TSTP Solution File: SWV374+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV374+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.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 0.14s 0.36s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SWV374+1 : TPTP v8.1.0. Released v3.3.0.
% 0.00/0.10 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.09/0.30 % Computer : n008.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Sun Sep 4 02:47:40 EDT 2022
% 0.09/0.30 % CPUTime :
% 0.09/0.30 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.09/0.30 Usage: tptp [options] [-file:]file
% 0.09/0.30 -h, -? prints this message.
% 0.09/0.30 -smt2 print SMT-LIB2 benchmark.
% 0.09/0.30 -m, -model generate model.
% 0.09/0.30 -p, -proof generate proof.
% 0.09/0.30 -c, -core generate unsat core of named formulas.
% 0.09/0.30 -st, -statistics display statistics.
% 0.09/0.30 -t:timeout set timeout (in second).
% 0.09/0.30 -smt2status display status in smt2 format instead of SZS.
% 0.09/0.30 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.09/0.30 -<param>:<value> configuration parameter and value.
% 0.09/0.30 -o:<output-file> file to place output in.
% 0.14/0.36 % SZS status Theorem
% 0.14/0.36 % SZS output start Proof
% 0.14/0.36 tff(less_than_type, type, (
% 0.14/0.36 less_than: ( $i * $i ) > $o)).
% 0.14/0.36 tff(findmin_cpq_res_type, type, (
% 0.14/0.36 findmin_cpq_res: $i > $i)).
% 0.14/0.36 tff(triple_type, type, (
% 0.14/0.36 triple: ( $i * $i * $i ) > $i)).
% 0.14/0.36 tff(tptp_fun_W_0_type, type, (
% 0.14/0.36 tptp_fun_W_0: $i)).
% 0.14/0.36 tff(tptp_fun_V_1_type, type, (
% 0.14/0.36 tptp_fun_V_1: $i)).
% 0.14/0.36 tff(tptp_fun_U_2_type, type, (
% 0.14/0.36 tptp_fun_U_2: $i)).
% 0.14/0.36 tff(lookup_slb_type, type, (
% 0.14/0.36 lookup_slb: ( $i * $i ) > $i)).
% 0.14/0.36 tff(findmin_pqp_res_type, type, (
% 0.14/0.36 findmin_pqp_res: $i > $i)).
% 0.14/0.36 tff(create_slb_type, type, (
% 0.14/0.36 create_slb: $i)).
% 0.14/0.36 tff(bad_type, type, (
% 0.14/0.36 bad: $i)).
% 0.14/0.36 tff(update_slb_type, type, (
% 0.14/0.36 update_slb: ( $i * $i ) > $i)).
% 0.14/0.36 tff(findmin_cpq_eff_type, type, (
% 0.14/0.36 findmin_cpq_eff: $i > $i)).
% 0.14/0.36 tff(ok_type, type, (
% 0.14/0.36 ok: $i > $o)).
% 0.14/0.36 tff(contains_slb_type, type, (
% 0.14/0.36 contains_slb: ( $i * $i ) > $o)).
% 0.14/0.36 tff(strictly_less_than_type, type, (
% 0.14/0.36 strictly_less_than: ( $i * $i ) > $o)).
% 0.14/0.36 tff(1,assumption,(V!1 = create_slb), introduced(assumption)).
% 0.14/0.36 tff(2,plain,
% 0.14/0.36 (create_slb = V!1),
% 0.14/0.36 inference(symmetry,[status(thm)],[1])).
% 0.14/0.36 tff(3,plain,
% 0.14/0.36 (^[U: $i] : refl((update_slb(create_slb, U) = create_slb) <=> (update_slb(create_slb, U) = create_slb))),
% 0.14/0.36 inference(bind,[status(th)],[])).
% 0.14/0.36 tff(4,plain,
% 0.14/0.36 (![U: $i] : (update_slb(create_slb, U) = create_slb) <=> ![U: $i] : (update_slb(create_slb, U) = create_slb)),
% 0.14/0.36 inference(quant_intro,[status(thm)],[3])).
% 0.14/0.36 tff(5,plain,
% 0.14/0.36 (![U: $i] : (update_slb(create_slb, U) = create_slb) <=> ![U: $i] : (update_slb(create_slb, U) = create_slb)),
% 0.14/0.36 inference(rewrite,[status(thm)],[])).
% 0.14/0.36 tff(6,axiom,(![U: $i] : (update_slb(create_slb, U) = create_slb)), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+2.ax','ax28')).
% 0.14/0.36 tff(7,plain,
% 0.14/0.36 (![U: $i] : (update_slb(create_slb, U) = create_slb)),
% 0.14/0.36 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.14/0.36 tff(8,plain,(
% 0.14/0.36 ![U: $i] : (update_slb(create_slb, U) = create_slb)),
% 0.14/0.36 inference(skolemize,[status(sab)],[7])).
% 0.14/0.36 tff(9,plain,
% 0.14/0.36 (![U: $i] : (update_slb(create_slb, U) = create_slb)),
% 0.14/0.36 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.14/0.36 tff(10,plain,
% 0.14/0.36 ((~![U: $i] : (update_slb(create_slb, U) = create_slb)) | (update_slb(create_slb, findmin_pqp_res(U!2)) = create_slb)),
% 0.14/0.36 inference(quant_inst,[status(thm)],[])).
% 0.14/0.36 tff(11,plain,
% 0.14/0.36 (update_slb(create_slb, findmin_pqp_res(U!2)) = create_slb),
% 0.14/0.36 inference(unit_resolution,[status(thm)],[10, 9])).
% 0.14/0.36 tff(12,plain,
% 0.14/0.36 (update_slb(V!1, findmin_pqp_res(U!2)) = update_slb(create_slb, findmin_pqp_res(U!2))),
% 0.14/0.36 inference(monotonicity,[status(thm)],[1])).
% 0.14/0.36 tff(13,plain,
% 0.14/0.36 (update_slb(V!1, findmin_pqp_res(U!2)) = V!1),
% 0.14/0.36 inference(transitivity,[status(thm)],[12, 11, 2])).
% 0.14/0.36 tff(14,plain,
% 0.14/0.36 (triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad) = triple(U!2, V!1, bad)),
% 0.14/0.36 inference(monotonicity,[status(thm)],[13])).
% 0.14/0.36 tff(15,plain,
% 0.14/0.36 (triple(U!2, V!1, bad) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad)),
% 0.14/0.36 inference(symmetry,[status(thm)],[14])).
% 0.14/0.36 tff(16,plain,
% 0.14/0.36 (triple(U!2, V!1, bad) = triple(U!2, create_slb, bad)),
% 0.14/0.36 inference(monotonicity,[status(thm)],[1])).
% 0.14/0.36 tff(17,plain,
% 0.14/0.36 (triple(U!2, create_slb, bad) = triple(U!2, V!1, bad)),
% 0.14/0.36 inference(symmetry,[status(thm)],[16])).
% 0.14/0.36 tff(18,plain,
% 0.14/0.36 (^[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)))),
% 0.14/0.36 inference(bind,[status(th)],[])).
% 0.14/0.36 tff(19,plain,
% 0.14/0.36 (![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))),
% 0.14/0.36 inference(quant_intro,[status(thm)],[18])).
% 0.14/0.36 tff(20,plain,
% 0.14/0.36 (![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))),
% 0.14/0.36 inference(rewrite,[status(thm)],[])).
% 0.14/0.36 tff(21,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')).
% 0.14/0.36 tff(22,plain,
% 0.14/0.36 (![U: $i, V: $i] : (findmin_cpq_eff(triple(U, create_slb, V)) = triple(U, create_slb, bad))),
% 0.14/0.36 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.14/0.36 tff(23,plain,(
% 0.14/0.36 ![U: $i, V: $i] : (findmin_cpq_eff(triple(U, create_slb, V)) = triple(U, create_slb, bad))),
% 0.14/0.36 inference(skolemize,[status(sab)],[22])).
% 0.14/0.36 tff(24,plain,
% 0.14/0.36 (![U: $i, V: $i] : (findmin_cpq_eff(triple(U, create_slb, V)) = triple(U, create_slb, bad))),
% 0.14/0.36 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.14/0.36 tff(25,plain,
% 0.14/0.36 ((~![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, W!0)) = triple(U!2, create_slb, bad))),
% 0.14/0.36 inference(quant_inst,[status(thm)],[])).
% 0.14/0.36 tff(26,plain,
% 0.14/0.36 (findmin_cpq_eff(triple(U!2, create_slb, W!0)) = triple(U!2, create_slb, bad)),
% 0.14/0.36 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.14/0.36 tff(27,plain,
% 0.14/0.36 (triple(U!2, create_slb, W!0) = triple(U!2, V!1, W!0)),
% 0.14/0.36 inference(monotonicity,[status(thm)],[2])).
% 0.14/0.36 tff(28,plain,
% 0.14/0.36 (triple(U!2, V!1, W!0) = triple(U!2, create_slb, W!0)),
% 0.14/0.36 inference(symmetry,[status(thm)],[27])).
% 0.14/0.36 tff(29,plain,
% 0.14/0.36 (findmin_cpq_eff(triple(U!2, V!1, W!0)) = findmin_cpq_eff(triple(U!2, create_slb, W!0))),
% 0.14/0.36 inference(monotonicity,[status(thm)],[28])).
% 0.14/0.36 tff(30,plain,
% 0.14/0.36 (findmin_cpq_eff(triple(U!2, V!1, W!0)) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad)),
% 0.14/0.36 inference(transitivity,[status(thm)],[29, 26, 17, 15])).
% 0.14/0.36 tff(31,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)).
% 0.14/0.36 tff(32,plain,
% 0.14/0.36 (triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad) = findmin_cpq_eff(triple(U!2, V!1, W!0))),
% 0.14/0.36 inference(symmetry,[status(thm)],[31])).
% 0.14/0.36 tff(33,plain,
% 0.14/0.36 (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)))),
% 0.14/0.36 inference(monotonicity,[status(thm)],[32])).
% 0.14/0.36 tff(34,plain,
% 0.14/0.36 (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))),
% 0.14/0.36 inference(symmetry,[status(thm)],[33])).
% 0.14/0.36 tff(35,plain,
% 0.14/0.36 ((~![U: $i, V: $i, W: $i] : ((~ok(findmin_cpq_eff(triple(U, V, W)))) | ((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))) <=> (~![U: $i, V: $i, W: $i] : ((~ok(findmin_cpq_eff(triple(U, V, W)))) | ((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))))),
% 0.14/0.36 inference(rewrite,[status(thm)],[])).
% 0.14/0.36 tff(36,plain,
% 0.14/0.36 ((~![U: $i, V: $i, W: $i] : (ok(findmin_cpq_eff(triple(U, V, W))) => (((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))) <=> (~![U: $i, V: $i, W: $i] : ((~ok(findmin_cpq_eff(triple(U, V, W)))) | ((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))))),
% 0.14/0.36 inference(rewrite,[status(thm)],[])).
% 0.14/0.36 tff(37,axiom,(~![U: $i, V: $i, W: $i] : (ok(findmin_cpq_eff(triple(U, V, W))) => (((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l10_co')).
% 0.14/0.36 tff(38,plain,
% 0.14/0.36 (~![U: $i, V: $i, W: $i] : ((~ok(findmin_cpq_eff(triple(U, V, W)))) | ((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))),
% 0.14/0.36 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.14/0.36 tff(39,plain,
% 0.14/0.36 (~![U: $i, V: $i, W: $i] : ((~ok(findmin_cpq_eff(triple(U, V, W)))) | ((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))),
% 0.14/0.36 inference(modus_ponens,[status(thm)],[38, 35])).
% 0.14/0.36 tff(40,plain,
% 0.14/0.36 (~![U: $i, V: $i, W: $i] : ((~ok(findmin_cpq_eff(triple(U, V, W)))) | ((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))),
% 0.14/0.37 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.14/0.37 tff(41,plain,
% 0.14/0.37 (~![U: $i, V: $i, W: $i] : ((~ok(findmin_cpq_eff(triple(U, V, W)))) | ((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))),
% 0.14/0.37 inference(modus_ponens,[status(thm)],[40, 35])).
% 0.14/0.37 tff(42,plain,
% 0.14/0.37 (~![U: $i, V: $i, W: $i] : ((~ok(findmin_cpq_eff(triple(U, V, W)))) | ((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))),
% 0.14/0.37 inference(modus_ponens,[status(thm)],[41, 35])).
% 0.14/0.37 tff(43,plain,
% 0.14/0.37 (~![U: $i, V: $i, W: $i] : ((~ok(findmin_cpq_eff(triple(U, V, W)))) | ((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))),
% 0.14/0.37 inference(modus_ponens,[status(thm)],[42, 35])).
% 0.14/0.37 tff(44,plain,
% 0.14/0.37 (~![U: $i, V: $i, W: $i] : ((~ok(findmin_cpq_eff(triple(U, V, W)))) | ((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))),
% 0.14/0.37 inference(modus_ponens,[status(thm)],[43, 35])).
% 0.14/0.37 tff(45,plain,(
% 0.14/0.37 ~((~ok(findmin_cpq_eff(triple(U!2, V!1, W!0)))) | ((~(V!1 = create_slb)) & contains_slb(V!1, findmin_pqp_res(U!2)) & less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_pqp_res(U!2))))),
% 0.14/0.37 inference(skolemize,[status(sab)],[44])).
% 0.14/0.37 tff(46,plain,
% 0.14/0.37 (ok(findmin_cpq_eff(triple(U!2, V!1, W!0)))),
% 0.14/0.37 inference(or_elim,[status(thm)],[45])).
% 0.14/0.37 tff(47,plain,
% 0.14/0.37 (ok(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad))),
% 0.14/0.37 inference(modus_ponens,[status(thm)],[46, 34])).
% 0.14/0.37 tff(48,plain,
% 0.14/0.37 (^[U: $i, V: $i] : refl((~ok(triple(U, V, bad))) <=> (~ok(triple(U, V, bad))))),
% 0.14/0.37 inference(bind,[status(th)],[])).
% 0.14/0.37 tff(49,plain,
% 0.14/0.37 (![U: $i, V: $i] : (~ok(triple(U, V, bad))) <=> ![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.14/0.37 inference(quant_intro,[status(thm)],[48])).
% 0.14/0.37 tff(50,plain,
% 0.14/0.37 (![U: $i, V: $i] : (~ok(triple(U, V, bad))) <=> ![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.14/0.37 inference(rewrite,[status(thm)],[])).
% 0.14/0.37 tff(51,plain,
% 0.14/0.37 (^[U: $i, V: $i] : rewrite((ok(triple(U, V, bad)) <=> $false) <=> (~ok(triple(U, V, bad))))),
% 0.14/0.37 inference(bind,[status(th)],[])).
% 0.14/0.37 tff(52,plain,
% 0.14/0.37 (![U: $i, V: $i] : (ok(triple(U, V, bad)) <=> $false) <=> ![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.14/0.37 inference(quant_intro,[status(thm)],[51])).
% 0.14/0.37 tff(53,axiom,(![U: $i, V: $i] : (ok(triple(U, V, bad)) <=> $false)), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax','ax40')).
% 0.14/0.37 tff(54,plain,
% 0.14/0.37 (![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.14/0.37 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.14/0.37 tff(55,plain,
% 0.14/0.37 (![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.14/0.37 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.14/0.37 tff(56,plain,(
% 0.14/0.37 ![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.14/0.37 inference(skolemize,[status(sab)],[55])).
% 0.14/0.37 tff(57,plain,
% 0.14/0.37 (![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.14/0.37 inference(modus_ponens,[status(thm)],[56, 49])).
% 0.14/0.37 tff(58,plain,
% 0.14/0.37 ((~![U: $i, V: $i] : (~ok(triple(U, V, bad)))) | (~ok(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad)))),
% 0.14/0.37 inference(quant_inst,[status(thm)],[])).
% 0.14/0.37 tff(59,plain,
% 0.14/0.37 (~ok(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad))),
% 0.14/0.37 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.14/0.37 tff(60,plain,
% 0.14/0.37 ($false),
% 0.14/0.37 inference(unit_resolution,[status(thm)],[59, 47])).
% 0.14/0.37 tff(61,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,[]))).
% 0.14/0.37 tff(62,plain,
% 0.14/0.37 ($false),
% 0.14/0.37 inference(unit_resolution,[status(thm)],[61, 30])).
% 0.14/0.37 tff(63,plain,(~(V!1 = create_slb)), inference(lemma,lemma(discharge,[]))).
% 0.14/0.37 tff(64,plain,
% 0.14/0.37 (^[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))))),
% 0.14/0.37 inference(bind,[status(th)],[])).
% 0.14/0.37 tff(65,plain,
% 0.14/0.37 (![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)))),
% 0.14/0.37 inference(quant_intro,[status(thm)],[64])).
% 0.14/0.37 tff(66,plain,
% 0.14/0.37 (![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)))),
% 0.14/0.37 inference(rewrite,[status(thm)],[])).
% 0.14/0.37 tff(67,plain,
% 0.14/0.37 (![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)))),
% 0.14/0.37 inference(elim_unused_vars,[status(thm)],[])).
% 0.14/0.37 tff(68,plain,
% 0.14/0.37 (^[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))))),
% 0.14/0.37 inference(bind,[status(th)],[])).
% 0.14/0.37 tff(69,plain,
% 0.14/0.37 (![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)))),
% 0.14/0.37 inference(quant_intro,[status(thm)],[68])).
% 0.14/0.37 tff(70,plain,
% 0.14/0.37 (![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)))),
% 0.14/0.37 inference(transitivity,[status(thm)],[69, 67])).
% 0.14/0.37 tff(71,axiom,(![U: $i, V: $i, W: $i, X: $i] : ((~(V = create_slb)) => (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax','ax51')).
% 0.14/0.37 tff(72,plain,
% 0.14/0.37 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.14/0.37 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.14/0.37 tff(73,plain,
% 0.14/0.37 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.14/0.37 inference(modus_ponens,[status(thm)],[72, 66])).
% 0.14/0.37 tff(74,plain,(
% 0.14/0.37 ![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.14/0.37 inference(skolemize,[status(sab)],[73])).
% 0.14/0.37 tff(75,plain,
% 0.14/0.37 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.14/0.37 inference(modus_ponens,[status(thm)],[74, 65])).
% 0.14/0.37 tff(76,plain,
% 0.14/0.37 (((~![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)))),
% 0.14/0.37 inference(rewrite,[status(thm)],[])).
% 0.14/0.37 tff(77,plain,
% 0.14/0.37 ((~![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)))),
% 0.14/0.37 inference(quant_inst,[status(thm)],[])).
% 0.14/0.37 tff(78,plain,
% 0.14/0.37 ((~![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))),
% 0.14/0.37 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.14/0.37 tff(79,plain,
% 0.14/0.37 ((V!1 = create_slb) | (findmin_cpq_res(triple(U!2, V!1, W!0)) = findmin_pqp_res(U!2))),
% 0.14/0.37 inference(unit_resolution,[status(thm)],[78, 75])).
% 0.14/0.37 tff(80,plain,
% 0.14/0.37 (findmin_cpq_res(triple(U!2, V!1, W!0)) = findmin_pqp_res(U!2)),
% 0.14/0.37 inference(unit_resolution,[status(thm)],[79, 63])).
% 0.14/0.37 tff(81,plain,
% 0.14/0.37 (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))),
% 0.14/0.37 inference(monotonicity,[status(thm)],[80])).
% 0.14/0.37 tff(82,plain,
% 0.14/0.37 (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)))),
% 0.14/0.37 inference(symmetry,[status(thm)],[81])).
% 0.14/0.37 tff(83,plain,
% 0.14/0.37 ((~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))))),
% 0.14/0.37 inference(monotonicity,[status(thm)],[82])).
% 0.14/0.37 tff(84,plain,
% 0.14/0.37 (^[U: $i, V: $i, W: $i] : refl((contains_slb(V, findmin_pqp_res(U)) | (V = create_slb) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> (contains_slb(V, findmin_pqp_res(U)) | (V = create_slb) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))))),
% 0.14/0.37 inference(bind,[status(th)],[])).
% 0.14/0.37 tff(85,plain,
% 0.14/0.37 (![U: $i, V: $i, W: $i] : (contains_slb(V, findmin_pqp_res(U)) | (V = create_slb) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ![U: $i, V: $i, W: $i] : (contains_slb(V, findmin_pqp_res(U)) | (V = create_slb) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.14/0.37 inference(quant_intro,[status(thm)],[84])).
% 0.14/0.37 tff(86,plain,
% 0.14/0.37 (^[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))) <=> (contains_slb(V, findmin_pqp_res(U)) | (V = create_slb) | (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))) <=> (contains_slb(V, findmin_pqp_res(U)) | (V = create_slb) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))))),
% 0.14/0.37 inference(bind,[status(th)],[])).
% 0.14/0.37 tff(87,plain,
% 0.14/0.37 (![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] : (contains_slb(V, findmin_pqp_res(U)) | (V = create_slb) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.14/0.37 inference(quant_intro,[status(thm)],[86])).
% 0.14/0.37 tff(88,plain,
% 0.14/0.37 (![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)))),
% 0.14/0.37 inference(rewrite,[status(thm)],[])).
% 0.14/0.37 tff(89,plain,
% 0.14/0.37 (![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)))),
% 0.14/0.37 inference(elim_unused_vars,[status(thm)],[])).
% 0.14/0.37 tff(90,plain,
% 0.14/0.37 (^[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))))),
% 0.14/0.37 inference(bind,[status(th)],[])).
% 0.14/0.37 tff(91,plain,
% 0.14/0.37 (![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)))),
% 0.14/0.37 inference(quant_intro,[status(thm)],[90])).
% 0.14/0.37 tff(92,plain,
% 0.14/0.37 (![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)))),
% 0.14/0.37 inference(transitivity,[status(thm)],[91, 89])).
% 0.14/0.37 tff(93,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')).
% 0.14/0.37 tff(94,plain,
% 0.14/0.37 (![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)))),
% 0.14/0.37 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.14/0.37 tff(95,plain,
% 0.14/0.37 (![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)))),
% 0.14/0.37 inference(modus_ponens,[status(thm)],[94, 88])).
% 0.14/0.37 tff(96,plain,(
% 0.14/0.37 ![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)))),
% 0.14/0.37 inference(skolemize,[status(sab)],[95])).
% 0.14/0.37 tff(97,plain,
% 0.14/0.37 (![U: $i, V: $i, W: $i] : (contains_slb(V, findmin_pqp_res(U)) | (V = create_slb) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.14/0.37 inference(modus_ponens,[status(thm)],[96, 87])).
% 0.14/0.37 tff(98,plain,
% 0.14/0.37 (![U: $i, V: $i, W: $i] : (contains_slb(V, findmin_pqp_res(U)) | (V = create_slb) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.14/0.37 inference(modus_ponens,[status(thm)],[97, 85])).
% 0.14/0.37 tff(99,plain,
% 0.14/0.37 (((~![U: $i, V: $i, W: $i] : (contains_slb(V, findmin_pqp_res(U)) | (V = create_slb) | (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] : (contains_slb(V, findmin_pqp_res(U)) | (V = create_slb) | (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)))),
% 0.14/0.37 inference(rewrite,[status(thm)],[])).
% 0.14/0.37 tff(100,plain,
% 0.14/0.37 ((contains_slb(V!1, findmin_pqp_res(U!2)) | (V!1 = create_slb) | (findmin_cpq_eff(triple(U!2, V!1, W!0)) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), 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)))),
% 0.14/0.37 inference(rewrite,[status(thm)],[])).
% 0.14/0.37 tff(101,plain,
% 0.14/0.37 (((~![U: $i, V: $i, W: $i] : (contains_slb(V, findmin_pqp_res(U)) | (V = create_slb) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))) | (contains_slb(V!1, findmin_pqp_res(U!2)) | (V!1 = create_slb) | (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] : (contains_slb(V, findmin_pqp_res(U)) | (V = create_slb) | (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))))),
% 0.14/0.38 inference(monotonicity,[status(thm)],[100])).
% 0.14/0.38 tff(102,plain,
% 0.14/0.38 (((~![U: $i, V: $i, W: $i] : (contains_slb(V, findmin_pqp_res(U)) | (V = create_slb) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))) | (contains_slb(V!1, findmin_pqp_res(U!2)) | (V!1 = create_slb) | (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] : (contains_slb(V, findmin_pqp_res(U)) | (V = create_slb) | (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)))),
% 0.14/0.38 inference(transitivity,[status(thm)],[101, 99])).
% 0.14/0.38 tff(103,plain,
% 0.14/0.38 ((~![U: $i, V: $i, W: $i] : (contains_slb(V, findmin_pqp_res(U)) | (V = create_slb) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))) | (contains_slb(V!1, findmin_pqp_res(U!2)) | (V!1 = create_slb) | (findmin_cpq_eff(triple(U!2, V!1, W!0)) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad)))),
% 0.14/0.38 inference(quant_inst,[status(thm)],[])).
% 0.14/0.38 tff(104,plain,
% 0.14/0.38 ((~![U: $i, V: $i, W: $i] : (contains_slb(V, findmin_pqp_res(U)) | (V = create_slb) | (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))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.14/0.38 tff(105,plain,
% 0.14/0.38 ((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))),
% 0.14/0.38 inference(unit_resolution,[status(thm)],[104, 98])).
% 0.14/0.38 tff(106,plain,
% 0.14/0.38 (contains_slb(V!1, findmin_pqp_res(U!2))),
% 0.14/0.38 inference(unit_resolution,[status(thm)],[105, 63, 61])).
% 0.14/0.38 tff(107,plain,
% 0.14/0.38 ((~(~((V!1 = create_slb) | (~contains_slb(V!1, findmin_pqp_res(U!2))) | (~less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_pqp_res(U!2)))))) <=> ((V!1 = create_slb) | (~contains_slb(V!1, findmin_pqp_res(U!2))) | (~less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_pqp_res(U!2))))),
% 0.14/0.38 inference(rewrite,[status(thm)],[])).
% 0.14/0.38 tff(108,plain,
% 0.14/0.38 (((~(V!1 = create_slb)) & contains_slb(V!1, findmin_pqp_res(U!2)) & less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_pqp_res(U!2))) <=> (~((V!1 = create_slb) | (~contains_slb(V!1, findmin_pqp_res(U!2))) | (~less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_pqp_res(U!2)))))),
% 0.14/0.38 inference(rewrite,[status(thm)],[])).
% 0.14/0.38 tff(109,plain,
% 0.14/0.38 ((~((~(V!1 = create_slb)) & contains_slb(V!1, findmin_pqp_res(U!2)) & less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_pqp_res(U!2)))) <=> (~(~((V!1 = create_slb) | (~contains_slb(V!1, findmin_pqp_res(U!2))) | (~less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_pqp_res(U!2))))))),
% 0.14/0.38 inference(monotonicity,[status(thm)],[108])).
% 0.14/0.38 tff(110,plain,
% 0.14/0.38 ((~((~(V!1 = create_slb)) & contains_slb(V!1, findmin_pqp_res(U!2)) & less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_pqp_res(U!2)))) <=> ((V!1 = create_slb) | (~contains_slb(V!1, findmin_pqp_res(U!2))) | (~less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_pqp_res(U!2))))),
% 0.14/0.38 inference(transitivity,[status(thm)],[109, 107])).
% 0.14/0.38 tff(111,plain,
% 0.14/0.38 (~((~(V!1 = create_slb)) & contains_slb(V!1, findmin_pqp_res(U!2)) & less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_pqp_res(U!2)))),
% 0.14/0.38 inference(or_elim,[status(thm)],[45])).
% 0.14/0.38 tff(112,plain,
% 0.14/0.38 ((V!1 = create_slb) | (~contains_slb(V!1, findmin_pqp_res(U!2))) | (~less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_pqp_res(U!2)))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.14/0.38 tff(113,plain,
% 0.14/0.38 (~less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_pqp_res(U!2))),
% 0.14/0.38 inference(unit_resolution,[status(thm)],[112, 106, 63])).
% 0.14/0.38 tff(114,plain,
% 0.14/0.38 (~less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_cpq_res(triple(U!2, V!1, W!0)))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[113, 83])).
% 0.14/0.38 tff(115,plain,
% 0.14/0.38 (^[U: $i, V: $i] : refl((strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U)))) <=> (strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U)))))),
% 0.14/0.38 inference(bind,[status(th)],[])).
% 0.14/0.38 tff(116,plain,
% 0.14/0.38 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U)))) <=> ![U: $i, V: $i] : (strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U))))),
% 0.14/0.38 inference(quant_intro,[status(thm)],[115])).
% 0.14/0.38 tff(117,plain,
% 0.14/0.38 (^[U: $i, V: $i] : rewrite((strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U)))) <=> (strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U)))))),
% 0.14/0.38 inference(bind,[status(th)],[])).
% 0.14/0.38 tff(118,plain,
% 0.14/0.38 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U)))) <=> ![U: $i, V: $i] : (strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U))))),
% 0.14/0.38 inference(quant_intro,[status(thm)],[117])).
% 0.14/0.38 tff(119,plain,
% 0.14/0.38 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U)))) <=> ![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.14/0.38 inference(rewrite,[status(thm)],[])).
% 0.14/0.38 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')).
% 0.14/0.38 tff(121,plain,
% 0.14/0.38 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.14/0.38 tff(122,plain,(
% 0.14/0.38 ![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.14/0.38 inference(skolemize,[status(sab)],[121])).
% 0.14/0.38 tff(123,plain,
% 0.14/0.38 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U))))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[122, 118])).
% 0.14/0.38 tff(124,plain,
% 0.14/0.38 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U))))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[123, 116])).
% 0.14/0.38 tff(125,plain,
% 0.14/0.38 ((~![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))))))),
% 0.14/0.38 inference(quant_inst,[status(thm)],[])).
% 0.14/0.38 tff(126,plain,
% 0.14/0.38 (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)))))),
% 0.14/0.38 inference(unit_resolution,[status(thm)],[125, 124])).
% 0.14/0.38 tff(127,plain,
% 0.14/0.38 (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)))),
% 0.14/0.38 inference(monotonicity,[status(thm)],[80])).
% 0.14/0.38 tff(128,plain,
% 0.14/0.38 (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)))),
% 0.14/0.38 inference(symmetry,[status(thm)],[127])).
% 0.14/0.38 tff(129,plain,
% 0.14/0.38 ((~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))))),
% 0.14/0.38 inference(monotonicity,[status(thm)],[128])).
% 0.14/0.38 tff(130,plain,
% 0.14/0.38 (^[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))))))),
% 0.14/0.38 inference(bind,[status(th)],[])).
% 0.14/0.38 tff(131,plain,
% 0.14/0.38 (![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)))))),
% 0.14/0.38 inference(quant_intro,[status(thm)],[130])).
% 0.14/0.38 tff(132,plain,
% 0.14/0.38 (^[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)))))))),
% 0.14/0.38 inference(bind,[status(th)],[])).
% 0.14/0.38 tff(133,plain,
% 0.14/0.38 (![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)))))),
% 0.14/0.38 inference(quant_intro,[status(thm)],[132])).
% 0.14/0.38 tff(134,plain,
% 0.14/0.38 (![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)))),
% 0.14/0.38 inference(rewrite,[status(thm)],[])).
% 0.14/0.38 tff(135,plain,
% 0.14/0.38 (![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)))),
% 0.14/0.38 inference(elim_unused_vars,[status(thm)],[])).
% 0.14/0.38 tff(136,plain,
% 0.14/0.38 (^[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)))))),
% 0.14/0.38 inference(bind,[status(th)],[])).
% 0.14/0.38 tff(137,plain,
% 0.14/0.38 (![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)))),
% 0.14/0.38 inference(quant_intro,[status(thm)],[136])).
% 0.14/0.38 tff(138,plain,
% 0.14/0.38 (![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)))),
% 0.14/0.38 inference(transitivity,[status(thm)],[137, 135])).
% 0.14/0.38 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')).
% 0.14/0.38 tff(140,plain,
% 0.14/0.38 (![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)))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.14/0.38 tff(141,plain,
% 0.14/0.38 (![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)))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[140, 134])).
% 0.14/0.38 tff(142,plain,(
% 0.14/0.38 ![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)))),
% 0.14/0.38 inference(skolemize,[status(sab)],[141])).
% 0.14/0.38 tff(143,plain,
% 0.14/0.38 (![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)))))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[142, 133])).
% 0.14/0.38 tff(144,plain,
% 0.14/0.38 (![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)))))),
% 0.14/0.38 inference(modus_ponens,[status(thm)],[143, 131])).
% 0.14/0.38 tff(145,plain,
% 0.14/0.38 (((~![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)))))),
% 0.14/0.38 inference(rewrite,[status(thm)],[])).
% 0.14/0.38 tff(146,plain,
% 0.14/0.38 ((~![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)))))),
% 0.14/0.39 inference(quant_inst,[status(thm)],[])).
% 0.14/0.39 tff(147,plain,
% 0.14/0.39 ((~![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))))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.14/0.39 tff(148,plain,
% 0.14/0.39 ((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))))),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[147, 144])).
% 0.14/0.39 tff(149,plain,
% 0.14/0.39 (~strictly_less_than(findmin_pqp_res(U!2), lookup_slb(V!1, findmin_pqp_res(U!2)))),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[148, 106, 61, 63])).
% 0.14/0.39 tff(150,plain,
% 0.14/0.39 (~strictly_less_than(findmin_cpq_res(triple(U!2, V!1, W!0)), lookup_slb(V!1, findmin_pqp_res(U!2)))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[149, 129])).
% 0.14/0.39 tff(151,plain,
% 0.14/0.39 ((~(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))))),
% 0.14/0.39 inference(tautology,[status(thm)],[])).
% 0.14/0.39 tff(152,plain,
% 0.14/0.39 ((~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)))),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[151, 150, 126])).
% 0.14/0.39 tff(153,plain,
% 0.14/0.39 ((~((~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)))),
% 0.14/0.39 inference(tautology,[status(thm)],[])).
% 0.14/0.39 tff(154,plain,
% 0.14/0.39 (~less_than(findmin_cpq_res(triple(U!2, V!1, W!0)), lookup_slb(V!1, findmin_pqp_res(U!2)))),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[153, 114, 152])).
% 0.14/0.39 tff(155,plain,
% 0.14/0.39 (^[U: $i, V: $i] : refl((less_than(V, U) | less_than(U, V)) <=> (less_than(V, U) | less_than(U, V)))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(156,plain,
% 0.14/0.39 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.14/0.39 inference(quant_intro,[status(thm)],[155])).
% 0.14/0.39 tff(157,plain,
% 0.14/0.39 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(158,plain,
% 0.14/0.39 (^[U: $i, V: $i] : rewrite((less_than(U, V) | less_than(V, U)) <=> (less_than(V, U) | less_than(U, V)))),
% 0.14/0.39 inference(bind,[status(th)],[])).
% 0.14/0.39 tff(159,plain,
% 0.14/0.39 (![U: $i, V: $i] : (less_than(U, V) | less_than(V, U)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.14/0.39 inference(quant_intro,[status(thm)],[158])).
% 0.14/0.39 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')).
% 0.14/0.39 tff(161,plain,
% 0.14/0.39 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.14/0.39 tff(162,plain,
% 0.14/0.39 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[161, 157])).
% 0.14/0.39 tff(163,plain,(
% 0.14/0.39 ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.14/0.39 inference(skolemize,[status(sab)],[162])).
% 0.14/0.39 tff(164,plain,
% 0.14/0.39 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[163, 156])).
% 0.14/0.39 tff(165,plain,
% 0.14/0.39 (((~![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))))),
% 0.14/0.39 inference(rewrite,[status(thm)],[])).
% 0.14/0.39 tff(166,plain,
% 0.14/0.39 ((~![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))))),
% 0.14/0.39 inference(quant_inst,[status(thm)],[])).
% 0.14/0.39 tff(167,plain,
% 0.14/0.39 ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | less_than(findmin_cpq_res(triple(U!2, V!1, W!0)), lookup_slb(V!1, findmin_pqp_res(U!2))) | less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_cpq_res(triple(U!2, V!1, W!0)))),
% 0.14/0.39 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.14/0.39 tff(168,plain,
% 0.14/0.39 (less_than(findmin_cpq_res(triple(U!2, V!1, W!0)), lookup_slb(V!1, findmin_pqp_res(U!2))) | less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_cpq_res(triple(U!2, V!1, W!0)))),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[167, 164])).
% 0.14/0.39 tff(169,plain,
% 0.14/0.39 ($false),
% 0.14/0.39 inference(unit_resolution,[status(thm)],[168, 154, 114])).
% 0.14/0.39 % SZS output end Proof
%------------------------------------------------------------------------------