%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV390+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:32:21 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 : SWV390+1 : TPTP v9.0.0. Released v3.3.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.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 09:48:50 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 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(tptp_fun_Y_0_type, type, (
% 0.12/0.38 tptp_fun_Y_0: $i > $i)).
% 0.12/0.38 tff(tptp_fun_V_3_type, type, (
% 0.12/0.38 tptp_fun_V_3: $i)).
% 0.12/0.38 tff(tptp_fun_X_1_type, type, (
% 0.12/0.38 tptp_fun_X_1: $i > $i)).
% 0.12/0.38 tff(bottom_type, type, (
% 0.12/0.38 bottom: $i)).
% 0.12/0.38 tff(tptp_fun_X_5_type, type, (
% 0.12/0.38 tptp_fun_X_5: $i)).
% 0.12/0.38 tff(insert_slb_type, type, (
% 0.12/0.38 insert_slb: ( $i * $i ) > $i)).
% 0.12/0.38 tff(pair_type, type, (
% 0.12/0.38 pair: ( $i * $i ) > $i)).
% 0.12/0.38 tff(less_than_type, type, (
% 0.12/0.38 less_than: ( $i * $i ) > $o)).
% 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_W_2_type, type, (
% 0.12/0.38 tptp_fun_W_2: $i)).
% 0.12/0.38 tff(tptp_fun_U_4_type, type, (
% 0.12/0.38 tptp_fun_U_4: $i)).
% 0.12/0.38 tff(insert_cpq_type, type, (
% 0.12/0.38 insert_cpq: ( $i * $i ) > $i)).
% 0.12/0.38 tff(insert_pqp_type, type, (
% 0.12/0.38 insert_pqp: ( $i * $i ) > $i)).
% 0.12/0.38 tff(1,plain,
% 0.12/0.38 (^[U: $i, V: $i, W: $i] : refl((~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V)))))))) <=> (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V)))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 (![U: $i, V: $i, W: $i] : (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V)))))))) <=> ![U: $i, V: $i, W: $i] : (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V))))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (^[U: $i, V: $i, W: $i] : rewrite((~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V)))))))) <=> (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V)))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 (![U: $i, V: $i, W: $i] : (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V)))))))) <=> ![U: $i, V: $i, W: $i] : (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V))))))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[3])).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (![U: $i, V: $i, W: $i] : (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V)))))))) <=> ![U: $i, V: $i, W: $i] : (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V))))))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[4, 2])).
% 0.12/0.38 tff(6,plain,
% 0.12/0.38 (^[U: $i, V: $i, W: $i] : trans(monotonicity(rewrite(((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X))) <=> ((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))), ((((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X))) & (check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V)))))) <=> (((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X))) & (check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V)))))))), rewrite((((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X))) & (check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V)))))) <=> (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V))))))))), ((((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X))) & (check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V)))))) <=> (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V))))))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(7,plain,
% 0.12/0.39 (![U: $i, V: $i, W: $i] : (((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X))) & (check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V)))))) <=> ![U: $i, V: $i, W: $i] : (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V))))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[6])).
% 0.12/0.39 tff(8,plain,
% 0.12/0.39 (![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) <=> ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X))) <=> ![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) <=> ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(9,plain,
% 0.12/0.39 (^[U: $i, V: $i, W: $i] : rewrite((check_cpq(triple(U, V, W)) <=> ![X: $i, Y: $i] : (pair_in_list(V, X, Y) => less_than(Y, X))) <=> (check_cpq(triple(U, V, W)) <=> ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(10,plain,
% 0.12/0.39 (![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) <=> ![X: $i, Y: $i] : (pair_in_list(V, X, Y) => less_than(Y, X))) <=> ![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) <=> ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[9])).
% 0.12/0.39 tff(11,axiom,(![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) <=> ![X: $i, Y: $i] : (pair_in_list(V, X, Y) => less_than(Y, X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l26_li4142')).
% 0.12/0.39 tff(12,plain,
% 0.12/0.39 (![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) <=> ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.12/0.39 tff(13,plain,
% 0.12/0.39 (![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) <=> ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.12/0.39 tff(14,plain,(
% 0.12/0.39 ![U: $i, V: $i, W: $i] : (((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X))) & (check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V))))))),
% 0.12/0.39 inference(skolemize,[status(sab)],[13])).
% 0.12/0.39 tff(15,plain,
% 0.12/0.39 (![U: $i, V: $i, W: $i] : (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V))))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.12/0.39 tff(16,plain,
% 0.12/0.39 (![U: $i, V: $i, W: $i] : (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V))))))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.12/0.39 tff(17,plain,
% 0.12/0.39 ((~![U: $i, V: $i, W: $i] : (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V))))))))) | (~((~((~check_cpq(triple(U!4, V!3, W!2))) | ![X: $i, Y: $i] : ((~pair_in_list(V!3, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U!4, V!3, W!2)) | (~((~pair_in_list(V!3, tptp_fun_X_1(V!3), tptp_fun_Y_0(V!3))) | less_than(tptp_fun_Y_0(V!3), tptp_fun_X_1(V!3))))))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(18,plain,
% 0.12/0.39 (~((~((~check_cpq(triple(U!4, V!3, W!2))) | ![X: $i, Y: $i] : ((~pair_in_list(V!3, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U!4, V!3, W!2)) | (~((~pair_in_list(V!3, tptp_fun_X_1(V!3), tptp_fun_Y_0(V!3))) | less_than(tptp_fun_Y_0(V!3), tptp_fun_X_1(V!3)))))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.12/0.39 tff(19,plain,
% 0.12/0.39 (((~((~check_cpq(triple(U!4, V!3, W!2))) | ![X: $i, Y: $i] : ((~pair_in_list(V!3, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U!4, V!3, W!2)) | (~((~pair_in_list(V!3, tptp_fun_X_1(V!3), tptp_fun_Y_0(V!3))) | less_than(tptp_fun_Y_0(V!3), tptp_fun_X_1(V!3))))))) | (check_cpq(triple(U!4, V!3, W!2)) | (~((~pair_in_list(V!3, tptp_fun_X_1(V!3), tptp_fun_Y_0(V!3))) | less_than(tptp_fun_Y_0(V!3), tptp_fun_X_1(V!3)))))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(20,plain,
% 0.12/0.39 (check_cpq(triple(U!4, V!3, W!2)) | (~((~pair_in_list(V!3, tptp_fun_X_1(V!3), tptp_fun_Y_0(V!3))) | less_than(tptp_fun_Y_0(V!3), tptp_fun_X_1(V!3))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.12/0.39 tff(21,plain,
% 0.12/0.39 ((~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | ![X: $i] : (~check_cpq(insert_cpq(triple(U, V, W), X))))) <=> (~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | ![X: $i] : (~check_cpq(insert_cpq(triple(U, V, W), X)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(22,plain,
% 0.12/0.39 ((~![U: $i, V: $i, W: $i] : ((~check_cpq(triple(U, V, W))) => ![X: $i] : (~check_cpq(insert_cpq(triple(U, V, W), X))))) <=> (~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | ![X: $i] : (~check_cpq(insert_cpq(triple(U, V, W), X)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(23,axiom,(~![U: $i, V: $i, W: $i] : ((~check_cpq(triple(U, V, W))) => ![X: $i] : (~check_cpq(insert_cpq(triple(U, V, W), X))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l26_co')).
% 0.12/0.39 tff(24,plain,
% 0.12/0.39 (~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | ![X: $i] : (~check_cpq(insert_cpq(triple(U, V, W), X))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.12/0.39 tff(25,plain,
% 0.12/0.39 (~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | ![X: $i] : (~check_cpq(insert_cpq(triple(U, V, W), X))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.12/0.39 tff(26,plain,
% 0.12/0.39 (~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | ![X: $i] : (~check_cpq(insert_cpq(triple(U, V, W), X))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.12/0.39 tff(27,plain,
% 0.12/0.39 (~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | ![X: $i] : (~check_cpq(insert_cpq(triple(U, V, W), X))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[26, 21])).
% 0.12/0.39 tff(28,plain,
% 0.12/0.39 (~check_cpq(triple(U!4, V!3, W!2))),
% 0.12/0.39 inference(and_elim,[status(thm)],[27])).
% 0.12/0.39 tff(29,plain,
% 0.12/0.39 ((~(check_cpq(triple(U!4, V!3, W!2)) | (~((~pair_in_list(V!3, tptp_fun_X_1(V!3), tptp_fun_Y_0(V!3))) | less_than(tptp_fun_Y_0(V!3), tptp_fun_X_1(V!3)))))) | check_cpq(triple(U!4, V!3, W!2)) | (~((~pair_in_list(V!3, tptp_fun_X_1(V!3), tptp_fun_Y_0(V!3))) | less_than(tptp_fun_Y_0(V!3), tptp_fun_X_1(V!3))))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(30,plain,
% 0.12/0.39 ((~(check_cpq(triple(U!4, V!3, W!2)) | (~((~pair_in_list(V!3, tptp_fun_X_1(V!3), tptp_fun_Y_0(V!3))) | less_than(tptp_fun_Y_0(V!3), tptp_fun_X_1(V!3)))))) | (~((~pair_in_list(V!3, tptp_fun_X_1(V!3), tptp_fun_Y_0(V!3))) | less_than(tptp_fun_Y_0(V!3), tptp_fun_X_1(V!3))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[29, 28])).
% 0.12/0.39 tff(31,plain,
% 0.12/0.39 (~((~pair_in_list(V!3, tptp_fun_X_1(V!3), tptp_fun_Y_0(V!3))) | less_than(tptp_fun_Y_0(V!3), tptp_fun_X_1(V!3)))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[30, 20])).
% 0.12/0.39 tff(32,plain,
% 0.12/0.39 (((~pair_in_list(V!3, tptp_fun_X_1(V!3), tptp_fun_Y_0(V!3))) | less_than(tptp_fun_Y_0(V!3), tptp_fun_X_1(V!3))) | pair_in_list(V!3, tptp_fun_X_1(V!3), tptp_fun_Y_0(V!3))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(33,plain,
% 0.12/0.39 (pair_in_list(V!3, tptp_fun_X_1(V!3), tptp_fun_Y_0(V!3))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.12/0.39 tff(34,plain,
% 0.12/0.39 (((~((~(X!5 = tptp_fun_X_1(V!3))) | (~(bottom = tptp_fun_Y_0(V!3))))) | pair_in_list(V!3, tptp_fun_X_1(V!3), tptp_fun_Y_0(V!3))) | (~pair_in_list(V!3, tptp_fun_X_1(V!3), tptp_fun_Y_0(V!3)))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(35,plain,
% 0.12/0.39 ((~((~(X!5 = tptp_fun_X_1(V!3))) | (~(bottom = tptp_fun_Y_0(V!3))))) | pair_in_list(V!3, tptp_fun_X_1(V!3), tptp_fun_Y_0(V!3))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.12/0.39 tff(36,plain,
% 0.12/0.39 ((~![U: $i, V: $i, W: $i] : (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V))))))))) | (~((~((~check_cpq(triple(insert_pqp(U!4, X!5), insert_slb(V!3, pair(X!5, bottom)), W!2))) | ![X: $i, Y: $i] : ((~pair_in_list(insert_slb(V!3, pair(X!5, bottom)), X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(insert_pqp(U!4, X!5), insert_slb(V!3, pair(X!5, bottom)), W!2)) | (~((~pair_in_list(insert_slb(V!3, pair(X!5, bottom)), tptp_fun_X_1(insert_slb(V!3, pair(X!5, bottom))), tptp_fun_Y_0(insert_slb(V!3, pair(X!5, bottom))))) | less_than(tptp_fun_Y_0(insert_slb(V!3, pair(X!5, bottom))), tptp_fun_X_1(insert_slb(V!3, pair(X!5, bottom))))))))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(37,plain,
% 0.12/0.39 (~((~((~check_cpq(triple(insert_pqp(U!4, X!5), insert_slb(V!3, pair(X!5, bottom)), W!2))) | ![X: $i, Y: $i] : ((~pair_in_list(insert_slb(V!3, pair(X!5, bottom)), X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(insert_pqp(U!4, X!5), insert_slb(V!3, pair(X!5, bottom)), W!2)) | (~((~pair_in_list(insert_slb(V!3, pair(X!5, bottom)), tptp_fun_X_1(insert_slb(V!3, pair(X!5, bottom))), tptp_fun_Y_0(insert_slb(V!3, pair(X!5, bottom))))) | less_than(tptp_fun_Y_0(insert_slb(V!3, pair(X!5, bottom))), tptp_fun_X_1(insert_slb(V!3, pair(X!5, bottom)))))))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[36, 16])).
% 0.12/0.39 tff(38,plain,
% 0.12/0.39 (((~((~check_cpq(triple(insert_pqp(U!4, X!5), insert_slb(V!3, pair(X!5, bottom)), W!2))) | ![X: $i, Y: $i] : ((~pair_in_list(insert_slb(V!3, pair(X!5, bottom)), X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(insert_pqp(U!4, X!5), insert_slb(V!3, pair(X!5, bottom)), W!2)) | (~((~pair_in_list(insert_slb(V!3, pair(X!5, bottom)), tptp_fun_X_1(insert_slb(V!3, pair(X!5, bottom))), tptp_fun_Y_0(insert_slb(V!3, pair(X!5, bottom))))) | less_than(tptp_fun_Y_0(insert_slb(V!3, pair(X!5, bottom))), tptp_fun_X_1(insert_slb(V!3, pair(X!5, bottom))))))))) | ((~check_cpq(triple(insert_pqp(U!4, X!5), insert_slb(V!3, pair(X!5, bottom)), W!2))) | ![X: $i, Y: $i] : ((~pair_in_list(insert_slb(V!3, pair(X!5, bottom)), X, Y)) | less_than(Y, X)))),
% 0.12/0.39 inference(tautology,[status(thm)],[])).
% 0.12/0.39 tff(39,plain,
% 0.12/0.39 ((~check_cpq(triple(insert_pqp(U!4, X!5), insert_slb(V!3, pair(X!5, bottom)), W!2))) | ![X: $i, Y: $i] : ((~pair_in_list(insert_slb(V!3, pair(X!5, bottom)), X, Y)) | less_than(Y, X))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.12/0.39 tff(40,plain,
% 0.12/0.39 (^[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)))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(41,plain,
% 0.12/0.39 (![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))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[40])).
% 0.12/0.39 tff(42,plain,
% 0.12/0.39 (![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))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(43,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')).
% 0.12/0.39 tff(44,plain,
% 0.12/0.39 (![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))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.12/0.39 tff(45,plain,(
% 0.12/0.39 ![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))),
% 0.12/0.39 inference(skolemize,[status(sab)],[44])).
% 0.12/0.39 tff(46,plain,
% 0.12/0.39 (![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))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.12/0.39 tff(47,plain,
% 0.12/0.39 ((~![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!4, V!3, W!2), X!5) = triple(insert_pqp(U!4, X!5), insert_slb(V!3, pair(X!5, bottom)), W!2))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(48,plain,
% 0.12/0.39 (insert_cpq(triple(U!4, V!3, W!2), X!5) = triple(insert_pqp(U!4, X!5), insert_slb(V!3, pair(X!5, bottom)), W!2)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.12/0.39 tff(49,plain,
% 0.12/0.39 (triple(insert_pqp(U!4, X!5), insert_slb(V!3, pair(X!5, bottom)), W!2) = insert_cpq(triple(U!4, V!3, W!2), X!5)),
% 0.12/0.39 inference(symmetry,[status(thm)],[48])).
% 0.12/0.39 tff(50,plain,
% 0.12/0.39 (check_cpq(triple(insert_pqp(U!4, X!5), insert_slb(V!3, pair(X!5, bottom)), W!2)) <=> check_cpq(insert_cpq(triple(U!4, V!3, W!2), X!5))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[49])).
% 0.12/0.39 tff(51,plain,
% 0.12/0.39 (check_cpq(insert_cpq(triple(U!4, V!3, W!2), X!5)) <=> check_cpq(triple(insert_pqp(U!4, X!5), insert_slb(V!3, pair(X!5, bottom)), W!2))),
% 0.12/0.39 inference(symmetry,[status(thm)],[50])).
% 0.12/0.39 tff(52,plain,
% 0.12/0.39 (check_cpq(insert_cpq(triple(U!4, V!3, W!2), X!5))),
% 0.12/0.39 inference(and_elim,[status(thm)],[27])).
% 0.12/0.39 tff(53,plain,
% 0.12/0.39 (check_cpq(triple(insert_pqp(U!4, X!5), insert_slb(V!3, pair(X!5, bottom)), W!2))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.12/0.40 tff(54,plain,
% 0.12/0.40 ((~((~check_cpq(triple(insert_pqp(U!4, X!5), insert_slb(V!3, pair(X!5, bottom)), W!2))) | ![X: $i, Y: $i] : ((~pair_in_list(insert_slb(V!3, pair(X!5, bottom)), X, Y)) | less_than(Y, X)))) | (~check_cpq(triple(insert_pqp(U!4, X!5), insert_slb(V!3, pair(X!5, bottom)), W!2))) | ![X: $i, Y: $i] : ((~pair_in_list(insert_slb(V!3, pair(X!5, bottom)), X, Y)) | less_than(Y, X))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(55,plain,
% 0.12/0.40 (![X: $i, Y: $i] : ((~pair_in_list(insert_slb(V!3, pair(X!5, bottom)), X, Y)) | less_than(Y, X))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[54, 53, 39])).
% 0.12/0.40 tff(56,plain,
% 0.12/0.40 (((~pair_in_list(V!3, tptp_fun_X_1(V!3), tptp_fun_Y_0(V!3))) | less_than(tptp_fun_Y_0(V!3), tptp_fun_X_1(V!3))) | (~less_than(tptp_fun_Y_0(V!3), tptp_fun_X_1(V!3)))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(57,plain,
% 0.12/0.40 (~less_than(tptp_fun_Y_0(V!3), tptp_fun_X_1(V!3))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[56, 31])).
% 0.12/0.40 tff(58,plain,
% 0.12/0.40 (((~![X: $i, Y: $i] : ((~pair_in_list(insert_slb(V!3, pair(X!5, bottom)), X, Y)) | less_than(Y, X))) | ((~pair_in_list(insert_slb(V!3, pair(X!5, bottom)), tptp_fun_X_1(V!3), tptp_fun_Y_0(V!3))) | less_than(tptp_fun_Y_0(V!3), tptp_fun_X_1(V!3)))) <=> ((~![X: $i, Y: $i] : ((~pair_in_list(insert_slb(V!3, pair(X!5, bottom)), X, Y)) | less_than(Y, X))) | (~pair_in_list(insert_slb(V!3, pair(X!5, bottom)), tptp_fun_X_1(V!3), tptp_fun_Y_0(V!3))) | less_than(tptp_fun_Y_0(V!3), tptp_fun_X_1(V!3)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(59,plain,
% 0.12/0.40 ((~![X: $i, Y: $i] : ((~pair_in_list(insert_slb(V!3, pair(X!5, bottom)), X, Y)) | less_than(Y, X))) | ((~pair_in_list(insert_slb(V!3, pair(X!5, bottom)), tptp_fun_X_1(V!3), tptp_fun_Y_0(V!3))) | less_than(tptp_fun_Y_0(V!3), tptp_fun_X_1(V!3)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(60,plain,
% 0.12/0.40 ((~![X: $i, Y: $i] : ((~pair_in_list(insert_slb(V!3, pair(X!5, bottom)), X, Y)) | less_than(Y, X))) | (~pair_in_list(insert_slb(V!3, pair(X!5, bottom)), tptp_fun_X_1(V!3), tptp_fun_Y_0(V!3))) | less_than(tptp_fun_Y_0(V!3), tptp_fun_X_1(V!3))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.12/0.40 tff(61,plain,
% 0.12/0.40 (~pair_in_list(insert_slb(V!3, pair(X!5, bottom)), tptp_fun_X_1(V!3), tptp_fun_Y_0(V!3))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[60, 57, 55])).
% 0.12/0.40 tff(62,plain,
% 0.12/0.40 ((~(pair_in_list(insert_slb(V!3, pair(X!5, bottom)), tptp_fun_X_1(V!3), tptp_fun_Y_0(V!3)) <=> ((~((~(X!5 = tptp_fun_X_1(V!3))) | (~(bottom = tptp_fun_Y_0(V!3))))) | pair_in_list(V!3, tptp_fun_X_1(V!3), tptp_fun_Y_0(V!3))))) | pair_in_list(insert_slb(V!3, pair(X!5, bottom)), tptp_fun_X_1(V!3), tptp_fun_Y_0(V!3)) | (~((~((~(X!5 = tptp_fun_X_1(V!3))) | (~(bottom = tptp_fun_Y_0(V!3))))) | pair_in_list(V!3, tptp_fun_X_1(V!3), tptp_fun_Y_0(V!3))))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(63,plain,
% 0.12/0.40 (~(pair_in_list(insert_slb(V!3, pair(X!5, bottom)), tptp_fun_X_1(V!3), tptp_fun_Y_0(V!3)) <=> ((~((~(X!5 = tptp_fun_X_1(V!3))) | (~(bottom = tptp_fun_Y_0(V!3))))) | pair_in_list(V!3, tptp_fun_X_1(V!3), tptp_fun_Y_0(V!3))))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[62, 61, 35])).
% 0.12/0.40 tff(64,plain,
% 0.12/0.40 (^[U: $i, V: $i, W: $i, X: $i, Y: $i] : refl((pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> ((~((~(V = W)) | (~(X = Y)))) | pair_in_list(U, W, Y))) <=> (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> ((~((~(V = W)) | (~(X = Y)))) | pair_in_list(U, W, Y))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(65,plain,
% 0.12/0.40 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> ((~((~(V = W)) | (~(X = Y)))) | pair_in_list(U, W, Y))) <=> ![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> ((~((~(V = W)) | (~(X = Y)))) | pair_in_list(U, W, Y)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[64])).
% 0.12/0.40 tff(66,plain,
% 0.12/0.40 (^[U: $i, V: $i, W: $i, X: $i, Y: $i] : rewrite((pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> (((V = W) & (X = Y)) | pair_in_list(U, W, Y))) <=> (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> ((~((~(V = W)) | (~(X = Y)))) | pair_in_list(U, W, Y))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(67,plain,
% 0.12/0.40 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> (((V = W) & (X = Y)) | pair_in_list(U, W, Y))) <=> ![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> ((~((~(V = W)) | (~(X = Y)))) | pair_in_list(U, W, Y)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[66])).
% 0.12/0.40 tff(68,plain,
% 0.12/0.40 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> (((V = W) & (X = Y)) | pair_in_list(U, W, Y))) <=> ![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> (((V = W) & (X = Y)) | pair_in_list(U, W, Y)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(69,plain,
% 0.12/0.40 (^[U: $i, V: $i, W: $i, X: $i, Y: $i] : rewrite((pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> (pair_in_list(U, W, Y) | ((V = W) & (X = Y)))) <=> (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> (((V = W) & (X = Y)) | pair_in_list(U, W, Y))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(70,plain,
% 0.12/0.40 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> (pair_in_list(U, W, Y) | ((V = W) & (X = Y)))) <=> ![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> (((V = W) & (X = Y)) | pair_in_list(U, W, Y)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[69])).
% 0.12/0.40 tff(71,axiom,(![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> (pair_in_list(U, W, Y) | ((V = W) & (X = Y))))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+2.ax','ax23')).
% 0.12/0.40 tff(72,plain,
% 0.12/0.40 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> (((V = W) & (X = Y)) | pair_in_list(U, W, Y)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.12/0.40 tff(73,plain,
% 0.12/0.40 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> (((V = W) & (X = Y)) | pair_in_list(U, W, Y)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.12/0.40 tff(74,plain,(
% 0.12/0.40 ![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> (((V = W) & (X = Y)) | pair_in_list(U, W, Y)))),
% 0.12/0.40 inference(skolemize,[status(sab)],[73])).
% 0.12/0.40 tff(75,plain,
% 0.12/0.40 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> ((~((~(V = W)) | (~(X = Y)))) | pair_in_list(U, W, Y)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[74, 67])).
% 0.12/0.40 tff(76,plain,
% 0.12/0.40 (![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> ((~((~(V = W)) | (~(X = Y)))) | pair_in_list(U, W, Y)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[75, 65])).
% 0.12/0.40 tff(77,plain,
% 0.12/0.40 ((~![U: $i, V: $i, W: $i, X: $i, Y: $i] : (pair_in_list(insert_slb(U, pair(V, X)), W, Y) <=> ((~((~(V = W)) | (~(X = Y)))) | pair_in_list(U, W, Y)))) | (pair_in_list(insert_slb(V!3, pair(X!5, bottom)), tptp_fun_X_1(V!3), tptp_fun_Y_0(V!3)) <=> ((~((~(X!5 = tptp_fun_X_1(V!3))) | (~(bottom = tptp_fun_Y_0(V!3))))) | pair_in_list(V!3, tptp_fun_X_1(V!3), tptp_fun_Y_0(V!3))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(78,plain,
% 0.12/0.40 ($false),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[77, 76, 63])).
% 0.12/0.40 % SZS output end Proof
% 0.12/0.40 % E exiting
%------------------------------------------------------------------------------