TSTP Solution File: SWV408+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV408+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.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 15:11:40 EDT 2022
% Result : Theorem 0.21s 0.42s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SWV408+1 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n027.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Sep 4 03:08:51 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.36 Usage: tptp [options] [-file:]file
% 0.14/0.36 -h, -? prints this message.
% 0.14/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.36 -m, -model generate model.
% 0.14/0.36 -p, -proof generate proof.
% 0.14/0.36 -c, -core generate unsat core of named formulas.
% 0.14/0.36 -st, -statistics display statistics.
% 0.14/0.36 -t:timeout set timeout (in second).
% 0.14/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.36 -<param>:<value> configuration parameter and value.
% 0.14/0.36 -o:<output-file> file to place output in.
% 0.21/0.42 % SZS status Theorem
% 0.21/0.42 % SZS output start Proof
% 0.21/0.42 tff(contains_slb_type, type, (
% 0.21/0.42 contains_slb: ( $i * $i ) > $o)).
% 0.21/0.42 tff(tptp_fun_X_1_type, type, (
% 0.21/0.42 tptp_fun_X_1: $i)).
% 0.21/0.42 tff(create_slb_type, type, (
% 0.21/0.42 create_slb: $i)).
% 0.21/0.42 tff(tptp_fun_V_3_type, type, (
% 0.21/0.42 tptp_fun_V_3: $i)).
% 0.21/0.42 tff(findmin_pqp_res_type, type, (
% 0.21/0.42 findmin_pqp_res: $i > $i)).
% 0.21/0.42 tff(tptp_fun_U_4_type, type, (
% 0.21/0.42 tptp_fun_U_4: $i)).
% 0.21/0.42 tff(findmin_cpq_res_type, type, (
% 0.21/0.42 findmin_cpq_res: $i > $i)).
% 0.21/0.42 tff(triple_type, type, (
% 0.21/0.42 triple: ( $i * $i * $i ) > $i)).
% 0.21/0.42 tff(tptp_fun_W_2_type, type, (
% 0.21/0.42 tptp_fun_W_2: $i)).
% 0.21/0.42 tff(strictly_less_than_type, type, (
% 0.21/0.42 strictly_less_than: ( $i * $i ) > $o)).
% 0.21/0.42 tff(pair_in_list_type, type, (
% 0.21/0.42 pair_in_list: ( $i * $i * $i ) > $o)).
% 0.21/0.42 tff(update_slb_type, type, (
% 0.21/0.42 update_slb: ( $i * $i ) > $i)).
% 0.21/0.42 tff(less_than_type, type, (
% 0.21/0.42 less_than: ( $i * $i ) > $o)).
% 0.21/0.42 tff(tptp_fun_X_0_type, type, (
% 0.21/0.42 tptp_fun_X_0: ( $i * $i * $i ) > $i)).
% 0.21/0.42 tff(1,assumption,(findmin_cpq_res(triple(U!4, V!3, W!2)) = findmin_pqp_res(U!4)), introduced(assumption)).
% 0.21/0.42 tff(2,plain,
% 0.21/0.42 (findmin_pqp_res(U!4) = findmin_cpq_res(triple(U!4, V!3, W!2))),
% 0.21/0.42 inference(symmetry,[status(thm)],[1])).
% 0.21/0.42 tff(3,plain,
% 0.21/0.42 (strictly_less_than(X!1, findmin_pqp_res(U!4)) <=> strictly_less_than(X!1, findmin_cpq_res(triple(U!4, V!3, W!2)))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[2])).
% 0.21/0.42 tff(4,plain,
% 0.21/0.42 (strictly_less_than(X!1, findmin_cpq_res(triple(U!4, V!3, W!2))) <=> strictly_less_than(X!1, findmin_pqp_res(U!4))),
% 0.21/0.42 inference(symmetry,[status(thm)],[3])).
% 0.21/0.42 tff(5,plain,
% 0.21/0.42 ((![Y: $i] : (~(pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, Y) & less_than(findmin_pqp_res(U!4), Y))) & (~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, findmin_pqp_res(U!4))) & (contains_slb(V!3, X!1) & strictly_less_than(X!1, findmin_cpq_res(triple(U!4, V!3, W!2))))) <=> (![Y: $i] : (~(pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, Y) & less_than(findmin_pqp_res(U!4), Y))) & (~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, findmin_pqp_res(U!4))) & contains_slb(V!3, X!1) & strictly_less_than(X!1, findmin_cpq_res(triple(U!4, V!3, W!2))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(6,plain,
% 0.21/0.42 ((~(~(contains_slb(V!3, X!1) & strictly_less_than(X!1, findmin_cpq_res(triple(U!4, V!3, W!2)))))) <=> (contains_slb(V!3, X!1) & strictly_less_than(X!1, findmin_cpq_res(triple(U!4, V!3, W!2))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(7,plain,
% 0.21/0.42 ((![Y: $i] : (~(pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, Y) & less_than(findmin_pqp_res(U!4), Y))) & (~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, findmin_pqp_res(U!4))) & (~(~(contains_slb(V!3, X!1) & strictly_less_than(X!1, findmin_cpq_res(triple(U!4, V!3, W!2))))))) <=> (![Y: $i] : (~(pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, Y) & less_than(findmin_pqp_res(U!4), Y))) & (~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, findmin_pqp_res(U!4))) & (contains_slb(V!3, X!1) & strictly_less_than(X!1, findmin_cpq_res(triple(U!4, V!3, W!2)))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[6])).
% 0.21/0.42 tff(8,plain,
% 0.21/0.42 ((![Y: $i] : (~(pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, Y) & less_than(findmin_pqp_res(U!4), Y))) & (~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, findmin_pqp_res(U!4))) & (~(~(contains_slb(V!3, X!1) & strictly_less_than(X!1, findmin_cpq_res(triple(U!4, V!3, W!2))))))) <=> (![Y: $i] : (~(pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, Y) & less_than(findmin_pqp_res(U!4), Y))) & (~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, findmin_pqp_res(U!4))) & contains_slb(V!3, X!1) & strictly_less_than(X!1, findmin_cpq_res(triple(U!4, V!3, W!2))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[7, 5])).
% 0.21/0.42 tff(9,plain,
% 0.21/0.42 ((~![U: $i, V: $i, W: $i, X: $i] : (?[Y: $i] : (pair_in_list(update_slb(V, findmin_pqp_res(U)), X, Y) & less_than(findmin_pqp_res(U), Y)) | pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~(contains_slb(V, X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))))) <=> (~![U: $i, V: $i, W: $i, X: $i] : (?[Y: $i] : (pair_in_list(update_slb(V, findmin_pqp_res(U)), X, Y) & less_than(findmin_pqp_res(U), Y)) | pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~(contains_slb(V, X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(10,plain,
% 0.21/0.42 ((~![U: $i, V: $i, W: $i, X: $i] : ((contains_slb(V, X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))) => (pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | ?[Y: $i] : (pair_in_list(update_slb(V, findmin_pqp_res(U)), X, Y) & less_than(findmin_pqp_res(U), Y))))) <=> (~![U: $i, V: $i, W: $i, X: $i] : (?[Y: $i] : (pair_in_list(update_slb(V, findmin_pqp_res(U)), X, Y) & less_than(findmin_pqp_res(U), Y)) | pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~(contains_slb(V, X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(11,axiom,(~![U: $i, V: $i, W: $i, X: $i] : ((contains_slb(V, X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))) => (pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | ?[Y: $i] : (pair_in_list(update_slb(V, findmin_pqp_res(U)), X, Y) & less_than(findmin_pqp_res(U), Y))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l44_co')).
% 0.21/0.42 tff(12,plain,
% 0.21/0.42 (~![U: $i, V: $i, W: $i, X: $i] : (?[Y: $i] : (pair_in_list(update_slb(V, findmin_pqp_res(U)), X, Y) & less_than(findmin_pqp_res(U), Y)) | pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~(contains_slb(V, X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.21/0.42 tff(13,plain,
% 0.21/0.42 (~![U: $i, V: $i, W: $i, X: $i] : (?[Y: $i] : (pair_in_list(update_slb(V, findmin_pqp_res(U)), X, Y) & less_than(findmin_pqp_res(U), Y)) | pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~(contains_slb(V, X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[12, 9])).
% 0.21/0.42 tff(14,plain,
% 0.21/0.42 (~![U: $i, V: $i, W: $i, X: $i] : (?[Y: $i] : (pair_in_list(update_slb(V, findmin_pqp_res(U)), X, Y) & less_than(findmin_pqp_res(U), Y)) | pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~(contains_slb(V, X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[13, 9])).
% 0.21/0.42 tff(15,plain,
% 0.21/0.42 (~![U: $i, V: $i, W: $i, X: $i] : (?[Y: $i] : (pair_in_list(update_slb(V, findmin_pqp_res(U)), X, Y) & less_than(findmin_pqp_res(U), Y)) | pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~(contains_slb(V, X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[14, 9])).
% 0.21/0.42 tff(16,plain,
% 0.21/0.42 (~![U: $i, V: $i, W: $i, X: $i] : (?[Y: $i] : (pair_in_list(update_slb(V, findmin_pqp_res(U)), X, Y) & less_than(findmin_pqp_res(U), Y)) | pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~(contains_slb(V, X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[15, 9])).
% 0.21/0.42 tff(17,plain,
% 0.21/0.42 (~![U: $i, V: $i, W: $i, X: $i] : (?[Y: $i] : (pair_in_list(update_slb(V, findmin_pqp_res(U)), X, Y) & less_than(findmin_pqp_res(U), Y)) | pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~(contains_slb(V, X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[16, 9])).
% 0.21/0.42 tff(18,plain,
% 0.21/0.42 (~![U: $i, V: $i, W: $i, X: $i] : (?[Y: $i] : (pair_in_list(update_slb(V, findmin_pqp_res(U)), X, Y) & less_than(findmin_pqp_res(U), Y)) | pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~(contains_slb(V, X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[17, 9])).
% 0.21/0.42 tff(19,plain,
% 0.21/0.42 (![Y: $i] : (~(pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, Y) & less_than(findmin_pqp_res(U!4), Y))) & (~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, findmin_pqp_res(U!4))) & contains_slb(V!3, X!1) & strictly_less_than(X!1, findmin_cpq_res(triple(U!4, V!3, W!2)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[18, 8])).
% 0.21/0.42 tff(20,plain,
% 0.21/0.42 (strictly_less_than(X!1, findmin_cpq_res(triple(U!4, V!3, W!2)))),
% 0.21/0.42 inference(and_elim,[status(thm)],[19])).
% 0.21/0.42 tff(21,plain,
% 0.21/0.42 (strictly_less_than(X!1, findmin_pqp_res(U!4))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[20, 4])).
% 0.21/0.42 tff(22,assumption,(~((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, tptp_fun_X_0(findmin_pqp_res(U!4), X!1, V!3))) | (~less_than(findmin_pqp_res(U!4), tptp_fun_X_0(findmin_pqp_res(U!4), X!1, V!3))))), introduced(assumption)).
% 0.21/0.42 tff(23,plain,
% 0.21/0.42 (((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, tptp_fun_X_0(findmin_pqp_res(U!4), X!1, V!3))) | (~less_than(findmin_pqp_res(U!4), tptp_fun_X_0(findmin_pqp_res(U!4), X!1, V!3)))) | less_than(findmin_pqp_res(U!4), tptp_fun_X_0(findmin_pqp_res(U!4), X!1, V!3))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(24,plain,
% 0.21/0.42 (less_than(findmin_pqp_res(U!4), tptp_fun_X_0(findmin_pqp_res(U!4), X!1, V!3))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.21/0.42 tff(25,plain,
% 0.21/0.42 (((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, tptp_fun_X_0(findmin_pqp_res(U!4), X!1, V!3))) | (~less_than(findmin_pqp_res(U!4), tptp_fun_X_0(findmin_pqp_res(U!4), X!1, V!3)))) | pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, tptp_fun_X_0(findmin_pqp_res(U!4), X!1, V!3))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(26,plain,
% 0.21/0.42 (pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, tptp_fun_X_0(findmin_pqp_res(U!4), X!1, V!3))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[25, 22])).
% 0.21/0.42 tff(27,plain,
% 0.21/0.42 (^[Y: $i] : refl(((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, Y)) | (~less_than(findmin_pqp_res(U!4), Y))) <=> ((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, Y)) | (~less_than(findmin_pqp_res(U!4), Y))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(28,plain,
% 0.21/0.42 (![Y: $i] : ((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, Y)) | (~less_than(findmin_pqp_res(U!4), Y))) <=> ![Y: $i] : ((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, Y)) | (~less_than(findmin_pqp_res(U!4), Y)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[27])).
% 0.21/0.42 tff(29,plain,
% 0.21/0.42 (^[Y: $i] : trans(monotonicity(rewrite((pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, Y) & less_than(findmin_pqp_res(U!4), Y)) <=> (~((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, Y)) | (~less_than(findmin_pqp_res(U!4), Y))))), ((~(pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, Y) & less_than(findmin_pqp_res(U!4), Y))) <=> (~(~((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, Y)) | (~less_than(findmin_pqp_res(U!4), Y))))))), rewrite((~(~((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, Y)) | (~less_than(findmin_pqp_res(U!4), Y))))) <=> ((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, Y)) | (~less_than(findmin_pqp_res(U!4), Y)))), ((~(pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, Y) & less_than(findmin_pqp_res(U!4), Y))) <=> ((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, Y)) | (~less_than(findmin_pqp_res(U!4), Y)))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(30,plain,
% 0.21/0.42 (![Y: $i] : (~(pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, Y) & less_than(findmin_pqp_res(U!4), Y))) <=> ![Y: $i] : ((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, Y)) | (~less_than(findmin_pqp_res(U!4), Y)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[29])).
% 0.21/0.42 tff(31,plain,
% 0.21/0.42 (![Y: $i] : (~(pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, Y) & less_than(findmin_pqp_res(U!4), Y)))),
% 0.21/0.42 inference(and_elim,[status(thm)],[19])).
% 0.21/0.42 tff(32,plain,
% 0.21/0.42 (![Y: $i] : ((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, Y)) | (~less_than(findmin_pqp_res(U!4), Y)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.21/0.42 tff(33,plain,
% 0.21/0.42 (![Y: $i] : ((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, Y)) | (~less_than(findmin_pqp_res(U!4), Y)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.21/0.43 tff(34,plain,
% 0.21/0.43 (((~![Y: $i] : ((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, Y)) | (~less_than(findmin_pqp_res(U!4), Y)))) | ((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, tptp_fun_X_0(findmin_pqp_res(U!4), X!1, V!3))) | (~less_than(findmin_pqp_res(U!4), tptp_fun_X_0(findmin_pqp_res(U!4), X!1, V!3))))) <=> ((~![Y: $i] : ((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, Y)) | (~less_than(findmin_pqp_res(U!4), Y)))) | (~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, tptp_fun_X_0(findmin_pqp_res(U!4), X!1, V!3))) | (~less_than(findmin_pqp_res(U!4), tptp_fun_X_0(findmin_pqp_res(U!4), X!1, V!3))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(35,plain,
% 0.21/0.43 ((~![Y: $i] : ((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, Y)) | (~less_than(findmin_pqp_res(U!4), Y)))) | ((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, tptp_fun_X_0(findmin_pqp_res(U!4), X!1, V!3))) | (~less_than(findmin_pqp_res(U!4), tptp_fun_X_0(findmin_pqp_res(U!4), X!1, V!3))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(36,plain,
% 0.21/0.43 ((~![Y: $i] : ((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, Y)) | (~less_than(findmin_pqp_res(U!4), Y)))) | (~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, tptp_fun_X_0(findmin_pqp_res(U!4), X!1, V!3))) | (~less_than(findmin_pqp_res(U!4), tptp_fun_X_0(findmin_pqp_res(U!4), X!1, V!3)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.21/0.43 tff(37,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[36, 33, 26, 24])).
% 0.21/0.43 tff(38,plain,((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, tptp_fun_X_0(findmin_pqp_res(U!4), X!1, V!3))) | (~less_than(findmin_pqp_res(U!4), tptp_fun_X_0(findmin_pqp_res(U!4), X!1, V!3)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(39,plain,
% 0.21/0.43 (contains_slb(V!3, X!1)),
% 0.21/0.43 inference(and_elim,[status(thm)],[19])).
% 0.21/0.43 tff(40,plain,
% 0.21/0.43 (~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, findmin_pqp_res(U!4))),
% 0.21/0.43 inference(and_elim,[status(thm)],[19])).
% 0.21/0.43 tff(41,plain,
% 0.21/0.43 (^[U: $i, V: $i, W: $i] : refl((pair_in_list(update_slb(U, W), V, W) | (~strictly_less_than(V, W)) | (~contains_slb(U, V)) | (~((~pair_in_list(update_slb(U, W), V, tptp_fun_X_0(W, V, U))) | (~less_than(W, tptp_fun_X_0(W, V, U)))))) <=> (pair_in_list(update_slb(U, W), V, W) | (~strictly_less_than(V, W)) | (~contains_slb(U, V)) | (~((~pair_in_list(update_slb(U, W), V, tptp_fun_X_0(W, V, U))) | (~less_than(W, tptp_fun_X_0(W, V, U)))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(42,plain,
% 0.21/0.43 (![U: $i, V: $i, W: $i] : (pair_in_list(update_slb(U, W), V, W) | (~strictly_less_than(V, W)) | (~contains_slb(U, V)) | (~((~pair_in_list(update_slb(U, W), V, tptp_fun_X_0(W, V, U))) | (~less_than(W, tptp_fun_X_0(W, V, U)))))) <=> ![U: $i, V: $i, W: $i] : (pair_in_list(update_slb(U, W), V, W) | (~strictly_less_than(V, W)) | (~contains_slb(U, V)) | (~((~pair_in_list(update_slb(U, W), V, tptp_fun_X_0(W, V, U))) | (~less_than(W, tptp_fun_X_0(W, V, U))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[41])).
% 0.21/0.43 tff(43,plain,
% 0.21/0.43 (^[U: $i, V: $i, W: $i] : trans(monotonicity(trans(monotonicity(rewrite((contains_slb(U, V) & strictly_less_than(V, W)) <=> (~((~contains_slb(U, V)) | (~strictly_less_than(V, W))))), ((~(contains_slb(U, V) & strictly_less_than(V, W))) <=> (~(~((~contains_slb(U, V)) | (~strictly_less_than(V, W))))))), rewrite((~(~((~contains_slb(U, V)) | (~strictly_less_than(V, W))))) <=> ((~contains_slb(U, V)) | (~strictly_less_than(V, W)))), ((~(contains_slb(U, V) & strictly_less_than(V, W))) <=> ((~contains_slb(U, V)) | (~strictly_less_than(V, W))))), rewrite((pair_in_list(update_slb(U, W), V, tptp_fun_X_0(W, V, U)) & less_than(W, tptp_fun_X_0(W, V, U))) <=> (~((~pair_in_list(update_slb(U, W), V, tptp_fun_X_0(W, V, U))) | (~less_than(W, tptp_fun_X_0(W, V, U)))))), ((pair_in_list(update_slb(U, W), V, W) | (~(contains_slb(U, V) & strictly_less_than(V, W))) | (pair_in_list(update_slb(U, W), V, tptp_fun_X_0(W, V, U)) & less_than(W, tptp_fun_X_0(W, V, U)))) <=> (pair_in_list(update_slb(U, W), V, W) | ((~contains_slb(U, V)) | (~strictly_less_than(V, W))) | (~((~pair_in_list(update_slb(U, W), V, tptp_fun_X_0(W, V, U))) | (~less_than(W, tptp_fun_X_0(W, V, U)))))))), rewrite((pair_in_list(update_slb(U, W), V, W) | ((~contains_slb(U, V)) | (~strictly_less_than(V, W))) | (~((~pair_in_list(update_slb(U, W), V, tptp_fun_X_0(W, V, U))) | (~less_than(W, tptp_fun_X_0(W, V, U)))))) <=> (pair_in_list(update_slb(U, W), V, W) | (~strictly_less_than(V, W)) | (~contains_slb(U, V)) | (~((~pair_in_list(update_slb(U, W), V, tptp_fun_X_0(W, V, U))) | (~less_than(W, tptp_fun_X_0(W, V, U))))))), ((pair_in_list(update_slb(U, W), V, W) | (~(contains_slb(U, V) & strictly_less_than(V, W))) | (pair_in_list(update_slb(U, W), V, tptp_fun_X_0(W, V, U)) & less_than(W, tptp_fun_X_0(W, V, U)))) <=> (pair_in_list(update_slb(U, W), V, W) | (~strictly_less_than(V, W)) | (~contains_slb(U, V)) | (~((~pair_in_list(update_slb(U, W), V, tptp_fun_X_0(W, V, U))) | (~less_than(W, tptp_fun_X_0(W, V, U))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(44,plain,
% 0.21/0.43 (![U: $i, V: $i, W: $i] : (pair_in_list(update_slb(U, W), V, W) | (~(contains_slb(U, V) & strictly_less_than(V, W))) | (pair_in_list(update_slb(U, W), V, tptp_fun_X_0(W, V, U)) & less_than(W, tptp_fun_X_0(W, V, U)))) <=> ![U: $i, V: $i, W: $i] : (pair_in_list(update_slb(U, W), V, W) | (~strictly_less_than(V, W)) | (~contains_slb(U, V)) | (~((~pair_in_list(update_slb(U, W), V, tptp_fun_X_0(W, V, U))) | (~less_than(W, tptp_fun_X_0(W, V, U))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[43])).
% 0.21/0.43 tff(45,plain,
% 0.21/0.43 (^[U: $i, V: $i, W: $i] : rewrite(((pair_in_list(update_slb(U, W), V, tptp_fun_X_0(W, V, U)) & less_than(W, tptp_fun_X_0(W, V, U))) | pair_in_list(update_slb(U, W), V, W) | (~(contains_slb(U, V) & strictly_less_than(V, W)))) <=> (pair_in_list(update_slb(U, W), V, W) | (~(contains_slb(U, V) & strictly_less_than(V, W))) | (pair_in_list(update_slb(U, W), V, tptp_fun_X_0(W, V, U)) & less_than(W, tptp_fun_X_0(W, V, U)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(46,plain,
% 0.21/0.43 (![U: $i, V: $i, W: $i] : ((pair_in_list(update_slb(U, W), V, tptp_fun_X_0(W, V, U)) & less_than(W, tptp_fun_X_0(W, V, U))) | pair_in_list(update_slb(U, W), V, W) | (~(contains_slb(U, V) & strictly_less_than(V, W)))) <=> ![U: $i, V: $i, W: $i] : (pair_in_list(update_slb(U, W), V, W) | (~(contains_slb(U, V) & strictly_less_than(V, W))) | (pair_in_list(update_slb(U, W), V, tptp_fun_X_0(W, V, U)) & less_than(W, tptp_fun_X_0(W, V, U))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[45])).
% 0.21/0.43 tff(47,plain,
% 0.21/0.43 (![U: $i, V: $i, W: $i] : (?[X: $i] : (pair_in_list(update_slb(U, W), V, X) & less_than(W, X)) | pair_in_list(update_slb(U, W), V, W) | (~(contains_slb(U, V) & strictly_less_than(V, W)))) <=> ![U: $i, V: $i, W: $i] : (?[X: $i] : (pair_in_list(update_slb(U, W), V, X) & less_than(W, X)) | pair_in_list(update_slb(U, W), V, W) | (~(contains_slb(U, V) & strictly_less_than(V, W))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(48,plain,
% 0.21/0.43 (^[U: $i, V: $i, W: $i] : trans(monotonicity(rewrite((pair_in_list(update_slb(U, W), V, W) | ?[X: $i] : (pair_in_list(update_slb(U, W), V, X) & less_than(W, X))) <=> (pair_in_list(update_slb(U, W), V, W) | ?[X: $i] : (pair_in_list(update_slb(U, W), V, X) & less_than(W, X)))), (((contains_slb(U, V) & strictly_less_than(V, W)) => (pair_in_list(update_slb(U, W), V, W) | ?[X: $i] : (pair_in_list(update_slb(U, W), V, X) & less_than(W, X)))) <=> ((contains_slb(U, V) & strictly_less_than(V, W)) => (pair_in_list(update_slb(U, W), V, W) | ?[X: $i] : (pair_in_list(update_slb(U, W), V, X) & less_than(W, X)))))), rewrite(((contains_slb(U, V) & strictly_less_than(V, W)) => (pair_in_list(update_slb(U, W), V, W) | ?[X: $i] : (pair_in_list(update_slb(U, W), V, X) & less_than(W, X)))) <=> (?[X: $i] : (pair_in_list(update_slb(U, W), V, X) & less_than(W, X)) | pair_in_list(update_slb(U, W), V, W) | (~(contains_slb(U, V) & strictly_less_than(V, W))))), (((contains_slb(U, V) & strictly_less_than(V, W)) => (pair_in_list(update_slb(U, W), V, W) | ?[X: $i] : (pair_in_list(update_slb(U, W), V, X) & less_than(W, X)))) <=> (?[X: $i] : (pair_in_list(update_slb(U, W), V, X) & less_than(W, X)) | pair_in_list(update_slb(U, W), V, W) | (~(contains_slb(U, V) & strictly_less_than(V, W))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(49,plain,
% 0.21/0.43 (![U: $i, V: $i, W: $i] : ((contains_slb(U, V) & strictly_less_than(V, W)) => (pair_in_list(update_slb(U, W), V, W) | ?[X: $i] : (pair_in_list(update_slb(U, W), V, X) & less_than(W, X)))) <=> ![U: $i, V: $i, W: $i] : (?[X: $i] : (pair_in_list(update_slb(U, W), V, X) & less_than(W, X)) | pair_in_list(update_slb(U, W), V, W) | (~(contains_slb(U, V) & strictly_less_than(V, W))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[48])).
% 0.21/0.43 tff(50,axiom,(![U: $i, V: $i, W: $i] : ((contains_slb(U, V) & strictly_less_than(V, W)) => (pair_in_list(update_slb(U, W), V, W) | ?[X: $i] : (pair_in_list(update_slb(U, W), V, X) & less_than(W, X))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l44_l45')).
% 0.21/0.43 tff(51,plain,
% 0.21/0.43 (![U: $i, V: $i, W: $i] : (?[X: $i] : (pair_in_list(update_slb(U, W), V, X) & less_than(W, X)) | pair_in_list(update_slb(U, W), V, W) | (~(contains_slb(U, V) & strictly_less_than(V, W))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.21/0.43 tff(52,plain,
% 0.21/0.43 (![U: $i, V: $i, W: $i] : (?[X: $i] : (pair_in_list(update_slb(U, W), V, X) & less_than(W, X)) | pair_in_list(update_slb(U, W), V, W) | (~(contains_slb(U, V) & strictly_less_than(V, W))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.21/0.43 tff(53,plain,(
% 0.21/0.43 ![U: $i, V: $i, W: $i] : ((pair_in_list(update_slb(U, W), V, tptp_fun_X_0(W, V, U)) & less_than(W, tptp_fun_X_0(W, V, U))) | pair_in_list(update_slb(U, W), V, W) | (~(contains_slb(U, V) & strictly_less_than(V, W))))),
% 0.21/0.43 inference(skolemize,[status(sab)],[52])).
% 0.21/0.43 tff(54,plain,
% 0.21/0.43 (![U: $i, V: $i, W: $i] : (pair_in_list(update_slb(U, W), V, W) | (~(contains_slb(U, V) & strictly_less_than(V, W))) | (pair_in_list(update_slb(U, W), V, tptp_fun_X_0(W, V, U)) & less_than(W, tptp_fun_X_0(W, V, U))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[53, 46])).
% 0.21/0.43 tff(55,plain,
% 0.21/0.43 (![U: $i, V: $i, W: $i] : (pair_in_list(update_slb(U, W), V, W) | (~strictly_less_than(V, W)) | (~contains_slb(U, V)) | (~((~pair_in_list(update_slb(U, W), V, tptp_fun_X_0(W, V, U))) | (~less_than(W, tptp_fun_X_0(W, V, U))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[54, 44])).
% 0.21/0.43 tff(56,plain,
% 0.21/0.43 (![U: $i, V: $i, W: $i] : (pair_in_list(update_slb(U, W), V, W) | (~strictly_less_than(V, W)) | (~contains_slb(U, V)) | (~((~pair_in_list(update_slb(U, W), V, tptp_fun_X_0(W, V, U))) | (~less_than(W, tptp_fun_X_0(W, V, U))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[55, 42])).
% 0.21/0.43 tff(57,plain,
% 0.21/0.43 (((~![U: $i, V: $i, W: $i] : (pair_in_list(update_slb(U, W), V, W) | (~strictly_less_than(V, W)) | (~contains_slb(U, V)) | (~((~pair_in_list(update_slb(U, W), V, tptp_fun_X_0(W, V, U))) | (~less_than(W, tptp_fun_X_0(W, V, U))))))) | (pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, findmin_pqp_res(U!4)) | (~strictly_less_than(X!1, findmin_pqp_res(U!4))) | (~contains_slb(V!3, X!1)) | (~((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, tptp_fun_X_0(findmin_pqp_res(U!4), X!1, V!3))) | (~less_than(findmin_pqp_res(U!4), tptp_fun_X_0(findmin_pqp_res(U!4), X!1, V!3))))))) <=> ((~![U: $i, V: $i, W: $i] : (pair_in_list(update_slb(U, W), V, W) | (~strictly_less_than(V, W)) | (~contains_slb(U, V)) | (~((~pair_in_list(update_slb(U, W), V, tptp_fun_X_0(W, V, U))) | (~less_than(W, tptp_fun_X_0(W, V, U))))))) | pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, findmin_pqp_res(U!4)) | (~strictly_less_than(X!1, findmin_pqp_res(U!4))) | (~contains_slb(V!3, X!1)) | (~((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, tptp_fun_X_0(findmin_pqp_res(U!4), X!1, V!3))) | (~less_than(findmin_pqp_res(U!4), tptp_fun_X_0(findmin_pqp_res(U!4), X!1, V!3))))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(58,plain,
% 0.21/0.43 ((~![U: $i, V: $i, W: $i] : (pair_in_list(update_slb(U, W), V, W) | (~strictly_less_than(V, W)) | (~contains_slb(U, V)) | (~((~pair_in_list(update_slb(U, W), V, tptp_fun_X_0(W, V, U))) | (~less_than(W, tptp_fun_X_0(W, V, U))))))) | (pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, findmin_pqp_res(U!4)) | (~strictly_less_than(X!1, findmin_pqp_res(U!4))) | (~contains_slb(V!3, X!1)) | (~((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, tptp_fun_X_0(findmin_pqp_res(U!4), X!1, V!3))) | (~less_than(findmin_pqp_res(U!4), tptp_fun_X_0(findmin_pqp_res(U!4), X!1, V!3))))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(59,plain,
% 0.21/0.43 ((~![U: $i, V: $i, W: $i] : (pair_in_list(update_slb(U, W), V, W) | (~strictly_less_than(V, W)) | (~contains_slb(U, V)) | (~((~pair_in_list(update_slb(U, W), V, tptp_fun_X_0(W, V, U))) | (~less_than(W, tptp_fun_X_0(W, V, U))))))) | pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, findmin_pqp_res(U!4)) | (~strictly_less_than(X!1, findmin_pqp_res(U!4))) | (~contains_slb(V!3, X!1)) | (~((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, tptp_fun_X_0(findmin_pqp_res(U!4), X!1, V!3))) | (~less_than(findmin_pqp_res(U!4), tptp_fun_X_0(findmin_pqp_res(U!4), X!1, V!3)))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.21/0.43 tff(60,plain,
% 0.21/0.43 ((~strictly_less_than(X!1, findmin_pqp_res(U!4))) | (~((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, tptp_fun_X_0(findmin_pqp_res(U!4), X!1, V!3))) | (~less_than(findmin_pqp_res(U!4), tptp_fun_X_0(findmin_pqp_res(U!4), X!1, V!3)))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[59, 56, 40, 39])).
% 0.21/0.43 tff(61,plain,
% 0.21/0.43 (~strictly_less_than(X!1, findmin_pqp_res(U!4))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[60, 38])).
% 0.21/0.43 tff(62,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[61, 21])).
% 0.21/0.43 tff(63,plain,(~(findmin_cpq_res(triple(U!4, V!3, W!2)) = findmin_pqp_res(U!4))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(64,plain,
% 0.21/0.43 (^[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))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(65,plain,
% 0.21/0.43 (![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)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[64])).
% 0.21/0.43 tff(66,plain,
% 0.21/0.43 (![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)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(67,plain,
% 0.21/0.43 (![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)))),
% 0.21/0.43 inference(elim_unused_vars,[status(thm)],[])).
% 0.21/0.43 tff(68,plain,
% 0.21/0.43 (^[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))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(69,plain,
% 0.21/0.43 (![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)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[68])).
% 0.21/0.43 tff(70,plain,
% 0.21/0.43 (![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)))),
% 0.21/0.43 inference(transitivity,[status(thm)],[69, 67])).
% 0.21/0.43 tff(71,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')).
% 0.21/0.43 tff(72,plain,
% 0.21/0.43 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.21/0.43 tff(73,plain,
% 0.21/0.43 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[72, 66])).
% 0.21/0.44 tff(74,plain,(
% 0.21/0.44 ![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.21/0.44 inference(skolemize,[status(sab)],[73])).
% 0.21/0.44 tff(75,plain,
% 0.21/0.44 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[74, 65])).
% 0.21/0.44 tff(76,plain,
% 0.21/0.44 (((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))) | ((V!3 = create_slb) | (findmin_cpq_res(triple(U!4, V!3, W!2)) = findmin_pqp_res(U!4)))) <=> ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))) | (V!3 = create_slb) | (findmin_cpq_res(triple(U!4, V!3, W!2)) = findmin_pqp_res(U!4)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(77,plain,
% 0.21/0.44 ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))) | ((V!3 = create_slb) | (findmin_cpq_res(triple(U!4, V!3, W!2)) = findmin_pqp_res(U!4)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(78,plain,
% 0.21/0.44 ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))) | (V!3 = create_slb) | (findmin_cpq_res(triple(U!4, V!3, W!2)) = findmin_pqp_res(U!4))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.21/0.44 tff(79,plain,
% 0.21/0.44 ((V!3 = create_slb) | (findmin_cpq_res(triple(U!4, V!3, W!2)) = findmin_pqp_res(U!4))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[78, 75])).
% 0.21/0.44 tff(80,plain,
% 0.21/0.44 (V!3 = create_slb),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[79, 63])).
% 0.21/0.44 tff(81,plain,
% 0.21/0.44 (create_slb = V!3),
% 0.21/0.44 inference(symmetry,[status(thm)],[80])).
% 0.21/0.44 tff(82,plain,
% 0.21/0.44 (contains_slb(create_slb, X!1) <=> contains_slb(V!3, X!1)),
% 0.21/0.44 inference(monotonicity,[status(thm)],[81])).
% 0.21/0.44 tff(83,plain,
% 0.21/0.44 (contains_slb(V!3, X!1) <=> contains_slb(create_slb, X!1)),
% 0.21/0.44 inference(symmetry,[status(thm)],[82])).
% 0.21/0.44 tff(84,plain,
% 0.21/0.44 (contains_slb(create_slb, X!1)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[39, 83])).
% 0.21/0.44 tff(85,plain,
% 0.21/0.44 (^[U: $i] : refl((~contains_slb(create_slb, U)) <=> (~contains_slb(create_slb, U)))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(86,plain,
% 0.21/0.44 (![U: $i] : (~contains_slb(create_slb, U)) <=> ![U: $i] : (~contains_slb(create_slb, U))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[85])).
% 0.21/0.44 tff(87,plain,
% 0.21/0.44 (![U: $i] : (~contains_slb(create_slb, U)) <=> ![U: $i] : (~contains_slb(create_slb, U))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(88,axiom,(![U: $i] : (~contains_slb(create_slb, U))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+2.ax','ax20')).
% 0.21/0.44 tff(89,plain,
% 0.21/0.44 (![U: $i] : (~contains_slb(create_slb, U))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.21/0.44 tff(90,plain,(
% 0.21/0.44 ![U: $i] : (~contains_slb(create_slb, U))),
% 0.21/0.44 inference(skolemize,[status(sab)],[89])).
% 0.21/0.44 tff(91,plain,
% 0.21/0.44 (![U: $i] : (~contains_slb(create_slb, U))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[90, 86])).
% 0.21/0.44 tff(92,plain,
% 0.21/0.44 ((~![U: $i] : (~contains_slb(create_slb, U))) | (~contains_slb(create_slb, X!1))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(93,plain,
% 0.21/0.44 (~contains_slb(create_slb, X!1)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.21/0.44 tff(94,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[93, 84])).
% 0.21/0.44 % SZS output end Proof
%------------------------------------------------------------------------------