TSTP Solution File: SWV408+2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV408+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.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
% 0.03/0.13 % Problem : SWV408+2 : TPTP v8.1.0. Released v3.3.0.
% 0.14/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n007.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
% 0.14/0.36 % DateTime : Sun Sep 4 02:39:04 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.21/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.21/0.36 Usage: tptp [options] [-file:]file
% 0.21/0.36 -h, -? prints this message.
% 0.21/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.21/0.36 -m, -model generate model.
% 0.21/0.36 -p, -proof generate proof.
% 0.21/0.36 -c, -core generate unsat core of named formulas.
% 0.21/0.36 -st, -statistics display statistics.
% 0.21/0.36 -t:timeout set timeout (in second).
% 0.21/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.21/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.21/0.36 -<param>:<value> configuration parameter and value.
% 0.21/0.36 -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(pair_in_list_type, type, (
% 0.21/0.42 pair_in_list: ( $i * $i * $i ) > $o)).
% 0.21/0.42 tff(tptp_fun_W_0_type, type, (
% 0.21/0.42 tptp_fun_W_0: ( $i * $i ) > $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(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(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(less_than_type, type, (
% 0.21/0.42 less_than: ( $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(strictly_less_than_type, type, (
% 0.21/0.42 strictly_less_than: ( $i * $i ) > $o)).
% 0.21/0.42 tff(contains_slb_type, type, (
% 0.21/0.42 contains_slb: ( $i * $i ) > $o)).
% 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 (less_than(tptp_fun_W_0(X!1, V!3), findmin_cpq_res(triple(U!4, V!3, W!2))) <=> less_than(tptp_fun_W_0(X!1, V!3), findmin_pqp_res(U!4))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[1])).
% 0.21/0.42 tff(3,plain,
% 0.21/0.42 (less_than(tptp_fun_W_0(X!1, V!3), findmin_pqp_res(U!4)) <=> less_than(tptp_fun_W_0(X!1, V!3), findmin_cpq_res(triple(U!4, V!3, W!2)))),
% 0.21/0.42 inference(symmetry,[status(thm)],[2])).
% 0.21/0.42 tff(4,plain,
% 0.21/0.42 ((~less_than(tptp_fun_W_0(X!1, V!3), findmin_pqp_res(U!4))) <=> (~less_than(tptp_fun_W_0(X!1, V!3), findmin_cpq_res(triple(U!4, V!3, W!2))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[3])).
% 0.21/0.42 tff(5,plain,
% 0.21/0.42 (less_than(findmin_cpq_res(triple(U!4, V!3, W!2)), tptp_fun_W_0(X!1, V!3)) <=> less_than(findmin_pqp_res(U!4), tptp_fun_W_0(X!1, V!3))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[1])).
% 0.21/0.42 tff(6,plain,
% 0.21/0.42 ((~less_than(findmin_cpq_res(triple(U!4, V!3, W!2)), tptp_fun_W_0(X!1, V!3))) <=> (~less_than(findmin_pqp_res(U!4), tptp_fun_W_0(X!1, V!3)))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[5])).
% 0.21/0.42 tff(7,plain,
% 0.21/0.42 (update_slb(V!3, findmin_cpq_res(triple(U!4, V!3, W!2))) = update_slb(V!3, findmin_pqp_res(U!4))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[1])).
% 0.21/0.42 tff(8,plain,
% 0.21/0.42 (pair_in_list(update_slb(V!3, findmin_cpq_res(triple(U!4, V!3, W!2))), X!1, tptp_fun_W_0(X!1, V!3)) <=> pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, tptp_fun_W_0(X!1, V!3))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[7])).
% 0.21/0.42 tff(9,plain,
% 0.21/0.42 (pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, tptp_fun_W_0(X!1, V!3)) <=> pair_in_list(update_slb(V!3, findmin_cpq_res(triple(U!4, V!3, W!2))), X!1, tptp_fun_W_0(X!1, V!3))),
% 0.21/0.42 inference(symmetry,[status(thm)],[8])).
% 0.21/0.42 tff(10,plain,
% 0.21/0.42 ((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, tptp_fun_W_0(X!1, V!3))) <=> (~pair_in_list(update_slb(V!3, findmin_cpq_res(triple(U!4, V!3, W!2))), X!1, tptp_fun_W_0(X!1, V!3)))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[9])).
% 0.21/0.42 tff(11,assumption,(less_than(findmin_cpq_res(triple(U!4, V!3, W!2)), tptp_fun_W_0(X!1, V!3))), introduced(assumption)).
% 0.21/0.42 tff(12,plain,
% 0.21/0.42 (less_than(findmin_pqp_res(U!4), tptp_fun_W_0(X!1, V!3))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[11, 5])).
% 0.21/0.42 tff(13,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(14,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)],[13])).
% 0.21/0.42 tff(15,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)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(16,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))) <=> ![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)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[15])).
% 0.21/0.43 tff(17,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, 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))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(18,plain,
% 0.21/0.43 ((~(~(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))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(19,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, 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)))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[18])).
% 0.21/0.43 tff(20,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, 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))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[19, 17])).
% 0.21/0.43 tff(21,plain,
% 0.21/0.43 ((~![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)))))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(22,plain,
% 0.21/0.43 ((~![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)))))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(23,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/sandbox2/benchmark/theBenchmark.p','l44_co')).
% 0.21/0.43 tff(24,plain,
% 0.21/0.43 (~![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))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.21/0.43 tff(25,plain,
% 0.21/0.43 (~![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))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.21/0.43 tff(26,plain,
% 0.21/0.43 (~![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))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.21/0.43 tff(27,plain,
% 0.21/0.43 (~![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))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[26, 21])).
% 0.21/0.43 tff(28,plain,
% 0.21/0.43 (~![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))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[27, 21])).
% 0.21/0.43 tff(29,plain,
% 0.21/0.43 (~![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))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.21/0.43 tff(30,plain,
% 0.21/0.43 (~![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))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[29, 21])).
% 0.21/0.43 tff(31,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, 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)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[30, 20])).
% 0.21/0.43 tff(32,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)))),
% 0.21/0.43 inference(and_elim,[status(thm)],[31])).
% 0.21/0.43 tff(33,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)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[32, 16])).
% 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)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[33, 14])).
% 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)))) | ((~less_than(findmin_pqp_res(U!4), tptp_fun_W_0(X!1, V!3))) | (~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, tptp_fun_W_0(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)))) | (~less_than(findmin_pqp_res(U!4), tptp_fun_W_0(X!1, V!3))) | (~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, tptp_fun_W_0(X!1, V!3))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(36,plain,
% 0.21/0.43 (((~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, tptp_fun_W_0(X!1, V!3))) | (~less_than(findmin_pqp_res(U!4), tptp_fun_W_0(X!1, V!3)))) <=> ((~less_than(findmin_pqp_res(U!4), tptp_fun_W_0(X!1, V!3))) | (~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, tptp_fun_W_0(X!1, V!3))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(37,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_W_0(X!1, V!3))) | (~less_than(findmin_pqp_res(U!4), tptp_fun_W_0(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)))) | ((~less_than(findmin_pqp_res(U!4), tptp_fun_W_0(X!1, V!3))) | (~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, tptp_fun_W_0(X!1, V!3)))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[36])).
% 0.21/0.43 tff(38,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_W_0(X!1, V!3))) | (~less_than(findmin_pqp_res(U!4), tptp_fun_W_0(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)))) | (~less_than(findmin_pqp_res(U!4), tptp_fun_W_0(X!1, V!3))) | (~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, tptp_fun_W_0(X!1, V!3))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[37, 35])).
% 0.21/0.43 tff(39,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_W_0(X!1, V!3))) | (~less_than(findmin_pqp_res(U!4), tptp_fun_W_0(X!1, V!3))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(40,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)))) | (~less_than(findmin_pqp_res(U!4), tptp_fun_W_0(X!1, V!3))) | (~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, tptp_fun_W_0(X!1, V!3)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.21/0.43 tff(41,plain,
% 0.21/0.43 (~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, tptp_fun_W_0(X!1, V!3))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[40, 34, 12])).
% 0.21/0.43 tff(42,plain,
% 0.21/0.43 (~pair_in_list(update_slb(V!3, findmin_cpq_res(triple(U!4, V!3, W!2))), X!1, tptp_fun_W_0(X!1, V!3))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[41, 10])).
% 0.21/0.43 tff(43,plain,
% 0.21/0.43 (contains_slb(V!3, X!1)),
% 0.21/0.43 inference(and_elim,[status(thm)],[31])).
% 0.21/0.43 tff(44,plain,
% 0.21/0.43 (^[U: $i, V: $i] : refl(((~contains_slb(U, V)) | pair_in_list(U, V, tptp_fun_W_0(V, U))) <=> ((~contains_slb(U, V)) | pair_in_list(U, V, tptp_fun_W_0(V, U))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(45,plain,
% 0.21/0.43 (![U: $i, V: $i] : ((~contains_slb(U, V)) | pair_in_list(U, V, tptp_fun_W_0(V, U))) <=> ![U: $i, V: $i] : ((~contains_slb(U, V)) | pair_in_list(U, V, tptp_fun_W_0(V, U)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[44])).
% 0.21/0.43 tff(46,plain,
% 0.21/0.43 (![U: $i, V: $i] : ((~contains_slb(U, V)) | ?[W: $i] : pair_in_list(U, V, W)) <=> ![U: $i, V: $i] : ((~contains_slb(U, V)) | ?[W: $i] : pair_in_list(U, V, W))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(47,plain,
% 0.21/0.43 (^[U: $i, V: $i] : rewrite((contains_slb(U, V) => ?[W: $i] : pair_in_list(U, V, W)) <=> ((~contains_slb(U, V)) | ?[W: $i] : pair_in_list(U, V, W)))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(48,plain,
% 0.21/0.43 (![U: $i, V: $i] : (contains_slb(U, V) => ?[W: $i] : pair_in_list(U, V, W)) <=> ![U: $i, V: $i] : ((~contains_slb(U, V)) | ?[W: $i] : pair_in_list(U, V, W))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[47])).
% 0.21/0.43 tff(49,axiom,(![U: $i, V: $i] : (contains_slb(U, V) => ?[W: $i] : pair_in_list(U, V, W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l45_li4647')).
% 0.21/0.43 tff(50,plain,
% 0.21/0.43 (![U: $i, V: $i] : ((~contains_slb(U, V)) | ?[W: $i] : pair_in_list(U, V, W))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.21/0.43 tff(51,plain,
% 0.21/0.43 (![U: $i, V: $i] : ((~contains_slb(U, V)) | ?[W: $i] : pair_in_list(U, V, W))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.21/0.43 tff(52,plain,(
% 0.21/0.43 ![U: $i, V: $i] : ((~contains_slb(U, V)) | pair_in_list(U, V, tptp_fun_W_0(V, U)))),
% 0.21/0.43 inference(skolemize,[status(sab)],[51])).
% 0.21/0.43 tff(53,plain,
% 0.21/0.43 (![U: $i, V: $i] : ((~contains_slb(U, V)) | pair_in_list(U, V, tptp_fun_W_0(V, U)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.21/0.43 tff(54,plain,
% 0.21/0.43 (((~![U: $i, V: $i] : ((~contains_slb(U, V)) | pair_in_list(U, V, tptp_fun_W_0(V, U)))) | ((~contains_slb(V!3, X!1)) | pair_in_list(V!3, X!1, tptp_fun_W_0(X!1, V!3)))) <=> ((~![U: $i, V: $i] : ((~contains_slb(U, V)) | pair_in_list(U, V, tptp_fun_W_0(V, U)))) | (~contains_slb(V!3, X!1)) | pair_in_list(V!3, X!1, tptp_fun_W_0(X!1, V!3)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(55,plain,
% 0.21/0.43 ((~![U: $i, V: $i] : ((~contains_slb(U, V)) | pair_in_list(U, V, tptp_fun_W_0(V, U)))) | ((~contains_slb(V!3, X!1)) | pair_in_list(V!3, X!1, tptp_fun_W_0(X!1, V!3)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(56,plain,
% 0.21/0.43 ((~![U: $i, V: $i] : ((~contains_slb(U, V)) | pair_in_list(U, V, tptp_fun_W_0(V, U)))) | (~contains_slb(V!3, X!1)) | pair_in_list(V!3, X!1, tptp_fun_W_0(X!1, V!3))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.21/0.43 tff(57,plain,
% 0.21/0.43 (pair_in_list(V!3, X!1, tptp_fun_W_0(X!1, V!3))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[56, 53, 43])).
% 0.21/0.43 tff(58,plain,
% 0.21/0.43 (^[U: $i, V: $i, W: $i, X: $i] : refl(((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W))) <=> ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(59,plain,
% 0.21/0.43 (![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[58])).
% 0.21/0.43 tff(60,plain,
% 0.21/0.43 (^[U: $i, V: $i, W: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((pair_in_list(U, V, W) & less_than(X, W)) <=> (~((~less_than(X, W)) | (~pair_in_list(U, V, W))))), ((~(pair_in_list(U, V, W) & less_than(X, W))) <=> (~(~((~less_than(X, W)) | (~pair_in_list(U, V, W))))))), rewrite((~(~((~less_than(X, W)) | (~pair_in_list(U, V, W))))) <=> ((~less_than(X, W)) | (~pair_in_list(U, V, W)))), ((~(pair_in_list(U, V, W) & less_than(X, W))) <=> ((~less_than(X, W)) | (~pair_in_list(U, V, W))))), (((~(pair_in_list(U, V, W) & less_than(X, W))) | pair_in_list(update_slb(U, X), V, W)) <=> (((~less_than(X, W)) | (~pair_in_list(U, V, W))) | pair_in_list(update_slb(U, X), V, W)))), rewrite((((~less_than(X, W)) | (~pair_in_list(U, V, W))) | pair_in_list(update_slb(U, X), V, W)) <=> ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W)))), (((~(pair_in_list(U, V, W) & less_than(X, W))) | pair_in_list(update_slb(U, X), V, W)) <=> ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(61,plain,
% 0.21/0.43 (![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & less_than(X, W))) | pair_in_list(update_slb(U, X), V, W)) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[60])).
% 0.21/0.44 tff(62,plain,
% 0.21/0.44 (![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & less_than(X, W))) | pair_in_list(update_slb(U, X), V, W)) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & less_than(X, W))) | pair_in_list(update_slb(U, X), V, W))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(63,plain,
% 0.21/0.44 (^[U: $i, V: $i, W: $i, X: $i] : rewrite(((pair_in_list(U, V, W) & less_than(X, W)) => pair_in_list(update_slb(U, X), V, W)) <=> ((~(pair_in_list(U, V, W) & less_than(X, W))) | pair_in_list(update_slb(U, X), V, W)))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(64,plain,
% 0.21/0.44 (![U: $i, V: $i, W: $i, X: $i] : ((pair_in_list(U, V, W) & less_than(X, W)) => pair_in_list(update_slb(U, X), V, W)) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & less_than(X, W))) | pair_in_list(update_slb(U, X), V, W))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[63])).
% 0.21/0.44 tff(65,axiom,(![U: $i, V: $i, W: $i, X: $i] : ((pair_in_list(U, V, W) & less_than(X, W)) => pair_in_list(update_slb(U, X), V, W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l49_li3637')).
% 0.21/0.44 tff(66,plain,
% 0.21/0.44 (![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & less_than(X, W))) | pair_in_list(update_slb(U, X), V, W))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.21/0.44 tff(67,plain,
% 0.21/0.44 (![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & less_than(X, W))) | pair_in_list(update_slb(U, X), V, W))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.21/0.44 tff(68,plain,(
% 0.21/0.44 ![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & less_than(X, W))) | pair_in_list(update_slb(U, X), V, W))),
% 0.21/0.44 inference(skolemize,[status(sab)],[67])).
% 0.21/0.44 tff(69,plain,
% 0.21/0.44 (![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[68, 61])).
% 0.21/0.44 tff(70,plain,
% 0.21/0.44 (![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[69, 59])).
% 0.21/0.44 tff(71,plain,
% 0.21/0.44 (((~![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W)))) | ((~pair_in_list(V!3, X!1, tptp_fun_W_0(X!1, V!3))) | (~less_than(findmin_cpq_res(triple(U!4, V!3, W!2)), tptp_fun_W_0(X!1, V!3))) | pair_in_list(update_slb(V!3, findmin_cpq_res(triple(U!4, V!3, W!2))), X!1, tptp_fun_W_0(X!1, V!3)))) <=> ((~![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W)))) | (~pair_in_list(V!3, X!1, tptp_fun_W_0(X!1, V!3))) | (~less_than(findmin_cpq_res(triple(U!4, V!3, W!2)), tptp_fun_W_0(X!1, V!3))) | pair_in_list(update_slb(V!3, findmin_cpq_res(triple(U!4, V!3, W!2))), X!1, tptp_fun_W_0(X!1, V!3)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(72,plain,
% 0.21/0.44 (((~less_than(findmin_cpq_res(triple(U!4, V!3, W!2)), tptp_fun_W_0(X!1, V!3))) | pair_in_list(update_slb(V!3, findmin_cpq_res(triple(U!4, V!3, W!2))), X!1, tptp_fun_W_0(X!1, V!3)) | (~pair_in_list(V!3, X!1, tptp_fun_W_0(X!1, V!3)))) <=> ((~pair_in_list(V!3, X!1, tptp_fun_W_0(X!1, V!3))) | (~less_than(findmin_cpq_res(triple(U!4, V!3, W!2)), tptp_fun_W_0(X!1, V!3))) | pair_in_list(update_slb(V!3, findmin_cpq_res(triple(U!4, V!3, W!2))), X!1, tptp_fun_W_0(X!1, V!3)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(73,plain,
% 0.21/0.44 (((~![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W)))) | ((~less_than(findmin_cpq_res(triple(U!4, V!3, W!2)), tptp_fun_W_0(X!1, V!3))) | pair_in_list(update_slb(V!3, findmin_cpq_res(triple(U!4, V!3, W!2))), X!1, tptp_fun_W_0(X!1, V!3)) | (~pair_in_list(V!3, X!1, tptp_fun_W_0(X!1, V!3))))) <=> ((~![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W)))) | ((~pair_in_list(V!3, X!1, tptp_fun_W_0(X!1, V!3))) | (~less_than(findmin_cpq_res(triple(U!4, V!3, W!2)), tptp_fun_W_0(X!1, V!3))) | pair_in_list(update_slb(V!3, findmin_cpq_res(triple(U!4, V!3, W!2))), X!1, tptp_fun_W_0(X!1, V!3))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[72])).
% 0.21/0.44 tff(74,plain,
% 0.21/0.44 (((~![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W)))) | ((~less_than(findmin_cpq_res(triple(U!4, V!3, W!2)), tptp_fun_W_0(X!1, V!3))) | pair_in_list(update_slb(V!3, findmin_cpq_res(triple(U!4, V!3, W!2))), X!1, tptp_fun_W_0(X!1, V!3)) | (~pair_in_list(V!3, X!1, tptp_fun_W_0(X!1, V!3))))) <=> ((~![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W)))) | (~pair_in_list(V!3, X!1, tptp_fun_W_0(X!1, V!3))) | (~less_than(findmin_cpq_res(triple(U!4, V!3, W!2)), tptp_fun_W_0(X!1, V!3))) | pair_in_list(update_slb(V!3, findmin_cpq_res(triple(U!4, V!3, W!2))), X!1, tptp_fun_W_0(X!1, V!3)))),
% 0.21/0.44 inference(transitivity,[status(thm)],[73, 71])).
% 0.21/0.44 tff(75,plain,
% 0.21/0.44 ((~![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W)))) | ((~less_than(findmin_cpq_res(triple(U!4, V!3, W!2)), tptp_fun_W_0(X!1, V!3))) | pair_in_list(update_slb(V!3, findmin_cpq_res(triple(U!4, V!3, W!2))), X!1, tptp_fun_W_0(X!1, V!3)) | (~pair_in_list(V!3, X!1, tptp_fun_W_0(X!1, V!3))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(76,plain,
% 0.21/0.44 ((~![U: $i, V: $i, W: $i, X: $i] : ((~less_than(X, W)) | pair_in_list(update_slb(U, X), V, W) | (~pair_in_list(U, V, W)))) | (~pair_in_list(V!3, X!1, tptp_fun_W_0(X!1, V!3))) | (~less_than(findmin_cpq_res(triple(U!4, V!3, W!2)), tptp_fun_W_0(X!1, V!3))) | pair_in_list(update_slb(V!3, findmin_cpq_res(triple(U!4, V!3, W!2))), X!1, tptp_fun_W_0(X!1, V!3))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.21/0.44 tff(77,plain,
% 0.21/0.44 (pair_in_list(update_slb(V!3, findmin_cpq_res(triple(U!4, V!3, W!2))), X!1, tptp_fun_W_0(X!1, V!3))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[76, 70, 57, 11])).
% 0.21/0.44 tff(78,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[77, 42])).
% 0.21/0.44 tff(79,plain,((~less_than(findmin_cpq_res(triple(U!4, V!3, W!2)), tptp_fun_W_0(X!1, V!3))) | (~(findmin_cpq_res(triple(U!4, V!3, W!2)) = findmin_pqp_res(U!4)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44 tff(80,plain,
% 0.21/0.44 (~less_than(findmin_cpq_res(triple(U!4, V!3, W!2)), tptp_fun_W_0(X!1, V!3))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[79, 1])).
% 0.21/0.44 tff(81,plain,
% 0.21/0.44 (~less_than(findmin_pqp_res(U!4), tptp_fun_W_0(X!1, V!3))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[80, 6])).
% 0.21/0.44 tff(82,plain,
% 0.21/0.44 (^[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)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(83,plain,
% 0.21/0.44 (![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))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[82])).
% 0.21/0.44 tff(84,plain,
% 0.21/0.44 (^[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)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(85,plain,
% 0.21/0.44 (![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))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[84])).
% 0.21/0.44 tff(86,plain,
% 0.21/0.44 (![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))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(87,axiom,(![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+0.ax','stricly_smaller_definition')).
% 0.21/0.44 tff(88,plain,
% 0.21/0.44 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.21/0.44 tff(89,plain,(
% 0.21/0.44 ![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.21/0.44 inference(skolemize,[status(sab)],[88])).
% 0.21/0.44 tff(90,plain,
% 0.21/0.44 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.21/0.44 tff(91,plain,
% 0.21/0.44 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[90, 83])).
% 0.21/0.44 tff(92,plain,
% 0.21/0.44 ((~![U: $i, V: $i] : (strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U))))) | (strictly_less_than(tptp_fun_W_0(X!1, V!3), findmin_pqp_res(U!4)) <=> (~((~less_than(tptp_fun_W_0(X!1, V!3), findmin_pqp_res(U!4))) | less_than(findmin_pqp_res(U!4), tptp_fun_W_0(X!1, V!3)))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(93,plain,
% 0.21/0.44 (strictly_less_than(tptp_fun_W_0(X!1, V!3), findmin_pqp_res(U!4)) <=> (~((~less_than(tptp_fun_W_0(X!1, V!3), findmin_pqp_res(U!4))) | less_than(findmin_pqp_res(U!4), tptp_fun_W_0(X!1, V!3))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[92, 91])).
% 0.21/0.44 tff(94,plain,
% 0.21/0.44 (~pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, findmin_pqp_res(U!4))),
% 0.21/0.44 inference(and_elim,[status(thm)],[31])).
% 0.21/0.44 tff(95,plain,
% 0.21/0.44 (^[U: $i, V: $i, W: $i, X: $i] : refl((pair_in_list(update_slb(U, X), V, X) | (~strictly_less_than(W, X)) | (~pair_in_list(U, V, W))) <=> (pair_in_list(update_slb(U, X), V, X) | (~strictly_less_than(W, X)) | (~pair_in_list(U, V, W))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(96,plain,
% 0.21/0.44 (![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~strictly_less_than(W, X)) | (~pair_in_list(U, V, W))) <=> ![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~strictly_less_than(W, X)) | (~pair_in_list(U, V, W)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[95])).
% 0.21/0.44 tff(97,plain,
% 0.21/0.44 (^[U: $i, V: $i, W: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((pair_in_list(U, V, W) & strictly_less_than(W, X)) <=> (~((~strictly_less_than(W, X)) | (~pair_in_list(U, V, W))))), ((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) <=> (~(~((~strictly_less_than(W, X)) | (~pair_in_list(U, V, W))))))), rewrite((~(~((~strictly_less_than(W, X)) | (~pair_in_list(U, V, W))))) <=> ((~strictly_less_than(W, X)) | (~pair_in_list(U, V, W)))), ((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) <=> ((~strictly_less_than(W, X)) | (~pair_in_list(U, V, W))))), (((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X)) <=> (((~strictly_less_than(W, X)) | (~pair_in_list(U, V, W))) | pair_in_list(update_slb(U, X), V, X)))), rewrite((((~strictly_less_than(W, X)) | (~pair_in_list(U, V, W))) | pair_in_list(update_slb(U, X), V, X)) <=> (pair_in_list(update_slb(U, X), V, X) | (~strictly_less_than(W, X)) | (~pair_in_list(U, V, W)))), (((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X)) <=> (pair_in_list(update_slb(U, X), V, X) | (~strictly_less_than(W, X)) | (~pair_in_list(U, V, W)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(98,plain,
% 0.21/0.44 (![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X)) <=> ![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~strictly_less_than(W, X)) | (~pair_in_list(U, V, W)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[97])).
% 0.21/0.44 tff(99,plain,
% 0.21/0.44 (![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X)) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(100,plain,
% 0.21/0.44 (^[U: $i, V: $i, W: $i, X: $i] : rewrite(((pair_in_list(U, V, W) & strictly_less_than(W, X)) => pair_in_list(update_slb(U, X), V, X)) <=> ((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X)))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(101,plain,
% 0.21/0.44 (![U: $i, V: $i, W: $i, X: $i] : ((pair_in_list(U, V, W) & strictly_less_than(W, X)) => pair_in_list(update_slb(U, X), V, X)) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[100])).
% 0.21/0.44 tff(102,axiom,(![U: $i, V: $i, W: $i, X: $i] : ((pair_in_list(U, V, W) & strictly_less_than(W, X)) => pair_in_list(update_slb(U, X), V, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l48_li3839')).
% 0.21/0.44 tff(103,plain,
% 0.21/0.44 (![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.21/0.44 tff(104,plain,
% 0.21/0.44 (![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[103, 99])).
% 0.21/0.44 tff(105,plain,(
% 0.21/0.44 ![U: $i, V: $i, W: $i, X: $i] : ((~(pair_in_list(U, V, W) & strictly_less_than(W, X))) | pair_in_list(update_slb(U, X), V, X))),
% 0.21/0.44 inference(skolemize,[status(sab)],[104])).
% 0.21/0.44 tff(106,plain,
% 0.21/0.44 (![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~strictly_less_than(W, X)) | (~pair_in_list(U, V, W)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[105, 98])).
% 0.21/0.44 tff(107,plain,
% 0.21/0.44 (![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~strictly_less_than(W, X)) | (~pair_in_list(U, V, W)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[106, 96])).
% 0.21/0.44 tff(108,plain,
% 0.21/0.44 (((~![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~strictly_less_than(W, X)) | (~pair_in_list(U, V, W)))) | (pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, findmin_pqp_res(U!4)) | (~strictly_less_than(tptp_fun_W_0(X!1, V!3), findmin_pqp_res(U!4))) | (~pair_in_list(V!3, X!1, tptp_fun_W_0(X!1, V!3))))) <=> ((~![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~strictly_less_than(W, X)) | (~pair_in_list(U, V, W)))) | pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, findmin_pqp_res(U!4)) | (~strictly_less_than(tptp_fun_W_0(X!1, V!3), findmin_pqp_res(U!4))) | (~pair_in_list(V!3, X!1, tptp_fun_W_0(X!1, V!3))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(109,plain,
% 0.21/0.44 ((~![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~strictly_less_than(W, X)) | (~pair_in_list(U, V, W)))) | (pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, findmin_pqp_res(U!4)) | (~strictly_less_than(tptp_fun_W_0(X!1, V!3), findmin_pqp_res(U!4))) | (~pair_in_list(V!3, X!1, tptp_fun_W_0(X!1, V!3))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(110,plain,
% 0.21/0.44 ((~![U: $i, V: $i, W: $i, X: $i] : (pair_in_list(update_slb(U, X), V, X) | (~strictly_less_than(W, X)) | (~pair_in_list(U, V, W)))) | pair_in_list(update_slb(V!3, findmin_pqp_res(U!4)), X!1, findmin_pqp_res(U!4)) | (~strictly_less_than(tptp_fun_W_0(X!1, V!3), findmin_pqp_res(U!4))) | (~pair_in_list(V!3, X!1, tptp_fun_W_0(X!1, V!3)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.21/0.44 tff(111,plain,
% 0.21/0.44 (~strictly_less_than(tptp_fun_W_0(X!1, V!3), findmin_pqp_res(U!4))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[110, 107, 94, 57])).
% 0.21/0.44 tff(112,plain,
% 0.21/0.44 ((~(strictly_less_than(tptp_fun_W_0(X!1, V!3), findmin_pqp_res(U!4)) <=> (~((~less_than(tptp_fun_W_0(X!1, V!3), findmin_pqp_res(U!4))) | less_than(findmin_pqp_res(U!4), tptp_fun_W_0(X!1, V!3)))))) | strictly_less_than(tptp_fun_W_0(X!1, V!3), findmin_pqp_res(U!4)) | ((~less_than(tptp_fun_W_0(X!1, V!3), findmin_pqp_res(U!4))) | less_than(findmin_pqp_res(U!4), tptp_fun_W_0(X!1, V!3)))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(113,plain,
% 0.21/0.44 ((~(strictly_less_than(tptp_fun_W_0(X!1, V!3), findmin_pqp_res(U!4)) <=> (~((~less_than(tptp_fun_W_0(X!1, V!3), findmin_pqp_res(U!4))) | less_than(findmin_pqp_res(U!4), tptp_fun_W_0(X!1, V!3)))))) | ((~less_than(tptp_fun_W_0(X!1, V!3), findmin_pqp_res(U!4))) | less_than(findmin_pqp_res(U!4), tptp_fun_W_0(X!1, V!3)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[112, 111])).
% 0.21/0.45 tff(114,plain,
% 0.21/0.45 ((~less_than(tptp_fun_W_0(X!1, V!3), findmin_pqp_res(U!4))) | less_than(findmin_pqp_res(U!4), tptp_fun_W_0(X!1, V!3))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[113, 93])).
% 0.21/0.45 tff(115,plain,
% 0.21/0.45 ((~((~less_than(tptp_fun_W_0(X!1, V!3), findmin_pqp_res(U!4))) | less_than(findmin_pqp_res(U!4), tptp_fun_W_0(X!1, V!3)))) | (~less_than(tptp_fun_W_0(X!1, V!3), findmin_pqp_res(U!4))) | less_than(findmin_pqp_res(U!4), tptp_fun_W_0(X!1, V!3))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(116,plain,
% 0.21/0.45 ((~less_than(tptp_fun_W_0(X!1, V!3), findmin_pqp_res(U!4))) | less_than(findmin_pqp_res(U!4), tptp_fun_W_0(X!1, V!3))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[115, 114])).
% 0.21/0.45 tff(117,plain,
% 0.21/0.45 (~less_than(tptp_fun_W_0(X!1, V!3), findmin_pqp_res(U!4))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[116, 81])).
% 0.21/0.45 tff(118,plain,
% 0.21/0.45 (~less_than(tptp_fun_W_0(X!1, V!3), findmin_cpq_res(triple(U!4, V!3, W!2)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[117, 4])).
% 0.21/0.45 tff(119,plain,
% 0.21/0.45 (^[U: $i, V: $i] : refl((less_than(V, U) | less_than(U, V)) <=> (less_than(V, U) | less_than(U, V)))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(120,plain,
% 0.21/0.45 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[119])).
% 0.21/0.45 tff(121,plain,
% 0.21/0.45 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(122,plain,
% 0.21/0.45 (^[U: $i, V: $i] : rewrite((less_than(U, V) | less_than(V, U)) <=> (less_than(V, U) | less_than(U, V)))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(123,plain,
% 0.21/0.45 (![U: $i, V: $i] : (less_than(U, V) | less_than(V, U)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[122])).
% 0.21/0.45 tff(124,axiom,(![U: $i, V: $i] : (less_than(U, V) | less_than(V, U))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+0.ax','totality')).
% 0.21/0.45 tff(125,plain,
% 0.21/0.45 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.21/0.45 tff(126,plain,
% 0.21/0.45 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[125, 121])).
% 0.21/0.45 tff(127,plain,(
% 0.21/0.45 ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.21/0.45 inference(skolemize,[status(sab)],[126])).
% 0.21/0.45 tff(128,plain,
% 0.21/0.45 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[127, 120])).
% 0.21/0.45 tff(129,plain,
% 0.21/0.45 (((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | (less_than(findmin_cpq_res(triple(U!4, V!3, W!2)), tptp_fun_W_0(X!1, V!3)) | less_than(tptp_fun_W_0(X!1, V!3), findmin_cpq_res(triple(U!4, V!3, W!2))))) <=> ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | less_than(findmin_cpq_res(triple(U!4, V!3, W!2)), tptp_fun_W_0(X!1, V!3)) | less_than(tptp_fun_W_0(X!1, V!3), findmin_cpq_res(triple(U!4, V!3, W!2))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(130,plain,
% 0.21/0.45 ((less_than(tptp_fun_W_0(X!1, V!3), findmin_cpq_res(triple(U!4, V!3, W!2))) | less_than(findmin_cpq_res(triple(U!4, V!3, W!2)), tptp_fun_W_0(X!1, V!3))) <=> (less_than(findmin_cpq_res(triple(U!4, V!3, W!2)), tptp_fun_W_0(X!1, V!3)) | less_than(tptp_fun_W_0(X!1, V!3), findmin_cpq_res(triple(U!4, V!3, W!2))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(131,plain,
% 0.21/0.45 (((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | (less_than(tptp_fun_W_0(X!1, V!3), findmin_cpq_res(triple(U!4, V!3, W!2))) | less_than(findmin_cpq_res(triple(U!4, V!3, W!2)), tptp_fun_W_0(X!1, V!3)))) <=> ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | (less_than(findmin_cpq_res(triple(U!4, V!3, W!2)), tptp_fun_W_0(X!1, V!3)) | less_than(tptp_fun_W_0(X!1, V!3), findmin_cpq_res(triple(U!4, V!3, W!2)))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[130])).
% 0.21/0.45 tff(132,plain,
% 0.21/0.45 (((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | (less_than(tptp_fun_W_0(X!1, V!3), findmin_cpq_res(triple(U!4, V!3, W!2))) | less_than(findmin_cpq_res(triple(U!4, V!3, W!2)), tptp_fun_W_0(X!1, V!3)))) <=> ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | less_than(findmin_cpq_res(triple(U!4, V!3, W!2)), tptp_fun_W_0(X!1, V!3)) | less_than(tptp_fun_W_0(X!1, V!3), findmin_cpq_res(triple(U!4, V!3, W!2))))),
% 0.21/0.45 inference(transitivity,[status(thm)],[131, 129])).
% 0.21/0.45 tff(133,plain,
% 0.21/0.45 ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | (less_than(tptp_fun_W_0(X!1, V!3), findmin_cpq_res(triple(U!4, V!3, W!2))) | less_than(findmin_cpq_res(triple(U!4, V!3, W!2)), tptp_fun_W_0(X!1, V!3)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(134,plain,
% 0.21/0.45 ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | less_than(findmin_cpq_res(triple(U!4, V!3, W!2)), tptp_fun_W_0(X!1, V!3)) | less_than(tptp_fun_W_0(X!1, V!3), findmin_cpq_res(triple(U!4, V!3, W!2)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.21/0.45 tff(135,plain,
% 0.21/0.45 (less_than(tptp_fun_W_0(X!1, V!3), findmin_cpq_res(triple(U!4, V!3, W!2)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[134, 128, 80])).
% 0.21/0.45 tff(136,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[135, 118])).
% 0.21/0.45 tff(137,plain,(~(findmin_cpq_res(triple(U!4, V!3, W!2)) = findmin_pqp_res(U!4))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.45 tff(138,plain,
% 0.21/0.45 (^[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))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(139,plain,
% 0.21/0.45 (![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)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[138])).
% 0.21/0.45 tff(140,plain,
% 0.21/0.45 (![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)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(141,plain,
% 0.21/0.45 (![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)))),
% 0.21/0.45 inference(elim_unused_vars,[status(thm)],[])).
% 0.21/0.45 tff(142,plain,
% 0.21/0.45 (^[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))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(143,plain,
% 0.21/0.45 (![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)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[142])).
% 0.21/0.45 tff(144,plain,
% 0.21/0.45 (![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)))),
% 0.21/0.45 inference(transitivity,[status(thm)],[143, 141])).
% 0.21/0.45 tff(145,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/sandbox2/benchmark/Axioms/SWV007+3.ax','ax51')).
% 0.21/0.45 tff(146,plain,
% 0.21/0.45 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.21/0.45 tff(147,plain,
% 0.21/0.45 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[146, 140])).
% 0.21/0.45 tff(148,plain,(
% 0.21/0.45 ![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.21/0.45 inference(skolemize,[status(sab)],[147])).
% 0.21/0.45 tff(149,plain,
% 0.21/0.45 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[148, 139])).
% 0.21/0.46 tff(150,plain,
% 0.21/0.46 (((~![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)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(151,plain,
% 0.21/0.46 ((~![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)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(152,plain,
% 0.21/0.46 ((~![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))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.21/0.46 tff(153,plain,
% 0.21/0.46 ((V!3 = create_slb) | (findmin_cpq_res(triple(U!4, V!3, W!2)) = findmin_pqp_res(U!4))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[152, 149])).
% 0.21/0.46 tff(154,plain,
% 0.21/0.46 (V!3 = create_slb),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[153, 137])).
% 0.21/0.46 tff(155,plain,
% 0.21/0.46 (create_slb = V!3),
% 0.21/0.46 inference(symmetry,[status(thm)],[154])).
% 0.21/0.46 tff(156,plain,
% 0.21/0.46 (pair_in_list(create_slb, X!1, tptp_fun_W_0(X!1, V!3)) <=> pair_in_list(V!3, X!1, tptp_fun_W_0(X!1, V!3))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[155])).
% 0.21/0.46 tff(157,plain,
% 0.21/0.46 (pair_in_list(V!3, X!1, tptp_fun_W_0(X!1, V!3)) <=> pair_in_list(create_slb, X!1, tptp_fun_W_0(X!1, V!3))),
% 0.21/0.46 inference(symmetry,[status(thm)],[156])).
% 0.21/0.46 tff(158,plain,
% 0.21/0.46 (pair_in_list(create_slb, X!1, tptp_fun_W_0(X!1, V!3))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[57, 157])).
% 0.21/0.46 tff(159,plain,
% 0.21/0.46 (^[U: $i, V: $i] : refl((~pair_in_list(create_slb, U, V)) <=> (~pair_in_list(create_slb, U, V)))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(160,plain,
% 0.21/0.46 (![U: $i, V: $i] : (~pair_in_list(create_slb, U, V)) <=> ![U: $i, V: $i] : (~pair_in_list(create_slb, U, V))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[159])).
% 0.21/0.46 tff(161,plain,
% 0.21/0.46 (![U: $i, V: $i] : (~pair_in_list(create_slb, U, V)) <=> ![U: $i, V: $i] : (~pair_in_list(create_slb, U, V))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(162,axiom,(![U: $i, V: $i] : (~pair_in_list(create_slb, U, V))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+2.ax','ax22')).
% 0.21/0.46 tff(163,plain,
% 0.21/0.46 (![U: $i, V: $i] : (~pair_in_list(create_slb, U, V))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.21/0.46 tff(164,plain,(
% 0.21/0.46 ![U: $i, V: $i] : (~pair_in_list(create_slb, U, V))),
% 0.21/0.46 inference(skolemize,[status(sab)],[163])).
% 0.21/0.46 tff(165,plain,
% 0.21/0.46 (![U: $i, V: $i] : (~pair_in_list(create_slb, U, V))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[164, 160])).
% 0.21/0.46 tff(166,plain,
% 0.21/0.46 ((~![U: $i, V: $i] : (~pair_in_list(create_slb, U, V))) | (~pair_in_list(create_slb, X!1, tptp_fun_W_0(X!1, V!3)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(167,plain,
% 0.21/0.46 (~pair_in_list(create_slb, X!1, tptp_fun_W_0(X!1, V!3))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[166, 165])).
% 0.21/0.46 tff(168,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[167, 158])).
% 0.21/0.46 % SZS output end Proof
%------------------------------------------------------------------------------