%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV412+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:32:24 AM UTC 2025
% Result : Theorem 0.13s 0.39s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWV412+1 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n005.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 : Fri Jun 20 09:45:20 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.39 % SZS status Theorem
% 0.13/0.39 % SZS output start Proof
% 0.13/0.39 tff(pair_in_list_type, type, (
% 0.13/0.39 pair_in_list: ( $i * $i * $i ) > $o)).
% 0.13/0.39 tff(tptp_fun_X_0_type, type, (
% 0.13/0.39 tptp_fun_X_0: $i)).
% 0.13/0.39 tff(tptp_fun_V_2_type, type, (
% 0.13/0.39 tptp_fun_V_2: $i)).
% 0.13/0.39 tff(update_slb_type, type, (
% 0.13/0.39 update_slb: ( $i * $i ) > $i)).
% 0.13/0.39 tff(tptp_fun_U_3_type, type, (
% 0.13/0.39 tptp_fun_U_3: $i)).
% 0.13/0.39 tff(strictly_less_than_type, type, (
% 0.13/0.39 strictly_less_than: ( $i * $i ) > $o)).
% 0.13/0.39 tff(tptp_fun_W_1_type, type, (
% 0.13/0.39 tptp_fun_W_1: $i)).
% 0.13/0.39 tff(1,plain,
% 0.13/0.39 ((~![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(V, X) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X))) <=> (~![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(V, X) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(2,plain,
% 0.13/0.39 ((~![U: $i, V: $i, W: $i, X: $i] : (((pair_in_list(U, V, W) & strictly_less_than(V, X)) & strictly_less_than(W, X)) => pair_in_list(update_slb(U, X), V, X))) <=> (~![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(V, X) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(3,axiom,(~![U: $i, V: $i, W: $i, X: $i] : (((pair_in_list(U, V, W) & strictly_less_than(V, X)) & strictly_less_than(W, X)) => pair_in_list(update_slb(U, X), V, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l48_co')).
% 0.13/0.39 tff(4,plain,
% 0.13/0.39 (~![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(V, X) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.13/0.39 tff(5,plain,
% 0.13/0.39 (~![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(V, X) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.13/0.39 tff(6,plain,
% 0.13/0.39 (~![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(V, X) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.13/0.39 tff(7,plain,
% 0.13/0.39 (~![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(V, X) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.13/0.39 tff(8,plain,(
% 0.13/0.39 ~((~(pair_in_list(U!3, V!2, W!1) & strictly_less_than(V!2, X!0) & strictly_less_than(W!1, X!0))) | pair_in_list(update_slb(U!3, X!0), V!2, X!0))),
% 0.13/0.39 inference(skolemize,[status(sab)],[7])).
% 0.13/0.39 tff(9,plain,
% 0.13/0.39 (~pair_in_list(update_slb(U!3, X!0), V!2, X!0)),
% 0.13/0.39 inference(or_elim,[status(thm)],[8])).
% 0.13/0.39 tff(10,plain,
% 0.13/0.39 (pair_in_list(U!3, V!2, W!1) & strictly_less_than(V!2, X!0) & strictly_less_than(W!1, X!0)),
% 0.13/0.39 inference(or_elim,[status(thm)],[8])).
% 0.13/0.39 tff(11,plain,
% 0.13/0.39 (strictly_less_than(W!1, X!0)),
% 0.13/0.39 inference(and_elim,[status(thm)],[10])).
% 0.13/0.39 tff(12,plain,
% 0.13/0.39 (pair_in_list(U!3, V!2, W!1)),
% 0.13/0.39 inference(and_elim,[status(thm)],[10])).
% 0.13/0.39 tff(13,plain,
% 0.13/0.39 (^[U: $i, V: $i, W: $i, X: $i] : refl((pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(W, X))) <=> (pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(W, X))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(14,plain,
% 0.13/0.39 (![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(W, X))) <=> ![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(W, X)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[13])).
% 0.13/0.39 tff(15,plain,
% 0.13/0.39 (^[U: $i, V: $i, W: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((pair_in_list(U, V, W) & strictly_less_than(W, X)) <=> (~((~pair_in_list(U, V, W)) | (~strictly_less_than(W, X))))), ((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) <=> (~(~((~pair_in_list(U, V, W)) | (~strictly_less_than(W, X))))))), rewrite((~(~((~pair_in_list(U, V, W)) | (~strictly_less_than(W, X))))) <=> ((~pair_in_list(U, V, W)) | (~strictly_less_than(W, X)))), ((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) <=> ((~pair_in_list(U, V, W)) | (~strictly_less_than(W, X))))), (((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X)) <=> (((~pair_in_list(U, V, W)) | (~strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X)))), rewrite((((~pair_in_list(U, V, W)) | (~strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X)) <=> (pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(W, X)))), (((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X)) <=> (pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(W, X)))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(16,plain,
% 0.13/0.39 (![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X)) <=> ![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(W, X)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[15])).
% 0.13/0.39 tff(17,plain,
% 0.13/0.39 (![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X)) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(18,plain,
% 0.13/0.39 (^[U: $i, V: $i, W: $i, X: $i] : rewrite(((pair_in_list(U, V, W) & strictly_less_than(W, X)) => pair_in_list(update_slb(U, X), V, X)) <=> ((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X)))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(19,plain,
% 0.13/0.39 (![U: $i, V: $i, W: $i, X: $i] : ((pair_in_list(U, V, W) & strictly_less_than(W, X)) => pair_in_list(update_slb(U, X), V, X)) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[18])).
% 0.13/0.39 tff(20,axiom,(![U: $i, V: $i, W: $i, X: $i] : ((pair_in_list(U, V, W) & strictly_less_than(W, X)) => pair_in_list(update_slb(U, X), V, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l48_li3839')).
% 0.13/0.39 tff(21,plain,
% 0.13/0.39 (![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.13/0.39 tff(22,plain,
% 0.13/0.39 (![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.13/0.39 tff(23,plain,(
% 0.13/0.39 ![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X))),
% 0.13/0.39 inference(skolemize,[status(sab)],[22])).
% 0.13/0.39 tff(24,plain,
% 0.13/0.39 (![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(W, X)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.13/0.39 tff(25,plain,
% 0.13/0.39 (![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(W, X)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[24, 14])).
% 0.13/0.39 tff(26,plain,
% 0.13/0.39 (((~![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(W, X)))) | (pair_in_list(update_slb(U!3, X!0), V!2, X!0) | (~pair_in_list(U!3, V!2, W!1)) | (~strictly_less_than(W!1, X!0)))) <=> ((~![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(W, X)))) | pair_in_list(update_slb(U!3, X!0), V!2, X!0) | (~pair_in_list(U!3, V!2, W!1)) | (~strictly_less_than(W!1, X!0)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(27,plain,
% 0.13/0.39 ((~![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(W, X)))) | (pair_in_list(update_slb(U!3, X!0), V!2, X!0) | (~pair_in_list(U!3, V!2, W!1)) | (~strictly_less_than(W!1, X!0)))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(28,plain,
% 0.13/0.39 ((~![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~pair_in_list(U, V, W)) | (~strictly_less_than(W, X)))) | pair_in_list(update_slb(U!3, X!0), V!2, X!0) | (~pair_in_list(U!3, V!2, W!1)) | (~strictly_less_than(W!1, X!0))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.13/0.39 tff(29,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[28, 25, 12, 11, 9])).
% 0.13/0.39 % SZS output end Proof
% 0.13/0.39 % E exiting
%------------------------------------------------------------------------------