TSTP Solution File: KRS145+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KRS145+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.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 0.12s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : KRS145+1 : TPTP v8.1.0. Released v3.1.0.
% 0.10/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n026.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
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Sep 1 09:52:07 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(rp_type, type, (
% 0.12/0.38 rp: ( $i * $i ) > $o)).
% 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(tptp_fun_X_2_type, type, (
% 0.12/0.38 tptp_fun_X_2: $i)).
% 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(cc_type, type, (
% 0.12/0.38 cc: $i > $o)).
% 0.12/0.38 tff(tptp_fun_Y2_3_type, type, (
% 0.12/0.38 tptp_fun_Y2_3: $i)).
% 0.12/0.38 tff(tptp_fun_Y1_4_type, type, (
% 0.12/0.38 tptp_fun_Y1_4: $i)).
% 0.12/0.38 tff(tptp_fun_Y0_5_type, type, (
% 0.12/0.38 tptp_fun_Y0_5: $i)).
% 0.12/0.38 tff(xsd_integer_type, type, (
% 0.12/0.38 xsd_integer: $i > $o)).
% 0.12/0.38 tff(xsd_string_type, type, (
% 0.12/0.38 xsd_string: $i > $o)).
% 0.12/0.38 tff(cowlNothing_type, type, (
% 0.12/0.38 cowlNothing: $i > $o)).
% 0.12/0.38 tff(cowlThing_type, type, (
% 0.12/0.38 cowlThing: $i > $o)).
% 0.12/0.38 tff(1,plain,
% 0.12/0.38 (((~(~cc(X!2))) & (![Y0: $i, Y1: $i] : (~(rp(X!2, Y0) & rp(X!2, Y1) & (~(Y0 = Y1)))) | (~((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) & (![Y0: $i, Y1: $i] : (~(rp(X!2, Y0) & rp(X!2, Y1) & (~(Y0 = Y1)))) | (~((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)))))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(2,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(3,plain,
% 0.12/0.38 ((~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![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(4,plain,
% 0.12/0.38 ((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![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] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![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(5,plain,
% 0.12/0.38 ((~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![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] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![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(monotonicity,[status(thm)],[4])).
% 0.12/0.38 tff(6,plain,
% 0.12/0.38 ((~((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X)))) & ![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] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![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)],[])).
% 0.12/0.39 tff(7,axiom,(~((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X)))) & ![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/sandbox2/benchmark/theBenchmark.p','the_axiom')).
% 0.12/0.39 tff(8,plain,
% 0.12/0.39 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![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)))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.12/0.39 tff(9,plain,
% 0.12/0.39 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![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)))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.12/0.39 tff(10,plain,
% 0.12/0.39 (~![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))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[9, 3])).
% 0.12/0.39 tff(11,plain,
% 0.12/0.39 (~![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))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.12/0.39 tff(12,plain,
% 0.12/0.39 (~![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))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[11, 2])).
% 0.12/0.39 tff(13,plain,
% 0.12/0.39 (~![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))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.12/0.39 tff(14,plain,
% 0.12/0.39 (~![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))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[13, 2])).
% 0.12/0.39 tff(15,plain,
% 0.12/0.39 (~![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))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[14, 2])).
% 0.12/0.39 tff(16,plain,
% 0.12/0.39 (cc(X!2) & (![Y0: $i, Y1: $i] : (~(rp(X!2, Y0) & rp(X!2, Y1) & (~(Y0 = Y1)))) | (~((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))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[15, 1])).
% 0.12/0.39 tff(17,plain,
% 0.12/0.39 (cc(X!2)),
% 0.12/0.39 inference(and_elim,[status(thm)],[16])).
% 0.12/0.39 tff(18,plain,
% 0.12/0.39 (^[X: $i] : rewrite(((~cc(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)))) | (~rp(X, tptp_fun_Y0_1(X))) | (~rp(X, tptp_fun_Y1_0(X)))))) <=> ((~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))))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(19,plain,
% 0.12/0.39 (![X: $i] : ((~cc(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)))) | (~rp(X, tptp_fun_Y0_1(X))) | (~rp(X, tptp_fun_Y1_0(X)))))) <=> ![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)))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[18])).
% 0.12/0.39 tff(20,plain,
% 0.12/0.39 (^[X: $i] : refl(((~cc(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)))) | (~rp(X, tptp_fun_Y0_1(X))) | (~rp(X, tptp_fun_Y1_0(X)))))) <=> ((~cc(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)))) | (~rp(X, tptp_fun_Y0_1(X))) | (~rp(X, tptp_fun_Y1_0(X)))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(21,plain,
% 0.12/0.39 (![X: $i] : ((~cc(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)))) | (~rp(X, tptp_fun_Y0_1(X))) | (~rp(X, tptp_fun_Y1_0(X)))))) <=> ![X: $i] : ((~cc(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)))) | (~rp(X, tptp_fun_Y0_1(X))) | (~rp(X, tptp_fun_Y1_0(X))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[20])).
% 0.12/0.39 tff(22,plain,
% 0.12/0.39 (^[X: $i] : rewrite(((~cc(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)))) | (~rp(X, tptp_fun_Y0_1(X))) | (~rp(X, tptp_fun_Y1_0(X)))))) <=> ((~cc(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)))) | (~rp(X, tptp_fun_Y0_1(X))) | (~rp(X, tptp_fun_Y1_0(X)))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(23,plain,
% 0.12/0.39 (![X: $i] : ((~cc(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)))) | (~rp(X, tptp_fun_Y0_1(X))) | (~rp(X, tptp_fun_Y1_0(X)))))) <=> ![X: $i] : ((~cc(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)))) | (~rp(X, tptp_fun_Y0_1(X))) | (~rp(X, tptp_fun_Y1_0(X))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[22])).
% 0.12/0.39 tff(24,plain,
% 0.12/0.39 (![X: $i] : ((~cc(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)))) | (~rp(X, tptp_fun_Y0_1(X))) | (~rp(X, tptp_fun_Y1_0(X)))))) <=> ![X: $i] : ((~cc(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)))) | (~rp(X, tptp_fun_Y0_1(X))) | (~rp(X, tptp_fun_Y1_0(X))))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[23, 21])).
% 0.12/0.39 tff(25,plain,
% 0.12/0.39 (^[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)) | (~((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)))) | (~rp(X, tptp_fun_Y0_1(X))) | (~rp(X, tptp_fun_Y1_0(X)))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(26,plain,
% 0.12/0.39 (![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)) | (~((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)))) | (~rp(X, tptp_fun_Y0_1(X))) | (~rp(X, tptp_fun_Y1_0(X))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[25])).
% 0.12/0.39 tff(27,plain,
% 0.12/0.39 (^[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))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(28,plain,
% 0.12/0.39 (![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)))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[27])).
% 0.12/0.39 tff(29,plain,
% 0.12/0.39 (![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)))) & ?[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)))) & ?[Y0: $i, Y1: $i] : (rp(X, Y0) & rp(X, Y1) & (~(Y0 = Y1)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(30,plain,
% 0.12/0.39 (^[X: $i] : trans(monotonicity(rewrite((![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)))) & ?[Y0: $i, Y1: $i] : (rp(X, Y0) & rp(X, Y1) & (~(Y0 = Y1))))), ((cc(X) => (![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))))) <=> (cc(X) => (![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~(rp(X, Y0) & rp(X, Y1) & rp(X, Y2)))) & ?[Y0: $i, Y1: $i] : (rp(X, Y0) & rp(X, Y1) & (~(Y0 = Y1))))))), rewrite((cc(X) => (![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~(rp(X, Y0) & rp(X, Y1) & rp(X, Y2)))) & ?[Y0: $i, Y1: $i] : (rp(X, Y0) & rp(X, Y1) & (~(Y0 = Y1))))) <=> ((~cc(X)) | (![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~(rp(X, Y0) & rp(X, Y1) & rp(X, Y2)))) & ?[Y0: $i, Y1: $i] : (rp(X, Y0) & rp(X, Y1) & (~(Y0 = Y1)))))), ((cc(X) => (![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))))) <=> ((~cc(X)) | (![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~(rp(X, Y0) & rp(X, Y1) & rp(X, Y2)))) & ?[Y0: $i, Y1: $i] : (rp(X, Y0) & rp(X, Y1) & (~(Y0 = Y1)))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(31,plain,
% 0.12/0.39 (![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))) & ?[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)))) & ?[Y0: $i, Y1: $i] : (rp(X, Y0) & rp(X, Y1) & (~(Y0 = Y1)))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[30])).
% 0.12/0.39 tff(32,axiom,(![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))) & ?[Y0: $i, Y1: $i] : ((rp(X, Y0) & rp(X, Y1)) & (~(Y0 = Y1)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_2')).
% 0.12/0.39 tff(33,plain,
% 0.12/0.39 (![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)))) & ?[Y0: $i, Y1: $i] : (rp(X, Y0) & rp(X, Y1) & (~(Y0 = Y1)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.12/0.39 tff(34,plain,
% 0.12/0.39 (![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)))) & ?[Y0: $i, Y1: $i] : (rp(X, Y0) & rp(X, Y1) & (~(Y0 = Y1)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.12/0.39 tff(35,plain,(
% 0.12/0.39 ![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))))))),
% 0.12/0.39 inference(skolemize,[status(sab)],[34])).
% 0.12/0.39 tff(36,plain,
% 0.12/0.39 (![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)))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.12/0.39 tff(37,plain,
% 0.12/0.39 (![X: $i] : ((~cc(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)))) | (~rp(X, tptp_fun_Y0_1(X))) | (~rp(X, tptp_fun_Y1_0(X))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[36, 26])).
% 0.12/0.39 tff(38,plain,
% 0.12/0.39 (![X: $i] : ((~cc(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)))) | (~rp(X, tptp_fun_Y0_1(X))) | (~rp(X, tptp_fun_Y1_0(X))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[37, 24])).
% 0.12/0.39 tff(39,plain,
% 0.12/0.39 (![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)))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[38, 19])).
% 0.12/0.39 tff(40,plain,
% 0.12/0.39 (((~![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, Y1)) | (~rp(X!2, Y2)) | (~rp(X!2, Y0)))))))) <=> ((~![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, Y1)) | (~rp(X!2, Y2)) | (~rp(X!2, Y0)))))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(41,plain,
% 0.12/0.39 (((~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))))))) <=> ((~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, Y1)) | (~rp(X!2, Y2)) | (~rp(X!2, Y0)))))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(42,plain,
% 0.12/0.39 (((~![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, Y1)) | (~rp(X!2, Y2)) | (~rp(X!2, Y0))))))))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[41])).
% 0.12/0.40 tff(43,plain,
% 0.12/0.40 (((~![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, Y1)) | (~rp(X!2, Y2)) | (~rp(X!2, Y0)))))))),
% 0.12/0.40 inference(transitivity,[status(thm)],[42, 40])).
% 0.12/0.40 tff(44,plain,
% 0.12/0.40 ((~![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)))))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(45,plain,
% 0.12/0.40 ((~![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, Y1)) | (~rp(X!2, Y2)) | (~rp(X!2, Y0))))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.12/0.40 tff(46,plain,
% 0.12/0.40 (~((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, Y1)) | (~rp(X!2, Y2)) | (~rp(X!2, Y0)))))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[45, 39, 17])).
% 0.12/0.40 tff(47,plain,
% 0.12/0.40 (((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, Y1)) | (~rp(X!2, Y2)) | (~rp(X!2, Y0))))) | rp(X!2, tptp_fun_Y1_0(X!2))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(48,plain,
% 0.12/0.40 (rp(X!2, tptp_fun_Y1_0(X!2))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.12/0.40 tff(49,plain,
% 0.12/0.40 (((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, Y1)) | (~rp(X!2, Y2)) | (~rp(X!2, Y0))))) | rp(X!2, tptp_fun_Y0_1(X!2))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(50,plain,
% 0.12/0.40 (rp(X!2, tptp_fun_Y0_1(X!2))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[49, 46])).
% 0.12/0.40 tff(51,plain,
% 0.12/0.40 (((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, Y1)) | (~rp(X!2, Y2)) | (~rp(X!2, Y0))))) | (~(tptp_fun_Y0_1(X!2) = tptp_fun_Y1_0(X!2)))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(52,plain,
% 0.12/0.40 (~(tptp_fun_Y0_1(X!2) = tptp_fun_Y1_0(X!2))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[51, 46])).
% 0.12/0.40 tff(53,plain,
% 0.12/0.40 (((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, Y1)) | (~rp(X!2, Y2)) | (~rp(X!2, Y0))))) | ![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X!2, Y1)) | (~rp(X!2, Y2)) | (~rp(X!2, Y0)))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(54,plain,
% 0.12/0.40 (![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X!2, Y1)) | (~rp(X!2, Y2)) | (~rp(X!2, Y0)))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[53, 46])).
% 0.12/0.40 tff(55,assumption,(~((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)).
% 0.12/0.40 tff(56,plain,
% 0.12/0.40 (((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)),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(57,plain,
% 0.12/0.40 (rp(X!2, Y2!3)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.12/0.40 tff(58,plain,
% 0.12/0.40 (((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)),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(59,plain,
% 0.12/0.40 (rp(X!2, Y1!4)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[58, 55])).
% 0.12/0.40 tff(60,plain,
% 0.12/0.40 (((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)),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(61,plain,
% 0.12/0.40 (rp(X!2, Y0!5)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[60, 55])).
% 0.12/0.40 tff(62,plain,
% 0.12/0.40 (((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))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(63,plain,
% 0.12/0.40 (~(Y0!5 = Y2!3)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[62, 55])).
% 0.12/0.40 tff(64,plain,
% 0.12/0.40 (((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))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(65,plain,
% 0.12/0.40 (~(Y0!5 = Y1!4)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[64, 55])).
% 0.12/0.40 tff(66,plain,
% 0.12/0.40 (((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))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(67,plain,
% 0.12/0.40 (~(Y1!4 = Y2!3)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[66, 55])).
% 0.12/0.40 tff(68,plain,
% 0.12/0.40 (((~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X!2, Y1)) | (~rp(X!2, Y2)) | (~rp(X!2, Y0)))) | ((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, Y1)) | (~rp(X!2, Y2)) | (~rp(X!2, Y0)))) | (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)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(69,plain,
% 0.12/0.40 (((Y1!4 = Y2!3) | (Y0!5 = Y1!4) | (Y0!5 = Y2!3) | (~rp(X!2, Y1!4)) | (~rp(X!2, Y2!3)) | (~rp(X!2, Y0!5))) <=> ((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)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(70,plain,
% 0.12/0.40 (((~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X!2, Y1)) | (~rp(X!2, Y2)) | (~rp(X!2, Y0)))) | ((Y1!4 = Y2!3) | (Y0!5 = Y1!4) | (Y0!5 = Y2!3) | (~rp(X!2, Y1!4)) | (~rp(X!2, Y2!3)) | (~rp(X!2, Y0!5)))) <=> ((~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X!2, Y1)) | (~rp(X!2, Y2)) | (~rp(X!2, Y0)))) | ((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))))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[69])).
% 0.12/0.40 tff(71,plain,
% 0.12/0.40 (((~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X!2, Y1)) | (~rp(X!2, Y2)) | (~rp(X!2, Y0)))) | ((Y1!4 = Y2!3) | (Y0!5 = Y1!4) | (Y0!5 = Y2!3) | (~rp(X!2, Y1!4)) | (~rp(X!2, Y2!3)) | (~rp(X!2, Y0!5)))) <=> ((~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X!2, Y1)) | (~rp(X!2, Y2)) | (~rp(X!2, Y0)))) | (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)))),
% 0.12/0.40 inference(transitivity,[status(thm)],[70, 68])).
% 0.12/0.41 tff(72,plain,
% 0.12/0.41 ((~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X!2, Y1)) | (~rp(X!2, Y2)) | (~rp(X!2, Y0)))) | ((Y1!4 = Y2!3) | (Y0!5 = Y1!4) | (Y0!5 = Y2!3) | (~rp(X!2, Y1!4)) | (~rp(X!2, Y2!3)) | (~rp(X!2, Y0!5)))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(73,plain,
% 0.12/0.41 ((~![Y0: $i, Y1: $i, Y2: $i] : ((Y1 = Y2) | (Y0 = Y1) | (Y0 = Y2) | (~rp(X!2, Y1)) | (~rp(X!2, Y2)) | (~rp(X!2, Y0)))) | (Y1!4 = Y2!3) | (Y0!5 = Y1!4) | (Y0!5 = Y2!3) | (~rp(X!2, Y0!5)) | (~rp(X!2, Y1!4)) | (~rp(X!2, Y2!3))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.12/0.41 tff(74,plain,
% 0.12/0.41 ($false),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[73, 67, 65, 63, 61, 59, 57, 54])).
% 0.12/0.41 tff(75,plain,((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,[]))).
% 0.12/0.41 tff(76,plain,
% 0.12/0.41 ((![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!2, Y0)) | (~rp(X!2, Y1))) | (~((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) | (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] : ((Y0 = Y1) | (~rp(X!2, Y0)) | (~rp(X!2, Y1))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(77,plain,
% 0.12/0.41 ((~((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) | (Y0!5 = Y1!4) | (Y0!5 = Y2!3) | (~rp(X!2, Y0!5)) | (~rp(X!2, Y1!4)) | (~rp(X!2, Y2!3))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(78,plain,
% 0.12/0.41 ((![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!2, Y0)) | (~rp(X!2, Y1))) | (~((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] : ((Y0 = Y1) | (~rp(X!2, Y0)) | (~rp(X!2, Y1))) | (~((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)))))),
% 0.12/0.41 inference(monotonicity,[status(thm)],[77])).
% 0.12/0.41 tff(79,plain,
% 0.12/0.41 ((![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!2, Y0)) | (~rp(X!2, Y1))) | (~((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) | (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] : ((Y0 = Y1) | (~rp(X!2, Y0)) | (~rp(X!2, Y1))))),
% 0.12/0.41 inference(transitivity,[status(thm)],[78, 76])).
% 0.12/0.41 tff(80,plain,
% 0.12/0.41 ((![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!2, Y0)) | (~rp(X!2, Y1))) | (~((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] : ((Y0 = Y1) | (~rp(X!2, Y0)) | (~rp(X!2, Y1))) | (~((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)))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(81,plain,
% 0.12/0.41 ((![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!2, Y0)) | (~rp(X!2, Y1))) | (~((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] : ((Y0 = Y1) | (~rp(X!2, Y0)) | (~rp(X!2, Y1))) | (~((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)))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(82,plain,
% 0.12/0.41 ((~((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) | (Y0!5 = Y1!4) | (Y0!5 = Y2!3) | (~rp(X!2, Y0!5)) | (~rp(X!2, Y1!4)) | (~rp(X!2, Y2!3))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(83,plain,
% 0.12/0.41 (^[Y0: $i, Y1: $i] : trans(monotonicity(rewrite((rp(X!2, Y0) & rp(X!2, Y1) & (~(Y0 = Y1))) <=> (~((Y0 = Y1) | (~rp(X!2, Y0)) | (~rp(X!2, Y1))))), ((~(rp(X!2, Y0) & rp(X!2, Y1) & (~(Y0 = Y1)))) <=> (~(~((Y0 = Y1) | (~rp(X!2, Y0)) | (~rp(X!2, Y1))))))), rewrite((~(~((Y0 = Y1) | (~rp(X!2, Y0)) | (~rp(X!2, Y1))))) <=> ((Y0 = Y1) | (~rp(X!2, Y0)) | (~rp(X!2, Y1)))), ((~(rp(X!2, Y0) & rp(X!2, Y1) & (~(Y0 = Y1)))) <=> ((Y0 = Y1) | (~rp(X!2, Y0)) | (~rp(X!2, Y1)))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(84,plain,
% 0.19/0.41 (![Y0: $i, Y1: $i] : (~(rp(X!2, Y0) & rp(X!2, Y1) & (~(Y0 = Y1)))) <=> ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!2, Y0)) | (~rp(X!2, Y1)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[83])).
% 0.19/0.41 tff(85,plain,
% 0.19/0.41 ((![Y0: $i, Y1: $i] : (~(rp(X!2, Y0) & rp(X!2, Y1) & (~(Y0 = Y1)))) | (~((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] : ((Y0 = Y1) | (~rp(X!2, Y0)) | (~rp(X!2, Y1))) | (~((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)))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[84, 82])).
% 0.19/0.41 tff(86,plain,
% 0.19/0.41 ((![Y0: $i, Y1: $i] : (~(rp(X!2, Y0) & rp(X!2, Y1) & (~(Y0 = Y1)))) | (~((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] : ((Y0 = Y1) | (~rp(X!2, Y0)) | (~rp(X!2, Y1))) | (~((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)))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[85, 81])).
% 0.19/0.41 tff(87,plain,
% 0.19/0.41 (![Y0: $i, Y1: $i] : (~(rp(X!2, Y0) & rp(X!2, Y1) & (~(Y0 = Y1)))) | (~((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)))))),
% 0.19/0.41 inference(and_elim,[status(thm)],[16])).
% 0.19/0.41 tff(88,plain,
% 0.19/0.41 (![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!2, Y0)) | (~rp(X!2, Y1))) | (~((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))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.19/0.41 tff(89,plain,
% 0.19/0.41 (![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!2, Y0)) | (~rp(X!2, Y1))) | (~((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))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[88, 80])).
% 0.19/0.41 tff(90,plain,
% 0.19/0.41 ((~((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] : ((Y0 = Y1) | (~rp(X!2, Y0)) | (~rp(X!2, Y1)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[89, 79])).
% 0.19/0.41 tff(91,plain,
% 0.19/0.41 (![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!2, Y0)) | (~rp(X!2, Y1)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[90, 75])).
% 0.19/0.41 tff(92,plain,
% 0.19/0.41 (((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!2, Y0)) | (~rp(X!2, Y1)))) | ((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] : ((Y0 = Y1) | (~rp(X!2, Y0)) | (~rp(X!2, Y1)))) | (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))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(93,plain,
% 0.19/0.41 ((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!2, Y0)) | (~rp(X!2, Y1)))) | ((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))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(94,plain,
% 0.19/0.41 ((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!2, Y0)) | (~rp(X!2, Y1)))) | (tptp_fun_Y0_1(X!2) = tptp_fun_Y1_0(X!2)) | (~rp(X!2, tptp_fun_Y0_1(X!2))) | (~rp(X!2, tptp_fun_Y1_0(X!2)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.19/0.41 tff(95,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[94, 91, 52, 50, 48])).
% 0.19/0.41 % SZS output end Proof
%------------------------------------------------------------------------------