%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS143+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:13:28 AM UTC 2025
% Result : Theorem 0.20s 0.37s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KRS143+1 : TPTP v9.0.0. Released v3.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n001.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 19:15:49 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.20/0.37 % SZS status Theorem
% 0.20/0.37 % SZS output start Proof
% 0.20/0.37 tff(xsd_string_type, type, (
% 0.20/0.37 xsd_string: $i > $o)).
% 0.20/0.37 tff(tptp_fun_X_2_type, type, (
% 0.20/0.37 tptp_fun_X_2: $i)).
% 0.20/0.37 tff(xsd_integer_type, type, (
% 0.20/0.37 xsd_integer: $i > $o)).
% 0.20/0.37 tff(cowlThing_type, type, (
% 0.20/0.37 cowlThing: $i > $o)).
% 0.20/0.37 tff(tptp_fun_X_1_type, type, (
% 0.20/0.37 tptp_fun_X_1: $i)).
% 0.20/0.37 tff(cowlNothing_type, type, (
% 0.20/0.37 cowlNothing: $i > $o)).
% 0.20/0.37 tff(rp_type, type, (
% 0.20/0.37 rp: ( $i * $i ) > $o)).
% 0.20/0.37 tff(tptp_fun_X_3_type, type, (
% 0.20/0.37 tptp_fun_X_3: $i)).
% 0.20/0.37 tff(tptp_fun_Y1_4_type, type, (
% 0.20/0.37 tptp_fun_Y1_4: $i)).
% 0.20/0.37 tff(tptp_fun_Y0_5_type, type, (
% 0.20/0.37 tptp_fun_Y0_5: $i)).
% 0.20/0.37 tff(cc_type, type, (
% 0.20/0.37 cc: $i > $o)).
% 0.20/0.37 tff(tptp_fun_Y0_0_type, type, (
% 0.20/0.37 tptp_fun_Y0_0: $i > $i)).
% 0.20/0.37 tff(1,assumption,(cowlNothing(X!1) | (~cowlThing(X!1))), introduced(assumption)).
% 0.20/0.37 tff(2,plain,
% 0.20/0.37 (^[X: $i] : refl((~(cowlNothing(X) | (~cowlThing(X)))) <=> (~(cowlNothing(X) | (~cowlThing(X)))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(3,plain,
% 0.20/0.37 (![X: $i] : (~(cowlNothing(X) | (~cowlThing(X)))) <=> ![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.37 tff(4,plain,
% 0.20/0.37 (^[X: $i] : rewrite((cowlThing(X) & (~cowlNothing(X))) <=> (~(cowlNothing(X) | (~cowlThing(X)))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(5,plain,
% 0.20/0.37 (![X: $i] : (cowlThing(X) & (~cowlNothing(X))) <=> ![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.37 tff(6,plain,
% 0.20/0.37 (![X: $i] : (cowlThing(X) & (~cowlNothing(X))) <=> ![X: $i] : (cowlThing(X) & (~cowlNothing(X)))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(7,axiom,(![X: $i] : (cowlThing(X) & (~cowlNothing(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_0')).
% 0.20/0.37 tff(8,plain,
% 0.20/0.37 (![X: $i] : (cowlThing(X) & (~cowlNothing(X)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.20/0.37 tff(9,plain,(
% 0.20/0.37 ![X: $i] : (cowlThing(X) & (~cowlNothing(X)))),
% 0.20/0.37 inference(skolemize,[status(sab)],[8])).
% 0.20/0.37 tff(10,plain,
% 0.20/0.37 (![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.20/0.37 tff(11,plain,
% 0.20/0.37 (![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.20/0.37 tff(12,plain,
% 0.20/0.37 ((~![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))) | (~(cowlNothing(X!1) | (~cowlThing(X!1))))),
% 0.20/0.37 inference(quant_inst,[status(thm)],[])).
% 0.20/0.37 tff(13,plain,
% 0.20/0.37 ($false),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[12, 11, 1])).
% 0.20/0.37 tff(14,plain,(~(cowlNothing(X!1) | (~cowlThing(X!1)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.37 tff(15,plain,
% 0.20/0.37 ((cowlNothing(X!1) | (~cowlThing(X!1))) | cowlThing(X!1)),
% 0.20/0.37 inference(tautology,[status(thm)],[])).
% 0.20/0.37 tff(16,plain,
% 0.20/0.37 (cowlThing(X!1)),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[15, 14])).
% 0.20/0.37 tff(17,plain,
% 0.20/0.37 ((cowlNothing(X!1) | (~cowlThing(X!1))) | (~cowlNothing(X!1))),
% 0.20/0.37 inference(tautology,[status(thm)],[])).
% 0.20/0.37 tff(18,plain,
% 0.20/0.37 (~cowlNothing(X!1)),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[17, 14])).
% 0.20/0.37 tff(19,assumption,(~((~cc(X!3)) | (~((~((~rp(X!3, Y0!5)) | (~rp(X!3, Y1!4)) | (Y0!5 = Y1!4))) | ![Y0: $i] : (~rp(X!3, Y0)))))), introduced(assumption)).
% 0.20/0.37 tff(20,plain,
% 0.20/0.37 (((~cc(X!3)) | (~((~((~rp(X!3, Y0!5)) | (~rp(X!3, Y1!4)) | (Y0!5 = Y1!4))) | ![Y0: $i] : (~rp(X!3, Y0))))) | cc(X!3)),
% 0.20/0.37 inference(tautology,[status(thm)],[])).
% 0.20/0.37 tff(21,plain,
% 0.20/0.37 (cc(X!3)),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.20/0.37 tff(22,plain,
% 0.20/0.37 (^[X: $i] : refl(((~cc(X)) | rp(X, tptp_fun_Y0_0(X))) <=> ((~cc(X)) | rp(X, tptp_fun_Y0_0(X))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(23,plain,
% 0.20/0.37 (![X: $i] : ((~cc(X)) | rp(X, tptp_fun_Y0_0(X))) <=> ![X: $i] : ((~cc(X)) | rp(X, tptp_fun_Y0_0(X)))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[22])).
% 0.20/0.37 tff(24,plain,
% 0.20/0.37 (![X: $i] : ((~cc(X)) | ?[Y0: $i] : rp(X, Y0)) <=> ![X: $i] : ((~cc(X)) | ?[Y0: $i] : rp(X, Y0))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(25,plain,
% 0.20/0.37 (^[X: $i] : rewrite((cc(X) => ?[Y0: $i] : rp(X, Y0)) <=> ((~cc(X)) | ?[Y0: $i] : rp(X, Y0)))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(26,plain,
% 0.20/0.37 (![X: $i] : (cc(X) => ?[Y0: $i] : rp(X, Y0)) <=> ![X: $i] : ((~cc(X)) | ?[Y0: $i] : rp(X, Y0))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[25])).
% 0.20/0.37 tff(27,axiom,(![X: $i] : (cc(X) => ?[Y0: $i] : rp(X, Y0))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_2')).
% 0.20/0.37 tff(28,plain,
% 0.20/0.37 (![X: $i] : ((~cc(X)) | ?[Y0: $i] : rp(X, Y0))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.20/0.37 tff(29,plain,
% 0.20/0.37 (![X: $i] : ((~cc(X)) | ?[Y0: $i] : rp(X, Y0))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.20/0.37 tff(30,plain,(
% 0.20/0.37 ![X: $i] : ((~cc(X)) | rp(X, tptp_fun_Y0_0(X)))),
% 0.20/0.37 inference(skolemize,[status(sab)],[29])).
% 0.20/0.37 tff(31,plain,
% 0.20/0.37 (![X: $i] : ((~cc(X)) | rp(X, tptp_fun_Y0_0(X)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.20/0.37 tff(32,plain,
% 0.20/0.37 (((~![X: $i] : ((~cc(X)) | rp(X, tptp_fun_Y0_0(X)))) | ((~cc(X!3)) | rp(X!3, tptp_fun_Y0_0(X!3)))) <=> ((~![X: $i] : ((~cc(X)) | rp(X, tptp_fun_Y0_0(X)))) | (~cc(X!3)) | rp(X!3, tptp_fun_Y0_0(X!3)))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(33,plain,
% 0.20/0.37 ((~![X: $i] : ((~cc(X)) | rp(X, tptp_fun_Y0_0(X)))) | ((~cc(X!3)) | rp(X!3, tptp_fun_Y0_0(X!3)))),
% 0.20/0.37 inference(quant_inst,[status(thm)],[])).
% 0.20/0.37 tff(34,plain,
% 0.20/0.37 ((~![X: $i] : ((~cc(X)) | rp(X, tptp_fun_Y0_0(X)))) | (~cc(X!3)) | rp(X!3, tptp_fun_Y0_0(X!3))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.20/0.37 tff(35,plain,
% 0.20/0.37 (rp(X!3, tptp_fun_Y0_0(X!3))),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[34, 31, 21])).
% 0.20/0.37 tff(36,plain,
% 0.20/0.37 (^[X: $i] : refl(((~cc(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y0)) | (~rp(X, Y1)))) <=> ((~cc(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y0)) | (~rp(X, Y1)))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(37,plain,
% 0.20/0.37 (![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y0)) | (~rp(X, Y1)))) <=> ![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y0)) | (~rp(X, Y1))))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[36])).
% 0.20/0.37 tff(38,plain,
% 0.20/0.37 (^[X: $i] : rewrite(((~cc(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y0)) | (~rp(X, Y1)))) <=> ((~cc(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y0)) | (~rp(X, Y1)))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(39,plain,
% 0.20/0.37 (![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y0)) | (~rp(X, Y1)))) <=> ![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y0)) | (~rp(X, Y1))))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[38])).
% 0.20/0.37 tff(40,plain,
% 0.20/0.37 (![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y0)) | (~rp(X, Y1)))) <=> ![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y0)) | (~rp(X, Y1))))),
% 0.20/0.37 inference(transitivity,[status(thm)],[39, 37])).
% 0.20/0.37 tff(41,plain,
% 0.20/0.37 (^[X: $i] : rewrite(((~cc(X)) | ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1))) <=> ((~cc(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y0)) | (~rp(X, Y1)))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(42,plain,
% 0.20/0.37 (![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1))) <=> ![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y0)) | (~rp(X, Y1))))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[41])).
% 0.20/0.37 tff(43,plain,
% 0.20/0.37 (![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1))) <=> ![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1)))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(44,plain,
% 0.20/0.37 (^[X: $i] : trans(monotonicity(quant_intro(proof_bind(^[Y0: $i, Y1: $i] : rewrite(((rp(X, Y0) & rp(X, Y1)) => (Y0 = Y1)) <=> ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1)))), (![Y0: $i, Y1: $i] : ((rp(X, Y0) & rp(X, Y1)) => (Y0 = Y1)) <=> ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1)))), ((cc(X) => ![Y0: $i, Y1: $i] : ((rp(X, Y0) & rp(X, Y1)) => (Y0 = Y1))) <=> (cc(X) => ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1))))), rewrite((cc(X) => ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1))) <=> ((~cc(X)) | ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1)))), ((cc(X) => ![Y0: $i, Y1: $i] : ((rp(X, Y0) & rp(X, Y1)) => (Y0 = Y1))) <=> ((~cc(X)) | ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1)))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(45,plain,
% 0.20/0.38 (![X: $i] : (cc(X) => ![Y0: $i, Y1: $i] : ((rp(X, Y0) & rp(X, Y1)) => (Y0 = Y1))) <=> ![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[44])).
% 0.20/0.38 tff(46,axiom,(![X: $i] : (cc(X) => ![Y0: $i, Y1: $i] : ((rp(X, Y0) & rp(X, Y1)) => (Y0 = Y1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_3')).
% 0.20/0.38 tff(47,plain,
% 0.20/0.38 (![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.20/0.38 tff(48,plain,
% 0.20/0.38 (![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.20/0.38 tff(49,plain,(
% 0.20/0.38 ![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1)))),
% 0.20/0.38 inference(skolemize,[status(sab)],[48])).
% 0.20/0.38 tff(50,plain,
% 0.20/0.38 (![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y0)) | (~rp(X, Y1))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.20/0.38 tff(51,plain,
% 0.20/0.38 (![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y0)) | (~rp(X, Y1))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[50, 40])).
% 0.20/0.38 tff(52,plain,
% 0.20/0.38 (((~![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y0)) | (~rp(X, Y1))))) | ((~cc(X!3)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!3, Y1)) | (~rp(X!3, Y0))))) <=> ((~![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y0)) | (~rp(X, Y1))))) | (~cc(X!3)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!3, Y1)) | (~rp(X!3, Y0))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(53,plain,
% 0.20/0.38 (((~cc(X!3)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!3, Y0)) | (~rp(X!3, Y1)))) <=> ((~cc(X!3)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!3, Y1)) | (~rp(X!3, Y0))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(54,plain,
% 0.20/0.38 (((~![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y0)) | (~rp(X, Y1))))) | ((~cc(X!3)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!3, Y0)) | (~rp(X!3, Y1))))) <=> ((~![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y0)) | (~rp(X, Y1))))) | ((~cc(X!3)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!3, Y1)) | (~rp(X!3, Y0)))))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[53])).
% 0.20/0.38 tff(55,plain,
% 0.20/0.38 (((~![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y0)) | (~rp(X, Y1))))) | ((~cc(X!3)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!3, Y0)) | (~rp(X!3, Y1))))) <=> ((~![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y0)) | (~rp(X, Y1))))) | (~cc(X!3)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!3, Y1)) | (~rp(X!3, Y0))))),
% 0.20/0.38 inference(transitivity,[status(thm)],[54, 52])).
% 0.20/0.38 tff(56,plain,
% 0.20/0.38 ((~![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y0)) | (~rp(X, Y1))))) | ((~cc(X!3)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!3, Y0)) | (~rp(X!3, Y1))))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(57,plain,
% 0.20/0.38 ((~![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y0)) | (~rp(X, Y1))))) | (~cc(X!3)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!3, Y1)) | (~rp(X!3, Y0)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.20/0.38 tff(58,plain,
% 0.20/0.38 (![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!3, Y1)) | (~rp(X!3, Y0)))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[57, 51, 21])).
% 0.20/0.38 tff(59,assumption,(~![Y0: $i] : (~rp(X!3, Y0))), introduced(assumption)).
% 0.20/0.38 tff(60,plain,
% 0.20/0.38 (((~cc(X!3)) | (~((~((~rp(X!3, Y0!5)) | (~rp(X!3, Y1!4)) | (Y0!5 = Y1!4))) | ![Y0: $i] : (~rp(X!3, Y0))))) | ((~((~rp(X!3, Y0!5)) | (~rp(X!3, Y1!4)) | (Y0!5 = Y1!4))) | ![Y0: $i] : (~rp(X!3, Y0)))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(61,plain,
% 0.20/0.38 ((~((~rp(X!3, Y0!5)) | (~rp(X!3, Y1!4)) | (Y0!5 = Y1!4))) | ![Y0: $i] : (~rp(X!3, Y0))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[60, 19])).
% 0.20/0.38 tff(62,plain,
% 0.20/0.38 ((~((~((~rp(X!3, Y0!5)) | (~rp(X!3, Y1!4)) | (Y0!5 = Y1!4))) | ![Y0: $i] : (~rp(X!3, Y0)))) | (~((~rp(X!3, Y0!5)) | (~rp(X!3, Y1!4)) | (Y0!5 = Y1!4))) | ![Y0: $i] : (~rp(X!3, Y0))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(63,plain,
% 0.20/0.38 (~((~rp(X!3, Y0!5)) | (~rp(X!3, Y1!4)) | (Y0!5 = Y1!4))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[62, 61, 59])).
% 0.20/0.38 tff(64,plain,
% 0.20/0.38 (((~rp(X!3, Y0!5)) | (~rp(X!3, Y1!4)) | (Y0!5 = Y1!4)) | (~(Y0!5 = Y1!4))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(65,plain,
% 0.20/0.38 (~(Y0!5 = Y1!4)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.20/0.38 tff(66,plain,
% 0.20/0.38 (((~rp(X!3, Y0!5)) | (~rp(X!3, Y1!4)) | (Y0!5 = Y1!4)) | rp(X!3, Y1!4)),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(67,plain,
% 0.20/0.38 (rp(X!3, Y1!4)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[66, 63])).
% 0.20/0.38 tff(68,plain,
% 0.20/0.38 (((~rp(X!3, Y0!5)) | (~rp(X!3, Y1!4)) | (Y0!5 = Y1!4)) | rp(X!3, Y0!5)),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(69,plain,
% 0.20/0.38 (rp(X!3, Y0!5)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[68, 63])).
% 0.20/0.38 tff(70,plain,
% 0.20/0.38 (((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!3, Y1)) | (~rp(X!3, Y0)))) | ((~rp(X!3, Y0!5)) | (~rp(X!3, Y1!4)) | (Y0!5 = Y1!4))) <=> ((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!3, Y1)) | (~rp(X!3, Y0)))) | (~rp(X!3, Y0!5)) | (~rp(X!3, Y1!4)) | (Y0!5 = Y1!4))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(71,plain,
% 0.20/0.38 (((Y0!5 = Y1!4) | (~rp(X!3, Y1!4)) | (~rp(X!3, Y0!5))) <=> ((~rp(X!3, Y0!5)) | (~rp(X!3, Y1!4)) | (Y0!5 = Y1!4))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(72,plain,
% 0.20/0.38 (((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!3, Y1)) | (~rp(X!3, Y0)))) | ((Y0!5 = Y1!4) | (~rp(X!3, Y1!4)) | (~rp(X!3, Y0!5)))) <=> ((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!3, Y1)) | (~rp(X!3, Y0)))) | ((~rp(X!3, Y0!5)) | (~rp(X!3, Y1!4)) | (Y0!5 = Y1!4)))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[71])).
% 0.20/0.38 tff(73,plain,
% 0.20/0.38 (((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!3, Y1)) | (~rp(X!3, Y0)))) | ((Y0!5 = Y1!4) | (~rp(X!3, Y1!4)) | (~rp(X!3, Y0!5)))) <=> ((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!3, Y1)) | (~rp(X!3, Y0)))) | (~rp(X!3, Y0!5)) | (~rp(X!3, Y1!4)) | (Y0!5 = Y1!4))),
% 0.20/0.38 inference(transitivity,[status(thm)],[72, 70])).
% 0.20/0.38 tff(74,plain,
% 0.20/0.38 ((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!3, Y1)) | (~rp(X!3, Y0)))) | ((Y0!5 = Y1!4) | (~rp(X!3, Y1!4)) | (~rp(X!3, Y0!5)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(75,plain,
% 0.20/0.38 ((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!3, Y1)) | (~rp(X!3, Y0)))) | (~rp(X!3, Y0!5)) | (~rp(X!3, Y1!4)) | (Y0!5 = Y1!4)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.20/0.38 tff(76,plain,
% 0.20/0.38 ($false),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[75, 69, 67, 65, 58])).
% 0.20/0.38 tff(77,plain,(((~cc(X!3)) | (~((~((~rp(X!3, Y0!5)) | (~rp(X!3, Y1!4)) | (Y0!5 = Y1!4))) | ![Y0: $i] : (~rp(X!3, Y0))))) | ![Y0: $i] : (~rp(X!3, Y0))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.38 tff(78,plain,
% 0.20/0.38 (![Y0: $i] : (~rp(X!3, Y0))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[77, 19])).
% 0.20/0.38 tff(79,plain,
% 0.20/0.38 ((~![Y0: $i] : (~rp(X!3, Y0))) | (~rp(X!3, tptp_fun_Y0_0(X!3)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(80,plain,
% 0.20/0.38 ($false),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[79, 78, 35])).
% 0.20/0.38 tff(81,plain,((~cc(X!3)) | (~((~((~rp(X!3, Y0!5)) | (~rp(X!3, Y1!4)) | (Y0!5 = Y1!4))) | ![Y0: $i] : (~rp(X!3, Y0))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.38 tff(82,plain,
% 0.20/0.38 (((~((~cc(X!3)) | (~((~((~rp(X!3, Y0!5)) | (~rp(X!3, Y1!4)) | (Y0!5 = Y1!4))) | ![Y0: $i] : (~rp(X!3, Y0)))))) | (~cowlThing(X!1)) | (xsd_integer(X!2) <=> xsd_string(X!2)) | cowlNothing(X!1)) <=> ((~cowlThing(X!1)) | (xsd_integer(X!2) <=> xsd_string(X!2)) | cowlNothing(X!1) | (~((~cc(X!3)) | (~((~((~rp(X!3, Y0!5)) | (~rp(X!3, Y1!4)) | (Y0!5 = Y1!4))) | ![Y0: $i] : (~rp(X!3, Y0)))))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(83,plain,
% 0.20/0.38 (((~((~rp(X!3, Y0!5)) | (~rp(X!3, Y1!4)) | (Y0!5 = Y1!4))) | ![Y0: $i] : (~rp(X!3, Y0))) <=> ((~((~rp(X!3, Y0!5)) | (~rp(X!3, Y1!4)) | (Y0!5 = Y1!4))) | ![Y0: $i] : (~rp(X!3, Y0)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(84,plain,
% 0.20/0.38 ((~((~((~rp(X!3, Y0!5)) | (~rp(X!3, Y1!4)) | (Y0!5 = Y1!4))) | ![Y0: $i] : (~rp(X!3, Y0)))) <=> (~((~((~rp(X!3, Y0!5)) | (~rp(X!3, Y1!4)) | (Y0!5 = Y1!4))) | ![Y0: $i] : (~rp(X!3, Y0))))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[83])).
% 0.20/0.38 tff(85,plain,
% 0.20/0.38 (((~cc(X!3)) | (~((~((~rp(X!3, Y0!5)) | (~rp(X!3, Y1!4)) | (Y0!5 = Y1!4))) | ![Y0: $i] : (~rp(X!3, Y0))))) <=> ((~cc(X!3)) | (~((~((~rp(X!3, Y0!5)) | (~rp(X!3, Y1!4)) | (Y0!5 = Y1!4))) | ![Y0: $i] : (~rp(X!3, Y0)))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[84])).
% 0.20/0.39 tff(86,plain,
% 0.20/0.39 ((~((~cc(X!3)) | (~((~((~rp(X!3, Y0!5)) | (~rp(X!3, Y1!4)) | (Y0!5 = Y1!4))) | ![Y0: $i] : (~rp(X!3, Y0)))))) <=> (~((~cc(X!3)) | (~((~((~rp(X!3, Y0!5)) | (~rp(X!3, Y1!4)) | (Y0!5 = Y1!4))) | ![Y0: $i] : (~rp(X!3, Y0))))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[85])).
% 0.20/0.39 tff(87,plain,
% 0.20/0.39 (((~((~cc(X!3)) | (~((~((~rp(X!3, Y0!5)) | (~rp(X!3, Y1!4)) | (Y0!5 = Y1!4))) | ![Y0: $i] : (~rp(X!3, Y0)))))) | (~cowlThing(X!1)) | (xsd_integer(X!2) <=> xsd_string(X!2)) | cowlNothing(X!1)) <=> ((~((~cc(X!3)) | (~((~((~rp(X!3, Y0!5)) | (~rp(X!3, Y1!4)) | (Y0!5 = Y1!4))) | ![Y0: $i] : (~rp(X!3, Y0)))))) | (~cowlThing(X!1)) | (xsd_integer(X!2) <=> xsd_string(X!2)) | cowlNothing(X!1))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[86])).
% 0.20/0.39 tff(88,plain,
% 0.20/0.39 (((~((~cc(X!3)) | (~((~((~rp(X!3, Y0!5)) | (~rp(X!3, Y1!4)) | (Y0!5 = Y1!4))) | ![Y0: $i] : (~rp(X!3, Y0)))))) | (~cowlThing(X!1)) | (xsd_integer(X!2) <=> xsd_string(X!2)) | cowlNothing(X!1)) <=> ((~cowlThing(X!1)) | (xsd_integer(X!2) <=> xsd_string(X!2)) | cowlNothing(X!1) | (~((~cc(X!3)) | (~((~((~rp(X!3, Y0!5)) | (~rp(X!3, Y1!4)) | (Y0!5 = Y1!4))) | ![Y0: $i] : (~rp(X!3, Y0)))))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[87, 82])).
% 0.20/0.39 tff(89,plain,
% 0.20/0.39 (((~((~cc(X!3)) | (~((~((~rp(X!3, Y0!5)) | (~rp(X!3, Y1!4)) | (Y0!5 = Y1!4))) | ![Y0: $i] : (~rp(X!3, Y0)))))) | (~cowlThing(X!1)) | (xsd_integer(X!2) <=> xsd_string(X!2)) | cowlNothing(X!1)) <=> ((~((~cc(X!3)) | (~((~((~rp(X!3, Y0!5)) | (~rp(X!3, Y1!4)) | (Y0!5 = Y1!4))) | ![Y0: $i] : (~rp(X!3, Y0)))))) | (~cowlThing(X!1)) | (xsd_integer(X!2) <=> xsd_string(X!2)) | cowlNothing(X!1))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(90,plain,
% 0.20/0.39 ((((~cowlThing(X!1)) | cowlNothing(X!1)) | (xsd_integer(X!2) <=> xsd_string(X!2)) | (~((~cc(X!3)) | (~((~((~rp(X!3, Y0!5)) | (~rp(X!3, Y1!4)) | (Y0!5 = Y1!4))) | ![Y0: $i] : (~rp(X!3, Y0))))))) <=> ((~((~cc(X!3)) | (~((~((~rp(X!3, Y0!5)) | (~rp(X!3, Y1!4)) | (Y0!5 = Y1!4))) | ![Y0: $i] : (~rp(X!3, Y0)))))) | (~cowlThing(X!1)) | (xsd_integer(X!2) <=> xsd_string(X!2)) | cowlNothing(X!1))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(91,plain,
% 0.20/0.39 ((cc(X!3) & ((~((~rp(X!3, Y0!5)) | (~rp(X!3, Y1!4)) | (Y0!5 = Y1!4))) | ![Y0: $i] : (~rp(X!3, Y0)))) <=> (~((~cc(X!3)) | (~((~((~rp(X!3, Y0!5)) | (~rp(X!3, Y1!4)) | (Y0!5 = Y1!4))) | ![Y0: $i] : (~rp(X!3, Y0))))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(92,plain,
% 0.20/0.39 (((~((~(rp(X!3, Y0!5) & rp(X!3, Y1!4))) | (Y0!5 = Y1!4))) | ![Y0: $i] : (~rp(X!3, Y0))) <=> ((~((~rp(X!3, Y0!5)) | (~rp(X!3, Y1!4)) | (Y0!5 = Y1!4))) | ![Y0: $i] : (~rp(X!3, Y0)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(93,plain,
% 0.20/0.39 ((cc(X!3) & ((~((~(rp(X!3, Y0!5) & rp(X!3, Y1!4))) | (Y0!5 = Y1!4))) | ![Y0: $i] : (~rp(X!3, Y0)))) <=> (cc(X!3) & ((~((~rp(X!3, Y0!5)) | (~rp(X!3, Y1!4)) | (Y0!5 = Y1!4))) | ![Y0: $i] : (~rp(X!3, Y0))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[92])).
% 0.20/0.39 tff(94,plain,
% 0.20/0.39 ((cc(X!3) & ((~((~(rp(X!3, Y0!5) & rp(X!3, Y1!4))) | (Y0!5 = Y1!4))) | ![Y0: $i] : (~rp(X!3, Y0)))) <=> (~((~cc(X!3)) | (~((~((~rp(X!3, Y0!5)) | (~rp(X!3, Y1!4)) | (Y0!5 = Y1!4))) | ![Y0: $i] : (~rp(X!3, Y0))))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[93, 91])).
% 0.20/0.39 tff(95,plain,
% 0.20/0.39 ((~(~((~cowlThing(X!1)) | cowlNothing(X!1)))) <=> ((~cowlThing(X!1)) | cowlNothing(X!1))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(96,plain,
% 0.20/0.39 ((cowlThing(X!1) & (~cowlNothing(X!1))) <=> (~((~cowlThing(X!1)) | cowlNothing(X!1)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(97,plain,
% 0.20/0.39 ((~(cowlThing(X!1) & (~cowlNothing(X!1)))) <=> (~(~((~cowlThing(X!1)) | cowlNothing(X!1))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[96])).
% 0.20/0.39 tff(98,plain,
% 0.20/0.39 ((~(cowlThing(X!1) & (~cowlNothing(X!1)))) <=> ((~cowlThing(X!1)) | cowlNothing(X!1))),
% 0.20/0.39 inference(transitivity,[status(thm)],[97, 95])).
% 0.20/0.39 tff(99,plain,
% 0.20/0.39 (((~(cowlThing(X!1) & (~cowlNothing(X!1)))) | (xsd_integer(X!2) <=> xsd_string(X!2)) | (cc(X!3) & ((~((~(rp(X!3, Y0!5) & rp(X!3, Y1!4))) | (Y0!5 = Y1!4))) | ![Y0: $i] : (~rp(X!3, Y0))))) <=> (((~cowlThing(X!1)) | cowlNothing(X!1)) | (xsd_integer(X!2) <=> xsd_string(X!2)) | (~((~cc(X!3)) | (~((~((~rp(X!3, Y0!5)) | (~rp(X!3, Y1!4)) | (Y0!5 = Y1!4))) | ![Y0: $i] : (~rp(X!3, Y0)))))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[98, 94])).
% 0.20/0.39 tff(100,plain,
% 0.20/0.39 (((~(cowlThing(X!1) & (~cowlNothing(X!1)))) | (xsd_integer(X!2) <=> xsd_string(X!2)) | (cc(X!3) & ((~((~(rp(X!3, Y0!5) & rp(X!3, Y1!4))) | (Y0!5 = Y1!4))) | ![Y0: $i] : (~rp(X!3, Y0))))) <=> ((~((~cc(X!3)) | (~((~((~rp(X!3, Y0!5)) | (~rp(X!3, Y1!4)) | (Y0!5 = Y1!4))) | ![Y0: $i] : (~rp(X!3, Y0)))))) | (~cowlThing(X!1)) | (xsd_integer(X!2) <=> xsd_string(X!2)) | cowlNothing(X!1))),
% 0.20/0.39 inference(transitivity,[status(thm)],[99, 90])).
% 0.20/0.39 tff(101,plain,
% 0.20/0.39 (((~(cowlThing(X!1) & (~cowlNothing(X!1)))) | (xsd_integer(X!2) <=> xsd_string(X!2)) | (cc(X!3) & (![Y0: $i] : (~rp(X!3, Y0)) | (~((~(rp(X!3, Y0!5) & rp(X!3, Y1!4))) | (Y0!5 = Y1!4)))))) <=> ((~(cowlThing(X!1) & (~cowlNothing(X!1)))) | (xsd_integer(X!2) <=> xsd_string(X!2)) | (cc(X!3) & ((~((~(rp(X!3, Y0!5) & rp(X!3, Y1!4))) | (Y0!5 = Y1!4))) | ![Y0: $i] : (~rp(X!3, Y0)))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(102,plain,
% 0.20/0.39 ((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i] : ((~cc(X)) | (?[Y0: $i] : rp(X, Y0) & ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1))))) <=> (![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i] : ((~cc(X)) | (?[Y0: $i] : rp(X, Y0) & ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1)))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(103,plain,
% 0.20/0.39 ((~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i] : ((~cc(X)) | (?[Y0: $i] : rp(X, Y0) & ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1)))))) <=> (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i] : ((~cc(X)) | (?[Y0: $i] : rp(X, Y0) & ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1))))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[102])).
% 0.20/0.39 tff(104,plain,
% 0.20/0.39 ((~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i] : ((~cc(X)) | (?[Y0: $i] : rp(X, Y0) & ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1)))))) <=> (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i] : ((~cc(X)) | (?[Y0: $i] : rp(X, Y0) & ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1))))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(105,plain,
% 0.20/0.39 ((~((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X)))) & ![X: $i] : (cc(X) => (?[Y0: $i] : rp(X, Y0) & ![Y0: $i, Y1: $i] : ((rp(X, Y0) & rp(X, Y1)) => (Y0 = Y1)))))) <=> (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i] : ((~cc(X)) | (?[Y0: $i] : rp(X, Y0) & ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1))))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(106,axiom,(~((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X)))) & ![X: $i] : (cc(X) => (?[Y0: $i] : rp(X, Y0) & ![Y0: $i, Y1: $i] : ((rp(X, Y0) & rp(X, Y1)) => (Y0 = Y1)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','the_axiom')).
% 0.20/0.39 tff(107,plain,
% 0.20/0.39 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i] : ((~cc(X)) | (?[Y0: $i] : rp(X, Y0) & ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1)))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.20/0.39 tff(108,plain,
% 0.20/0.39 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i] : ((~cc(X)) | (?[Y0: $i] : rp(X, Y0) & ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1)))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[107, 103])).
% 0.20/0.39 tff(109,plain,
% 0.20/0.39 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i] : ((~cc(X)) | (?[Y0: $i] : rp(X, Y0) & ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1)))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[108, 104])).
% 0.20/0.39 tff(110,plain,
% 0.20/0.39 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i] : ((~cc(X)) | (?[Y0: $i] : rp(X, Y0) & ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1)))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[109, 103])).
% 0.20/0.39 unexpected number of arguments: (let ((a!1 (forall ((X $i)) (and (cowlThing X) (not (cowlNothing X)))))
% 0.20/0.39 (a!2 (not (and (cowlThing X!1) (not (cowlNothing X!1)))))
% 0.20/0.39 (a!3 (forall ((X $i)) (not (= (xsd_integer X) (xsd_string X)))))
% 0.20/0.39 (a!5 (forall ((X $i))
% 0.20/0.39 (let ((a!1 (forall ((Y0 $i) (Y1 $i))
% 0.20/0.39 (or (not (and (rp X Y0) (rp X Y1))) (= Y0 Y1)))))
% 0.20/0.39 (or (not (cc X)) (and (exists ((Y0 $i)) (rp X Y0)) a!1)))))
% 0.20/0.39 (a!6 (exists ((Y0 $i)) (rp X!3 Y0)))
% 0.20/0.39 (a!7 (forall ((Y0 $i) (Y1 $i))
% 0.20/0.39 (or (not (and (rp X!3 Y0) (rp X!3 Y1))) (= Y0 Y1))))
% 0.20/0.39 (a!9 (lambda ((Y0 $i)) (refl (~ (not (rp X!3 Y0)) (not (rp X!3 Y0))))))
% 0.20/0.39 (a!10 (forall ((Y0 $i)) (not (rp X!3 Y0))))
% 0.20/0.39 (a!11 (or (not (and (rp X!3 Y0!5) (rp X!3 Y1!4))) (= Y0!5 Y1!4))))
% 0.20/0.39 (let ((a!4 (sk (~ (not a!3) (= (xsd_integer X!2) (xsd_string X!2)))))
% 0.20/0.39 (a!8 (not (or (not (cc X!3)) (and a!6 a!7))))
% 0.20/0.39 (a!12 (nnf-neg (nnf-neg (proof-bind a!9) (~ (not a!6) a!10))
% 0.20/0.39 (sk (~ (not a!7) (not a!11)))
% 0.20/0.39 (~ (not (and a!6 a!7)) (or a!10 (not a!11)))))
% 0.20/0.39 (a!15 (~ (not a!5) (and (cc X!3) (or a!10 (not a!11)))))
% 0.20/0.39 (a!17 (or a!2
% 0.20/0.39 (= (xsd_integer X!2) (xsd_string X!2))
% 0.20/0.39 (and (cc X!3) (or a!10 (not a!11))))))
% 0.20/0.39 (let ((a!13 (~ a!8 (and (cc X!3) (or a!10 (not a!11))))))
% 0.20/0.39 (let ((a!14 (nnf-neg (refl (~ (cc X!3) (cc X!3))) a!12 a!13)))
% 0.20/0.40 (let ((a!16 (trans (sk (~ (not a!5) a!8)) a!14 a!15)))
% 0.20/0.40 (nnf-neg (sk (~ (not a!1) a!2)) a!4 a!16 (~ (not (and a!1 a!3 a!5)) a!17)))))))
% 0.20/0.40 Proof display could not be completed: unexpected number of arguments
% 0.20/0.40 % E exiting
%------------------------------------------------------------------------------