%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS144+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 0.12s 0.38s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : KRS144+1 : TPTP v9.0.0. Released v3.1.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n002.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 19:13:16 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(xsd_string_type, type, (
% 0.12/0.38 xsd_string: $i > $o)).
% 0.12/0.38 tff(tptp_fun_X_3_type, type, (
% 0.12/0.38 tptp_fun_X_3: $i)).
% 0.12/0.38 tff(xsd_integer_type, type, (
% 0.12/0.38 xsd_integer: $i > $o)).
% 0.12/0.38 tff(rp_type, type, (
% 0.12/0.38 rp: ( $i * $i ) > $o)).
% 0.12/0.38 tff(tptp_fun_X_8_type, type, (
% 0.12/0.38 tptp_fun_X_8: $i)).
% 0.12/0.38 tff(cc_type, type, (
% 0.12/0.38 cc: $i > $o)).
% 0.12/0.38 tff(tptp_fun_Y0_1_type, type, (
% 0.12/0.38 tptp_fun_Y0_1: $i > $i)).
% 0.12/0.38 tff(tptp_fun_Y1_0_type, type, (
% 0.12/0.38 tptp_fun_Y1_0: $i > $i)).
% 0.12/0.38 tff(cowlThing_type, type, (
% 0.12/0.38 cowlThing: $i > $o)).
% 0.12/0.38 tff(tptp_fun_X_2_type, type, (
% 0.12/0.38 tptp_fun_X_2: $i)).
% 0.12/0.38 tff(cowlNothing_type, type, (
% 0.12/0.38 cowlNothing: $i > $o)).
% 0.12/0.38 tff(tptp_fun_X_4_type, type, (
% 0.12/0.38 tptp_fun_X_4: $i)).
% 0.12/0.38 tff(tptp_fun_Y2_5_type, type, (
% 0.12/0.38 tptp_fun_Y2_5: $i)).
% 0.12/0.38 tff(tptp_fun_Y0_7_type, type, (
% 0.12/0.38 tptp_fun_Y0_7: $i)).
% 0.12/0.38 tff(tptp_fun_Y1_6_type, type, (
% 0.12/0.38 tptp_fun_Y1_6: $i)).
% 0.12/0.38 tff(1,assumption,(~((~cc(X!8)) | (~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!8, Y0)) | (~rp(X!8, Y1)))))), introduced(assumption)).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 (((~cc(X!8)) | (~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!8, Y0)) | (~rp(X!8, Y1))))) | cc(X!8)),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (cc(X!8)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 (^[X: $i] : rewrite(((~cc(X)) | (~((~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X, Y0)) | (~rp(X, Y1)) | (~rp(X, Y2)))) | (~rp(X, tptp_fun_Y0_1(X))) | (~rp(X, tptp_fun_Y1_0(X))) | (tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X))))) <=> ((~cc(X)) | (~((~rp(X, tptp_fun_Y0_1(X))) | (~rp(X, tptp_fun_Y1_0(X))) | (tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X, Y0)) | (~rp(X, Y1)) | (~rp(X, Y2))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (![X: $i] : ((~cc(X)) | (~((~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X, Y0)) | (~rp(X, Y1)) | (~rp(X, Y2)))) | (~rp(X, tptp_fun_Y0_1(X))) | (~rp(X, tptp_fun_Y1_0(X))) | (tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X))))) <=> ![X: $i] : ((~cc(X)) | (~((~rp(X, tptp_fun_Y0_1(X))) | (~rp(X, tptp_fun_Y1_0(X))) | (tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X, Y0)) | (~rp(X, Y1)) | (~rp(X, Y2)))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[4])).
% 0.12/0.38 tff(6,plain,
% 0.12/0.38 (^[X: $i] : refl(((~cc(X)) | (~((~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X, Y0)) | (~rp(X, Y1)) | (~rp(X, Y2)))) | (~rp(X, tptp_fun_Y0_1(X))) | (~rp(X, tptp_fun_Y1_0(X))) | (tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X))))) <=> ((~cc(X)) | (~((~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X, Y0)) | (~rp(X, Y1)) | (~rp(X, Y2)))) | (~rp(X, tptp_fun_Y0_1(X))) | (~rp(X, tptp_fun_Y1_0(X))) | (tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 (![X: $i] : ((~cc(X)) | (~((~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X, Y0)) | (~rp(X, Y1)) | (~rp(X, Y2)))) | (~rp(X, tptp_fun_Y0_1(X))) | (~rp(X, tptp_fun_Y1_0(X))) | (tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X))))) <=> ![X: $i] : ((~cc(X)) | (~((~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X, Y0)) | (~rp(X, Y1)) | (~rp(X, Y2)))) | (~rp(X, tptp_fun_Y0_1(X))) | (~rp(X, tptp_fun_Y1_0(X))) | (tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X)))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[6])).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 (^[X: $i] : rewrite(((~cc(X)) | (~((~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X, Y0)) | (~rp(X, Y1)) | (~rp(X, Y2)))) | (~rp(X, tptp_fun_Y0_1(X))) | (~rp(X, tptp_fun_Y1_0(X))) | (tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X))))) <=> ((~cc(X)) | (~((~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X, Y0)) | (~rp(X, Y1)) | (~rp(X, Y2)))) | (~rp(X, tptp_fun_Y0_1(X))) | (~rp(X, tptp_fun_Y1_0(X))) | (tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (![X: $i] : ((~cc(X)) | (~((~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X, Y0)) | (~rp(X, Y1)) | (~rp(X, Y2)))) | (~rp(X, tptp_fun_Y0_1(X))) | (~rp(X, tptp_fun_Y1_0(X))) | (tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X))))) <=> ![X: $i] : ((~cc(X)) | (~((~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X, Y0)) | (~rp(X, Y1)) | (~rp(X, Y2)))) | (~rp(X, tptp_fun_Y0_1(X))) | (~rp(X, tptp_fun_Y1_0(X))) | (tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X)))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[8])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 (![X: $i] : ((~cc(X)) | (~((~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X, Y0)) | (~rp(X, Y1)) | (~rp(X, Y2)))) | (~rp(X, tptp_fun_Y0_1(X))) | (~rp(X, tptp_fun_Y1_0(X))) | (tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X))))) <=> ![X: $i] : ((~cc(X)) | (~((~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X, Y0)) | (~rp(X, Y1)) | (~rp(X, Y2)))) | (~rp(X, tptp_fun_Y0_1(X))) | (~rp(X, tptp_fun_Y1_0(X))) | (tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X)))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[9, 7])).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 (^[X: $i] : rewrite(((~cc(X)) | (rp(X, tptp_fun_Y0_1(X)) & rp(X, tptp_fun_Y1_0(X)) & (~(tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X))) & ![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~(rp(X, Y0) & rp(X, Y1) & rp(X, Y2)))))) <=> ((~cc(X)) | (~((~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X, Y0)) | (~rp(X, Y1)) | (~rp(X, Y2)))) | (~rp(X, tptp_fun_Y0_1(X))) | (~rp(X, tptp_fun_Y1_0(X))) | (tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 (![X: $i] : ((~cc(X)) | (rp(X, tptp_fun_Y0_1(X)) & rp(X, tptp_fun_Y1_0(X)) & (~(tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X))) & ![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~(rp(X, Y0) & rp(X, Y1) & rp(X, Y2)))))) <=> ![X: $i] : ((~cc(X)) | (~((~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X, Y0)) | (~rp(X, Y1)) | (~rp(X, Y2)))) | (~rp(X, tptp_fun_Y0_1(X))) | (~rp(X, tptp_fun_Y1_0(X))) | (tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X)))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[11])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (^[X: $i] : rewrite(((~cc(X)) | ((rp(X, tptp_fun_Y0_1(X)) & rp(X, tptp_fun_Y1_0(X)) & (~(tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X)))) & ![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~(rp(X, Y0) & rp(X, Y1) & rp(X, Y2)))))) <=> ((~cc(X)) | (rp(X, tptp_fun_Y0_1(X)) & rp(X, tptp_fun_Y1_0(X)) & (~(tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X))) & ![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~(rp(X, Y0) & rp(X, Y1) & rp(X, Y2)))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 (![X: $i] : ((~cc(X)) | ((rp(X, tptp_fun_Y0_1(X)) & rp(X, tptp_fun_Y1_0(X)) & (~(tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X)))) & ![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~(rp(X, Y0) & rp(X, Y1) & rp(X, Y2)))))) <=> ![X: $i] : ((~cc(X)) | (rp(X, tptp_fun_Y0_1(X)) & rp(X, tptp_fun_Y1_0(X)) & (~(tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X))) & ![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~(rp(X, Y0) & rp(X, Y1) & rp(X, Y2))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[13])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (![X: $i] : ((~cc(X)) | (?[Y0: $i, Y1: $i] : (rp(X, Y0) & rp(X, Y1) & (~(Y0 = Y1))) & ![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~(rp(X, Y0) & rp(X, Y1) & rp(X, Y2)))))) <=> ![X: $i] : ((~cc(X)) | (?[Y0: $i, Y1: $i] : (rp(X, Y0) & rp(X, Y1) & (~(Y0 = Y1))) & ![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~(rp(X, Y0) & rp(X, Y1) & rp(X, Y2))))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 (^[X: $i] : trans(monotonicity(rewrite((?[Y0: $i, Y1: $i] : ((rp(X, Y0) & rp(X, Y1)) & (~(Y0 = Y1))) & ![Y0: $i, Y1: $i, Y2: $i] : (((rp(X, Y0) & rp(X, Y1)) & rp(X, Y2)) => (((Y0 = Y1) | (Y0 = Y2)) | (Y1 = Y2)))) <=> (?[Y0: $i, Y1: $i] : (rp(X, Y0) & rp(X, Y1) & (~(Y0 = Y1))) & ![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~(rp(X, Y0) & rp(X, Y1) & rp(X, Y2)))))), ((cc(X) => (?[Y0: $i, Y1: $i] : ((rp(X, Y0) & rp(X, Y1)) & (~(Y0 = Y1))) & ![Y0: $i, Y1: $i, Y2: $i] : (((rp(X, Y0) & rp(X, Y1)) & rp(X, Y2)) => (((Y0 = Y1) | (Y0 = Y2)) | (Y1 = Y2))))) <=> (cc(X) => (?[Y0: $i, Y1: $i] : (rp(X, Y0) & rp(X, Y1) & (~(Y0 = Y1))) & ![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~(rp(X, Y0) & rp(X, Y1) & rp(X, Y2)))))))), rewrite((cc(X) => (?[Y0: $i, Y1: $i] : (rp(X, Y0) & rp(X, Y1) & (~(Y0 = Y1))) & ![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~(rp(X, Y0) & rp(X, Y1) & rp(X, Y2)))))) <=> ((~cc(X)) | (?[Y0: $i, Y1: $i] : (rp(X, Y0) & rp(X, Y1) & (~(Y0 = Y1))) & ![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~(rp(X, Y0) & rp(X, Y1) & rp(X, Y2))))))), ((cc(X) => (?[Y0: $i, Y1: $i] : ((rp(X, Y0) & rp(X, Y1)) & (~(Y0 = Y1))) & ![Y0: $i, Y1: $i, Y2: $i] : (((rp(X, Y0) & rp(X, Y1)) & rp(X, Y2)) => (((Y0 = Y1) | (Y0 = Y2)) | (Y1 = Y2))))) <=> ((~cc(X)) | (?[Y0: $i, Y1: $i] : (rp(X, Y0) & rp(X, Y1) & (~(Y0 = Y1))) & ![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~(rp(X, Y0) & rp(X, Y1) & rp(X, Y2))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 (![X: $i] : (cc(X) => (?[Y0: $i, Y1: $i] : ((rp(X, Y0) & rp(X, Y1)) & (~(Y0 = Y1))) & ![Y0: $i, Y1: $i, Y2: $i] : (((rp(X, Y0) & rp(X, Y1)) & rp(X, Y2)) => (((Y0 = Y1) | (Y0 = Y2)) | (Y1 = Y2))))) <=> ![X: $i] : ((~cc(X)) | (?[Y0: $i, Y1: $i] : (rp(X, Y0) & rp(X, Y1) & (~(Y0 = Y1))) & ![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~(rp(X, Y0) & rp(X, Y1) & rp(X, Y2))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[16])).
% 0.12/0.38 tff(18,axiom,(![X: $i] : (cc(X) => (?[Y0: $i, Y1: $i] : ((rp(X, Y0) & rp(X, Y1)) & (~(Y0 = Y1))) & ![Y0: $i, Y1: $i, Y2: $i] : (((rp(X, Y0) & rp(X, Y1)) & rp(X, Y2)) => (((Y0 = Y1) | (Y0 = Y2)) | (Y1 = Y2)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_2')).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (![X: $i] : ((~cc(X)) | (?[Y0: $i, Y1: $i] : (rp(X, Y0) & rp(X, Y1) & (~(Y0 = Y1))) & ![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~(rp(X, Y0) & rp(X, Y1) & rp(X, Y2))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 (![X: $i] : ((~cc(X)) | (?[Y0: $i, Y1: $i] : (rp(X, Y0) & rp(X, Y1) & (~(Y0 = Y1))) & ![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~(rp(X, Y0) & rp(X, Y1) & rp(X, Y2))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.12/0.38 tff(21,plain,(
% 0.12/0.38 ![X: $i] : ((~cc(X)) | ((rp(X, tptp_fun_Y0_1(X)) & rp(X, tptp_fun_Y1_0(X)) & (~(tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X)))) & ![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~(rp(X, Y0) & rp(X, Y1) & rp(X, Y2))))))),
% 0.12/0.38 inference(skolemize,[status(sab)],[20])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 (![X: $i] : ((~cc(X)) | (rp(X, tptp_fun_Y0_1(X)) & rp(X, tptp_fun_Y1_0(X)) & (~(tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X))) & ![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~(rp(X, Y0) & rp(X, Y1) & rp(X, Y2))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 (![X: $i] : ((~cc(X)) | (~((~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X, Y0)) | (~rp(X, Y1)) | (~rp(X, Y2)))) | (~rp(X, tptp_fun_Y0_1(X))) | (~rp(X, tptp_fun_Y1_0(X))) | (tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X)))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[22, 12])).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 (![X: $i] : ((~cc(X)) | (~((~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X, Y0)) | (~rp(X, Y1)) | (~rp(X, Y2)))) | (~rp(X, tptp_fun_Y0_1(X))) | (~rp(X, tptp_fun_Y1_0(X))) | (tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X)))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[23, 10])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 (![X: $i] : ((~cc(X)) | (~((~rp(X, tptp_fun_Y0_1(X))) | (~rp(X, tptp_fun_Y1_0(X))) | (tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X, Y0)) | (~rp(X, Y1)) | (~rp(X, Y2)))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[24, 5])).
% 0.12/0.38 tff(26,plain,
% 0.12/0.38 (((~![X: $i] : ((~cc(X)) | (~((~rp(X, tptp_fun_Y0_1(X))) | (~rp(X, tptp_fun_Y1_0(X))) | (tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X, Y0)) | (~rp(X, Y1)) | (~rp(X, Y2)))))))) | ((~cc(X!8)) | (~((tptp_fun_Y0_1(X!8) = tptp_fun_Y1_0(X!8)) | (~rp(X!8, tptp_fun_Y1_0(X!8))) | (~rp(X!8, tptp_fun_Y0_1(X!8))) | (~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X!8, Y1)) | (~rp(X!8, Y2)) | (~rp(X!8, Y0)))))))) <=> ((~![X: $i] : ((~cc(X)) | (~((~rp(X, tptp_fun_Y0_1(X))) | (~rp(X, tptp_fun_Y1_0(X))) | (tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X, Y0)) | (~rp(X, Y1)) | (~rp(X, Y2)))))))) | (~cc(X!8)) | (~((tptp_fun_Y0_1(X!8) = tptp_fun_Y1_0(X!8)) | (~rp(X!8, tptp_fun_Y1_0(X!8))) | (~rp(X!8, tptp_fun_Y0_1(X!8))) | (~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X!8, Y1)) | (~rp(X!8, Y2)) | (~rp(X!8, Y0)))))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(27,plain,
% 0.12/0.39 (((~cc(X!8)) | (~((~rp(X!8, tptp_fun_Y0_1(X!8))) | (~rp(X!8, tptp_fun_Y1_0(X!8))) | (tptp_fun_Y0_1(X!8) = tptp_fun_Y1_0(X!8)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X!8, Y0)) | (~rp(X!8, Y1)) | (~rp(X!8, Y2))))))) <=> ((~cc(X!8)) | (~((tptp_fun_Y0_1(X!8) = tptp_fun_Y1_0(X!8)) | (~rp(X!8, tptp_fun_Y1_0(X!8))) | (~rp(X!8, tptp_fun_Y0_1(X!8))) | (~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X!8, Y1)) | (~rp(X!8, Y2)) | (~rp(X!8, Y0)))))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(28,plain,
% 0.12/0.39 (((~![X: $i] : ((~cc(X)) | (~((~rp(X, tptp_fun_Y0_1(X))) | (~rp(X, tptp_fun_Y1_0(X))) | (tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X, Y0)) | (~rp(X, Y1)) | (~rp(X, Y2)))))))) | ((~cc(X!8)) | (~((~rp(X!8, tptp_fun_Y0_1(X!8))) | (~rp(X!8, tptp_fun_Y1_0(X!8))) | (tptp_fun_Y0_1(X!8) = tptp_fun_Y1_0(X!8)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X!8, Y0)) | (~rp(X!8, Y1)) | (~rp(X!8, Y2)))))))) <=> ((~![X: $i] : ((~cc(X)) | (~((~rp(X, tptp_fun_Y0_1(X))) | (~rp(X, tptp_fun_Y1_0(X))) | (tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X, Y0)) | (~rp(X, Y1)) | (~rp(X, Y2)))))))) | ((~cc(X!8)) | (~((tptp_fun_Y0_1(X!8) = tptp_fun_Y1_0(X!8)) | (~rp(X!8, tptp_fun_Y1_0(X!8))) | (~rp(X!8, tptp_fun_Y0_1(X!8))) | (~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X!8, Y1)) | (~rp(X!8, Y2)) | (~rp(X!8, Y0))))))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[27])).
% 0.12/0.39 tff(29,plain,
% 0.12/0.39 (((~![X: $i] : ((~cc(X)) | (~((~rp(X, tptp_fun_Y0_1(X))) | (~rp(X, tptp_fun_Y1_0(X))) | (tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X, Y0)) | (~rp(X, Y1)) | (~rp(X, Y2)))))))) | ((~cc(X!8)) | (~((~rp(X!8, tptp_fun_Y0_1(X!8))) | (~rp(X!8, tptp_fun_Y1_0(X!8))) | (tptp_fun_Y0_1(X!8) = tptp_fun_Y1_0(X!8)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X!8, Y0)) | (~rp(X!8, Y1)) | (~rp(X!8, Y2)))))))) <=> ((~![X: $i] : ((~cc(X)) | (~((~rp(X, tptp_fun_Y0_1(X))) | (~rp(X, tptp_fun_Y1_0(X))) | (tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X, Y0)) | (~rp(X, Y1)) | (~rp(X, Y2)))))))) | (~cc(X!8)) | (~((tptp_fun_Y0_1(X!8) = tptp_fun_Y1_0(X!8)) | (~rp(X!8, tptp_fun_Y1_0(X!8))) | (~rp(X!8, tptp_fun_Y0_1(X!8))) | (~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X!8, Y1)) | (~rp(X!8, Y2)) | (~rp(X!8, Y0)))))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[28, 26])).
% 0.12/0.39 tff(30,plain,
% 0.12/0.39 ((~![X: $i] : ((~cc(X)) | (~((~rp(X, tptp_fun_Y0_1(X))) | (~rp(X, tptp_fun_Y1_0(X))) | (tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X, Y0)) | (~rp(X, Y1)) | (~rp(X, Y2)))))))) | ((~cc(X!8)) | (~((~rp(X!8, tptp_fun_Y0_1(X!8))) | (~rp(X!8, tptp_fun_Y1_0(X!8))) | (tptp_fun_Y0_1(X!8) = tptp_fun_Y1_0(X!8)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X!8, Y0)) | (~rp(X!8, Y1)) | (~rp(X!8, Y2)))))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(31,plain,
% 0.12/0.39 ((~![X: $i] : ((~cc(X)) | (~((~rp(X, tptp_fun_Y0_1(X))) | (~rp(X, tptp_fun_Y1_0(X))) | (tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X, Y0)) | (~rp(X, Y1)) | (~rp(X, Y2)))))))) | (~cc(X!8)) | (~((tptp_fun_Y0_1(X!8) = tptp_fun_Y1_0(X!8)) | (~rp(X!8, tptp_fun_Y1_0(X!8))) | (~rp(X!8, tptp_fun_Y0_1(X!8))) | (~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X!8, Y1)) | (~rp(X!8, Y2)) | (~rp(X!8, Y0))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.12/0.39 tff(32,plain,
% 0.12/0.39 (~((tptp_fun_Y0_1(X!8) = tptp_fun_Y1_0(X!8)) | (~rp(X!8, tptp_fun_Y1_0(X!8))) | (~rp(X!8, tptp_fun_Y0_1(X!8))) | (~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X!8, Y1)) | (~rp(X!8, Y2)) | (~rp(X!8, Y0)))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[31, 25, 3])).
% 0.12/0.39 tff(33,plain,
% 0.12/0.39 (((tptp_fun_Y0_1(X!8) = tptp_fun_Y1_0(X!8)) | (~rp(X!8, tptp_fun_Y1_0(X!8))) | (~rp(X!8, tptp_fun_Y0_1(X!8))) | (~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X!8, Y1)) | (~rp(X!8, Y2)) | (~rp(X!8, Y0))))) | rp(X!8, tptp_fun_Y0_1(X!8))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(34,plain,
% 0.12/0.39 (rp(X!8, tptp_fun_Y0_1(X!8))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.12/0.39 tff(35,plain,
% 0.12/0.39 (((tptp_fun_Y0_1(X!8) = tptp_fun_Y1_0(X!8)) | (~rp(X!8, tptp_fun_Y1_0(X!8))) | (~rp(X!8, tptp_fun_Y0_1(X!8))) | (~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X!8, Y1)) | (~rp(X!8, Y2)) | (~rp(X!8, Y0))))) | rp(X!8, tptp_fun_Y1_0(X!8))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(36,plain,
% 0.12/0.39 (rp(X!8, tptp_fun_Y1_0(X!8))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[35, 32])).
% 0.12/0.39 tff(37,plain,
% 0.12/0.39 (((tptp_fun_Y0_1(X!8) = tptp_fun_Y1_0(X!8)) | (~rp(X!8, tptp_fun_Y1_0(X!8))) | (~rp(X!8, tptp_fun_Y0_1(X!8))) | (~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X!8, Y1)) | (~rp(X!8, Y2)) | (~rp(X!8, Y0))))) | (~(tptp_fun_Y0_1(X!8) = tptp_fun_Y1_0(X!8)))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(38,plain,
% 0.12/0.39 (~(tptp_fun_Y0_1(X!8) = tptp_fun_Y1_0(X!8))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[37, 32])).
% 0.12/0.39 tff(39,plain,
% 0.12/0.39 (((~cc(X!8)) | (~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!8, Y0)) | (~rp(X!8, Y1))))) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!8, Y0)) | (~rp(X!8, Y1)))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(40,plain,
% 0.12/0.39 (![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!8, Y0)) | (~rp(X!8, Y1)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[39, 1])).
% 0.12/0.39 tff(41,plain,
% 0.12/0.39 (((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!8, Y0)) | (~rp(X!8, Y1)))) | ((tptp_fun_Y0_1(X!8) = tptp_fun_Y1_0(X!8)) | (~rp(X!8, tptp_fun_Y1_0(X!8))) | (~rp(X!8, tptp_fun_Y0_1(X!8))))) <=> ((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!8, Y0)) | (~rp(X!8, Y1)))) | (tptp_fun_Y0_1(X!8) = tptp_fun_Y1_0(X!8)) | (~rp(X!8, tptp_fun_Y1_0(X!8))) | (~rp(X!8, tptp_fun_Y0_1(X!8))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(42,plain,
% 0.12/0.39 (((tptp_fun_Y0_1(X!8) = tptp_fun_Y1_0(X!8)) | (~rp(X!8, tptp_fun_Y0_1(X!8))) | (~rp(X!8, tptp_fun_Y1_0(X!8)))) <=> ((tptp_fun_Y0_1(X!8) = tptp_fun_Y1_0(X!8)) | (~rp(X!8, tptp_fun_Y1_0(X!8))) | (~rp(X!8, tptp_fun_Y0_1(X!8))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(43,plain,
% 0.12/0.39 (((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!8, Y0)) | (~rp(X!8, Y1)))) | ((tptp_fun_Y0_1(X!8) = tptp_fun_Y1_0(X!8)) | (~rp(X!8, tptp_fun_Y0_1(X!8))) | (~rp(X!8, tptp_fun_Y1_0(X!8))))) <=> ((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!8, Y0)) | (~rp(X!8, Y1)))) | ((tptp_fun_Y0_1(X!8) = tptp_fun_Y1_0(X!8)) | (~rp(X!8, tptp_fun_Y1_0(X!8))) | (~rp(X!8, tptp_fun_Y0_1(X!8)))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[42])).
% 0.12/0.39 tff(44,plain,
% 0.12/0.39 (((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!8, Y0)) | (~rp(X!8, Y1)))) | ((tptp_fun_Y0_1(X!8) = tptp_fun_Y1_0(X!8)) | (~rp(X!8, tptp_fun_Y0_1(X!8))) | (~rp(X!8, tptp_fun_Y1_0(X!8))))) <=> ((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!8, Y0)) | (~rp(X!8, Y1)))) | (tptp_fun_Y0_1(X!8) = tptp_fun_Y1_0(X!8)) | (~rp(X!8, tptp_fun_Y1_0(X!8))) | (~rp(X!8, tptp_fun_Y0_1(X!8))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[43, 41])).
% 0.12/0.39 tff(45,plain,
% 0.12/0.39 ((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!8, Y0)) | (~rp(X!8, Y1)))) | ((tptp_fun_Y0_1(X!8) = tptp_fun_Y1_0(X!8)) | (~rp(X!8, tptp_fun_Y0_1(X!8))) | (~rp(X!8, tptp_fun_Y1_0(X!8))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(46,plain,
% 0.12/0.39 ((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!8, Y0)) | (~rp(X!8, Y1)))) | (tptp_fun_Y0_1(X!8) = tptp_fun_Y1_0(X!8)) | (~rp(X!8, tptp_fun_Y1_0(X!8))) | (~rp(X!8, tptp_fun_Y0_1(X!8)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.12/0.39 tff(47,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[46, 40, 38, 36, 34])).
% 0.12/0.39 tff(48,plain,((~cc(X!8)) | (~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!8, Y0)) | (~rp(X!8, Y1))))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.39 tff(49,assumption,(cowlNothing(X!2) | (~cowlThing(X!2))), introduced(assumption)).
% 0.12/0.39 tff(50,plain,
% 0.12/0.39 (^[X: $i] : refl((~(cowlNothing(X) | (~cowlThing(X)))) <=> (~(cowlNothing(X) | (~cowlThing(X)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(51,plain,
% 0.12/0.39 (![X: $i] : (~(cowlNothing(X) | (~cowlThing(X)))) <=> ![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[50])).
% 0.12/0.39 tff(52,plain,
% 0.12/0.39 (^[X: $i] : rewrite((cowlThing(X) & (~cowlNothing(X))) <=> (~(cowlNothing(X) | (~cowlThing(X)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(53,plain,
% 0.12/0.39 (![X: $i] : (cowlThing(X) & (~cowlNothing(X))) <=> ![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[52])).
% 0.12/0.39 tff(54,plain,
% 0.12/0.39 (![X: $i] : (cowlThing(X) & (~cowlNothing(X))) <=> ![X: $i] : (cowlThing(X) & (~cowlNothing(X)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(55,axiom,(![X: $i] : (cowlThing(X) & (~cowlNothing(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_0')).
% 0.12/0.39 tff(56,plain,
% 0.12/0.39 (![X: $i] : (cowlThing(X) & (~cowlNothing(X)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.12/0.39 tff(57,plain,(
% 0.12/0.39 ![X: $i] : (cowlThing(X) & (~cowlNothing(X)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[56])).
% 0.12/0.39 tff(58,plain,
% 0.12/0.39 (![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.12/0.39 tff(59,plain,
% 0.12/0.39 (![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.12/0.39 tff(60,plain,
% 0.12/0.39 ((~![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))) | (~(cowlNothing(X!2) | (~cowlThing(X!2))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(61,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[60, 59, 49])).
% 0.12/0.39 tff(62,plain,(~(cowlNothing(X!2) | (~cowlThing(X!2)))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.39 tff(63,plain,
% 0.12/0.39 ((cowlNothing(X!2) | (~cowlThing(X!2))) | cowlThing(X!2)),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(64,plain,
% 0.12/0.39 (cowlThing(X!2)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.12/0.39 tff(65,plain,
% 0.12/0.39 ((cowlNothing(X!2) | (~cowlThing(X!2))) | (~cowlNothing(X!2))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(66,plain,
% 0.12/0.39 (~cowlNothing(X!2)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[65, 62])).
% 0.12/0.39 tff(67,assumption,(~((~rp(X!4, Y0!7)) | (~rp(X!4, Y1!6)) | (~rp(X!4, Y2!5)) | (Y1!6 = Y2!5) | (Y0!7 = Y1!6) | (Y0!7 = Y2!5) | (~cc(X!4)))), introduced(assumption)).
% 0.12/0.39 tff(68,plain,
% 0.12/0.39 (((~rp(X!4, Y0!7)) | (~rp(X!4, Y1!6)) | (~rp(X!4, Y2!5)) | (Y1!6 = Y2!5) | (Y0!7 = Y1!6) | (Y0!7 = Y2!5) | (~cc(X!4))) | cc(X!4)),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(69,plain,
% 0.12/0.39 (cc(X!4)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.12/0.39 tff(70,plain,
% 0.12/0.39 (((~![X: $i] : ((~cc(X)) | (~((~rp(X, tptp_fun_Y0_1(X))) | (~rp(X, tptp_fun_Y1_0(X))) | (tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X, Y0)) | (~rp(X, Y1)) | (~rp(X, Y2)))))))) | ((~cc(X!4)) | (~((~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X!4, Y0)) | (~rp(X!4, Y1)) | (~rp(X!4, Y2)))) | (tptp_fun_Y0_1(X!4) = tptp_fun_Y1_0(X!4)) | (~rp(X!4, tptp_fun_Y1_0(X!4))) | (~rp(X!4, tptp_fun_Y0_1(X!4))))))) <=> ((~![X: $i] : ((~cc(X)) | (~((~rp(X, tptp_fun_Y0_1(X))) | (~rp(X, tptp_fun_Y1_0(X))) | (tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X, Y0)) | (~rp(X, Y1)) | (~rp(X, Y2)))))))) | (~cc(X!4)) | (~((~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X!4, Y0)) | (~rp(X!4, Y1)) | (~rp(X!4, Y2)))) | (tptp_fun_Y0_1(X!4) = tptp_fun_Y1_0(X!4)) | (~rp(X!4, tptp_fun_Y1_0(X!4))) | (~rp(X!4, tptp_fun_Y0_1(X!4))))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(71,plain,
% 0.12/0.40 (((~cc(X!4)) | (~((~rp(X!4, tptp_fun_Y0_1(X!4))) | (~rp(X!4, tptp_fun_Y1_0(X!4))) | (tptp_fun_Y0_1(X!4) = tptp_fun_Y1_0(X!4)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X!4, Y0)) | (~rp(X!4, Y1)) | (~rp(X!4, Y2))))))) <=> ((~cc(X!4)) | (~((~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X!4, Y0)) | (~rp(X!4, Y1)) | (~rp(X!4, Y2)))) | (tptp_fun_Y0_1(X!4) = tptp_fun_Y1_0(X!4)) | (~rp(X!4, tptp_fun_Y1_0(X!4))) | (~rp(X!4, tptp_fun_Y0_1(X!4))))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(72,plain,
% 0.12/0.40 (((~![X: $i] : ((~cc(X)) | (~((~rp(X, tptp_fun_Y0_1(X))) | (~rp(X, tptp_fun_Y1_0(X))) | (tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X, Y0)) | (~rp(X, Y1)) | (~rp(X, Y2)))))))) | ((~cc(X!4)) | (~((~rp(X!4, tptp_fun_Y0_1(X!4))) | (~rp(X!4, tptp_fun_Y1_0(X!4))) | (tptp_fun_Y0_1(X!4) = tptp_fun_Y1_0(X!4)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X!4, Y0)) | (~rp(X!4, Y1)) | (~rp(X!4, Y2)))))))) <=> ((~![X: $i] : ((~cc(X)) | (~((~rp(X, tptp_fun_Y0_1(X))) | (~rp(X, tptp_fun_Y1_0(X))) | (tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X, Y0)) | (~rp(X, Y1)) | (~rp(X, Y2)))))))) | ((~cc(X!4)) | (~((~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X!4, Y0)) | (~rp(X!4, Y1)) | (~rp(X!4, Y2)))) | (tptp_fun_Y0_1(X!4) = tptp_fun_Y1_0(X!4)) | (~rp(X!4, tptp_fun_Y1_0(X!4))) | (~rp(X!4, tptp_fun_Y0_1(X!4)))))))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[71])).
% 0.12/0.40 tff(73,plain,
% 0.12/0.40 (((~![X: $i] : ((~cc(X)) | (~((~rp(X, tptp_fun_Y0_1(X))) | (~rp(X, tptp_fun_Y1_0(X))) | (tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X, Y0)) | (~rp(X, Y1)) | (~rp(X, Y2)))))))) | ((~cc(X!4)) | (~((~rp(X!4, tptp_fun_Y0_1(X!4))) | (~rp(X!4, tptp_fun_Y1_0(X!4))) | (tptp_fun_Y0_1(X!4) = tptp_fun_Y1_0(X!4)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X!4, Y0)) | (~rp(X!4, Y1)) | (~rp(X!4, Y2)))))))) <=> ((~![X: $i] : ((~cc(X)) | (~((~rp(X, tptp_fun_Y0_1(X))) | (~rp(X, tptp_fun_Y1_0(X))) | (tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X, Y0)) | (~rp(X, Y1)) | (~rp(X, Y2)))))))) | (~cc(X!4)) | (~((~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X!4, Y0)) | (~rp(X!4, Y1)) | (~rp(X!4, Y2)))) | (tptp_fun_Y0_1(X!4) = tptp_fun_Y1_0(X!4)) | (~rp(X!4, tptp_fun_Y1_0(X!4))) | (~rp(X!4, tptp_fun_Y0_1(X!4))))))),
% 0.12/0.40 inference(transitivity,[status(thm)],[72, 70])).
% 0.12/0.40 tff(74,plain,
% 0.12/0.40 ((~![X: $i] : ((~cc(X)) | (~((~rp(X, tptp_fun_Y0_1(X))) | (~rp(X, tptp_fun_Y1_0(X))) | (tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X, Y0)) | (~rp(X, Y1)) | (~rp(X, Y2)))))))) | ((~cc(X!4)) | (~((~rp(X!4, tptp_fun_Y0_1(X!4))) | (~rp(X!4, tptp_fun_Y1_0(X!4))) | (tptp_fun_Y0_1(X!4) = tptp_fun_Y1_0(X!4)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X!4, Y0)) | (~rp(X!4, Y1)) | (~rp(X!4, Y2)))))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(75,plain,
% 0.12/0.40 ((~![X: $i] : ((~cc(X)) | (~((~rp(X, tptp_fun_Y0_1(X))) | (~rp(X, tptp_fun_Y1_0(X))) | (tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X)) | (~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X, Y0)) | (~rp(X, Y1)) | (~rp(X, Y2)))))))) | (~cc(X!4)) | (~((~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X!4, Y0)) | (~rp(X!4, Y1)) | (~rp(X!4, Y2)))) | (tptp_fun_Y0_1(X!4) = tptp_fun_Y1_0(X!4)) | (~rp(X!4, tptp_fun_Y1_0(X!4))) | (~rp(X!4, tptp_fun_Y0_1(X!4)))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.12/0.40 tff(76,plain,
% 0.12/0.40 (~((~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X!4, Y0)) | (~rp(X!4, Y1)) | (~rp(X!4, Y2)))) | (tptp_fun_Y0_1(X!4) = tptp_fun_Y1_0(X!4)) | (~rp(X!4, tptp_fun_Y1_0(X!4))) | (~rp(X!4, tptp_fun_Y0_1(X!4))))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[75, 25, 69])).
% 0.12/0.40 tff(77,plain,
% 0.12/0.40 (((~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X!4, Y0)) | (~rp(X!4, Y1)) | (~rp(X!4, Y2)))) | (tptp_fun_Y0_1(X!4) = tptp_fun_Y1_0(X!4)) | (~rp(X!4, tptp_fun_Y1_0(X!4))) | (~rp(X!4, tptp_fun_Y0_1(X!4)))) | ![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X!4, Y0)) | (~rp(X!4, Y1)) | (~rp(X!4, Y2)))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(78,plain,
% 0.12/0.40 (![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X!4, Y0)) | (~rp(X!4, Y1)) | (~rp(X!4, Y2)))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.12/0.40 tff(79,plain,
% 0.12/0.40 (((~rp(X!4, Y0!7)) | (~rp(X!4, Y1!6)) | (~rp(X!4, Y2!5)) | (Y1!6 = Y2!5) | (Y0!7 = Y1!6) | (Y0!7 = Y2!5) | (~cc(X!4))) | (~(Y0!7 = Y2!5))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(80,plain,
% 0.12/0.40 (~(Y0!7 = Y2!5)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[79, 67])).
% 0.12/0.40 tff(81,plain,
% 0.12/0.40 (((~rp(X!4, Y0!7)) | (~rp(X!4, Y1!6)) | (~rp(X!4, Y2!5)) | (Y1!6 = Y2!5) | (Y0!7 = Y1!6) | (Y0!7 = Y2!5) | (~cc(X!4))) | (~(Y0!7 = Y1!6))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(82,plain,
% 0.12/0.40 (~(Y0!7 = Y1!6)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[81, 67])).
% 0.12/0.40 tff(83,plain,
% 0.12/0.40 (((~rp(X!4, Y0!7)) | (~rp(X!4, Y1!6)) | (~rp(X!4, Y2!5)) | (Y1!6 = Y2!5) | (Y0!7 = Y1!6) | (Y0!7 = Y2!5) | (~cc(X!4))) | (~(Y1!6 = Y2!5))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(84,plain,
% 0.12/0.40 (~(Y1!6 = Y2!5)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[83, 67])).
% 0.12/0.40 tff(85,plain,
% 0.12/0.40 (((~rp(X!4, Y0!7)) | (~rp(X!4, Y1!6)) | (~rp(X!4, Y2!5)) | (Y1!6 = Y2!5) | (Y0!7 = Y1!6) | (Y0!7 = Y2!5) | (~cc(X!4))) | rp(X!4, Y2!5)),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(86,plain,
% 0.12/0.40 (rp(X!4, Y2!5)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[85, 67])).
% 0.12/0.40 tff(87,plain,
% 0.12/0.40 (((~rp(X!4, Y0!7)) | (~rp(X!4, Y1!6)) | (~rp(X!4, Y2!5)) | (Y1!6 = Y2!5) | (Y0!7 = Y1!6) | (Y0!7 = Y2!5) | (~cc(X!4))) | rp(X!4, Y1!6)),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(88,plain,
% 0.12/0.40 (rp(X!4, Y1!6)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[87, 67])).
% 0.12/0.40 tff(89,plain,
% 0.12/0.40 (((~rp(X!4, Y0!7)) | (~rp(X!4, Y1!6)) | (~rp(X!4, Y2!5)) | (Y1!6 = Y2!5) | (Y0!7 = Y1!6) | (Y0!7 = Y2!5) | (~cc(X!4))) | rp(X!4, Y0!7)),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(90,plain,
% 0.12/0.40 (rp(X!4, Y0!7)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[89, 67])).
% 0.12/0.40 tff(91,plain,
% 0.12/0.40 (((~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X!4, Y0)) | (~rp(X!4, Y1)) | (~rp(X!4, Y2)))) | ((~rp(X!4, Y0!7)) | (~rp(X!4, Y1!6)) | (~rp(X!4, Y2!5)) | (Y1!6 = Y2!5) | (Y0!7 = Y1!6) | (Y0!7 = Y2!5))) <=> ((~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X!4, Y0)) | (~rp(X!4, Y1)) | (~rp(X!4, Y2)))) | (~rp(X!4, Y0!7)) | (~rp(X!4, Y1!6)) | (~rp(X!4, Y2!5)) | (Y1!6 = Y2!5) | (Y0!7 = Y1!6) | (Y0!7 = Y2!5))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(92,plain,
% 0.12/0.40 (((Y1!6 = Y2!5) | (Y0!7 = Y1!6) | (Y0!7 = Y2!5) | (~rp(X!4, Y0!7)) | (~rp(X!4, Y1!6)) | (~rp(X!4, Y2!5))) <=> ((~rp(X!4, Y0!7)) | (~rp(X!4, Y1!6)) | (~rp(X!4, Y2!5)) | (Y1!6 = Y2!5) | (Y0!7 = Y1!6) | (Y0!7 = Y2!5))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(93,plain,
% 0.12/0.40 (((~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X!4, Y0)) | (~rp(X!4, Y1)) | (~rp(X!4, Y2)))) | ((Y1!6 = Y2!5) | (Y0!7 = Y1!6) | (Y0!7 = Y2!5) | (~rp(X!4, Y0!7)) | (~rp(X!4, Y1!6)) | (~rp(X!4, Y2!5)))) <=> ((~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X!4, Y0)) | (~rp(X!4, Y1)) | (~rp(X!4, Y2)))) | ((~rp(X!4, Y0!7)) | (~rp(X!4, Y1!6)) | (~rp(X!4, Y2!5)) | (Y1!6 = Y2!5) | (Y0!7 = Y1!6) | (Y0!7 = Y2!5)))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[92])).
% 0.12/0.40 tff(94,plain,
% 0.12/0.40 (((~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X!4, Y0)) | (~rp(X!4, Y1)) | (~rp(X!4, Y2)))) | ((Y1!6 = Y2!5) | (Y0!7 = Y1!6) | (Y0!7 = Y2!5) | (~rp(X!4, Y0!7)) | (~rp(X!4, Y1!6)) | (~rp(X!4, Y2!5)))) <=> ((~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X!4, Y0)) | (~rp(X!4, Y1)) | (~rp(X!4, Y2)))) | (~rp(X!4, Y0!7)) | (~rp(X!4, Y1!6)) | (~rp(X!4, Y2!5)) | (Y1!6 = Y2!5) | (Y0!7 = Y1!6) | (Y0!7 = Y2!5))),
% 0.12/0.41 inference(transitivity,[status(thm)],[93, 91])).
% 0.12/0.41 tff(95,plain,
% 0.12/0.41 ((~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X!4, Y0)) | (~rp(X!4, Y1)) | (~rp(X!4, Y2)))) | ((Y1!6 = Y2!5) | (Y0!7 = Y1!6) | (Y0!7 = Y2!5) | (~rp(X!4, Y0!7)) | (~rp(X!4, Y1!6)) | (~rp(X!4, Y2!5)))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(96,plain,
% 0.12/0.41 ((~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X!4, Y0)) | (~rp(X!4, Y1)) | (~rp(X!4, Y2)))) | (~rp(X!4, Y0!7)) | (~rp(X!4, Y1!6)) | (~rp(X!4, Y2!5)) | (Y1!6 = Y2!5) | (Y0!7 = Y1!6) | (Y0!7 = Y2!5)),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.12/0.41 tff(97,plain,
% 0.12/0.41 ($false),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[96, 90, 88, 86, 84, 82, 80, 78])).
% 0.12/0.41 tff(98,plain,((~rp(X!4, Y0!7)) | (~rp(X!4, Y1!6)) | (~rp(X!4, Y2!5)) | (Y1!6 = Y2!5) | (Y0!7 = Y1!6) | (Y0!7 = Y2!5) | (~cc(X!4))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.41 tff(99,plain,
% 0.12/0.41 (((~((~rp(X!4, Y0!7)) | (~rp(X!4, Y1!6)) | (~rp(X!4, Y2!5)) | (Y1!6 = Y2!5) | (Y0!7 = Y1!6) | (Y0!7 = Y2!5) | (~cc(X!4)))) | (~cowlThing(X!2)) | cowlNothing(X!2) | (xsd_integer(X!3) <=> xsd_string(X!3)) | (~((~cc(X!8)) | (~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!8, Y0)) | (~rp(X!8, Y1))))))) <=> ((~((~rp(X!4, Y0!7)) | (~rp(X!4, Y1!6)) | (~rp(X!4, Y2!5)) | (Y1!6 = Y2!5) | (Y0!7 = Y1!6) | (Y0!7 = Y2!5) | (~cc(X!4)))) | (~cowlThing(X!2)) | cowlNothing(X!2) | (xsd_integer(X!3) <=> xsd_string(X!3)) | (~((~cc(X!8)) | (~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!8, Y0)) | (~rp(X!8, Y1)))))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(100,plain,
% 0.12/0.41 ((((~cowlThing(X!2)) | cowlNothing(X!2)) | (xsd_integer(X!3) <=> xsd_string(X!3)) | (~((~rp(X!4, Y0!7)) | (~rp(X!4, Y1!6)) | (~rp(X!4, Y2!5)) | (Y1!6 = Y2!5) | (Y0!7 = Y1!6) | (Y0!7 = Y2!5) | (~cc(X!4)))) | (~((~cc(X!8)) | (~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!8, Y0)) | (~rp(X!8, Y1))))))) <=> ((~((~rp(X!4, Y0!7)) | (~rp(X!4, Y1!6)) | (~rp(X!4, Y2!5)) | (Y1!6 = Y2!5) | (Y0!7 = Y1!6) | (Y0!7 = Y2!5) | (~cc(X!4)))) | (~cowlThing(X!2)) | cowlNothing(X!2) | (xsd_integer(X!3) <=> xsd_string(X!3)) | (~((~cc(X!8)) | (~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!8, Y0)) | (~rp(X!8, Y1)))))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(101,plain,
% 0.12/0.41 ((cc(X!8) & ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!8, Y0)) | (~rp(X!8, Y1)))) <=> (~((~cc(X!8)) | (~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!8, Y0)) | (~rp(X!8, Y1))))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(102,plain,
% 0.12/0.41 (^[Y0: $i, Y1: $i] : trans(monotonicity(rewrite((rp(X!8, Y0) & rp(X!8, Y1) & (~(Y0 = Y1))) <=> (~((Y0 = Y1) | (~rp(X!8, Y0)) | (~rp(X!8, Y1))))), ((~(rp(X!8, Y0) & rp(X!8, Y1) & (~(Y0 = Y1)))) <=> (~(~((Y0 = Y1) | (~rp(X!8, Y0)) | (~rp(X!8, Y1))))))), rewrite((~(~((Y0 = Y1) | (~rp(X!8, Y0)) | (~rp(X!8, Y1))))) <=> ((Y0 = Y1) | (~rp(X!8, Y0)) | (~rp(X!8, Y1)))), ((~(rp(X!8, Y0) & rp(X!8, Y1) & (~(Y0 = Y1)))) <=> ((Y0 = Y1) | (~rp(X!8, Y0)) | (~rp(X!8, Y1)))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(103,plain,
% 0.12/0.41 (![Y0: $i, Y1: $i] : (~(rp(X!8, Y0) & rp(X!8, Y1) & (~(Y0 = Y1)))) <=> ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!8, Y0)) | (~rp(X!8, Y1)))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[102])).
% 0.12/0.41 tff(104,plain,
% 0.12/0.41 ((cc(X!8) & ![Y0: $i, Y1: $i] : (~(rp(X!8, Y0) & rp(X!8, Y1) & (~(Y0 = Y1))))) <=> (cc(X!8) & ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!8, Y0)) | (~rp(X!8, Y1))))),
% 0.12/0.41 inference(monotonicity,[status(thm)],[103])).
% 0.12/0.41 tff(105,plain,
% 0.12/0.41 ((cc(X!8) & ![Y0: $i, Y1: $i] : (~(rp(X!8, Y0) & rp(X!8, Y1) & (~(Y0 = Y1))))) <=> (~((~cc(X!8)) | (~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!8, Y0)) | (~rp(X!8, Y1))))))),
% 0.12/0.41 inference(transitivity,[status(thm)],[104, 101])).
% 0.12/0.41 tff(106,plain,
% 0.12/0.41 ((cc(X!4) & (~((~rp(X!4, Y0!7)) | (~rp(X!4, Y1!6)) | (~rp(X!4, Y2!5)) | (Y1!6 = Y2!5) | (Y0!7 = Y1!6) | (Y0!7 = Y2!5)))) <=> (~((~rp(X!4, Y0!7)) | (~rp(X!4, Y1!6)) | (~rp(X!4, Y2!5)) | (Y1!6 = Y2!5) | (Y0!7 = Y1!6) | (Y0!7 = Y2!5) | (~cc(X!4))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(107,plain,
% 0.12/0.41 ((~((Y1!6 = Y2!5) | (Y0!7 = Y1!6) | (Y0!7 = Y2!5) | (~(rp(X!4, Y0!7) & rp(X!4, Y1!6) & rp(X!4, Y2!5))))) <=> (~((~rp(X!4, Y0!7)) | (~rp(X!4, Y1!6)) | (~rp(X!4, Y2!5)) | (Y1!6 = Y2!5) | (Y0!7 = Y1!6) | (Y0!7 = Y2!5)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(108,plain,
% 0.12/0.41 ((cc(X!4) & (~((Y1!6 = Y2!5) | (Y0!7 = Y1!6) | (Y0!7 = Y2!5) | (~(rp(X!4, Y0!7) & rp(X!4, Y1!6) & rp(X!4, Y2!5)))))) <=> (cc(X!4) & (~((~rp(X!4, Y0!7)) | (~rp(X!4, Y1!6)) | (~rp(X!4, Y2!5)) | (Y1!6 = Y2!5) | (Y0!7 = Y1!6) | (Y0!7 = Y2!5))))),
% 0.12/0.41 inference(monotonicity,[status(thm)],[107])).
% 0.12/0.41 tff(109,plain,
% 0.12/0.41 ((cc(X!4) & (~((Y1!6 = Y2!5) | (Y0!7 = Y1!6) | (Y0!7 = Y2!5) | (~(rp(X!4, Y0!7) & rp(X!4, Y1!6) & rp(X!4, Y2!5)))))) <=> (~((~rp(X!4, Y0!7)) | (~rp(X!4, Y1!6)) | (~rp(X!4, Y2!5)) | (Y1!6 = Y2!5) | (Y0!7 = Y1!6) | (Y0!7 = Y2!5) | (~cc(X!4))))),
% 0.12/0.41 inference(transitivity,[status(thm)],[108, 106])).
% 0.12/0.41 tff(110,plain,
% 0.12/0.41 ((~(~((~cowlThing(X!2)) | cowlNothing(X!2)))) <=> ((~cowlThing(X!2)) | cowlNothing(X!2))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(111,plain,
% 0.12/0.41 ((cowlThing(X!2) & (~cowlNothing(X!2))) <=> (~((~cowlThing(X!2)) | cowlNothing(X!2)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(112,plain,
% 0.12/0.41 ((~(cowlThing(X!2) & (~cowlNothing(X!2)))) <=> (~(~((~cowlThing(X!2)) | cowlNothing(X!2))))),
% 0.12/0.41 inference(monotonicity,[status(thm)],[111])).
% 0.12/0.41 tff(113,plain,
% 0.12/0.41 ((~(cowlThing(X!2) & (~cowlNothing(X!2)))) <=> ((~cowlThing(X!2)) | cowlNothing(X!2))),
% 0.12/0.41 inference(transitivity,[status(thm)],[112, 110])).
% 0.12/0.41 tff(114,plain,
% 0.12/0.41 (((~(cowlThing(X!2) & (~cowlNothing(X!2)))) | (xsd_integer(X!3) <=> xsd_string(X!3)) | (cc(X!4) & (~((Y1!6 = Y2!5) | (Y0!7 = Y1!6) | (Y0!7 = Y2!5) | (~(rp(X!4, Y0!7) & rp(X!4, Y1!6) & rp(X!4, Y2!5)))))) | (cc(X!8) & ![Y0: $i, Y1: $i] : (~(rp(X!8, Y0) & rp(X!8, Y1) & (~(Y0 = Y1)))))) <=> (((~cowlThing(X!2)) | cowlNothing(X!2)) | (xsd_integer(X!3) <=> xsd_string(X!3)) | (~((~rp(X!4, Y0!7)) | (~rp(X!4, Y1!6)) | (~rp(X!4, Y2!5)) | (Y1!6 = Y2!5) | (Y0!7 = Y1!6) | (Y0!7 = Y2!5) | (~cc(X!4)))) | (~((~cc(X!8)) | (~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!8, Y0)) | (~rp(X!8, Y1)))))))),
% 0.12/0.41 inference(monotonicity,[status(thm)],[113, 109, 105])).
% 0.12/0.41 tff(115,plain,
% 0.12/0.41 (((~(cowlThing(X!2) & (~cowlNothing(X!2)))) | (xsd_integer(X!3) <=> xsd_string(X!3)) | (cc(X!4) & (~((Y1!6 = Y2!5) | (Y0!7 = Y1!6) | (Y0!7 = Y2!5) | (~(rp(X!4, Y0!7) & rp(X!4, Y1!6) & rp(X!4, Y2!5)))))) | (cc(X!8) & ![Y0: $i, Y1: $i] : (~(rp(X!8, Y0) & rp(X!8, Y1) & (~(Y0 = Y1)))))) <=> ((~((~rp(X!4, Y0!7)) | (~rp(X!4, Y1!6)) | (~rp(X!4, Y2!5)) | (Y1!6 = Y2!5) | (Y0!7 = Y1!6) | (Y0!7 = Y2!5) | (~cc(X!4)))) | (~cowlThing(X!2)) | cowlNothing(X!2) | (xsd_integer(X!3) <=> xsd_string(X!3)) | (~((~cc(X!8)) | (~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!8, Y0)) | (~rp(X!8, Y1)))))))),
% 0.12/0.41 inference(transitivity,[status(thm)],[114, 100])).
% 0.12/0.41 tff(116,plain,
% 0.12/0.41 ((cc(X!8) & ![Y0: $i, Y1: $i] : (~(rp(X!8, Y0) & rp(X!8, Y1) & (~(Y0 = Y1))))) <=> (cc(X!8) & ![Y0: $i, Y1: $i] : (~(rp(X!8, Y0) & rp(X!8, Y1) & (~(Y0 = Y1)))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(117,plain,
% 0.12/0.41 ((~((Y1!6 = Y2!5) | (Y0!7 = Y1!6) | (Y0!7 = Y2!5) | (~(rp(X!4, Y0!7) & rp(X!4, Y1!6) & rp(X!4, Y2!5))))) <=> (~((Y1!6 = Y2!5) | (Y0!7 = Y1!6) | (Y0!7 = Y2!5) | (~(rp(X!4, Y0!7) & rp(X!4, Y1!6) & rp(X!4, Y2!5)))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(118,plain,
% 0.12/0.41 ((cc(X!4) & (~((Y1!6 = Y2!5) | (Y0!7 = Y1!6) | (Y0!7 = Y2!5) | (~(rp(X!4, Y0!7) & rp(X!4, Y1!6) & rp(X!4, Y2!5)))))) <=> (cc(X!4) & (~((Y1!6 = Y2!5) | (Y0!7 = Y1!6) | (Y0!7 = Y2!5) | (~(rp(X!4, Y0!7) & rp(X!4, Y1!6) & rp(X!4, Y2!5))))))),
% 0.12/0.41 inference(monotonicity,[status(thm)],[117])).
% 0.12/0.41 tff(119,plain,
% 0.12/0.41 (((~(cowlThing(X!2) & (~cowlNothing(X!2)))) | (xsd_integer(X!3) <=> xsd_string(X!3)) | (cc(X!4) & (~((Y1!6 = Y2!5) | (Y0!7 = Y1!6) | (Y0!7 = Y2!5) | (~(rp(X!4, Y0!7) & rp(X!4, Y1!6) & rp(X!4, Y2!5)))))) | (cc(X!8) & ![Y0: $i, Y1: $i] : (~(rp(X!8, Y0) & rp(X!8, Y1) & (~(Y0 = Y1)))))) <=> ((~(cowlThing(X!2) & (~cowlNothing(X!2)))) | (xsd_integer(X!3) <=> xsd_string(X!3)) | (cc(X!4) & (~((Y1!6 = Y2!5) | (Y0!7 = Y1!6) | (Y0!7 = Y2!5) | (~(rp(X!4, Y0!7) & rp(X!4, Y1!6) & rp(X!4, Y2!5)))))) | (cc(X!8) & ![Y0: $i, Y1: $i] : (~(rp(X!8, Y0) & rp(X!8, Y1) & (~(Y0 = Y1))))))),
% 0.12/0.41 inference(monotonicity,[status(thm)],[118, 116])).
% 0.12/0.41 tff(120,plain,
% 0.12/0.41 ((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~(rp(X, Y0) & rp(X, Y1) & rp(X, Y2))))) & ![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, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~(rp(X, Y0) & rp(X, Y1) & rp(X, Y2))))) & ![X: $i] : ((~cc(X)) | ?[Y0: $i, Y1: $i] : (rp(X, Y0) & rp(X, Y1) & (~(Y0 = Y1)))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(121,plain,
% 0.12/0.41 ((~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~(rp(X, Y0) & rp(X, Y1) & rp(X, Y2))))) & ![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, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~(rp(X, Y0) & rp(X, Y1) & rp(X, Y2))))) & ![X: $i] : ((~cc(X)) | ?[Y0: $i, Y1: $i] : (rp(X, Y0) & rp(X, Y1) & (~(Y0 = Y1))))))),
% 0.12/0.41 inference(monotonicity,[status(thm)],[120])).
% 0.12/0.41 tff(122,plain,
% 0.12/0.41 ((~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~(rp(X, Y0) & rp(X, Y1) & rp(X, Y2))))) & ![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, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~(rp(X, Y0) & rp(X, Y1) & rp(X, Y2))))) & ![X: $i] : ((~cc(X)) | ?[Y0: $i, Y1: $i] : (rp(X, Y0) & rp(X, Y1) & (~(Y0 = Y1))))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(123,plain,
% 0.12/0.41 ((~(((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X)))) & ![X: $i] : (cc(X) => ![Y0: $i, Y1: $i, Y2: $i] : (((rp(X, Y0) & rp(X, Y1)) & rp(X, Y2)) => (((Y0 = Y1) | (Y0 = Y2)) | (Y1 = Y2))))) & ![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, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~(rp(X, Y0) & rp(X, Y1) & rp(X, Y2))))) & ![X: $i] : ((~cc(X)) | ?[Y0: $i, Y1: $i] : (rp(X, Y0) & rp(X, Y1) & (~(Y0 = Y1))))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(124,axiom,(~(((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X)))) & ![X: $i] : (cc(X) => ![Y0: $i, Y1: $i, Y2: $i] : (((rp(X, Y0) & rp(X, Y1)) & rp(X, Y2)) => (((Y0 = Y1) | (Y0 = Y2)) | (Y1 = Y2))))) & ![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')).
% 0.12/0.41 tff(125,plain,
% 0.12/0.41 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~(rp(X, Y0) & rp(X, Y1) & rp(X, Y2))))) & ![X: $i] : ((~cc(X)) | ?[Y0: $i, Y1: $i] : (rp(X, Y0) & rp(X, Y1) & (~(Y0 = Y1)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.20/0.42 tff(126,plain,
% 0.20/0.42 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~(rp(X, Y0) & rp(X, Y1) & rp(X, Y2))))) & ![X: $i] : ((~cc(X)) | ?[Y0: $i, Y1: $i] : (rp(X, Y0) & rp(X, Y1) & (~(Y0 = Y1)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[125, 121])).
% 0.20/0.42 tff(127,plain,
% 0.20/0.42 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~(rp(X, Y0) & rp(X, Y1) & rp(X, Y2))))) & ![X: $i] : ((~cc(X)) | ?[Y0: $i, Y1: $i] : (rp(X, Y0) & rp(X, Y1) & (~(Y0 = Y1)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[126, 122])).
% 0.20/0.42 tff(128,plain,
% 0.20/0.42 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (~(xsd_integer(X) <=> xsd_string(X))) & ![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~(rp(X, Y0) & rp(X, Y1) & rp(X, Y2))))) & ![X: $i] : ((~cc(X)) | ?[Y0: $i, Y1: $i] : (rp(X, Y0) & rp(X, Y1) & (~(Y0 = Y1)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[127, 121])).
% 0.20/0.42 unexpected number of arguments: (let ((a!1 (forall ((X $i)) (and (cowlThing X) (not (cowlNothing X)))))
% 0.20/0.42 (a!2 (not (and (cowlThing X!2) (not (cowlNothing X!2)))))
% 0.20/0.42 (a!3 (forall ((X $i)) (not (= (xsd_integer X) (xsd_string X)))))
% 0.20/0.42 (a!5 (forall ((X $i))
% 0.20/0.42 (let ((a!1 (forall ((Y0 $i) (Y1 $i) (Y2 $i))
% 0.20/0.42 (or (= Y1 Y2)
% 0.20/0.42 (= Y0 Y1)
% 0.20/0.42 (= Y0 Y2)
% 0.20/0.42 (not (and (rp X Y0) (rp X Y1) (rp X Y2)))))))
% 0.20/0.42 (or (not (cc X)) a!1))))
% 0.20/0.42 (a!6 (forall ((Y0 $i) (Y1 $i) (Y2 $i))
% 0.20/0.42 (or (= Y1 Y2)
% 0.20/0.42 (= Y0 Y1)
% 0.20/0.42 (= Y0 Y2)
% 0.20/0.42 (not (and (rp X!4 Y0) (rp X!4 Y1) (rp X!4 Y2))))))
% 0.20/0.42 (a!8 (or (= Y1!6 Y2!5)
% 0.20/0.42 (= Y0!7 Y1!6)
% 0.20/0.42 (= Y0!7 Y2!5)
% 0.20/0.42 (not (and (rp X!4 Y0!7) (rp X!4 Y1!6) (rp X!4 Y2!5)))))
% 0.20/0.42 (a!11 (forall ((X $i))
% 0.20/0.42 (let ((a!1 (exists ((Y0 $i) (Y1 $i))
% 0.20/0.42 (and (rp X Y0) (rp X Y1) (not (= Y0 Y1))))))
% 0.20/0.42 (or (not (cc X)) a!1))))
% 0.20/0.42 (a!12 (exists ((Y0 $i) (Y1 $i))
% 0.20/0.42 (and (rp X!8 Y0) (rp X!8 Y1) (not (= Y0 Y1)))))
% 0.20/0.42 (a!14 (lambda ((Y0 $i) (Y1 $i))
% 0.20/0.42 (let ((a!1 (and (rp X!8 Y0) (rp X!8 Y1) (not (= Y0 Y1)))))
% 0.20/0.42 (refl (~ (not a!1) (not a!1))))))
% 0.20/0.42 (a!15 (forall ((Y0 $i) (Y1 $i))
% 0.20/0.42 (let ((a!1 (and (rp X!8 Y0) (rp X!8 Y1) (not (= Y0 Y1)))))
% 0.20/0.42 (not a!1)))))
% 0.20/0.42 (let ((a!4 (sk (~ (not a!3) (= (xsd_integer X!3) (xsd_string X!3)))))
% 0.20/0.42 (a!7 (not (or (not (cc X!4)) a!6)))
% 0.20/0.42 (a!13 (not (or (not (cc X!8)) a!12)))
% 0.20/0.42 (a!18 (~ (not (and a!1 a!3 a!5 a!11))
% 0.20/0.42 (or a!2
% 0.20/0.42 (= (xsd_integer X!3) (xsd_string X!3))
% 0.20/0.42 (and (cc X!4) (not a!8))
% 0.20/0.42 (and (cc X!8) a!15)))))
% 0.20/0.42 (let ((a!9 (nnf-neg (refl (~ (cc X!4) (cc X!4)))
% 0.20/0.42 (sk (~ (not a!6) (not a!8)))
% 0.20/0.42 (~ a!7 (and (cc X!4) (not a!8)))))
% 0.20/0.42 (a!16 (nnf-neg (refl (~ (cc X!8) (cc X!8)))
% 0.20/0.42 (nnf-neg (proof-bind a!14) (~ (not a!12) a!15))
% 0.20/0.42 (~ a!13 (and (cc X!8) a!15)))))
% 0.20/0.42 (let ((a!10 (trans (sk (~ (not a!5) a!7))
% 0.20/0.42 a!9
% 0.20/0.42 (~ (not a!5) (and (cc X!4) (not a!8)))))
% 0.20/0.42 (a!17 (trans (sk (~ (not a!11) a!13))
% 0.20/0.42 a!16
% 0.20/0.42 (~ (not a!11) (and (cc X!8) a!15)))))
% 0.20/0.42 (nnf-neg (sk (~ (not a!1) a!2)) a!4 a!10 a!17 a!18)))))
% 0.20/0.42 Proof display could not be completed: unexpected number of arguments
% 0.20/0.43 % E exiting
%------------------------------------------------------------------------------