%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV405+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 05:32:23 AM UTC 2025
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV405+1 : TPTP v9.0.0. Released v3.3.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 09:45:24 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(check_cpq_type, type, (
% 0.12/0.38 check_cpq: $i > $o)).
% 0.12/0.38 tff(triple_type, type, (
% 0.12/0.38 triple: ( $i * $i * $i ) > $i)).
% 0.12/0.38 tff(tptp_fun_V_0_type, type, (
% 0.12/0.38 tptp_fun_V_0: $i)).
% 0.12/0.38 tff(create_slb_type, type, (
% 0.12/0.38 create_slb: $i)).
% 0.12/0.38 tff(tptp_fun_U_1_type, type, (
% 0.12/0.38 tptp_fun_U_1: $i)).
% 0.12/0.38 tff(less_than_type, type, (
% 0.12/0.38 less_than: ( $i * $i ) > $o)).
% 0.12/0.38 tff(tptp_fun_W_3_type, type, (
% 0.12/0.38 tptp_fun_W_3: $i)).
% 0.12/0.38 tff(tptp_fun_X_2_type, type, (
% 0.12/0.38 tptp_fun_X_2: $i)).
% 0.12/0.38 tff(pair_in_list_type, type, (
% 0.12/0.38 pair_in_list: ( $i * $i * $i ) > $o)).
% 0.12/0.38 tff(1,assumption,(pair_in_list(create_slb, W!3, X!2)), introduced(assumption)).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 (^[U: $i, V: $i] : refl((~pair_in_list(create_slb, U, V)) <=> (~pair_in_list(create_slb, U, V)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (![U: $i, V: $i] : (~pair_in_list(create_slb, U, V)) <=> ![U: $i, V: $i] : (~pair_in_list(create_slb, U, V))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 (![U: $i, V: $i] : (~pair_in_list(create_slb, U, V)) <=> ![U: $i, V: $i] : (~pair_in_list(create_slb, U, V))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(5,axiom,(![U: $i, V: $i] : (~pair_in_list(create_slb, U, V))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+2.ax','ax22')).
% 0.12/0.38 tff(6,plain,
% 0.12/0.38 (![U: $i, V: $i] : (~pair_in_list(create_slb, U, V))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.12/0.38 tff(7,plain,(
% 0.12/0.38 ![U: $i, V: $i] : (~pair_in_list(create_slb, U, V))),
% 0.12/0.38 inference(skolemize,[status(sab)],[6])).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 (![U: $i, V: $i] : (~pair_in_list(create_slb, U, V))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 ((~![U: $i, V: $i] : (~pair_in_list(create_slb, U, V))) | (~pair_in_list(create_slb, W!3, X!2))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.12/0.38 tff(11,plain,(~pair_in_list(create_slb, W!3, X!2)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 (((~pair_in_list(create_slb, W!3, X!2)) | less_than(X!2, W!3)) | pair_in_list(create_slb, W!3, X!2)),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 ((~pair_in_list(create_slb, W!3, X!2)) | less_than(X!2, W!3)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[12, 11])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 ((check_cpq(triple(U!1, create_slb, V!0)) | ![W: $i, X: $i] : ((~pair_in_list(create_slb, W, X)) | less_than(X, W))) <=> (check_cpq(triple(U!1, create_slb, V!0)) | ![W: $i, X: $i] : ((~pair_in_list(create_slb, W, X)) | less_than(X, W)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (((check_cpq(triple(U!1, create_slb, V!0)) | ![W: $i, X: $i] : ((~pair_in_list(create_slb, W, X)) | less_than(X, W))) & ((~check_cpq(triple(U!1, create_slb, V!0))) | (~((~pair_in_list(create_slb, W!3, X!2)) | less_than(X!2, W!3))))) <=> ((check_cpq(triple(U!1, create_slb, V!0)) | ![W: $i, X: $i] : ((~pair_in_list(create_slb, W, X)) | less_than(X, W))) & ((~check_cpq(triple(U!1, create_slb, V!0))) | (~((~pair_in_list(create_slb, W!3, X!2)) | less_than(X!2, W!3)))))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[14])).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 ((~![U: $i, V: $i] : (check_cpq(triple(U, create_slb, V)) <=> ![W: $i, X: $i] : ((~pair_in_list(create_slb, W, X)) | less_than(X, W)))) <=> (~![U: $i, V: $i] : (check_cpq(triple(U, create_slb, V)) <=> ![W: $i, X: $i] : ((~pair_in_list(create_slb, W, X)) | less_than(X, W))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 ((~![U: $i, V: $i] : (check_cpq(triple(U, create_slb, V)) <=> ![W: $i, X: $i] : (pair_in_list(create_slb, W, X) => less_than(X, W)))) <=> (~![U: $i, V: $i] : (check_cpq(triple(U, create_slb, V)) <=> ![W: $i, X: $i] : ((~pair_in_list(create_slb, W, X)) | less_than(X, W))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(18,axiom,(~![U: $i, V: $i] : (check_cpq(triple(U, create_slb, V)) <=> ![W: $i, X: $i] : (pair_in_list(create_slb, W, X) => less_than(X, W)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l41_co')).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (~![U: $i, V: $i] : (check_cpq(triple(U, create_slb, V)) <=> ![W: $i, X: $i] : ((~pair_in_list(create_slb, W, X)) | less_than(X, W)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.12/0.39 tff(20,plain,
% 0.12/0.39 (~![U: $i, V: $i] : (check_cpq(triple(U, create_slb, V)) <=> ![W: $i, X: $i] : ((~pair_in_list(create_slb, W, X)) | less_than(X, W)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[19, 16])).
% 0.12/0.39 tff(21,plain,
% 0.12/0.39 (~![U: $i, V: $i] : (check_cpq(triple(U, create_slb, V)) <=> ![W: $i, X: $i] : ((~pair_in_list(create_slb, W, X)) | less_than(X, W)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.12/0.39 tff(22,plain,
% 0.12/0.39 (~![U: $i, V: $i] : (check_cpq(triple(U, create_slb, V)) <=> ![W: $i, X: $i] : ((~pair_in_list(create_slb, W, X)) | less_than(X, W)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[21, 16])).
% 0.12/0.39 tff(23,plain,
% 0.12/0.39 ((check_cpq(triple(U!1, create_slb, V!0)) | ![W: $i, X: $i] : ((~pair_in_list(create_slb, W, X)) | less_than(X, W))) & ((~check_cpq(triple(U!1, create_slb, V!0))) | (~((~pair_in_list(create_slb, W!3, X!2)) | less_than(X!2, W!3))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.12/0.39 tff(24,plain,
% 0.12/0.39 ((~check_cpq(triple(U!1, create_slb, V!0))) | (~((~pair_in_list(create_slb, W!3, X!2)) | less_than(X!2, W!3)))),
% 0.12/0.39 inference(and_elim,[status(thm)],[23])).
% 0.12/0.39 tff(25,plain,
% 0.12/0.39 (~check_cpq(triple(U!1, create_slb, V!0))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[24, 13])).
% 0.12/0.39 tff(26,plain,
% 0.12/0.39 (^[U: $i, V: $i] : refl(check_cpq(triple(U, create_slb, V)) <=> check_cpq(triple(U, create_slb, V)))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(27,plain,
% 0.12/0.39 (![U: $i, V: $i] : check_cpq(triple(U, create_slb, V)) <=> ![U: $i, V: $i] : check_cpq(triple(U, create_slb, V))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[26])).
% 0.12/0.39 tff(28,plain,
% 0.12/0.39 (![U: $i, V: $i] : check_cpq(triple(U, create_slb, V)) <=> ![U: $i, V: $i] : check_cpq(triple(U, create_slb, V))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(29,axiom,(![U: $i, V: $i] : check_cpq(triple(U, create_slb, V))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax','ax36')).
% 0.12/0.39 tff(30,plain,
% 0.12/0.39 (![U: $i, V: $i] : check_cpq(triple(U, create_slb, V))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.12/0.39 tff(31,plain,(
% 0.12/0.39 ![U: $i, V: $i] : check_cpq(triple(U, create_slb, V))),
% 0.12/0.39 inference(skolemize,[status(sab)],[30])).
% 0.12/0.39 tff(32,plain,
% 0.12/0.39 (![U: $i, V: $i] : check_cpq(triple(U, create_slb, V))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.12/0.39 tff(33,plain,
% 0.12/0.39 ((~![U: $i, V: $i] : check_cpq(triple(U, create_slb, V))) | check_cpq(triple(U!1, create_slb, V!0))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(34,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[33, 32, 25])).
% 0.12/0.39 % SZS output end Proof
% 0.12/0.39 % E exiting
%------------------------------------------------------------------------------