TSTP Solution File: SWV407+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV407+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.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 15:11:39 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
% 0.07/0.13 % Problem : SWV407+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n004.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 02:50:04 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -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(check_cpq_type, type, (
% 0.21/0.42 check_cpq: $i > $o)).
% 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_3_type, type, (
% 0.21/0.42 tptp_fun_W_3: $i)).
% 0.21/0.42 tff(update_slb_type, type, (
% 0.21/0.42 update_slb: ( $i * $i ) > $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_5_type, type, (
% 0.21/0.42 tptp_fun_U_5: $i)).
% 0.21/0.42 tff(tptp_fun_V_4_type, type, (
% 0.21/0.42 tptp_fun_V_4: $i)).
% 0.21/0.42 tff(findmin_cpq_eff_type, type, (
% 0.21/0.42 findmin_cpq_eff: $i > $i)).
% 0.21/0.42 tff(bad_type, type, (
% 0.21/0.42 bad: $i)).
% 0.21/0.42 tff(less_than_type, type, (
% 0.21/0.42 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(tptp_fun_X_6_type, type, (
% 0.21/0.42 tptp_fun_X_6: $i)).
% 0.21/0.42 tff(tptp_fun_Y_2_type, type, (
% 0.21/0.42 tptp_fun_Y_2: ( $i * $i * $i ) > $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(create_slb_type, type, (
% 0.21/0.42 create_slb: $i)).
% 0.21/0.42 tff(contains_slb_type, type, (
% 0.21/0.42 contains_slb: ( $i * $i ) > $o)).
% 0.21/0.42 tff(contains_cpq_type, type, (
% 0.21/0.42 contains_cpq: ( $i * $i ) > $o)).
% 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(tptp_fun_X_1_type, type, (
% 0.21/0.42 tptp_fun_X_1: $i > $i)).
% 0.21/0.42 tff(tptp_fun_Y_0_type, type, (
% 0.21/0.42 tptp_fun_Y_0: $i > $i)).
% 0.21/0.42 tff(lookup_slb_type, type, (
% 0.21/0.42 lookup_slb: ( $i * $i ) > $i)).
% 0.21/0.42 tff(1,assumption,(less_than(tptp_fun_Y_2(X!6, V!4, U!5), X!6)), introduced(assumption)).
% 0.21/0.42 tff(2,assumption,(V!4 = create_slb), introduced(assumption)).
% 0.21/0.42 tff(3,plain,
% 0.21/0.42 (create_slb = V!4),
% 0.21/0.42 inference(symmetry,[status(thm)],[2])).
% 0.21/0.42 tff(4,plain,
% 0.21/0.42 (contains_slb(create_slb, X!6) <=> contains_slb(V!4, X!6)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[3])).
% 0.21/0.42 tff(5,plain,
% 0.21/0.42 (contains_slb(V!4, X!6) <=> contains_slb(create_slb, X!6)),
% 0.21/0.42 inference(symmetry,[status(thm)],[4])).
% 0.21/0.42 tff(6,plain,
% 0.21/0.42 (^[U: $i, V: $i, W: $i, X: $i] : refl((contains_cpq(triple(U, V, W), X) <=> contains_slb(V, X)) <=> (contains_cpq(triple(U, V, W), X) <=> contains_slb(V, X)))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(7,plain,
% 0.21/0.42 (![U: $i, V: $i, W: $i, X: $i] : (contains_cpq(triple(U, V, W), X) <=> contains_slb(V, X)) <=> ![U: $i, V: $i, W: $i, X: $i] : (contains_cpq(triple(U, V, W), X) <=> contains_slb(V, X))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[6])).
% 0.21/0.42 tff(8,plain,
% 0.21/0.42 (![U: $i, V: $i, W: $i, X: $i] : (contains_cpq(triple(U, V, W), X) <=> contains_slb(V, X)) <=> ![U: $i, V: $i, W: $i, X: $i] : (contains_cpq(triple(U, V, W), X) <=> contains_slb(V, X))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(9,axiom,(![U: $i, V: $i, W: $i, X: $i] : (contains_cpq(triple(U, V, W), X) <=> contains_slb(V, X))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax','ax39')).
% 0.21/0.42 tff(10,plain,
% 0.21/0.42 (![U: $i, V: $i, W: $i, X: $i] : (contains_cpq(triple(U, V, W), X) <=> contains_slb(V, X))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.21/0.42 tff(11,plain,(
% 0.21/0.42 ![U: $i, V: $i, W: $i, X: $i] : (contains_cpq(triple(U, V, W), X) <=> contains_slb(V, X))),
% 0.21/0.42 inference(skolemize,[status(sab)],[10])).
% 0.21/0.42 tff(12,plain,
% 0.21/0.42 (![U: $i, V: $i, W: $i, X: $i] : (contains_cpq(triple(U, V, W), X) <=> contains_slb(V, X))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.21/0.42 tff(13,plain,
% 0.21/0.42 ((~![U: $i, V: $i, W: $i, X: $i] : (contains_cpq(triple(U, V, W), X) <=> contains_slb(V, X))) | (contains_cpq(triple(U!5, V!4, W!3), X!6) <=> contains_slb(V!4, X!6))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(14,plain,
% 0.21/0.42 (contains_cpq(triple(U!5, V!4, W!3), X!6) <=> contains_slb(V!4, X!6)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.21/0.42 tff(15,plain,
% 0.21/0.42 ((check_cpq(findmin_cpq_eff(triple(U!5, V!4, W!3))) & (contains_cpq(triple(U!5, V!4, W!3), X!6) & strictly_less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3))))) <=> (check_cpq(findmin_cpq_eff(triple(U!5, V!4, W!3))) & contains_cpq(triple(U!5, V!4, W!3), X!6) & strictly_less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(16,plain,
% 0.21/0.42 ((~(~check_cpq(findmin_cpq_eff(triple(U!5, V!4, W!3))))) <=> check_cpq(findmin_cpq_eff(triple(U!5, V!4, W!3)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(17,plain,
% 0.21/0.42 (((~(~check_cpq(findmin_cpq_eff(triple(U!5, V!4, W!3))))) & (contains_cpq(triple(U!5, V!4, W!3), X!6) & strictly_less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3))))) <=> (check_cpq(findmin_cpq_eff(triple(U!5, V!4, W!3))) & (contains_cpq(triple(U!5, V!4, W!3), X!6) & strictly_less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[16])).
% 0.21/0.42 tff(18,plain,
% 0.21/0.42 (((~(~check_cpq(findmin_cpq_eff(triple(U!5, V!4, W!3))))) & (contains_cpq(triple(U!5, V!4, W!3), X!6) & strictly_less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3))))) <=> (check_cpq(findmin_cpq_eff(triple(U!5, V!4, W!3))) & contains_cpq(triple(U!5, V!4, W!3), X!6) & strictly_less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[17, 15])).
% 0.21/0.42 tff(19,plain,
% 0.21/0.42 ((~![U: $i, V: $i, W: $i] : ((~check_cpq(findmin_cpq_eff(triple(U, V, W)))) | (~?[X: $i] : (contains_cpq(triple(U, V, W), X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))))) <=> (~![U: $i, V: $i, W: $i] : ((~check_cpq(findmin_cpq_eff(triple(U, V, W)))) | (~?[X: $i] : (contains_cpq(triple(U, V, W), 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(20,plain,
% 0.21/0.42 ((~![U: $i, V: $i, W: $i] : (?[X: $i] : (contains_cpq(triple(U, V, W), X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))) => (~check_cpq(findmin_cpq_eff(triple(U, V, W)))))) <=> (~![U: $i, V: $i, W: $i] : ((~check_cpq(findmin_cpq_eff(triple(U, V, W)))) | (~?[X: $i] : (contains_cpq(triple(U, V, W), 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(21,axiom,(~![U: $i, V: $i, W: $i] : (?[X: $i] : (contains_cpq(triple(U, V, W), X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))) => (~check_cpq(findmin_cpq_eff(triple(U, V, W)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l43_co')).
% 0.21/0.42 tff(22,plain,
% 0.21/0.42 (~![U: $i, V: $i, W: $i] : ((~check_cpq(findmin_cpq_eff(triple(U, V, W)))) | (~?[X: $i] : (contains_cpq(triple(U, V, W), X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.21/0.42 tff(23,plain,
% 0.21/0.42 (~![U: $i, V: $i, W: $i] : ((~check_cpq(findmin_cpq_eff(triple(U, V, W)))) | (~?[X: $i] : (contains_cpq(triple(U, V, W), X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[22, 19])).
% 0.21/0.42 tff(24,plain,
% 0.21/0.42 (~![U: $i, V: $i, W: $i] : ((~check_cpq(findmin_cpq_eff(triple(U, V, W)))) | (~?[X: $i] : (contains_cpq(triple(U, V, W), X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.21/0.42 tff(25,plain,
% 0.21/0.42 (~![U: $i, V: $i, W: $i] : ((~check_cpq(findmin_cpq_eff(triple(U, V, W)))) | (~?[X: $i] : (contains_cpq(triple(U, V, W), X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[24, 19])).
% 0.21/0.42 tff(26,plain,
% 0.21/0.42 (~![U: $i, V: $i, W: $i] : ((~check_cpq(findmin_cpq_eff(triple(U, V, W)))) | (~?[X: $i] : (contains_cpq(triple(U, V, W), X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[25, 19])).
% 0.21/0.42 tff(27,plain,
% 0.21/0.42 (~![U: $i, V: $i, W: $i] : ((~check_cpq(findmin_cpq_eff(triple(U, V, W)))) | (~?[X: $i] : (contains_cpq(triple(U, V, W), X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.21/0.42 tff(28,plain,
% 0.21/0.42 (~![U: $i, V: $i, W: $i] : ((~check_cpq(findmin_cpq_eff(triple(U, V, W)))) | (~?[X: $i] : (contains_cpq(triple(U, V, W), X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[27, 19])).
% 0.21/0.42 tff(29,plain,
% 0.21/0.42 (check_cpq(findmin_cpq_eff(triple(U!5, V!4, W!3))) & contains_cpq(triple(U!5, V!4, W!3), X!6) & strictly_less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[28, 18])).
% 0.21/0.42 tff(30,plain,
% 0.21/0.42 (contains_cpq(triple(U!5, V!4, W!3), X!6)),
% 0.21/0.42 inference(and_elim,[status(thm)],[29])).
% 0.21/0.43 tff(31,plain,
% 0.21/0.43 ((~(contains_cpq(triple(U!5, V!4, W!3), X!6) <=> contains_slb(V!4, X!6))) | (~contains_cpq(triple(U!5, V!4, W!3), X!6)) | contains_slb(V!4, X!6)),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(32,plain,
% 0.21/0.43 ((~(contains_cpq(triple(U!5, V!4, W!3), X!6) <=> contains_slb(V!4, X!6))) | contains_slb(V!4, X!6)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.21/0.43 tff(33,plain,
% 0.21/0.43 (contains_slb(V!4, X!6)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[32, 14])).
% 0.21/0.43 tff(34,plain,
% 0.21/0.43 (contains_slb(create_slb, X!6)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[33, 5])).
% 0.21/0.43 tff(35,plain,
% 0.21/0.43 (^[U: $i] : refl((~contains_slb(create_slb, U)) <=> (~contains_slb(create_slb, U)))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(36,plain,
% 0.21/0.43 (![U: $i] : (~contains_slb(create_slb, U)) <=> ![U: $i] : (~contains_slb(create_slb, U))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[35])).
% 0.21/0.43 tff(37,plain,
% 0.21/0.43 (![U: $i] : (~contains_slb(create_slb, U)) <=> ![U: $i] : (~contains_slb(create_slb, U))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(38,axiom,(![U: $i] : (~contains_slb(create_slb, U))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+2.ax','ax20')).
% 0.21/0.43 tff(39,plain,
% 0.21/0.43 (![U: $i] : (~contains_slb(create_slb, U))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.21/0.43 tff(40,plain,(
% 0.21/0.43 ![U: $i] : (~contains_slb(create_slb, U))),
% 0.21/0.43 inference(skolemize,[status(sab)],[39])).
% 0.21/0.43 tff(41,plain,
% 0.21/0.43 (![U: $i] : (~contains_slb(create_slb, U))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.21/0.43 tff(42,plain,
% 0.21/0.43 ((~![U: $i] : (~contains_slb(create_slb, U))) | (~contains_slb(create_slb, X!6))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(43,plain,
% 0.21/0.43 (~contains_slb(create_slb, X!6)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.21/0.43 tff(44,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[43, 34])).
% 0.21/0.43 tff(45,plain,(~(V!4 = create_slb)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(46,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(47,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)],[46])).
% 0.21/0.43 tff(48,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(49,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(50,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(51,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)],[50])).
% 0.21/0.43 tff(52,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)],[51, 49])).
% 0.21/0.43 tff(53,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')).
% 0.21/0.43 tff(54,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)],[53, 52])).
% 0.21/0.43 tff(55,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)],[54, 48])).
% 0.21/0.43 tff(56,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(skolemize,[status(sab)],[55])).
% 0.21/0.43 tff(57,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)],[56, 47])).
% 0.21/0.43 tff(58,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)))) | ((V!4 = create_slb) | (findmin_cpq_res(triple(U!5, V!4, W!3)) = findmin_pqp_res(U!5)))) <=> ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))) | (V!4 = create_slb) | (findmin_cpq_res(triple(U!5, V!4, W!3)) = findmin_pqp_res(U!5)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(59,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)))) | ((V!4 = create_slb) | (findmin_cpq_res(triple(U!5, V!4, W!3)) = findmin_pqp_res(U!5)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(60,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)))) | (V!4 = create_slb) | (findmin_cpq_res(triple(U!5, V!4, W!3)) = findmin_pqp_res(U!5))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.21/0.43 tff(61,plain,
% 0.21/0.43 ((V!4 = create_slb) | (findmin_cpq_res(triple(U!5, V!4, W!3)) = findmin_pqp_res(U!5))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[60, 57])).
% 0.21/0.43 tff(62,plain,
% 0.21/0.43 (findmin_cpq_res(triple(U!5, V!4, W!3)) = findmin_pqp_res(U!5)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[61, 45])).
% 0.21/0.43 tff(63,plain,
% 0.21/0.43 (less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_Y_2(X!6, V!4, U!5)) <=> less_than(findmin_pqp_res(U!5), tptp_fun_Y_2(X!6, V!4, U!5))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[62])).
% 0.21/0.43 tff(64,plain,
% 0.21/0.43 (less_than(findmin_pqp_res(U!5), tptp_fun_Y_2(X!6, V!4, U!5)) <=> less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_Y_2(X!6, V!4, U!5))),
% 0.21/0.43 inference(symmetry,[status(thm)],[63])).
% 0.21/0.43 tff(65,assumption,(~(V!4 = create_slb)), introduced(assumption)).
% 0.21/0.43 tff(66,assumption,(pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_pqp_res(U!5))), introduced(assumption)).
% 0.21/0.43 tff(67,plain,
% 0.21/0.43 (findmin_cpq_res(triple(U!5, V!4, W!3)) = findmin_pqp_res(U!5)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[61, 65])).
% 0.21/0.43 tff(68,assumption,(findmin_cpq_res(triple(U!5, V!4, W!3)) = findmin_pqp_res(U!5)), introduced(assumption)).
% 0.21/0.43 tff(69,plain,
% 0.21/0.43 (pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_cpq_res(triple(U!5, V!4, W!3))) <=> pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_pqp_res(U!5))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[68])).
% 0.21/0.43 tff(70,plain,
% 0.21/0.43 (pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_pqp_res(U!5)) <=> pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))),
% 0.21/0.43 inference(symmetry,[status(thm)],[69])).
% 0.21/0.43 tff(71,plain,
% 0.21/0.43 (pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[66, 70])).
% 0.21/0.43 tff(72,assumption,(~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))), introduced(assumption)).
% 0.21/0.43 tff(73,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.21/0.43 tff(74,plain,(pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_cpq_res(triple(U!5, V!4, W!3))) | (~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_pqp_res(U!5))) | (~(findmin_cpq_res(triple(U!5, V!4, W!3)) = findmin_pqp_res(U!5)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(75,plain,
% 0.21/0.43 (pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[74, 67, 66])).
% 0.21/0.43 tff(76,assumption,(![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X))), introduced(assumption)).
% 0.21/0.43 tff(77,assumption,(pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))), introduced(assumption)).
% 0.21/0.43 tff(78,plain,
% 0.21/0.43 (^[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)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(79,plain,
% 0.21/0.43 (![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))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[78])).
% 0.21/0.43 tff(80,plain,
% 0.21/0.43 (^[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)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(81,plain,
% 0.21/0.43 (![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))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[80])).
% 0.21/0.43 tff(82,plain,
% 0.21/0.43 (![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))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(83,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')).
% 0.21/0.43 tff(84,plain,
% 0.21/0.43 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.21/0.43 tff(85,plain,(
% 0.21/0.43 ![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.21/0.43 inference(skolemize,[status(sab)],[84])).
% 0.21/0.43 tff(86,plain,
% 0.21/0.43 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[85, 81])).
% 0.21/0.43 tff(87,plain,
% 0.21/0.43 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[86, 79])).
% 0.21/0.43 tff(88,plain,
% 0.21/0.43 ((~![U: $i, V: $i] : (strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U))))) | (strictly_less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3))) <=> (~((~less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), X!6))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(89,plain,
% 0.21/0.43 (strictly_less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3))) <=> (~((~less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), X!6)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.21/0.43 tff(90,plain,
% 0.21/0.43 (strictly_less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))),
% 0.21/0.43 inference(and_elim,[status(thm)],[29])).
% 0.21/0.43 tff(91,plain,
% 0.21/0.43 ((~(strictly_less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3))) <=> (~((~less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), X!6))))) | (~strictly_less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))) | (~((~less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), X!6)))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(92,plain,
% 0.21/0.43 ((~(strictly_less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3))) <=> (~((~less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), X!6))))) | (~((~less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), X!6)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.21/0.43 tff(93,plain,
% 0.21/0.43 (~((~less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), X!6))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[92, 89])).
% 0.21/0.43 tff(94,plain,
% 0.21/0.43 (((~less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), X!6)) | (~less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), X!6))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(95,plain,
% 0.21/0.43 (~less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), X!6)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.21/0.43 tff(96,plain,
% 0.21/0.43 (((~![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X))) | ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), X!6))) <=> ((~![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X))) | (~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), X!6))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(97,plain,
% 0.21/0.43 ((~![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X))) | ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), X!6))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(98,plain,
% 0.21/0.43 ((~![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X))) | (~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), X!6)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.21/0.43 tff(99,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[98, 95, 77, 76])).
% 0.21/0.43 tff(100,plain,((~![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X))) | (~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_cpq_res(triple(U!5, V!4, W!3))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(101,plain,
% 0.21/0.43 (~![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[100, 75])).
% 0.21/0.43 tff(102,assumption,(findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad)), introduced(assumption)).
% 0.21/0.43 tff(103,plain,
% 0.21/0.43 (triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad) = findmin_cpq_eff(triple(U!5, V!4, W!3))),
% 0.21/0.43 inference(symmetry,[status(thm)],[102])).
% 0.21/0.43 tff(104,plain,
% 0.21/0.43 (check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad)) <=> check_cpq(findmin_cpq_eff(triple(U!5, V!4, W!3)))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[103])).
% 0.21/0.43 tff(105,plain,
% 0.21/0.43 (check_cpq(findmin_cpq_eff(triple(U!5, V!4, W!3))) <=> check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad))),
% 0.21/0.43 inference(symmetry,[status(thm)],[104])).
% 0.21/0.43 tff(106,plain,
% 0.21/0.43 (check_cpq(findmin_cpq_eff(triple(U!5, V!4, W!3)))),
% 0.21/0.43 inference(and_elim,[status(thm)],[29])).
% 0.21/0.43 tff(107,plain,
% 0.21/0.43 (check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.21/0.43 tff(108,plain,
% 0.21/0.43 (^[U: $i, V: $i, W: $i] : refl((~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V)))))))) <=> (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V)))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(109,plain,
% 0.21/0.43 (![U: $i, V: $i, W: $i] : (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V)))))))) <=> ![U: $i, V: $i, W: $i] : (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V))))))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[108])).
% 0.21/0.44 tff(110,plain,
% 0.21/0.44 (^[U: $i, V: $i, W: $i] : rewrite((~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V)))))))) <=> (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V)))))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(111,plain,
% 0.21/0.44 (![U: $i, V: $i, W: $i] : (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V)))))))) <=> ![U: $i, V: $i, W: $i] : (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V))))))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[110])).
% 0.21/0.44 tff(112,plain,
% 0.21/0.44 (![U: $i, V: $i, W: $i] : (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V)))))))) <=> ![U: $i, V: $i, W: $i] : (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V))))))))),
% 0.21/0.44 inference(transitivity,[status(thm)],[111, 109])).
% 0.21/0.44 tff(113,plain,
% 0.21/0.44 (^[U: $i, V: $i, W: $i] : trans(monotonicity(rewrite(((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X))) <=> ((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))), ((((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X))) & (check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V)))))) <=> (((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X))) & (check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V)))))))), rewrite((((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X))) & (check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V)))))) <=> (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V))))))))), ((((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X))) & (check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V)))))) <=> (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V))))))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(114,plain,
% 0.21/0.44 (![U: $i, V: $i, W: $i] : (((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X))) & (check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V)))))) <=> ![U: $i, V: $i, W: $i] : (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V))))))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[113])).
% 0.21/0.44 tff(115,plain,
% 0.21/0.44 (![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) <=> ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X))) <=> ![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) <=> ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(116,plain,
% 0.21/0.44 (^[U: $i, V: $i, W: $i] : rewrite((check_cpq(triple(U, V, W)) <=> ![X: $i, Y: $i] : (pair_in_list(V, X, Y) => less_than(Y, X))) <=> (check_cpq(triple(U, V, W)) <=> ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(117,plain,
% 0.21/0.44 (![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) <=> ![X: $i, Y: $i] : (pair_in_list(V, X, Y) => less_than(Y, X))) <=> ![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) <=> ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[116])).
% 0.21/0.44 tff(118,axiom,(![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) <=> ![X: $i, Y: $i] : (pair_in_list(V, X, Y) => less_than(Y, X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l43_li4142')).
% 0.21/0.44 tff(119,plain,
% 0.21/0.44 (![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) <=> ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.21/0.44 tff(120,plain,
% 0.21/0.44 (![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) <=> ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[119, 115])).
% 0.21/0.44 tff(121,plain,(
% 0.21/0.44 ![U: $i, V: $i, W: $i] : (((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X))) & (check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V))))))),
% 0.21/0.44 inference(skolemize,[status(sab)],[120])).
% 0.21/0.44 tff(122,plain,
% 0.21/0.44 (![U: $i, V: $i, W: $i] : (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V))))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[121, 114])).
% 0.21/0.44 tff(123,plain,
% 0.21/0.44 (![U: $i, V: $i, W: $i] : (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V))))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[122, 112])).
% 0.21/0.44 tff(124,plain,
% 0.21/0.44 ((~![U: $i, V: $i, W: $i] : (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V))))))))) | (~((~((~check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad))) | ![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad)) | (~((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), tptp_fun_X_1(update_slb(V!4, findmin_pqp_res(U!5))), tptp_fun_Y_0(update_slb(V!4, findmin_pqp_res(U!5))))) | less_than(tptp_fun_Y_0(update_slb(V!4, findmin_pqp_res(U!5))), tptp_fun_X_1(update_slb(V!4, findmin_pqp_res(U!5))))))))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(125,plain,
% 0.21/0.44 (~((~((~check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad))) | ![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad)) | (~((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), tptp_fun_X_1(update_slb(V!4, findmin_pqp_res(U!5))), tptp_fun_Y_0(update_slb(V!4, findmin_pqp_res(U!5))))) | less_than(tptp_fun_Y_0(update_slb(V!4, findmin_pqp_res(U!5))), tptp_fun_X_1(update_slb(V!4, findmin_pqp_res(U!5)))))))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[124, 123])).
% 0.21/0.44 tff(126,plain,
% 0.21/0.44 (((~((~check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad))) | ![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad)) | (~((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), tptp_fun_X_1(update_slb(V!4, findmin_pqp_res(U!5))), tptp_fun_Y_0(update_slb(V!4, findmin_pqp_res(U!5))))) | less_than(tptp_fun_Y_0(update_slb(V!4, findmin_pqp_res(U!5))), tptp_fun_X_1(update_slb(V!4, findmin_pqp_res(U!5))))))))) | ((~check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad))) | ![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X)))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(127,plain,
% 0.21/0.44 ((~check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad))) | ![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[126, 125])).
% 0.21/0.44 tff(128,assumption,(~![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X))), introduced(assumption)).
% 0.21/0.44 tff(129,plain,
% 0.21/0.44 ((~((~check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad))) | ![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X)))) | (~check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad))) | ![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(130,plain,
% 0.21/0.44 ((~((~check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad))) | ![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X)))) | (~check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[129, 128])).
% 0.21/0.44 tff(131,plain,
% 0.21/0.44 (~check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[130, 127])).
% 0.21/0.44 tff(132,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[131, 107])).
% 0.21/0.44 tff(133,plain,((~(findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad))) | ![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44 tff(134,plain,
% 0.21/0.44 (~(findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[133, 101])).
% 0.21/0.44 tff(135,plain,
% 0.21/0.44 (less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_cpq_res(triple(U!5, V!4, W!3))) <=> less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_pqp_res(U!5))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[67])).
% 0.21/0.44 tff(136,plain,
% 0.21/0.44 (less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_pqp_res(U!5)) <=> less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_cpq_res(triple(U!5, V!4, W!3)))),
% 0.21/0.44 inference(symmetry,[status(thm)],[135])).
% 0.21/0.44 tff(137,plain,
% 0.21/0.44 ((~less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_pqp_res(U!5))) <=> (~less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_cpq_res(triple(U!5, V!4, W!3))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[136])).
% 0.21/0.44 tff(138,assumption,(~(findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3))), introduced(assumption)).
% 0.21/0.44 tff(139,assumption,(~(findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad))), introduced(assumption)).
% 0.21/0.44 tff(140,plain,
% 0.21/0.44 (^[U: $i, V: $i, W: $i] : refl(((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(141,plain,
% 0.21/0.44 (![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[140])).
% 0.21/0.44 tff(142,plain,
% 0.21/0.44 (^[U: $i, V: $i, W: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U)))) <=> (~((V = create_slb) | contains_slb(V, findmin_pqp_res(U))))), ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) <=> (~(~((V = create_slb) | contains_slb(V, findmin_pqp_res(U))))))), rewrite((~(~((V = create_slb) | contains_slb(V, findmin_pqp_res(U))))) <=> ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)))), ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) <=> ((V = create_slb) | contains_slb(V, findmin_pqp_res(U))))), (((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> (((V = create_slb) | contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))))), rewrite((((V = create_slb) | contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))), (((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(143,plain,
% 0.21/0.44 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[142])).
% 0.21/0.44 tff(144,plain,
% 0.21/0.44 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(145,plain,
% 0.21/0.45 (![U: $i, V: $i, W: $i, X: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.21/0.45 inference(elim_unused_vars,[status(thm)],[])).
% 0.21/0.45 tff(146,plain,
% 0.21/0.45 (^[U: $i, V: $i, W: $i, X: $i] : rewrite((((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U)))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(147,plain,
% 0.21/0.45 (![U: $i, V: $i, W: $i, X: $i] : (((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U)))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[146])).
% 0.21/0.45 tff(148,plain,
% 0.21/0.45 (![U: $i, V: $i, W: $i, X: $i] : (((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U)))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.21/0.45 inference(transitivity,[status(thm)],[147, 145])).
% 0.21/0.45 tff(149,axiom,(![U: $i, V: $i, W: $i, X: $i] : (((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U)))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax','ax47')).
% 0.21/0.45 tff(150,plain,
% 0.21/0.45 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.21/0.45 tff(151,plain,
% 0.21/0.45 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[150, 144])).
% 0.21/0.45 tff(152,plain,(
% 0.21/0.45 ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.21/0.45 inference(skolemize,[status(sab)],[151])).
% 0.21/0.45 tff(153,plain,
% 0.21/0.45 (![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[152, 143])).
% 0.21/0.45 tff(154,plain,
% 0.21/0.45 (![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[153, 141])).
% 0.21/0.45 tff(155,plain,
% 0.21/0.45 (((~![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))) | ((V!4 = create_slb) | contains_slb(V!4, findmin_pqp_res(U!5)) | (findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad)))) <=> ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))) | (V!4 = create_slb) | contains_slb(V!4, findmin_pqp_res(U!5)) | (findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(156,plain,
% 0.21/0.45 ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))) | ((V!4 = create_slb) | contains_slb(V!4, findmin_pqp_res(U!5)) | (findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(157,plain,
% 0.21/0.45 ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))) | (V!4 = create_slb) | contains_slb(V!4, findmin_pqp_res(U!5)) | (findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.21/0.45 tff(158,plain,
% 0.21/0.45 ((V!4 = create_slb) | contains_slb(V!4, findmin_pqp_res(U!5)) | (findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[157, 154])).
% 0.21/0.45 tff(159,plain,
% 0.21/0.45 (contains_slb(V!4, findmin_pqp_res(U!5))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[158, 139, 65])).
% 0.21/0.45 tff(160,plain,
% 0.21/0.45 (^[U: $i, V: $i, W: $i] : refl(((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) <=> ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(161,plain,
% 0.21/0.45 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) <=> ![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[160])).
% 0.21/0.45 tff(162,plain,
% 0.21/0.45 (^[U: $i, V: $i, W: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))) <=> (~((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))))), ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) <=> (~(~((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))))))), rewrite((~(~((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))))) <=> ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))), ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) <=> ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))))), (((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))) <=> (((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))))), rewrite((((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))) <=> ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))), (((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))) <=> ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(163,plain,
% 0.21/0.45 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))) <=> ![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[162])).
% 0.21/0.45 tff(164,plain,
% 0.21/0.45 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))) <=> ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(165,plain,
% 0.21/0.45 (![U: $i, V: $i, W: $i, X: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))) <=> ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)))),
% 0.21/0.45 inference(elim_unused_vars,[status(thm)],[])).
% 0.21/0.45 tff(166,plain,
% 0.21/0.45 (^[U: $i, V: $i, W: $i, X: $i] : trans(monotonicity(rewrite((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))) <=> ((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))), (((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))) <=> (((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))))), rewrite((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))) <=> ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)))), (((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))) <=> ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(167,plain,
% 0.21/0.45 (![U: $i, V: $i, W: $i, X: $i] : ((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[166])).
% 0.21/0.45 tff(168,plain,
% 0.21/0.45 (![U: $i, V: $i, W: $i, X: $i] : ((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))) <=> ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)))),
% 0.21/0.45 inference(transitivity,[status(thm)],[167, 165])).
% 0.21/0.45 tff(169,axiom,(![U: $i, V: $i, W: $i, X: $i] : ((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax','ax49')).
% 0.21/0.45 tff(170,plain,
% 0.21/0.45 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.21/0.45 tff(171,plain,
% 0.21/0.45 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[170, 164])).
% 0.21/0.45 tff(172,plain,(
% 0.21/0.45 ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)))),
% 0.21/0.45 inference(skolemize,[status(sab)],[171])).
% 0.21/0.45 tff(173,plain,
% 0.21/0.45 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[172, 163])).
% 0.21/0.45 tff(174,plain,
% 0.21/0.45 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[173, 161])).
% 0.21/0.45 tff(175,plain,
% 0.21/0.45 (((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))) | ((V!4 = create_slb) | (~contains_slb(V!4, findmin_pqp_res(U!5))) | (findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3)) | (~less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_pqp_res(U!5))))) <=> ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))) | (V!4 = create_slb) | (~contains_slb(V!4, findmin_pqp_res(U!5))) | (findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3)) | (~less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_pqp_res(U!5))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(176,plain,
% 0.21/0.45 ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))) | ((V!4 = create_slb) | (~contains_slb(V!4, findmin_pqp_res(U!5))) | (findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3)) | (~less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_pqp_res(U!5))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(177,plain,
% 0.21/0.45 ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))) | (V!4 = create_slb) | (~contains_slb(V!4, findmin_pqp_res(U!5))) | (findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3)) | (~less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_pqp_res(U!5)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.21/0.46 tff(178,plain,
% 0.21/0.46 ((V!4 = create_slb) | (~contains_slb(V!4, findmin_pqp_res(U!5))) | (findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3)) | (~less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_pqp_res(U!5)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[177, 174])).
% 0.21/0.46 tff(179,plain,
% 0.21/0.46 (~less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_pqp_res(U!5))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[178, 159, 65, 138])).
% 0.21/0.46 tff(180,plain,
% 0.21/0.46 (~less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_cpq_res(triple(U!5, V!4, W!3)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[179, 137])).
% 0.21/0.46 tff(181,plain,
% 0.21/0.46 ((~![U: $i, V: $i] : (strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U))))) | (strictly_less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), lookup_slb(V!4, findmin_pqp_res(U!5))) <=> (~((~less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), lookup_slb(V!4, findmin_pqp_res(U!5)))) | less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_cpq_res(triple(U!5, V!4, W!3))))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(182,plain,
% 0.21/0.46 (strictly_less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), lookup_slb(V!4, findmin_pqp_res(U!5))) <=> (~((~less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), lookup_slb(V!4, findmin_pqp_res(U!5)))) | less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_cpq_res(triple(U!5, V!4, W!3)))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[181, 87])).
% 0.21/0.46 tff(183,plain,
% 0.21/0.46 (strictly_less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), lookup_slb(V!4, findmin_pqp_res(U!5))) <=> strictly_less_than(findmin_pqp_res(U!5), lookup_slb(V!4, findmin_pqp_res(U!5)))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[67])).
% 0.21/0.46 tff(184,plain,
% 0.21/0.46 (strictly_less_than(findmin_pqp_res(U!5), lookup_slb(V!4, findmin_pqp_res(U!5))) <=> strictly_less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), lookup_slb(V!4, findmin_pqp_res(U!5)))),
% 0.21/0.46 inference(symmetry,[status(thm)],[183])).
% 0.21/0.46 tff(185,plain,
% 0.21/0.46 ((~strictly_less_than(findmin_pqp_res(U!5), lookup_slb(V!4, findmin_pqp_res(U!5)))) <=> (~strictly_less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), lookup_slb(V!4, findmin_pqp_res(U!5))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[184])).
% 0.21/0.46 tff(186,plain,
% 0.21/0.46 (^[U: $i, V: $i, W: $i] : refl(((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) <=> ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(187,plain,
% 0.21/0.46 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) <=> ![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[186])).
% 0.21/0.46 tff(188,plain,
% 0.21/0.46 (^[U: $i, V: $i, W: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))) <=> (~((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))))), ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) <=> (~(~((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))))))), rewrite((~(~((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))))) <=> ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))))), ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) <=> ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))))), (((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> (((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))))), rewrite((((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))))), (((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(189,plain,
% 0.21/0.46 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[188])).
% 0.21/0.46 tff(190,plain,
% 0.21/0.46 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(191,plain,
% 0.21/0.46 (![U: $i, V: $i, W: $i, X: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.21/0.46 inference(elim_unused_vars,[status(thm)],[])).
% 0.21/0.46 tff(192,plain,
% 0.21/0.46 (^[U: $i, V: $i, W: $i, X: $i] : trans(monotonicity(rewrite((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))) <=> ((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))), (((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> (((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))))), rewrite((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))), (((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(193,plain,
% 0.21/0.46 (![U: $i, V: $i, W: $i, X: $i] : ((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[192])).
% 0.21/0.46 tff(194,plain,
% 0.21/0.46 (![U: $i, V: $i, W: $i, X: $i] : ((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.21/0.46 inference(transitivity,[status(thm)],[193, 191])).
% 0.21/0.46 tff(195,axiom,(![U: $i, V: $i, W: $i, X: $i] : ((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax','ax48')).
% 0.21/0.46 tff(196,plain,
% 0.21/0.46 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.21/0.46 tff(197,plain,
% 0.21/0.46 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[196, 190])).
% 0.21/0.46 tff(198,plain,(
% 0.21/0.46 ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.21/0.46 inference(skolemize,[status(sab)],[197])).
% 0.21/0.46 tff(199,plain,
% 0.21/0.46 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[198, 189])).
% 0.21/0.46 tff(200,plain,
% 0.21/0.46 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[199, 187])).
% 0.21/0.46 tff(201,plain,
% 0.21/0.46 (((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))))) | ((V!4 = create_slb) | (~contains_slb(V!4, findmin_pqp_res(U!5))) | (findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad)) | (~strictly_less_than(findmin_pqp_res(U!5), lookup_slb(V!4, findmin_pqp_res(U!5)))))) <=> ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))))) | (V!4 = create_slb) | (~contains_slb(V!4, findmin_pqp_res(U!5))) | (findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad)) | (~strictly_less_than(findmin_pqp_res(U!5), lookup_slb(V!4, findmin_pqp_res(U!5)))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(202,plain,
% 0.21/0.46 ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))))) | ((V!4 = create_slb) | (~contains_slb(V!4, findmin_pqp_res(U!5))) | (findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad)) | (~strictly_less_than(findmin_pqp_res(U!5), lookup_slb(V!4, findmin_pqp_res(U!5)))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(203,plain,
% 0.21/0.46 ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))))) | (V!4 = create_slb) | (~contains_slb(V!4, findmin_pqp_res(U!5))) | (findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad)) | (~strictly_less_than(findmin_pqp_res(U!5), lookup_slb(V!4, findmin_pqp_res(U!5))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.21/0.46 tff(204,plain,
% 0.21/0.46 ((V!4 = create_slb) | (~contains_slb(V!4, findmin_pqp_res(U!5))) | (findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad)) | (~strictly_less_than(findmin_pqp_res(U!5), lookup_slb(V!4, findmin_pqp_res(U!5))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[203, 200])).
% 0.21/0.46 tff(205,plain,
% 0.21/0.46 (~strictly_less_than(findmin_pqp_res(U!5), lookup_slb(V!4, findmin_pqp_res(U!5)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[204, 159, 65, 139])).
% 0.21/0.46 tff(206,plain,
% 0.21/0.46 (~strictly_less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), lookup_slb(V!4, findmin_pqp_res(U!5)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[205, 185])).
% 0.21/0.46 tff(207,plain,
% 0.21/0.46 ((~(strictly_less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), lookup_slb(V!4, findmin_pqp_res(U!5))) <=> (~((~less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), lookup_slb(V!4, findmin_pqp_res(U!5)))) | less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_cpq_res(triple(U!5, V!4, W!3))))))) | strictly_less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), lookup_slb(V!4, findmin_pqp_res(U!5))) | ((~less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), lookup_slb(V!4, findmin_pqp_res(U!5)))) | less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_cpq_res(triple(U!5, V!4, W!3))))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(208,plain,
% 0.21/0.46 ((~less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), lookup_slb(V!4, findmin_pqp_res(U!5)))) | less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_cpq_res(triple(U!5, V!4, W!3)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[207, 206, 182])).
% 0.21/0.46 tff(209,plain,
% 0.21/0.46 ((~((~less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), lookup_slb(V!4, findmin_pqp_res(U!5)))) | less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_cpq_res(triple(U!5, V!4, W!3))))) | (~less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), lookup_slb(V!4, findmin_pqp_res(U!5)))) | less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_cpq_res(triple(U!5, V!4, W!3)))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(210,plain,
% 0.21/0.46 (~less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), lookup_slb(V!4, findmin_pqp_res(U!5)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[209, 180, 208])).
% 0.21/0.46 tff(211,plain,
% 0.21/0.46 (^[U: $i, V: $i] : refl((less_than(V, U) | less_than(U, V)) <=> (less_than(V, U) | less_than(U, V)))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(212,plain,
% 0.21/0.46 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[211])).
% 0.21/0.46 tff(213,plain,
% 0.21/0.46 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(214,plain,
% 0.21/0.46 (^[U: $i, V: $i] : rewrite((less_than(U, V) | less_than(V, U)) <=> (less_than(V, U) | less_than(U, V)))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(215,plain,
% 0.21/0.46 (![U: $i, V: $i] : (less_than(U, V) | less_than(V, U)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[214])).
% 0.21/0.46 tff(216,axiom,(![U: $i, V: $i] : (less_than(U, V) | less_than(V, U))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+0.ax','totality')).
% 0.21/0.46 tff(217,plain,
% 0.21/0.46 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.21/0.46 tff(218,plain,
% 0.21/0.46 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[217, 213])).
% 0.21/0.46 tff(219,plain,(
% 0.21/0.46 ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.21/0.46 inference(skolemize,[status(sab)],[218])).
% 0.21/0.46 tff(220,plain,
% 0.21/0.46 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[219, 212])).
% 0.21/0.46 tff(221,plain,
% 0.21/0.46 (((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | (less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), lookup_slb(V!4, findmin_pqp_res(U!5))) | less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_cpq_res(triple(U!5, V!4, W!3))))) <=> ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), lookup_slb(V!4, findmin_pqp_res(U!5))) | less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_cpq_res(triple(U!5, V!4, W!3))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(222,plain,
% 0.21/0.46 ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | (less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), lookup_slb(V!4, findmin_pqp_res(U!5))) | less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_cpq_res(triple(U!5, V!4, W!3))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(223,plain,
% 0.21/0.46 ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), lookup_slb(V!4, findmin_pqp_res(U!5))) | less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_cpq_res(triple(U!5, V!4, W!3)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[222, 221])).
% 0.21/0.46 tff(224,plain,
% 0.21/0.46 (less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), lookup_slb(V!4, findmin_pqp_res(U!5))) | less_than(lookup_slb(V!4, findmin_pqp_res(U!5)), findmin_cpq_res(triple(U!5, V!4, W!3)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[223, 220])).
% 0.21/0.46 tff(225,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[224, 210, 180])).
% 0.21/0.46 tff(226,plain,((findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad)) | (V!4 = create_slb) | (findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.46 tff(227,plain,
% 0.21/0.46 (findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[226, 134, 65])).
% 0.21/0.46 tff(228,plain,
% 0.21/0.46 (triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3) = findmin_cpq_eff(triple(U!5, V!4, W!3))),
% 0.21/0.46 inference(symmetry,[status(thm)],[227])).
% 0.21/0.46 tff(229,plain,
% 0.21/0.46 (check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3)) <=> check_cpq(findmin_cpq_eff(triple(U!5, V!4, W!3)))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[228])).
% 0.21/0.46 tff(230,plain,
% 0.21/0.46 (check_cpq(findmin_cpq_eff(triple(U!5, V!4, W!3))) <=> check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3))),
% 0.21/0.46 inference(symmetry,[status(thm)],[229])).
% 0.21/0.46 tff(231,plain,
% 0.21/0.46 (check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[106, 230])).
% 0.21/0.46 tff(232,plain,
% 0.21/0.46 ((~![U: $i, V: $i, W: $i] : (~((~((~check_cpq(triple(U, V, W))) | ![X: $i, Y: $i] : ((~pair_in_list(V, X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U, V, W)) | (~((~pair_in_list(V, tptp_fun_X_1(V), tptp_fun_Y_0(V))) | less_than(tptp_fun_Y_0(V), tptp_fun_X_1(V))))))))) | (~((~((~check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3))) | ![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3)) | (~((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), tptp_fun_X_1(update_slb(V!4, findmin_pqp_res(U!5))), tptp_fun_Y_0(update_slb(V!4, findmin_pqp_res(U!5))))) | less_than(tptp_fun_Y_0(update_slb(V!4, findmin_pqp_res(U!5))), tptp_fun_X_1(update_slb(V!4, findmin_pqp_res(U!5))))))))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(233,plain,
% 0.21/0.46 (~((~((~check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3))) | ![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3)) | (~((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), tptp_fun_X_1(update_slb(V!4, findmin_pqp_res(U!5))), tptp_fun_Y_0(update_slb(V!4, findmin_pqp_res(U!5))))) | less_than(tptp_fun_Y_0(update_slb(V!4, findmin_pqp_res(U!5))), tptp_fun_X_1(update_slb(V!4, findmin_pqp_res(U!5)))))))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[232, 123])).
% 0.21/0.46 tff(234,plain,
% 0.21/0.46 (((~((~check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3))) | ![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X)))) | (~(check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3)) | (~((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), tptp_fun_X_1(update_slb(V!4, findmin_pqp_res(U!5))), tptp_fun_Y_0(update_slb(V!4, findmin_pqp_res(U!5))))) | less_than(tptp_fun_Y_0(update_slb(V!4, findmin_pqp_res(U!5))), tptp_fun_X_1(update_slb(V!4, findmin_pqp_res(U!5))))))))) | ((~check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3))) | ![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X)))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(235,plain,
% 0.21/0.46 ((~check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3))) | ![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[234, 233])).
% 0.21/0.46 tff(236,plain,
% 0.21/0.46 ((~((~check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3))) | ![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X)))) | (~check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3))) | ![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(237,plain,
% 0.21/0.46 ((~((~check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3))) | ![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X)))) | (~check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[236, 101])).
% 0.21/0.46 tff(238,plain,
% 0.21/0.46 (~check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[237, 235])).
% 0.21/0.46 tff(239,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[238, 231])).
% 0.21/0.46 tff(240,plain,((V!4 = create_slb) | (~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_pqp_res(U!5)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.46 tff(241,plain,
% 0.21/0.46 (~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_pqp_res(U!5))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[240, 45])).
% 0.21/0.46 tff(242,plain,
% 0.21/0.46 (^[U: $i, V: $i, W: $i, X: $i] : refl(((~contains_slb(V, X)) | pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))) | (~((~pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U))) | (~less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U)))))) <=> ((~contains_slb(V, X)) | pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))) | (~((~pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U))) | (~less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U)))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(243,plain,
% 0.21/0.47 (![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))) | (~((~pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U))) | (~less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U)))))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))) | (~((~pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U))) | (~less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U))))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[242])).
% 0.21/0.47 tff(244,plain,
% 0.21/0.47 (^[U: $i, V: $i, W: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((contains_slb(V, X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))) <=> (~((~contains_slb(V, X)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))))), ((~(contains_slb(V, X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))) <=> (~(~((~contains_slb(V, X)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))))))), rewrite((~(~((~contains_slb(V, X)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))))) <=> ((~contains_slb(V, X)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))))), ((~(contains_slb(V, X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))) <=> ((~contains_slb(V, X)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))))), rewrite((pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U)) & less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U))) <=> (~((~pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U))) | (~less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U)))))), ((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))))) | (pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U)) & less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U)))) <=> (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))))) | (~((~pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U))) | (~less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U)))))))), rewrite((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))))) | (~((~pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U))) | (~less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U)))))) <=> ((~contains_slb(V, X)) | pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))) | (~((~pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U))) | (~less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U))))))), ((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))))) | (pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U)) & less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U)))) <=> ((~contains_slb(V, X)) | pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))) | (~((~pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U))) | (~less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U))))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(245,plain,
% 0.21/0.47 (![U: $i, V: $i, W: $i, X: $i] : (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))))) | (pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U)) & less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U)))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))) | (~((~pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U))) | (~less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U))))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[244])).
% 0.21/0.47 tff(246,plain,
% 0.21/0.47 (^[U: $i, V: $i, W: $i, X: $i] : rewrite(((pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U)) & less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U))) | 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)))))) <=> (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))))) | (pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U)) & less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U)))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(247,plain,
% 0.21/0.47 (![U: $i, V: $i, W: $i, X: $i] : ((pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U)) & less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U))) | 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] : (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))))) | (pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U)) & less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[246])).
% 0.21/0.47 tff(248,plain,
% 0.21/0.47 (![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))))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(249,plain,
% 0.21/0.47 (^[U: $i, V: $i, W: $i, X: $i] : trans(monotonicity(rewrite((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))) <=> (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)))), (((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)))) <=> ((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)))))), rewrite(((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)))) <=> (?[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))))))), (((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)))) <=> (?[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))))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(250,plain,
% 0.21/0.47 (![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))))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[249])).
% 0.21/0.47 tff(251,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','l43_l44')).
% 0.21/0.47 tff(252,plain,
% 0.21/0.47 (![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))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.21/0.47 tff(253,plain,
% 0.21/0.47 (![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))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[252, 248])).
% 0.21/0.47 tff(254,plain,(
% 0.21/0.47 ![U: $i, V: $i, W: $i, X: $i] : ((pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U)) & less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U))) | 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))))))),
% 0.21/0.47 inference(skolemize,[status(sab)],[253])).
% 0.21/0.47 tff(255,plain,
% 0.21/0.47 (![U: $i, V: $i, W: $i, X: $i] : (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))))) | (pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U)) & less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[254, 247])).
% 0.21/0.47 tff(256,plain,
% 0.21/0.47 (![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))) | (~((~pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U))) | (~less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[255, 245])).
% 0.21/0.47 tff(257,plain,
% 0.21/0.47 (![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))) | (~((~pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U))) | (~less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[256, 243])).
% 0.21/0.47 tff(258,plain,
% 0.21/0.47 (((~![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))) | (~((~pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U))) | (~less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U))))))) | ((~contains_slb(V!4, X!6)) | (~strictly_less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))) | pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_pqp_res(U!5)) | (~((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, tptp_fun_Y_2(X!6, V!4, U!5))) | (~less_than(findmin_pqp_res(U!5), tptp_fun_Y_2(X!6, V!4, U!5))))))) <=> ((~![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))) | (~((~pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U))) | (~less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U))))))) | (~contains_slb(V!4, X!6)) | (~strictly_less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))) | pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_pqp_res(U!5)) | (~((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, tptp_fun_Y_2(X!6, V!4, U!5))) | (~less_than(findmin_pqp_res(U!5), tptp_fun_Y_2(X!6, V!4, U!5))))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(259,plain,
% 0.21/0.47 (((~contains_slb(V!4, X!6)) | pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_pqp_res(U!5)) | (~strictly_less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))) | (~((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, tptp_fun_Y_2(X!6, V!4, U!5))) | (~less_than(findmin_pqp_res(U!5), tptp_fun_Y_2(X!6, V!4, U!5)))))) <=> ((~contains_slb(V!4, X!6)) | (~strictly_less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))) | pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_pqp_res(U!5)) | (~((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, tptp_fun_Y_2(X!6, V!4, U!5))) | (~less_than(findmin_pqp_res(U!5), tptp_fun_Y_2(X!6, V!4, U!5))))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(260,plain,
% 0.21/0.47 ((~((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, tptp_fun_Y_2(X!6, V!4, U!5))) | (~less_than(findmin_pqp_res(U!5), tptp_fun_Y_2(X!6, V!4, U!5))))) <=> (~((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, tptp_fun_Y_2(X!6, V!4, U!5))) | (~less_than(findmin_pqp_res(U!5), tptp_fun_Y_2(X!6, V!4, U!5)))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(261,plain,
% 0.21/0.47 (((~contains_slb(V!4, X!6)) | pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_pqp_res(U!5)) | (~strictly_less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))) | (~((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, tptp_fun_Y_2(X!6, V!4, U!5))) | (~less_than(findmin_pqp_res(U!5), tptp_fun_Y_2(X!6, V!4, U!5)))))) <=> ((~contains_slb(V!4, X!6)) | pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_pqp_res(U!5)) | (~strictly_less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))) | (~((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, tptp_fun_Y_2(X!6, V!4, U!5))) | (~less_than(findmin_pqp_res(U!5), tptp_fun_Y_2(X!6, V!4, U!5))))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[260])).
% 0.21/0.47 tff(262,plain,
% 0.21/0.47 (((~contains_slb(V!4, X!6)) | pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_pqp_res(U!5)) | (~strictly_less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))) | (~((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, tptp_fun_Y_2(X!6, V!4, U!5))) | (~less_than(findmin_pqp_res(U!5), tptp_fun_Y_2(X!6, V!4, U!5)))))) <=> ((~contains_slb(V!4, X!6)) | (~strictly_less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))) | pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_pqp_res(U!5)) | (~((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, tptp_fun_Y_2(X!6, V!4, U!5))) | (~less_than(findmin_pqp_res(U!5), tptp_fun_Y_2(X!6, V!4, U!5))))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[261, 259])).
% 0.21/0.47 tff(263,plain,
% 0.21/0.47 (((~![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))) | (~((~pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U))) | (~less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U))))))) | ((~contains_slb(V!4, X!6)) | pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_pqp_res(U!5)) | (~strictly_less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))) | (~((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, tptp_fun_Y_2(X!6, V!4, U!5))) | (~less_than(findmin_pqp_res(U!5), tptp_fun_Y_2(X!6, V!4, U!5))))))) <=> ((~![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))) | (~((~pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U))) | (~less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U))))))) | ((~contains_slb(V!4, X!6)) | (~strictly_less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))) | pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_pqp_res(U!5)) | (~((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, tptp_fun_Y_2(X!6, V!4, U!5))) | (~less_than(findmin_pqp_res(U!5), tptp_fun_Y_2(X!6, V!4, U!5)))))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[262])).
% 0.21/0.47 tff(264,plain,
% 0.21/0.47 (((~![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))) | (~((~pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U))) | (~less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U))))))) | ((~contains_slb(V!4, X!6)) | pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_pqp_res(U!5)) | (~strictly_less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))) | (~((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, tptp_fun_Y_2(X!6, V!4, U!5))) | (~less_than(findmin_pqp_res(U!5), tptp_fun_Y_2(X!6, V!4, U!5))))))) <=> ((~![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))) | (~((~pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U))) | (~less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U))))))) | (~contains_slb(V!4, X!6)) | (~strictly_less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))) | pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_pqp_res(U!5)) | (~((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, tptp_fun_Y_2(X!6, V!4, U!5))) | (~less_than(findmin_pqp_res(U!5), tptp_fun_Y_2(X!6, V!4, U!5))))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[263, 258])).
% 0.21/0.47 tff(265,plain,
% 0.21/0.47 ((~![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))) | (~((~pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U))) | (~less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U))))))) | ((~contains_slb(V!4, X!6)) | pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_pqp_res(U!5)) | (~strictly_less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))) | (~((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, tptp_fun_Y_2(X!6, V!4, U!5))) | (~less_than(findmin_pqp_res(U!5), tptp_fun_Y_2(X!6, V!4, U!5))))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(266,plain,
% 0.21/0.47 ((~![U: $i, V: $i, W: $i, X: $i] : ((~contains_slb(V, X)) | pair_in_list(update_slb(V, findmin_pqp_res(U)), X, findmin_pqp_res(U)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))) | (~((~pair_in_list(update_slb(V, findmin_pqp_res(U)), X, tptp_fun_Y_2(X, V, U))) | (~less_than(findmin_pqp_res(U), tptp_fun_Y_2(X, V, U))))))) | (~contains_slb(V!4, X!6)) | (~strictly_less_than(X!6, findmin_cpq_res(triple(U!5, V!4, W!3)))) | pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_pqp_res(U!5)) | (~((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, tptp_fun_Y_2(X!6, V!4, U!5))) | (~less_than(findmin_pqp_res(U!5), tptp_fun_Y_2(X!6, V!4, U!5)))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[265, 264])).
% 0.21/0.47 tff(267,plain,
% 0.21/0.47 ((~contains_slb(V!4, X!6)) | pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_pqp_res(U!5)) | (~((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, tptp_fun_Y_2(X!6, V!4, U!5))) | (~less_than(findmin_pqp_res(U!5), tptp_fun_Y_2(X!6, V!4, U!5)))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[266, 257, 90])).
% 0.21/0.47 tff(268,plain,
% 0.21/0.47 (pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, findmin_pqp_res(U!5)) | (~((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, tptp_fun_Y_2(X!6, V!4, U!5))) | (~less_than(findmin_pqp_res(U!5), tptp_fun_Y_2(X!6, V!4, U!5)))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[267, 33])).
% 0.21/0.47 tff(269,plain,
% 0.21/0.47 (~((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, tptp_fun_Y_2(X!6, V!4, U!5))) | (~less_than(findmin_pqp_res(U!5), tptp_fun_Y_2(X!6, V!4, U!5))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[268, 241])).
% 0.21/0.47 tff(270,plain,
% 0.21/0.47 (((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, tptp_fun_Y_2(X!6, V!4, U!5))) | (~less_than(findmin_pqp_res(U!5), tptp_fun_Y_2(X!6, V!4, U!5)))) | less_than(findmin_pqp_res(U!5), tptp_fun_Y_2(X!6, V!4, U!5))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(271,plain,
% 0.21/0.47 (less_than(findmin_pqp_res(U!5), tptp_fun_Y_2(X!6, V!4, U!5))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[270, 269])).
% 0.21/0.47 tff(272,plain,
% 0.21/0.47 (less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_Y_2(X!6, V!4, U!5))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[271, 64])).
% 0.21/0.47 tff(273,plain,
% 0.21/0.47 (![U: $i, V: $i, W: $i] : (less_than(U, W) | (~less_than(V, W)) | (~less_than(U, V))) <=> ![U: $i, V: $i, W: $i] : (less_than(U, W) | (~less_than(V, W)) | (~less_than(U, V)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(274,plain,
% 0.21/0.47 (^[U: $i, V: $i, W: $i] : trans(monotonicity(trans(monotonicity(rewrite((less_than(U, V) & less_than(V, W)) <=> (~((~less_than(V, W)) | (~less_than(U, V))))), ((~(less_than(U, V) & less_than(V, W))) <=> (~(~((~less_than(V, W)) | (~less_than(U, V))))))), rewrite((~(~((~less_than(V, W)) | (~less_than(U, V))))) <=> ((~less_than(V, W)) | (~less_than(U, V)))), ((~(less_than(U, V) & less_than(V, W))) <=> ((~less_than(V, W)) | (~less_than(U, V))))), (((~(less_than(U, V) & less_than(V, W))) | less_than(U, W)) <=> (((~less_than(V, W)) | (~less_than(U, V))) | less_than(U, W)))), rewrite((((~less_than(V, W)) | (~less_than(U, V))) | less_than(U, W)) <=> (less_than(U, W) | (~less_than(V, W)) | (~less_than(U, V)))), (((~(less_than(U, V) & less_than(V, W))) | less_than(U, W)) <=> (less_than(U, W) | (~less_than(V, W)) | (~less_than(U, V)))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(275,plain,
% 0.21/0.47 (![U: $i, V: $i, W: $i] : ((~(less_than(U, V) & less_than(V, W))) | less_than(U, W)) <=> ![U: $i, V: $i, W: $i] : (less_than(U, W) | (~less_than(V, W)) | (~less_than(U, V)))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[274])).
% 0.21/0.47 tff(276,plain,
% 0.21/0.47 (![U: $i, V: $i, W: $i] : ((~(less_than(U, V) & less_than(V, W))) | less_than(U, W)) <=> ![U: $i, V: $i, W: $i] : ((~(less_than(U, V) & less_than(V, W))) | less_than(U, W))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(277,plain,
% 0.21/0.47 (^[U: $i, V: $i, W: $i] : rewrite(((less_than(U, V) & less_than(V, W)) => less_than(U, W)) <=> ((~(less_than(U, V) & less_than(V, W))) | less_than(U, W)))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(278,plain,
% 0.21/0.47 (![U: $i, V: $i, W: $i] : ((less_than(U, V) & less_than(V, W)) => less_than(U, W)) <=> ![U: $i, V: $i, W: $i] : ((~(less_than(U, V) & less_than(V, W))) | less_than(U, W))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[277])).
% 0.21/0.47 tff(279,axiom,(![U: $i, V: $i, W: $i] : ((less_than(U, V) & less_than(V, W)) => less_than(U, W))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+0.ax','transitivity')).
% 0.21/0.47 tff(280,plain,
% 0.21/0.47 (![U: $i, V: $i, W: $i] : ((~(less_than(U, V) & less_than(V, W))) | less_than(U, W))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[279, 278])).
% 0.21/0.47 tff(281,plain,
% 0.21/0.47 (![U: $i, V: $i, W: $i] : ((~(less_than(U, V) & less_than(V, W))) | less_than(U, W))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[280, 276])).
% 0.21/0.47 tff(282,plain,(
% 0.21/0.47 ![U: $i, V: $i, W: $i] : ((~(less_than(U, V) & less_than(V, W))) | less_than(U, W))),
% 0.21/0.47 inference(skolemize,[status(sab)],[281])).
% 0.21/0.47 tff(283,plain,
% 0.21/0.47 (![U: $i, V: $i, W: $i] : (less_than(U, W) | (~less_than(V, W)) | (~less_than(U, V)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[282, 275])).
% 0.21/0.47 tff(284,plain,
% 0.21/0.47 (![U: $i, V: $i, W: $i] : (less_than(U, W) | (~less_than(V, W)) | (~less_than(U, V)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[283, 273])).
% 0.21/0.47 tff(285,plain,
% 0.21/0.47 (((~![U: $i, V: $i, W: $i] : (less_than(U, W) | (~less_than(V, W)) | (~less_than(U, V)))) | (less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), X!6) | (~less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_Y_2(X!6, V!4, U!5))) | (~less_than(tptp_fun_Y_2(X!6, V!4, U!5), X!6)))) <=> ((~![U: $i, V: $i, W: $i] : (less_than(U, W) | (~less_than(V, W)) | (~less_than(U, V)))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), X!6) | (~less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_Y_2(X!6, V!4, U!5))) | (~less_than(tptp_fun_Y_2(X!6, V!4, U!5), X!6)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(286,plain,
% 0.21/0.47 ((less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), X!6) | (~less_than(tptp_fun_Y_2(X!6, V!4, U!5), X!6)) | (~less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_Y_2(X!6, V!4, U!5)))) <=> (less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), X!6) | (~less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_Y_2(X!6, V!4, U!5))) | (~less_than(tptp_fun_Y_2(X!6, V!4, U!5), X!6)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(287,plain,
% 0.21/0.47 (((~![U: $i, V: $i, W: $i] : (less_than(U, W) | (~less_than(V, W)) | (~less_than(U, V)))) | (less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), X!6) | (~less_than(tptp_fun_Y_2(X!6, V!4, U!5), X!6)) | (~less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_Y_2(X!6, V!4, U!5))))) <=> ((~![U: $i, V: $i, W: $i] : (less_than(U, W) | (~less_than(V, W)) | (~less_than(U, V)))) | (less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), X!6) | (~less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_Y_2(X!6, V!4, U!5))) | (~less_than(tptp_fun_Y_2(X!6, V!4, U!5), X!6))))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[286])).
% 0.21/0.47 tff(288,plain,
% 0.21/0.47 (((~![U: $i, V: $i, W: $i] : (less_than(U, W) | (~less_than(V, W)) | (~less_than(U, V)))) | (less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), X!6) | (~less_than(tptp_fun_Y_2(X!6, V!4, U!5), X!6)) | (~less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_Y_2(X!6, V!4, U!5))))) <=> ((~![U: $i, V: $i, W: $i] : (less_than(U, W) | (~less_than(V, W)) | (~less_than(U, V)))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), X!6) | (~less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_Y_2(X!6, V!4, U!5))) | (~less_than(tptp_fun_Y_2(X!6, V!4, U!5), X!6)))),
% 0.21/0.48 inference(transitivity,[status(thm)],[287, 285])).
% 0.21/0.48 tff(289,plain,
% 0.21/0.48 ((~![U: $i, V: $i, W: $i] : (less_than(U, W) | (~less_than(V, W)) | (~less_than(U, V)))) | (less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), X!6) | (~less_than(tptp_fun_Y_2(X!6, V!4, U!5), X!6)) | (~less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_Y_2(X!6, V!4, U!5))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(290,plain,
% 0.21/0.48 ((~![U: $i, V: $i, W: $i] : (less_than(U, W) | (~less_than(V, W)) | (~less_than(U, V)))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), X!6) | (~less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_Y_2(X!6, V!4, U!5))) | (~less_than(tptp_fun_Y_2(X!6, V!4, U!5), X!6))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[289, 288])).
% 0.21/0.48 tff(291,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[290, 284, 95, 272, 1])).
% 0.21/0.48 tff(292,plain,(~less_than(tptp_fun_Y_2(X!6, V!4, U!5), X!6)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(293,plain,
% 0.21/0.48 (((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, tptp_fun_Y_2(X!6, V!4, U!5))) | (~less_than(findmin_pqp_res(U!5), tptp_fun_Y_2(X!6, V!4, U!5)))) | pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, tptp_fun_Y_2(X!6, V!4, U!5))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(294,plain,
% 0.21/0.48 (pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, tptp_fun_Y_2(X!6, V!4, U!5))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[293, 269])).
% 0.21/0.48 tff(295,plain,
% 0.21/0.48 (((~![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X))) | ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, tptp_fun_Y_2(X!6, V!4, U!5))) | less_than(tptp_fun_Y_2(X!6, V!4, U!5), X!6))) <=> ((~![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X))) | (~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, tptp_fun_Y_2(X!6, V!4, U!5))) | less_than(tptp_fun_Y_2(X!6, V!4, U!5), X!6))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(296,plain,
% 0.21/0.48 ((~![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X))) | ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, tptp_fun_Y_2(X!6, V!4, U!5))) | less_than(tptp_fun_Y_2(X!6, V!4, U!5), X!6))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(297,plain,
% 0.21/0.48 ((~![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X))) | (~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X!6, tptp_fun_Y_2(X!6, V!4, U!5))) | less_than(tptp_fun_Y_2(X!6, V!4, U!5), X!6)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[296, 295])).
% 0.21/0.48 tff(298,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[297, 294, 76, 292])).
% 0.21/0.48 tff(299,plain,(~![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(300,plain,
% 0.21/0.48 (~(findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[133, 299])).
% 0.21/0.48 tff(301,plain,
% 0.21/0.48 ((findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad)) | (findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[226, 45])).
% 0.21/0.48 tff(302,plain,
% 0.21/0.48 (findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[301, 300])).
% 0.21/0.48 tff(303,plain,
% 0.21/0.48 (triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3) = findmin_cpq_eff(triple(U!5, V!4, W!3))),
% 0.21/0.48 inference(symmetry,[status(thm)],[302])).
% 0.21/0.48 tff(304,plain,
% 0.21/0.48 (check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3)) <=> check_cpq(findmin_cpq_eff(triple(U!5, V!4, W!3)))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[303])).
% 0.21/0.48 tff(305,plain,
% 0.21/0.48 (check_cpq(findmin_cpq_eff(triple(U!5, V!4, W!3))) <=> check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3))),
% 0.21/0.48 inference(symmetry,[status(thm)],[304])).
% 0.21/0.48 tff(306,plain,
% 0.21/0.48 (check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[106, 305])).
% 0.21/0.48 tff(307,plain,
% 0.21/0.48 ((~((~check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3))) | ![X: $i, Y: $i] : ((~pair_in_list(update_slb(V!4, findmin_pqp_res(U!5)), X, Y)) | less_than(Y, X)))) | (~check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[236, 299])).
% 0.21/0.48 tff(308,plain,
% 0.21/0.48 (~check_cpq(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), W!3))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[307, 235])).
% 0.21/0.48 tff(309,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[308, 306])).
% 0.21/0.48 % SZS output end Proof
%------------------------------------------------------------------------------