TSTP Solution File: KRS135+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KRS135+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.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 17:44:55 EDT 2022
% Result : Theorem 0.12s 0.39s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : KRS135+1 : TPTP v8.1.0. Released v3.1.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Sep 1 09:37:39 EDT 2022
% 0.12/0.34 % 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.
% 0.12/0.39 % SZS status Theorem
% 0.12/0.39 % SZS output start Proof
% 0.12/0.39 tff(rprop_type, type, (
% 0.12/0.39 rprop: ( $i * $i ) > $o)).
% 0.12/0.39 tff(tptp_fun_X_1_type, type, (
% 0.12/0.39 tptp_fun_X_1: $i)).
% 0.12/0.39 tff(cA_type, type, (
% 0.12/0.39 cA: $i > $o)).
% 0.12/0.39 tff(cowlThing_type, type, (
% 0.12/0.39 cowlThing: $i > $o)).
% 0.12/0.39 tff(cowlNothing_type, type, (
% 0.12/0.39 cowlNothing: $i > $o)).
% 0.12/0.39 tff(tptp_fun_Y_0_type, type, (
% 0.12/0.39 tptp_fun_Y_0: $i)).
% 0.12/0.39 tff(xsd_integer_type, type, (
% 0.12/0.39 xsd_integer: $i > $o)).
% 0.12/0.39 tff(xsd_string_type, type, (
% 0.12/0.39 xsd_string: $i > $o)).
% 0.12/0.39 tff(1,plain,
% 0.12/0.39 (^[X: $i] : refl((~(cowlNothing(X) | (~cowlThing(X)))) <=> (~(cowlNothing(X) | (~cowlThing(X)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(2,plain,
% 0.12/0.39 (![X: $i] : (~(cowlNothing(X) | (~cowlThing(X)))) <=> ![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.39 tff(3,plain,
% 0.12/0.39 (^[X: $i] : rewrite((cowlThing(X) & (~cowlNothing(X))) <=> (~(cowlNothing(X) | (~cowlThing(X)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(4,plain,
% 0.12/0.39 (![X: $i] : (cowlThing(X) & (~cowlNothing(X))) <=> ![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.12/0.39 tff(5,plain,
% 0.12/0.39 (![X: $i] : (cowlThing(X) & (~cowlNothing(X))) <=> ![X: $i] : (cowlThing(X) & (~cowlNothing(X)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(6,axiom,(![X: $i] : (cowlThing(X) & (~cowlNothing(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_0')).
% 0.12/0.39 tff(7,plain,
% 0.12/0.39 (![X: $i] : (cowlThing(X) & (~cowlNothing(X)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.12/0.39 tff(8,plain,(
% 0.12/0.39 ![X: $i] : (cowlThing(X) & (~cowlNothing(X)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[7])).
% 0.12/0.39 tff(9,plain,
% 0.12/0.39 (![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.12/0.39 tff(10,plain,
% 0.12/0.39 (![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.12/0.39 tff(11,plain,
% 0.12/0.39 ((~![X: $i] : (~(cowlNothing(X) | (~cowlThing(X))))) | (~(cowlNothing(X!1) | (~cowlThing(X!1))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(12,plain,
% 0.12/0.39 (~(cowlNothing(X!1) | (~cowlThing(X!1)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.12/0.39 tff(13,plain,
% 0.12/0.39 ((cowlNothing(X!1) | (~cowlThing(X!1))) | cowlThing(X!1)),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(14,plain,
% 0.12/0.39 (cowlThing(X!1)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.12/0.39 tff(15,plain,
% 0.12/0.39 (^[X: $i] : refl(((~cowlThing(X)) | ![Y: $i] : (cA(Y) | (~rprop(X, Y)))) <=> ((~cowlThing(X)) | ![Y: $i] : (cA(Y) | (~rprop(X, Y)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(16,plain,
% 0.12/0.39 (![X: $i] : ((~cowlThing(X)) | ![Y: $i] : (cA(Y) | (~rprop(X, Y)))) <=> ![X: $i] : ((~cowlThing(X)) | ![Y: $i] : (cA(Y) | (~rprop(X, Y))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[15])).
% 0.12/0.39 tff(17,plain,
% 0.12/0.39 (^[X: $i] : rewrite(((~cowlThing(X)) | ![Y: $i] : (cA(Y) | (~rprop(X, Y)))) <=> ((~cowlThing(X)) | ![Y: $i] : (cA(Y) | (~rprop(X, Y)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(18,plain,
% 0.12/0.39 (![X: $i] : ((~cowlThing(X)) | ![Y: $i] : (cA(Y) | (~rprop(X, Y)))) <=> ![X: $i] : ((~cowlThing(X)) | ![Y: $i] : (cA(Y) | (~rprop(X, Y))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[17])).
% 0.12/0.39 tff(19,plain,
% 0.12/0.39 (![X: $i] : ((~cowlThing(X)) | ![Y: $i] : (cA(Y) | (~rprop(X, Y)))) <=> ![X: $i] : ((~cowlThing(X)) | ![Y: $i] : (cA(Y) | (~rprop(X, Y))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[18, 16])).
% 0.12/0.39 tff(20,plain,
% 0.12/0.39 (![X: $i] : ((~cowlThing(X)) | ![Y: $i] : (cA(Y) | (~rprop(X, Y)))) <=> ![X: $i] : ((~cowlThing(X)) | ![Y: $i] : (cA(Y) | (~rprop(X, Y))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(21,plain,
% 0.12/0.39 (^[X: $i] : trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : rewrite((rprop(X, Y) => cA(Y)) <=> (cA(Y) | (~rprop(X, Y))))), (![Y: $i] : (rprop(X, Y) => cA(Y)) <=> ![Y: $i] : (cA(Y) | (~rprop(X, Y))))), ((cowlThing(X) => ![Y: $i] : (rprop(X, Y) => cA(Y))) <=> (cowlThing(X) => ![Y: $i] : (cA(Y) | (~rprop(X, Y)))))), rewrite((cowlThing(X) => ![Y: $i] : (cA(Y) | (~rprop(X, Y)))) <=> ((~cowlThing(X)) | ![Y: $i] : (cA(Y) | (~rprop(X, Y))))), ((cowlThing(X) => ![Y: $i] : (rprop(X, Y) => cA(Y))) <=> ((~cowlThing(X)) | ![Y: $i] : (cA(Y) | (~rprop(X, Y))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(22,plain,
% 0.12/0.39 (![X: $i] : (cowlThing(X) => ![Y: $i] : (rprop(X, Y) => cA(Y))) <=> ![X: $i] : ((~cowlThing(X)) | ![Y: $i] : (cA(Y) | (~rprop(X, Y))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[21])).
% 0.12/0.39 tff(23,axiom,(![X: $i] : (cowlThing(X) => ![Y: $i] : (rprop(X, Y) => cA(Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_2')).
% 0.12/0.39 tff(24,plain,
% 0.12/0.39 (![X: $i] : ((~cowlThing(X)) | ![Y: $i] : (cA(Y) | (~rprop(X, Y))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.12/0.39 tff(25,plain,
% 0.12/0.39 (![X: $i] : ((~cowlThing(X)) | ![Y: $i] : (cA(Y) | (~rprop(X, Y))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.12/0.39 tff(26,plain,(
% 0.12/0.39 ![X: $i] : ((~cowlThing(X)) | ![Y: $i] : (cA(Y) | (~rprop(X, Y))))),
% 0.12/0.39 inference(skolemize,[status(sab)],[25])).
% 0.12/0.39 tff(27,plain,
% 0.12/0.39 (![X: $i] : ((~cowlThing(X)) | ![Y: $i] : (cA(Y) | (~rprop(X, Y))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.12/0.39 tff(28,plain,
% 0.12/0.39 (((~![X: $i] : ((~cowlThing(X)) | ![Y: $i] : (cA(Y) | (~rprop(X, Y))))) | ((~cowlThing(X!1)) | ![Y: $i] : (cA(Y) | (~rprop(X!1, Y))))) <=> ((~![X: $i] : ((~cowlThing(X)) | ![Y: $i] : (cA(Y) | (~rprop(X, Y))))) | (~cowlThing(X!1)) | ![Y: $i] : (cA(Y) | (~rprop(X!1, Y))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(29,plain,
% 0.12/0.39 ((~![X: $i] : ((~cowlThing(X)) | ![Y: $i] : (cA(Y) | (~rprop(X, Y))))) | ((~cowlThing(X!1)) | ![Y: $i] : (cA(Y) | (~rprop(X!1, Y))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(30,plain,
% 0.12/0.39 ((~![X: $i] : ((~cowlThing(X)) | ![Y: $i] : (cA(Y) | (~rprop(X, Y))))) | (~cowlThing(X!1)) | ![Y: $i] : (cA(Y) | (~rprop(X!1, Y)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.12/0.39 tff(31,plain,
% 0.12/0.39 (![Y: $i] : (cA(Y) | (~rprop(X!1, Y)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[30, 27, 14])).
% 0.12/0.39 tff(32,plain,
% 0.12/0.39 ((~![X: $i, Y: $i] : (cA(Y) | (~rprop(X, Y)))) <=> (~![X: $i, Y: $i] : (cA(Y) | (~rprop(X, Y))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(33,plain,
% 0.12/0.39 ((~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![X: $i, Y: $i] : (cA(Y) | (~rprop(X, Y))))) <=> (~![X: $i, Y: $i] : (cA(Y) | (~rprop(X, Y))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(34,plain,
% 0.12/0.39 ((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![X: $i, Y: $i] : (cA(Y) | (~rprop(X, Y)))) <=> (![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![X: $i, Y: $i] : (cA(Y) | (~rprop(X, Y))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(35,plain,
% 0.12/0.39 ((~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![X: $i, Y: $i] : (cA(Y) | (~rprop(X, Y))))) <=> (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![X: $i, Y: $i] : (cA(Y) | (~rprop(X, Y)))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[34])).
% 0.12/0.39 tff(36,plain,
% 0.12/0.39 ((~((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X)))) & ![X: $i, Y: $i] : (rprop(X, Y) => cA(Y)))) <=> (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![X: $i, Y: $i] : (cA(Y) | (~rprop(X, Y)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(37,axiom,(~((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X)))) & ![X: $i, Y: $i] : (rprop(X, Y) => cA(Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','the_axiom')).
% 0.12/0.39 tff(38,plain,
% 0.12/0.39 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![X: $i, Y: $i] : (cA(Y) | (~rprop(X, Y))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.12/0.39 tff(39,plain,
% 0.12/0.39 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & ![X: $i, Y: $i] : (cA(Y) | (~rprop(X, Y))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[38, 35])).
% 0.12/0.39 tff(40,plain,
% 0.12/0.39 (~![X: $i, Y: $i] : (cA(Y) | (~rprop(X, Y)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[39, 33])).
% 0.12/0.39 tff(41,plain,
% 0.12/0.39 (~![X: $i, Y: $i] : (cA(Y) | (~rprop(X, Y)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[40, 32])).
% 0.12/0.39 tff(42,plain,
% 0.12/0.39 (~![X: $i, Y: $i] : (cA(Y) | (~rprop(X, Y)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[41, 32])).
% 0.12/0.39 tff(43,plain,
% 0.12/0.39 (~![X: $i, Y: $i] : (cA(Y) | (~rprop(X, Y)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[42, 32])).
% 0.12/0.39 tff(44,plain,
% 0.12/0.39 (~![X: $i, Y: $i] : (cA(Y) | (~rprop(X, Y)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[43, 32])).
% 0.12/0.39 tff(45,plain,
% 0.12/0.39 (~![X: $i, Y: $i] : (cA(Y) | (~rprop(X, Y)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[44, 32])).
% 0.12/0.39 tff(46,plain,(
% 0.12/0.39 ~(cA(Y!0) | (~rprop(X!1, Y!0)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[45])).
% 0.12/0.39 tff(47,plain,
% 0.12/0.39 (rprop(X!1, Y!0)),
% 0.12/0.39 inference(or_elim,[status(thm)],[46])).
% 0.12/0.39 tff(48,plain,
% 0.12/0.39 (~cA(Y!0)),
% 0.12/0.39 inference(or_elim,[status(thm)],[46])).
% 0.12/0.39 tff(49,plain,
% 0.12/0.39 (((~![Y: $i] : (cA(Y) | (~rprop(X!1, Y)))) | (cA(Y!0) | (~rprop(X!1, Y!0)))) <=> ((~![Y: $i] : (cA(Y) | (~rprop(X!1, Y)))) | cA(Y!0) | (~rprop(X!1, Y!0)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(50,plain,
% 0.12/0.39 ((~![Y: $i] : (cA(Y) | (~rprop(X!1, Y)))) | (cA(Y!0) | (~rprop(X!1, Y!0)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(51,plain,
% 0.12/0.39 ((~![Y: $i] : (cA(Y) | (~rprop(X!1, Y)))) | cA(Y!0) | (~rprop(X!1, Y!0))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.12/0.39 tff(52,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[51, 48, 47, 31])).
% 0.12/0.39 % SZS output end Proof
%------------------------------------------------------------------------------