TSTP Solution File: SWV385+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV385+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.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 : Thu Sep 29 15:11:34 EDT 2022
% Result : Theorem 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV385+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n016.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 : Sun Sep 4 03:10:08 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 tff(check_cpq_type, type, (
% 0.20/0.41 check_cpq: $i > $o)).
% 0.20/0.41 tff(triple_type, type, (
% 0.20/0.41 triple: ( $i * $i * $i ) > $i)).
% 0.20/0.41 tff(tptp_fun_W_0_type, type, (
% 0.20/0.41 tptp_fun_W_0: $i)).
% 0.20/0.41 tff(tptp_fun_V_1_type, type, (
% 0.20/0.41 tptp_fun_V_1: $i)).
% 0.20/0.41 tff(tptp_fun_U_2_type, type, (
% 0.20/0.41 tptp_fun_U_2: $i)).
% 0.20/0.41 tff(im_succ_cpq_type, type, (
% 0.20/0.41 im_succ_cpq: $i > $i)).
% 0.20/0.41 tff(ok_type, type, (
% 0.20/0.41 ok: $i > $o)).
% 0.20/0.41 tff(1,plain,
% 0.20/0.41 ((~((~ok(im_succ_cpq(triple(U!2, V!1, W!0)))) | (~check_cpq(im_succ_cpq(triple(U!2, V!1, W!0)))) | (~((~check_cpq(triple(U!2, V!1, W!0))) | (~ok(triple(U!2, V!1, W!0))))))) <=> (~((~ok(im_succ_cpq(triple(U!2, V!1, W!0)))) | (~check_cpq(im_succ_cpq(triple(U!2, V!1, W!0)))) | (~((~check_cpq(triple(U!2, V!1, W!0))) | (~ok(triple(U!2, V!1, W!0)))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(2,plain,
% 0.20/0.41 ((~![U: $i, V: $i, W: $i] : ((~ok(im_succ_cpq(triple(U, V, W)))) | (~check_cpq(im_succ_cpq(triple(U, V, W)))) | (~((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W))))))) <=> (~![U: $i, V: $i, W: $i] : ((~ok(im_succ_cpq(triple(U, V, W)))) | (~check_cpq(im_succ_cpq(triple(U, V, W)))) | (~((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W)))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(3,plain,
% 0.20/0.41 ((~![U: $i, V: $i, W: $i] : (((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W)))) => ((~check_cpq(im_succ_cpq(triple(U, V, W)))) | (~ok(im_succ_cpq(triple(U, V, W))))))) <=> (~![U: $i, V: $i, W: $i] : ((~ok(im_succ_cpq(triple(U, V, W)))) | (~check_cpq(im_succ_cpq(triple(U, V, W)))) | (~((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W)))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(4,axiom,(~![U: $i, V: $i, W: $i] : (((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W)))) => ((~check_cpq(im_succ_cpq(triple(U, V, W)))) | (~ok(im_succ_cpq(triple(U, V, W))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l21_co')).
% 0.20/0.41 tff(5,plain,
% 0.20/0.41 (~![U: $i, V: $i, W: $i] : ((~ok(im_succ_cpq(triple(U, V, W)))) | (~check_cpq(im_succ_cpq(triple(U, V, W)))) | (~((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.41 tff(6,plain,
% 0.20/0.41 (~![U: $i, V: $i, W: $i] : ((~ok(im_succ_cpq(triple(U, V, W)))) | (~check_cpq(im_succ_cpq(triple(U, V, W)))) | (~((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.20/0.41 tff(7,plain,
% 0.20/0.41 (~![U: $i, V: $i, W: $i] : ((~ok(im_succ_cpq(triple(U, V, W)))) | (~check_cpq(im_succ_cpq(triple(U, V, W)))) | (~((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.41 tff(8,plain,
% 0.20/0.41 (~![U: $i, V: $i, W: $i] : ((~ok(im_succ_cpq(triple(U, V, W)))) | (~check_cpq(im_succ_cpq(triple(U, V, W)))) | (~((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.20/0.41 tff(9,plain,
% 0.20/0.41 (~![U: $i, V: $i, W: $i] : ((~ok(im_succ_cpq(triple(U, V, W)))) | (~check_cpq(im_succ_cpq(triple(U, V, W)))) | (~((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[8, 2])).
% 0.20/0.41 tff(10,plain,
% 0.20/0.41 (~![U: $i, V: $i, W: $i] : ((~ok(im_succ_cpq(triple(U, V, W)))) | (~check_cpq(im_succ_cpq(triple(U, V, W)))) | (~((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.20/0.41 tff(11,plain,
% 0.20/0.41 (~![U: $i, V: $i, W: $i] : ((~ok(im_succ_cpq(triple(U, V, W)))) | (~check_cpq(im_succ_cpq(triple(U, V, W)))) | (~((~check_cpq(triple(U, V, W))) | (~ok(triple(U, V, W))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.20/0.41 tff(12,plain,(
% 0.20/0.41 ~((~ok(im_succ_cpq(triple(U!2, V!1, W!0)))) | (~check_cpq(im_succ_cpq(triple(U!2, V!1, W!0)))) | (~((~check_cpq(triple(U!2, V!1, W!0))) | (~ok(triple(U!2, V!1, W!0))))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[11])).
% 0.20/0.41 tff(13,plain,
% 0.20/0.41 (~((~ok(im_succ_cpq(triple(U!2, V!1, W!0)))) | (~check_cpq(im_succ_cpq(triple(U!2, V!1, W!0)))) | (~((~check_cpq(triple(U!2, V!1, W!0))) | (~ok(triple(U!2, V!1, W!0))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[12, 1])).
% 0.20/0.41 tff(14,plain,
% 0.20/0.41 (check_cpq(im_succ_cpq(triple(U!2, V!1, W!0)))),
% 0.20/0.41 inference(or_elim,[status(thm)],[13])).
% 0.20/0.41 tff(15,plain,
% 0.20/0.41 (ok(im_succ_cpq(triple(U!2, V!1, W!0)))),
% 0.20/0.41 inference(or_elim,[status(thm)],[13])).
% 0.20/0.41 tff(16,plain,
% 0.20/0.41 (^[U: $i, V: $i, W: $i] : refl(((~ok(im_succ_cpq(triple(U, V, W)))) | (~check_cpq(im_succ_cpq(triple(U, V, W)))) | check_cpq(triple(U, V, W))) <=> ((~ok(im_succ_cpq(triple(U, V, W)))) | (~check_cpq(im_succ_cpq(triple(U, V, W)))) | check_cpq(triple(U, V, W))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(17,plain,
% 0.20/0.41 (![U: $i, V: $i, W: $i] : ((~ok(im_succ_cpq(triple(U, V, W)))) | (~check_cpq(im_succ_cpq(triple(U, V, W)))) | check_cpq(triple(U, V, W))) <=> ![U: $i, V: $i, W: $i] : ((~ok(im_succ_cpq(triple(U, V, W)))) | (~check_cpq(im_succ_cpq(triple(U, V, W)))) | check_cpq(triple(U, V, W)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[16])).
% 0.20/0.41 tff(18,plain,
% 0.20/0.41 (![U: $i, V: $i, W: $i] : ((~ok(im_succ_cpq(triple(U, V, W)))) | (~check_cpq(im_succ_cpq(triple(U, V, W)))) | check_cpq(triple(U, V, W))) <=> ![U: $i, V: $i, W: $i] : ((~ok(im_succ_cpq(triple(U, V, W)))) | (~check_cpq(im_succ_cpq(triple(U, V, W)))) | check_cpq(triple(U, V, W)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(19,plain,
% 0.20/0.41 (^[U: $i, V: $i, W: $i] : rewrite(((~check_cpq(triple(U, V, W))) => ((~check_cpq(im_succ_cpq(triple(U, V, W)))) | (~ok(im_succ_cpq(triple(U, V, W)))))) <=> ((~ok(im_succ_cpq(triple(U, V, W)))) | (~check_cpq(im_succ_cpq(triple(U, V, W)))) | check_cpq(triple(U, V, W))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(20,plain,
% 0.20/0.41 (![U: $i, V: $i, W: $i] : ((~check_cpq(triple(U, V, W))) => ((~check_cpq(im_succ_cpq(triple(U, V, W)))) | (~ok(im_succ_cpq(triple(U, V, W)))))) <=> ![U: $i, V: $i, W: $i] : ((~ok(im_succ_cpq(triple(U, V, W)))) | (~check_cpq(im_succ_cpq(triple(U, V, W)))) | check_cpq(triple(U, V, W)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[19])).
% 0.20/0.41 tff(21,axiom,(![U: $i, V: $i, W: $i] : ((~check_cpq(triple(U, V, W))) => ((~check_cpq(im_succ_cpq(triple(U, V, W)))) | (~ok(im_succ_cpq(triple(U, V, W))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l21_li2225')).
% 0.20/0.41 tff(22,plain,
% 0.20/0.41 (![U: $i, V: $i, W: $i] : ((~ok(im_succ_cpq(triple(U, V, W)))) | (~check_cpq(im_succ_cpq(triple(U, V, W)))) | check_cpq(triple(U, V, W)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.20/0.41 tff(23,plain,
% 0.20/0.41 (![U: $i, V: $i, W: $i] : ((~ok(im_succ_cpq(triple(U, V, W)))) | (~check_cpq(im_succ_cpq(triple(U, V, W)))) | check_cpq(triple(U, V, W)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.20/0.41 tff(24,plain,(
% 0.20/0.41 ![U: $i, V: $i, W: $i] : ((~ok(im_succ_cpq(triple(U, V, W)))) | (~check_cpq(im_succ_cpq(triple(U, V, W)))) | check_cpq(triple(U, V, W)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[23])).
% 0.20/0.41 tff(25,plain,
% 0.20/0.41 (![U: $i, V: $i, W: $i] : ((~ok(im_succ_cpq(triple(U, V, W)))) | (~check_cpq(im_succ_cpq(triple(U, V, W)))) | check_cpq(triple(U, V, W)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.20/0.41 tff(26,plain,
% 0.20/0.41 (((~![U: $i, V: $i, W: $i] : ((~ok(im_succ_cpq(triple(U, V, W)))) | (~check_cpq(im_succ_cpq(triple(U, V, W)))) | check_cpq(triple(U, V, W)))) | ((~ok(im_succ_cpq(triple(U!2, V!1, W!0)))) | (~check_cpq(im_succ_cpq(triple(U!2, V!1, W!0)))) | check_cpq(triple(U!2, V!1, W!0)))) <=> ((~![U: $i, V: $i, W: $i] : ((~ok(im_succ_cpq(triple(U, V, W)))) | (~check_cpq(im_succ_cpq(triple(U, V, W)))) | check_cpq(triple(U, V, W)))) | (~ok(im_succ_cpq(triple(U!2, V!1, W!0)))) | (~check_cpq(im_succ_cpq(triple(U!2, V!1, W!0)))) | check_cpq(triple(U!2, V!1, W!0)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(27,plain,
% 0.20/0.41 ((~![U: $i, V: $i, W: $i] : ((~ok(im_succ_cpq(triple(U, V, W)))) | (~check_cpq(im_succ_cpq(triple(U, V, W)))) | check_cpq(triple(U, V, W)))) | ((~ok(im_succ_cpq(triple(U!2, V!1, W!0)))) | (~check_cpq(im_succ_cpq(triple(U!2, V!1, W!0)))) | check_cpq(triple(U!2, V!1, W!0)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(28,plain,
% 0.20/0.41 ((~![U: $i, V: $i, W: $i] : ((~ok(im_succ_cpq(triple(U, V, W)))) | (~check_cpq(im_succ_cpq(triple(U, V, W)))) | check_cpq(triple(U, V, W)))) | (~ok(im_succ_cpq(triple(U!2, V!1, W!0)))) | (~check_cpq(im_succ_cpq(triple(U!2, V!1, W!0)))) | check_cpq(triple(U!2, V!1, W!0))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.20/0.42 tff(29,plain,
% 0.20/0.42 (check_cpq(triple(U!2, V!1, W!0))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[28, 25, 15, 14])).
% 0.20/0.42 tff(30,plain,
% 0.20/0.42 (^[U: $i, V: $i, W: $i] : refl((ok(triple(U, V, W)) | (~ok(im_succ_cpq(triple(U, V, W))))) <=> (ok(triple(U, V, W)) | (~ok(im_succ_cpq(triple(U, V, W))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(31,plain,
% 0.20/0.42 (![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~ok(im_succ_cpq(triple(U, V, W))))) <=> ![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~ok(im_succ_cpq(triple(U, V, W)))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[30])).
% 0.20/0.42 tff(32,plain,
% 0.20/0.42 (![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~ok(im_succ_cpq(triple(U, V, W))))) <=> ![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~ok(im_succ_cpq(triple(U, V, W)))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(33,plain,
% 0.20/0.42 (^[U: $i, V: $i, W: $i] : rewrite(((~ok(triple(U, V, W))) => (~ok(im_succ_cpq(triple(U, V, W))))) <=> (ok(triple(U, V, W)) | (~ok(im_succ_cpq(triple(U, V, W))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(34,plain,
% 0.20/0.42 (![U: $i, V: $i, W: $i] : ((~ok(triple(U, V, W))) => (~ok(im_succ_cpq(triple(U, V, W))))) <=> ![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~ok(im_succ_cpq(triple(U, V, W)))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[33])).
% 0.20/0.42 tff(35,axiom,(![U: $i, V: $i, W: $i] : ((~ok(triple(U, V, W))) => (~ok(im_succ_cpq(triple(U, V, W)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l21_li1316')).
% 0.20/0.42 tff(36,plain,
% 0.20/0.42 (![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~ok(im_succ_cpq(triple(U, V, W)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.20/0.42 tff(37,plain,
% 0.20/0.42 (![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~ok(im_succ_cpq(triple(U, V, W)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.20/0.42 tff(38,plain,(
% 0.20/0.42 ![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~ok(im_succ_cpq(triple(U, V, W)))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[37])).
% 0.20/0.42 tff(39,plain,
% 0.20/0.42 (![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~ok(im_succ_cpq(triple(U, V, W)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.20/0.42 tff(40,plain,
% 0.20/0.42 (((~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~ok(im_succ_cpq(triple(U, V, W)))))) | (ok(triple(U!2, V!1, W!0)) | (~ok(im_succ_cpq(triple(U!2, V!1, W!0)))))) <=> ((~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~ok(im_succ_cpq(triple(U, V, W)))))) | ok(triple(U!2, V!1, W!0)) | (~ok(im_succ_cpq(triple(U!2, V!1, W!0)))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(41,plain,
% 0.20/0.42 ((~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~ok(im_succ_cpq(triple(U, V, W)))))) | (ok(triple(U!2, V!1, W!0)) | (~ok(im_succ_cpq(triple(U!2, V!1, W!0)))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(42,plain,
% 0.20/0.42 ((~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~ok(im_succ_cpq(triple(U, V, W)))))) | ok(triple(U!2, V!1, W!0)) | (~ok(im_succ_cpq(triple(U!2, V!1, W!0))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.20/0.42 tff(43,plain,
% 0.20/0.42 (ok(triple(U!2, V!1, W!0))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[42, 39, 15])).
% 0.20/0.42 tff(44,plain,
% 0.20/0.42 ((~check_cpq(triple(U!2, V!1, W!0))) | (~ok(triple(U!2, V!1, W!0)))),
% 0.20/0.42 inference(or_elim,[status(thm)],[13])).
% 0.20/0.42 tff(45,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[44, 43, 29])).
% 0.20/0.42 % SZS output end Proof
%------------------------------------------------------------------------------