%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS142+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 0.38s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : KRS142+1 : TPTP v9.0.0. Released v3.1.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 19:10:56 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.38 % SZS status Theorem
% 0.20/0.38 % SZS output start Proof
% 0.20/0.38 tff(xsd_string_type, type, (
% 0.20/0.38 xsd_string: $i > $o)).
% 0.20/0.38 tff(tptp_fun_X_2_type, type, (
% 0.20/0.38 tptp_fun_X_2: $i)).
% 0.20/0.38 tff(xsd_integer_type, type, (
% 0.20/0.38 xsd_integer: $i > $o)).
% 0.20/0.38 tff(rp_type, type, (
% 0.20/0.38 rp: ( $i * $i ) > $o)).
% 0.20/0.38 tff(tptp_fun_X_3_type, type, (
% 0.20/0.38 tptp_fun_X_3: $i)).
% 0.20/0.38 tff(cc_type, type, (
% 0.20/0.38 cc: $i > $o)).
% 0.20/0.38 tff(tptp_fun_Y0_0_type, type, (
% 0.20/0.38 tptp_fun_Y0_0: $i > $i)).
% 0.20/0.38 tff(cowlThing_type, type, (
% 0.20/0.38 cowlThing: $i > $o)).
% 0.20/0.38 tff(tptp_fun_X_1_type, type, (
% 0.20/0.38 tptp_fun_X_1: $i)).
% 0.20/0.38 tff(cowlNothing_type, type, (
% 0.20/0.38 cowlNothing: $i > $o)).
% 0.20/0.38 tff(tptp_fun_Y1_5_type, type, (
% 0.20/0.38 tptp_fun_Y1_5: $i)).
% 0.20/0.38 tff(tptp_fun_Y0_6_type, type, (
% 0.20/0.38 tptp_fun_Y0_6: $i)).
% 0.20/0.38 tff(tptp_fun_X_4_type, type, (
% 0.20/0.38 tptp_fun_X_4: $i)).
% 0.20/0.38 tff(1,assumption,(~((~cc(X!3)) | (~![Y0: $i] : (~rp(X!3, Y0))))), introduced(assumption)).
% 0.20/0.38 tff(2,plain,
% 0.20/0.38 (((~cc(X!3)) | (~![Y0: $i] : (~rp(X!3, Y0)))) | cc(X!3)),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(3,plain,
% 0.20/0.38 (cc(X!3)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.20/0.38 tff(4,plain,
% 0.20/0.38 (^[X: $i] : refl(((~cc(X)) | (~((~rp(X, tptp_fun_Y0_0(X))) | (~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y0)) | (~rp(X, Y1))))))) <=> ((~cc(X)) | (~((~rp(X, tptp_fun_Y0_0(X))) | (~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y0)) | (~rp(X, Y1))))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(5,plain,
% 0.20/0.38 (![X: $i] : ((~cc(X)) | (~((~rp(X, tptp_fun_Y0_0(X))) | (~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y0)) | (~rp(X, Y1))))))) <=> ![X: $i] : ((~cc(X)) | (~((~rp(X, tptp_fun_Y0_0(X))) | (~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y0)) | (~rp(X, Y1)))))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.38 tff(6,plain,
% 0.20/0.38 (^[X: $i] : rewrite(((~cc(X)) | (~((~rp(X, tptp_fun_Y0_0(X))) | (~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y0)) | (~rp(X, Y1))))))) <=> ((~cc(X)) | (~((~rp(X, tptp_fun_Y0_0(X))) | (~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y0)) | (~rp(X, Y1))))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(7,plain,
% 0.20/0.38 (![X: $i] : ((~cc(X)) | (~((~rp(X, tptp_fun_Y0_0(X))) | (~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y0)) | (~rp(X, Y1))))))) <=> ![X: $i] : ((~cc(X)) | (~((~rp(X, tptp_fun_Y0_0(X))) | (~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y0)) | (~rp(X, Y1)))))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[6])).
% 0.20/0.38 tff(8,plain,
% 0.20/0.38 (![X: $i] : ((~cc(X)) | (~((~rp(X, tptp_fun_Y0_0(X))) | (~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y0)) | (~rp(X, Y1))))))) <=> ![X: $i] : ((~cc(X)) | (~((~rp(X, tptp_fun_Y0_0(X))) | (~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y0)) | (~rp(X, Y1)))))))),
% 0.20/0.38 inference(transitivity,[status(thm)],[7, 5])).
% 0.20/0.38 tff(9,plain,
% 0.20/0.38 (^[X: $i] : rewrite(((~cc(X)) | (rp(X, tptp_fun_Y0_0(X)) & ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1)))) <=> ((~cc(X)) | (~((~rp(X, tptp_fun_Y0_0(X))) | (~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y0)) | (~rp(X, Y1))))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(10,plain,
% 0.20/0.38 (![X: $i] : ((~cc(X)) | (rp(X, tptp_fun_Y0_0(X)) & ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1)))) <=> ![X: $i] : ((~cc(X)) | (~((~rp(X, tptp_fun_Y0_0(X))) | (~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y0)) | (~rp(X, Y1)))))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[9])).
% 0.20/0.38 tff(11,plain,
% 0.20/0.38 (![X: $i] : ((~cc(X)) | (?[Y0: $i] : rp(X, Y0) & ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1)))) <=> ![X: $i] : ((~cc(X)) | (?[Y0: $i] : rp(X, Y0) & ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(12,plain,
% 0.20/0.38 (^[X: $i] : trans(monotonicity(rewrite((?[Y0: $i] : rp(X, Y0) & ![Y0: $i, Y1: $i] : ((rp(X, Y0) & rp(X, Y1)) => (Y0 = Y1))) <=> (?[Y0: $i] : rp(X, Y0) & ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1)))), ((cc(X) => (?[Y0: $i] : rp(X, Y0) & ![Y0: $i, Y1: $i] : ((rp(X, Y0) & rp(X, Y1)) => (Y0 = Y1)))) <=> (cc(X) => (?[Y0: $i] : rp(X, Y0) & ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1)))))), rewrite((cc(X) => (?[Y0: $i] : rp(X, Y0) & ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1)))) <=> ((~cc(X)) | (?[Y0: $i] : rp(X, Y0) & ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1))))), ((cc(X) => (?[Y0: $i] : rp(X, Y0) & ![Y0: $i, Y1: $i] : ((rp(X, Y0) & rp(X, Y1)) => (Y0 = Y1)))) <=> ((~cc(X)) | (?[Y0: $i] : rp(X, Y0) & ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(13,plain,
% 0.20/0.38 (![X: $i] : (cc(X) => (?[Y0: $i] : rp(X, Y0) & ![Y0: $i, Y1: $i] : ((rp(X, Y0) & rp(X, Y1)) => (Y0 = Y1)))) <=> ![X: $i] : ((~cc(X)) | (?[Y0: $i] : rp(X, Y0) & ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[12])).
% 0.20/0.38 tff(14,axiom,(![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','axiom_2')).
% 0.20/0.38 tff(15,plain,
% 0.20/0.38 (![X: $i] : ((~cc(X)) | (?[Y0: $i] : rp(X, Y0) & ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.20/0.38 tff(16,plain,
% 0.20/0.38 (![X: $i] : ((~cc(X)) | (?[Y0: $i] : rp(X, Y0) & ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.20/0.38 tff(17,plain,(
% 0.20/0.38 ![X: $i] : ((~cc(X)) | (rp(X, tptp_fun_Y0_0(X)) & ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1))))),
% 0.20/0.38 inference(skolemize,[status(sab)],[16])).
% 0.20/0.38 tff(18,plain,
% 0.20/0.38 (![X: $i] : ((~cc(X)) | (~((~rp(X, tptp_fun_Y0_0(X))) | (~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y0)) | (~rp(X, Y1)))))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.20/0.38 tff(19,plain,
% 0.20/0.38 (![X: $i] : ((~cc(X)) | (~((~rp(X, tptp_fun_Y0_0(X))) | (~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y0)) | (~rp(X, Y1)))))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[18, 8])).
% 0.20/0.38 tff(20,plain,
% 0.20/0.38 (((~![X: $i] : ((~cc(X)) | (~((~rp(X, tptp_fun_Y0_0(X))) | (~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y0)) | (~rp(X, Y1)))))))) | ((~cc(X!3)) | (~((~rp(X!3, tptp_fun_Y0_0(X!3))) | (~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!3, Y1)) | (~rp(X!3, Y0)))))))) <=> ((~![X: $i] : ((~cc(X)) | (~((~rp(X, tptp_fun_Y0_0(X))) | (~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y0)) | (~rp(X, Y1)))))))) | (~cc(X!3)) | (~((~rp(X!3, tptp_fun_Y0_0(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(21,plain,
% 0.20/0.38 (((~cc(X!3)) | (~((~rp(X!3, tptp_fun_Y0_0(X!3))) | (~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!3, Y0)) | (~rp(X!3, Y1))))))) <=> ((~cc(X!3)) | (~((~rp(X!3, tptp_fun_Y0_0(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(22,plain,
% 0.20/0.38 (((~![X: $i] : ((~cc(X)) | (~((~rp(X, tptp_fun_Y0_0(X))) | (~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y0)) | (~rp(X, Y1)))))))) | ((~cc(X!3)) | (~((~rp(X!3, tptp_fun_Y0_0(X!3))) | (~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!3, Y0)) | (~rp(X!3, Y1)))))))) <=> ((~![X: $i] : ((~cc(X)) | (~((~rp(X, tptp_fun_Y0_0(X))) | (~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y0)) | (~rp(X, Y1)))))))) | ((~cc(X!3)) | (~((~rp(X!3, tptp_fun_Y0_0(X!3))) | (~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!3, Y1)) | (~rp(X!3, Y0))))))))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[21])).
% 0.20/0.38 tff(23,plain,
% 0.20/0.38 (((~![X: $i] : ((~cc(X)) | (~((~rp(X, tptp_fun_Y0_0(X))) | (~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y0)) | (~rp(X, Y1)))))))) | ((~cc(X!3)) | (~((~rp(X!3, tptp_fun_Y0_0(X!3))) | (~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!3, Y0)) | (~rp(X!3, Y1)))))))) <=> ((~![X: $i] : ((~cc(X)) | (~((~rp(X, tptp_fun_Y0_0(X))) | (~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y0)) | (~rp(X, Y1)))))))) | (~cc(X!3)) | (~((~rp(X!3, tptp_fun_Y0_0(X!3))) | (~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!3, Y1)) | (~rp(X!3, Y0)))))))),
% 0.20/0.38 inference(transitivity,[status(thm)],[22, 20])).
% 0.20/0.38 tff(24,plain,
% 0.20/0.38 ((~![X: $i] : ((~cc(X)) | (~((~rp(X, tptp_fun_Y0_0(X))) | (~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y0)) | (~rp(X, Y1)))))))) | ((~cc(X!3)) | (~((~rp(X!3, tptp_fun_Y0_0(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(25,plain,
% 0.20/0.38 ((~![X: $i] : ((~cc(X)) | (~((~rp(X, tptp_fun_Y0_0(X))) | (~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y0)) | (~rp(X, Y1)))))))) | (~cc(X!3)) | (~((~rp(X!3, tptp_fun_Y0_0(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)],[24, 23])).
% 0.20/0.38 tff(26,plain,
% 0.20/0.38 (~((~rp(X!3, tptp_fun_Y0_0(X!3))) | (~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!3, Y1)) | (~rp(X!3, Y0)))))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[25, 19, 3])).
% 0.20/0.38 tff(27,plain,
% 0.20/0.38 (((~rp(X!3, tptp_fun_Y0_0(X!3))) | (~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!3, Y1)) | (~rp(X!3, Y0))))) | rp(X!3, tptp_fun_Y0_0(X!3))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(28,plain,
% 0.20/0.38 (rp(X!3, tptp_fun_Y0_0(X!3))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.20/0.38 tff(29,plain,
% 0.20/0.38 (((~cc(X!3)) | (~![Y0: $i] : (~rp(X!3, Y0)))) | ![Y0: $i] : (~rp(X!3, Y0))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(30,plain,
% 0.20/0.38 (![Y0: $i] : (~rp(X!3, Y0))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[29, 1])).
% 0.20/0.38 tff(31,plain,
% 0.20/0.38 ((~![Y0: $i] : (~rp(X!3, Y0))) | (~rp(X!3, tptp_fun_Y0_0(X!3)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(32,plain,
% 0.20/0.38 ($false),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[31, 30, 28])).
% 0.20/0.38 tff(33,plain,((~cc(X!3)) | (~![Y0: $i] : (~rp(X!3, Y0)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.38 tff(34,assumption,(cowlNothing(X!1) | (~cowlThing(X!1))), introduced(assumption)).
% 0.20/0.38 tff(35,plain,
% 0.20/0.38 (^[X: $i] : refl((~(cowlNothing(X) | (~cowlThing(X)))) <=> (~(cowlNothing(X) | (~cowlThing(X)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(36,plain,
% 0.20/0.38 (![X: $i] : (~(cowlNothing(X) | (~cowlThing(X)))) <=> ![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[35])).
% 0.20/0.38 tff(37,plain,
% 0.20/0.38 (^[X: $i] : rewrite((cowlThing(X) & (~cowlNothing(X))) <=> (~(cowlNothing(X) | (~cowlThing(X)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(38,plain,
% 0.20/0.38 (![X: $i] : (cowlThing(X) & (~cowlNothing(X))) <=> ![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[37])).
% 0.20/0.38 tff(39,plain,
% 0.20/0.38 (![X: $i] : (cowlThing(X) & (~cowlNothing(X))) <=> ![X: $i] : (cowlThing(X) & (~cowlNothing(X)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(40,axiom,(![X: $i] : (cowlThing(X) & (~cowlNothing(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_0')).
% 0.20/0.38 tff(41,plain,
% 0.20/0.38 (![X: $i] : (cowlThing(X) & (~cowlNothing(X)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.20/0.38 tff(42,plain,(
% 0.20/0.38 ![X: $i] : (cowlThing(X) & (~cowlNothing(X)))),
% 0.20/0.38 inference(skolemize,[status(sab)],[41])).
% 0.20/0.38 tff(43,plain,
% 0.20/0.38 (![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.20/0.38 tff(44,plain,
% 0.20/0.38 (![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.20/0.38 tff(45,plain,
% 0.20/0.38 ((~![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))) | (~(cowlNothing(X!1) | (~cowlThing(X!1))))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(46,plain,
% 0.20/0.38 ($false),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[45, 44, 34])).
% 0.20/0.38 tff(47,plain,(~(cowlNothing(X!1) | (~cowlThing(X!1)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.38 tff(48,plain,
% 0.20/0.38 ((cowlNothing(X!1) | (~cowlThing(X!1))) | cowlThing(X!1)),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(49,plain,
% 0.20/0.38 (cowlThing(X!1)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.20/0.38 tff(50,plain,
% 0.20/0.38 ((cowlNothing(X!1) | (~cowlThing(X!1))) | (~cowlNothing(X!1))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(51,plain,
% 0.20/0.38 (~cowlNothing(X!1)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[50, 47])).
% 0.20/0.38 tff(52,assumption,(~((~rp(X!4, Y0!6)) | (~rp(X!4, Y1!5)) | (~cc(X!4)) | (Y0!6 = Y1!5))), introduced(assumption)).
% 0.20/0.38 tff(53,plain,
% 0.20/0.38 (((~rp(X!4, Y0!6)) | (~rp(X!4, Y1!5)) | (~cc(X!4)) | (Y0!6 = Y1!5)) | cc(X!4)),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(54,plain,
% 0.20/0.38 (cc(X!4)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.20/0.38 tff(55,plain,
% 0.20/0.38 (((~![X: $i] : ((~cc(X)) | (~((~rp(X, tptp_fun_Y0_0(X))) | (~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y0)) | (~rp(X, Y1)))))))) | ((~cc(X!4)) | (~((~rp(X!4, tptp_fun_Y0_0(X!4))) | (~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!4, Y0)) | (~rp(X!4, Y1)))))))) <=> ((~![X: $i] : ((~cc(X)) | (~((~rp(X, tptp_fun_Y0_0(X))) | (~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y0)) | (~rp(X, Y1)))))))) | (~cc(X!4)) | (~((~rp(X!4, tptp_fun_Y0_0(X!4))) | (~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!4, Y0)) | (~rp(X!4, Y1)))))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(56,plain,
% 0.20/0.38 ((~![X: $i] : ((~cc(X)) | (~((~rp(X, tptp_fun_Y0_0(X))) | (~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y0)) | (~rp(X, Y1)))))))) | ((~cc(X!4)) | (~((~rp(X!4, tptp_fun_Y0_0(X!4))) | (~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!4, Y0)) | (~rp(X!4, 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)) | (~((~rp(X, tptp_fun_Y0_0(X))) | (~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y0)) | (~rp(X, Y1)))))))) | (~cc(X!4)) | (~((~rp(X!4, tptp_fun_Y0_0(X!4))) | (~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!4, Y0)) | (~rp(X!4, Y1))))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.20/0.38 tff(58,plain,
% 0.20/0.38 (~((~rp(X!4, tptp_fun_Y0_0(X!4))) | (~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!4, Y0)) | (~rp(X!4, Y1)))))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[57, 19, 54])).
% 0.20/0.38 tff(59,plain,
% 0.20/0.38 (((~rp(X!4, tptp_fun_Y0_0(X!4))) | (~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!4, Y0)) | (~rp(X!4, Y1))))) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!4, Y0)) | (~rp(X!4, Y1)))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(60,plain,
% 0.20/0.38 (![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!4, Y0)) | (~rp(X!4, Y1)))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.20/0.38 tff(61,plain,
% 0.20/0.38 (((~rp(X!4, Y0!6)) | (~rp(X!4, Y1!5)) | (~cc(X!4)) | (Y0!6 = Y1!5)) | (~(Y0!6 = Y1!5))),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(62,plain,
% 0.20/0.38 (~(Y0!6 = Y1!5)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[61, 52])).
% 0.20/0.38 tff(63,plain,
% 0.20/0.38 (((~rp(X!4, Y0!6)) | (~rp(X!4, Y1!5)) | (~cc(X!4)) | (Y0!6 = Y1!5)) | rp(X!4, Y1!5)),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(64,plain,
% 0.20/0.38 (rp(X!4, Y1!5)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[63, 52])).
% 0.20/0.38 tff(65,plain,
% 0.20/0.38 (((~rp(X!4, Y0!6)) | (~rp(X!4, Y1!5)) | (~cc(X!4)) | (Y0!6 = Y1!5)) | rp(X!4, Y0!6)),
% 0.20/0.38 inference(tautology,[status(thm)],[])).
% 0.20/0.38 tff(66,plain,
% 0.20/0.38 (rp(X!4, Y0!6)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[65, 52])).
% 0.20/0.38 tff(67,plain,
% 0.20/0.38 (((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!4, Y0)) | (~rp(X!4, Y1)))) | ((~rp(X!4, Y0!6)) | (~rp(X!4, Y1!5)) | (Y0!6 = Y1!5))) <=> ((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!4, Y0)) | (~rp(X!4, Y1)))) | (~rp(X!4, Y0!6)) | (~rp(X!4, Y1!5)) | (Y0!6 = Y1!5))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(68,plain,
% 0.20/0.38 (((Y0!6 = Y1!5) | (~rp(X!4, Y0!6)) | (~rp(X!4, Y1!5))) <=> ((~rp(X!4, Y0!6)) | (~rp(X!4, Y1!5)) | (Y0!6 = Y1!5))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(69,plain,
% 0.20/0.38 (((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!4, Y0)) | (~rp(X!4, Y1)))) | ((Y0!6 = Y1!5) | (~rp(X!4, Y0!6)) | (~rp(X!4, Y1!5)))) <=> ((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!4, Y0)) | (~rp(X!4, Y1)))) | ((~rp(X!4, Y0!6)) | (~rp(X!4, Y1!5)) | (Y0!6 = Y1!5)))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[68])).
% 0.20/0.38 tff(70,plain,
% 0.20/0.38 (((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!4, Y0)) | (~rp(X!4, Y1)))) | ((Y0!6 = Y1!5) | (~rp(X!4, Y0!6)) | (~rp(X!4, Y1!5)))) <=> ((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!4, Y0)) | (~rp(X!4, Y1)))) | (~rp(X!4, Y0!6)) | (~rp(X!4, Y1!5)) | (Y0!6 = Y1!5))),
% 0.20/0.38 inference(transitivity,[status(thm)],[69, 67])).
% 0.20/0.38 tff(71,plain,
% 0.20/0.38 ((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!4, Y0)) | (~rp(X!4, Y1)))) | ((Y0!6 = Y1!5) | (~rp(X!4, Y0!6)) | (~rp(X!4, Y1!5)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(72,plain,
% 0.20/0.38 ((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!4, Y0)) | (~rp(X!4, Y1)))) | (~rp(X!4, Y0!6)) | (~rp(X!4, Y1!5)) | (Y0!6 = Y1!5)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.20/0.38 tff(73,plain,
% 0.20/0.38 ($false),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[72, 66, 64, 62, 60])).
% 0.20/0.38 tff(74,plain,((~rp(X!4, Y0!6)) | (~rp(X!4, Y1!5)) | (~cc(X!4)) | (Y0!6 = Y1!5)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(75,plain,
% 0.20/0.39 (((~((~rp(X!4, Y0!6)) | (~rp(X!4, Y1!5)) | (~cc(X!4)) | (Y0!6 = Y1!5))) | (~cowlThing(X!1)) | (~((~cc(X!3)) | (~![Y0: $i] : (~rp(X!3, Y0))))) | cowlNothing(X!1) | (xsd_integer(X!2) <=> xsd_string(X!2))) <=> ((~((~rp(X!4, Y0!6)) | (~rp(X!4, Y1!5)) | (~cc(X!4)) | (Y0!6 = Y1!5))) | (~cowlThing(X!1)) | cowlNothing(X!1) | (xsd_integer(X!2) <=> xsd_string(X!2)) | (~((~cc(X!3)) | (~![Y0: $i] : (~rp(X!3, Y0))))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(76,plain,
% 0.20/0.39 ((~![Y0: $i] : (~rp(X!3, Y0))) <=> (~![Y0: $i] : (~rp(X!3, Y0)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(77,plain,
% 0.20/0.39 (((~cc(X!3)) | (~![Y0: $i] : (~rp(X!3, Y0)))) <=> ((~cc(X!3)) | (~![Y0: $i] : (~rp(X!3, Y0))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[76])).
% 0.20/0.39 tff(78,plain,
% 0.20/0.39 ((~((~cc(X!3)) | (~![Y0: $i] : (~rp(X!3, Y0))))) <=> (~((~cc(X!3)) | (~![Y0: $i] : (~rp(X!3, Y0)))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[77])).
% 0.20/0.39 tff(79,plain,
% 0.20/0.39 ((~((~rp(X!4, Y0!6)) | (~rp(X!4, Y1!5)) | (~cc(X!4)) | (Y0!6 = Y1!5))) <=> (~((~rp(X!4, Y0!6)) | (~rp(X!4, Y1!5)) | (~cc(X!4)) | (Y0!6 = Y1!5)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(80,plain,
% 0.20/0.39 (((~((~rp(X!4, Y0!6)) | (~rp(X!4, Y1!5)) | (~cc(X!4)) | (Y0!6 = Y1!5))) | (~cowlThing(X!1)) | (~((~cc(X!3)) | (~![Y0: $i] : (~rp(X!3, Y0))))) | cowlNothing(X!1) | (xsd_integer(X!2) <=> xsd_string(X!2))) <=> ((~((~rp(X!4, Y0!6)) | (~rp(X!4, Y1!5)) | (~cc(X!4)) | (Y0!6 = Y1!5))) | (~cowlThing(X!1)) | (~((~cc(X!3)) | (~![Y0: $i] : (~rp(X!3, Y0))))) | cowlNothing(X!1) | (xsd_integer(X!2) <=> xsd_string(X!2)))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[79, 78])).
% 0.20/0.39 tff(81,plain,
% 0.20/0.39 (((~((~rp(X!4, Y0!6)) | (~rp(X!4, Y1!5)) | (~cc(X!4)) | (Y0!6 = Y1!5))) | (~cowlThing(X!1)) | (~((~cc(X!3)) | (~![Y0: $i] : (~rp(X!3, Y0))))) | cowlNothing(X!1) | (xsd_integer(X!2) <=> xsd_string(X!2))) <=> ((~((~rp(X!4, Y0!6)) | (~rp(X!4, Y1!5)) | (~cc(X!4)) | (Y0!6 = Y1!5))) | (~cowlThing(X!1)) | cowlNothing(X!1) | (xsd_integer(X!2) <=> xsd_string(X!2)) | (~((~cc(X!3)) | (~![Y0: $i] : (~rp(X!3, Y0))))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[80, 75])).
% 0.20/0.39 tff(82,plain,
% 0.20/0.39 (((~((~rp(X!4, Y0!6)) | (~rp(X!4, Y1!5)) | (~cc(X!4)) | (Y0!6 = Y1!5))) | (~cowlThing(X!1)) | (~((~cc(X!3)) | (~![Y0: $i] : (~rp(X!3, Y0))))) | cowlNothing(X!1) | (xsd_integer(X!2) <=> xsd_string(X!2))) <=> ((~((~rp(X!4, Y0!6)) | (~rp(X!4, Y1!5)) | (~cc(X!4)) | (Y0!6 = Y1!5))) | (~cowlThing(X!1)) | (~((~cc(X!3)) | (~![Y0: $i] : (~rp(X!3, Y0))))) | cowlNothing(X!1) | (xsd_integer(X!2) <=> xsd_string(X!2)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(83,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!4, Y0!6)) | (~rp(X!4, Y1!5)) | (~cc(X!4)) | (Y0!6 = Y1!5)))) <=> ((~((~rp(X!4, Y0!6)) | (~rp(X!4, Y1!5)) | (~cc(X!4)) | (Y0!6 = Y1!5))) | (~cowlThing(X!1)) | (~((~cc(X!3)) | (~![Y0: $i] : (~rp(X!3, Y0))))) | cowlNothing(X!1) | (xsd_integer(X!2) <=> xsd_string(X!2)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(84,plain,
% 0.20/0.39 ((cc(X!4) & (~((~rp(X!4, Y0!6)) | (~rp(X!4, Y1!5)) | (Y0!6 = Y1!5)))) <=> (~((~rp(X!4, Y0!6)) | (~rp(X!4, Y1!5)) | (~cc(X!4)) | (Y0!6 = Y1!5)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(85,plain,
% 0.20/0.39 ((~((~(rp(X!4, Y0!6) & rp(X!4, Y1!5))) | (Y0!6 = Y1!5))) <=> (~((~rp(X!4, Y0!6)) | (~rp(X!4, Y1!5)) | (Y0!6 = Y1!5)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(86,plain,
% 0.20/0.39 ((cc(X!4) & (~((~(rp(X!4, Y0!6) & rp(X!4, Y1!5))) | (Y0!6 = Y1!5)))) <=> (cc(X!4) & (~((~rp(X!4, Y0!6)) | (~rp(X!4, Y1!5)) | (Y0!6 = Y1!5))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[85])).
% 0.20/0.39 tff(87,plain,
% 0.20/0.39 ((cc(X!4) & (~((~(rp(X!4, Y0!6) & rp(X!4, Y1!5))) | (Y0!6 = Y1!5)))) <=> (~((~rp(X!4, Y0!6)) | (~rp(X!4, Y1!5)) | (~cc(X!4)) | (Y0!6 = Y1!5)))),
% 0.20/0.39 inference(transitivity,[status(thm)],[86, 84])).
% 0.20/0.39 tff(88,plain,
% 0.20/0.39 ((cc(X!3) & ![Y0: $i] : (~rp(X!3, Y0))) <=> (~((~cc(X!3)) | (~![Y0: $i] : (~rp(X!3, Y0)))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(89,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(90,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(91,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)],[90])).
% 0.20/0.39 tff(92,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)],[91, 89])).
% 0.20/0.39 tff(93,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))) | (cc(X!4) & (~((~(rp(X!4, Y0!6) & rp(X!4, Y1!5))) | (Y0!6 = Y1!5))))) <=> (((~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!4, Y0!6)) | (~rp(X!4, Y1!5)) | (~cc(X!4)) | (Y0!6 = Y1!5))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[92, 88, 87])).
% 0.20/0.39 tff(94,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))) | (cc(X!4) & (~((~(rp(X!4, Y0!6) & rp(X!4, Y1!5))) | (Y0!6 = Y1!5))))) <=> ((~((~rp(X!4, Y0!6)) | (~rp(X!4, Y1!5)) | (~cc(X!4)) | (Y0!6 = Y1!5))) | (~cowlThing(X!1)) | (~((~cc(X!3)) | (~![Y0: $i] : (~rp(X!3, Y0))))) | cowlNothing(X!1) | (xsd_integer(X!2) <=> xsd_string(X!2)))),
% 0.20/0.39 inference(transitivity,[status(thm)],[93, 83])).
% 0.20/0.39 tff(95,plain,
% 0.20/0.39 ((cc(X!3) & ![Y0: $i] : (~rp(X!3, Y0))) <=> (cc(X!3) & ![Y0: $i] : (~rp(X!3, Y0)))),
% 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)))) | (xsd_integer(X!2) <=> xsd_string(X!2)) | (cc(X!3) & ![Y0: $i] : (~rp(X!3, Y0))) | (cc(X!4) & (~((~(rp(X!4, Y0!6) & rp(X!4, Y1!5))) | (Y0!6 = Y1!5))))) <=> ((~(cowlThing(X!1) & (~cowlNothing(X!1)))) | (xsd_integer(X!2) <=> xsd_string(X!2)) | (cc(X!3) & ![Y0: $i] : (~rp(X!3, Y0))) | (cc(X!4) & (~((~(rp(X!4, Y0!6) & rp(X!4, Y1!5))) | (Y0!6 = Y1!5)))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[95])).
% 0.20/0.39 tff(97,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)) & ![X: $i] : ((~cc(X)) | ![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)) & ![X: $i] : ((~cc(X)) | ![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(98,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)) & ![X: $i] : ((~cc(X)) | ![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)) & ![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1)))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[97])).
% 0.20/0.39 tff(99,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)) & ![X: $i] : ((~cc(X)) | ![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)) & ![X: $i] : ((~cc(X)) | ![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(100,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))) & ![X: $i] : (cc(X) => ![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)) & ![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(101,axiom,(~(((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X)))) & ![X: $i] : (cc(X) => ?[Y0: $i] : rp(X, Y0))) & ![X: $i] : (cc(X) => ![Y0: $i, Y1: $i] : ((rp(X, Y0) & rp(X, Y1)) => (Y0 = Y1))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','the_axiom')).
% 0.20/0.40 tff(102,plain,
% 0.20/0.40 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i] : ((~cc(X)) | ?[Y0: $i] : rp(X, Y0)) & ![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.20/0.40 tff(103,plain,
% 0.20/0.40 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i] : ((~cc(X)) | ?[Y0: $i] : rp(X, Y0)) & ![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[102, 98])).
% 0.20/0.40 tff(104,plain,
% 0.20/0.40 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i] : ((~cc(X)) | ?[Y0: $i] : rp(X, Y0)) & ![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[103, 99])).
% 0.20/0.40 tff(105,plain,
% 0.20/0.40 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i] : ((~cc(X)) | ?[Y0: $i] : rp(X, Y0)) & ![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[104, 98])).
% 0.20/0.40 unexpected number of arguments: (let ((a!1 (forall ((X $i)) (and (cowlThing X) (not (cowlNothing X)))))
% 0.20/0.40 (a!2 (not (and (cowlThing X!1) (not (cowlNothing X!1)))))
% 0.20/0.40 (a!3 (forall ((X $i)) (not (= (xsd_integer X) (xsd_string X)))))
% 0.20/0.40 (a!5 (forall ((X $i)) (or (not (cc X)) (exists ((Y0 $i)) (rp X Y0)))))
% 0.20/0.40 (a!6 (exists ((Y0 $i)) (rp X!3 Y0)))
% 0.20/0.40 (a!8 (lambda ((Y0 $i)) (refl (~ (not (rp X!3 Y0)) (not (rp X!3 Y0))))))
% 0.20/0.40 (a!9 (forall ((Y0 $i)) (not (rp X!3 Y0))))
% 0.20/0.40 (a!12 (forall ((X $i))
% 0.20/0.40 (let ((a!1 (forall ((Y0 $i) (Y1 $i))
% 0.20/0.40 (or (not (and (rp X Y0) (rp X Y1))) (= Y0 Y1)))))
% 0.20/0.40 (or (not (cc X)) a!1))))
% 0.20/0.40 (a!13 (forall ((Y0 $i) (Y1 $i))
% 0.20/0.40 (or (not (and (rp X!4 Y0) (rp X!4 Y1))) (= Y0 Y1))))
% 0.20/0.40 (a!15 (or (not (and (rp X!4 Y0!6) (rp X!4 Y1!5))) (= Y0!6 Y1!5))))
% 0.20/0.40 (let ((a!4 (sk (~ (not a!3) (= (xsd_integer X!2) (xsd_string X!2)))))
% 0.20/0.40 (a!7 (not (or (not (cc X!3)) a!6)))
% 0.20/0.40 (a!14 (not (or (not (cc X!4)) a!13)))
% 0.20/0.40 (a!18 (~ (not (and a!1 a!3 a!5 a!12))
% 0.20/0.40 (or a!2
% 0.20/0.40 (= (xsd_integer X!2) (xsd_string X!2))
% 0.20/0.40 (and (cc X!3) a!9)
% 0.20/0.40 (and (cc X!4) (not a!15))))))
% 0.20/0.40 (let ((a!10 (nnf-neg (refl (~ (cc X!3) (cc X!3)))
% 0.20/0.40 (nnf-neg (proof-bind a!8) (~ (not a!6) a!9))
% 0.20/0.40 (~ a!7 (and (cc X!3) a!9))))
% 0.20/0.40 (a!16 (nnf-neg (refl (~ (cc X!4) (cc X!4)))
% 0.20/0.40 (sk (~ (not a!13) (not a!15)))
% 0.20/0.40 (~ a!14 (and (cc X!4) (not a!15))))))
% 0.20/0.40 (let ((a!11 (trans (sk (~ (not a!5) a!7)) a!10 (~ (not a!5) (and (cc X!3) a!9))))
% 0.20/0.40 (a!17 (trans (sk (~ (not a!12) a!14))
% 0.20/0.40 a!16
% 0.20/0.40 (~ (not a!12) (and (cc X!4) (not a!15))))))
% 0.20/0.40 (nnf-neg (sk (~ (not a!1) a!2)) a!4 a!11 a!17 a!18)))))
% 0.20/0.40 Proof display could not be completed: unexpected number of arguments
% 0.20/0.40 % E exiting
%------------------------------------------------------------------------------