%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV397+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:32:22 AM UTC 2025
% Result : Theorem 0.23s 0.42s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.15 % Problem : SWV397+1 : TPTP v9.0.0. Released v3.3.0.
% 0.08/0.15 % Command : run_E %s %d THM
% 0.15/0.37 % Computer : n015.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Fri Jun 20 09:45:26 EDT 2025
% 0.15/0.37 % CPUTime :
% 0.23/0.42 % SZS status Theorem
% 0.23/0.42 % SZS output start Proof
% 0.23/0.42 tff(ok_type, type, (
% 0.23/0.42 ok: $i > $o)).
% 0.23/0.42 tff(triple_type, type, (
% 0.23/0.42 triple: ( $i * $i * $i ) > $i)).
% 0.23/0.42 tff(bad_type, type, (
% 0.23/0.42 bad: $i)).
% 0.23/0.42 tff(tptp_fun_V_2_type, type, (
% 0.23/0.42 tptp_fun_V_2: $i)).
% 0.23/0.42 tff(tptp_fun_U_3_type, type, (
% 0.23/0.42 tptp_fun_U_3: $i)).
% 0.23/0.42 tff(remove_cpq_type, type, (
% 0.23/0.42 remove_cpq: ( $i * $i ) > $i)).
% 0.23/0.42 tff(tptp_fun_X_0_type, type, (
% 0.23/0.42 tptp_fun_X_0: $i)).
% 0.23/0.42 tff(tptp_fun_W_1_type, type, (
% 0.23/0.42 tptp_fun_W_1: $i)).
% 0.23/0.42 tff(contains_slb_type, type, (
% 0.23/0.42 contains_slb: ( $i * $i ) > $o)).
% 0.23/0.42 tff(1,plain,
% 0.23/0.42 ((~![U: $i, V: $i, W: $i, X: $i] : ((~ok(remove_cpq(triple(U, V, W), X))) | contains_slb(V, X))) <=> (~![U: $i, V: $i, W: $i, X: $i] : ((~ok(remove_cpq(triple(U, V, W), X))) | contains_slb(V, X)))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(2,plain,
% 0.23/0.42 ((~![U: $i, V: $i, W: $i, X: $i] : (ok(remove_cpq(triple(U, V, W), X)) => contains_slb(V, X))) <=> (~![U: $i, V: $i, W: $i, X: $i] : ((~ok(remove_cpq(triple(U, V, W), X))) | contains_slb(V, X)))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(3,axiom,(~![U: $i, V: $i, W: $i, X: $i] : (ok(remove_cpq(triple(U, V, W), X)) => contains_slb(V, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l33_co')).
% 0.23/0.42 tff(4,plain,
% 0.23/0.42 (~![U: $i, V: $i, W: $i, X: $i] : ((~ok(remove_cpq(triple(U, V, W), X))) | contains_slb(V, X))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.23/0.42 tff(5,plain,
% 0.23/0.42 (~![U: $i, V: $i, W: $i, X: $i] : ((~ok(remove_cpq(triple(U, V, W), X))) | contains_slb(V, X))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.23/0.42 tff(6,plain,
% 0.23/0.42 (~![U: $i, V: $i, W: $i, X: $i] : ((~ok(remove_cpq(triple(U, V, W), X))) | contains_slb(V, X))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.23/0.42 tff(7,plain,
% 0.23/0.42 (~![U: $i, V: $i, W: $i, X: $i] : ((~ok(remove_cpq(triple(U, V, W), X))) | contains_slb(V, X))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.23/0.42 tff(8,plain,(
% 0.23/0.42 ~((~ok(remove_cpq(triple(U!3, V!2, W!1), X!0))) | contains_slb(V!2, X!0))),
% 0.23/0.42 inference(skolemize,[status(sab)],[7])).
% 0.23/0.42 tff(9,plain,
% 0.23/0.42 (~contains_slb(V!2, X!0)),
% 0.23/0.42 inference(or_elim,[status(thm)],[8])).
% 0.23/0.42 tff(10,plain,
% 0.23/0.42 (^[U: $i, V: $i, W: $i, X: $i] : refl((contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad))) <=> (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad))))),
% 0.23/0.42 inference(bind,[status(th)],[])).
% 0.23/0.42 tff(11,plain,
% 0.23/0.42 (![U: $i, V: $i, W: $i, X: $i] : (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad))) <=> ![U: $i, V: $i, W: $i, X: $i] : (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad)))),
% 0.23/0.42 inference(quant_intro,[status(thm)],[10])).
% 0.23/0.42 tff(12,plain,
% 0.23/0.42 (![U: $i, V: $i, W: $i, X: $i] : (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad))) <=> ![U: $i, V: $i, W: $i, X: $i] : (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad)))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(13,plain,
% 0.23/0.42 (^[U: $i, V: $i, W: $i, X: $i] : rewrite(((~contains_slb(V, X)) => (remove_cpq(triple(U, V, W), X) = triple(U, V, bad))) <=> (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad))))),
% 0.23/0.42 inference(bind,[status(th)],[])).
% 0.23/0.42 tff(14,plain,
% 0.23/0.42 (![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) => (remove_cpq(triple(U, V, W), X) = triple(U, V, bad))) <=> ![U: $i, V: $i, W: $i, X: $i] : (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad)))),
% 0.23/0.42 inference(quant_intro,[status(thm)],[13])).
% 0.23/0.42 tff(15,axiom,(![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) => (remove_cpq(triple(U, V, W), X) = triple(U, V, bad)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax','ax43')).
% 0.23/0.42 tff(16,plain,
% 0.23/0.42 (![U: $i, V: $i, W: $i, X: $i] : (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad)))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.23/0.42 tff(17,plain,
% 0.23/0.42 (![U: $i, V: $i, W: $i, X: $i] : (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad)))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.23/0.42 tff(18,plain,(
% 0.23/0.42 ![U: $i, V: $i, W: $i, X: $i] : (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad)))),
% 0.23/0.43 inference(skolemize,[status(sab)],[17])).
% 0.23/0.43 tff(19,plain,
% 0.23/0.43 (![U: $i, V: $i, W: $i, X: $i] : (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad)))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.23/0.43 tff(20,plain,
% 0.23/0.43 (((~![U: $i, V: $i, W: $i, X: $i] : (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad)))) | (contains_slb(V!2, X!0) | (remove_cpq(triple(U!3, V!2, W!1), X!0) = triple(U!3, V!2, bad)))) <=> ((~![U: $i, V: $i, W: $i, X: $i] : (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad)))) | contains_slb(V!2, X!0) | (remove_cpq(triple(U!3, V!2, W!1), X!0) = triple(U!3, V!2, bad)))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(21,plain,
% 0.23/0.43 ((~![U: $i, V: $i, W: $i, X: $i] : (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad)))) | (contains_slb(V!2, X!0) | (remove_cpq(triple(U!3, V!2, W!1), X!0) = triple(U!3, V!2, bad)))),
% 0.23/0.43 inference(quant_inst,[status(thm)],[])).
% 0.23/0.43 tff(22,plain,
% 0.23/0.43 ((~![U: $i, V: $i, W: $i, X: $i] : (contains_slb(V, X) | (remove_cpq(triple(U, V, W), X) = triple(U, V, bad)))) | contains_slb(V!2, X!0) | (remove_cpq(triple(U!3, V!2, W!1), X!0) = triple(U!3, V!2, bad))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.23/0.43 tff(23,plain,
% 0.23/0.43 (remove_cpq(triple(U!3, V!2, W!1), X!0) = triple(U!3, V!2, bad)),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[22, 19, 9])).
% 0.23/0.43 tff(24,plain,
% 0.23/0.43 (triple(U!3, V!2, bad) = remove_cpq(triple(U!3, V!2, W!1), X!0)),
% 0.23/0.43 inference(symmetry,[status(thm)],[23])).
% 0.23/0.43 tff(25,plain,
% 0.23/0.43 (ok(triple(U!3, V!2, bad)) <=> ok(remove_cpq(triple(U!3, V!2, W!1), X!0))),
% 0.23/0.43 inference(monotonicity,[status(thm)],[24])).
% 0.23/0.43 tff(26,plain,
% 0.23/0.43 (ok(remove_cpq(triple(U!3, V!2, W!1), X!0)) <=> ok(triple(U!3, V!2, bad))),
% 0.23/0.43 inference(symmetry,[status(thm)],[25])).
% 0.23/0.43 tff(27,plain,
% 0.23/0.43 (ok(remove_cpq(triple(U!3, V!2, W!1), X!0))),
% 0.23/0.43 inference(or_elim,[status(thm)],[8])).
% 0.23/0.43 tff(28,plain,
% 0.23/0.43 (ok(triple(U!3, V!2, bad))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.23/0.43 tff(29,plain,
% 0.23/0.43 (^[U: $i, V: $i] : refl((~ok(triple(U, V, bad))) <=> (~ok(triple(U, V, bad))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(30,plain,
% 0.23/0.43 (![U: $i, V: $i] : (~ok(triple(U, V, bad))) <=> ![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[29])).
% 0.23/0.43 tff(31,plain,
% 0.23/0.43 (![U: $i, V: $i] : (~ok(triple(U, V, bad))) <=> ![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(32,plain,
% 0.23/0.43 (^[U: $i, V: $i] : rewrite((ok(triple(U, V, bad)) <=> $false) <=> (~ok(triple(U, V, bad))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(33,plain,
% 0.23/0.43 (![U: $i, V: $i] : (ok(triple(U, V, bad)) <=> $false) <=> ![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[32])).
% 0.23/0.43 tff(34,axiom,(![U: $i, V: $i] : (ok(triple(U, V, bad)) <=> $false)), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax','ax40')).
% 0.23/0.43 tff(35,plain,
% 0.23/0.43 (![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.23/0.43 tff(36,plain,
% 0.23/0.43 (![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.23/0.43 tff(37,plain,(
% 0.23/0.43 ![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.23/0.43 inference(skolemize,[status(sab)],[36])).
% 0.23/0.43 tff(38,plain,
% 0.23/0.43 (![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.23/0.43 tff(39,plain,
% 0.23/0.43 ((~![U: $i, V: $i] : (~ok(triple(U, V, bad)))) | (~ok(triple(U!3, V!2, bad)))),
% 0.23/0.43 inference(quant_inst,[status(thm)],[])).
% 0.23/0.43 tff(40,plain,
% 0.23/0.43 (~ok(triple(U!3, V!2, bad))),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.23/0.43 tff(41,plain,
% 0.23/0.43 ($false),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[40, 28])).
% 0.23/0.43 % SZS output end Proof
% 0.23/0.43 % E exiting
%------------------------------------------------------------------------------