TSTP Solution File: KRS143+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KRS143+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.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 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KRS143+1 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.32 % Computer : n005.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Thu Sep 1 09:37:48 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -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_Y0_0_type, type, (
% 0.12/0.38 tptp_fun_Y0_0: $i > $i)).
% 0.12/0.38 tff(tptp_fun_X_1_type, type, (
% 0.12/0.38 tptp_fun_X_1: $i)).
% 0.12/0.38 tff(cc_type, type, (
% 0.12/0.38 cc: $i > $o)).
% 0.12/0.38 tff(tptp_fun_Y1_2_type, type, (
% 0.12/0.38 tptp_fun_Y1_2: $i)).
% 0.12/0.38 tff(tptp_fun_Y0_3_type, type, (
% 0.12/0.38 tptp_fun_Y0_3: $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!1))) & (![Y0: $i] : (~rp(X!1, Y0)) | (~((~(rp(X!1, Y0!3) & rp(X!1, Y1!2))) | (Y0!3 = Y1!2))))) <=> (cc(X!1) & (![Y0: $i] : (~rp(X!1, Y0)) | (~((~(rp(X!1, Y0!3) & rp(X!1, Y1!2))) | (Y0!3 = Y1!2)))))),
% 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] : rp(X, Y0) & ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1))))) <=> (~![X: $i] : ((~cc(X)) | (?[Y0: $i] : rp(X, Y0) & ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1)))))),
% 0.12/0.38 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] : rp(X, Y0) & ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1)))))) <=> (~![X: $i] : ((~cc(X)) | (?[Y0: $i] : rp(X, Y0) & ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1)))))),
% 0.12/0.38 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] : rp(X, Y0) & ![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] : rp(X, Y0) & ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1)))))),
% 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] : rp(X, Y0) & ![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] : rp(X, Y0) & ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1))))))),
% 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] : rp(X, Y0) & ![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] : rp(X, Y0) & ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1))))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(7,axiom,(~((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X)))) & ![X: $i] : (cc(X) => (?[Y0: $i] : rp(X, Y0) & ![Y0: $i, Y1: $i] : ((rp(X, Y0) & rp(X, Y1)) => (Y0 = Y1)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','the_axiom')).
% 0.12/0.38 tff(8,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] : rp(X, Y0) & ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1)))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.12/0.38 tff(9,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] : rp(X, Y0) & ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1)))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 (~![X: $i] : ((~cc(X)) | (?[Y0: $i] : rp(X, Y0) & ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[9, 3])).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 (~![X: $i] : ((~cc(X)) | (?[Y0: $i] : rp(X, Y0) & ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 (~![X: $i] : ((~cc(X)) | (?[Y0: $i] : rp(X, Y0) & ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[11, 2])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (~![X: $i] : ((~cc(X)) | (?[Y0: $i] : rp(X, Y0) & ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 (~![X: $i] : ((~cc(X)) | (?[Y0: $i] : rp(X, Y0) & ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[13, 2])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (~![X: $i] : ((~cc(X)) | (?[Y0: $i] : rp(X, Y0) & ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[14, 2])).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 (cc(X!1) & (![Y0: $i] : (~rp(X!1, Y0)) | (~((~(rp(X!1, Y0!3) & rp(X!1, Y1!2))) | (Y0!3 = Y1!2))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[15, 1])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 (cc(X!1)),
% 0.12/0.38 inference(and_elim,[status(thm)],[16])).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 (^[X: $i] : refl(((~cc(X)) | rp(X, tptp_fun_Y0_0(X))) <=> ((~cc(X)) | rp(X, tptp_fun_Y0_0(X))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (![X: $i] : ((~cc(X)) | rp(X, tptp_fun_Y0_0(X))) <=> ![X: $i] : ((~cc(X)) | rp(X, tptp_fun_Y0_0(X)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[18])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 (![X: $i] : ((~cc(X)) | ?[Y0: $i] : rp(X, Y0)) <=> ![X: $i] : ((~cc(X)) | ?[Y0: $i] : rp(X, Y0))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 (^[X: $i] : rewrite((cc(X) => ?[Y0: $i] : rp(X, Y0)) <=> ((~cc(X)) | ?[Y0: $i] : rp(X, Y0)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 (![X: $i] : (cc(X) => ?[Y0: $i] : rp(X, Y0)) <=> ![X: $i] : ((~cc(X)) | ?[Y0: $i] : rp(X, Y0))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[21])).
% 0.12/0.38 tff(23,axiom,(![X: $i] : (cc(X) => ?[Y0: $i] : rp(X, Y0))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_2')).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 (![X: $i] : ((~cc(X)) | ?[Y0: $i] : rp(X, Y0))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 (![X: $i] : ((~cc(X)) | ?[Y0: $i] : rp(X, Y0))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.12/0.38 tff(26,plain,(
% 0.12/0.38 ![X: $i] : ((~cc(X)) | rp(X, tptp_fun_Y0_0(X)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[25])).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 (![X: $i] : ((~cc(X)) | rp(X, tptp_fun_Y0_0(X)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.12/0.38 tff(28,plain,
% 0.12/0.38 (((~![X: $i] : ((~cc(X)) | rp(X, tptp_fun_Y0_0(X)))) | ((~cc(X!1)) | rp(X!1, tptp_fun_Y0_0(X!1)))) <=> ((~![X: $i] : ((~cc(X)) | rp(X, tptp_fun_Y0_0(X)))) | (~cc(X!1)) | rp(X!1, tptp_fun_Y0_0(X!1)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(29,plain,
% 0.12/0.38 ((~![X: $i] : ((~cc(X)) | rp(X, tptp_fun_Y0_0(X)))) | ((~cc(X!1)) | rp(X!1, tptp_fun_Y0_0(X!1)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 ((~![X: $i] : ((~cc(X)) | rp(X, tptp_fun_Y0_0(X)))) | (~cc(X!1)) | rp(X!1, tptp_fun_Y0_0(X!1))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.12/0.38 tff(31,plain,
% 0.12/0.38 (rp(X!1, tptp_fun_Y0_0(X!1))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[30, 27, 17])).
% 0.12/0.38 tff(32,plain,
% 0.12/0.38 (^[X: $i] : refl(((~cc(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y1)) | (~rp(X, Y0)))) <=> ((~cc(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y1)) | (~rp(X, Y0)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(33,plain,
% 0.12/0.38 (![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y1)) | (~rp(X, Y0)))) <=> ![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y1)) | (~rp(X, Y0))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[32])).
% 0.12/0.38 tff(34,plain,
% 0.12/0.38 (^[X: $i] : rewrite(((~cc(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y1)) | (~rp(X, Y0)))) <=> ((~cc(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y1)) | (~rp(X, Y0)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(35,plain,
% 0.12/0.38 (![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y1)) | (~rp(X, Y0)))) <=> ![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y1)) | (~rp(X, Y0))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[34])).
% 0.12/0.38 tff(36,plain,
% 0.12/0.38 (![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y1)) | (~rp(X, Y0)))) <=> ![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y1)) | (~rp(X, Y0))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[35, 33])).
% 0.12/0.38 tff(37,plain,
% 0.12/0.38 (^[X: $i] : rewrite(((~cc(X)) | ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1))) <=> ((~cc(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y1)) | (~rp(X, Y0)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(38,plain,
% 0.12/0.38 (![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1))) <=> ![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y1)) | (~rp(X, Y0))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[37])).
% 0.12/0.38 tff(39,plain,
% 0.12/0.38 (![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1))) <=> ![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(40,plain,
% 0.12/0.38 (^[X: $i] : trans(monotonicity(quant_intro(proof_bind(^[Y0: $i, Y1: $i] : rewrite(((rp(X, Y0) & rp(X, Y1)) => (Y0 = Y1)) <=> ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1)))), (![Y0: $i, Y1: $i] : ((rp(X, Y0) & rp(X, Y1)) => (Y0 = Y1)) <=> ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1)))), ((cc(X) => ![Y0: $i, Y1: $i] : ((rp(X, Y0) & rp(X, Y1)) => (Y0 = Y1))) <=> (cc(X) => ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1))))), rewrite((cc(X) => ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1))) <=> ((~cc(X)) | ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1)))), ((cc(X) => ![Y0: $i, Y1: $i] : ((rp(X, Y0) & rp(X, Y1)) => (Y0 = Y1))) <=> ((~cc(X)) | ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(41,plain,
% 0.12/0.38 (![X: $i] : (cc(X) => ![Y0: $i, Y1: $i] : ((rp(X, Y0) & rp(X, Y1)) => (Y0 = Y1))) <=> ![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[40])).
% 0.12/0.38 tff(42,axiom,(![X: $i] : (cc(X) => ![Y0: $i, Y1: $i] : ((rp(X, Y0) & rp(X, Y1)) => (Y0 = Y1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_3')).
% 0.12/0.38 tff(43,plain,
% 0.12/0.38 (![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.12/0.38 tff(44,plain,
% 0.12/0.38 (![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.12/0.38 tff(45,plain,(
% 0.12/0.38 ![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i] : ((~(rp(X, Y0) & rp(X, Y1))) | (Y0 = Y1)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[44])).
% 0.12/0.38 tff(46,plain,
% 0.12/0.38 (![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y1)) | (~rp(X, Y0))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[45, 38])).
% 0.12/0.38 tff(47,plain,
% 0.12/0.38 (![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y1)) | (~rp(X, Y0))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[46, 36])).
% 0.12/0.38 tff(48,plain,
% 0.12/0.38 (((~![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y1)) | (~rp(X, Y0))))) | ((~cc(X!1)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!1, Y1)) | (~rp(X!1, Y0))))) <=> ((~![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y1)) | (~rp(X, Y0))))) | (~cc(X!1)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!1, Y1)) | (~rp(X!1, Y0))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(49,plain,
% 0.12/0.38 ((~![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y1)) | (~rp(X, Y0))))) | ((~cc(X!1)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!1, Y1)) | (~rp(X!1, Y0))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(50,plain,
% 0.12/0.38 ((~![X: $i] : ((~cc(X)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X, Y1)) | (~rp(X, Y0))))) | (~cc(X!1)) | ![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!1, Y1)) | (~rp(X!1, Y0)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.12/0.38 tff(51,plain,
% 0.12/0.38 (![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!1, Y1)) | (~rp(X!1, Y0)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[50, 47, 17])).
% 0.18/0.39 tff(52,assumption,(~((Y0!3 = Y1!2) | (~rp(X!1, Y0!3)) | (~rp(X!1, Y1!2)))), introduced(assumption)).
% 0.18/0.39 tff(53,plain,
% 0.18/0.39 (((Y0!3 = Y1!2) | (~rp(X!1, Y0!3)) | (~rp(X!1, Y1!2))) | rp(X!1, Y1!2)),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(54,plain,
% 0.18/0.39 (rp(X!1, Y1!2)),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.18/0.39 tff(55,plain,
% 0.18/0.39 (((Y0!3 = Y1!2) | (~rp(X!1, Y0!3)) | (~rp(X!1, Y1!2))) | rp(X!1, Y0!3)),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(56,plain,
% 0.18/0.39 (rp(X!1, Y0!3)),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[55, 52])).
% 0.18/0.39 tff(57,plain,
% 0.18/0.39 (((Y0!3 = Y1!2) | (~rp(X!1, Y0!3)) | (~rp(X!1, Y1!2))) | (~(Y0!3 = Y1!2))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(58,plain,
% 0.18/0.39 (~(Y0!3 = Y1!2)),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[57, 52])).
% 0.18/0.39 tff(59,plain,
% 0.18/0.39 (((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!1, Y1)) | (~rp(X!1, Y0)))) | ((Y0!3 = Y1!2) | (~rp(X!1, Y0!3)) | (~rp(X!1, Y1!2)))) <=> ((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!1, Y1)) | (~rp(X!1, Y0)))) | (Y0!3 = Y1!2) | (~rp(X!1, Y0!3)) | (~rp(X!1, Y1!2)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(60,plain,
% 0.18/0.39 (((Y0!3 = Y1!2) | (~rp(X!1, Y1!2)) | (~rp(X!1, Y0!3))) <=> ((Y0!3 = Y1!2) | (~rp(X!1, Y0!3)) | (~rp(X!1, Y1!2)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(61,plain,
% 0.18/0.39 (((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!1, Y1)) | (~rp(X!1, Y0)))) | ((Y0!3 = Y1!2) | (~rp(X!1, Y1!2)) | (~rp(X!1, Y0!3)))) <=> ((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!1, Y1)) | (~rp(X!1, Y0)))) | ((Y0!3 = Y1!2) | (~rp(X!1, Y0!3)) | (~rp(X!1, Y1!2))))),
% 0.18/0.39 inference(monotonicity,[status(thm)],[60])).
% 0.18/0.39 tff(62,plain,
% 0.18/0.39 (((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!1, Y1)) | (~rp(X!1, Y0)))) | ((Y0!3 = Y1!2) | (~rp(X!1, Y1!2)) | (~rp(X!1, Y0!3)))) <=> ((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!1, Y1)) | (~rp(X!1, Y0)))) | (Y0!3 = Y1!2) | (~rp(X!1, Y0!3)) | (~rp(X!1, Y1!2)))),
% 0.18/0.39 inference(transitivity,[status(thm)],[61, 59])).
% 0.18/0.39 tff(63,plain,
% 0.18/0.39 ((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!1, Y1)) | (~rp(X!1, Y0)))) | ((Y0!3 = Y1!2) | (~rp(X!1, Y1!2)) | (~rp(X!1, Y0!3)))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(64,plain,
% 0.18/0.39 ((~![Y0: $i, Y1: $i] : ((Y0 = Y1) | (~rp(X!1, Y1)) | (~rp(X!1, Y0)))) | (Y0!3 = Y1!2) | (~rp(X!1, Y0!3)) | (~rp(X!1, Y1!2))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.18/0.39 tff(65,plain,
% 0.18/0.39 ($false),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[64, 58, 56, 54, 51])).
% 0.18/0.39 tff(66,plain,((Y0!3 = Y1!2) | (~rp(X!1, Y0!3)) | (~rp(X!1, Y1!2))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.39 tff(67,plain,
% 0.18/0.39 ((![Y0: $i] : (~rp(X!1, Y0)) | (~((Y0!3 = Y1!2) | (~rp(X!1, Y0!3)) | (~rp(X!1, Y1!2))))) <=> ((~((Y0!3 = Y1!2) | (~rp(X!1, Y0!3)) | (~rp(X!1, Y1!2)))) | ![Y0: $i] : (~rp(X!1, Y0)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(68,plain,
% 0.18/0.39 ((~((Y0!3 = Y1!2) | (~rp(X!1, Y0!3)) | (~rp(X!1, Y1!2)))) <=> (~((Y0!3 = Y1!2) | (~rp(X!1, Y0!3)) | (~rp(X!1, Y1!2))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(69,plain,
% 0.18/0.39 ((![Y0: $i] : (~rp(X!1, Y0)) | (~((Y0!3 = Y1!2) | (~rp(X!1, Y0!3)) | (~rp(X!1, Y1!2))))) <=> (![Y0: $i] : (~rp(X!1, Y0)) | (~((Y0!3 = Y1!2) | (~rp(X!1, Y0!3)) | (~rp(X!1, Y1!2)))))),
% 0.18/0.39 inference(monotonicity,[status(thm)],[68])).
% 0.18/0.39 tff(70,plain,
% 0.18/0.39 ((![Y0: $i] : (~rp(X!1, Y0)) | (~((Y0!3 = Y1!2) | (~rp(X!1, Y0!3)) | (~rp(X!1, Y1!2))))) <=> ((~((Y0!3 = Y1!2) | (~rp(X!1, Y0!3)) | (~rp(X!1, Y1!2)))) | ![Y0: $i] : (~rp(X!1, Y0)))),
% 0.18/0.39 inference(transitivity,[status(thm)],[69, 67])).
% 0.18/0.39 tff(71,plain,
% 0.18/0.39 ((![Y0: $i] : (~rp(X!1, Y0)) | (~((Y0!3 = Y1!2) | (~rp(X!1, Y0!3)) | (~rp(X!1, Y1!2))))) <=> (![Y0: $i] : (~rp(X!1, Y0)) | (~((Y0!3 = Y1!2) | (~rp(X!1, Y0!3)) | (~rp(X!1, Y1!2)))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(72,plain,
% 0.18/0.39 ((![Y0: $i] : (~rp(X!1, Y0)) | (~((Y0!3 = Y1!2) | (~rp(X!1, Y0!3)) | (~rp(X!1, Y1!2))))) <=> (![Y0: $i] : (~rp(X!1, Y0)) | (~((Y0!3 = Y1!2) | (~rp(X!1, Y0!3)) | (~rp(X!1, Y1!2)))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(73,plain,
% 0.18/0.39 ((~((~(rp(X!1, Y0!3) & rp(X!1, Y1!2))) | (Y0!3 = Y1!2))) <=> (~((Y0!3 = Y1!2) | (~rp(X!1, Y0!3)) | (~rp(X!1, Y1!2))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(74,plain,
% 0.18/0.39 ((![Y0: $i] : (~rp(X!1, Y0)) | (~((~(rp(X!1, Y0!3) & rp(X!1, Y1!2))) | (Y0!3 = Y1!2)))) <=> (![Y0: $i] : (~rp(X!1, Y0)) | (~((Y0!3 = Y1!2) | (~rp(X!1, Y0!3)) | (~rp(X!1, Y1!2)))))),
% 0.18/0.39 inference(monotonicity,[status(thm)],[73])).
% 0.18/0.39 tff(75,plain,
% 0.18/0.39 ((![Y0: $i] : (~rp(X!1, Y0)) | (~((~(rp(X!1, Y0!3) & rp(X!1, Y1!2))) | (Y0!3 = Y1!2)))) <=> (![Y0: $i] : (~rp(X!1, Y0)) | (~((Y0!3 = Y1!2) | (~rp(X!1, Y0!3)) | (~rp(X!1, Y1!2)))))),
% 0.18/0.39 inference(transitivity,[status(thm)],[74, 72])).
% 0.18/0.39 tff(76,plain,
% 0.18/0.39 (![Y0: $i] : (~rp(X!1, Y0)) | (~((~(rp(X!1, Y0!3) & rp(X!1, Y1!2))) | (Y0!3 = Y1!2)))),
% 0.18/0.39 inference(and_elim,[status(thm)],[16])).
% 0.18/0.39 tff(77,plain,
% 0.18/0.39 (![Y0: $i] : (~rp(X!1, Y0)) | (~((Y0!3 = Y1!2) | (~rp(X!1, Y0!3)) | (~rp(X!1, Y1!2))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.18/0.39 tff(78,plain,
% 0.18/0.39 (![Y0: $i] : (~rp(X!1, Y0)) | (~((Y0!3 = Y1!2) | (~rp(X!1, Y0!3)) | (~rp(X!1, Y1!2))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[77, 71])).
% 0.18/0.39 tff(79,plain,
% 0.18/0.39 ((~((Y0!3 = Y1!2) | (~rp(X!1, Y0!3)) | (~rp(X!1, Y1!2)))) | ![Y0: $i] : (~rp(X!1, Y0))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[78, 70])).
% 0.18/0.39 tff(80,plain,
% 0.18/0.39 (![Y0: $i] : (~rp(X!1, Y0))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[79, 66])).
% 0.18/0.39 tff(81,plain,
% 0.18/0.39 ((~![Y0: $i] : (~rp(X!1, Y0))) | (~rp(X!1, tptp_fun_Y0_0(X!1)))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(82,plain,
% 0.18/0.39 ($false),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[81, 80, 31])).
% 0.18/0.39 % SZS output end Proof
%------------------------------------------------------------------------------