_fun_Y_0(X), tptp_fun_Z_1(X)) & (rf(tptp_fun_Z_1(X), tptp_fun_W_2(X)) & (~cp1(tptp_fun_W_2(X))))) & cp1(tptp_fun_Y_0(X)))) & (cUnsatisfiable(X) | ![Y: $i] : ((~rf(X, Y)) | ![Z: $i] : ((~rinvF(Y, Z)) | ![W: $i] : (~(rf(Z, W) & (~cp1(W))))) | (~cp1(Y)))))),
% 0.11/0.39 inference(skolemize,[status(sab)],[61])).
% 0.11/0.39 tff(63,plain,
% 0.11/0.39 (![X: $i] : (((~cUnsatisfiable(X)) | (rf(X, tptp_fun_Y_0(X)) & rinvF(tptp_fun_Y_0(X), tptp_fun_Z_1(X)) & rf(tptp_fun_Z_1(X), tptp_fun_W_2(X)) & (~cp1(tptp_fun_W_2(X))) & cp1(tptp_fun_Y_0(X)))) & (cUnsatisfiable(X) | ![Y: $i] : ((~cp1(Y)) | (~rf(X, Y)) | ![Z: $i] : ((~rinvF(Y, Z)) | ![W: $i] : (~(rf(Z, W) & (~cp1(W))))))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[62, 55])).
% 0.11/0.39 tff(64,plain,
% 0.11/0.39 (![X: $i] : (~((~((~cUnsatisfiable(X)) | (~(cp1(tptp_fun_W_2(X)) | (~rf(X, tptp_fun_Y_0(X))) | (~rinvF(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | (~rf(tptp_fun_Z_1(X), tptp_fun_W_2(X))) | (~cp1(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~cp1(Y)) | (~rf(X, Y)) | ![Z: $i] : ((~rinvF(Y, Z)) | ![W: $i] : (cp1(W) | (~rf(Z, W)))))))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[63, 53])).
% 0.11/0.39 tff(65,plain,
% 0.11/0.39 (![X: $i] : (~((~((~cUnsatisfiable(X)) | (~(cp1(tptp_fun_W_2(X)) | (~rf(X, tptp_fun_Y_0(X))) | (~rinvF(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | (~rf(tptp_fun_Z_1(X), tptp_fun_W_2(X))) | (~cp1(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~cp1(Y)) | (~rf(X, Y)) | ![Z: $i] : ((~rinvF(Y, Z)) | ![W: $i] : (cp1(W) | (~rf(Z, W)))))))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[64, 51])).
% 0.11/0.39 tff(66,plain,
% 0.11/0.39 (((~![X: $i] : (~((~((~cUnsatisfiable(X)) | (~(cp1(tptp_fun_W_2(X)) | (~rf(X, tptp_fun_Y_0(X))) | (~rinvF(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | (~rf(tptp_fun_Z_1(X), tptp_fun_W_2(X))) | (~cp1(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~cp1(Y)) | (~rf(X, Y)) | ![Z: $i] : ((~rinvF(Y, Z)) | ![W: $i] : (cp1(W) | (~rf(Z, W)))))))))) | (~((~((~cUnsatisfiable(i2003_11_14_17_19_42328)) | (~((~cp1(tptp_fun_Y_0(i2003_11_14_17_19_42328))) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), tptp_fun_W_2(i2003_11_14_17_19_42328))) | (~rinvF(tptp_fun_Y_0(i2003_11_14_17_19_42328), tptp_fun_Z_1(i2003_11_14_17_19_42328))) | (~rf(i2003_11_14_17_19_42328, tptp_fun_Y_0(i2003_11_14_17_19_42328))) | cp1(tptp_fun_W_2(i2003_11_14_17_19_42328)))))) | (~(cUnsatisfiable(i2003_11_14_17_19_42328) | ![Y: $i] : ((~cp1(Y)) | (~rf(i2003_11_14_17_19_42328, Y)) | ![Z: $i] : ((~rinvF(Y, Z)) | ![W: $i] : (cp1(W) | (~rf(Z, W)))))))))) <=> ((~![X: $i] : (~((~((~cUnsatisfiable(X)) | (~(cp1(tptp_fun_W_2(X)) | (~rf(X, tptp_fun_Y_0(X))) | (~rinvF(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | (~rf(tptp_fun_Z_1(X), tptp_fun_W_2(X))) | (~cp1(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~cp1(Y)) | (~rf(X, Y)) | ![Z: $i] : ((~rinvF(Y, Z)) | ![W: $i] : (cp1(W) | (~rf(Z, W)))))))))) | (~((~((~cUnsatisfiable(i2003_11_14_17_19_42328)) | (~((~cp1(tptp_fun_Y_0(i2003_11_14_17_19_42328))) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), tptp_fun_W_2(i2003_11_14_17_19_42328))) | (~rinvF(tptp_fun_Y_0(i2003_11_14_17_19_42328), tptp_fun_Z_1(i2003_11_14_17_19_42328))) | (~rf(i2003_11_14_17_19_42328, tptp_fun_Y_0(i2003_11_14_17_19_42328))) | cp1(tptp_fun_W_2(i2003_11_14_17_19_42328)))))) | (~(cUnsatisfiable(i2003_11_14_17_19_42328) | ![Y: $i] : ((~cp1(Y)) | (~rf(i2003_11_14_17_19_42328, Y)) | ![Z: $i] : ((~rinvF(Y, Z)) | ![W: $i] : (cp1(W) | (~rf(Z, W))))))))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(67,plain,
% 0.11/0.39 ((~((~((~cUnsatisfiable(i2003_11_14_17_19_42328)) | (~(cp1(tptp_fun_W_2(i2003_11_14_17_19_42328)) | (~rf(i2003_11_14_17_19_42328, tptp_fun_Y_0(i2003_11_14_17_19_42328))) | (~rinvF(tptp_fun_Y_0(i2003_11_14_17_19_42328), tptp_fun_Z_1(i2003_11_14_17_19_42328))) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), tptp_fun_W_2(i2003_11_14_17_19_42328))) | (~cp1(tptp_fun_Y_0(i2003_11_14_17_19_42328))))))) | (~(cUnsatisfiable(i2003_11_14_17_19_42328) | ![Y: $i] : ((~cp1(Y)) | (~rf(i2003_11_14_17_19_42328, Y)) | ![Z: $i] : ((~rinvF(Y, Z)) | ![W: $i] : (cp1(W) | (~rf(Z, W))))))))) <=> (~((~((~cUnsatisfiable(i2003_11_14_17_19_42328)) | (~((~cp1(tptp_fun_Y_0(i2003_11_14_17_19_42328))) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), tptp_fun_W_2(i2003_11_14_17_19_42328))) | (~rinvF(tptp_fun_Y_0(i2003_11_14_17_19_42328), tptp_fun_Z_1(i2003_11_14_17_19_42328))) | (~rf(i2003_11_14_17_19_42328, tptp_fun_Y_0(i2003_11_14_17_19_42328))) | cp1(tptp_fun_W_2(i2003_11_14_17_19_42328)))))) | (~(cUnsatisfiable(i2003_11_14_17_19_42328) | ![Y: $i] : ((~cp1(Y)) | (~rf(i2003_11_14_17_19_42328, Y)) | ![Z: $i] : ((~rinvF(Y, Z)) | ![W: $i] : (cp1(W) | (~rf(Z, W)))))))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(68,plain,
% 0.11/0.39 (((~![X: $i] : (~((~((~cUnsatisfiable(X)) | (~(cp1(tptp_fun_W_2(X)) | (~rf(X, tptp_fun_Y_0(X))) | (~rinvF(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | (~rf(tptp_fun_Z_1(X), tptp_fun_W_2(X))) | (~cp1(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~cp1(Y)) | (~rf(X, Y)) | ![Z: $i] : ((~rinvF(Y, Z)) | ![W: $i] : (cp1(W) | (~rf(Z, W)))))))))) | (~((~((~cUnsatisfiable(i2003_11_14_17_19_42328)) | (~(cp1(tptp_fun_W_2(i2003_11_14_17_19_42328)) | (~rf(i2003_11_14_17_19_42328, tptp_fun_Y_0(i2003_11_14_17_19_42328))) | (~rinvF(tptp_fun_Y_0(i2003_11_14_17_19_42328), tptp_fun_Z_1(i2003_11_14_17_19_42328))) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), tptp_fun_W_2(i2003_11_14_17_19_42328))) | (~cp1(tptp_fun_Y_0(i2003_11_14_17_19_42328))))))) | (~(cUnsatisfiable(i2003_11_14_17_19_42328) | ![Y: $i] : ((~cp1(Y)) | (~rf(i2003_11_14_17_19_42328, Y)) | ![Z: $i] : ((~rinvF(Y, Z)) | ![W: $i] : (cp1(W) | (~rf(Z, W)))))))))) <=> ((~![X: $i] : (~((~((~cUnsatisfiable(X)) | (~(cp1(tptp_fun_W_2(X)) | (~rf(X, tptp_fun_Y_0(X))) | (~rinvF(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | (~rf(tptp_fun_Z_1(X), tptp_fun_W_2(X))) | (~cp1(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~cp1(Y)) | (~rf(X, Y)) | ![Z: $i] : ((~rinvF(Y, Z)) | ![W: $i] : (cp1(W) | (~rf(Z, W)))))))))) | (~((~((~cUnsatisfiable(i2003_11_14_17_19_42328)) | (~((~cp1(tptp_fun_Y_0(i2003_11_14_17_19_42328))) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), tptp_fun_W_2(i2003_11_14_17_19_42328))) | (~rinvF(tptp_fun_Y_0(i2003_11_14_17_19_42328), tptp_fun_Z_1(i2003_11_14_17_19_42328))) | (~rf(i2003_11_14_17_19_42328, tptp_fun_Y_0(i2003_11_14_17_19_42328))) | cp1(tptp_fun_W_2(i2003_11_14_17_19_42328)))))) | (~(cUnsatisfiable(i2003_11_14_17_19_42328) | ![Y: $i] : ((~cp1(Y)) | (~rf(i2003_11_14_17_19_42328, Y)) | ![Z: $i] : ((~rinvF(Y, Z)) | ![W: $i] : (cp1(W) | (~rf(Z, W))))))))))),
% 0.11/0.39 inference(monotonicity,[status(thm)],[67])).
% 0.11/0.39 tff(69,plain,
% 0.11/0.39 (((~![X: $i] : (~((~((~cUnsatisfiable(X)) | (~(cp1(tptp_fun_W_2(X)) | (~rf(X, tptp_fun_Y_0(X))) | (~rinvF(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | (~rf(tptp_fun_Z_1(X), tptp_fun_W_2(X))) | (~cp1(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~cp1(Y)) | (~rf(X, Y)) | ![Z: $i] : ((~rinvF(Y, Z)) | ![W: $i] : (cp1(W) | (~rf(Z, W)))))))))) | (~((~((~cUnsatisfiable(i2003_11_14_17_19_42328)) | (~(cp1(tptp_fun_W_2(i2003_11_14_17_19_42328)) | (~rf(i2003_11_14_17_19_42328, tptp_fun_Y_0(i2003_11_14_17_19_42328))) | (~rinvF(tptp_fun_Y_0(i2003_11_14_17_19_42328), tptp_fun_Z_1(i2003_11_14_17_19_42328))) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), tptp_fun_W_2(i2003_11_14_17_19_42328))) | (~cp1(tptp_fun_Y_0(i2003_11_14_17_19_42328))))))) | (~(cUnsatisfiable(i2003_11_14_17_19_42328) | ![Y: $i] : ((~cp1(Y)) | (~rf(i2003_11_14_17_19_42328, Y)) | ![Z: $i] : ((~rinvF(Y, Z)) | ![W: $i] : (cp1(W) | (~rf(Z, W)))))))))) <=> ((~![X: $i] : (~((~((~cUnsatisfiable(X)) | (~(cp1(tptp_fun_W_2(X)) | (~rf(X, tptp_fun_Y_0(X))) | (~rinvF(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | (~rf(tptp_fun_Z_1(X), tptp_fun_W_2(X))) | (~cp1(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~cp1(Y)) | (~rf(X, Y)) | ![Z: $i] : ((~rinvF(Y, Z)) | ![W: $i] : (cp1(W) | (~rf(Z, W)))))))))) | (~((~((~cUnsatisfiable(i2003_11_14_17_19_42328)) | (~((~cp1(tptp_fun_Y_0(i2003_11_14_17_19_42328))) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), tptp_fun_W_2(i2003_11_14_17_19_42328))) | (~rinvF(tptp_fun_Y_0(i2003_11_14_17_19_42328), tptp_fun_Z_1(i2003_11_14_17_19_42328))) | (~rf(i2003_11_14_17_19_42328, tptp_fun_Y_0(i2003_11_14_17_19_42328))) | cp1(tptp_fun_W_2(i2003_11_14_17_19_42328)))))) | (~(cUnsatisfiable(i2003_11_14_17_19_42328) | ![Y: $i] : ((~cp1(Y)) | (~rf(i2003_11_14_17_19_42328, Y)) | ![Z: $i] : ((~rinvF(Y, Z)) | ![W: $i] : (cp1(W) | (~rf(Z, W))))))))))),
% 0.11/0.40 inference(transitivity,[status(thm)],[68, 66])).
% 0.11/0.40 tff(70,plain,
% 0.11/0.40 ((~![X: $i] : (~((~((~cUnsatisfiable(X)) | (~(cp1(tptp_fun_W_2(X)) | (~rf(X, tptp_fun_Y_0(X))) | (~rinvF(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | (~rf(tptp_fun_Z_1(X), tptp_fun_W_2(X))) | (~cp1(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~cp1(Y)) | (~rf(X, Y)) | ![Z: $i] : ((~rinvF(Y, Z)) | ![W: $i] : (cp1(W) | (~rf(Z, W)))))))))) | (~((~((~cUnsatisfiable(i2003_11_14_17_19_42328)) | (~(cp1(tptp_fun_W_2(i2003_11_14_17_19_42328)) | (~rf(i2003_11_14_17_19_42328, tptp_fun_Y_0(i2003_11_14_17_19_42328))) | (~rinvF(tptp_fun_Y_0(i2003_11_14_17_19_42328), tptp_fun_Z_1(i2003_11_14_17_19_42328))) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), tptp_fun_W_2(i2003_11_14_17_19_42328))) | (~cp1(tptp_fun_Y_0(i2003_11_14_17_19_42328))))))) | (~(cUnsatisfiable(i2003_11_14_17_19_42328) | ![Y: $i] : ((~cp1(Y)) | (~rf(i2003_11_14_17_19_42328, Y)) | ![Z: $i] : ((~rinvF(Y, Z)) | ![W: $i] : (cp1(W) | (~rf(Z, W)))))))))),
% 0.11/0.40 inference(quant_inst,[status(thm)],[])).
% 0.11/0.40 tff(71,plain,
% 0.11/0.40 ((~![X: $i] : (~((~((~cUnsatisfiable(X)) | (~(cp1(tptp_fun_W_2(X)) | (~rf(X, tptp_fun_Y_0(X))) | (~rinvF(tptp_fun_Y_0(X), tptp_fun_Z_1(X))) | (~rf(tptp_fun_Z_1(X), tptp_fun_W_2(X))) | (~cp1(tptp_fun_Y_0(X))))))) | (~(cUnsatisfiable(X) | ![Y: $i] : ((~cp1(Y)) | (~rf(X, Y)) | ![Z: $i] : ((~rinvF(Y, Z)) | ![W: $i] : (cp1(W) | (~rf(Z, W)))))))))) | (~((~((~cUnsatisfiable(i2003_11_14_17_19_42328)) | (~((~cp1(tptp_fun_Y_0(i2003_11_14_17_19_42328))) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), tptp_fun_W_2(i2003_11_14_17_19_42328))) | (~rinvF(tptp_fun_Y_0(i2003_11_14_17_19_42328), tptp_fun_Z_1(i2003_11_14_17_19_42328))) | (~rf(i2003_11_14_17_19_42328, tptp_fun_Y_0(i2003_11_14_17_19_42328))) | cp1(tptp_fun_W_2(i2003_11_14_17_19_42328)))))) | (~(cUnsatisfiable(i2003_11_14_17_19_42328) | ![Y: $i] : ((~cp1(Y)) | (~rf(i2003_11_14_17_19_42328, Y)) | ![Z: $i] : ((~rinvF(Y, Z)) | ![W: $i] : (cp1(W) | (~rf(Z, W)))))))))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.11/0.40 tff(72,plain,
% 0.11/0.40 (~((~((~cUnsatisfiable(i2003_11_14_17_19_42328)) | (~((~cp1(tptp_fun_Y_0(i2003_11_14_17_19_42328))) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), tptp_fun_W_2(i2003_11_14_17_19_42328))) | (~rinvF(tptp_fun_Y_0(i2003_11_14_17_19_42328), tptp_fun_Z_1(i2003_11_14_17_19_42328))) | (~rf(i2003_11_14_17_19_42328, tptp_fun_Y_0(i2003_11_14_17_19_42328))) | cp1(tptp_fun_W_2(i2003_11_14_17_19_42328)))))) | (~(cUnsatisfiable(i2003_11_14_17_19_42328) | ![Y: $i] : ((~cp1(Y)) | (~rf(i2003_11_14_17_19_42328, Y)) | ![Z: $i] : ((~rinvF(Y, Z)) | ![W: $i] : (cp1(W) | (~rf(Z, W))))))))),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[71, 65])).
% 0.11/0.40 tff(73,plain,
% 0.11/0.40 (((~((~cUnsatisfiable(i2003_11_14_17_19_42328)) | (~((~cp1(tptp_fun_Y_0(i2003_11_14_17_19_42328))) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), tptp_fun_W_2(i2003_11_14_17_19_42328))) | (~rinvF(tptp_fun_Y_0(i2003_11_14_17_19_42328), tptp_fun_Z_1(i2003_11_14_17_19_42328))) | (~rf(i2003_11_14_17_19_42328, tptp_fun_Y_0(i2003_11_14_17_19_42328))) | cp1(tptp_fun_W_2(i2003_11_14_17_19_42328)))))) | (~(cUnsatisfiable(i2003_11_14_17_19_42328) | ![Y: $i] : ((~cp1(Y)) | (~rf(i2003_11_14_17_19_42328, Y)) | ![Z: $i] : ((~rinvF(Y, Z)) | ![W: $i] : (cp1(W) | (~rf(Z, W)))))))) | ((~cUnsatisfiable(i2003_11_14_17_19_42328)) | (~((~cp1(tptp_fun_Y_0(i2003_11_14_17_19_42328))) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), tptp_fun_W_2(i2003_11_14_17_19_42328))) | (~rinvF(tptp_fun_Y_0(i2003_11_14_17_19_42328), tptp_fun_Z_1(i2003_11_14_17_19_42328))) | (~rf(i2003_11_14_17_19_42328, tptp_fun_Y_0(i2003_11_14_17_19_42328))) | cp1(tptp_fun_W_2(i2003_11_14_17_19_42328)))))),
% 0.11/0.40 inference(tautology,[status(thm)],[])).
% 0.11/0.40 tff(74,plain,
% 0.11/0.40 ((~cUnsatisfiable(i2003_11_14_17_19_42328)) | (~((~cp1(tptp_fun_Y_0(i2003_11_14_17_19_42328))) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), tptp_fun_W_2(i2003_11_14_17_19_42328))) | (~rinvF(tptp_fun_Y_0(i2003_11_14_17_19_42328), tptp_fun_Z_1(i2003_11_14_17_19_42328))) | (~rf(i2003_11_14_17_19_42328, tptp_fun_Y_0(i2003_11_14_17_19_42328))) | cp1(tptp_fun_W_2(i2003_11_14_17_19_42328))))),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.11/0.40 tff(75,plain,
% 0.11/0.40 (cUnsatisfiable(i2003_11_14_17_19_42328) <=> cUnsatisfiable(i2003_11_14_17_19_42328)),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(76,axiom,(cUnsatisfiable(i2003_11_14_17_19_42328)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_7')).
% 0.11/0.40 tff(77,plain,
% 0.11/0.40 (cUnsatisfiable(i2003_11_14_17_19_42328)),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.11/0.40 tff(78,plain,
% 0.11/0.40 ((~((~cUnsatisfiable(i2003_11_14_17_19_42328)) | (~((~cp1(tptp_fun_Y_0(i2003_11_14_17_19_42328))) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), tptp_fun_W_2(i2003_11_14_17_19_42328))) | (~rinvF(tptp_fun_Y_0(i2003_11_14_17_19_42328), tptp_fun_Z_1(i2003_11_14_17_19_42328))) | (~rf(i2003_11_14_17_19_42328, tptp_fun_Y_0(i2003_11_14_17_19_42328))) | cp1(tptp_fun_W_2(i2003_11_14_17_19_42328)))))) | (~cUnsatisfiable(i2003_11_14_17_19_42328)) | (~((~cp1(tptp_fun_Y_0(i2003_11_14_17_19_42328))) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), tptp_fun_W_2(i2003_11_14_17_19_42328))) | (~rinvF(tptp_fun_Y_0(i2003_11_14_17_19_42328), tptp_fun_Z_1(i2003_11_14_17_19_42328))) | (~rf(i2003_11_14_17_19_42328, tptp_fun_Y_0(i2003_11_14_17_19_42328))) | cp1(tptp_fun_W_2(i2003_11_14_17_19_42328))))),
% 0.11/0.40 inference(tautology,[status(thm)],[])).
% 0.11/0.40 tff(79,plain,
% 0.11/0.40 ((~((~cUnsatisfiable(i2003_11_14_17_19_42328)) | (~((~cp1(tptp_fun_Y_0(i2003_11_14_17_19_42328))) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), tptp_fun_W_2(i2003_11_14_17_19_42328))) | (~rinvF(tptp_fun_Y_0(i2003_11_14_17_19_42328), tptp_fun_Z_1(i2003_11_14_17_19_42328))) | (~rf(i2003_11_14_17_19_42328, tptp_fun_Y_0(i2003_11_14_17_19_42328))) | cp1(tptp_fun_W_2(i2003_11_14_17_19_42328)))))) | (~((~cp1(tptp_fun_Y_0(i2003_11_14_17_19_42328))) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), tptp_fun_W_2(i2003_11_14_17_19_42328))) | (~rinvF(tptp_fun_Y_0(i2003_11_14_17_19_42328), tptp_fun_Z_1(i2003_11_14_17_19_42328))) | (~rf(i2003_11_14_17_19_42328, tptp_fun_Y_0(i2003_11_14_17_19_42328))) | cp1(tptp_fun_W_2(i2003_11_14_17_19_42328))))),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.11/0.40 tff(80,plain,
% 0.11/0.40 (~((~cp1(tptp_fun_Y_0(i2003_11_14_17_19_42328))) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), tptp_fun_W_2(i2003_11_14_17_19_42328))) | (~rinvF(tptp_fun_Y_0(i2003_11_14_17_19_42328), tptp_fun_Z_1(i2003_11_14_17_19_42328))) | (~rf(i2003_11_14_17_19_42328, tptp_fun_Y_0(i2003_11_14_17_19_42328))) | cp1(tptp_fun_W_2(i2003_11_14_17_19_42328)))),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[79, 74])).
% 0.11/0.40 tff(81,plain,
% 0.11/0.40 (((~cp1(tptp_fun_Y_0(i2003_11_14_17_19_42328))) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), tptp_fun_W_2(i2003_11_14_17_19_42328))) | (~rinvF(tptp_fun_Y_0(i2003_11_14_17_19_42328), tptp_fun_Z_1(i2003_11_14_17_19_42328))) | (~rf(i2003_11_14_17_19_42328, tptp_fun_Y_0(i2003_11_14_17_19_42328))) | cp1(tptp_fun_W_2(i2003_11_14_17_19_42328))) | rinvF(tptp_fun_Y_0(i2003_11_14_17_19_42328), tptp_fun_Z_1(i2003_11_14_17_19_42328))),
% 0.11/0.40 inference(tautology,[status(thm)],[])).
% 0.11/0.40 tff(82,plain,
% 0.11/0.40 (rinvF(tptp_fun_Y_0(i2003_11_14_17_19_42328), tptp_fun_Z_1(i2003_11_14_17_19_42328))),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.11/0.40 tff(83,plain,
% 0.11/0.40 ((~(rinvF(tptp_fun_Y_0(i2003_11_14_17_19_42328), tptp_fun_Z_1(i2003_11_14_17_19_42328)) <=> rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), tptp_fun_Y_0(i2003_11_14_17_19_42328)))) | (~rinvF(tptp_fun_Y_0(i2003_11_14_17_19_42328), tptp_fun_Z_1(i2003_11_14_17_19_42328))) | rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), tptp_fun_Y_0(i2003_11_14_17_19_42328))),
% 0.11/0.40 inference(tautology,[status(thm)],[])).
% 0.11/0.40 tff(84,plain,
% 0.11/0.40 ((~(rinvF(tptp_fun_Y_0(i2003_11_14_17_19_42328), tptp_fun_Z_1(i2003_11_14_17_19_42328)) <=> rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), tptp_fun_Y_0(i2003_11_14_17_19_42328)))) | rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), tptp_fun_Y_0(i2003_11_14_17_19_42328))),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.11/0.40 tff(85,plain,
% 0.11/0.40 (rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), tptp_fun_Y_0(i2003_11_14_17_19_42328))),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[84, 46])).
% 0.11/0.40 tff(86,plain,
% 0.11/0.40 (((~cp1(tptp_fun_Y_0(i2003_11_14_17_19_42328))) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), tptp_fun_W_2(i2003_11_14_17_19_42328))) | (~rinvF(tptp_fun_Y_0(i2003_11_14_17_19_42328), tptp_fun_Z_1(i2003_11_14_17_19_42328))) | (~rf(i2003_11_14_17_19_42328, tptp_fun_Y_0(i2003_11_14_17_19_42328))) | cp1(tptp_fun_W_2(i2003_11_14_17_19_42328))) | rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), tptp_fun_W_2(i2003_11_14_17_19_42328))),
% 0.11/0.40 inference(tautology,[status(thm)],[])).
% 0.11/0.40 tff(87,plain,
% 0.11/0.40 (rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), tptp_fun_W_2(i2003_11_14_17_19_42328))),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[86, 80])).
% 0.11/0.40 tff(88,plain,
% 0.11/0.40 (((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), Y0)) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), Y1)))) | ((~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), tptp_fun_W_2(i2003_11_14_17_19_42328))) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), tptp_fun_Y_0(i2003_11_14_17_19_42328))) | (tptp_fun_W_2(i2003_11_14_17_19_42328) = tptp_fun_Y_0(i2003_11_14_17_19_42328)))) <=> ((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), Y0)) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), Y1)))) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), tptp_fun_W_2(i2003_11_14_17_19_42328))) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), tptp_fun_Y_0(i2003_11_14_17_19_42328))) | (tptp_fun_W_2(i2003_11_14_17_19_42328) = tptp_fun_Y_0(i2003_11_14_17_19_42328)))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(89,plain,
% 0.11/0.40 (((tptp_fun_W_2(i2003_11_14_17_19_42328) = tptp_fun_Y_0(i2003_11_14_17_19_42328)) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), tptp_fun_W_2(i2003_11_14_17_19_42328))) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), tptp_fun_Y_0(i2003_11_14_17_19_42328)))) <=> ((~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), tptp_fun_W_2(i2003_11_14_17_19_42328))) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), tptp_fun_Y_0(i2003_11_14_17_19_42328))) | (tptp_fun_W_2(i2003_11_14_17_19_42328) = tptp_fun_Y_0(i2003_11_14_17_19_42328)))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(90,plain,
% 0.11/0.40 (((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), Y0)) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), Y1)))) | ((tptp_fun_W_2(i2003_11_14_17_19_42328) = tptp_fun_Y_0(i2003_11_14_17_19_42328)) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), tptp_fun_W_2(i2003_11_14_17_19_42328))) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), tptp_fun_Y_0(i2003_11_14_17_19_42328))))) <=> ((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), Y0)) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), Y1)))) | ((~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), tptp_fun_W_2(i2003_11_14_17_19_42328))) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), tptp_fun_Y_0(i2003_11_14_17_19_42328))) | (tptp_fun_W_2(i2003_11_14_17_19_42328) = tptp_fun_Y_0(i2003_11_14_17_19_42328))))),
% 0.11/0.40 inference(monotonicity,[status(thm)],[89])).
% 0.11/0.40 tff(91,plain,
% 0.11/0.40 (((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), Y0)) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), Y1)))) | ((tptp_fun_W_2(i2003_11_14_17_19_42328) = tptp_fun_Y_0(i2003_11_14_17_19_42328)) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), tptp_fun_W_2(i2003_11_14_17_19_42328))) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), tptp_fun_Y_0(i2003_11_14_17_19_42328))))) <=> ((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), Y0)) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), Y1)))) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), tptp_fun_W_2(i2003_11_14_17_19_42328))) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), tptp_fun_Y_0(i2003_11_14_17_19_42328))) | (tptp_fun_W_2(i2003_11_14_17_19_42328) = tptp_fun_Y_0(i2003_11_14_17_19_42328)))),
% 0.11/0.40 inference(transitivity,[status(thm)],[90, 88])).
% 0.11/0.40 tff(92,plain,
% 0.11/0.40 ((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), Y0)) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), Y1)))) | ((tptp_fun_W_2(i2003_11_14_17_19_42328) = tptp_fun_Y_0(i2003_11_14_17_19_42328)) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), tptp_fun_W_2(i2003_11_14_17_19_42328))) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), tptp_fun_Y_0(i2003_11_14_17_19_42328))))),
% 0.11/0.40 inference(quant_inst,[status(thm)],[])).
% 0.11/0.40 tff(93,plain,
% 0.11/0.40 ((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), Y0)) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), Y1)))) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), tptp_fun_W_2(i2003_11_14_17_19_42328))) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), tptp_fun_Y_0(i2003_11_14_17_19_42328))) | (tptp_fun_W_2(i2003_11_14_17_19_42328) = tptp_fun_Y_0(i2003_11_14_17_19_42328))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.11/0.40 tff(94,plain,
% 0.11/0.40 (tptp_fun_W_2(i2003_11_14_17_19_42328) = tptp_fun_Y_0(i2003_11_14_17_19_42328)),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[93, 87, 85, 37])).
% 0.11/0.40 tff(95,plain,
% 0.11/0.40 (cp1(tptp_fun_W_2(i2003_11_14_17_19_42328)) <=> cp1(tptp_fun_Y_0(i2003_11_14_17_19_42328))),
% 0.11/0.40 inference(monotonicity,[status(thm)],[94])).
% 0.11/0.40 tff(96,plain,
% 0.11/0.40 (cp1(tptp_fun_Y_0(i2003_11_14_17_19_42328)) <=> cp1(tptp_fun_W_2(i2003_11_14_17_19_42328))),
% 0.11/0.40 inference(symmetry,[status(thm)],[95])).
% 0.11/0.40 tff(97,plain,
% 0.11/0.40 (((~cp1(tptp_fun_Y_0(i2003_11_14_17_19_42328))) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), tptp_fun_W_2(i2003_11_14_17_19_42328))) | (~rinvF(tptp_fun_Y_0(i2003_11_14_17_19_42328), tptp_fun_Z_1(i2003_11_14_17_19_42328))) | (~rf(i2003_11_14_17_19_42328, tptp_fun_Y_0(i2003_11_14_17_19_42328))) | cp1(tptp_fun_W_2(i2003_11_14_17_19_42328))) | cp1(tptp_fun_Y_0(i2003_11_14_17_19_42328))),
% 0.11/0.40 inference(tautology,[status(thm)],[])).
% 0.11/0.40 tff(98,plain,
% 0.11/0.40 (cp1(tptp_fun_Y_0(i2003_11_14_17_19_42328))),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[97, 80])).
% 0.11/0.40 tff(99,plain,
% 0.11/0.40 (cp1(tptp_fun_W_2(i2003_11_14_17_19_42328))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[98, 96])).
% 0.11/0.40 tff(100,plain,
% 0.11/0.40 (((~cp1(tptp_fun_Y_0(i2003_11_14_17_19_42328))) | (~rf(tptp_fun_Z_1(i2003_11_14_17_19_42328), tptp_fun_W_2(i2003_11_14_17_19_42328))) | (~rinvF(tptp_fun_Y_0(i2003_11_14_17_19_42328), tptp_fun_Z_1(i2003_11_14_17_19_42328))) | (~rf(i2003_11_14_17_19_42328, tptp_fun_Y_0(i2003_11_14_17_19_42328))) | cp1(tptp_fun_W_2(i2003_11_14_17_19_42328))) | (~cp1(tptp_fun_W_2(i2003_11_14_17_19_42328)))),
% 0.11/0.40 inference(tautology,[status(thm)],[])).
% 0.11/0.40 tff(101,plain,
% 0.11/0.40 (~cp1(tptp_fun_W_2(i2003_11_14_17_19_42328))),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[100, 80])).
% 0.11/0.40 tff(102,plain,
% 0.11/0.40 ($false),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[101, 99])).
% 0.11/0.40 % SZS output end Proof
% 0.11/0.40 % E exiting
%------------------------------------------------------------------------------