TSTP Solution File: SWV379+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV379+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 15:11:32 EDT 2022
% Result : Theorem 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWV379+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Sep 4 03:01:51 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.40 % SZS status Theorem
% 0.19/0.40 % SZS output start Proof
% 0.19/0.40 tff(triple_type, type, (
% 0.19/0.40 triple: ( $i * $i * $i ) > $i)).
% 0.19/0.40 tff(bad_type, type, (
% 0.19/0.40 bad: $i)).
% 0.19/0.40 tff(update_slb_type, type, (
% 0.19/0.40 update_slb: ( $i * $i ) > $i)).
% 0.19/0.40 tff(findmin_pqp_res_type, type, (
% 0.19/0.40 findmin_pqp_res: $i > $i)).
% 0.19/0.40 tff(tptp_fun_U_2_type, type, (
% 0.19/0.40 tptp_fun_U_2: $i)).
% 0.19/0.40 tff(tptp_fun_V_1_type, type, (
% 0.19/0.40 tptp_fun_V_1: $i)).
% 0.19/0.40 tff(findmin_cpq_eff_type, type, (
% 0.19/0.40 findmin_cpq_eff: $i > $i)).
% 0.19/0.40 tff(tptp_fun_W_0_type, type, (
% 0.19/0.40 tptp_fun_W_0: $i)).
% 0.19/0.40 tff(ok_type, type, (
% 0.19/0.40 ok: $i > $o)).
% 0.19/0.40 tff(create_slb_type, type, (
% 0.19/0.40 create_slb: $i)).
% 0.19/0.40 tff(less_than_type, type, (
% 0.19/0.40 less_than: ( $i * $i ) > $o)).
% 0.19/0.40 tff(findmin_cpq_res_type, type, (
% 0.19/0.40 findmin_cpq_res: $i > $i)).
% 0.19/0.40 tff(lookup_slb_type, type, (
% 0.19/0.40 lookup_slb: ( $i * $i ) > $i)).
% 0.19/0.40 tff(contains_slb_type, type, (
% 0.19/0.40 contains_slb: ( $i * $i ) > $o)).
% 0.19/0.40 tff(strictly_less_than_type, type, (
% 0.19/0.40 strictly_less_than: ( $i * $i ) > $o)).
% 0.19/0.40 tff(1,plain,
% 0.19/0.40 ((~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~ok(findmin_cpq_eff(triple(U, V, W)))))) <=> (~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~ok(findmin_cpq_eff(triple(U, V, W))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(2,plain,
% 0.19/0.40 ((~![U: $i, V: $i, W: $i] : ((~ok(triple(U, V, W))) => (~ok(findmin_cpq_eff(triple(U, V, W)))))) <=> (~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~ok(findmin_cpq_eff(triple(U, V, W))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(3,axiom,(~![U: $i, V: $i, W: $i] : ((~ok(triple(U, V, W))) => (~ok(findmin_cpq_eff(triple(U, V, W)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l15_co')).
% 0.19/0.40 tff(4,plain,
% 0.19/0.40 (~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~ok(findmin_cpq_eff(triple(U, V, W)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.19/0.40 tff(5,plain,
% 0.19/0.40 (~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~ok(findmin_cpq_eff(triple(U, V, W)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.19/0.40 tff(6,plain,
% 0.19/0.40 (~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~ok(findmin_cpq_eff(triple(U, V, W)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.19/0.40 tff(7,plain,
% 0.19/0.40 (~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~ok(findmin_cpq_eff(triple(U, V, W)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.19/0.40 tff(8,plain,
% 0.19/0.40 (~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~ok(findmin_cpq_eff(triple(U, V, W)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.19/0.40 tff(9,plain,
% 0.19/0.40 (~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~ok(findmin_cpq_eff(triple(U, V, W)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.19/0.40 tff(10,plain,
% 0.19/0.40 (~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~ok(findmin_cpq_eff(triple(U, V, W)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.19/0.40 tff(11,plain,(
% 0.19/0.40 ~(ok(triple(U!2, V!1, W!0)) | (~ok(findmin_cpq_eff(triple(U!2, V!1, W!0)))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[10])).
% 0.19/0.40 tff(12,plain,
% 0.19/0.40 (~ok(triple(U!2, V!1, W!0))),
% 0.19/0.40 inference(or_elim,[status(thm)],[11])).
% 0.19/0.40 tff(13,plain,
% 0.19/0.40 (^[U: $i, V: $i, W: $i] : refl((ok(triple(U, V, W)) | (W = bad)) <=> (ok(triple(U, V, W)) | (W = bad)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(14,plain,
% 0.19/0.40 (![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad)) <=> ![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[13])).
% 0.19/0.40 tff(15,plain,
% 0.19/0.40 (![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad)) <=> ![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(16,plain,
% 0.19/0.40 (^[U: $i, V: $i, W: $i] : rewrite(((~ok(triple(U, V, W))) => (W = bad)) <=> (ok(triple(U, V, W)) | (W = bad)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(17,plain,
% 0.19/0.40 (![U: $i, V: $i, W: $i] : ((~ok(triple(U, V, W))) => (W = bad)) <=> ![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[16])).
% 0.19/0.40 tff(18,axiom,(![U: $i, V: $i, W: $i] : ((~ok(triple(U, V, W))) => (W = bad))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax','ax41')).
% 0.19/0.40 tff(19,plain,
% 0.19/0.40 (![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.19/0.40 tff(20,plain,
% 0.19/0.40 (![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.19/0.40 tff(21,plain,(
% 0.19/0.40 ![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))),
% 0.19/0.40 inference(skolemize,[status(sab)],[20])).
% 0.19/0.40 tff(22,plain,
% 0.19/0.40 (![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.19/0.40 tff(23,plain,
% 0.19/0.40 (((~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))) | (ok(triple(U!2, V!1, W!0)) | (W!0 = bad))) <=> ((~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))) | ok(triple(U!2, V!1, W!0)) | (W!0 = bad))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(24,plain,
% 0.19/0.40 ((~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))) | (ok(triple(U!2, V!1, W!0)) | (W!0 = bad))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(25,plain,
% 0.19/0.40 ((~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))) | ok(triple(U!2, V!1, W!0)) | (W!0 = bad)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.19/0.40 tff(26,plain,
% 0.19/0.40 (W!0 = bad),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[25, 22, 12])).
% 0.19/0.40 tff(27,plain,
% 0.19/0.40 (bad = W!0),
% 0.19/0.40 inference(symmetry,[status(thm)],[26])).
% 0.19/0.40 tff(28,assumption,(~(V!1 = create_slb)), introduced(assumption)).
% 0.19/0.40 tff(29,plain,
% 0.19/0.40 (^[U: $i, V: $i, W: $i] : refl(((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U))) <=> ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(30,plain,
% 0.19/0.40 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U))) <=> ![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[29])).
% 0.19/0.40 tff(31,plain,
% 0.19/0.40 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U))) <=> ![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(32,plain,
% 0.19/0.40 (![U: $i, V: $i, W: $i, X: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U))) <=> ![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.19/0.40 inference(elim_unused_vars,[status(thm)],[])).
% 0.19/0.40 tff(33,plain,
% 0.19/0.40 (^[U: $i, V: $i, W: $i, X: $i] : rewrite(((~(V = create_slb)) => (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U))) <=> ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(34,plain,
% 0.19/0.40 (![U: $i, V: $i, W: $i, X: $i] : ((~(V = create_slb)) => (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[33])).
% 0.19/0.40 tff(35,plain,
% 0.19/0.40 (![U: $i, V: $i, W: $i, X: $i] : ((~(V = create_slb)) => (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U))) <=> ![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.19/0.40 inference(transitivity,[status(thm)],[34, 32])).
% 0.19/0.40 tff(36,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')).
% 0.19/0.40 tff(37,plain,
% 0.19/0.40 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.19/0.40 tff(38,plain,
% 0.19/0.40 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[37, 31])).
% 0.19/0.40 tff(39,plain,(
% 0.19/0.40 ![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[38])).
% 0.19/0.40 tff(40,plain,
% 0.19/0.40 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[39, 30])).
% 0.19/0.41 tff(41,plain,
% 0.19/0.41 (((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))) | ((V!1 = create_slb) | (findmin_cpq_res(triple(U!2, V!1, W!0)) = findmin_pqp_res(U!2)))) <=> ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))) | (V!1 = create_slb) | (findmin_cpq_res(triple(U!2, V!1, W!0)) = findmin_pqp_res(U!2)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(42,plain,
% 0.19/0.41 ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))) | ((V!1 = create_slb) | (findmin_cpq_res(triple(U!2, V!1, W!0)) = findmin_pqp_res(U!2)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(43,plain,
% 0.19/0.41 ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))) | (V!1 = create_slb) | (findmin_cpq_res(triple(U!2, V!1, W!0)) = findmin_pqp_res(U!2))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.19/0.41 tff(44,plain,
% 0.19/0.41 ((V!1 = create_slb) | (findmin_cpq_res(triple(U!2, V!1, W!0)) = findmin_pqp_res(U!2))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[43, 40])).
% 0.19/0.41 tff(45,plain,
% 0.19/0.41 (findmin_cpq_res(triple(U!2, V!1, W!0)) = findmin_pqp_res(U!2)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[44, 28])).
% 0.19/0.41 tff(46,plain,
% 0.19/0.41 (less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_cpq_res(triple(U!2, V!1, W!0))) <=> less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_pqp_res(U!2))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[45])).
% 0.19/0.41 tff(47,plain,
% 0.19/0.41 (less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_pqp_res(U!2)) <=> less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_cpq_res(triple(U!2, V!1, W!0)))),
% 0.19/0.41 inference(symmetry,[status(thm)],[46])).
% 0.19/0.41 tff(48,plain,
% 0.19/0.41 ((~less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_pqp_res(U!2))) <=> (~less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_cpq_res(triple(U!2, V!1, W!0))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[47])).
% 0.19/0.41 tff(49,plain,
% 0.19/0.41 (triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[26])).
% 0.19/0.41 tff(50,plain,
% 0.19/0.41 ((findmin_cpq_eff(triple(U!2, V!1, W!0)) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0)) <=> (findmin_cpq_eff(triple(U!2, V!1, W!0)) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[49])).
% 0.19/0.41 tff(51,plain,
% 0.19/0.41 ((findmin_cpq_eff(triple(U!2, V!1, W!0)) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad)) <=> (findmin_cpq_eff(triple(U!2, V!1, W!0)) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0))),
% 0.19/0.41 inference(symmetry,[status(thm)],[50])).
% 0.19/0.41 tff(52,plain,
% 0.19/0.41 ((~(findmin_cpq_eff(triple(U!2, V!1, W!0)) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad))) <=> (~(findmin_cpq_eff(triple(U!2, V!1, W!0)) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0)))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[51])).
% 0.19/0.41 tff(53,assumption,(findmin_cpq_eff(triple(U!2, V!1, W!0)) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad)), introduced(assumption)).
% 0.19/0.41 tff(54,plain,
% 0.19/0.41 (triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad) = findmin_cpq_eff(triple(U!2, V!1, W!0))),
% 0.19/0.41 inference(symmetry,[status(thm)],[53])).
% 0.19/0.41 tff(55,plain,
% 0.19/0.41 (ok(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad)) <=> ok(findmin_cpq_eff(triple(U!2, V!1, W!0)))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[54])).
% 0.19/0.41 tff(56,plain,
% 0.19/0.41 (ok(findmin_cpq_eff(triple(U!2, V!1, W!0))) <=> ok(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad))),
% 0.19/0.41 inference(symmetry,[status(thm)],[55])).
% 0.19/0.41 tff(57,plain,
% 0.19/0.41 (ok(findmin_cpq_eff(triple(U!2, V!1, W!0)))),
% 0.19/0.41 inference(or_elim,[status(thm)],[11])).
% 0.19/0.41 tff(58,plain,
% 0.19/0.41 (ok(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.19/0.41 tff(59,plain,
% 0.19/0.41 (^[U: $i, V: $i] : refl((~ok(triple(U, V, bad))) <=> (~ok(triple(U, V, bad))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(60,plain,
% 0.19/0.41 (![U: $i, V: $i] : (~ok(triple(U, V, bad))) <=> ![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[59])).
% 0.19/0.41 tff(61,plain,
% 0.19/0.41 (![U: $i, V: $i] : (~ok(triple(U, V, bad))) <=> ![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(62,plain,
% 0.19/0.41 (^[U: $i, V: $i] : rewrite((ok(triple(U, V, bad)) <=> $false) <=> (~ok(triple(U, V, bad))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(63,plain,
% 0.19/0.41 (![U: $i, V: $i] : (ok(triple(U, V, bad)) <=> $false) <=> ![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[62])).
% 0.19/0.41 tff(64,axiom,(![U: $i, V: $i] : (ok(triple(U, V, bad)) <=> $false)), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax','ax40')).
% 0.19/0.41 tff(65,plain,
% 0.19/0.41 (![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.19/0.41 tff(66,plain,
% 0.19/0.41 (![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.19/0.41 tff(67,plain,(
% 0.19/0.41 ![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[66])).
% 0.19/0.41 tff(68,plain,
% 0.19/0.41 (![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[67, 60])).
% 0.19/0.41 tff(69,plain,
% 0.19/0.41 ((~![U: $i, V: $i] : (~ok(triple(U, V, bad)))) | (~ok(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(70,plain,
% 0.19/0.41 (~ok(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.19/0.41 tff(71,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[70, 58])).
% 0.19/0.41 tff(72,plain,(~(findmin_cpq_eff(triple(U!2, V!1, W!0)) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(73,plain,
% 0.19/0.41 (~(findmin_cpq_eff(triple(U!2, V!1, W!0)) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[72, 52])).
% 0.19/0.41 tff(74,plain,
% 0.19/0.41 (^[U: $i, V: $i, W: $i] : refl(((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(75,plain,
% 0.19/0.41 (![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[74])).
% 0.19/0.41 tff(76,plain,
% 0.19/0.41 (^[U: $i, V: $i, W: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U)))) <=> (~((V = create_slb) | contains_slb(V, findmin_pqp_res(U))))), ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) <=> (~(~((V = create_slb) | contains_slb(V, findmin_pqp_res(U))))))), rewrite((~(~((V = create_slb) | contains_slb(V, findmin_pqp_res(U))))) <=> ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)))), ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) <=> ((V = create_slb) | contains_slb(V, findmin_pqp_res(U))))), (((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> (((V = create_slb) | contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))))), rewrite((((V = create_slb) | contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))), (((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(77,plain,
% 0.19/0.41 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[76])).
% 0.19/0.41 tff(78,plain,
% 0.19/0.41 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(79,plain,
% 0.19/0.41 (![U: $i, V: $i, W: $i, X: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.19/0.41 inference(elim_unused_vars,[status(thm)],[])).
% 0.19/0.41 tff(80,plain,
% 0.19/0.41 (^[U: $i, V: $i, W: $i, X: $i] : rewrite((((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U)))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(81,plain,
% 0.19/0.41 (![U: $i, V: $i, W: $i, X: $i] : (((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U)))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[80])).
% 0.19/0.41 tff(82,plain,
% 0.19/0.41 (![U: $i, V: $i, W: $i, X: $i] : (((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U)))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.19/0.41 inference(transitivity,[status(thm)],[81, 79])).
% 0.19/0.41 tff(83,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')).
% 0.19/0.41 tff(84,plain,
% 0.19/0.41 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.19/0.41 tff(85,plain,
% 0.19/0.41 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[84, 78])).
% 0.19/0.41 tff(86,plain,(
% 0.19/0.41 ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[85])).
% 0.19/0.41 tff(87,plain,
% 0.19/0.41 (![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[86, 77])).
% 0.19/0.41 tff(88,plain,
% 0.19/0.41 (![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[87, 75])).
% 0.19/0.41 tff(89,plain,
% 0.19/0.41 (((~![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))) | ((V!1 = create_slb) | contains_slb(V!1, findmin_pqp_res(U!2)) | (findmin_cpq_eff(triple(U!2, V!1, W!0)) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), 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!1 = create_slb) | contains_slb(V!1, findmin_pqp_res(U!2)) | (findmin_cpq_eff(triple(U!2, V!1, W!0)) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(90,plain,
% 0.19/0.41 ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))) | ((V!1 = create_slb) | contains_slb(V!1, findmin_pqp_res(U!2)) | (findmin_cpq_eff(triple(U!2, V!1, W!0)) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(91,plain,
% 0.19/0.41 ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))) | (V!1 = create_slb) | contains_slb(V!1, findmin_pqp_res(U!2)) | (findmin_cpq_eff(triple(U!2, V!1, W!0)) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.19/0.41 tff(92,plain,
% 0.19/0.41 ((V!1 = create_slb) | contains_slb(V!1, findmin_pqp_res(U!2)) | (findmin_cpq_eff(triple(U!2, V!1, W!0)) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[91, 88])).
% 0.19/0.41 tff(93,plain,
% 0.19/0.41 (contains_slb(V!1, findmin_pqp_res(U!2))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[92, 28, 72])).
% 0.19/0.41 tff(94,plain,
% 0.19/0.41 (^[U: $i, V: $i, W: $i] : refl(((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), 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)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(95,plain,
% 0.19/0.41 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), 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))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[94])).
% 0.19/0.41 tff(96,plain,
% 0.19/0.41 (^[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))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(97,plain,
% 0.19/0.41 (![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))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[96])).
% 0.19/0.41 tff(98,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(99,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(elim_unused_vars,[status(thm)],[])).
% 0.19/0.41 tff(100,plain,
% 0.19/0.41 (^[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)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(101,plain,
% 0.19/0.42 (![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)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[100])).
% 0.19/0.42 tff(102,plain,
% 0.19/0.42 (![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)))),
% 0.19/0.42 inference(transitivity,[status(thm)],[101, 99])).
% 0.19/0.42 tff(103,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')).
% 0.19/0.42 tff(104,plain,
% 0.19/0.42 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.19/0.42 tff(105,plain,
% 0.19/0.42 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[104, 98])).
% 0.19/0.42 tff(106,plain,(
% 0.19/0.42 ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[105])).
% 0.19/0.42 tff(107,plain,
% 0.19/0.42 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[106, 97])).
% 0.19/0.42 tff(108,plain,
% 0.19/0.42 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[107, 95])).
% 0.19/0.42 tff(109,plain,
% 0.19/0.42 (((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))) | ((V!1 = create_slb) | (~contains_slb(V!1, findmin_pqp_res(U!2))) | (findmin_cpq_eff(triple(U!2, V!1, W!0)) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0)) | (~less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_pqp_res(U!2))))) <=> ((~![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!1 = create_slb) | (~contains_slb(V!1, findmin_pqp_res(U!2))) | (findmin_cpq_eff(triple(U!2, V!1, W!0)) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0)) | (~less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_pqp_res(U!2))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(110,plain,
% 0.19/0.42 ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))) | ((V!1 = create_slb) | (~contains_slb(V!1, findmin_pqp_res(U!2))) | (findmin_cpq_eff(triple(U!2, V!1, W!0)) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0)) | (~less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_pqp_res(U!2))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(111,plain,
% 0.19/0.42 ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))) | (V!1 = create_slb) | (~contains_slb(V!1, findmin_pqp_res(U!2))) | (findmin_cpq_eff(triple(U!2, V!1, W!0)) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0)) | (~less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_pqp_res(U!2)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.19/0.42 tff(112,plain,
% 0.19/0.42 ((V!1 = create_slb) | (~contains_slb(V!1, findmin_pqp_res(U!2))) | (findmin_cpq_eff(triple(U!2, V!1, W!0)) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0)) | (~less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_pqp_res(U!2)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[111, 108])).
% 0.19/0.42 tff(113,plain,
% 0.19/0.42 (~less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_pqp_res(U!2))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[112, 93, 73, 28])).
% 0.19/0.42 tff(114,plain,
% 0.19/0.42 (~less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_cpq_res(triple(U!2, V!1, W!0)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[113, 48])).
% 0.19/0.42 tff(115,plain,
% 0.19/0.42 (^[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)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(116,plain,
% 0.19/0.42 (![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))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[115])).
% 0.19/0.42 tff(117,plain,
% 0.19/0.42 (^[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)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(118,plain,
% 0.19/0.42 (![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))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[117])).
% 0.19/0.42 tff(119,plain,
% 0.19/0.42 (![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))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(120,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')).
% 0.19/0.42 tff(121,plain,
% 0.19/0.42 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.19/0.42 tff(122,plain,(
% 0.19/0.42 ![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.19/0.42 inference(skolemize,[status(sab)],[121])).
% 0.19/0.42 tff(123,plain,
% 0.19/0.42 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[122, 118])).
% 0.19/0.42 tff(124,plain,
% 0.19/0.42 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[123, 116])).
% 0.19/0.42 tff(125,plain,
% 0.19/0.42 ((~![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!2, V!1, W!0)), lookup_slb(V!1, findmin_pqp_res(U!2))) <=> (~((~less_than(findmin_cpq_res(triple(U!2, V!1, W!0)), lookup_slb(V!1, findmin_pqp_res(U!2)))) | less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_cpq_res(triple(U!2, V!1, W!0))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(126,plain,
% 0.19/0.42 (strictly_less_than(findmin_cpq_res(triple(U!2, V!1, W!0)), lookup_slb(V!1, findmin_pqp_res(U!2))) <=> (~((~less_than(findmin_cpq_res(triple(U!2, V!1, W!0)), lookup_slb(V!1, findmin_pqp_res(U!2)))) | less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_cpq_res(triple(U!2, V!1, W!0)))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[125, 124])).
% 0.19/0.42 tff(127,plain,
% 0.19/0.42 (strictly_less_than(findmin_cpq_res(triple(U!2, V!1, W!0)), lookup_slb(V!1, findmin_pqp_res(U!2))) <=> strictly_less_than(findmin_pqp_res(U!2), lookup_slb(V!1, findmin_pqp_res(U!2)))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[45])).
% 0.19/0.42 tff(128,plain,
% 0.19/0.42 (strictly_less_than(findmin_pqp_res(U!2), lookup_slb(V!1, findmin_pqp_res(U!2))) <=> strictly_less_than(findmin_cpq_res(triple(U!2, V!1, W!0)), lookup_slb(V!1, findmin_pqp_res(U!2)))),
% 0.19/0.42 inference(symmetry,[status(thm)],[127])).
% 0.19/0.42 tff(129,plain,
% 0.19/0.42 ((~strictly_less_than(findmin_pqp_res(U!2), lookup_slb(V!1, findmin_pqp_res(U!2)))) <=> (~strictly_less_than(findmin_cpq_res(triple(U!2, V!1, W!0)), lookup_slb(V!1, findmin_pqp_res(U!2))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[128])).
% 0.19/0.42 tff(130,plain,
% 0.19/0.42 (^[U: $i, V: $i, W: $i] : refl(((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) <=> ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(131,plain,
% 0.19/0.42 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) <=> ![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[130])).
% 0.19/0.42 tff(132,plain,
% 0.19/0.42 (^[U: $i, V: $i, W: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))) <=> (~((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))))), ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) <=> (~(~((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))))))), rewrite((~(~((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))))) <=> ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))))), ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) <=> ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))))), (((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> (((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))))), rewrite((((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))))), (((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(133,plain,
% 0.19/0.42 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[132])).
% 0.19/0.42 tff(134,plain,
% 0.19/0.42 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(135,plain,
% 0.19/0.42 (![U: $i, V: $i, W: $i, X: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.19/0.42 inference(elim_unused_vars,[status(thm)],[])).
% 0.19/0.42 tff(136,plain,
% 0.19/0.42 (^[U: $i, V: $i, W: $i, X: $i] : trans(monotonicity(rewrite((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))) <=> ((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))), (((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> (((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))))), rewrite((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))), (((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(137,plain,
% 0.19/0.42 (![U: $i, V: $i, W: $i, X: $i] : ((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[136])).
% 0.19/0.42 tff(138,plain,
% 0.19/0.42 (![U: $i, V: $i, W: $i, X: $i] : ((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.19/0.42 inference(transitivity,[status(thm)],[137, 135])).
% 0.19/0.42 tff(139,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')).
% 0.19/0.42 tff(140,plain,
% 0.19/0.42 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.19/0.42 tff(141,plain,
% 0.19/0.42 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[140, 134])).
% 0.19/0.42 tff(142,plain,(
% 0.19/0.42 ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.19/0.43 inference(skolemize,[status(sab)],[141])).
% 0.19/0.43 tff(143,plain,
% 0.19/0.43 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[142, 133])).
% 0.19/0.43 tff(144,plain,
% 0.19/0.43 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[143, 131])).
% 0.19/0.43 tff(145,plain,
% 0.19/0.43 (((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))))) | ((V!1 = create_slb) | (~contains_slb(V!1, findmin_pqp_res(U!2))) | (findmin_cpq_eff(triple(U!2, V!1, W!0)) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad)) | (~strictly_less_than(findmin_pqp_res(U!2), lookup_slb(V!1, findmin_pqp_res(U!2)))))) <=> ((~![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!1 = create_slb) | (~contains_slb(V!1, findmin_pqp_res(U!2))) | (findmin_cpq_eff(triple(U!2, V!1, W!0)) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad)) | (~strictly_less_than(findmin_pqp_res(U!2), lookup_slb(V!1, findmin_pqp_res(U!2)))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(146,plain,
% 0.19/0.43 ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))))) | ((V!1 = create_slb) | (~contains_slb(V!1, findmin_pqp_res(U!2))) | (findmin_cpq_eff(triple(U!2, V!1, W!0)) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad)) | (~strictly_less_than(findmin_pqp_res(U!2), lookup_slb(V!1, findmin_pqp_res(U!2)))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(147,plain,
% 0.19/0.43 ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))))) | (V!1 = create_slb) | (~contains_slb(V!1, findmin_pqp_res(U!2))) | (findmin_cpq_eff(triple(U!2, V!1, W!0)) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad)) | (~strictly_less_than(findmin_pqp_res(U!2), lookup_slb(V!1, findmin_pqp_res(U!2))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.19/0.43 tff(148,plain,
% 0.19/0.43 ((V!1 = create_slb) | (~contains_slb(V!1, findmin_pqp_res(U!2))) | (findmin_cpq_eff(triple(U!2, V!1, W!0)) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad)) | (~strictly_less_than(findmin_pqp_res(U!2), lookup_slb(V!1, findmin_pqp_res(U!2))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[147, 144])).
% 0.19/0.43 tff(149,plain,
% 0.19/0.43 (~strictly_less_than(findmin_pqp_res(U!2), lookup_slb(V!1, findmin_pqp_res(U!2)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[148, 93, 72, 28])).
% 0.19/0.43 tff(150,plain,
% 0.19/0.43 (~strictly_less_than(findmin_cpq_res(triple(U!2, V!1, W!0)), lookup_slb(V!1, findmin_pqp_res(U!2)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[149, 129])).
% 0.19/0.43 tff(151,plain,
% 0.19/0.43 ((~(strictly_less_than(findmin_cpq_res(triple(U!2, V!1, W!0)), lookup_slb(V!1, findmin_pqp_res(U!2))) <=> (~((~less_than(findmin_cpq_res(triple(U!2, V!1, W!0)), lookup_slb(V!1, findmin_pqp_res(U!2)))) | less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_cpq_res(triple(U!2, V!1, W!0))))))) | strictly_less_than(findmin_cpq_res(triple(U!2, V!1, W!0)), lookup_slb(V!1, findmin_pqp_res(U!2))) | ((~less_than(findmin_cpq_res(triple(U!2, V!1, W!0)), lookup_slb(V!1, findmin_pqp_res(U!2)))) | less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_cpq_res(triple(U!2, V!1, W!0))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(152,plain,
% 0.19/0.43 ((~less_than(findmin_cpq_res(triple(U!2, V!1, W!0)), lookup_slb(V!1, findmin_pqp_res(U!2)))) | less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_cpq_res(triple(U!2, V!1, W!0)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[151, 150, 126])).
% 0.19/0.43 tff(153,plain,
% 0.19/0.43 ((~((~less_than(findmin_cpq_res(triple(U!2, V!1, W!0)), lookup_slb(V!1, findmin_pqp_res(U!2)))) | less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_cpq_res(triple(U!2, V!1, W!0))))) | (~less_than(findmin_cpq_res(triple(U!2, V!1, W!0)), lookup_slb(V!1, findmin_pqp_res(U!2)))) | less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_cpq_res(triple(U!2, V!1, W!0)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(154,plain,
% 0.19/0.43 (~less_than(findmin_cpq_res(triple(U!2, V!1, W!0)), lookup_slb(V!1, findmin_pqp_res(U!2)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[153, 114, 152])).
% 0.19/0.43 tff(155,plain,
% 0.19/0.43 (^[U: $i, V: $i] : refl((less_than(V, U) | less_than(U, V)) <=> (less_than(V, U) | less_than(U, V)))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(156,plain,
% 0.19/0.43 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[155])).
% 0.19/0.43 tff(157,plain,
% 0.19/0.43 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(158,plain,
% 0.19/0.43 (^[U: $i, V: $i] : rewrite((less_than(U, V) | less_than(V, U)) <=> (less_than(V, U) | less_than(U, V)))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(159,plain,
% 0.19/0.43 (![U: $i, V: $i] : (less_than(U, V) | less_than(V, U)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[158])).
% 0.19/0.43 tff(160,axiom,(![U: $i, V: $i] : (less_than(U, V) | less_than(V, U))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+0.ax','totality')).
% 0.19/0.43 tff(161,plain,
% 0.19/0.43 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.19/0.43 tff(162,plain,
% 0.19/0.43 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[161, 157])).
% 0.19/0.43 tff(163,plain,(
% 0.19/0.43 ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.19/0.43 inference(skolemize,[status(sab)],[162])).
% 0.19/0.43 tff(164,plain,
% 0.19/0.43 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[163, 156])).
% 0.19/0.43 tff(165,plain,
% 0.19/0.43 (((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | (less_than(findmin_cpq_res(triple(U!2, V!1, W!0)), lookup_slb(V!1, findmin_pqp_res(U!2))) | less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_cpq_res(triple(U!2, V!1, W!0))))) <=> ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | less_than(findmin_cpq_res(triple(U!2, V!1, W!0)), lookup_slb(V!1, findmin_pqp_res(U!2))) | less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_cpq_res(triple(U!2, V!1, W!0))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(166,plain,
% 0.19/0.43 ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | (less_than(findmin_cpq_res(triple(U!2, V!1, W!0)), lookup_slb(V!1, findmin_pqp_res(U!2))) | less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_cpq_res(triple(U!2, V!1, W!0))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(167,plain,
% 0.19/0.43 ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | less_than(findmin_cpq_res(triple(U!2, V!1, W!0)), lookup_slb(V!1, findmin_pqp_res(U!2))) | less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_cpq_res(triple(U!2, V!1, W!0)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.19/0.43 tff(168,plain,
% 0.19/0.43 (less_than(findmin_cpq_res(triple(U!2, V!1, W!0)), lookup_slb(V!1, findmin_pqp_res(U!2))) | less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_cpq_res(triple(U!2, V!1, W!0)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[167, 164])).
% 0.19/0.43 tff(169,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[168, 154, 114])).
% 0.19/0.43 tff(170,plain,(V!1 = create_slb), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(171,plain,
% 0.19/0.43 (create_slb = V!1),
% 0.19/0.43 inference(symmetry,[status(thm)],[170])).
% 0.19/0.43 tff(172,plain,
% 0.19/0.43 (^[U: $i] : refl((update_slb(create_slb, U) = create_slb) <=> (update_slb(create_slb, U) = create_slb))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(173,plain,
% 0.19/0.43 (![U: $i] : (update_slb(create_slb, U) = create_slb) <=> ![U: $i] : (update_slb(create_slb, U) = create_slb)),
% 0.19/0.43 inference(quant_intro,[status(thm)],[172])).
% 0.19/0.43 tff(174,plain,
% 0.19/0.43 (![U: $i] : (update_slb(create_slb, U) = create_slb) <=> ![U: $i] : (update_slb(create_slb, U) = create_slb)),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(175,axiom,(![U: $i] : (update_slb(create_slb, U) = create_slb)), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+2.ax','ax28')).
% 0.19/0.43 tff(176,plain,
% 0.19/0.43 (![U: $i] : (update_slb(create_slb, U) = create_slb)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.19/0.43 tff(177,plain,(
% 0.19/0.43 ![U: $i] : (update_slb(create_slb, U) = create_slb)),
% 0.19/0.43 inference(skolemize,[status(sab)],[176])).
% 0.19/0.43 tff(178,plain,
% 0.19/0.43 (![U: $i] : (update_slb(create_slb, U) = create_slb)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[177, 173])).
% 0.19/0.43 tff(179,plain,
% 0.19/0.43 ((~![U: $i] : (update_slb(create_slb, U) = create_slb)) | (update_slb(create_slb, findmin_pqp_res(U!2)) = create_slb)),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(180,plain,
% 0.19/0.43 (update_slb(create_slb, findmin_pqp_res(U!2)) = create_slb),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[179, 178])).
% 0.19/0.43 tff(181,plain,
% 0.19/0.43 (update_slb(V!1, findmin_pqp_res(U!2)) = update_slb(create_slb, findmin_pqp_res(U!2))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[170])).
% 0.19/0.43 tff(182,plain,
% 0.19/0.43 (update_slb(V!1, findmin_pqp_res(U!2)) = V!1),
% 0.19/0.43 inference(transitivity,[status(thm)],[181, 180, 171])).
% 0.19/0.43 tff(183,plain,
% 0.19/0.43 (triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad) = triple(U!2, V!1, W!0)),
% 0.19/0.43 inference(monotonicity,[status(thm)],[182, 27])).
% 0.19/0.43 tff(184,plain,
% 0.19/0.43 (triple(U!2, V!1, W!0) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad)),
% 0.19/0.43 inference(symmetry,[status(thm)],[183])).
% 0.19/0.43 tff(185,plain,
% 0.19/0.43 (triple(U!2, create_slb, bad) = triple(U!2, V!1, W!0)),
% 0.19/0.43 inference(monotonicity,[status(thm)],[171, 27])).
% 0.19/0.43 tff(186,plain,
% 0.19/0.43 (^[U: $i, V: $i] : refl((findmin_cpq_eff(triple(U, create_slb, V)) = triple(U, create_slb, bad)) <=> (findmin_cpq_eff(triple(U, create_slb, V)) = triple(U, create_slb, bad)))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(187,plain,
% 0.19/0.43 (![U: $i, V: $i] : (findmin_cpq_eff(triple(U, create_slb, V)) = triple(U, create_slb, bad)) <=> ![U: $i, V: $i] : (findmin_cpq_eff(triple(U, create_slb, V)) = triple(U, create_slb, bad))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[186])).
% 0.19/0.43 tff(188,plain,
% 0.19/0.43 (![U: $i, V: $i] : (findmin_cpq_eff(triple(U, create_slb, V)) = triple(U, create_slb, bad)) <=> ![U: $i, V: $i] : (findmin_cpq_eff(triple(U, create_slb, V)) = triple(U, create_slb, bad))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(189,axiom,(![U: $i, V: $i] : (findmin_cpq_eff(triple(U, create_slb, V)) = triple(U, create_slb, bad))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax','ax46')).
% 0.19/0.43 tff(190,plain,
% 0.19/0.43 (![U: $i, V: $i] : (findmin_cpq_eff(triple(U, create_slb, V)) = triple(U, create_slb, bad))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[189, 188])).
% 0.19/0.43 tff(191,plain,(
% 0.19/0.43 ![U: $i, V: $i] : (findmin_cpq_eff(triple(U, create_slb, V)) = triple(U, create_slb, bad))),
% 0.19/0.43 inference(skolemize,[status(sab)],[190])).
% 0.19/0.43 tff(192,plain,
% 0.19/0.43 (![U: $i, V: $i] : (findmin_cpq_eff(triple(U, create_slb, V)) = triple(U, create_slb, bad))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[191, 187])).
% 0.19/0.43 tff(193,plain,
% 0.19/0.43 ((~![U: $i, V: $i] : (findmin_cpq_eff(triple(U, create_slb, V)) = triple(U, create_slb, bad))) | (findmin_cpq_eff(triple(U!2, create_slb, bad)) = triple(U!2, create_slb, bad))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(194,plain,
% 0.19/0.43 (findmin_cpq_eff(triple(U!2, create_slb, bad)) = triple(U!2, create_slb, bad)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[193, 192])).
% 0.19/0.44 tff(195,plain,
% 0.19/0.44 (triple(U!2, V!1, W!0) = triple(U!2, create_slb, bad)),
% 0.19/0.44 inference(symmetry,[status(thm)],[185])).
% 0.19/0.44 tff(196,plain,
% 0.19/0.44 (findmin_cpq_eff(triple(U!2, V!1, W!0)) = findmin_cpq_eff(triple(U!2, create_slb, bad))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[195])).
% 0.19/0.44 tff(197,plain,
% 0.19/0.44 (findmin_cpq_eff(triple(U!2, V!1, W!0)) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad)),
% 0.19/0.44 inference(transitivity,[status(thm)],[196, 194, 185, 184])).
% 0.19/0.44 tff(198,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[72, 197])).
% 0.19/0.44 % SZS output end Proof
%------------------------------------------------------------------------------