TSTP Solution File: KRS171+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KRS171+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.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 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KRS171+1 : TPTP v8.1.0. Released v3.1.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n019.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 09:43:50 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.13/0.39 % SZS status Theorem
% 0.13/0.39 % SZS output start Proof
% 0.13/0.39 tff(rhasLeader_type, type, (
% 0.13/0.39 rhasLeader: ( $i * $i ) > $o)).
% 0.13/0.39 tff(tptp_fun_Y_0_type, type, (
% 0.13/0.39 tptp_fun_Y_0: $i)).
% 0.13/0.39 tff(tptp_fun_X_1_type, type, (
% 0.13/0.39 tptp_fun_X_1: $i)).
% 0.13/0.39 tff(rhasHead_type, type, (
% 0.13/0.39 rhasHead: ( $i * $i ) > $o)).
% 0.13/0.39 tff(xsd_integer_type, type, (
% 0.13/0.39 xsd_integer: $i > $o)).
% 0.13/0.39 tff(xsd_string_type, type, (
% 0.13/0.39 xsd_string: $i > $o)).
% 0.13/0.39 tff(cowlNothing_type, type, (
% 0.13/0.39 cowlNothing: $i > $o)).
% 0.13/0.39 tff(cowlThing_type, type, (
% 0.13/0.39 cowlThing: $i > $o)).
% 0.13/0.39 tff(1,assumption,(~rhasLeader(X!1, Y!0)), introduced(assumption)).
% 0.13/0.39 tff(2,plain,
% 0.13/0.39 ((~(rhasLeader(X!1, Y!0) <=> rhasHead(X!1, Y!0))) <=> ((~rhasLeader(X!1, Y!0)) <=> rhasHead(X!1, Y!0))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(3,plain,
% 0.13/0.39 ((~![X: $i, Y: $i] : (rhasLeader(X, Y) <=> rhasHead(X, Y))) <=> (~![X: $i, Y: $i] : (rhasLeader(X, Y) <=> rhasHead(X, Y)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(4,plain,
% 0.13/0.39 ((~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![X: $i, Y: $i] : (rhasLeader(X, Y) <=> rhasHead(X, Y)))) <=> (~![X: $i, Y: $i] : (rhasLeader(X, Y) <=> rhasHead(X, Y)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(5,plain,
% 0.13/0.39 ((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![X: $i, Y: $i] : (rhasLeader(X, Y) <=> rhasHead(X, Y))) <=> (![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![X: $i, Y: $i] : (rhasLeader(X, Y) <=> rhasHead(X, Y)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(6,plain,
% 0.13/0.39 ((~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![X: $i, Y: $i] : (rhasLeader(X, Y) <=> rhasHead(X, Y)))) <=> (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![X: $i, Y: $i] : (rhasLeader(X, Y) <=> rhasHead(X, Y))))),
% 0.13/0.39 inference(monotonicity,[status(thm)],[5])).
% 0.13/0.39 tff(7,plain,
% 0.13/0.39 ((~((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X)))) & ![X: $i, Y: $i] : (rhasLeader(X, Y) <=> rhasHead(X, Y)))) <=> (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![X: $i, Y: $i] : (rhasLeader(X, Y) <=> rhasHead(X, Y))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(8,axiom,(~((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X)))) & ![X: $i, Y: $i] : (rhasLeader(X, Y) <=> rhasHead(X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','the_axiom')).
% 0.13/0.39 tff(9,plain,
% 0.13/0.39 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![X: $i, Y: $i] : (rhasLeader(X, Y) <=> rhasHead(X, Y)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.13/0.39 tff(10,plain,
% 0.13/0.39 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![X: $i, Y: $i] : (rhasLeader(X, Y) <=> rhasHead(X, Y)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[9, 6])).
% 0.13/0.39 tff(11,plain,
% 0.13/0.39 (~![X: $i, Y: $i] : (rhasLeader(X, Y) <=> rhasHead(X, Y))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[10, 4])).
% 0.13/0.39 tff(12,plain,
% 0.13/0.39 (~![X: $i, Y: $i] : (rhasLeader(X, Y) <=> rhasHead(X, Y))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[11, 3])).
% 0.13/0.39 tff(13,plain,
% 0.13/0.39 (~![X: $i, Y: $i] : (rhasLeader(X, Y) <=> rhasHead(X, Y))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[12, 3])).
% 0.13/0.39 tff(14,plain,
% 0.13/0.39 (~![X: $i, Y: $i] : (rhasLeader(X, Y) <=> rhasHead(X, Y))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[13, 3])).
% 0.13/0.39 tff(15,plain,
% 0.13/0.39 (~![X: $i, Y: $i] : (rhasLeader(X, Y) <=> rhasHead(X, Y))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[14, 3])).
% 0.13/0.39 tff(16,plain,
% 0.13/0.39 (~![X: $i, Y: $i] : (rhasLeader(X, Y) <=> rhasHead(X, Y))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[15, 3])).
% 0.13/0.39 tff(17,plain,(
% 0.13/0.39 ~(rhasLeader(X!1, Y!0) <=> rhasHead(X!1, Y!0))),
% 0.13/0.39 inference(skolemize,[status(sab)],[16])).
% 0.13/0.39 tff(18,plain,
% 0.13/0.39 ((~rhasLeader(X!1, Y!0)) <=> rhasHead(X!1, Y!0)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[17, 2])).
% 0.13/0.39 tff(19,plain,
% 0.13/0.39 (rhasLeader(X!1, Y!0) | rhasHead(X!1, Y!0) | (~((~rhasLeader(X!1, Y!0)) <=> rhasHead(X!1, Y!0)))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(20,plain,
% 0.13/0.39 (rhasLeader(X!1, Y!0) | rhasHead(X!1, Y!0)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.13/0.39 tff(21,plain,
% 0.13/0.39 (rhasHead(X!1, Y!0)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[20, 1])).
% 0.13/0.39 tff(22,plain,
% 0.13/0.39 (^[X: $i, Y: $i] : refl(((~rhasHead(X, Y)) | rhasLeader(X, Y)) <=> ((~rhasHead(X, Y)) | rhasLeader(X, Y)))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(23,plain,
% 0.13/0.39 (![X: $i, Y: $i] : ((~rhasHead(X, Y)) | rhasLeader(X, Y)) <=> ![X: $i, Y: $i] : ((~rhasHead(X, Y)) | rhasLeader(X, Y))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[22])).
% 0.13/0.39 tff(24,plain,
% 0.13/0.39 (![X: $i, Y: $i] : ((~rhasHead(X, Y)) | rhasLeader(X, Y)) <=> ![X: $i, Y: $i] : ((~rhasHead(X, Y)) | rhasLeader(X, Y))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(25,plain,
% 0.13/0.39 (^[X: $i, Y: $i] : rewrite((rhasHead(X, Y) => rhasLeader(X, Y)) <=> ((~rhasHead(X, Y)) | rhasLeader(X, Y)))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(26,plain,
% 0.13/0.39 (![X: $i, Y: $i] : (rhasHead(X, Y) => rhasLeader(X, Y)) <=> ![X: $i, Y: $i] : ((~rhasHead(X, Y)) | rhasLeader(X, Y))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[25])).
% 0.13/0.39 tff(27,axiom,(![X: $i, Y: $i] : (rhasHead(X, Y) => rhasLeader(X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_2')).
% 0.13/0.39 tff(28,plain,
% 0.13/0.39 (![X: $i, Y: $i] : ((~rhasHead(X, Y)) | rhasLeader(X, Y))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.13/0.39 tff(29,plain,
% 0.13/0.39 (![X: $i, Y: $i] : ((~rhasHead(X, Y)) | rhasLeader(X, Y))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.13/0.39 tff(30,plain,(
% 0.13/0.39 ![X: $i, Y: $i] : ((~rhasHead(X, Y)) | rhasLeader(X, Y))),
% 0.13/0.39 inference(skolemize,[status(sab)],[29])).
% 0.13/0.39 tff(31,plain,
% 0.13/0.39 (![X: $i, Y: $i] : ((~rhasHead(X, Y)) | rhasLeader(X, Y))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.13/0.39 tff(32,plain,
% 0.13/0.39 (((~![X: $i, Y: $i] : ((~rhasHead(X, Y)) | rhasLeader(X, Y))) | ((~rhasHead(X!1, Y!0)) | rhasLeader(X!1, Y!0))) <=> ((~![X: $i, Y: $i] : ((~rhasHead(X, Y)) | rhasLeader(X, Y))) | (~rhasHead(X!1, Y!0)) | rhasLeader(X!1, Y!0))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(33,plain,
% 0.13/0.39 ((~![X: $i, Y: $i] : ((~rhasHead(X, Y)) | rhasLeader(X, Y))) | ((~rhasHead(X!1, Y!0)) | rhasLeader(X!1, Y!0))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(34,plain,
% 0.13/0.39 ((~![X: $i, Y: $i] : ((~rhasHead(X, Y)) | rhasLeader(X, Y))) | (~rhasHead(X!1, Y!0)) | rhasLeader(X!1, Y!0)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.13/0.39 tff(35,plain,
% 0.13/0.39 ((~rhasHead(X!1, Y!0)) | rhasLeader(X!1, Y!0)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[34, 31])).
% 0.13/0.39 tff(36,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[35, 21, 1])).
% 0.13/0.39 tff(37,plain,(rhasLeader(X!1, Y!0)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.39 tff(38,plain,
% 0.13/0.39 ((~rhasLeader(X!1, Y!0)) | (~rhasHead(X!1, Y!0)) | (~((~rhasLeader(X!1, Y!0)) <=> rhasHead(X!1, Y!0)))),
% 0.13/0.39 inference(tautology,[status(thm)],[])).
% 0.13/0.39 tff(39,plain,
% 0.13/0.39 ((~rhasLeader(X!1, Y!0)) | (~rhasHead(X!1, Y!0))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[38, 18])).
% 0.13/0.39 tff(40,plain,
% 0.13/0.39 (~rhasHead(X!1, Y!0)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[39, 37])).
% 0.13/0.39 tff(41,plain,
% 0.13/0.39 (^[X: $i, Y: $i] : refl(((~rhasLeader(X, Y)) | rhasHead(X, Y)) <=> ((~rhasLeader(X, Y)) | rhasHead(X, Y)))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(42,plain,
% 0.13/0.39 (![X: $i, Y: $i] : ((~rhasLeader(X, Y)) | rhasHead(X, Y)) <=> ![X: $i, Y: $i] : ((~rhasLeader(X, Y)) | rhasHead(X, Y))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[41])).
% 0.13/0.39 tff(43,plain,
% 0.13/0.39 (![X: $i, Y: $i] : ((~rhasLeader(X, Y)) | rhasHead(X, Y)) <=> ![X: $i, Y: $i] : ((~rhasLeader(X, Y)) | rhasHead(X, Y))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(44,plain,
% 0.13/0.39 (^[X: $i, Y: $i] : rewrite((rhasLeader(X, Y) => rhasHead(X, Y)) <=> ((~rhasLeader(X, Y)) | rhasHead(X, Y)))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(45,plain,
% 0.13/0.39 (![X: $i, Y: $i] : (rhasLeader(X, Y) => rhasHead(X, Y)) <=> ![X: $i, Y: $i] : ((~rhasLeader(X, Y)) | rhasHead(X, Y))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[44])).
% 0.13/0.39 tff(46,axiom,(![X: $i, Y: $i] : (rhasLeader(X, Y) => rhasHead(X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_3')).
% 0.13/0.39 tff(47,plain,
% 0.13/0.39 (![X: $i, Y: $i] : ((~rhasLeader(X, Y)) | rhasHead(X, Y))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.13/0.39 tff(48,plain,
% 0.13/0.39 (![X: $i, Y: $i] : ((~rhasLeader(X, Y)) | rhasHead(X, Y))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.13/0.39 tff(49,plain,(
% 0.13/0.39 ![X: $i, Y: $i] : ((~rhasLeader(X, Y)) | rhasHead(X, Y))),
% 0.13/0.39 inference(skolemize,[status(sab)],[48])).
% 0.13/0.39 tff(50,plain,
% 0.13/0.39 (![X: $i, Y: $i] : ((~rhasLeader(X, Y)) | rhasHead(X, Y))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.13/0.39 tff(51,plain,
% 0.13/0.39 (((~![X: $i, Y: $i] : ((~rhasLeader(X, Y)) | rhasHead(X, Y))) | ((~rhasLeader(X!1, Y!0)) | rhasHead(X!1, Y!0))) <=> ((~![X: $i, Y: $i] : ((~rhasLeader(X, Y)) | rhasHead(X, Y))) | (~rhasLeader(X!1, Y!0)) | rhasHead(X!1, Y!0))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(52,plain,
% 0.13/0.39 ((~![X: $i, Y: $i] : ((~rhasLeader(X, Y)) | rhasHead(X, Y))) | ((~rhasLeader(X!1, Y!0)) | rhasHead(X!1, Y!0))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(53,plain,
% 0.13/0.39 ((~![X: $i, Y: $i] : ((~rhasLeader(X, Y)) | rhasHead(X, Y))) | (~rhasLeader(X!1, Y!0)) | rhasHead(X!1, Y!0)),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.13/0.39 tff(54,plain,
% 0.13/0.39 ((~rhasLeader(X!1, Y!0)) | rhasHead(X!1, Y!0)),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[53, 50])).
% 0.13/0.39 tff(55,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[54, 40, 37])).
% 0.13/0.39 % SZS output end Proof
%------------------------------------------------------------------------------