TSTP Solution File: SWV377+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV377+1 : TPTP v8.1.0. Released v3.3.0.
% 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 : Thu Sep 29 15:11:32 EDT 2022
% Result : Theorem 0.22s 0.42s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWV377+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.15/0.35 % Computer : n019.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sun Sep 4 02:48:05 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.15/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.15/0.36 Usage: tptp [options] [-file:]file
% 0.15/0.36 -h, -? prints this message.
% 0.15/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.15/0.36 -m, -model generate model.
% 0.15/0.36 -p, -proof generate proof.
% 0.15/0.36 -c, -core generate unsat core of named formulas.
% 0.15/0.36 -st, -statistics display statistics.
% 0.15/0.36 -t:timeout set timeout (in second).
% 0.15/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.15/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.15/0.36 -<param>:<value> configuration parameter and value.
% 0.15/0.36 -o:<output-file> file to place output in.
% 0.22/0.42 % SZS status Theorem
% 0.22/0.42 % SZS output start Proof
% 0.22/0.42 tff(ok_type, type, (
% 0.22/0.42 ok: $i > $o)).
% 0.22/0.42 tff(triple_type, type, (
% 0.22/0.42 triple: ( $i * $i * $i ) > $i)).
% 0.22/0.42 tff(bad_type, type, (
% 0.22/0.42 bad: $i)).
% 0.22/0.42 tff(insert_slb_type, type, (
% 0.22/0.42 insert_slb: ( $i * $i ) > $i)).
% 0.22/0.42 tff(pair_type, type, (
% 0.22/0.42 pair: ( $i * $i ) > $i)).
% 0.22/0.42 tff(bottom_type, type, (
% 0.22/0.42 bottom: $i)).
% 0.22/0.42 tff(tptp_fun_X_0_type, type, (
% 0.22/0.42 tptp_fun_X_0: $i)).
% 0.22/0.42 tff(tptp_fun_V_2_type, type, (
% 0.22/0.42 tptp_fun_V_2: $i)).
% 0.22/0.42 tff(insert_pqp_type, type, (
% 0.22/0.42 insert_pqp: ( $i * $i ) > $i)).
% 0.22/0.42 tff(tptp_fun_U_3_type, type, (
% 0.22/0.42 tptp_fun_U_3: $i)).
% 0.22/0.42 tff(insert_cpq_type, type, (
% 0.22/0.42 insert_cpq: ( $i * $i ) > $i)).
% 0.22/0.42 tff(tptp_fun_W_1_type, type, (
% 0.22/0.42 tptp_fun_W_1: $i)).
% 0.22/0.42 tff(1,plain,
% 0.22/0.42 (^[U: $i, V: $i, W: $i, X: $i] : refl((insert_cpq(triple(U, V, W), X) = triple(insert_pqp(U, X), insert_slb(V, pair(X, bottom)), W)) <=> (insert_cpq(triple(U, V, W), X) = triple(insert_pqp(U, X), insert_slb(V, pair(X, bottom)), W)))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(2,plain,
% 0.22/0.42 (![U: $i, V: $i, W: $i, X: $i] : (insert_cpq(triple(U, V, W), X) = triple(insert_pqp(U, X), insert_slb(V, pair(X, bottom)), W)) <=> ![U: $i, V: $i, W: $i, X: $i] : (insert_cpq(triple(U, V, W), X) = triple(insert_pqp(U, X), insert_slb(V, pair(X, bottom)), W))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[1])).
% 0.22/0.42 tff(3,plain,
% 0.22/0.42 (![U: $i, V: $i, W: $i, X: $i] : (insert_cpq(triple(U, V, W), X) = triple(insert_pqp(U, X), insert_slb(V, pair(X, bottom)), W)) <=> ![U: $i, V: $i, W: $i, X: $i] : (insert_cpq(triple(U, V, W), X) = triple(insert_pqp(U, X), insert_slb(V, pair(X, bottom)), W))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(4,axiom,(![U: $i, V: $i, W: $i, X: $i] : (insert_cpq(triple(U, V, W), X) = triple(insert_pqp(U, X), insert_slb(V, pair(X, bottom)), W))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax','ax42')).
% 0.22/0.42 tff(5,plain,
% 0.22/0.42 (![U: $i, V: $i, W: $i, X: $i] : (insert_cpq(triple(U, V, W), X) = triple(insert_pqp(U, X), insert_slb(V, pair(X, bottom)), W))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.22/0.42 tff(6,plain,(
% 0.22/0.42 ![U: $i, V: $i, W: $i, X: $i] : (insert_cpq(triple(U, V, W), X) = triple(insert_pqp(U, X), insert_slb(V, pair(X, bottom)), W))),
% 0.22/0.42 inference(skolemize,[status(sab)],[5])).
% 0.22/0.42 tff(7,plain,
% 0.22/0.42 (![U: $i, V: $i, W: $i, X: $i] : (insert_cpq(triple(U, V, W), X) = triple(insert_pqp(U, X), insert_slb(V, pair(X, bottom)), W))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.22/0.42 tff(8,plain,
% 0.22/0.42 ((~![U: $i, V: $i, W: $i, X: $i] : (insert_cpq(triple(U, V, W), X) = triple(insert_pqp(U, X), insert_slb(V, pair(X, bottom)), W))) | (insert_cpq(triple(U!3, V!2, W!1), X!0) = triple(insert_pqp(U!3, X!0), insert_slb(V!2, pair(X!0, bottom)), W!1))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(9,plain,
% 0.22/0.42 (insert_cpq(triple(U!3, V!2, W!1), X!0) = triple(insert_pqp(U!3, X!0), insert_slb(V!2, pair(X!0, bottom)), W!1)),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.22/0.42 tff(10,plain,
% 0.22/0.42 (triple(insert_pqp(U!3, X!0), insert_slb(V!2, pair(X!0, bottom)), W!1) = insert_cpq(triple(U!3, V!2, W!1), X!0)),
% 0.22/0.42 inference(symmetry,[status(thm)],[9])).
% 0.22/0.42 tff(11,plain,
% 0.22/0.42 ((~![U: $i, V: $i, W: $i, X: $i] : (ok(triple(U, V, W)) | (~ok(insert_cpq(triple(U, V, W), X))))) <=> (~![U: $i, V: $i, W: $i, X: $i] : (ok(triple(U, V, W)) | (~ok(insert_cpq(triple(U, V, W), X)))))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(12,plain,
% 0.22/0.42 ((~![U: $i, V: $i, W: $i, X: $i] : ((~ok(triple(U, V, W))) => (~ok(insert_cpq(triple(U, V, W), X))))) <=> (~![U: $i, V: $i, W: $i, X: $i] : (ok(triple(U, V, W)) | (~ok(insert_cpq(triple(U, V, W), X)))))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(13,axiom,(~![U: $i, V: $i, W: $i, X: $i] : ((~ok(triple(U, V, W))) => (~ok(insert_cpq(triple(U, V, W), X))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l13_co')).
% 0.22/0.42 tff(14,plain,
% 0.22/0.42 (~![U: $i, V: $i, W: $i, X: $i] : (ok(triple(U, V, W)) | (~ok(insert_cpq(triple(U, V, W), X))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.22/0.42 tff(15,plain,
% 0.22/0.42 (~![U: $i, V: $i, W: $i, X: $i] : (ok(triple(U, V, W)) | (~ok(insert_cpq(triple(U, V, W), X))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[14, 11])).
% 0.22/0.42 tff(16,plain,
% 0.22/0.42 (~![U: $i, V: $i, W: $i, X: $i] : (ok(triple(U, V, W)) | (~ok(insert_cpq(triple(U, V, W), X))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.22/0.42 tff(17,plain,
% 0.22/0.42 (~![U: $i, V: $i, W: $i, X: $i] : (ok(triple(U, V, W)) | (~ok(insert_cpq(triple(U, V, W), X))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[16, 11])).
% 0.22/0.42 tff(18,plain,
% 0.22/0.42 (~![U: $i, V: $i, W: $i, X: $i] : (ok(triple(U, V, W)) | (~ok(insert_cpq(triple(U, V, W), X))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[17, 11])).
% 0.22/0.42 tff(19,plain,
% 0.22/0.42 (~![U: $i, V: $i, W: $i, X: $i] : (ok(triple(U, V, W)) | (~ok(insert_cpq(triple(U, V, W), X))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.22/0.42 tff(20,plain,
% 0.22/0.42 (~![U: $i, V: $i, W: $i, X: $i] : (ok(triple(U, V, W)) | (~ok(insert_cpq(triple(U, V, W), X))))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[19, 11])).
% 0.22/0.42 tff(21,plain,(
% 0.22/0.42 ~(ok(triple(U!3, V!2, W!1)) | (~ok(insert_cpq(triple(U!3, V!2, W!1), X!0))))),
% 0.22/0.42 inference(skolemize,[status(sab)],[20])).
% 0.22/0.42 tff(22,plain,
% 0.22/0.42 (~ok(triple(U!3, V!2, W!1))),
% 0.22/0.42 inference(or_elim,[status(thm)],[21])).
% 0.22/0.42 tff(23,plain,
% 0.22/0.42 (^[U: $i, V: $i, W: $i] : refl((ok(triple(U, V, W)) | (W = bad)) <=> (ok(triple(U, V, W)) | (W = bad)))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(24,plain,
% 0.22/0.42 (![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad)) <=> ![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[23])).
% 0.22/0.42 tff(25,plain,
% 0.22/0.42 (![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad)) <=> ![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(26,plain,
% 0.22/0.42 (^[U: $i, V: $i, W: $i] : rewrite(((~ok(triple(U, V, W))) => (W = bad)) <=> (ok(triple(U, V, W)) | (W = bad)))),
% 0.22/0.42 inference(bind,[status(th)],[])).
% 0.22/0.42 tff(27,plain,
% 0.22/0.42 (![U: $i, V: $i, W: $i] : ((~ok(triple(U, V, W))) => (W = bad)) <=> ![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))),
% 0.22/0.42 inference(quant_intro,[status(thm)],[26])).
% 0.22/0.42 tff(28,axiom,(![U: $i, V: $i, W: $i] : ((~ok(triple(U, V, W))) => (W = bad))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax','ax41')).
% 0.22/0.42 tff(29,plain,
% 0.22/0.42 (![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.22/0.42 tff(30,plain,
% 0.22/0.42 (![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.22/0.42 tff(31,plain,(
% 0.22/0.42 ![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))),
% 0.22/0.42 inference(skolemize,[status(sab)],[30])).
% 0.22/0.42 tff(32,plain,
% 0.22/0.42 (![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.22/0.42 tff(33,plain,
% 0.22/0.42 (((~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))) | (ok(triple(U!3, V!2, W!1)) | (W!1 = bad))) <=> ((~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))) | ok(triple(U!3, V!2, W!1)) | (W!1 = bad))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(34,plain,
% 0.22/0.42 ((~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))) | (ok(triple(U!3, V!2, W!1)) | (W!1 = bad))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(35,plain,
% 0.22/0.42 ((~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))) | ok(triple(U!3, V!2, W!1)) | (W!1 = bad)),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.22/0.42 tff(36,plain,
% 0.22/0.42 (W!1 = bad),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[35, 32, 22])).
% 0.22/0.42 tff(37,plain,
% 0.22/0.42 (bad = W!1),
% 0.22/0.42 inference(symmetry,[status(thm)],[36])).
% 0.22/0.42 tff(38,plain,
% 0.22/0.42 (triple(insert_pqp(U!3, X!0), insert_slb(V!2, pair(X!0, bottom)), bad) = triple(insert_pqp(U!3, X!0), insert_slb(V!2, pair(X!0, bottom)), W!1)),
% 0.22/0.42 inference(monotonicity,[status(thm)],[37])).
% 0.22/0.42 tff(39,plain,
% 0.22/0.42 (triple(insert_pqp(U!3, X!0), insert_slb(V!2, pair(X!0, bottom)), bad) = insert_cpq(triple(U!3, V!2, W!1), X!0)),
% 0.22/0.42 inference(transitivity,[status(thm)],[38, 10])).
% 0.22/0.42 tff(40,plain,
% 0.22/0.42 (ok(triple(insert_pqp(U!3, X!0), insert_slb(V!2, pair(X!0, bottom)), bad)) <=> ok(insert_cpq(triple(U!3, V!2, W!1), X!0))),
% 0.22/0.42 inference(monotonicity,[status(thm)],[39])).
% 0.22/0.42 tff(41,plain,
% 0.22/0.43 (ok(insert_cpq(triple(U!3, V!2, W!1), X!0)) <=> ok(triple(insert_pqp(U!3, X!0), insert_slb(V!2, pair(X!0, bottom)), bad))),
% 0.22/0.43 inference(symmetry,[status(thm)],[40])).
% 0.22/0.43 tff(42,plain,
% 0.22/0.43 (ok(insert_cpq(triple(U!3, V!2, W!1), X!0))),
% 0.22/0.43 inference(or_elim,[status(thm)],[21])).
% 0.22/0.43 tff(43,plain,
% 0.22/0.43 (ok(triple(insert_pqp(U!3, X!0), insert_slb(V!2, pair(X!0, bottom)), bad))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.22/0.43 tff(44,plain,
% 0.22/0.43 (^[U: $i, V: $i] : refl((~ok(triple(U, V, bad))) <=> (~ok(triple(U, V, bad))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(45,plain,
% 0.22/0.43 (![U: $i, V: $i] : (~ok(triple(U, V, bad))) <=> ![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[44])).
% 0.22/0.43 tff(46,plain,
% 0.22/0.43 (![U: $i, V: $i] : (~ok(triple(U, V, bad))) <=> ![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(47,plain,
% 0.22/0.43 (^[U: $i, V: $i] : rewrite((ok(triple(U, V, bad)) <=> $false) <=> (~ok(triple(U, V, bad))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(48,plain,
% 0.22/0.43 (![U: $i, V: $i] : (ok(triple(U, V, bad)) <=> $false) <=> ![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[47])).
% 0.22/0.43 tff(49,axiom,(![U: $i, V: $i] : (ok(triple(U, V, bad)) <=> $false)), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax','ax40')).
% 0.22/0.43 tff(50,plain,
% 0.22/0.43 (![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.22/0.43 tff(51,plain,
% 0.22/0.43 (![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.22/0.43 tff(52,plain,(
% 0.22/0.43 ![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.22/0.43 inference(skolemize,[status(sab)],[51])).
% 0.22/0.43 tff(53,plain,
% 0.22/0.43 (![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.22/0.43 tff(54,plain,
% 0.22/0.43 ((~![U: $i, V: $i] : (~ok(triple(U, V, bad)))) | (~ok(triple(insert_pqp(U!3, X!0), insert_slb(V!2, pair(X!0, bottom)), bad)))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(55,plain,
% 0.22/0.43 (~ok(triple(insert_pqp(U!3, X!0), insert_slb(V!2, pair(X!0, bottom)), bad))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.22/0.43 tff(56,plain,
% 0.22/0.43 ($false),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[55, 43])).
% 0.22/0.43 % SZS output end Proof
%------------------------------------------------------------------------------