%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV377+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 Jun 21 05:32:20 AM UTC 2025
% Result : Theorem 0.24s 0.41s
% Output : Proof 0.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : SWV377+1 : TPTP v9.0.0. Released v3.3.0.
% 0.04/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n012.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 09:43:40 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.24/0.41 % SZS status Theorem
% 0.24/0.41 % SZS output start Proof
% 0.24/0.41 tff(ok_type, type, (
% 0.24/0.41 ok: $i > $o)).
% 0.24/0.41 tff(triple_type, type, (
% 0.24/0.41 triple: ( $i * $i * $i ) > $i)).
% 0.24/0.41 tff(bad_type, type, (
% 0.24/0.41 bad: $i)).
% 0.24/0.41 tff(insert_slb_type, type, (
% 0.24/0.41 insert_slb: ( $i * $i ) > $i)).
% 0.24/0.41 tff(pair_type, type, (
% 0.24/0.41 pair: ( $i * $i ) > $i)).
% 0.24/0.41 tff(bottom_type, type, (
% 0.24/0.41 bottom: $i)).
% 0.24/0.41 tff(tptp_fun_X_0_type, type, (
% 0.24/0.41 tptp_fun_X_0: $i)).
% 0.24/0.41 tff(tptp_fun_V_2_type, type, (
% 0.24/0.41 tptp_fun_V_2: $i)).
% 0.24/0.41 tff(insert_pqp_type, type, (
% 0.24/0.41 insert_pqp: ( $i * $i ) > $i)).
% 0.24/0.41 tff(tptp_fun_U_3_type, type, (
% 0.24/0.41 tptp_fun_U_3: $i)).
% 0.24/0.41 tff(insert_cpq_type, type, (
% 0.24/0.41 insert_cpq: ( $i * $i ) > $i)).
% 0.24/0.41 tff(tptp_fun_W_1_type, type, (
% 0.24/0.41 tptp_fun_W_1: $i)).
% 0.24/0.41 tff(1,plain,
% 0.24/0.41 (^[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)))),
% 0.24/0.41 inference(bind,[status(th)],[])).
% 0.24/0.41 tff(2,plain,
% 0.24/0.41 (![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))),
% 0.24/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.24/0.41 tff(3,plain,
% 0.24/0.41 (![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))),
% 0.24/0.41 inference(rewrite,[status(thm)],[])).
% 0.24/0.41 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/sandbox2/benchmark/Axioms/SWV007+3.ax','ax42')).
% 0.24/0.41 tff(5,plain,
% 0.24/0.41 (![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))),
% 0.24/0.41 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.24/0.41 tff(6,plain,(
% 0.24/0.41 ![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))),
% 0.24/0.41 inference(skolemize,[status(sab)],[5])).
% 0.24/0.41 tff(7,plain,
% 0.24/0.41 (![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))),
% 0.24/0.41 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.24/0.41 tff(8,plain,
% 0.24/0.41 ((~![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))),
% 0.24/0.41 inference(quant_inst,[status(thm)],[])).
% 0.24/0.41 tff(9,plain,
% 0.24/0.41 (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)),
% 0.24/0.41 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.24/0.41 tff(10,plain,
% 0.24/0.41 (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)),
% 0.24/0.41 inference(symmetry,[status(thm)],[9])).
% 0.24/0.41 tff(11,plain,
% 0.24/0.41 ((~![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)))))),
% 0.24/0.41 inference(rewrite,[status(thm)],[])).
% 0.24/0.41 tff(12,plain,
% 0.24/0.41 ((~![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)))))),
% 0.24/0.41 inference(rewrite,[status(thm)],[])).
% 0.24/0.41 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/sandbox2/benchmark/theBenchmark.p','l13_co')).
% 0.24/0.41 tff(14,plain,
% 0.24/0.41 (~![U: $i, V: $i, W: $i, X: $i] : (ok(triple(U, V, W)) | (~ok(insert_cpq(triple(U, V, W), X))))),
% 0.24/0.41 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.24/0.41 tff(15,plain,
% 0.24/0.41 (~![U: $i, V: $i, W: $i, X: $i] : (ok(triple(U, V, W)) | (~ok(insert_cpq(triple(U, V, W), X))))),
% 0.24/0.41 inference(modus_ponens,[status(thm)],[14, 11])).
% 0.24/0.42 tff(16,plain,
% 0.24/0.42 (~![U: $i, V: $i, W: $i, X: $i] : (ok(triple(U, V, W)) | (~ok(insert_cpq(triple(U, V, W), X))))),
% 0.24/0.42 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.24/0.42 tff(17,plain,
% 0.24/0.42 (~![U: $i, V: $i, W: $i, X: $i] : (ok(triple(U, V, W)) | (~ok(insert_cpq(triple(U, V, W), X))))),
% 0.24/0.42 inference(modus_ponens,[status(thm)],[16, 11])).
% 0.24/0.42 tff(18,plain,(
% 0.24/0.42 ~(ok(triple(U!3, V!2, W!1)) | (~ok(insert_cpq(triple(U!3, V!2, W!1), X!0))))),
% 0.24/0.42 inference(skolemize,[status(sab)],[17])).
% 0.24/0.42 tff(19,plain,
% 0.24/0.42 (~ok(triple(U!3, V!2, W!1))),
% 0.24/0.42 inference(or_elim,[status(thm)],[18])).
% 0.24/0.42 tff(20,plain,
% 0.24/0.42 (^[U: $i, V: $i, W: $i] : refl((ok(triple(U, V, W)) | (W = bad)) <=> (ok(triple(U, V, W)) | (W = bad)))),
% 0.24/0.42 inference(bind,[status(th)],[])).
% 0.24/0.42 tff(21,plain,
% 0.24/0.42 (![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))),
% 0.24/0.42 inference(quant_intro,[status(thm)],[20])).
% 0.24/0.42 tff(22,plain,
% 0.24/0.42 (![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))),
% 0.24/0.42 inference(rewrite,[status(thm)],[])).
% 0.24/0.42 tff(23,plain,
% 0.24/0.42 (^[U: $i, V: $i, W: $i] : rewrite(((~ok(triple(U, V, W))) => (W = bad)) <=> (ok(triple(U, V, W)) | (W = bad)))),
% 0.24/0.42 inference(bind,[status(th)],[])).
% 0.24/0.42 tff(24,plain,
% 0.24/0.42 (![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))),
% 0.24/0.42 inference(quant_intro,[status(thm)],[23])).
% 0.24/0.42 tff(25,axiom,(![U: $i, V: $i, W: $i] : ((~ok(triple(U, V, W))) => (W = bad))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax','ax41')).
% 0.24/0.42 tff(26,plain,
% 0.24/0.42 (![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))),
% 0.24/0.42 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.24/0.42 tff(27,plain,
% 0.24/0.42 (![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))),
% 0.24/0.42 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.24/0.42 tff(28,plain,(
% 0.24/0.42 ![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))),
% 0.24/0.42 inference(skolemize,[status(sab)],[27])).
% 0.24/0.42 tff(29,plain,
% 0.24/0.42 (![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))),
% 0.24/0.42 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.24/0.42 tff(30,plain,
% 0.24/0.42 (((~![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))),
% 0.24/0.42 inference(rewrite,[status(thm)],[])).
% 0.24/0.42 tff(31,plain,
% 0.24/0.42 ((~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))) | (ok(triple(U!3, V!2, W!1)) | (W!1 = bad))),
% 0.24/0.42 inference(quant_inst,[status(thm)],[])).
% 0.24/0.42 tff(32,plain,
% 0.24/0.42 ((~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))) | ok(triple(U!3, V!2, W!1)) | (W!1 = bad)),
% 0.24/0.42 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.24/0.42 tff(33,plain,
% 0.24/0.42 (W!1 = bad),
% 0.24/0.42 inference(unit_resolution,[status(thm)],[32, 29, 19])).
% 0.24/0.42 tff(34,plain,
% 0.24/0.42 (bad = W!1),
% 0.24/0.42 inference(symmetry,[status(thm)],[33])).
% 0.24/0.42 tff(35,plain,
% 0.24/0.42 (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)),
% 0.24/0.42 inference(monotonicity,[status(thm)],[34])).
% 0.24/0.42 tff(36,plain,
% 0.24/0.42 (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)),
% 0.24/0.42 inference(transitivity,[status(thm)],[35, 10])).
% 0.24/0.42 tff(37,plain,
% 0.24/0.42 (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))),
% 0.24/0.42 inference(monotonicity,[status(thm)],[36])).
% 0.24/0.42 tff(38,plain,
% 0.24/0.42 (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))),
% 0.24/0.42 inference(symmetry,[status(thm)],[37])).
% 0.24/0.42 tff(39,plain,
% 0.24/0.42 (ok(insert_cpq(triple(U!3, V!2, W!1), X!0))),
% 0.24/0.42 inference(or_elim,[status(thm)],[18])).
% 0.24/0.42 tff(40,plain,
% 0.24/0.42 (ok(triple(insert_pqp(U!3, X!0), insert_slb(V!2, pair(X!0, bottom)), bad))),
% 0.24/0.42 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.24/0.42 tff(41,plain,
% 0.24/0.42 (^[U: $i, V: $i] : refl((~ok(triple(U, V, bad))) <=> (~ok(triple(U, V, bad))))),
% 0.24/0.42 inference(bind,[status(th)],[])).
% 0.24/0.42 tff(42,plain,
% 0.24/0.42 (![U: $i, V: $i] : (~ok(triple(U, V, bad))) <=> ![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.24/0.42 inference(quant_intro,[status(thm)],[41])).
% 0.24/0.42 tff(43,plain,
% 0.24/0.42 (![U: $i, V: $i] : (~ok(triple(U, V, bad))) <=> ![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.24/0.42 inference(rewrite,[status(thm)],[])).
% 0.24/0.42 tff(44,plain,
% 0.24/0.42 (^[U: $i, V: $i] : rewrite((ok(triple(U, V, bad)) <=> $false) <=> (~ok(triple(U, V, bad))))),
% 0.24/0.42 inference(bind,[status(th)],[])).
% 0.24/0.42 tff(45,plain,
% 0.24/0.42 (![U: $i, V: $i] : (ok(triple(U, V, bad)) <=> $false) <=> ![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.24/0.42 inference(quant_intro,[status(thm)],[44])).
% 0.24/0.42 tff(46,axiom,(![U: $i, V: $i] : (ok(triple(U, V, bad)) <=> $false)), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax','ax40')).
% 0.24/0.42 tff(47,plain,
% 0.24/0.42 (![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.24/0.42 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.24/0.42 tff(48,plain,
% 0.24/0.42 (![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.24/0.42 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.24/0.42 tff(49,plain,(
% 0.24/0.42 ![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.24/0.42 inference(skolemize,[status(sab)],[48])).
% 0.24/0.42 tff(50,plain,
% 0.24/0.42 (![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.24/0.42 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.24/0.42 tff(51,plain,
% 0.24/0.42 ((~![U: $i, V: $i] : (~ok(triple(U, V, bad)))) | (~ok(triple(insert_pqp(U!3, X!0), insert_slb(V!2, pair(X!0, bottom)), bad)))),
% 0.24/0.42 inference(quant_inst,[status(thm)],[])).
% 0.24/0.42 tff(52,plain,
% 0.24/0.42 (~ok(triple(insert_pqp(U!3, X!0), insert_slb(V!2, pair(X!0, bottom)), bad))),
% 0.24/0.42 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.24/0.42 tff(53,plain,
% 0.24/0.42 ($false),
% 0.24/0.42 inference(unit_resolution,[status(thm)],[52, 40])).
% 0.24/0.42 % SZS output end Proof
% 0.24/0.42 % E exiting
%------------------------------------------------------------------------------