%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV398+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV398+1 : TPTP v9.0.0. Released v3.3.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 09:45:32 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.39 % SZS status Theorem
% 0.20/0.39 % SZS output start Proof
% 0.20/0.39 tff(pair_in_list_type, type, (
% 0.20/0.39 pair_in_list: ( $i * $i * $i ) > $o)).
% 0.20/0.39 tff(tptp_fun_Z_2_type, type, (
% 0.20/0.39 tptp_fun_Z_2: ( $i * $i ) > $i)).
% 0.20/0.39 tff(tptp_fun_V_5_type, type, (
% 0.20/0.39 tptp_fun_V_5: $i)).
% 0.20/0.39 tff(findmin_cpq_res_type, type, (
% 0.20/0.39 findmin_cpq_res: $i > $i)).
% 0.20/0.39 tff(triple_type, type, (
% 0.20/0.39 triple: ( $i * $i * $i ) > $i)).
% 0.20/0.39 tff(tptp_fun_W_4_type, type, (
% 0.20/0.39 tptp_fun_W_4: $i)).
% 0.20/0.39 tff(tptp_fun_U_6_type, type, (
% 0.20/0.39 tptp_fun_U_6: $i)).
% 0.20/0.39 tff(tptp_fun_Y_3_type, type, (
% 0.20/0.39 tptp_fun_Y_3: ( $i * $i ) > $i)).
% 0.20/0.39 tff(update_slb_type, type, (
% 0.20/0.39 update_slb: ( $i * $i ) > $i)).
% 0.20/0.39 tff(findmin_pqp_res_type, type, (
% 0.20/0.39 findmin_pqp_res: $i > $i)).
% 0.20/0.39 tff(create_slb_type, type, (
% 0.20/0.39 create_slb: $i)).
% 0.20/0.39 tff(tptp_fun_Y_0_type, type, (
% 0.20/0.39 tptp_fun_Y_0: $i > $i)).
% 0.20/0.39 tff(tptp_fun_X_1_type, type, (
% 0.20/0.39 tptp_fun_X_1: $i > $i)).
% 0.20/0.39 tff(less_than_type, type, (
% 0.20/0.39 less_than: ( $i * $i ) > $o)).
% 0.20/0.39 tff(check_cpq_type, type, (
% 0.20/0.39 check_cpq: $i > $o)).
% 0.20/0.39 tff(findmin_cpq_eff_type, type, (
% 0.20/0.39 findmin_cpq_eff: $i > $i)).
% 0.20/0.39 tff(strictly_less_than_type, type, (
% 0.20/0.39 strictly_less_than: ( $i * $i ) > $o)).
% 0.20/0.39 tff(bad_type, type, (
% 0.20/0.39 bad: $i)).
% 0.20/0.39 tff(lookup_slb_type, type, (
% 0.20/0.39 lookup_slb: ( $i * $i ) > $i)).
% 0.20/0.39 tff(contains_slb_type, type, (
% 0.20/0.39 contains_slb: ( $i * $i ) > $o)).
% 0.20/0.39 tff(1,assumption,(V!5 = create_slb), introduced(assumption)).
% 0.20/0.39 tff(2,plain,
% 0.20/0.39 (create_slb = V!5),
% 0.20/0.39 inference(symmetry,[status(thm)],[1])).
% 0.20/0.39 tff(3,plain,
% 0.20/0.39 (pair_in_list(create_slb, tptp_fun_X_1(V!5), tptp_fun_Y_0(V!5)) <=> pair_in_list(V!5, tptp_fun_X_1(V!5), tptp_fun_Y_0(V!5))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[2])).
% 0.20/0.39 tff(4,plain,
% 0.20/0.39 (pair_in_list(V!5, tptp_fun_X_1(V!5), tptp_fun_Y_0(V!5)) <=> pair_in_list(create_slb, tptp_fun_X_1(V!5), tptp_fun_Y_0(V!5))),
% 0.20/0.39 inference(symmetry,[status(thm)],[3])).
% 0.20/0.39 tff(5,plain,
% 0.20/0.39 (^[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)))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(6,plain,
% 0.20/0.39 (![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))))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[5])).
% 0.20/0.39 tff(7,plain,
% 0.20/0.39 (^[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)) | (~((~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)))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(8,plain,
% 0.20/0.39 (![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))))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[7])).
% 0.20/0.39 tff(9,plain,
% 0.20/0.39 (![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))))))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[8, 6])).
% 0.20/0.39 tff(10,plain,
% 0.20/0.39 (^[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))))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(11,plain,
% 0.20/0.39 (![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))))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[10])).
% 0.20/0.39 tff(12,plain,
% 0.20/0.39 (![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)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(13,plain,
% 0.20/0.39 (^[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))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(14,plain,
% 0.20/0.39 (![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)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.39 tff(15,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')).
% 0.20/0.40 tff(16,plain,
% 0.20/0.40 (![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)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.20/0.40 tff(17,plain,
% 0.20/0.40 (![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)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.20/0.40 tff(18,plain,(
% 0.20/0.40 ![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))))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[17])).
% 0.20/0.40 tff(19,plain,
% 0.20/0.40 (![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))))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.20/0.40 tff(20,plain,
% 0.20/0.40 (![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))))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[19, 9])).
% 0.20/0.40 tff(21,plain,
% 0.20/0.40 ((~![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!6, V!5, W!4))) | ![X: $i, Y: $i] : ((~pair_in_list(V!5, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U!6, V!5, W!4)) | (~((~pair_in_list(V!5, tptp_fun_X_1(V!5), tptp_fun_Y_0(V!5))) | less_than(tptp_fun_Y_0(V!5), tptp_fun_X_1(V!5))))))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(22,plain,
% 0.20/0.40 (~((~((~check_cpq(triple(U!6, V!5, W!4))) | ![X: $i, Y: $i] : ((~pair_in_list(V!5, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U!6, V!5, W!4)) | (~((~pair_in_list(V!5, tptp_fun_X_1(V!5), tptp_fun_Y_0(V!5))) | less_than(tptp_fun_Y_0(V!5), tptp_fun_X_1(V!5)))))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.20/0.40 tff(23,plain,
% 0.20/0.40 (((~((~check_cpq(triple(U!6, V!5, W!4))) | ![X: $i, Y: $i] : ((~pair_in_list(V!5, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U!6, V!5, W!4)) | (~((~pair_in_list(V!5, tptp_fun_X_1(V!5), tptp_fun_Y_0(V!5))) | less_than(tptp_fun_Y_0(V!5), tptp_fun_X_1(V!5))))))) | (check_cpq(triple(U!6, V!5, W!4)) | (~((~pair_in_list(V!5, tptp_fun_X_1(V!5), tptp_fun_Y_0(V!5))) | less_than(tptp_fun_Y_0(V!5), tptp_fun_X_1(V!5)))))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(24,plain,
% 0.20/0.40 (check_cpq(triple(U!6, V!5, W!4)) | (~((~pair_in_list(V!5, tptp_fun_X_1(V!5), tptp_fun_Y_0(V!5))) | less_than(tptp_fun_Y_0(V!5), tptp_fun_X_1(V!5))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.20/0.40 tff(25,plain,
% 0.20/0.40 ((~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~check_cpq(findmin_cpq_eff(triple(U, V, W)))))) <=> (~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~check_cpq(findmin_cpq_eff(triple(U, V, W))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(26,plain,
% 0.20/0.40 ((~![U: $i, V: $i, W: $i] : ((~check_cpq(triple(U, V, W))) => (~check_cpq(findmin_cpq_eff(triple(U, V, W)))))) <=> (~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~check_cpq(findmin_cpq_eff(triple(U, V, W))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(27,axiom,(~![U: $i, V: $i, W: $i] : ((~check_cpq(triple(U, V, W))) => (~check_cpq(findmin_cpq_eff(triple(U, V, W)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l24_co')).
% 0.20/0.40 tff(28,plain,
% 0.20/0.40 (~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~check_cpq(findmin_cpq_eff(triple(U, V, W)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.20/0.40 tff(29,plain,
% 0.20/0.40 (~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~check_cpq(findmin_cpq_eff(triple(U, V, W)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[28, 25])).
% 0.20/0.40 tff(30,plain,
% 0.20/0.40 (~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~check_cpq(findmin_cpq_eff(triple(U, V, W)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.20/0.40 tff(31,plain,
% 0.20/0.40 (~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~check_cpq(findmin_cpq_eff(triple(U, V, W)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[30, 25])).
% 0.20/0.40 tff(32,plain,(
% 0.20/0.40 ~(check_cpq(triple(U!6, V!5, W!4)) | (~check_cpq(findmin_cpq_eff(triple(U!6, V!5, W!4)))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[31])).
% 0.20/0.40 tff(33,plain,
% 0.20/0.40 (~check_cpq(triple(U!6, V!5, W!4))),
% 0.20/0.40 inference(or_elim,[status(thm)],[32])).
% 0.20/0.40 tff(34,plain,
% 0.20/0.40 ((~(check_cpq(triple(U!6, V!5, W!4)) | (~((~pair_in_list(V!5, tptp_fun_X_1(V!5), tptp_fun_Y_0(V!5))) | less_than(tptp_fun_Y_0(V!5), tptp_fun_X_1(V!5)))))) | check_cpq(triple(U!6, V!5, W!4)) | (~((~pair_in_list(V!5, tptp_fun_X_1(V!5), tptp_fun_Y_0(V!5))) | less_than(tptp_fun_Y_0(V!5), tptp_fun_X_1(V!5))))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(35,plain,
% 0.20/0.40 ((~(check_cpq(triple(U!6, V!5, W!4)) | (~((~pair_in_list(V!5, tptp_fun_X_1(V!5), tptp_fun_Y_0(V!5))) | less_than(tptp_fun_Y_0(V!5), tptp_fun_X_1(V!5)))))) | (~((~pair_in_list(V!5, tptp_fun_X_1(V!5), tptp_fun_Y_0(V!5))) | less_than(tptp_fun_Y_0(V!5), tptp_fun_X_1(V!5))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.20/0.40 tff(36,plain,
% 0.20/0.40 (~((~pair_in_list(V!5, tptp_fun_X_1(V!5), tptp_fun_Y_0(V!5))) | less_than(tptp_fun_Y_0(V!5), tptp_fun_X_1(V!5)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[35, 24])).
% 0.20/0.40 tff(37,plain,
% 0.20/0.40 (((~pair_in_list(V!5, tptp_fun_X_1(V!5), tptp_fun_Y_0(V!5))) | less_than(tptp_fun_Y_0(V!5), tptp_fun_X_1(V!5))) | pair_in_list(V!5, tptp_fun_X_1(V!5), tptp_fun_Y_0(V!5))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(38,plain,
% 0.20/0.40 (pair_in_list(V!5, tptp_fun_X_1(V!5), tptp_fun_Y_0(V!5))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.20/0.40 tff(39,plain,
% 0.20/0.40 (pair_in_list(create_slb, tptp_fun_X_1(V!5), tptp_fun_Y_0(V!5))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[38, 4])).
% 0.20/0.40 tff(40,plain,
% 0.20/0.40 (^[U: $i, V: $i] : refl((~pair_in_list(create_slb, U, V)) <=> (~pair_in_list(create_slb, U, V)))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(41,plain,
% 0.20/0.40 (![U: $i, V: $i] : (~pair_in_list(create_slb, U, V)) <=> ![U: $i, V: $i] : (~pair_in_list(create_slb, U, V))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[40])).
% 0.20/0.40 tff(42,plain,
% 0.20/0.40 (![U: $i, V: $i] : (~pair_in_list(create_slb, U, V)) <=> ![U: $i, V: $i] : (~pair_in_list(create_slb, U, V))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(43,axiom,(![U: $i, V: $i] : (~pair_in_list(create_slb, U, V))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+2.ax','ax22')).
% 0.20/0.40 tff(44,plain,
% 0.20/0.40 (![U: $i, V: $i] : (~pair_in_list(create_slb, U, V))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.20/0.40 tff(45,plain,(
% 0.20/0.40 ![U: $i, V: $i] : (~pair_in_list(create_slb, U, V))),
% 0.20/0.40 inference(skolemize,[status(sab)],[44])).
% 0.20/0.40 tff(46,plain,
% 0.20/0.40 (![U: $i, V: $i] : (~pair_in_list(create_slb, U, V))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.20/0.40 tff(47,plain,
% 0.20/0.40 ((~![U: $i, V: $i] : (~pair_in_list(create_slb, U, V))) | (~pair_in_list(create_slb, tptp_fun_X_1(V!5), tptp_fun_Y_0(V!5)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(48,plain,
% 0.20/0.40 (~pair_in_list(create_slb, tptp_fun_X_1(V!5), tptp_fun_Y_0(V!5))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.20/0.40 tff(49,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[48, 39])).
% 0.20/0.40 tff(50,plain,(~(V!5 = create_slb)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(51,plain,
% 0.20/0.40 (^[U: $i, V: $i, W: $i] : refl(((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U))) <=> ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(52,plain,
% 0.20/0.40 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U))) <=> ![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[51])).
% 0.20/0.40 tff(53,plain,
% 0.20/0.40 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U))) <=> ![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(54,plain,
% 0.20/0.40 (![U: $i, V: $i, W: $i, X: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U))) <=> ![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.20/0.40 inference(elim_unused_vars,[status(thm)],[])).
% 0.20/0.40 tff(55,plain,
% 0.20/0.40 (^[U: $i, V: $i, W: $i, X: $i] : rewrite(((~(V = create_slb)) => (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U))) <=> ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(56,plain,
% 0.20/0.40 (![U: $i, V: $i, W: $i, X: $i] : ((~(V = create_slb)) => (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[55])).
% 0.20/0.40 tff(57,plain,
% 0.20/0.40 (![U: $i, V: $i, W: $i, X: $i] : ((~(V = create_slb)) => (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U))) <=> ![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.20/0.40 inference(transitivity,[status(thm)],[56, 54])).
% 0.20/0.40 tff(58,axiom,(![U: $i, V: $i, W: $i, X: $i] : ((~(V = create_slb)) => (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax','ax51')).
% 0.20/0.40 tff(59,plain,
% 0.20/0.40 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.20/0.40 tff(60,plain,
% 0.20/0.40 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[59, 53])).
% 0.20/0.40 tff(61,plain,(
% 0.20/0.40 ![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.20/0.40 inference(skolemize,[status(sab)],[60])).
% 0.20/0.40 tff(62,plain,
% 0.20/0.40 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[61, 52])).
% 0.20/0.40 tff(63,plain,
% 0.20/0.40 (((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))) | ((V!5 = create_slb) | (findmin_cpq_res(triple(U!6, V!5, W!4)) = findmin_pqp_res(U!6)))) <=> ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))) | (V!5 = create_slb) | (findmin_cpq_res(triple(U!6, V!5, W!4)) = findmin_pqp_res(U!6)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(64,plain,
% 0.20/0.40 ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))) | ((V!5 = create_slb) | (findmin_cpq_res(triple(U!6, V!5, W!4)) = findmin_pqp_res(U!6)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(65,plain,
% 0.20/0.40 ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))) | (V!5 = create_slb) | (findmin_cpq_res(triple(U!6, V!5, W!4)) = findmin_pqp_res(U!6))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.20/0.40 tff(66,plain,
% 0.20/0.40 ((V!5 = create_slb) | (findmin_cpq_res(triple(U!6, V!5, W!4)) = findmin_pqp_res(U!6))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[65, 62])).
% 0.20/0.40 tff(67,plain,
% 0.20/0.40 (findmin_cpq_res(triple(U!6, V!5, W!4)) = findmin_pqp_res(U!6)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[66, 50])).
% 0.20/0.40 tff(68,plain,
% 0.20/0.40 (update_slb(V!5, findmin_cpq_res(triple(U!6, V!5, W!4))) = update_slb(V!5, findmin_pqp_res(U!6))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[67])).
% 0.20/0.40 tff(69,plain,
% 0.20/0.40 (update_slb(V!5, findmin_pqp_res(U!6)) = update_slb(V!5, findmin_cpq_res(triple(U!6, V!5, W!4)))),
% 0.20/0.40 inference(symmetry,[status(thm)],[68])).
% 0.20/0.40 tff(70,plain,
% 0.20/0.40 (pair_in_list(update_slb(V!5, findmin_pqp_res(U!6)), tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5)) <=> pair_in_list(update_slb(V!5, findmin_cpq_res(triple(U!6, V!5, W!4))), tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[69])).
% 0.20/0.40 tff(71,plain,
% 0.20/0.40 (pair_in_list(update_slb(V!5, findmin_cpq_res(triple(U!6, V!5, W!4))), tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5)) <=> pair_in_list(update_slb(V!5, findmin_pqp_res(U!6)), tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5))),
% 0.20/0.40 inference(symmetry,[status(thm)],[70])).
% 0.20/0.40 tff(72,plain,
% 0.20/0.40 (^[U: $i, V: $i] : refl((~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V))) <=> (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(73,plain,
% 0.20/0.40 (![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V))) <=> ![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[72])).
% 0.20/0.40 tff(74,plain,
% 0.20/0.40 (^[U: $i, V: $i] : trans(trans(monotonicity(rewrite((less_than(U, V) & (~less_than(V, U))) <=> (~((~less_than(U, V)) | less_than(V, U)))), ((strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U)))) <=> (strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U)))))), rewrite((strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U)))) <=> (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))), ((strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U)))) <=> (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V))))), rewrite((~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V))) <=> (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))), ((strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U)))) <=> (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(75,plain,
% 0.20/0.40 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U)))) <=> ![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[74])).
% 0.20/0.40 tff(76,plain,
% 0.20/0.40 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U)))) <=> ![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(77,axiom,(![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax','stricly_smaller_definition')).
% 0.20/0.40 tff(78,plain,
% 0.20/0.40 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.20/0.40 tff(79,plain,(
% 0.20/0.40 ![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[78])).
% 0.20/0.40 tff(80,plain,
% 0.20/0.40 (![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.20/0.40 tff(81,plain,
% 0.20/0.40 (![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[80, 73])).
% 0.20/0.40 tff(82,plain,
% 0.20/0.40 ((~![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))) | (~(((~less_than(tptp_fun_X_1(V!5), tptp_fun_Y_0(V!5))) | less_than(tptp_fun_Y_0(V!5), tptp_fun_X_1(V!5))) <=> strictly_less_than(tptp_fun_X_1(V!5), tptp_fun_Y_0(V!5))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(83,plain,
% 0.20/0.40 (~(((~less_than(tptp_fun_X_1(V!5), tptp_fun_Y_0(V!5))) | less_than(tptp_fun_Y_0(V!5), tptp_fun_X_1(V!5))) <=> strictly_less_than(tptp_fun_X_1(V!5), tptp_fun_Y_0(V!5)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.20/0.40 tff(84,plain,
% 0.20/0.40 (((~pair_in_list(V!5, tptp_fun_X_1(V!5), tptp_fun_Y_0(V!5))) | less_than(tptp_fun_Y_0(V!5), tptp_fun_X_1(V!5))) | (~less_than(tptp_fun_Y_0(V!5), tptp_fun_X_1(V!5)))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(85,plain,
% 0.20/0.40 (~less_than(tptp_fun_Y_0(V!5), tptp_fun_X_1(V!5))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[84, 36])).
% 0.20/0.40 tff(86,plain,
% 0.20/0.40 (^[U: $i, V: $i] : refl((less_than(V, U) | less_than(U, V)) <=> (less_than(V, U) | less_than(U, V)))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(87,plain,
% 0.20/0.40 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[86])).
% 0.20/0.40 tff(88,plain,
% 0.20/0.40 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(89,plain,
% 0.20/0.40 (^[U: $i, V: $i] : rewrite((less_than(U, V) | less_than(V, U)) <=> (less_than(V, U) | less_than(U, V)))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(90,plain,
% 0.20/0.40 (![U: $i, V: $i] : (less_than(U, V) | less_than(V, U)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[89])).
% 0.20/0.40 tff(91,axiom,(![U: $i, V: $i] : (less_than(U, V) | less_than(V, U))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax','totality')).
% 0.20/0.40 tff(92,plain,
% 0.20/0.40 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.20/0.40 tff(93,plain,
% 0.20/0.40 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[92, 88])).
% 0.20/0.40 tff(94,plain,(
% 0.20/0.40 ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.20/0.40 inference(skolemize,[status(sab)],[93])).
% 0.20/0.40 tff(95,plain,
% 0.20/0.40 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[94, 87])).
% 0.20/0.40 tff(96,plain,
% 0.20/0.40 (((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | (less_than(tptp_fun_X_1(V!5), tptp_fun_Y_0(V!5)) | less_than(tptp_fun_Y_0(V!5), tptp_fun_X_1(V!5)))) <=> ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | less_than(tptp_fun_X_1(V!5), tptp_fun_Y_0(V!5)) | less_than(tptp_fun_Y_0(V!5), tptp_fun_X_1(V!5)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(97,plain,
% 0.20/0.40 ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | (less_than(tptp_fun_X_1(V!5), tptp_fun_Y_0(V!5)) | less_than(tptp_fun_Y_0(V!5), tptp_fun_X_1(V!5)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(98,plain,
% 0.20/0.40 ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | less_than(tptp_fun_X_1(V!5), tptp_fun_Y_0(V!5)) | less_than(tptp_fun_Y_0(V!5), tptp_fun_X_1(V!5))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.20/0.40 tff(99,plain,
% 0.20/0.40 (less_than(tptp_fun_X_1(V!5), tptp_fun_Y_0(V!5))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[98, 95, 85])).
% 0.20/0.40 tff(100,plain,
% 0.20/0.40 ((~((~less_than(tptp_fun_X_1(V!5), tptp_fun_Y_0(V!5))) | less_than(tptp_fun_Y_0(V!5), tptp_fun_X_1(V!5)))) | (~less_than(tptp_fun_X_1(V!5), tptp_fun_Y_0(V!5))) | less_than(tptp_fun_Y_0(V!5), tptp_fun_X_1(V!5))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(101,plain,
% 0.20/0.41 ((~((~less_than(tptp_fun_X_1(V!5), tptp_fun_Y_0(V!5))) | less_than(tptp_fun_Y_0(V!5), tptp_fun_X_1(V!5)))) | (~less_than(tptp_fun_X_1(V!5), tptp_fun_Y_0(V!5)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[100, 85])).
% 0.20/0.41 tff(102,plain,
% 0.20/0.41 (~((~less_than(tptp_fun_X_1(V!5), tptp_fun_Y_0(V!5))) | less_than(tptp_fun_Y_0(V!5), tptp_fun_X_1(V!5)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[101, 99])).
% 0.20/0.41 tff(103,plain,
% 0.20/0.41 ((((~less_than(tptp_fun_X_1(V!5), tptp_fun_Y_0(V!5))) | less_than(tptp_fun_Y_0(V!5), tptp_fun_X_1(V!5))) <=> strictly_less_than(tptp_fun_X_1(V!5), tptp_fun_Y_0(V!5))) | ((~less_than(tptp_fun_X_1(V!5), tptp_fun_Y_0(V!5))) | less_than(tptp_fun_Y_0(V!5), tptp_fun_X_1(V!5))) | strictly_less_than(tptp_fun_X_1(V!5), tptp_fun_Y_0(V!5))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(104,plain,
% 0.20/0.41 (strictly_less_than(tptp_fun_X_1(V!5), tptp_fun_Y_0(V!5))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[103, 102, 83])).
% 0.20/0.41 tff(105,plain,
% 0.20/0.41 (^[U: $i, X: $i, V: $i, W: $i] : trans(monotonicity(rewrite((~((~pair_in_list(update_slb(U, X), tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))) | (~strictly_less_than(tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))))) <=> (~((~pair_in_list(update_slb(U, X), tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))) | (~strictly_less_than(tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U)))))), ((((~strictly_less_than(V, W)) | (~pair_in_list(U, V, W))) | (~((~pair_in_list(update_slb(U, X), tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))) | (~strictly_less_than(tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U)))))) <=> (((~strictly_less_than(V, W)) | (~pair_in_list(U, V, W))) | (~((~pair_in_list(update_slb(U, X), tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))) | (~strictly_less_than(tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U)))))))), rewrite((((~strictly_less_than(V, W)) | (~pair_in_list(U, V, W))) | (~((~pair_in_list(update_slb(U, X), tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))) | (~strictly_less_than(tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U)))))) <=> ((~strictly_less_than(V, W)) | (~pair_in_list(U, V, W)) | (~((~pair_in_list(update_slb(U, X), tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))) | (~strictly_less_than(tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))))))), ((((~strictly_less_than(V, W)) | (~pair_in_list(U, V, W))) | (~((~pair_in_list(update_slb(U, X), tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))) | (~strictly_less_than(tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U)))))) <=> ((~strictly_less_than(V, W)) | (~pair_in_list(U, V, W)) | (~((~pair_in_list(update_slb(U, X), tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))) | (~strictly_less_than(tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(106,plain,
% 0.20/0.41 (![U: $i, X: $i, V: $i, W: $i] : (((~strictly_less_than(V, W)) | (~pair_in_list(U, V, W))) | (~((~pair_in_list(update_slb(U, X), tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))) | (~strictly_less_than(tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U)))))) <=> ![U: $i, X: $i, V: $i, W: $i] : ((~strictly_less_than(V, W)) | (~pair_in_list(U, V, W)) | (~((~pair_in_list(update_slb(U, X), tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))) | (~strictly_less_than(tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[105])).
% 0.20/0.41 tff(107,plain,
% 0.20/0.41 (^[U: $i, X: $i, V: $i, W: $i] : refl((((~strictly_less_than(V, W)) | (~pair_in_list(U, V, W))) | (~((~pair_in_list(update_slb(U, X), tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))) | (~strictly_less_than(tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U)))))) <=> (((~strictly_less_than(V, W)) | (~pair_in_list(U, V, W))) | (~((~pair_in_list(update_slb(U, X), tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))) | (~strictly_less_than(tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U)))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(108,plain,
% 0.20/0.41 (![U: $i, X: $i, V: $i, W: $i] : (((~strictly_less_than(V, W)) | (~pair_in_list(U, V, W))) | (~((~pair_in_list(update_slb(U, X), tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))) | (~strictly_less_than(tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U)))))) <=> ![U: $i, X: $i, V: $i, W: $i] : (((~strictly_less_than(V, W)) | (~pair_in_list(U, V, W))) | (~((~pair_in_list(update_slb(U, X), tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))) | (~strictly_less_than(tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[107])).
% 0.20/0.41 tff(109,plain,
% 0.20/0.41 (![U: $i] : ![X: $i, V: $i, W: $i] : (((~strictly_less_than(V, W)) | (~pair_in_list(U, V, W))) | (~((~pair_in_list(update_slb(U, X), tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))) | (~strictly_less_than(tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U)))))) <=> ![U: $i, X: $i, V: $i, W: $i] : (((~strictly_less_than(V, W)) | (~pair_in_list(U, V, W))) | (~((~pair_in_list(update_slb(U, X), tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))) | (~strictly_less_than(tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))))))),
% 0.20/0.41 inference(pull_quant,[status(thm)],[])).
% 0.20/0.41 tff(110,plain,
% 0.20/0.41 (^[U: $i] : pull_quant((![V: $i, W: $i] : ((~strictly_less_than(V, W)) | (~pair_in_list(U, V, W))) | ![X: $i] : (~((~pair_in_list(update_slb(U, X), tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))) | (~strictly_less_than(tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U)))))) <=> ![X: $i, V: $i, W: $i] : (((~strictly_less_than(V, W)) | (~pair_in_list(U, V, W))) | (~((~pair_in_list(update_slb(U, X), tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))) | (~strictly_less_than(tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U)))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(111,plain,
% 0.20/0.41 (![U: $i] : (![V: $i, W: $i] : ((~strictly_less_than(V, W)) | (~pair_in_list(U, V, W))) | ![X: $i] : (~((~pair_in_list(update_slb(U, X), tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))) | (~strictly_less_than(tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U)))))) <=> ![U: $i] : ![X: $i, V: $i, W: $i] : (((~strictly_less_than(V, W)) | (~pair_in_list(U, V, W))) | (~((~pair_in_list(update_slb(U, X), tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))) | (~strictly_less_than(tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[110])).
% 0.20/0.41 tff(112,plain,
% 0.20/0.41 (![U: $i] : (![V: $i, W: $i] : ((~strictly_less_than(V, W)) | (~pair_in_list(U, V, W))) | ![X: $i] : (~((~pair_in_list(update_slb(U, X), tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))) | (~strictly_less_than(tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U)))))) <=> ![U: $i, X: $i, V: $i, W: $i] : (((~strictly_less_than(V, W)) | (~pair_in_list(U, V, W))) | (~((~pair_in_list(update_slb(U, X), tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))) | (~strictly_less_than(tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[111, 109])).
% 0.20/0.41 tff(113,plain,
% 0.20/0.41 (![U: $i] : (![V: $i, W: $i] : ((~strictly_less_than(V, W)) | (~pair_in_list(U, V, W))) | ![X: $i] : (~((~pair_in_list(update_slb(U, X), tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))) | (~strictly_less_than(tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U)))))) <=> ![U: $i, X: $i, V: $i, W: $i] : (((~strictly_less_than(V, W)) | (~pair_in_list(U, V, W))) | (~((~pair_in_list(update_slb(U, X), tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))) | (~strictly_less_than(tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[112, 108])).
% 0.20/0.41 tff(114,plain,
% 0.20/0.41 (^[U: $i] : rewrite((![V: $i, W: $i] : ((~strictly_less_than(V, W)) | (~pair_in_list(U, V, W))) | ![X: $i] : (~((~pair_in_list(update_slb(U, X), tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))) | (~strictly_less_than(tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U)))))) <=> (![V: $i, W: $i] : ((~strictly_less_than(V, W)) | (~pair_in_list(U, V, W))) | ![X: $i] : (~((~pair_in_list(update_slb(U, X), tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))) | (~strictly_less_than(tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U)))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(115,plain,
% 0.20/0.41 (![U: $i] : (![V: $i, W: $i] : ((~strictly_less_than(V, W)) | (~pair_in_list(U, V, W))) | ![X: $i] : (~((~pair_in_list(update_slb(U, X), tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))) | (~strictly_less_than(tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U)))))) <=> ![U: $i] : (![V: $i, W: $i] : ((~strictly_less_than(V, W)) | (~pair_in_list(U, V, W))) | ![X: $i] : (~((~pair_in_list(update_slb(U, X), tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))) | (~strictly_less_than(tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[114])).
% 0.20/0.41 tff(116,plain,
% 0.20/0.41 (![U: $i] : (![V: $i, W: $i] : ((~strictly_less_than(V, W)) | (~pair_in_list(U, V, W))) | ![X: $i] : (~((~pair_in_list(update_slb(U, X), tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))) | (~strictly_less_than(tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U)))))) <=> ![U: $i, X: $i, V: $i, W: $i] : (((~strictly_less_than(V, W)) | (~pair_in_list(U, V, W))) | (~((~pair_in_list(update_slb(U, X), tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))) | (~strictly_less_than(tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[115, 113])).
% 0.20/0.41 tff(117,plain,
% 0.20/0.41 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i, W: $i] : trans(monotonicity(rewrite((pair_in_list(U, V, W) & strictly_less_than(V, W)) <=> (~((~strictly_less_than(V, W)) | (~pair_in_list(U, V, W))))), ((~(pair_in_list(U, V, W) & strictly_less_than(V, W))) <=> (~(~((~strictly_less_than(V, W)) | (~pair_in_list(U, V, W))))))), rewrite((~(~((~strictly_less_than(V, W)) | (~pair_in_list(U, V, W))))) <=> ((~strictly_less_than(V, W)) | (~pair_in_list(U, V, W)))), ((~(pair_in_list(U, V, W) & strictly_less_than(V, W))) <=> ((~strictly_less_than(V, W)) | (~pair_in_list(U, V, W)))))), (![V: $i, W: $i] : (~(pair_in_list(U, V, W) & strictly_less_than(V, W))) <=> ![V: $i, W: $i] : ((~strictly_less_than(V, W)) | (~pair_in_list(U, V, W))))), quant_intro(proof_bind(^[X: $i] : rewrite((pair_in_list(update_slb(U, X), tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U)) & strictly_less_than(tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))) <=> (~((~pair_in_list(update_slb(U, X), tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))) | (~strictly_less_than(tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))))))), (![X: $i] : (pair_in_list(update_slb(U, X), tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U)) & strictly_less_than(tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))) <=> ![X: $i] : (~((~pair_in_list(update_slb(U, X), tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))) | (~strictly_less_than(tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))))))), ((![V: $i, W: $i] : (~(pair_in_list(U, V, W) & strictly_less_than(V, W))) | ![X: $i] : (pair_in_list(update_slb(U, X), tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U)) & strictly_less_than(tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U)))) <=> (![V: $i, W: $i] : ((~strictly_less_than(V, W)) | (~pair_in_list(U, V, W))) | ![X: $i] : (~((~pair_in_list(update_slb(U, X), tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))) | (~strictly_less_than(tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U)))))))), rewrite((![V: $i, W: $i] : ((~strictly_less_than(V, W)) | (~pair_in_list(U, V, W))) | ![X: $i] : (~((~pair_in_list(update_slb(U, X), tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))) | (~strictly_less_than(tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U)))))) <=> (![V: $i, W: $i] : ((~strictly_less_than(V, W)) | (~pair_in_list(U, V, W))) | ![X: $i] : (~((~pair_in_list(update_slb(U, X), tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))) | (~strictly_less_than(tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))))))), ((![V: $i, W: $i] : (~(pair_in_list(U, V, W) & strictly_less_than(V, W))) | ![X: $i] : (pair_in_list(update_slb(U, X), tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U)) & strictly_less_than(tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U)))) <=> (![V: $i, W: $i] : ((~strictly_less_than(V, W)) | (~pair_in_list(U, V, W))) | ![X: $i] : (~((~pair_in_list(update_slb(U, X), tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))) | (~strictly_less_than(tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(118,plain,
% 0.20/0.41 (![U: $i] : (![V: $i, W: $i] : (~(pair_in_list(U, V, W) & strictly_less_than(V, W))) | ![X: $i] : (pair_in_list(update_slb(U, X), tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U)) & strictly_less_than(tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U)))) <=> ![U: $i] : (![V: $i, W: $i] : ((~strictly_less_than(V, W)) | (~pair_in_list(U, V, W))) | ![X: $i] : (~((~pair_in_list(update_slb(U, X), tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))) | (~strictly_less_than(tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[117])).
% 0.20/0.41 tff(119,plain,
% 0.20/0.41 (![U: $i] : ((~?[V: $i, W: $i] : (pair_in_list(U, V, W) & strictly_less_than(V, W))) | ![X: $i] : ?[Y: $i, Z: $i] : (pair_in_list(update_slb(U, X), Y, Z) & strictly_less_than(Y, Z))) <=> ![U: $i] : ((~?[V: $i, W: $i] : (pair_in_list(U, V, W) & strictly_less_than(V, W))) | ![X: $i] : ?[Y: $i, Z: $i] : (pair_in_list(update_slb(U, X), Y, Z) & strictly_less_than(Y, Z)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(120,plain,
% 0.20/0.41 (^[U: $i] : rewrite((?[V: $i, W: $i] : (pair_in_list(U, V, W) & strictly_less_than(V, W)) => ![X: $i] : ?[Y: $i, Z: $i] : (pair_in_list(update_slb(U, X), Y, Z) & strictly_less_than(Y, Z))) <=> ((~?[V: $i, W: $i] : (pair_in_list(U, V, W) & strictly_less_than(V, W))) | ![X: $i] : ?[Y: $i, Z: $i] : (pair_in_list(update_slb(U, X), Y, Z) & strictly_less_than(Y, Z))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(121,plain,
% 0.20/0.41 (![U: $i] : (?[V: $i, W: $i] : (pair_in_list(U, V, W) & strictly_less_than(V, W)) => ![X: $i] : ?[Y: $i, Z: $i] : (pair_in_list(update_slb(U, X), Y, Z) & strictly_less_than(Y, Z))) <=> ![U: $i] : ((~?[V: $i, W: $i] : (pair_in_list(U, V, W) & strictly_less_than(V, W))) | ![X: $i] : ?[Y: $i, Z: $i] : (pair_in_list(update_slb(U, X), Y, Z) & strictly_less_than(Y, Z)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[120])).
% 0.20/0.41 tff(122,axiom,(![U: $i] : (?[V: $i, W: $i] : (pair_in_list(U, V, W) & strictly_less_than(V, W)) => ![X: $i] : ?[Y: $i, Z: $i] : (pair_in_list(update_slb(U, X), Y, Z) & strictly_less_than(Y, Z)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l34_l35')).
% 0.20/0.41 tff(123,plain,
% 0.20/0.41 (![U: $i] : ((~?[V: $i, W: $i] : (pair_in_list(U, V, W) & strictly_less_than(V, W))) | ![X: $i] : ?[Y: $i, Z: $i] : (pair_in_list(update_slb(U, X), Y, Z) & strictly_less_than(Y, Z)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.20/0.41 tff(124,plain,
% 0.20/0.41 (![U: $i] : ((~?[V: $i, W: $i] : (pair_in_list(U, V, W) & strictly_less_than(V, W))) | ![X: $i] : ?[Y: $i, Z: $i] : (pair_in_list(update_slb(U, X), Y, Z) & strictly_less_than(Y, Z)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[123, 119])).
% 0.20/0.41 tff(125,plain,(
% 0.20/0.41 ![U: $i] : (![V: $i, W: $i] : (~(pair_in_list(U, V, W) & strictly_less_than(V, W))) | ![X: $i] : (pair_in_list(update_slb(U, X), tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U)) & strictly_less_than(tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[124])).
% 0.20/0.41 tff(126,plain,
% 0.20/0.41 (![U: $i] : (![V: $i, W: $i] : ((~strictly_less_than(V, W)) | (~pair_in_list(U, V, W))) | ![X: $i] : (~((~pair_in_list(update_slb(U, X), tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))) | (~strictly_less_than(tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[125, 118])).
% 0.20/0.41 tff(127,plain,
% 0.20/0.41 (![U: $i, X: $i, V: $i, W: $i] : (((~strictly_less_than(V, W)) | (~pair_in_list(U, V, W))) | (~((~pair_in_list(update_slb(U, X), tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))) | (~strictly_less_than(tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[126, 116])).
% 0.20/0.41 tff(128,plain,
% 0.20/0.41 (![U: $i, X: $i, V: $i, W: $i] : ((~strictly_less_than(V, W)) | (~pair_in_list(U, V, W)) | (~((~pair_in_list(update_slb(U, X), tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))) | (~strictly_less_than(tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[127, 106])).
% 0.20/0.41 tff(129,plain,
% 0.20/0.41 (((~![U: $i, X: $i, V: $i, W: $i] : ((~strictly_less_than(V, W)) | (~pair_in_list(U, V, W)) | (~((~pair_in_list(update_slb(U, X), tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))) | (~strictly_less_than(tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))))))) | ((~strictly_less_than(tptp_fun_X_1(V!5), tptp_fun_Y_0(V!5))) | (~pair_in_list(V!5, tptp_fun_X_1(V!5), tptp_fun_Y_0(V!5))) | (~((~pair_in_list(update_slb(V!5, findmin_cpq_res(triple(U!6, V!5, W!4))), tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5))) | (~strictly_less_than(tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5))))))) <=> ((~![U: $i, X: $i, V: $i, W: $i] : ((~strictly_less_than(V, W)) | (~pair_in_list(U, V, W)) | (~((~pair_in_list(update_slb(U, X), tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))) | (~strictly_less_than(tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))))))) | (~strictly_less_than(tptp_fun_X_1(V!5), tptp_fun_Y_0(V!5))) | (~pair_in_list(V!5, tptp_fun_X_1(V!5), tptp_fun_Y_0(V!5))) | (~((~pair_in_list(update_slb(V!5, findmin_cpq_res(triple(U!6, V!5, W!4))), tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5))) | (~strictly_less_than(tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(130,plain,
% 0.20/0.41 ((~![U: $i, X: $i, V: $i, W: $i] : ((~strictly_less_than(V, W)) | (~pair_in_list(U, V, W)) | (~((~pair_in_list(update_slb(U, X), tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))) | (~strictly_less_than(tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))))))) | ((~strictly_less_than(tptp_fun_X_1(V!5), tptp_fun_Y_0(V!5))) | (~pair_in_list(V!5, tptp_fun_X_1(V!5), tptp_fun_Y_0(V!5))) | (~((~pair_in_list(update_slb(V!5, findmin_cpq_res(triple(U!6, V!5, W!4))), tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5))) | (~strictly_less_than(tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5))))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(131,plain,
% 0.20/0.42 ((~![U: $i, X: $i, V: $i, W: $i] : ((~strictly_less_than(V, W)) | (~pair_in_list(U, V, W)) | (~((~pair_in_list(update_slb(U, X), tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))) | (~strictly_less_than(tptp_fun_Y_3(X, U), tptp_fun_Z_2(X, U))))))) | (~strictly_less_than(tptp_fun_X_1(V!5), tptp_fun_Y_0(V!5))) | (~pair_in_list(V!5, tptp_fun_X_1(V!5), tptp_fun_Y_0(V!5))) | (~((~pair_in_list(update_slb(V!5, findmin_cpq_res(triple(U!6, V!5, W!4))), tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5))) | (~strictly_less_than(tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.20/0.42 tff(132,plain,
% 0.20/0.42 (~((~pair_in_list(update_slb(V!5, findmin_cpq_res(triple(U!6, V!5, W!4))), tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5))) | (~strictly_less_than(tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[131, 128, 38, 104])).
% 0.20/0.42 tff(133,plain,
% 0.20/0.42 (((~pair_in_list(update_slb(V!5, findmin_cpq_res(triple(U!6, V!5, W!4))), tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5))) | (~strictly_less_than(tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5)))) | pair_in_list(update_slb(V!5, findmin_cpq_res(triple(U!6, V!5, W!4))), tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(134,plain,
% 0.20/0.42 (pair_in_list(update_slb(V!5, findmin_cpq_res(triple(U!6, V!5, W!4))), tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[133, 132])).
% 0.20/0.42 tff(135,plain,
% 0.20/0.42 (pair_in_list(update_slb(V!5, findmin_pqp_res(U!6)), tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[134, 71])).
% 0.20/0.42 tff(136,plain,
% 0.20/0.42 ((~![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))) | (~(((~less_than(tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5))) | less_than(tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5))) <=> strictly_less_than(tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(137,plain,
% 0.20/0.42 (~(((~less_than(tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5))) | less_than(tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5))) <=> strictly_less_than(tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[136, 81])).
% 0.20/0.42 tff(138,plain,
% 0.20/0.42 (((~pair_in_list(update_slb(V!5, findmin_cpq_res(triple(U!6, V!5, W!4))), tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5))) | (~strictly_less_than(tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5)))) | strictly_less_than(tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(139,plain,
% 0.20/0.42 (strictly_less_than(tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[138, 132])).
% 0.20/0.42 tff(140,plain,
% 0.20/0.42 ((((~less_than(tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5))) | less_than(tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5))) <=> strictly_less_than(tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5))) | (~((~less_than(tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5))) | less_than(tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5)))) | (~strictly_less_than(tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(141,plain,
% 0.20/0.42 ((((~less_than(tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5))) | less_than(tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5))) <=> strictly_less_than(tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5))) | (~((~less_than(tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5))) | less_than(tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.20/0.42 tff(142,plain,
% 0.20/0.42 (~((~less_than(tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5))) | less_than(tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[141, 137])).
% 0.20/0.42 tff(143,plain,
% 0.20/0.42 (((~less_than(tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5))) | less_than(tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5))) | (~less_than(tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(144,plain,
% 0.20/0.42 (~less_than(tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[143, 142])).
% 0.20/0.42 tff(145,plain,
% 0.20/0.42 ((~![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!6, update_slb(V!5, findmin_pqp_res(U!6)), bad))) | ![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!5, findmin_pqp_res(U!6)), X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U!6, update_slb(V!5, findmin_pqp_res(U!6)), bad)) | (~((~pair_in_list(update_slb(V!5, findmin_pqp_res(U!6)), tptp_fun_X_1(update_slb(V!5, findmin_pqp_res(U!6))), tptp_fun_Y_0(update_slb(V!5, findmin_pqp_res(U!6))))) | less_than(tptp_fun_Y_0(update_slb(V!5, findmin_pqp_res(U!6))), tptp_fun_X_1(update_slb(V!5, findmin_pqp_res(U!6))))))))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(146,plain,
% 0.20/0.42 (~((~((~check_cpq(triple(U!6, update_slb(V!5, findmin_pqp_res(U!6)), bad))) | ![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!5, findmin_pqp_res(U!6)), X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U!6, update_slb(V!5, findmin_pqp_res(U!6)), bad)) | (~((~pair_in_list(update_slb(V!5, findmin_pqp_res(U!6)), tptp_fun_X_1(update_slb(V!5, findmin_pqp_res(U!6))), tptp_fun_Y_0(update_slb(V!5, findmin_pqp_res(U!6))))) | less_than(tptp_fun_Y_0(update_slb(V!5, findmin_pqp_res(U!6))), tptp_fun_X_1(update_slb(V!5, findmin_pqp_res(U!6)))))))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[145, 20])).
% 0.20/0.42 tff(147,plain,
% 0.20/0.42 (((~((~check_cpq(triple(U!6, update_slb(V!5, findmin_pqp_res(U!6)), bad))) | ![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!5, findmin_pqp_res(U!6)), X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U!6, update_slb(V!5, findmin_pqp_res(U!6)), bad)) | (~((~pair_in_list(update_slb(V!5, findmin_pqp_res(U!6)), tptp_fun_X_1(update_slb(V!5, findmin_pqp_res(U!6))), tptp_fun_Y_0(update_slb(V!5, findmin_pqp_res(U!6))))) | less_than(tptp_fun_Y_0(update_slb(V!5, findmin_pqp_res(U!6))), tptp_fun_X_1(update_slb(V!5, findmin_pqp_res(U!6))))))))) | ((~check_cpq(triple(U!6, update_slb(V!5, findmin_pqp_res(U!6)), bad))) | ![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!5, findmin_pqp_res(U!6)), X, Y)) | less_than(Y, X)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(148,plain,
% 0.20/0.42 ((~check_cpq(triple(U!6, update_slb(V!5, findmin_pqp_res(U!6)), bad))) | ![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!5, findmin_pqp_res(U!6)), X, Y)) | less_than(Y, X))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[147, 146])).
% 0.20/0.42 tff(149,plain,
% 0.20/0.42 (strictly_less_than(findmin_cpq_res(triple(U!6, V!5, W!4)), lookup_slb(V!5, findmin_pqp_res(U!6))) <=> strictly_less_than(findmin_pqp_res(U!6), lookup_slb(V!5, findmin_pqp_res(U!6)))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[67])).
% 0.20/0.42 tff(150,plain,
% 0.20/0.42 (strictly_less_than(findmin_pqp_res(U!6), lookup_slb(V!5, findmin_pqp_res(U!6))) <=> strictly_less_than(findmin_cpq_res(triple(U!6, V!5, W!4)), lookup_slb(V!5, findmin_pqp_res(U!6)))),
% 0.20/0.42 inference(symmetry,[status(thm)],[149])).
% 0.20/0.42 tff(151,plain,
% 0.20/0.42 ((~strictly_less_than(findmin_pqp_res(U!6), lookup_slb(V!5, findmin_pqp_res(U!6)))) <=> (~strictly_less_than(findmin_cpq_res(triple(U!6, V!5, W!4)), lookup_slb(V!5, findmin_pqp_res(U!6))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[150])).
% 0.20/0.42 tff(152,assumption,(~(findmin_cpq_eff(triple(U!6, V!5, W!4)) = triple(U!6, update_slb(V!5, findmin_pqp_res(U!6)), bad))), introduced(assumption)).
% 0.20/0.42 tff(153,assumption,(~(V!5 = create_slb)), introduced(assumption)).
% 0.20/0.42 tff(154,assumption,(strictly_less_than(findmin_pqp_res(U!6), lookup_slb(V!5, findmin_pqp_res(U!6)))), introduced(assumption)).
% 0.20/0.42 tff(155,plain,
% 0.20/0.42 (^[U: $i, V: $i, W: $i] : refl(((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) <=> ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(156,plain,
% 0.20/0.42 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) <=> ![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[155])).
% 0.20/0.42 tff(157,plain,
% 0.20/0.42 (^[U: $i, V: $i, W: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))) <=> (~((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))))), ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) <=> (~(~((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))))))), rewrite((~(~((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))))) <=> ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))))), ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) <=> ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))))), (((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> (((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))))), rewrite((((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))))), (((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(158,plain,
% 0.20/0.42 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[157])).
% 0.20/0.42 tff(159,plain,
% 0.20/0.42 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(160,plain,
% 0.20/0.42 (![U: $i, V: $i, W: $i, X: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.20/0.42 inference(elim_unused_vars,[status(thm)],[])).
% 0.20/0.42 tff(161,plain,
% 0.20/0.42 (^[U: $i, V: $i, W: $i, X: $i] : trans(monotonicity(rewrite((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))) <=> ((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))), (((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> (((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))))), rewrite((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))), (((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(162,plain,
% 0.20/0.43 (![U: $i, V: $i, W: $i, X: $i] : ((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[161])).
% 0.20/0.43 tff(163,plain,
% 0.20/0.43 (![U: $i, V: $i, W: $i, X: $i] : ((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[162, 160])).
% 0.20/0.43 tff(164,axiom,(![U: $i, V: $i, W: $i, X: $i] : ((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax','ax48')).
% 0.20/0.43 tff(165,plain,
% 0.20/0.43 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.20/0.43 tff(166,plain,
% 0.20/0.43 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[165, 159])).
% 0.20/0.43 tff(167,plain,(
% 0.20/0.43 ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[166])).
% 0.20/0.43 tff(168,plain,
% 0.20/0.43 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[167, 158])).
% 0.20/0.43 tff(169,plain,
% 0.20/0.43 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[168, 156])).
% 0.20/0.43 tff(170,plain,
% 0.20/0.43 (((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))))) | ((V!5 = create_slb) | (~contains_slb(V!5, findmin_pqp_res(U!6))) | (findmin_cpq_eff(triple(U!6, V!5, W!4)) = triple(U!6, update_slb(V!5, findmin_pqp_res(U!6)), bad)) | (~strictly_less_than(findmin_pqp_res(U!6), lookup_slb(V!5, findmin_pqp_res(U!6)))))) <=> ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))))) | (V!5 = create_slb) | (~contains_slb(V!5, findmin_pqp_res(U!6))) | (findmin_cpq_eff(triple(U!6, V!5, W!4)) = triple(U!6, update_slb(V!5, findmin_pqp_res(U!6)), bad)) | (~strictly_less_than(findmin_pqp_res(U!6), lookup_slb(V!5, findmin_pqp_res(U!6)))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(171,plain,
% 0.20/0.43 ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))))) | ((V!5 = create_slb) | (~contains_slb(V!5, findmin_pqp_res(U!6))) | (findmin_cpq_eff(triple(U!6, V!5, W!4)) = triple(U!6, update_slb(V!5, findmin_pqp_res(U!6)), bad)) | (~strictly_less_than(findmin_pqp_res(U!6), lookup_slb(V!5, findmin_pqp_res(U!6)))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(172,plain,
% 0.20/0.43 ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))))) | (V!5 = create_slb) | (~contains_slb(V!5, findmin_pqp_res(U!6))) | (findmin_cpq_eff(triple(U!6, V!5, W!4)) = triple(U!6, update_slb(V!5, findmin_pqp_res(U!6)), bad)) | (~strictly_less_than(findmin_pqp_res(U!6), lookup_slb(V!5, findmin_pqp_res(U!6))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.20/0.43 tff(173,plain,
% 0.20/0.43 ((V!5 = create_slb) | (~contains_slb(V!5, findmin_pqp_res(U!6))) | (findmin_cpq_eff(triple(U!6, V!5, W!4)) = triple(U!6, update_slb(V!5, findmin_pqp_res(U!6)), bad)) | (~strictly_less_than(findmin_pqp_res(U!6), lookup_slb(V!5, findmin_pqp_res(U!6))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[172, 169])).
% 0.20/0.43 tff(174,plain,
% 0.20/0.43 (~contains_slb(V!5, findmin_pqp_res(U!6))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[173, 153, 152, 154])).
% 0.20/0.43 tff(175,plain,
% 0.20/0.43 (^[U: $i, V: $i, W: $i] : refl(((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(176,plain,
% 0.20/0.43 (![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[175])).
% 0.20/0.43 tff(177,plain,
% 0.20/0.43 (^[U: $i, V: $i, W: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U)))) <=> (~((V = create_slb) | contains_slb(V, findmin_pqp_res(U))))), ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) <=> (~(~((V = create_slb) | contains_slb(V, findmin_pqp_res(U))))))), rewrite((~(~((V = create_slb) | contains_slb(V, findmin_pqp_res(U))))) <=> ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)))), ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) <=> ((V = create_slb) | contains_slb(V, findmin_pqp_res(U))))), (((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> (((V = create_slb) | contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))))), rewrite((((V = create_slb) | contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))), (((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(178,plain,
% 0.20/0.43 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[177])).
% 0.20/0.43 tff(179,plain,
% 0.20/0.43 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(180,plain,
% 0.20/0.43 (![U: $i, V: $i, W: $i, X: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.20/0.43 inference(elim_unused_vars,[status(thm)],[])).
% 0.20/0.43 tff(181,plain,
% 0.20/0.43 (^[U: $i, V: $i, W: $i, X: $i] : rewrite((((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U)))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(182,plain,
% 0.20/0.43 (![U: $i, V: $i, W: $i, X: $i] : (((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U)))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[181])).
% 0.20/0.43 tff(183,plain,
% 0.20/0.43 (![U: $i, V: $i, W: $i, X: $i] : (((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U)))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[182, 180])).
% 0.20/0.43 tff(184,axiom,(![U: $i, V: $i, W: $i, X: $i] : (((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U)))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax','ax47')).
% 0.20/0.43 tff(185,plain,
% 0.20/0.43 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.20/0.43 tff(186,plain,
% 0.20/0.43 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[185, 179])).
% 0.20/0.43 tff(187,plain,(
% 0.20/0.43 ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[186])).
% 0.20/0.43 tff(188,plain,
% 0.20/0.43 (![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[187, 178])).
% 0.20/0.43 tff(189,plain,
% 0.20/0.43 (![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[188, 176])).
% 0.20/0.43 tff(190,plain,
% 0.20/0.43 (((~![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))) | ((V!5 = create_slb) | contains_slb(V!5, findmin_pqp_res(U!6)) | (findmin_cpq_eff(triple(U!6, V!5, W!4)) = triple(U!6, update_slb(V!5, findmin_pqp_res(U!6)), bad)))) <=> ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))) | (V!5 = create_slb) | contains_slb(V!5, findmin_pqp_res(U!6)) | (findmin_cpq_eff(triple(U!6, V!5, W!4)) = triple(U!6, update_slb(V!5, findmin_pqp_res(U!6)), bad)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(191,plain,
% 0.20/0.43 ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))) | ((V!5 = create_slb) | contains_slb(V!5, findmin_pqp_res(U!6)) | (findmin_cpq_eff(triple(U!6, V!5, W!4)) = triple(U!6, update_slb(V!5, findmin_pqp_res(U!6)), bad)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(192,plain,
% 0.20/0.43 ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))) | (V!5 = create_slb) | contains_slb(V!5, findmin_pqp_res(U!6)) | (findmin_cpq_eff(triple(U!6, V!5, W!4)) = triple(U!6, update_slb(V!5, findmin_pqp_res(U!6)), bad))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.20/0.43 tff(193,plain,
% 0.20/0.43 ((V!5 = create_slb) | contains_slb(V!5, findmin_pqp_res(U!6)) | (findmin_cpq_eff(triple(U!6, V!5, W!4)) = triple(U!6, update_slb(V!5, findmin_pqp_res(U!6)), bad))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[192, 189])).
% 0.20/0.43 tff(194,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[193, 174, 153, 152])).
% 0.20/0.43 tff(195,plain,((V!5 = create_slb) | (findmin_cpq_eff(triple(U!6, V!5, W!4)) = triple(U!6, update_slb(V!5, findmin_pqp_res(U!6)), bad)) | (~strictly_less_than(findmin_pqp_res(U!6), lookup_slb(V!5, findmin_pqp_res(U!6))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(196,plain,
% 0.20/0.44 ((findmin_cpq_eff(triple(U!6, V!5, W!4)) = triple(U!6, update_slb(V!5, findmin_pqp_res(U!6)), bad)) | (~strictly_less_than(findmin_pqp_res(U!6), lookup_slb(V!5, findmin_pqp_res(U!6))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[195, 50])).
% 0.20/0.44 tff(197,plain,
% 0.20/0.44 (~strictly_less_than(findmin_pqp_res(U!6), lookup_slb(V!5, findmin_pqp_res(U!6)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[196, 152])).
% 0.20/0.44 tff(198,plain,
% 0.20/0.44 (~strictly_less_than(findmin_cpq_res(triple(U!6, V!5, W!4)), lookup_slb(V!5, findmin_pqp_res(U!6)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[197, 151])).
% 0.20/0.44 tff(199,plain,
% 0.20/0.44 ((~![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))) | (~(((~less_than(findmin_cpq_res(triple(U!6, V!5, W!4)), lookup_slb(V!5, findmin_pqp_res(U!6)))) | less_than(lookup_slb(V!5, findmin_pqp_res(U!6)), findmin_cpq_res(triple(U!6, V!5, W!4)))) <=> strictly_less_than(findmin_cpq_res(triple(U!6, V!5, W!4)), lookup_slb(V!5, findmin_pqp_res(U!6)))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(200,plain,
% 0.20/0.44 (~(((~less_than(findmin_cpq_res(triple(U!6, V!5, W!4)), lookup_slb(V!5, findmin_pqp_res(U!6)))) | less_than(lookup_slb(V!5, findmin_pqp_res(U!6)), findmin_cpq_res(triple(U!6, V!5, W!4)))) <=> strictly_less_than(findmin_cpq_res(triple(U!6, V!5, W!4)), lookup_slb(V!5, findmin_pqp_res(U!6))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[199, 81])).
% 0.20/0.44 tff(201,plain,
% 0.20/0.44 (less_than(lookup_slb(V!5, findmin_pqp_res(U!6)), findmin_cpq_res(triple(U!6, V!5, W!4))) <=> less_than(lookup_slb(V!5, findmin_pqp_res(U!6)), findmin_pqp_res(U!6))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[67])).
% 0.20/0.44 tff(202,plain,
% 0.20/0.44 (less_than(lookup_slb(V!5, findmin_pqp_res(U!6)), findmin_pqp_res(U!6)) <=> less_than(lookup_slb(V!5, findmin_pqp_res(U!6)), findmin_cpq_res(triple(U!6, V!5, W!4)))),
% 0.20/0.44 inference(symmetry,[status(thm)],[201])).
% 0.20/0.44 tff(203,plain,
% 0.20/0.44 ((~less_than(lookup_slb(V!5, findmin_pqp_res(U!6)), findmin_pqp_res(U!6))) <=> (~less_than(lookup_slb(V!5, findmin_pqp_res(U!6)), findmin_cpq_res(triple(U!6, V!5, W!4))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[202])).
% 0.20/0.44 tff(204,plain,
% 0.20/0.44 (contains_slb(V!5, findmin_pqp_res(U!6)) | (findmin_cpq_eff(triple(U!6, V!5, W!4)) = triple(U!6, update_slb(V!5, findmin_pqp_res(U!6)), bad))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[193, 50])).
% 0.20/0.44 tff(205,plain,
% 0.20/0.44 (contains_slb(V!5, findmin_pqp_res(U!6))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[204, 152])).
% 0.20/0.44 tff(206,plain,
% 0.20/0.44 ((~![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!6, update_slb(V!5, findmin_pqp_res(U!6)), W!4))) | ![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!5, findmin_pqp_res(U!6)), X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U!6, update_slb(V!5, findmin_pqp_res(U!6)), W!4)) | (~((~pair_in_list(update_slb(V!5, findmin_pqp_res(U!6)), tptp_fun_X_1(update_slb(V!5, findmin_pqp_res(U!6))), tptp_fun_Y_0(update_slb(V!5, findmin_pqp_res(U!6))))) | less_than(tptp_fun_Y_0(update_slb(V!5, findmin_pqp_res(U!6))), tptp_fun_X_1(update_slb(V!5, findmin_pqp_res(U!6))))))))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(207,plain,
% 0.20/0.44 (~((~((~check_cpq(triple(U!6, update_slb(V!5, findmin_pqp_res(U!6)), W!4))) | ![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!5, findmin_pqp_res(U!6)), X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U!6, update_slb(V!5, findmin_pqp_res(U!6)), W!4)) | (~((~pair_in_list(update_slb(V!5, findmin_pqp_res(U!6)), tptp_fun_X_1(update_slb(V!5, findmin_pqp_res(U!6))), tptp_fun_Y_0(update_slb(V!5, findmin_pqp_res(U!6))))) | less_than(tptp_fun_Y_0(update_slb(V!5, findmin_pqp_res(U!6))), tptp_fun_X_1(update_slb(V!5, findmin_pqp_res(U!6)))))))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[206, 20])).
% 0.20/0.44 tff(208,plain,
% 0.20/0.44 (((~((~check_cpq(triple(U!6, update_slb(V!5, findmin_pqp_res(U!6)), W!4))) | ![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!5, findmin_pqp_res(U!6)), X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U!6, update_slb(V!5, findmin_pqp_res(U!6)), W!4)) | (~((~pair_in_list(update_slb(V!5, findmin_pqp_res(U!6)), tptp_fun_X_1(update_slb(V!5, findmin_pqp_res(U!6))), tptp_fun_Y_0(update_slb(V!5, findmin_pqp_res(U!6))))) | less_than(tptp_fun_Y_0(update_slb(V!5, findmin_pqp_res(U!6))), tptp_fun_X_1(update_slb(V!5, findmin_pqp_res(U!6))))))))) | ((~check_cpq(triple(U!6, update_slb(V!5, findmin_pqp_res(U!6)), W!4))) | ![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!5, findmin_pqp_res(U!6)), X, Y)) | less_than(Y, X)))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(209,plain,
% 0.20/0.44 ((~check_cpq(triple(U!6, update_slb(V!5, findmin_pqp_res(U!6)), W!4))) | ![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!5, findmin_pqp_res(U!6)), X, Y)) | less_than(Y, X))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[208, 207])).
% 0.20/0.44 tff(210,assumption,(findmin_cpq_eff(triple(U!6, V!5, W!4)) = triple(U!6, update_slb(V!5, findmin_pqp_res(U!6)), W!4)), introduced(assumption)).
% 0.20/0.44 tff(211,plain,
% 0.20/0.44 (triple(U!6, update_slb(V!5, findmin_pqp_res(U!6)), W!4) = findmin_cpq_eff(triple(U!6, V!5, W!4))),
% 0.20/0.44 inference(symmetry,[status(thm)],[210])).
% 0.20/0.44 tff(212,plain,
% 0.20/0.44 (check_cpq(triple(U!6, update_slb(V!5, findmin_pqp_res(U!6)), W!4)) <=> check_cpq(findmin_cpq_eff(triple(U!6, V!5, W!4)))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[211])).
% 0.20/0.44 tff(213,plain,
% 0.20/0.44 (check_cpq(findmin_cpq_eff(triple(U!6, V!5, W!4))) <=> check_cpq(triple(U!6, update_slb(V!5, findmin_pqp_res(U!6)), W!4))),
% 0.20/0.44 inference(symmetry,[status(thm)],[212])).
% 0.20/0.44 tff(214,plain,
% 0.20/0.44 (check_cpq(findmin_cpq_eff(triple(U!6, V!5, W!4)))),
% 0.20/0.44 inference(or_elim,[status(thm)],[32])).
% 0.20/0.44 tff(215,plain,
% 0.20/0.44 (check_cpq(triple(U!6, update_slb(V!5, findmin_pqp_res(U!6)), W!4))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[214, 213])).
% 0.20/0.44 tff(216,plain,
% 0.20/0.44 ((~((~check_cpq(triple(U!6, update_slb(V!5, findmin_pqp_res(U!6)), W!4))) | ![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!5, findmin_pqp_res(U!6)), X, Y)) | less_than(Y, X)))) | (~check_cpq(triple(U!6, update_slb(V!5, findmin_pqp_res(U!6)), W!4))) | ![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!5, findmin_pqp_res(U!6)), X, Y)) | less_than(Y, X))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(217,plain,
% 0.20/0.44 (![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!5, findmin_pqp_res(U!6)), X, Y)) | less_than(Y, X))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[216, 215, 209])).
% 0.20/0.44 tff(218,plain,
% 0.20/0.44 (((~![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!5, findmin_pqp_res(U!6)), X, Y)) | less_than(Y, X))) | ((~pair_in_list(update_slb(V!5, findmin_pqp_res(U!6)), tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5))) | less_than(tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5)))) <=> ((~![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!5, findmin_pqp_res(U!6)), X, Y)) | less_than(Y, X))) | (~pair_in_list(update_slb(V!5, findmin_pqp_res(U!6)), tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5))) | less_than(tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(219,plain,
% 0.20/0.44 ((~![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!5, findmin_pqp_res(U!6)), X, Y)) | less_than(Y, X))) | ((~pair_in_list(update_slb(V!5, findmin_pqp_res(U!6)), tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5))) | less_than(tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(220,plain,
% 0.20/0.44 ((~![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!5, findmin_pqp_res(U!6)), X, Y)) | less_than(Y, X))) | (~pair_in_list(update_slb(V!5, findmin_pqp_res(U!6)), tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5))) | less_than(tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.20/0.44 tff(221,plain,
% 0.20/0.44 (~pair_in_list(update_slb(V!5, findmin_pqp_res(U!6)), tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[220, 217, 144])).
% 0.20/0.44 tff(222,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[221, 135])).
% 0.20/0.44 tff(223,plain,(~(findmin_cpq_eff(triple(U!6, V!5, W!4)) = triple(U!6, update_slb(V!5, findmin_pqp_res(U!6)), W!4))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(224,plain,
% 0.20/0.44 (^[U: $i, V: $i, W: $i] : refl(((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) <=> ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(225,plain,
% 0.20/0.44 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) <=> ![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[224])).
% 0.20/0.44 tff(226,plain,
% 0.20/0.44 (^[U: $i, V: $i, W: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))) <=> (~((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))))), ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) <=> (~(~((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))))))), rewrite((~(~((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))))) <=> ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))), ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) <=> ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))))), (((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))) <=> (((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))))), rewrite((((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))) <=> ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))), (((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))) <=> ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(227,plain,
% 0.20/0.44 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))) <=> ![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[226])).
% 0.20/0.44 tff(228,plain,
% 0.20/0.44 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))) <=> ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(229,plain,
% 0.20/0.44 (![U: $i, V: $i, W: $i, X: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))) <=> ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)))),
% 0.20/0.44 inference(elim_unused_vars,[status(thm)],[])).
% 0.20/0.44 tff(230,plain,
% 0.20/0.44 (^[U: $i, V: $i, W: $i, X: $i] : trans(monotonicity(rewrite((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))) <=> ((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))), (((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))) <=> (((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))))), rewrite((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))) <=> ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)))), (((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))) <=> ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(231,plain,
% 0.20/0.44 (![U: $i, V: $i, W: $i, X: $i] : ((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[230])).
% 0.20/0.44 tff(232,plain,
% 0.20/0.44 (![U: $i, V: $i, W: $i, X: $i] : ((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))) <=> ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[231, 229])).
% 0.20/0.44 tff(233,axiom,(![U: $i, V: $i, W: $i, X: $i] : ((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax','ax49')).
% 0.20/0.44 tff(234,plain,
% 0.20/0.44 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[233, 232])).
% 0.20/0.44 tff(235,plain,
% 0.20/0.44 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[234, 228])).
% 0.20/0.44 tff(236,plain,(
% 0.20/0.44 ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[235])).
% 0.20/0.44 tff(237,plain,
% 0.20/0.44 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[236, 227])).
% 0.20/0.44 tff(238,plain,
% 0.20/0.44 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[237, 225])).
% 0.20/0.44 tff(239,plain,
% 0.20/0.44 (((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))) | ((V!5 = create_slb) | (~contains_slb(V!5, findmin_pqp_res(U!6))) | (findmin_cpq_eff(triple(U!6, V!5, W!4)) = triple(U!6, update_slb(V!5, findmin_pqp_res(U!6)), W!4)) | (~less_than(lookup_slb(V!5, findmin_pqp_res(U!6)), findmin_pqp_res(U!6))))) <=> ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))) | (V!5 = create_slb) | (~contains_slb(V!5, findmin_pqp_res(U!6))) | (findmin_cpq_eff(triple(U!6, V!5, W!4)) = triple(U!6, update_slb(V!5, findmin_pqp_res(U!6)), W!4)) | (~less_than(lookup_slb(V!5, findmin_pqp_res(U!6)), findmin_pqp_res(U!6))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(240,plain,
% 0.20/0.44 ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))) | ((V!5 = create_slb) | (~contains_slb(V!5, findmin_pqp_res(U!6))) | (findmin_cpq_eff(triple(U!6, V!5, W!4)) = triple(U!6, update_slb(V!5, findmin_pqp_res(U!6)), W!4)) | (~less_than(lookup_slb(V!5, findmin_pqp_res(U!6)), findmin_pqp_res(U!6))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(241,plain,
% 0.20/0.45 ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))) | (V!5 = create_slb) | (~contains_slb(V!5, findmin_pqp_res(U!6))) | (findmin_cpq_eff(triple(U!6, V!5, W!4)) = triple(U!6, update_slb(V!5, findmin_pqp_res(U!6)), W!4)) | (~less_than(lookup_slb(V!5, findmin_pqp_res(U!6)), findmin_pqp_res(U!6)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[240, 239])).
% 0.20/0.45 tff(242,plain,
% 0.20/0.45 ((V!5 = create_slb) | (~contains_slb(V!5, findmin_pqp_res(U!6))) | (findmin_cpq_eff(triple(U!6, V!5, W!4)) = triple(U!6, update_slb(V!5, findmin_pqp_res(U!6)), W!4)) | (~less_than(lookup_slb(V!5, findmin_pqp_res(U!6)), findmin_pqp_res(U!6)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[241, 238])).
% 0.20/0.45 tff(243,plain,
% 0.20/0.45 ((~contains_slb(V!5, findmin_pqp_res(U!6))) | (findmin_cpq_eff(triple(U!6, V!5, W!4)) = triple(U!6, update_slb(V!5, findmin_pqp_res(U!6)), W!4)) | (~less_than(lookup_slb(V!5, findmin_pqp_res(U!6)), findmin_pqp_res(U!6)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[242, 50])).
% 0.20/0.45 tff(244,plain,
% 0.20/0.45 ((~contains_slb(V!5, findmin_pqp_res(U!6))) | (~less_than(lookup_slb(V!5, findmin_pqp_res(U!6)), findmin_pqp_res(U!6)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[243, 223])).
% 0.20/0.45 tff(245,plain,
% 0.20/0.45 (~less_than(lookup_slb(V!5, findmin_pqp_res(U!6)), findmin_pqp_res(U!6))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[244, 205])).
% 0.20/0.45 tff(246,plain,
% 0.20/0.45 (~less_than(lookup_slb(V!5, findmin_pqp_res(U!6)), findmin_cpq_res(triple(U!6, V!5, W!4)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[245, 203])).
% 0.20/0.45 tff(247,assumption,((~less_than(findmin_cpq_res(triple(U!6, V!5, W!4)), lookup_slb(V!5, findmin_pqp_res(U!6)))) | less_than(lookup_slb(V!5, findmin_pqp_res(U!6)), findmin_cpq_res(triple(U!6, V!5, W!4)))), introduced(assumption)).
% 0.20/0.45 tff(248,assumption,(~less_than(lookup_slb(V!5, findmin_pqp_res(U!6)), findmin_cpq_res(triple(U!6, V!5, W!4)))), introduced(assumption)).
% 0.20/0.45 tff(249,plain,
% 0.20/0.45 (((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | (less_than(findmin_cpq_res(triple(U!6, V!5, W!4)), lookup_slb(V!5, findmin_pqp_res(U!6))) | less_than(lookup_slb(V!5, findmin_pqp_res(U!6)), findmin_cpq_res(triple(U!6, V!5, W!4))))) <=> ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | less_than(findmin_cpq_res(triple(U!6, V!5, W!4)), lookup_slb(V!5, findmin_pqp_res(U!6))) | less_than(lookup_slb(V!5, findmin_pqp_res(U!6)), findmin_cpq_res(triple(U!6, V!5, W!4))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(250,plain,
% 0.20/0.45 ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | (less_than(findmin_cpq_res(triple(U!6, V!5, W!4)), lookup_slb(V!5, findmin_pqp_res(U!6))) | less_than(lookup_slb(V!5, findmin_pqp_res(U!6)), findmin_cpq_res(triple(U!6, V!5, W!4))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(251,plain,
% 0.20/0.45 ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | less_than(findmin_cpq_res(triple(U!6, V!5, W!4)), lookup_slb(V!5, findmin_pqp_res(U!6))) | less_than(lookup_slb(V!5, findmin_pqp_res(U!6)), findmin_cpq_res(triple(U!6, V!5, W!4)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[250, 249])).
% 0.20/0.45 tff(252,plain,
% 0.20/0.45 (less_than(findmin_cpq_res(triple(U!6, V!5, W!4)), lookup_slb(V!5, findmin_pqp_res(U!6)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[251, 95, 248])).
% 0.20/0.45 tff(253,plain,
% 0.20/0.45 ((~((~less_than(findmin_cpq_res(triple(U!6, V!5, W!4)), lookup_slb(V!5, findmin_pqp_res(U!6)))) | less_than(lookup_slb(V!5, findmin_pqp_res(U!6)), findmin_cpq_res(triple(U!6, V!5, W!4))))) | (~less_than(findmin_cpq_res(triple(U!6, V!5, W!4)), lookup_slb(V!5, findmin_pqp_res(U!6)))) | less_than(lookup_slb(V!5, findmin_pqp_res(U!6)), findmin_cpq_res(triple(U!6, V!5, W!4)))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(254,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[253, 252, 248, 247])).
% 0.20/0.45 tff(255,plain,(less_than(lookup_slb(V!5, findmin_pqp_res(U!6)), findmin_cpq_res(triple(U!6, V!5, W!4))) | (~((~less_than(findmin_cpq_res(triple(U!6, V!5, W!4)), lookup_slb(V!5, findmin_pqp_res(U!6)))) | less_than(lookup_slb(V!5, findmin_pqp_res(U!6)), findmin_cpq_res(triple(U!6, V!5, W!4)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(256,plain,
% 0.20/0.45 (~((~less_than(findmin_cpq_res(triple(U!6, V!5, W!4)), lookup_slb(V!5, findmin_pqp_res(U!6)))) | less_than(lookup_slb(V!5, findmin_pqp_res(U!6)), findmin_cpq_res(triple(U!6, V!5, W!4))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[255, 246])).
% 0.20/0.45 tff(257,plain,
% 0.20/0.45 ((((~less_than(findmin_cpq_res(triple(U!6, V!5, W!4)), lookup_slb(V!5, findmin_pqp_res(U!6)))) | less_than(lookup_slb(V!5, findmin_pqp_res(U!6)), findmin_cpq_res(triple(U!6, V!5, W!4)))) <=> strictly_less_than(findmin_cpq_res(triple(U!6, V!5, W!4)), lookup_slb(V!5, findmin_pqp_res(U!6)))) | ((~less_than(findmin_cpq_res(triple(U!6, V!5, W!4)), lookup_slb(V!5, findmin_pqp_res(U!6)))) | less_than(lookup_slb(V!5, findmin_pqp_res(U!6)), findmin_cpq_res(triple(U!6, V!5, W!4)))) | strictly_less_than(findmin_cpq_res(triple(U!6, V!5, W!4)), lookup_slb(V!5, findmin_pqp_res(U!6)))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(258,plain,
% 0.20/0.45 (strictly_less_than(findmin_cpq_res(triple(U!6, V!5, W!4)), lookup_slb(V!5, findmin_pqp_res(U!6)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[257, 256, 200])).
% 0.20/0.45 tff(259,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[258, 198])).
% 0.20/0.45 tff(260,plain,(findmin_cpq_eff(triple(U!6, V!5, W!4)) = triple(U!6, update_slb(V!5, findmin_pqp_res(U!6)), bad)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(261,plain,
% 0.20/0.45 (triple(U!6, update_slb(V!5, findmin_pqp_res(U!6)), bad) = findmin_cpq_eff(triple(U!6, V!5, W!4))),
% 0.20/0.45 inference(symmetry,[status(thm)],[260])).
% 0.20/0.45 tff(262,plain,
% 0.20/0.45 (check_cpq(triple(U!6, update_slb(V!5, findmin_pqp_res(U!6)), bad)) <=> check_cpq(findmin_cpq_eff(triple(U!6, V!5, W!4)))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[261])).
% 0.20/0.45 tff(263,plain,
% 0.20/0.45 (check_cpq(findmin_cpq_eff(triple(U!6, V!5, W!4))) <=> check_cpq(triple(U!6, update_slb(V!5, findmin_pqp_res(U!6)), bad))),
% 0.20/0.45 inference(symmetry,[status(thm)],[262])).
% 0.20/0.45 tff(264,plain,
% 0.20/0.45 (check_cpq(triple(U!6, update_slb(V!5, findmin_pqp_res(U!6)), bad))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[214, 263])).
% 0.20/0.45 tff(265,plain,
% 0.20/0.45 ((~((~check_cpq(triple(U!6, update_slb(V!5, findmin_pqp_res(U!6)), bad))) | ![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!5, findmin_pqp_res(U!6)), X, Y)) | less_than(Y, X)))) | (~check_cpq(triple(U!6, update_slb(V!5, findmin_pqp_res(U!6)), bad))) | ![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!5, findmin_pqp_res(U!6)), X, Y)) | less_than(Y, X))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(266,plain,
% 0.20/0.45 (![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!5, findmin_pqp_res(U!6)), X, Y)) | less_than(Y, X))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[265, 264, 148])).
% 0.20/0.45 tff(267,plain,
% 0.20/0.45 (~pair_in_list(update_slb(V!5, findmin_pqp_res(U!6)), tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[220, 266, 144])).
% 0.20/0.45 tff(268,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[267, 135])).
% 0.20/0.45 % SZS output end Proof
% 0.20/0.45 % E exiting
%------------------------------------------------------------------------------