TSTP Solution File: KRS144+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KRS144+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.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 Sep 17 17:44:57 EDT 2022
% Result : Theorem 0.20s 0.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KRS144+1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Sep 1 09:34:34 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.40 % SZS status Theorem
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 tff(rp_type, type, (
% 0.20/0.40 rp: ( $i * $i ) > $o)).
% 0.20/0.40 tff(tptp_fun_Y1_0_type, type, (
% 0.20/0.40 tptp_fun_Y1_0: $i > $i)).
% 0.20/0.40 tff(tptp_fun_X_6_type, type, (
% 0.20/0.40 tptp_fun_X_6: $i)).
% 0.20/0.40 tff(tptp_fun_Y0_1_type, type, (
% 0.20/0.40 tptp_fun_Y0_1: $i > $i)).
% 0.20/0.40 tff(cc_type, type, (
% 0.20/0.40 cc: $i > $o)).
% 0.20/0.40 tff(tptp_fun_Y2_3_type, type, (
% 0.20/0.40 tptp_fun_Y2_3: $i)).
% 0.20/0.40 tff(tptp_fun_X_2_type, type, (
% 0.20/0.40 tptp_fun_X_2: $i)).
% 0.20/0.40 tff(tptp_fun_Y1_4_type, type, (
% 0.20/0.40 tptp_fun_Y1_4: $i)).
% 0.20/0.40 tff(tptp_fun_Y0_5_type, type, (
% 0.20/0.40 tptp_fun_Y0_5: $i)).
% 0.20/0.40 tff(xsd_integer_type, type, (
% 0.20/0.40 xsd_integer: $i > $o)).
% 0.20/0.40 tff(xsd_string_type, type, (
% 0.20/0.40 xsd_string: $i > $o)).
% 0.20/0.40 tff(cowlNothing_type, type, (
% 0.20/0.40 cowlNothing: $i > $o)).
% 0.20/0.40 tff(cowlThing_type, type, (
% 0.20/0.40 cowlThing: $i > $o)).
% 0.20/0.40 tff(1,assumption,(~((~cc(X!2)) | (Y1!4 = Y2!3) | (Y0!5 = Y1!4) | (Y0!5 = Y2!3) | (~rp(X!2, Y0!5)) | (~rp(X!2, Y1!4)) | (~rp(X!2, Y2!3)))), introduced(assumption)).
% 0.20/0.40 tff(2,plain,
% 0.20/0.40 (((~cc(X!2)) | (Y1!4 = Y2!3) | (Y0!5 = Y1!4) | (Y0!5 = Y2!3) | (~rp(X!2, Y0!5)) | (~rp(X!2, Y1!4)) | (~rp(X!2, Y2!3))) | cc(X!2)),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(3,plain,
% 0.20/0.40 (cc(X!2)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.20/0.40 tff(4,plain,
% 0.20/0.40 (^[X: $i] : refl(((~cc(X)) | (~((tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X)) | (~rp(X, tptp_fun_Y0_1(X))) | (~rp(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)) | (~((tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X)) | (~rp(X, tptp_fun_Y0_1(X))) | (~rp(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))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(5,plain,
% 0.20/0.40 (![X: $i] : ((~cc(X)) | (~((tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X)) | (~rp(X, tptp_fun_Y0_1(X))) | (~rp(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)) | (~((tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X)) | (~rp(X, tptp_fun_Y0_1(X))) | (~rp(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)))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.40 tff(6,plain,
% 0.20/0.40 (^[X: $i] : rewrite(((~cc(X)) | (~((tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X)) | (~rp(X, tptp_fun_Y0_1(X))) | (~rp(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)) | (~((tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X)) | (~rp(X, tptp_fun_Y0_1(X))) | (~rp(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))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(7,plain,
% 0.20/0.40 (![X: $i] : ((~cc(X)) | (~((tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X)) | (~rp(X, tptp_fun_Y0_1(X))) | (~rp(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)) | (~((tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X)) | (~rp(X, tptp_fun_Y0_1(X))) | (~rp(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)))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[6])).
% 0.20/0.40 tff(8,plain,
% 0.20/0.40 (![X: $i] : ((~cc(X)) | (~((tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X)) | (~rp(X, tptp_fun_Y0_1(X))) | (~rp(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)) | (~((tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X)) | (~rp(X, tptp_fun_Y0_1(X))) | (~rp(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)))))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[7, 5])).
% 0.20/0.40 tff(9,plain,
% 0.20/0.40 (^[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)) | (~((tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X)) | (~rp(X, tptp_fun_Y0_1(X))) | (~rp(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))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(10,plain,
% 0.20/0.40 (![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)))))) <=> ![X: $i] : ((~cc(X)) | (~((tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X)) | (~rp(X, tptp_fun_Y0_1(X))) | (~rp(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)))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[9])).
% 0.20/0.40 tff(11,plain,
% 0.20/0.40 (^[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)))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(12,plain,
% 0.20/0.40 (![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)))))) <=> ![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))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[11])).
% 0.20/0.40 tff(13,plain,
% 0.20/0.40 (![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))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(14,plain,
% 0.20/0.40 (^[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))))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(15,plain,
% 0.20/0.40 (![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))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[14])).
% 0.20/0.40 tff(16,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')).
% 0.20/0.40 tff(17,plain,
% 0.20/0.40 (![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))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.20/0.40 tff(18,plain,
% 0.20/0.40 (![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))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.20/0.40 tff(19,plain,(
% 0.20/0.40 ![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))))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[18])).
% 0.20/0.40 tff(20,plain,
% 0.20/0.40 (![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))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.20/0.40 tff(21,plain,
% 0.20/0.40 (![X: $i] : ((~cc(X)) | (~((tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X)) | (~rp(X, tptp_fun_Y0_1(X))) | (~rp(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)))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[20, 10])).
% 0.20/0.40 tff(22,plain,
% 0.20/0.40 (![X: $i] : ((~cc(X)) | (~((tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X)) | (~rp(X, tptp_fun_Y0_1(X))) | (~rp(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)))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[21, 8])).
% 0.20/0.40 tff(23,plain,
% 0.20/0.40 (((~![X: $i] : ((~cc(X)) | (~((tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X)) | (~rp(X, tptp_fun_Y0_1(X))) | (~rp(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!2)) | (~((tptp_fun_Y0_1(X!2) = tptp_fun_Y1_0(X!2)) | (~rp(X!2, tptp_fun_Y0_1(X!2))) | (~rp(X!2, tptp_fun_Y1_0(X!2))) | (~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X!2, Y0)) | (~rp(X!2, Y1)) | (~rp(X!2, Y2)))))))) <=> ((~![X: $i] : ((~cc(X)) | (~((tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X)) | (~rp(X, tptp_fun_Y0_1(X))) | (~rp(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!2)) | (~((tptp_fun_Y0_1(X!2) = tptp_fun_Y1_0(X!2)) | (~rp(X!2, tptp_fun_Y0_1(X!2))) | (~rp(X!2, tptp_fun_Y1_0(X!2))) | (~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X!2, Y0)) | (~rp(X!2, Y1)) | (~rp(X!2, Y2)))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(24,plain,
% 0.20/0.40 ((~![X: $i] : ((~cc(X)) | (~((tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X)) | (~rp(X, tptp_fun_Y0_1(X))) | (~rp(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!2)) | (~((tptp_fun_Y0_1(X!2) = tptp_fun_Y1_0(X!2)) | (~rp(X!2, tptp_fun_Y0_1(X!2))) | (~rp(X!2, tptp_fun_Y1_0(X!2))) | (~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X!2, Y0)) | (~rp(X!2, Y1)) | (~rp(X!2, Y2)))))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(25,plain,
% 0.20/0.40 ((~![X: $i] : ((~cc(X)) | (~((tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X)) | (~rp(X, tptp_fun_Y0_1(X))) | (~rp(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!2)) | (~((tptp_fun_Y0_1(X!2) = tptp_fun_Y1_0(X!2)) | (~rp(X!2, tptp_fun_Y0_1(X!2))) | (~rp(X!2, tptp_fun_Y1_0(X!2))) | (~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X!2, Y0)) | (~rp(X!2, Y1)) | (~rp(X!2, Y2))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.20/0.41 tff(26,plain,
% 0.20/0.41 (~((tptp_fun_Y0_1(X!2) = tptp_fun_Y1_0(X!2)) | (~rp(X!2, tptp_fun_Y0_1(X!2))) | (~rp(X!2, tptp_fun_Y1_0(X!2))) | (~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X!2, Y0)) | (~rp(X!2, Y1)) | (~rp(X!2, Y2)))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[25, 22, 3])).
% 0.20/0.41 tff(27,plain,
% 0.20/0.41 (((tptp_fun_Y0_1(X!2) = tptp_fun_Y1_0(X!2)) | (~rp(X!2, tptp_fun_Y0_1(X!2))) | (~rp(X!2, tptp_fun_Y1_0(X!2))) | (~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X!2, Y0)) | (~rp(X!2, Y1)) | (~rp(X!2, Y2))))) | ![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X!2, Y0)) | (~rp(X!2, Y1)) | (~rp(X!2, Y2)))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(28,plain,
% 0.20/0.41 (![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X!2, Y0)) | (~rp(X!2, Y1)) | (~rp(X!2, Y2)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.20/0.41 tff(29,plain,
% 0.20/0.41 (((~cc(X!2)) | (Y1!4 = Y2!3) | (Y0!5 = Y1!4) | (Y0!5 = Y2!3) | (~rp(X!2, Y0!5)) | (~rp(X!2, Y1!4)) | (~rp(X!2, Y2!3))) | rp(X!2, Y2!3)),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(30,plain,
% 0.20/0.41 (rp(X!2, Y2!3)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[29, 1])).
% 0.20/0.41 tff(31,plain,
% 0.20/0.41 (((~cc(X!2)) | (Y1!4 = Y2!3) | (Y0!5 = Y1!4) | (Y0!5 = Y2!3) | (~rp(X!2, Y0!5)) | (~rp(X!2, Y1!4)) | (~rp(X!2, Y2!3))) | rp(X!2, Y1!4)),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(32,plain,
% 0.20/0.41 (rp(X!2, Y1!4)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[31, 1])).
% 0.20/0.41 tff(33,plain,
% 0.20/0.41 (((~cc(X!2)) | (Y1!4 = Y2!3) | (Y0!5 = Y1!4) | (Y0!5 = Y2!3) | (~rp(X!2, Y0!5)) | (~rp(X!2, Y1!4)) | (~rp(X!2, Y2!3))) | rp(X!2, Y0!5)),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(34,plain,
% 0.20/0.41 (rp(X!2, Y0!5)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[33, 1])).
% 0.20/0.41 tff(35,plain,
% 0.20/0.41 (((~cc(X!2)) | (Y1!4 = Y2!3) | (Y0!5 = Y1!4) | (Y0!5 = Y2!3) | (~rp(X!2, Y0!5)) | (~rp(X!2, Y1!4)) | (~rp(X!2, Y2!3))) | (~(Y0!5 = Y2!3))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(36,plain,
% 0.20/0.41 (~(Y0!5 = Y2!3)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[35, 1])).
% 0.20/0.41 tff(37,plain,
% 0.20/0.41 (((~cc(X!2)) | (Y1!4 = Y2!3) | (Y0!5 = Y1!4) | (Y0!5 = Y2!3) | (~rp(X!2, Y0!5)) | (~rp(X!2, Y1!4)) | (~rp(X!2, Y2!3))) | (~(Y0!5 = Y1!4))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(38,plain,
% 0.20/0.41 (~(Y0!5 = Y1!4)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[37, 1])).
% 0.20/0.41 tff(39,plain,
% 0.20/0.41 (((~cc(X!2)) | (Y1!4 = Y2!3) | (Y0!5 = Y1!4) | (Y0!5 = Y2!3) | (~rp(X!2, Y0!5)) | (~rp(X!2, Y1!4)) | (~rp(X!2, Y2!3))) | (~(Y1!4 = Y2!3))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(40,plain,
% 0.20/0.41 (~(Y1!4 = Y2!3)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[39, 1])).
% 0.20/0.41 tff(41,plain,
% 0.20/0.41 (((~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X!2, Y0)) | (~rp(X!2, Y1)) | (~rp(X!2, Y2)))) | ((Y1!4 = Y2!3) | (Y0!5 = Y1!4) | (Y0!5 = Y2!3) | (~rp(X!2, Y0!5)) | (~rp(X!2, Y1!4)) | (~rp(X!2, Y2!3)))) <=> ((~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X!2, Y0)) | (~rp(X!2, Y1)) | (~rp(X!2, Y2)))) | (Y1!4 = Y2!3) | (Y0!5 = Y1!4) | (Y0!5 = Y2!3) | (~rp(X!2, Y0!5)) | (~rp(X!2, Y1!4)) | (~rp(X!2, Y2!3)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(42,plain,
% 0.20/0.41 ((~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X!2, Y0)) | (~rp(X!2, Y1)) | (~rp(X!2, Y2)))) | ((Y1!4 = Y2!3) | (Y0!5 = Y1!4) | (Y0!5 = Y2!3) | (~rp(X!2, Y0!5)) | (~rp(X!2, Y1!4)) | (~rp(X!2, Y2!3)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(43,plain,
% 0.20/0.41 ((~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X!2, Y0)) | (~rp(X!2, Y1)) | (~rp(X!2, Y2)))) | (Y1!4 = Y2!3) | (Y0!5 = Y1!4) | (Y0!5 = Y2!3) | (~rp(X!2, Y0!5)) | (~rp(X!2, Y1!4)) | (~rp(X!2, Y2!3))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.20/0.41 tff(44,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[43, 40, 38, 36, 34, 32, 30, 28])).
% 0.20/0.41 tff(45,plain,((~cc(X!2)) | (Y1!4 = Y2!3) | (Y0!5 = Y1!4) | (Y0!5 = Y2!3) | (~rp(X!2, Y0!5)) | (~rp(X!2, Y1!4)) | (~rp(X!2, Y2!3))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(46,plain,
% 0.20/0.41 (((~((~cc(X!2)) | (Y1!4 = Y2!3) | (Y0!5 = Y1!4) | (Y0!5 = Y2!3) | (~rp(X!2, Y0!5)) | (~rp(X!2, Y1!4)) | (~rp(X!2, Y2!3)))) | (~((~cc(X!6)) | (~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!6, Y0)) | (~rp(X!6, Y1))))))) <=> ((~((~cc(X!2)) | (Y1!4 = Y2!3) | (Y0!5 = Y1!4) | (Y0!5 = Y2!3) | (~rp(X!2, Y0!5)) | (~rp(X!2, Y1!4)) | (~rp(X!2, Y2!3)))) | (~((~cc(X!6)) | (~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!6, Y0)) | (~rp(X!6, Y1)))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(47,plain,
% 0.20/0.41 (((cc(X!2) & (~((Y1!4 = Y2!3) | (Y0!5 = Y1!4) | (Y0!5 = Y2!3) | (~(rp(X!2, Y0!5) & rp(X!2, Y1!4) & rp(X!2, Y2!3)))))) | (cc(X!6) & ![Y0: $i, Y1: $i] : (~(rp(X!6, Y0) & rp(X!6, Y1) & (~(Y0 = Y1)))))) <=> ((~((~cc(X!2)) | (Y1!4 = Y2!3) | (Y0!5 = Y1!4) | (Y0!5 = Y2!3) | (~rp(X!2, Y0!5)) | (~rp(X!2, Y1!4)) | (~rp(X!2, Y2!3)))) | (~((~cc(X!6)) | (~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!6, Y0)) | (~rp(X!6, Y1)))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(48,plain,
% 0.20/0.41 ((((~(~cc(X!2))) & (~((Y1!4 = Y2!3) | (Y0!5 = Y1!4) | (Y0!5 = Y2!3) | (~(rp(X!2, Y0!5) & rp(X!2, Y1!4) & rp(X!2, Y2!3)))))) | ((~(~cc(X!6))) & ![Y0: $i, Y1: $i] : (~(rp(X!6, Y0) & rp(X!6, Y1) & (~(Y0 = Y1)))))) <=> ((cc(X!2) & (~((Y1!4 = Y2!3) | (Y0!5 = Y1!4) | (Y0!5 = Y2!3) | (~(rp(X!2, Y0!5) & rp(X!2, Y1!4) & rp(X!2, Y2!3)))))) | (cc(X!6) & ![Y0: $i, Y1: $i] : (~(rp(X!6, Y0) & rp(X!6, Y1) & (~(Y0 = Y1))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(49,plain,
% 0.20/0.41 ((![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] : ((~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)))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(50,plain,
% 0.20/0.41 ((~(![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] : ((~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))))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[49])).
% 0.20/0.41 tff(51,plain,
% 0.20/0.41 ((~(![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] : ((~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))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(52,plain,
% 0.20/0.41 ((~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i, Y2: $i] : ((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] : ((~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))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(53,plain,
% 0.20/0.41 ((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i, Y2: $i] : ((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_string(X) <=> (~xsd_integer(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)))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(54,plain,
% 0.20/0.41 ((~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i, Y2: $i] : ((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_string(X) <=> (~xsd_integer(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))))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[53])).
% 0.20/0.41 tff(55,plain,
% 0.20/0.41 ((~(((![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_string(X) <=> (~xsd_integer(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))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(56,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')).
% 0.20/0.41 tff(57,plain,
% 0.20/0.41 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i, Y2: $i] : ((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)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.20/0.41 tff(58,plain,
% 0.20/0.41 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i, Y2: $i] : ((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)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[57, 54])).
% 0.20/0.41 tff(59,plain,
% 0.20/0.41 (~(![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)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[58, 52])).
% 0.20/0.41 tff(60,plain,
% 0.20/0.41 (~(![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)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[59, 51])).
% 0.20/0.41 tff(61,plain,
% 0.20/0.41 (~(![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)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[60, 50])).
% 0.20/0.41 tff(62,plain,
% 0.20/0.41 (~(![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)],[61, 50])).
% 0.20/0.42 tff(63,plain,
% 0.20/0.42 (~(![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)],[62, 50])).
% 0.20/0.42 tff(64,plain,
% 0.20/0.42 (~(![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)],[63, 50])).
% 0.20/0.42 unexpected number of arguments: (let ((a!1 (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!2 (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!2 Y0) (rp X!2 Y1) (rp X!2 Y2))))))
% 0.20/0.42 (a!4 (~ (not (not (cc X!2))) (not (not (cc X!2)))))
% 0.20/0.42 (a!5 (or (= Y1!4 Y2!3)
% 0.20/0.42 (= Y0!5 Y1!4)
% 0.20/0.42 (= Y0!5 Y2!3)
% 0.20/0.42 (not (and (rp X!2 Y0!5) (rp X!2 Y1!4) (rp X!2 Y2!3)))))
% 0.20/0.42 (a!9 (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!10 (exists ((Y0 $i) (Y1 $i))
% 0.20/0.42 (and (rp X!6 Y0) (rp X!6 Y1) (not (= Y0 Y1)))))
% 0.20/0.42 (a!12 (~ (not (not (cc X!6))) (not (not (cc X!6)))))
% 0.20/0.42 (a!13 (lambda ((Y0 $i) (Y1 $i))
% 0.20/0.42 (let ((a!1 (and (rp X!6 Y0) (rp X!6 Y1) (not (= Y0 Y1)))))
% 0.20/0.42 (refl (~ (not a!1) (not a!1))))))
% 0.20/0.42 (a!14 (forall ((Y0 $i) (Y1 $i))
% 0.20/0.42 (let ((a!1 (and (rp X!6 Y0) (rp X!6 Y1) (not (= Y0 Y1)))))
% 0.20/0.42 (not a!1)))))
% 0.20/0.42 (let ((a!3 (not (or (not (cc X!2)) a!2)))
% 0.20/0.42 (a!6 (and (not (not (cc X!2))) (not a!5)))
% 0.20/0.42 (a!11 (not (or (not (cc X!6)) a!10)))
% 0.20/0.42 (a!15 (and (not (not (cc X!6))) a!14)))
% 0.20/0.42 (let ((a!7 (nnf-neg (refl a!4) (sk (~ (not a!2) (not a!5))) (~ a!3 a!6)))
% 0.20/0.42 (a!16 (nnf-neg (refl a!12)
% 0.20/0.42 (nnf-neg (proof-bind a!13) (~ (not a!10) a!14))
% 0.20/0.42 (~ a!11 a!15))))
% 0.20/0.42 (let ((a!8 (trans (sk (~ (not a!1) a!3)) a!7 (~ (not a!1) a!6)))
% 0.20/0.42 (a!17 (trans (sk (~ (not a!9) a!11)) a!16 (~ (not a!9) a!15))))
% 0.20/0.42 (nnf-neg a!8 a!17 (~ (not (and a!1 a!9)) (or a!6 a!15)))))))
% 0.20/0.42 Proof display could not be completed: unexpected number of arguments
%------------------------------------------------------------------------------