TSTP Solution File: SWV398+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV398+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.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 : Thu Sep 29 15:11:37 EDT 2022
% Result : Theorem 0.16s 0.37s
% Output : Proof 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : SWV398+1 : TPTP v8.1.0. Released v3.3.0.
% 0.09/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.31 % Computer : n020.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Sun Sep 4 02:53:29 EDT 2022
% 0.10/0.31 % CPUTime :
% 0.16/0.31 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.16/0.31 Usage: tptp [options] [-file:]file
% 0.16/0.31 -h, -? prints this message.
% 0.16/0.31 -smt2 print SMT-LIB2 benchmark.
% 0.16/0.31 -m, -model generate model.
% 0.16/0.31 -p, -proof generate proof.
% 0.16/0.31 -c, -core generate unsat core of named formulas.
% 0.16/0.31 -st, -statistics display statistics.
% 0.16/0.31 -t:timeout set timeout (in second).
% 0.16/0.31 -smt2status display status in smt2 format instead of SZS.
% 0.16/0.31 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.16/0.31 -<param>:<value> configuration parameter and value.
% 0.16/0.31 -o:<output-file> file to place output in.
% 0.16/0.37 % SZS status Theorem
% 0.16/0.37 % SZS output start Proof
% 0.16/0.37 tff(pair_in_list_type, type, (
% 0.16/0.37 pair_in_list: ( $i * $i * $i ) > $o)).
% 0.16/0.37 tff(tptp_fun_Z_2_type, type, (
% 0.16/0.37 tptp_fun_Z_2: ( $i * $i ) > $i)).
% 0.16/0.37 tff(tptp_fun_V_5_type, type, (
% 0.16/0.37 tptp_fun_V_5: $i)).
% 0.16/0.37 tff(findmin_cpq_res_type, type, (
% 0.16/0.37 findmin_cpq_res: $i > $i)).
% 0.16/0.37 tff(triple_type, type, (
% 0.16/0.37 triple: ( $i * $i * $i ) > $i)).
% 0.16/0.37 tff(tptp_fun_W_4_type, type, (
% 0.16/0.37 tptp_fun_W_4: $i)).
% 0.16/0.37 tff(tptp_fun_U_6_type, type, (
% 0.16/0.37 tptp_fun_U_6: $i)).
% 0.16/0.37 tff(tptp_fun_Y_3_type, type, (
% 0.16/0.37 tptp_fun_Y_3: ( $i * $i ) > $i)).
% 0.16/0.37 tff(update_slb_type, type, (
% 0.16/0.37 update_slb: ( $i * $i ) > $i)).
% 0.16/0.37 tff(findmin_pqp_res_type, type, (
% 0.16/0.37 findmin_pqp_res: $i > $i)).
% 0.16/0.37 tff(create_slb_type, type, (
% 0.16/0.37 create_slb: $i)).
% 0.16/0.37 tff(tptp_fun_Y_0_type, type, (
% 0.16/0.37 tptp_fun_Y_0: $i > $i)).
% 0.16/0.37 tff(tptp_fun_X_1_type, type, (
% 0.16/0.37 tptp_fun_X_1: $i > $i)).
% 0.16/0.37 tff(less_than_type, type, (
% 0.16/0.37 less_than: ( $i * $i ) > $o)).
% 0.16/0.37 tff(check_cpq_type, type, (
% 0.16/0.37 check_cpq: $i > $o)).
% 0.16/0.37 tff(findmin_cpq_eff_type, type, (
% 0.16/0.37 findmin_cpq_eff: $i > $i)).
% 0.16/0.37 tff(strictly_less_than_type, type, (
% 0.16/0.37 strictly_less_than: ( $i * $i ) > $o)).
% 0.16/0.37 tff(lookup_slb_type, type, (
% 0.16/0.37 lookup_slb: ( $i * $i ) > $i)).
% 0.16/0.37 tff(bad_type, type, (
% 0.16/0.37 bad: $i)).
% 0.16/0.37 tff(contains_slb_type, type, (
% 0.16/0.37 contains_slb: ( $i * $i ) > $o)).
% 0.16/0.37 tff(1,assumption,(V!5 = create_slb), introduced(assumption)).
% 0.16/0.37 tff(2,plain,
% 0.16/0.37 (create_slb = V!5),
% 0.16/0.37 inference(symmetry,[status(thm)],[1])).
% 0.16/0.37 tff(3,plain,
% 0.16/0.37 (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))),
% 0.16/0.37 inference(monotonicity,[status(thm)],[2])).
% 0.16/0.37 tff(4,plain,
% 0.16/0.37 (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))),
% 0.16/0.37 inference(symmetry,[status(thm)],[3])).
% 0.16/0.37 tff(5,plain,
% 0.16/0.37 (^[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)))))))))),
% 0.16/0.37 inference(bind,[status(th)],[])).
% 0.16/0.37 tff(6,plain,
% 0.16/0.37 (![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))))))))),
% 0.16/0.37 inference(quant_intro,[status(thm)],[5])).
% 0.16/0.37 tff(7,plain,
% 0.16/0.37 (^[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)))))))))),
% 0.16/0.37 inference(bind,[status(th)],[])).
% 0.16/0.37 tff(8,plain,
% 0.16/0.37 (![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))))))))),
% 0.16/0.37 inference(quant_intro,[status(thm)],[7])).
% 0.16/0.37 tff(9,plain,
% 0.16/0.37 (![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))))))))),
% 0.16/0.37 inference(transitivity,[status(thm)],[8, 6])).
% 0.16/0.37 tff(10,plain,
% 0.16/0.37 (^[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))))))))))),
% 0.16/0.37 inference(bind,[status(th)],[])).
% 0.16/0.37 tff(11,plain,
% 0.16/0.37 (![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))))))))),
% 0.16/0.37 inference(quant_intro,[status(thm)],[10])).
% 0.16/0.37 tff(12,plain,
% 0.16/0.37 (![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)))),
% 0.16/0.37 inference(rewrite,[status(thm)],[])).
% 0.16/0.37 tff(13,plain,
% 0.16/0.37 (^[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))))),
% 0.16/0.37 inference(bind,[status(th)],[])).
% 0.16/0.37 tff(14,plain,
% 0.16/0.37 (![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)))),
% 0.16/0.37 inference(quant_intro,[status(thm)],[13])).
% 0.16/0.37 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')).
% 0.16/0.38 tff(16,plain,
% 0.16/0.38 (![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) <=> ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.16/0.38 tff(17,plain,
% 0.16/0.38 (![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) <=> ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.16/0.38 tff(18,plain,(
% 0.16/0.38 ![U: $i, V: $i, W: $i] : (((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X))) & (check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V))))))),
% 0.16/0.38 inference(skolemize,[status(sab)],[17])).
% 0.16/0.38 tff(19,plain,
% 0.16/0.38 (![U: $i, V: $i, W: $i] : (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V))))))))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.16/0.38 tff(20,plain,
% 0.16/0.38 (![U: $i, V: $i, W: $i] : (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V))))))))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[19, 9])).
% 0.16/0.38 tff(21,plain,
% 0.16/0.38 ((~![U: $i, V: $i, W: $i] : (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V))))))))) | (~((~((~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))))))))),
% 0.16/0.38 inference(quant_inst,[status(thm)],[])).
% 0.16/0.38 tff(22,plain,
% 0.16/0.38 (~((~((~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)))))))),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.16/0.38 tff(23,plain,
% 0.16/0.38 (((~((~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)))))),
% 0.16/0.38 inference(tautology,[status(thm)],[])).
% 0.16/0.38 tff(24,plain,
% 0.16/0.38 (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))))),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.16/0.38 tff(25,plain,
% 0.16/0.38 ((~![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))))))),
% 0.16/0.38 inference(rewrite,[status(thm)],[])).
% 0.16/0.38 tff(26,plain,
% 0.16/0.38 ((~![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))))))),
% 0.16/0.38 inference(rewrite,[status(thm)],[])).
% 0.16/0.38 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')).
% 0.16/0.38 tff(28,plain,
% 0.16/0.38 (~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~check_cpq(findmin_cpq_eff(triple(U, V, W)))))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.16/0.38 tff(29,plain,
% 0.16/0.38 (~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~check_cpq(findmin_cpq_eff(triple(U, V, W)))))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[28, 25])).
% 0.16/0.38 tff(30,plain,
% 0.16/0.38 (~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~check_cpq(findmin_cpq_eff(triple(U, V, W)))))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.16/0.38 tff(31,plain,
% 0.16/0.38 (~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~check_cpq(findmin_cpq_eff(triple(U, V, W)))))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[30, 25])).
% 0.16/0.38 tff(32,plain,
% 0.16/0.38 (~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~check_cpq(findmin_cpq_eff(triple(U, V, W)))))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[31, 25])).
% 0.16/0.38 tff(33,plain,
% 0.16/0.38 (~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~check_cpq(findmin_cpq_eff(triple(U, V, W)))))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.16/0.38 tff(34,plain,
% 0.16/0.38 (~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~check_cpq(findmin_cpq_eff(triple(U, V, W)))))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[33, 25])).
% 0.16/0.38 tff(35,plain,(
% 0.16/0.38 ~(check_cpq(triple(U!6, V!5, W!4)) | (~check_cpq(findmin_cpq_eff(triple(U!6, V!5, W!4)))))),
% 0.16/0.38 inference(skolemize,[status(sab)],[34])).
% 0.16/0.38 tff(36,plain,
% 0.16/0.38 (~check_cpq(triple(U!6, V!5, W!4))),
% 0.16/0.38 inference(or_elim,[status(thm)],[35])).
% 0.16/0.38 tff(37,plain,
% 0.16/0.38 ((~(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))))),
% 0.16/0.38 inference(tautology,[status(thm)],[])).
% 0.16/0.38 tff(38,plain,
% 0.16/0.38 ((~(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))))),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.16/0.38 tff(39,plain,
% 0.16/0.38 (~((~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)))),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[38, 24])).
% 0.16/0.38 tff(40,plain,
% 0.16/0.38 (((~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))),
% 0.16/0.38 inference(tautology,[status(thm)],[])).
% 0.16/0.38 tff(41,plain,
% 0.16/0.38 (pair_in_list(V!5, tptp_fun_X_1(V!5), tptp_fun_Y_0(V!5))),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.16/0.38 tff(42,plain,
% 0.16/0.38 (pair_in_list(create_slb, tptp_fun_X_1(V!5), tptp_fun_Y_0(V!5))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[41, 4])).
% 0.16/0.38 tff(43,plain,
% 0.16/0.38 (^[U: $i, V: $i] : refl((~pair_in_list(create_slb, U, V)) <=> (~pair_in_list(create_slb, U, V)))),
% 0.16/0.38 inference(bind,[status(th)],[])).
% 0.16/0.38 tff(44,plain,
% 0.16/0.38 (![U: $i, V: $i] : (~pair_in_list(create_slb, U, V)) <=> ![U: $i, V: $i] : (~pair_in_list(create_slb, U, V))),
% 0.16/0.38 inference(quant_intro,[status(thm)],[43])).
% 0.16/0.38 tff(45,plain,
% 0.16/0.38 (![U: $i, V: $i] : (~pair_in_list(create_slb, U, V)) <=> ![U: $i, V: $i] : (~pair_in_list(create_slb, U, V))),
% 0.16/0.38 inference(rewrite,[status(thm)],[])).
% 0.16/0.38 tff(46,axiom,(![U: $i, V: $i] : (~pair_in_list(create_slb, U, V))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+2.ax','ax22')).
% 0.16/0.38 tff(47,plain,
% 0.16/0.38 (![U: $i, V: $i] : (~pair_in_list(create_slb, U, V))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.16/0.38 tff(48,plain,(
% 0.16/0.38 ![U: $i, V: $i] : (~pair_in_list(create_slb, U, V))),
% 0.16/0.38 inference(skolemize,[status(sab)],[47])).
% 0.16/0.38 tff(49,plain,
% 0.16/0.38 (![U: $i, V: $i] : (~pair_in_list(create_slb, U, V))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.16/0.38 tff(50,plain,
% 0.16/0.38 ((~![U: $i, V: $i] : (~pair_in_list(create_slb, U, V))) | (~pair_in_list(create_slb, tptp_fun_X_1(V!5), tptp_fun_Y_0(V!5)))),
% 0.16/0.38 inference(quant_inst,[status(thm)],[])).
% 0.16/0.38 tff(51,plain,
% 0.16/0.38 (~pair_in_list(create_slb, tptp_fun_X_1(V!5), tptp_fun_Y_0(V!5))),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.16/0.38 tff(52,plain,
% 0.16/0.38 ($false),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[51, 42])).
% 0.16/0.38 tff(53,plain,(~(V!5 = create_slb)), inference(lemma,lemma(discharge,[]))).
% 0.16/0.38 tff(54,plain,
% 0.16/0.38 (^[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))))),
% 0.16/0.38 inference(bind,[status(th)],[])).
% 0.16/0.38 tff(55,plain,
% 0.16/0.38 (![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)))),
% 0.16/0.38 inference(quant_intro,[status(thm)],[54])).
% 0.16/0.38 tff(56,plain,
% 0.16/0.38 (![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)))),
% 0.16/0.38 inference(rewrite,[status(thm)],[])).
% 0.16/0.38 tff(57,plain,
% 0.16/0.38 (![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)))),
% 0.16/0.38 inference(elim_unused_vars,[status(thm)],[])).
% 0.16/0.38 tff(58,plain,
% 0.16/0.38 (^[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))))),
% 0.16/0.38 inference(bind,[status(th)],[])).
% 0.16/0.38 tff(59,plain,
% 0.16/0.38 (![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)))),
% 0.16/0.38 inference(quant_intro,[status(thm)],[58])).
% 0.16/0.38 tff(60,plain,
% 0.16/0.38 (![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)))),
% 0.16/0.38 inference(transitivity,[status(thm)],[59, 57])).
% 0.16/0.38 tff(61,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')).
% 0.16/0.38 tff(62,plain,
% 0.16/0.38 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.16/0.38 tff(63,plain,
% 0.16/0.38 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[62, 56])).
% 0.16/0.38 tff(64,plain,(
% 0.16/0.38 ![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.16/0.38 inference(skolemize,[status(sab)],[63])).
% 0.16/0.38 tff(65,plain,
% 0.16/0.38 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[64, 55])).
% 0.16/0.38 tff(66,plain,
% 0.16/0.38 (((~![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)))),
% 0.16/0.38 inference(rewrite,[status(thm)],[])).
% 0.16/0.38 tff(67,plain,
% 0.16/0.38 ((~![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)))),
% 0.16/0.38 inference(quant_inst,[status(thm)],[])).
% 0.16/0.38 tff(68,plain,
% 0.16/0.38 ((~![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))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.16/0.38 tff(69,plain,
% 0.16/0.38 ((V!5 = create_slb) | (findmin_cpq_res(triple(U!6, V!5, W!4)) = findmin_pqp_res(U!6))),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[68, 65])).
% 0.16/0.38 tff(70,plain,
% 0.16/0.38 (findmin_cpq_res(triple(U!6, V!5, W!4)) = findmin_pqp_res(U!6)),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[69, 53])).
% 0.16/0.38 tff(71,plain,
% 0.16/0.38 (update_slb(V!5, findmin_cpq_res(triple(U!6, V!5, W!4))) = update_slb(V!5, findmin_pqp_res(U!6))),
% 0.16/0.38 inference(monotonicity,[status(thm)],[70])).
% 0.16/0.38 tff(72,plain,
% 0.16/0.38 (update_slb(V!5, findmin_pqp_res(U!6)) = update_slb(V!5, findmin_cpq_res(triple(U!6, V!5, W!4)))),
% 0.16/0.38 inference(symmetry,[status(thm)],[71])).
% 0.16/0.38 tff(73,plain,
% 0.16/0.38 (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))),
% 0.16/0.38 inference(monotonicity,[status(thm)],[72])).
% 0.16/0.38 tff(74,plain,
% 0.16/0.38 (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))),
% 0.16/0.38 inference(symmetry,[status(thm)],[73])).
% 0.16/0.38 tff(75,plain,
% 0.16/0.38 (^[U: $i, V: $i] : refl((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)))))),
% 0.16/0.38 inference(bind,[status(th)],[])).
% 0.16/0.38 tff(76,plain,
% 0.16/0.38 (![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))))),
% 0.16/0.38 inference(quant_intro,[status(thm)],[75])).
% 0.16/0.38 tff(77,plain,
% 0.16/0.38 (^[U: $i, V: $i] : rewrite((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)))))),
% 0.16/0.38 inference(bind,[status(th)],[])).
% 0.16/0.38 tff(78,plain,
% 0.16/0.38 (![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))))),
% 0.16/0.38 inference(quant_intro,[status(thm)],[77])).
% 0.16/0.38 tff(79,plain,
% 0.16/0.38 (![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))))),
% 0.16/0.38 inference(rewrite,[status(thm)],[])).
% 0.16/0.38 tff(80,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')).
% 0.16/0.38 tff(81,plain,
% 0.16/0.38 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.16/0.38 tff(82,plain,(
% 0.16/0.38 ![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.16/0.38 inference(skolemize,[status(sab)],[81])).
% 0.16/0.38 tff(83,plain,
% 0.16/0.38 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U))))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.16/0.38 tff(84,plain,
% 0.16/0.38 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U))))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[83, 76])).
% 0.16/0.38 tff(85,plain,
% 0.16/0.38 ((~![U: $i, V: $i] : (strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U))))) | (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)))))),
% 0.16/0.38 inference(quant_inst,[status(thm)],[])).
% 0.16/0.38 tff(86,plain,
% 0.16/0.38 (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))))),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.16/0.38 tff(87,plain,
% 0.16/0.38 (((~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)))),
% 0.16/0.39 inference(tautology,[status(thm)],[])).
% 0.16/0.39 tff(88,plain,
% 0.16/0.39 (~less_than(tptp_fun_Y_0(V!5), tptp_fun_X_1(V!5))),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[87, 39])).
% 0.16/0.39 tff(89,plain,
% 0.16/0.39 (^[U: $i, V: $i] : refl((less_than(V, U) | less_than(U, V)) <=> (less_than(V, U) | less_than(U, V)))),
% 0.16/0.39 inference(bind,[status(th)],[])).
% 0.16/0.39 tff(90,plain,
% 0.16/0.39 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.16/0.39 inference(quant_intro,[status(thm)],[89])).
% 0.16/0.39 tff(91,plain,
% 0.16/0.39 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(92,plain,
% 0.16/0.39 (^[U: $i, V: $i] : rewrite((less_than(U, V) | less_than(V, U)) <=> (less_than(V, U) | less_than(U, V)))),
% 0.16/0.39 inference(bind,[status(th)],[])).
% 0.16/0.39 tff(93,plain,
% 0.16/0.39 (![U: $i, V: $i] : (less_than(U, V) | less_than(V, U)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.16/0.39 inference(quant_intro,[status(thm)],[92])).
% 0.16/0.39 tff(94,axiom,(![U: $i, V: $i] : (less_than(U, V) | less_than(V, U))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax','totality')).
% 0.16/0.39 tff(95,plain,
% 0.16/0.39 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.16/0.39 tff(96,plain,
% 0.16/0.39 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.16/0.39 tff(97,plain,(
% 0.16/0.39 ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.16/0.39 inference(skolemize,[status(sab)],[96])).
% 0.16/0.39 tff(98,plain,
% 0.16/0.39 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[97, 90])).
% 0.16/0.39 tff(99,plain,
% 0.16/0.39 (((~![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)))),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(100,plain,
% 0.16/0.39 ((~![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)))),
% 0.16/0.39 inference(quant_inst,[status(thm)],[])).
% 0.16/0.39 tff(101,plain,
% 0.16/0.39 ((~![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))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.16/0.39 tff(102,plain,
% 0.16/0.39 (less_than(tptp_fun_X_1(V!5), tptp_fun_Y_0(V!5))),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[101, 98, 88])).
% 0.16/0.39 tff(103,plain,
% 0.16/0.39 ((~((~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))),
% 0.16/0.39 inference(tautology,[status(thm)],[])).
% 0.16/0.39 tff(104,plain,
% 0.16/0.39 ((~((~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)))),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[103, 88])).
% 0.16/0.39 tff(105,plain,
% 0.16/0.39 (~((~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)))),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[104, 102])).
% 0.16/0.39 tff(106,plain,
% 0.16/0.39 ((~(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)) | ((~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)))),
% 0.16/0.39 inference(tautology,[status(thm)],[])).
% 0.16/0.39 tff(107,plain,
% 0.16/0.39 (strictly_less_than(tptp_fun_X_1(V!5), tptp_fun_Y_0(V!5))),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[106, 105, 86])).
% 0.16/0.39 tff(108,plain,
% 0.16/0.39 (^[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))))))))),
% 0.16/0.39 inference(bind,[status(th)],[])).
% 0.16/0.39 tff(109,plain,
% 0.16/0.39 (![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))))))),
% 0.16/0.39 inference(quant_intro,[status(thm)],[108])).
% 0.16/0.39 tff(110,plain,
% 0.16/0.39 (^[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)))))))),
% 0.16/0.39 inference(bind,[status(th)],[])).
% 0.16/0.39 tff(111,plain,
% 0.16/0.39 (![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))))))),
% 0.16/0.39 inference(quant_intro,[status(thm)],[110])).
% 0.16/0.39 tff(112,plain,
% 0.16/0.39 (![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))))))),
% 0.16/0.39 inference(pull_quant,[status(thm)],[])).
% 0.16/0.39 tff(113,plain,
% 0.16/0.39 (^[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)))))))),
% 0.16/0.39 inference(bind,[status(th)],[])).
% 0.16/0.39 tff(114,plain,
% 0.16/0.39 (![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))))))),
% 0.16/0.39 inference(quant_intro,[status(thm)],[113])).
% 0.16/0.39 tff(115,plain,
% 0.16/0.39 (![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))))))),
% 0.16/0.39 inference(transitivity,[status(thm)],[114, 112])).
% 0.16/0.39 tff(116,plain,
% 0.16/0.39 (![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))))))),
% 0.16/0.39 inference(transitivity,[status(thm)],[115, 111])).
% 0.16/0.39 tff(117,plain,
% 0.16/0.39 (^[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)))))))),
% 0.16/0.39 inference(bind,[status(th)],[])).
% 0.16/0.39 tff(118,plain,
% 0.16/0.39 (![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))))))),
% 0.16/0.39 inference(quant_intro,[status(thm)],[117])).
% 0.16/0.39 tff(119,plain,
% 0.16/0.39 (![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))))))),
% 0.16/0.39 inference(transitivity,[status(thm)],[118, 116])).
% 0.16/0.39 tff(120,plain,
% 0.16/0.39 (^[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))))))))),
% 0.17/0.39 inference(bind,[status(th)],[])).
% 0.17/0.39 tff(121,plain,
% 0.17/0.39 (![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))))))),
% 0.17/0.39 inference(quant_intro,[status(thm)],[120])).
% 0.17/0.39 tff(122,plain,
% 0.17/0.39 (![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)))),
% 0.17/0.39 inference(rewrite,[status(thm)],[])).
% 0.17/0.39 tff(123,plain,
% 0.17/0.39 (^[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))))),
% 0.17/0.39 inference(bind,[status(th)],[])).
% 0.17/0.39 tff(124,plain,
% 0.17/0.39 (![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)))),
% 0.17/0.39 inference(quant_intro,[status(thm)],[123])).
% 0.17/0.39 tff(125,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')).
% 0.17/0.39 tff(126,plain,
% 0.17/0.39 (![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)))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.17/0.39 tff(127,plain,
% 0.17/0.39 (![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)))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[126, 122])).
% 0.17/0.39 tff(128,plain,(
% 0.17/0.39 ![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))))),
% 0.17/0.39 inference(skolemize,[status(sab)],[127])).
% 0.17/0.39 tff(129,plain,
% 0.17/0.39 (![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))))))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[128, 121])).
% 0.17/0.39 tff(130,plain,
% 0.17/0.39 (![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))))))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[129, 119])).
% 0.17/0.39 tff(131,plain,
% 0.17/0.39 (![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))))))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[130, 109])).
% 0.17/0.39 tff(132,plain,
% 0.17/0.39 (((~![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))))))),
% 0.17/0.39 inference(rewrite,[status(thm)],[])).
% 0.17/0.39 tff(133,plain,
% 0.17/0.39 ((~![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))))))),
% 0.17/0.40 inference(quant_inst,[status(thm)],[])).
% 0.17/0.40 tff(134,plain,
% 0.17/0.40 ((~![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)))))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.17/0.40 tff(135,plain,
% 0.17/0.40 (~((~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))) | (~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))))),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[134, 131, 41, 107])).
% 0.17/0.40 tff(136,plain,
% 0.17/0.40 (((~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))) | (~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))),
% 0.17/0.40 inference(tautology,[status(thm)],[])).
% 0.17/0.40 tff(137,plain,
% 0.17/0.40 (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))),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[136, 135])).
% 0.17/0.40 tff(138,plain,
% 0.17/0.40 (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))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[137, 74])).
% 0.17/0.40 tff(139,plain,
% 0.17/0.40 ((~![U: $i, V: $i] : (strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U))))) | (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)))))),
% 0.17/0.40 inference(quant_inst,[status(thm)],[])).
% 0.17/0.40 tff(140,plain,
% 0.17/0.40 (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))))),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[139, 84])).
% 0.17/0.40 tff(141,plain,
% 0.17/0.40 (((~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))) | (~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))),
% 0.17/0.40 inference(tautology,[status(thm)],[])).
% 0.17/0.40 tff(142,plain,
% 0.17/0.40 (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))),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[141, 135])).
% 0.17/0.40 tff(143,plain,
% 0.17/0.40 ((~(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))) | (~((~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))))),
% 0.17/0.40 inference(tautology,[status(thm)],[])).
% 0.17/0.40 tff(144,plain,
% 0.17/0.40 ((~(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)))))) | (~((~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))))),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[143, 142])).
% 0.17/0.40 tff(145,plain,
% 0.17/0.40 (~((~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)))),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[144, 140])).
% 0.17/0.40 tff(146,plain,
% 0.17/0.40 (((~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)))),
% 0.17/0.40 inference(tautology,[status(thm)],[])).
% 0.17/0.40 tff(147,plain,
% 0.17/0.40 (~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))),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[146, 145])).
% 0.17/0.40 tff(148,plain,
% 0.17/0.40 ((~![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, 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))))))))))),
% 0.17/0.40 inference(quant_inst,[status(thm)],[])).
% 0.17/0.40 tff(149,plain,
% 0.17/0.40 (~((~((~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)))))))))),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[148, 20])).
% 0.17/0.40 tff(150,plain,
% 0.17/0.40 (((~((~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)))),
% 0.17/0.40 inference(tautology,[status(thm)],[])).
% 0.17/0.40 tff(151,plain,
% 0.17/0.40 ((~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))),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[150, 149])).
% 0.17/0.40 tff(152,plain,
% 0.17/0.40 (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))),
% 0.17/0.40 inference(monotonicity,[status(thm)],[70])).
% 0.17/0.40 tff(153,assumption,(~less_than(lookup_slb(V!5, findmin_pqp_res(U!6)), findmin_cpq_res(triple(U!6, V!5, W!4)))), introduced(assumption)).
% 0.17/0.40 tff(154,plain,
% 0.17/0.40 (((~![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))))),
% 0.17/0.40 inference(rewrite,[status(thm)],[])).
% 0.17/0.40 tff(155,plain,
% 0.17/0.40 ((~![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))))),
% 0.17/0.40 inference(quant_inst,[status(thm)],[])).
% 0.17/0.40 tff(156,plain,
% 0.17/0.40 ((~![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)))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.17/0.40 tff(157,plain,
% 0.17/0.40 (less_than(findmin_cpq_res(triple(U!6, V!5, W!4)), lookup_slb(V!5, findmin_pqp_res(U!6)))),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[156, 98, 153])).
% 0.17/0.40 tff(158,plain,
% 0.17/0.40 ((~![U: $i, V: $i] : (strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U))))) | (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))))))),
% 0.17/0.40 inference(quant_inst,[status(thm)],[])).
% 0.17/0.40 tff(159,plain,
% 0.17/0.40 (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)))))),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[158, 84])).
% 0.17/0.40 tff(160,plain,
% 0.17/0.40 (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)))),
% 0.17/0.40 inference(monotonicity,[status(thm)],[70])).
% 0.17/0.40 tff(161,plain,
% 0.17/0.41 (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)))),
% 0.17/0.41 inference(symmetry,[status(thm)],[160])).
% 0.17/0.41 tff(162,plain,
% 0.17/0.41 ((~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))))),
% 0.17/0.41 inference(monotonicity,[status(thm)],[161])).
% 0.17/0.41 tff(163,plain,
% 0.17/0.41 ((~![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))))))))))),
% 0.17/0.41 inference(quant_inst,[status(thm)],[])).
% 0.17/0.41 tff(164,plain,
% 0.17/0.41 (~((~((~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)))))))))),
% 0.17/0.41 inference(unit_resolution,[status(thm)],[163, 20])).
% 0.17/0.41 tff(165,plain,
% 0.17/0.41 (((~((~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)))),
% 0.17/0.41 inference(tautology,[status(thm)],[])).
% 0.17/0.41 tff(166,plain,
% 0.17/0.41 ((~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))),
% 0.17/0.41 inference(unit_resolution,[status(thm)],[165, 164])).
% 0.17/0.41 tff(167,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)).
% 0.17/0.41 tff(168,plain,
% 0.17/0.41 (triple(U!6, update_slb(V!5, findmin_pqp_res(U!6)), bad) = findmin_cpq_eff(triple(U!6, V!5, W!4))),
% 0.17/0.41 inference(symmetry,[status(thm)],[167])).
% 0.17/0.41 tff(169,plain,
% 0.17/0.41 (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)))),
% 0.17/0.41 inference(monotonicity,[status(thm)],[168])).
% 0.17/0.41 tff(170,plain,
% 0.17/0.41 (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))),
% 0.17/0.41 inference(symmetry,[status(thm)],[169])).
% 0.17/0.41 tff(171,plain,
% 0.17/0.41 (check_cpq(findmin_cpq_eff(triple(U!6, V!5, W!4)))),
% 0.17/0.41 inference(or_elim,[status(thm)],[35])).
% 0.17/0.41 tff(172,plain,
% 0.17/0.41 (check_cpq(triple(U!6, update_slb(V!5, findmin_pqp_res(U!6)), bad))),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.17/0.41 tff(173,plain,
% 0.17/0.41 ((~((~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))),
% 0.17/0.41 inference(tautology,[status(thm)],[])).
% 0.17/0.41 tff(174,plain,
% 0.17/0.41 (![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!5, findmin_pqp_res(U!6)), X, Y)) | less_than(Y, X))),
% 0.17/0.41 inference(unit_resolution,[status(thm)],[173, 172, 166])).
% 0.17/0.41 tff(175,plain,
% 0.17/0.41 (((~![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)))),
% 0.17/0.41 inference(rewrite,[status(thm)],[])).
% 0.17/0.41 tff(176,plain,
% 0.17/0.41 ((~![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)))),
% 0.17/0.41 inference(quant_inst,[status(thm)],[])).
% 0.17/0.41 tff(177,plain,
% 0.17/0.41 ((~![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!5, findmin_pqp_res(U!6)), X, Y)) | less_than(Y, X))) | (~pair_in_list(update_slb(V!5, findmin_pqp_res(U!6)), tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5))) | less_than(tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5))),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.17/0.41 tff(178,plain,
% 0.17/0.41 (~pair_in_list(update_slb(V!5, findmin_pqp_res(U!6)), tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5))),
% 0.17/0.41 inference(unit_resolution,[status(thm)],[177, 174, 147])).
% 0.17/0.41 tff(179,plain,
% 0.17/0.41 ($false),
% 0.17/0.41 inference(unit_resolution,[status(thm)],[178, 138])).
% 0.17/0.41 tff(180,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,[]))).
% 0.17/0.41 tff(181,assumption,(strictly_less_than(findmin_pqp_res(U!6), lookup_slb(V!5, findmin_pqp_res(U!6)))), introduced(assumption)).
% 0.17/0.41 tff(182,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)).
% 0.17/0.41 tff(183,plain,
% 0.17/0.41 (^[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))))),
% 0.17/0.41 inference(bind,[status(th)],[])).
% 0.17/0.41 tff(184,plain,
% 0.17/0.41 (![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)))),
% 0.17/0.41 inference(quant_intro,[status(thm)],[183])).
% 0.17/0.41 tff(185,plain,
% 0.17/0.41 (^[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)))))),
% 0.17/0.41 inference(bind,[status(th)],[])).
% 0.17/0.41 tff(186,plain,
% 0.17/0.41 (![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)))),
% 0.17/0.41 inference(quant_intro,[status(thm)],[185])).
% 0.17/0.41 tff(187,plain,
% 0.17/0.41 (![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)))),
% 0.17/0.41 inference(rewrite,[status(thm)],[])).
% 0.17/0.41 tff(188,plain,
% 0.17/0.41 (![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)))),
% 0.17/0.41 inference(elim_unused_vars,[status(thm)],[])).
% 0.17/0.41 tff(189,plain,
% 0.17/0.41 (^[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))))),
% 0.17/0.41 inference(bind,[status(th)],[])).
% 0.17/0.41 tff(190,plain,
% 0.17/0.41 (![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)))),
% 0.17/0.41 inference(quant_intro,[status(thm)],[189])).
% 0.17/0.41 tff(191,plain,
% 0.17/0.41 (![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)))),
% 0.17/0.41 inference(transitivity,[status(thm)],[190, 188])).
% 0.17/0.41 tff(192,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')).
% 0.17/0.41 tff(193,plain,
% 0.17/0.41 (![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)))),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.17/0.41 tff(194,plain,
% 0.17/0.41 (![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)))),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[193, 187])).
% 0.17/0.41 tff(195,plain,(
% 0.17/0.41 ![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)))),
% 0.17/0.41 inference(skolemize,[status(sab)],[194])).
% 0.17/0.41 tff(196,plain,
% 0.17/0.41 (![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)))),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[195, 186])).
% 0.17/0.41 tff(197,plain,
% 0.17/0.41 (![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)))),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[196, 184])).
% 0.17/0.41 tff(198,plain,
% 0.17/0.41 (((~![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)))),
% 0.17/0.41 inference(rewrite,[status(thm)],[])).
% 0.17/0.41 tff(199,plain,
% 0.17/0.41 ((~![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)))),
% 0.17/0.41 inference(quant_inst,[status(thm)],[])).
% 0.17/0.41 tff(200,plain,
% 0.17/0.41 ((~![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))),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.17/0.41 tff(201,plain,
% 0.17/0.41 ((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))),
% 0.17/0.41 inference(unit_resolution,[status(thm)],[200, 197])).
% 0.17/0.41 tff(202,plain,
% 0.17/0.41 (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))),
% 0.17/0.41 inference(unit_resolution,[status(thm)],[201, 53])).
% 0.17/0.41 tff(203,plain,
% 0.17/0.41 (contains_slb(V!5, findmin_pqp_res(U!6))),
% 0.17/0.41 inference(unit_resolution,[status(thm)],[202, 182])).
% 0.17/0.41 tff(204,plain,
% 0.17/0.41 (^[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))))))),
% 0.17/0.42 inference(bind,[status(th)],[])).
% 0.17/0.42 tff(205,plain,
% 0.17/0.42 (![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)))))),
% 0.17/0.42 inference(quant_intro,[status(thm)],[204])).
% 0.17/0.42 tff(206,plain,
% 0.17/0.42 (^[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)))))))),
% 0.17/0.42 inference(bind,[status(th)],[])).
% 0.17/0.42 tff(207,plain,
% 0.17/0.42 (![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)))))),
% 0.17/0.42 inference(quant_intro,[status(thm)],[206])).
% 0.17/0.42 tff(208,plain,
% 0.17/0.42 (![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)))),
% 0.17/0.42 inference(rewrite,[status(thm)],[])).
% 0.17/0.42 tff(209,plain,
% 0.17/0.42 (![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)))),
% 0.17/0.42 inference(elim_unused_vars,[status(thm)],[])).
% 0.17/0.42 tff(210,plain,
% 0.17/0.42 (^[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)))))),
% 0.17/0.42 inference(bind,[status(th)],[])).
% 0.17/0.42 tff(211,plain,
% 0.17/0.42 (![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, 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)))),
% 0.17/0.42 inference(quant_intro,[status(thm)],[210])).
% 0.17/0.42 tff(212,plain,
% 0.17/0.42 (![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)))),
% 0.17/0.42 inference(transitivity,[status(thm)],[211, 209])).
% 0.17/0.42 tff(213,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')).
% 0.17/0.42 tff(214,plain,
% 0.17/0.42 (![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)))),
% 0.17/0.42 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.17/0.42 tff(215,plain,
% 0.17/0.42 (![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)))),
% 0.17/0.42 inference(modus_ponens,[status(thm)],[214, 208])).
% 0.17/0.42 tff(216,plain,(
% 0.17/0.42 ![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)))),
% 0.17/0.42 inference(skolemize,[status(sab)],[215])).
% 0.17/0.42 tff(217,plain,
% 0.17/0.42 (![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)))))),
% 0.17/0.42 inference(modus_ponens,[status(thm)],[216, 207])).
% 0.17/0.42 tff(218,plain,
% 0.17/0.42 (![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)))))),
% 0.17/0.42 inference(modus_ponens,[status(thm)],[217, 205])).
% 0.17/0.42 tff(219,plain,
% 0.17/0.42 (((~![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)))))) | ((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)))))),
% 0.17/0.42 inference(rewrite,[status(thm)],[])).
% 0.17/0.42 tff(220,plain,
% 0.17/0.42 ((~![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)))))) | ((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)))))),
% 0.17/0.42 inference(quant_inst,[status(thm)],[])).
% 0.17/0.42 tff(221,plain,
% 0.17/0.42 ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))))) | (V!5 = create_slb) | (~contains_slb(V!5, findmin_pqp_res(U!6))) | (findmin_cpq_eff(triple(U!6, V!5, W!4)) = triple(U!6, update_slb(V!5, findmin_pqp_res(U!6)), bad)) | (~strictly_less_than(findmin_pqp_res(U!6), lookup_slb(V!5, findmin_pqp_res(U!6))))),
% 0.17/0.42 inference(modus_ponens,[status(thm)],[220, 219])).
% 0.17/0.42 tff(222,plain,
% 0.17/0.42 ((V!5 = create_slb) | (~contains_slb(V!5, findmin_pqp_res(U!6))) | (findmin_cpq_eff(triple(U!6, V!5, W!4)) = triple(U!6, update_slb(V!5, findmin_pqp_res(U!6)), bad)) | (~strictly_less_than(findmin_pqp_res(U!6), lookup_slb(V!5, findmin_pqp_res(U!6))))),
% 0.17/0.42 inference(unit_resolution,[status(thm)],[221, 218])).
% 0.17/0.42 tff(223,plain,
% 0.17/0.42 ((~contains_slb(V!5, findmin_pqp_res(U!6))) | (findmin_cpq_eff(triple(U!6, V!5, W!4)) = triple(U!6, update_slb(V!5, findmin_pqp_res(U!6)), bad)) | (~strictly_less_than(findmin_pqp_res(U!6), lookup_slb(V!5, findmin_pqp_res(U!6))))),
% 0.17/0.42 inference(unit_resolution,[status(thm)],[222, 53])).
% 0.17/0.42 tff(224,plain,
% 0.17/0.42 ($false),
% 0.17/0.42 inference(unit_resolution,[status(thm)],[223, 203, 182, 181])).
% 0.17/0.42 tff(225,plain,((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,[]))).
% 0.17/0.42 tff(226,plain,
% 0.17/0.42 (~strictly_less_than(findmin_pqp_res(U!6), lookup_slb(V!5, findmin_pqp_res(U!6)))),
% 0.17/0.42 inference(unit_resolution,[status(thm)],[225, 180])).
% 0.17/0.42 tff(227,plain,
% 0.17/0.42 (~strictly_less_than(findmin_cpq_res(triple(U!6, V!5, W!4)), lookup_slb(V!5, findmin_pqp_res(U!6)))),
% 0.17/0.42 inference(modus_ponens,[status(thm)],[226, 162])).
% 0.17/0.42 tff(228,plain,
% 0.17/0.42 ((~(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))) | ((~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))))),
% 0.17/0.42 inference(tautology,[status(thm)],[])).
% 0.17/0.42 tff(229,plain,
% 0.17/0.42 ((~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)))),
% 0.17/0.42 inference(unit_resolution,[status(thm)],[228, 227, 159])).
% 0.17/0.42 tff(230,plain,
% 0.17/0.42 ((~((~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)))),
% 0.17/0.42 inference(tautology,[status(thm)],[])).
% 0.17/0.42 tff(231,plain,
% 0.17/0.42 ((~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)))),
% 0.17/0.42 inference(unit_resolution,[status(thm)],[230, 229])).
% 0.17/0.42 tff(232,plain,
% 0.17/0.42 ($false),
% 0.17/0.42 inference(unit_resolution,[status(thm)],[231, 157, 153])).
% 0.17/0.42 tff(233,plain,(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,[]))).
% 0.17/0.42 tff(234,plain,
% 0.17/0.42 (less_than(lookup_slb(V!5, findmin_pqp_res(U!6)), findmin_pqp_res(U!6))),
% 0.17/0.42 inference(modus_ponens,[status(thm)],[233, 152])).
% 0.17/0.42 tff(235,plain,
% 0.17/0.42 (contains_slb(V!5, findmin_pqp_res(U!6))),
% 0.17/0.42 inference(unit_resolution,[status(thm)],[202, 180])).
% 0.17/0.42 tff(236,plain,
% 0.17/0.42 (^[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)), 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)))))),
% 0.17/0.42 inference(bind,[status(th)],[])).
% 0.17/0.42 tff(237,plain,
% 0.17/0.42 (![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)), 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))))),
% 0.17/0.42 inference(quant_intro,[status(thm)],[236])).
% 0.17/0.42 tff(238,plain,
% 0.17/0.42 (^[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))))))),
% 0.17/0.42 inference(bind,[status(th)],[])).
% 0.17/0.42 tff(239,plain,
% 0.17/0.42 (![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))))),
% 0.17/0.42 inference(quant_intro,[status(thm)],[238])).
% 0.17/0.42 tff(240,plain,
% 0.17/0.42 (![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)))),
% 0.17/0.43 inference(rewrite,[status(thm)],[])).
% 0.17/0.43 tff(241,plain,
% 0.17/0.43 (![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)))),
% 0.17/0.43 inference(elim_unused_vars,[status(thm)],[])).
% 0.17/0.43 tff(242,plain,
% 0.17/0.43 (^[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)))))),
% 0.17/0.43 inference(bind,[status(th)],[])).
% 0.17/0.43 tff(243,plain,
% 0.17/0.43 (![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)))),
% 0.17/0.43 inference(quant_intro,[status(thm)],[242])).
% 0.17/0.43 tff(244,plain,
% 0.17/0.43 (![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)))),
% 0.17/0.43 inference(transitivity,[status(thm)],[243, 241])).
% 0.17/0.43 tff(245,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')).
% 0.17/0.43 tff(246,plain,
% 0.17/0.43 (![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)))),
% 0.17/0.43 inference(modus_ponens,[status(thm)],[245, 244])).
% 0.17/0.43 tff(247,plain,
% 0.17/0.43 (![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)))),
% 0.17/0.43 inference(modus_ponens,[status(thm)],[246, 240])).
% 0.17/0.43 tff(248,plain,(
% 0.17/0.43 ![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)))),
% 0.17/0.43 inference(skolemize,[status(sab)],[247])).
% 0.17/0.43 tff(249,plain,
% 0.17/0.43 (![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)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))),
% 0.17/0.43 inference(modus_ponens,[status(thm)],[248, 239])).
% 0.17/0.43 tff(250,plain,
% 0.17/0.43 (![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)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))),
% 0.17/0.43 inference(modus_ponens,[status(thm)],[249, 237])).
% 0.17/0.43 tff(251,plain,
% 0.17/0.43 (((~![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)), 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))))),
% 0.17/0.43 inference(rewrite,[status(thm)],[])).
% 0.17/0.43 tff(252,plain,
% 0.17/0.43 ((~![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)), 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))))),
% 0.17/0.43 inference(quant_inst,[status(thm)],[])).
% 0.17/0.43 tff(253,plain,
% 0.17/0.43 ((~![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)), 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)))),
% 0.17/0.43 inference(modus_ponens,[status(thm)],[252, 251])).
% 0.17/0.43 tff(254,plain,
% 0.17/0.43 ((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)), W!4)) | (~less_than(lookup_slb(V!5, findmin_pqp_res(U!6)), findmin_pqp_res(U!6)))),
% 0.17/0.43 inference(unit_resolution,[status(thm)],[253, 250])).
% 0.17/0.43 tff(255,plain,
% 0.17/0.43 ((~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)))),
% 0.17/0.43 inference(unit_resolution,[status(thm)],[254, 53])).
% 0.17/0.43 tff(256,plain,
% 0.17/0.43 ((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)))),
% 0.17/0.43 inference(unit_resolution,[status(thm)],[255, 235])).
% 0.17/0.43 tff(257,plain,
% 0.17/0.43 (findmin_cpq_eff(triple(U!6, V!5, W!4)) = triple(U!6, update_slb(V!5, findmin_pqp_res(U!6)), W!4)),
% 0.17/0.43 inference(unit_resolution,[status(thm)],[256, 234])).
% 0.17/0.43 tff(258,plain,
% 0.17/0.43 (triple(U!6, update_slb(V!5, findmin_pqp_res(U!6)), W!4) = findmin_cpq_eff(triple(U!6, V!5, W!4))),
% 0.17/0.43 inference(symmetry,[status(thm)],[257])).
% 0.17/0.43 tff(259,plain,
% 0.17/0.43 (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)))),
% 0.17/0.43 inference(monotonicity,[status(thm)],[258])).
% 0.17/0.43 tff(260,plain,
% 0.17/0.43 (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))),
% 0.17/0.43 inference(symmetry,[status(thm)],[259])).
% 0.17/0.43 tff(261,plain,
% 0.17/0.43 (check_cpq(triple(U!6, update_slb(V!5, findmin_pqp_res(U!6)), W!4))),
% 0.17/0.43 inference(modus_ponens,[status(thm)],[171, 260])).
% 0.17/0.43 tff(262,plain,
% 0.17/0.43 ((~((~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))),
% 0.17/0.43 inference(tautology,[status(thm)],[])).
% 0.17/0.43 tff(263,plain,
% 0.17/0.43 (![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!5, findmin_pqp_res(U!6)), X, Y)) | less_than(Y, X))),
% 0.17/0.43 inference(unit_resolution,[status(thm)],[262, 261, 151])).
% 0.17/0.43 tff(264,plain,
% 0.17/0.43 (~pair_in_list(update_slb(V!5, findmin_pqp_res(U!6)), tptp_fun_Y_3(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5), tptp_fun_Z_2(findmin_cpq_res(triple(U!6, V!5, W!4)), V!5))),
% 0.17/0.43 inference(unit_resolution,[status(thm)],[177, 263, 147])).
% 0.17/0.43 tff(265,plain,
% 0.17/0.43 ($false),
% 0.17/0.43 inference(unit_resolution,[status(thm)],[264, 138])).
% 0.17/0.43 % SZS output end Proof
%------------------------------------------------------------------------------