TSTP Solution File: KRS172+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KRS172+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 17:45:04 EDT 2022
% Result : Theorem 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : KRS172+1 : TPTP v8.1.0. Released v3.1.0.
% 0.13/0.13 % 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 09:38:04 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.19/0.35 Usage: tptp [options] [-file:]file
% 0.19/0.35 -h, -? prints this message.
% 0.19/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.19/0.35 -m, -model generate model.
% 0.19/0.35 -p, -proof generate proof.
% 0.19/0.35 -c, -core generate unsat core of named formulas.
% 0.19/0.35 -st, -statistics display statistics.
% 0.19/0.35 -t:timeout set timeout (in second).
% 0.19/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.19/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.19/0.35 -<param>:<value> configuration parameter and value.
% 0.19/0.35 -o:<output-file> file to place output in.
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 tff(tptp_fun_Y_0_type, type, (
% 0.19/0.39 tptp_fun_Y_0: $i)).
% 0.19/0.39 tff(iv_type, type, (
% 0.19/0.39 iv: $i)).
% 0.19/0.39 tff(rp_type, type, (
% 0.19/0.39 rp: ( $i * $i ) > $o)).
% 0.19/0.39 tff(tptp_fun_X_1_type, type, (
% 0.19/0.39 tptp_fun_X_1: $i)).
% 0.19/0.39 tff(cd_type, type, (
% 0.19/0.39 cd: $i > $o)).
% 0.19/0.39 tff(rq_type, type, (
% 0.19/0.39 rq: ( $i * $i ) > $o)).
% 0.19/0.39 tff(xsd_integer_type, type, (
% 0.19/0.39 xsd_integer: $i > $o)).
% 0.19/0.39 tff(xsd_string_type, type, (
% 0.19/0.39 xsd_string: $i > $o)).
% 0.19/0.39 tff(cowlNothing_type, type, (
% 0.19/0.39 cowlNothing: $i > $o)).
% 0.19/0.39 tff(cowlThing_type, type, (
% 0.19/0.39 cowlThing: $i > $o)).
% 0.19/0.39 tff(1,plain,
% 0.19/0.39 (^[X: $i] : refl((cd(X) <=> rp(X, iv)) <=> (cd(X) <=> rp(X, iv)))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(2,plain,
% 0.19/0.39 (![X: $i] : (cd(X) <=> rp(X, iv)) <=> ![X: $i] : (cd(X) <=> rp(X, iv))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.39 tff(3,plain,
% 0.19/0.39 (![X: $i] : (cd(X) <=> rp(X, iv)) <=> ![X: $i] : (cd(X) <=> rp(X, iv))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(4,axiom,(![X: $i] : (cd(X) <=> rp(X, iv))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_3')).
% 0.19/0.39 tff(5,plain,
% 0.19/0.39 (![X: $i] : (cd(X) <=> rp(X, iv))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.39 tff(6,plain,(
% 0.19/0.39 ![X: $i] : (cd(X) <=> rp(X, iv))),
% 0.19/0.39 inference(skolemize,[status(sab)],[5])).
% 0.19/0.39 tff(7,plain,
% 0.19/0.39 (![X: $i] : (cd(X) <=> rp(X, iv))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.39 tff(8,plain,
% 0.19/0.39 ((~![X: $i] : (cd(X) <=> rp(X, iv))) | (cd(X!1) <=> rp(X!1, iv))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(9,plain,
% 0.19/0.39 (cd(X!1) <=> rp(X!1, iv)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.39 tff(10,assumption,(~rp(X!1, Y!0)), introduced(assumption)).
% 0.19/0.39 tff(11,plain,
% 0.19/0.39 ((~(rq(X!1, Y!0) <=> rp(X!1, Y!0))) <=> ((~rq(X!1, Y!0)) <=> rp(X!1, Y!0))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(12,plain,
% 0.19/0.39 ((~![X: $i, Y: $i] : (rq(X, Y) <=> rp(X, Y))) <=> (~![X: $i, Y: $i] : (rq(X, Y) <=> rp(X, Y)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(13,plain,
% 0.19/0.39 ((~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![X: $i, Y: $i] : (rq(X, Y) <=> rp(X, Y)))) <=> (~![X: $i, Y: $i] : (rq(X, Y) <=> rp(X, Y)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(14,plain,
% 0.19/0.39 ((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![X: $i, Y: $i] : (rq(X, Y) <=> rp(X, Y))) <=> (![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![X: $i, Y: $i] : (rq(X, Y) <=> rp(X, Y)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(15,plain,
% 0.19/0.39 ((~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![X: $i, Y: $i] : (rq(X, Y) <=> rp(X, Y)))) <=> (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![X: $i, Y: $i] : (rq(X, Y) <=> rp(X, Y))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[14])).
% 0.19/0.39 tff(16,plain,
% 0.19/0.39 ((~((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X)))) & ![X: $i, Y: $i] : (rq(X, Y) <=> rp(X, Y)))) <=> (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![X: $i, Y: $i] : (rq(X, Y) <=> rp(X, Y))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(17,axiom,(~((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X)))) & ![X: $i, Y: $i] : (rq(X, Y) <=> rp(X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','the_axiom')).
% 0.19/0.39 tff(18,plain,
% 0.19/0.39 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![X: $i, Y: $i] : (rq(X, Y) <=> rp(X, Y)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.19/0.39 tff(19,plain,
% 0.19/0.39 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![X: $i, Y: $i] : (rq(X, Y) <=> rp(X, Y)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[18, 15])).
% 0.19/0.39 tff(20,plain,
% 0.19/0.39 (~![X: $i, Y: $i] : (rq(X, Y) <=> rp(X, Y))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[19, 13])).
% 0.19/0.39 tff(21,plain,
% 0.19/0.39 (~![X: $i, Y: $i] : (rq(X, Y) <=> rp(X, Y))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[20, 12])).
% 0.19/0.40 tff(22,plain,
% 0.19/0.40 (~![X: $i, Y: $i] : (rq(X, Y) <=> rp(X, Y))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[21, 12])).
% 0.19/0.40 tff(23,plain,
% 0.19/0.40 (~![X: $i, Y: $i] : (rq(X, Y) <=> rp(X, Y))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[22, 12])).
% 0.19/0.40 tff(24,plain,
% 0.19/0.40 (~![X: $i, Y: $i] : (rq(X, Y) <=> rp(X, Y))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[23, 12])).
% 0.19/0.40 tff(25,plain,
% 0.19/0.40 (~![X: $i, Y: $i] : (rq(X, Y) <=> rp(X, Y))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[24, 12])).
% 0.19/0.40 tff(26,plain,(
% 0.19/0.40 ~(rq(X!1, Y!0) <=> rp(X!1, Y!0))),
% 0.19/0.40 inference(skolemize,[status(sab)],[25])).
% 0.19/0.40 tff(27,plain,
% 0.19/0.40 ((~rq(X!1, Y!0)) <=> rp(X!1, Y!0)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[26, 11])).
% 0.19/0.40 tff(28,plain,
% 0.19/0.40 (rq(X!1, Y!0) | rp(X!1, Y!0) | (~((~rq(X!1, Y!0)) <=> rp(X!1, Y!0)))),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(29,plain,
% 0.19/0.40 (rq(X!1, Y!0) | rp(X!1, Y!0)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.19/0.40 tff(30,plain,
% 0.19/0.40 (rq(X!1, Y!0)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[29, 10])).
% 0.19/0.40 tff(31,plain,
% 0.19/0.40 (^[X: $i, Y: $i] : refl((cd(X) | (~rq(X, Y))) <=> (cd(X) | (~rq(X, Y))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(32,plain,
% 0.19/0.40 (![X: $i, Y: $i] : (cd(X) | (~rq(X, Y))) <=> ![X: $i, Y: $i] : (cd(X) | (~rq(X, Y)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[31])).
% 0.19/0.40 tff(33,plain,
% 0.19/0.40 (![X: $i, Y: $i] : (cd(X) | (~rq(X, Y))) <=> ![X: $i, Y: $i] : (cd(X) | (~rq(X, Y)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(34,plain,
% 0.19/0.40 (^[X: $i, Y: $i] : rewrite((rq(X, Y) => cd(X)) <=> (cd(X) | (~rq(X, Y))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(35,plain,
% 0.19/0.40 (![X: $i, Y: $i] : (rq(X, Y) => cd(X)) <=> ![X: $i, Y: $i] : (cd(X) | (~rq(X, Y)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[34])).
% 0.19/0.40 tff(36,axiom,(![X: $i, Y: $i] : (rq(X, Y) => cd(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_7')).
% 0.19/0.40 tff(37,plain,
% 0.19/0.40 (![X: $i, Y: $i] : (cd(X) | (~rq(X, Y)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.19/0.40 tff(38,plain,
% 0.19/0.40 (![X: $i, Y: $i] : (cd(X) | (~rq(X, Y)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.19/0.40 tff(39,plain,(
% 0.19/0.40 ![X: $i, Y: $i] : (cd(X) | (~rq(X, Y)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[38])).
% 0.19/0.40 tff(40,plain,
% 0.19/0.40 (![X: $i, Y: $i] : (cd(X) | (~rq(X, Y)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.19/0.40 tff(41,plain,
% 0.19/0.40 (((~![X: $i, Y: $i] : (cd(X) | (~rq(X, Y)))) | (cd(X!1) | (~rq(X!1, Y!0)))) <=> ((~![X: $i, Y: $i] : (cd(X) | (~rq(X, Y)))) | cd(X!1) | (~rq(X!1, Y!0)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(42,plain,
% 0.19/0.40 ((~![X: $i, Y: $i] : (cd(X) | (~rq(X, Y)))) | (cd(X!1) | (~rq(X!1, Y!0)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(43,plain,
% 0.19/0.40 ((~![X: $i, Y: $i] : (cd(X) | (~rq(X, Y)))) | cd(X!1) | (~rq(X!1, Y!0))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.19/0.40 tff(44,plain,
% 0.19/0.40 (cd(X!1) | (~rq(X!1, Y!0))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[43, 40])).
% 0.19/0.40 tff(45,plain,
% 0.19/0.40 (cd(X!1)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[44, 30])).
% 0.19/0.40 tff(46,plain,
% 0.19/0.40 ((~(cd(X!1) <=> rp(X!1, iv))) | (~cd(X!1)) | rp(X!1, iv)),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(47,plain,
% 0.19/0.40 ((~(cd(X!1) <=> rp(X!1, iv))) | rp(X!1, iv)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.19/0.40 tff(48,plain,
% 0.19/0.40 (rp(X!1, iv)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[47, 9])).
% 0.19/0.40 tff(49,plain,
% 0.19/0.40 (^[A: $i, B: $i, C: $i] : refl((rp(C, B) | (~(A = B)) | (~rp(C, A))) <=> (rp(C, B) | (~(A = B)) | (~rp(C, A))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(50,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i] : (rp(C, B) | (~(A = B)) | (~rp(C, A))) <=> ![A: $i, B: $i, C: $i] : (rp(C, B) | (~(A = B)) | (~rp(C, A)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[49])).
% 0.19/0.40 tff(51,plain,
% 0.19/0.40 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((A = B) & rp(C, A)) <=> (~((~(A = B)) | (~rp(C, A))))), ((~((A = B) & rp(C, A))) <=> (~(~((~(A = B)) | (~rp(C, A))))))), rewrite((~(~((~(A = B)) | (~rp(C, A))))) <=> ((~(A = B)) | (~rp(C, A)))), ((~((A = B) & rp(C, A))) <=> ((~(A = B)) | (~rp(C, A))))), (((~((A = B) & rp(C, A))) | rp(C, B)) <=> (((~(A = B)) | (~rp(C, A))) | rp(C, B)))), rewrite((((~(A = B)) | (~rp(C, A))) | rp(C, B)) <=> (rp(C, B) | (~(A = B)) | (~rp(C, A)))), (((~((A = B) & rp(C, A))) | rp(C, B)) <=> (rp(C, B) | (~(A = B)) | (~rp(C, A)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(52,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i] : ((~((A = B) & rp(C, A))) | rp(C, B)) <=> ![A: $i, B: $i, C: $i] : (rp(C, B) | (~(A = B)) | (~rp(C, A)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[51])).
% 0.19/0.40 tff(53,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i] : ((~((A = B) & rp(C, A))) | rp(C, B)) <=> ![A: $i, B: $i, C: $i] : ((~((A = B) & rp(C, A))) | rp(C, B))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(54,plain,
% 0.19/0.40 (^[A: $i, B: $i, C: $i] : rewrite((((A = B) & rp(C, A)) => rp(C, B)) <=> ((~((A = B) & rp(C, A))) | rp(C, B)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(55,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i] : (((A = B) & rp(C, A)) => rp(C, B)) <=> ![A: $i, B: $i, C: $i] : ((~((A = B) & rp(C, A))) | rp(C, B))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[54])).
% 0.19/0.40 tff(56,axiom,(![A: $i, B: $i, C: $i] : (((A = B) & rp(C, A)) => rp(C, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rp_substitution_2')).
% 0.19/0.40 tff(57,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i] : ((~((A = B) & rp(C, A))) | rp(C, B))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.19/0.40 tff(58,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i] : ((~((A = B) & rp(C, A))) | rp(C, B))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.19/0.40 tff(59,plain,(
% 0.19/0.40 ![A: $i, B: $i, C: $i] : ((~((A = B) & rp(C, A))) | rp(C, B))),
% 0.19/0.40 inference(skolemize,[status(sab)],[58])).
% 0.19/0.40 tff(60,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i] : (rp(C, B) | (~(A = B)) | (~rp(C, A)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.19/0.40 tff(61,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i] : (rp(C, B) | (~(A = B)) | (~rp(C, A)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[60, 50])).
% 0.19/0.40 tff(62,plain,
% 0.19/0.40 (((~![A: $i, B: $i, C: $i] : (rp(C, B) | (~(A = B)) | (~rp(C, A)))) | (rp(X!1, Y!0) | (~rp(X!1, iv)) | (~(iv = Y!0)))) <=> ((~![A: $i, B: $i, C: $i] : (rp(C, B) | (~(A = B)) | (~rp(C, A)))) | rp(X!1, Y!0) | (~rp(X!1, iv)) | (~(iv = Y!0)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(63,plain,
% 0.19/0.40 ((rp(X!1, Y!0) | (~(iv = Y!0)) | (~rp(X!1, iv))) <=> (rp(X!1, Y!0) | (~rp(X!1, iv)) | (~(iv = Y!0)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(64,plain,
% 0.19/0.40 (((~![A: $i, B: $i, C: $i] : (rp(C, B) | (~(A = B)) | (~rp(C, A)))) | (rp(X!1, Y!0) | (~(iv = Y!0)) | (~rp(X!1, iv)))) <=> ((~![A: $i, B: $i, C: $i] : (rp(C, B) | (~(A = B)) | (~rp(C, A)))) | (rp(X!1, Y!0) | (~rp(X!1, iv)) | (~(iv = Y!0))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[63])).
% 0.19/0.40 tff(65,plain,
% 0.19/0.40 (((~![A: $i, B: $i, C: $i] : (rp(C, B) | (~(A = B)) | (~rp(C, A)))) | (rp(X!1, Y!0) | (~(iv = Y!0)) | (~rp(X!1, iv)))) <=> ((~![A: $i, B: $i, C: $i] : (rp(C, B) | (~(A = B)) | (~rp(C, A)))) | rp(X!1, Y!0) | (~rp(X!1, iv)) | (~(iv = Y!0)))),
% 0.19/0.40 inference(transitivity,[status(thm)],[64, 62])).
% 0.19/0.40 tff(66,plain,
% 0.19/0.40 ((~![A: $i, B: $i, C: $i] : (rp(C, B) | (~(A = B)) | (~rp(C, A)))) | (rp(X!1, Y!0) | (~(iv = Y!0)) | (~rp(X!1, iv)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(67,plain,
% 0.19/0.40 ((~![A: $i, B: $i, C: $i] : (rp(C, B) | (~(A = B)) | (~rp(C, A)))) | rp(X!1, Y!0) | (~rp(X!1, iv)) | (~(iv = Y!0))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.19/0.40 tff(68,plain,
% 0.19/0.40 (~(iv = Y!0)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[67, 61, 10, 48])).
% 0.19/0.40 tff(69,plain,
% 0.19/0.40 (^[X: $i] : refl((cd(X) <=> rq(X, iv)) <=> (cd(X) <=> rq(X, iv)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(70,plain,
% 0.19/0.40 (![X: $i] : (cd(X) <=> rq(X, iv)) <=> ![X: $i] : (cd(X) <=> rq(X, iv))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[69])).
% 0.19/0.40 tff(71,plain,
% 0.19/0.40 (![X: $i] : (cd(X) <=> rq(X, iv)) <=> ![X: $i] : (cd(X) <=> rq(X, iv))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(72,axiom,(![X: $i] : (cd(X) <=> rq(X, iv))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_2')).
% 0.19/0.40 tff(73,plain,
% 0.19/0.40 (![X: $i] : (cd(X) <=> rq(X, iv))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.19/0.40 tff(74,plain,(
% 0.19/0.40 ![X: $i] : (cd(X) <=> rq(X, iv))),
% 0.19/0.40 inference(skolemize,[status(sab)],[73])).
% 0.19/0.40 tff(75,plain,
% 0.19/0.40 (![X: $i] : (cd(X) <=> rq(X, iv))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.19/0.40 tff(76,plain,
% 0.19/0.40 ((~![X: $i] : (cd(X) <=> rq(X, iv))) | (cd(X!1) <=> rq(X!1, iv))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(77,plain,
% 0.19/0.40 (cd(X!1) <=> rq(X!1, iv)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.19/0.40 tff(78,plain,
% 0.19/0.40 ((~(cd(X!1) <=> rq(X!1, iv))) | (~cd(X!1)) | rq(X!1, iv)),
% 0.19/0.40 inference(tautology,[status(thm)],[])).
% 0.19/0.40 tff(79,plain,
% 0.19/0.40 ((~(cd(X!1) <=> rq(X!1, iv))) | rq(X!1, iv)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[78, 45])).
% 0.19/0.40 tff(80,plain,
% 0.19/0.40 (rq(X!1, iv)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[79, 77])).
% 0.19/0.40 tff(81,plain,
% 0.19/0.40 (^[X: $i, Y: $i, Z: $i] : refl(((Y = Z) | (~rq(X, Z)) | (~rq(X, Y))) <=> ((Y = Z) | (~rq(X, Z)) | (~rq(X, Y))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(82,plain,
% 0.19/0.40 (![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rq(X, Z)) | (~rq(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rq(X, Z)) | (~rq(X, Y)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[81])).
% 0.19/0.40 tff(83,plain,
% 0.19/0.40 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((rq(X, Y) & rq(X, Z)) <=> (~((~rq(X, Z)) | (~rq(X, Y))))), ((~(rq(X, Y) & rq(X, Z))) <=> (~(~((~rq(X, Z)) | (~rq(X, Y))))))), rewrite((~(~((~rq(X, Z)) | (~rq(X, Y))))) <=> ((~rq(X, Z)) | (~rq(X, Y)))), ((~(rq(X, Y) & rq(X, Z))) <=> ((~rq(X, Z)) | (~rq(X, Y))))), (((~(rq(X, Y) & rq(X, Z))) | (Y = Z)) <=> (((~rq(X, Z)) | (~rq(X, Y))) | (Y = Z)))), rewrite((((~rq(X, Z)) | (~rq(X, Y))) | (Y = Z)) <=> ((Y = Z) | (~rq(X, Z)) | (~rq(X, Y)))), (((~(rq(X, Y) & rq(X, Z))) | (Y = Z)) <=> ((Y = Z) | (~rq(X, Z)) | (~rq(X, Y)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(84,plain,
% 0.19/0.40 (![X: $i, Y: $i, Z: $i] : ((~(rq(X, Y) & rq(X, Z))) | (Y = Z)) <=> ![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rq(X, Z)) | (~rq(X, Y)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[83])).
% 0.19/0.40 tff(85,plain,
% 0.19/0.40 (![X: $i, Y: $i, Z: $i] : ((~(rq(X, Y) & rq(X, Z))) | (Y = Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(rq(X, Y) & rq(X, Z))) | (Y = Z))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(86,plain,
% 0.19/0.40 (^[X: $i, Y: $i, Z: $i] : rewrite(((rq(X, Y) & rq(X, Z)) => (Y = Z)) <=> ((~(rq(X, Y) & rq(X, Z))) | (Y = Z)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(87,plain,
% 0.19/0.40 (![X: $i, Y: $i, Z: $i] : ((rq(X, Y) & rq(X, Z)) => (Y = Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(rq(X, Y) & rq(X, Z))) | (Y = Z))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[86])).
% 0.19/0.40 tff(88,axiom,(![X: $i, Y: $i, Z: $i] : ((rq(X, Y) & rq(X, Z)) => (Y = Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_6')).
% 0.19/0.40 tff(89,plain,
% 0.19/0.40 (![X: $i, Y: $i, Z: $i] : ((~(rq(X, Y) & rq(X, Z))) | (Y = Z))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.19/0.40 tff(90,plain,
% 0.19/0.40 (![X: $i, Y: $i, Z: $i] : ((~(rq(X, Y) & rq(X, Z))) | (Y = Z))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.19/0.40 tff(91,plain,(
% 0.19/0.40 ![X: $i, Y: $i, Z: $i] : ((~(rq(X, Y) & rq(X, Z))) | (Y = Z))),
% 0.19/0.40 inference(skolemize,[status(sab)],[90])).
% 0.19/0.40 tff(92,plain,
% 0.19/0.40 (![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rq(X, Z)) | (~rq(X, Y)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[91, 84])).
% 0.19/0.40 tff(93,plain,
% 0.19/0.40 (![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rq(X, Z)) | (~rq(X, Y)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[92, 82])).
% 0.19/0.40 tff(94,plain,
% 0.19/0.40 (((~![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rq(X, Z)) | (~rq(X, Y)))) | ((~rq(X!1, Y!0)) | (iv = Y!0) | (~rq(X!1, iv)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rq(X, Z)) | (~rq(X, Y)))) | (~rq(X!1, Y!0)) | (iv = Y!0) | (~rq(X!1, iv)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(95,plain,
% 0.19/0.40 (((iv = Y!0) | (~rq(X!1, Y!0)) | (~rq(X!1, iv))) <=> ((~rq(X!1, Y!0)) | (iv = Y!0) | (~rq(X!1, iv)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(96,plain,
% 0.19/0.40 (((~![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rq(X, Z)) | (~rq(X, Y)))) | ((iv = Y!0) | (~rq(X!1, Y!0)) | (~rq(X!1, iv)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rq(X, Z)) | (~rq(X, Y)))) | ((~rq(X!1, Y!0)) | (iv = Y!0) | (~rq(X!1, iv))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[95])).
% 0.19/0.41 tff(97,plain,
% 0.19/0.41 (((~![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rq(X, Z)) | (~rq(X, Y)))) | ((iv = Y!0) | (~rq(X!1, Y!0)) | (~rq(X!1, iv)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rq(X, Z)) | (~rq(X, Y)))) | (~rq(X!1, Y!0)) | (iv = Y!0) | (~rq(X!1, iv)))),
% 0.19/0.41 inference(transitivity,[status(thm)],[96, 94])).
% 0.19/0.41 tff(98,plain,
% 0.19/0.41 ((~![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rq(X, Z)) | (~rq(X, Y)))) | ((iv = Y!0) | (~rq(X!1, Y!0)) | (~rq(X!1, iv)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(99,plain,
% 0.19/0.41 ((~![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rq(X, Z)) | (~rq(X, Y)))) | (~rq(X!1, Y!0)) | (iv = Y!0) | (~rq(X!1, iv))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.19/0.41 tff(100,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[99, 93, 30, 80, 68])).
% 0.19/0.41 tff(101,plain,(rp(X!1, Y!0)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(102,plain,
% 0.19/0.41 (^[X: $i, Y: $i] : refl((cd(X) | (~rp(X, Y))) <=> (cd(X) | (~rp(X, Y))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(103,plain,
% 0.19/0.41 (![X: $i, Y: $i] : (cd(X) | (~rp(X, Y))) <=> ![X: $i, Y: $i] : (cd(X) | (~rp(X, Y)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[102])).
% 0.19/0.41 tff(104,plain,
% 0.19/0.41 (![X: $i, Y: $i] : (cd(X) | (~rp(X, Y))) <=> ![X: $i, Y: $i] : (cd(X) | (~rp(X, Y)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(105,plain,
% 0.19/0.41 (^[X: $i, Y: $i] : rewrite((rp(X, Y) => cd(X)) <=> (cd(X) | (~rp(X, Y))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(106,plain,
% 0.19/0.41 (![X: $i, Y: $i] : (rp(X, Y) => cd(X)) <=> ![X: $i, Y: $i] : (cd(X) | (~rp(X, Y)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[105])).
% 0.19/0.41 tff(107,axiom,(![X: $i, Y: $i] : (rp(X, Y) => cd(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_5')).
% 0.19/0.41 tff(108,plain,
% 0.19/0.41 (![X: $i, Y: $i] : (cd(X) | (~rp(X, Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.19/0.41 tff(109,plain,
% 0.19/0.41 (![X: $i, Y: $i] : (cd(X) | (~rp(X, Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[108, 104])).
% 0.19/0.41 tff(110,plain,(
% 0.19/0.41 ![X: $i, Y: $i] : (cd(X) | (~rp(X, Y)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[109])).
% 0.19/0.41 tff(111,plain,
% 0.19/0.41 (![X: $i, Y: $i] : (cd(X) | (~rp(X, Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[110, 103])).
% 0.19/0.41 tff(112,plain,
% 0.19/0.41 (((~![X: $i, Y: $i] : (cd(X) | (~rp(X, Y)))) | (cd(X!1) | (~rp(X!1, Y!0)))) <=> ((~![X: $i, Y: $i] : (cd(X) | (~rp(X, Y)))) | cd(X!1) | (~rp(X!1, Y!0)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(113,plain,
% 0.19/0.41 ((~![X: $i, Y: $i] : (cd(X) | (~rp(X, Y)))) | (cd(X!1) | (~rp(X!1, Y!0)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(114,plain,
% 0.19/0.41 ((~![X: $i, Y: $i] : (cd(X) | (~rp(X, Y)))) | cd(X!1) | (~rp(X!1, Y!0))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.19/0.41 tff(115,plain,
% 0.19/0.41 (cd(X!1) | (~rp(X!1, Y!0))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[114, 111])).
% 0.19/0.41 tff(116,plain,
% 0.19/0.41 (cd(X!1)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[115, 101])).
% 0.19/0.41 tff(117,plain,
% 0.19/0.41 ((~(cd(X!1) <=> rp(X!1, iv))) | rp(X!1, iv)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[46, 116])).
% 0.19/0.41 tff(118,plain,
% 0.19/0.41 (rp(X!1, iv)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[117, 9])).
% 0.19/0.41 tff(119,plain,
% 0.19/0.41 (^[X: $i, Y: $i, Z: $i] : refl(((Y = Z) | (~rp(X, Z)) | (~rp(X, Y))) <=> ((Y = Z) | (~rp(X, Z)) | (~rp(X, Y))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(120,plain,
% 0.19/0.41 (![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rp(X, Z)) | (~rp(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rp(X, Z)) | (~rp(X, Y)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[119])).
% 0.19/0.41 tff(121,plain,
% 0.19/0.41 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((rp(X, Y) & rp(X, Z)) <=> (~((~rp(X, Z)) | (~rp(X, Y))))), ((~(rp(X, Y) & rp(X, Z))) <=> (~(~((~rp(X, Z)) | (~rp(X, Y))))))), rewrite((~(~((~rp(X, Z)) | (~rp(X, Y))))) <=> ((~rp(X, Z)) | (~rp(X, Y)))), ((~(rp(X, Y) & rp(X, Z))) <=> ((~rp(X, Z)) | (~rp(X, Y))))), (((~(rp(X, Y) & rp(X, Z))) | (Y = Z)) <=> (((~rp(X, Z)) | (~rp(X, Y))) | (Y = Z)))), rewrite((((~rp(X, Z)) | (~rp(X, Y))) | (Y = Z)) <=> ((Y = Z) | (~rp(X, Z)) | (~rp(X, Y)))), (((~(rp(X, Y) & rp(X, Z))) | (Y = Z)) <=> ((Y = Z) | (~rp(X, Z)) | (~rp(X, Y)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(122,plain,
% 0.19/0.41 (![X: $i, Y: $i, Z: $i] : ((~(rp(X, Y) & rp(X, Z))) | (Y = Z)) <=> ![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rp(X, Z)) | (~rp(X, Y)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[121])).
% 0.19/0.41 tff(123,plain,
% 0.19/0.41 (![X: $i, Y: $i, Z: $i] : ((~(rp(X, Y) & rp(X, Z))) | (Y = Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(rp(X, Y) & rp(X, Z))) | (Y = Z))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(124,plain,
% 0.19/0.41 (^[X: $i, Y: $i, Z: $i] : rewrite(((rp(X, Y) & rp(X, Z)) => (Y = Z)) <=> ((~(rp(X, Y) & rp(X, Z))) | (Y = Z)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(125,plain,
% 0.19/0.41 (![X: $i, Y: $i, Z: $i] : ((rp(X, Y) & rp(X, Z)) => (Y = Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(rp(X, Y) & rp(X, Z))) | (Y = Z))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[124])).
% 0.19/0.41 tff(126,axiom,(![X: $i, Y: $i, Z: $i] : ((rp(X, Y) & rp(X, Z)) => (Y = Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_4')).
% 0.19/0.41 tff(127,plain,
% 0.19/0.41 (![X: $i, Y: $i, Z: $i] : ((~(rp(X, Y) & rp(X, Z))) | (Y = Z))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.19/0.41 tff(128,plain,
% 0.19/0.41 (![X: $i, Y: $i, Z: $i] : ((~(rp(X, Y) & rp(X, Z))) | (Y = Z))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[127, 123])).
% 0.19/0.41 tff(129,plain,(
% 0.19/0.41 ![X: $i, Y: $i, Z: $i] : ((~(rp(X, Y) & rp(X, Z))) | (Y = Z))),
% 0.19/0.41 inference(skolemize,[status(sab)],[128])).
% 0.19/0.41 tff(130,plain,
% 0.19/0.41 (![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rp(X, Z)) | (~rp(X, Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[129, 122])).
% 0.19/0.41 tff(131,plain,
% 0.19/0.41 (![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rp(X, Z)) | (~rp(X, Y)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[130, 120])).
% 0.19/0.41 tff(132,plain,
% 0.19/0.41 (((~![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rp(X, Z)) | (~rp(X, Y)))) | ((~rp(X!1, Y!0)) | (~rp(X!1, iv)) | (iv = Y!0))) <=> ((~![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rp(X, Z)) | (~rp(X, Y)))) | (~rp(X!1, Y!0)) | (~rp(X!1, iv)) | (iv = Y!0))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(133,plain,
% 0.19/0.41 (((iv = Y!0) | (~rp(X!1, Y!0)) | (~rp(X!1, iv))) <=> ((~rp(X!1, Y!0)) | (~rp(X!1, iv)) | (iv = Y!0))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(134,plain,
% 0.19/0.41 (((~![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rp(X, Z)) | (~rp(X, Y)))) | ((iv = Y!0) | (~rp(X!1, Y!0)) | (~rp(X!1, iv)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rp(X, Z)) | (~rp(X, Y)))) | ((~rp(X!1, Y!0)) | (~rp(X!1, iv)) | (iv = Y!0)))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[133])).
% 0.19/0.41 tff(135,plain,
% 0.19/0.41 (((~![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rp(X, Z)) | (~rp(X, Y)))) | ((iv = Y!0) | (~rp(X!1, Y!0)) | (~rp(X!1, iv)))) <=> ((~![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rp(X, Z)) | (~rp(X, Y)))) | (~rp(X!1, Y!0)) | (~rp(X!1, iv)) | (iv = Y!0))),
% 0.19/0.41 inference(transitivity,[status(thm)],[134, 132])).
% 0.19/0.41 tff(136,plain,
% 0.19/0.41 ((~![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rp(X, Z)) | (~rp(X, Y)))) | ((iv = Y!0) | (~rp(X!1, Y!0)) | (~rp(X!1, iv)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(137,plain,
% 0.19/0.41 ((~![X: $i, Y: $i, Z: $i] : ((Y = Z) | (~rp(X, Z)) | (~rp(X, Y)))) | (~rp(X!1, Y!0)) | (~rp(X!1, iv)) | (iv = Y!0)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.19/0.41 tff(138,plain,
% 0.19/0.41 (iv = Y!0),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[137, 131, 101, 118])).
% 0.19/0.41 tff(139,plain,
% 0.19/0.41 ((~(cd(X!1) <=> rq(X!1, iv))) | rq(X!1, iv)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[78, 116])).
% 0.19/0.41 tff(140,plain,
% 0.19/0.41 (rq(X!1, iv)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[139, 77])).
% 0.19/0.41 tff(141,plain,
% 0.19/0.41 ((~rq(X!1, Y!0)) | (~rp(X!1, Y!0)) | (~((~rq(X!1, Y!0)) <=> rp(X!1, Y!0)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(142,plain,
% 0.19/0.41 ((~rq(X!1, Y!0)) | (~rp(X!1, Y!0))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[141, 27])).
% 0.19/0.41 tff(143,plain,
% 0.19/0.41 (~rq(X!1, Y!0)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[142, 101])).
% 0.19/0.41 tff(144,plain,
% 0.19/0.41 (^[A: $i, B: $i, C: $i] : refl((rq(C, B) | (~(A = B)) | (~rq(C, A))) <=> (rq(C, B) | (~(A = B)) | (~rq(C, A))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(145,plain,
% 0.19/0.41 (![A: $i, B: $i, C: $i] : (rq(C, B) | (~(A = B)) | (~rq(C, A))) <=> ![A: $i, B: $i, C: $i] : (rq(C, B) | (~(A = B)) | (~rq(C, A)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[144])).
% 0.19/0.41 tff(146,plain,
% 0.19/0.41 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((A = B) & rq(C, A)) <=> (~((~(A = B)) | (~rq(C, A))))), ((~((A = B) & rq(C, A))) <=> (~(~((~(A = B)) | (~rq(C, A))))))), rewrite((~(~((~(A = B)) | (~rq(C, A))))) <=> ((~(A = B)) | (~rq(C, A)))), ((~((A = B) & rq(C, A))) <=> ((~(A = B)) | (~rq(C, A))))), (((~((A = B) & rq(C, A))) | rq(C, B)) <=> (((~(A = B)) | (~rq(C, A))) | rq(C, B)))), rewrite((((~(A = B)) | (~rq(C, A))) | rq(C, B)) <=> (rq(C, B) | (~(A = B)) | (~rq(C, A)))), (((~((A = B) & rq(C, A))) | rq(C, B)) <=> (rq(C, B) | (~(A = B)) | (~rq(C, A)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(147,plain,
% 0.19/0.41 (![A: $i, B: $i, C: $i] : ((~((A = B) & rq(C, A))) | rq(C, B)) <=> ![A: $i, B: $i, C: $i] : (rq(C, B) | (~(A = B)) | (~rq(C, A)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[146])).
% 0.19/0.41 tff(148,plain,
% 0.19/0.41 (![A: $i, B: $i, C: $i] : ((~((A = B) & rq(C, A))) | rq(C, B)) <=> ![A: $i, B: $i, C: $i] : ((~((A = B) & rq(C, A))) | rq(C, B))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(149,plain,
% 0.19/0.41 (^[A: $i, B: $i, C: $i] : rewrite((((A = B) & rq(C, A)) => rq(C, B)) <=> ((~((A = B) & rq(C, A))) | rq(C, B)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(150,plain,
% 0.19/0.41 (![A: $i, B: $i, C: $i] : (((A = B) & rq(C, A)) => rq(C, B)) <=> ![A: $i, B: $i, C: $i] : ((~((A = B) & rq(C, A))) | rq(C, B))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[149])).
% 0.19/0.41 tff(151,axiom,(![A: $i, B: $i, C: $i] : (((A = B) & rq(C, A)) => rq(C, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rq_substitution_2')).
% 0.19/0.41 tff(152,plain,
% 0.19/0.41 (![A: $i, B: $i, C: $i] : ((~((A = B) & rq(C, A))) | rq(C, B))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.19/0.41 tff(153,plain,
% 0.19/0.41 (![A: $i, B: $i, C: $i] : ((~((A = B) & rq(C, A))) | rq(C, B))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[152, 148])).
% 0.19/0.41 tff(154,plain,(
% 0.19/0.41 ![A: $i, B: $i, C: $i] : ((~((A = B) & rq(C, A))) | rq(C, B))),
% 0.19/0.41 inference(skolemize,[status(sab)],[153])).
% 0.19/0.41 tff(155,plain,
% 0.19/0.41 (![A: $i, B: $i, C: $i] : (rq(C, B) | (~(A = B)) | (~rq(C, A)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[154, 147])).
% 0.19/0.41 tff(156,plain,
% 0.19/0.41 (![A: $i, B: $i, C: $i] : (rq(C, B) | (~(A = B)) | (~rq(C, A)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[155, 145])).
% 0.19/0.41 tff(157,plain,
% 0.19/0.41 (((~![A: $i, B: $i, C: $i] : (rq(C, B) | (~(A = B)) | (~rq(C, A)))) | (rq(X!1, Y!0) | (~(iv = Y!0)) | (~rq(X!1, iv)))) <=> ((~![A: $i, B: $i, C: $i] : (rq(C, B) | (~(A = B)) | (~rq(C, A)))) | rq(X!1, Y!0) | (~(iv = Y!0)) | (~rq(X!1, iv)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(158,plain,
% 0.19/0.41 ((~![A: $i, B: $i, C: $i] : (rq(C, B) | (~(A = B)) | (~rq(C, A)))) | (rq(X!1, Y!0) | (~(iv = Y!0)) | (~rq(X!1, iv)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(159,plain,
% 0.19/0.41 ((~![A: $i, B: $i, C: $i] : (rq(C, B) | (~(A = B)) | (~rq(C, A)))) | rq(X!1, Y!0) | (~(iv = Y!0)) | (~rq(X!1, iv))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.19/0.41 tff(160,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[159, 156, 143, 140, 138])).
% 0.19/0.41 % SZS output end Proof
%------------------------------------------------------------------------------