%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV379+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 : Sat Jun 21 05:32:20 AM UTC 2025
% Result : Theorem 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWV379+1 : TPTP v9.0.0. Released v3.3.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 09:44:54 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.38 % SZS status Theorem
% 0.19/0.38 % SZS output start Proof
% 0.19/0.38 tff(triple_type, type, (
% 0.19/0.38 triple: ( $i * $i * $i ) > $i)).
% 0.19/0.38 tff(bad_type, type, (
% 0.19/0.38 bad: $i)).
% 0.19/0.38 tff(update_slb_type, type, (
% 0.19/0.38 update_slb: ( $i * $i ) > $i)).
% 0.19/0.38 tff(findmin_pqp_res_type, type, (
% 0.19/0.38 findmin_pqp_res: $i > $i)).
% 0.19/0.38 tff(tptp_fun_U_2_type, type, (
% 0.19/0.38 tptp_fun_U_2: $i)).
% 0.19/0.38 tff(tptp_fun_V_1_type, type, (
% 0.19/0.38 tptp_fun_V_1: $i)).
% 0.19/0.38 tff(findmin_cpq_eff_type, type, (
% 0.19/0.38 findmin_cpq_eff: $i > $i)).
% 0.19/0.38 tff(tptp_fun_W_0_type, type, (
% 0.19/0.38 tptp_fun_W_0: $i)).
% 0.19/0.38 tff(ok_type, type, (
% 0.19/0.38 ok: $i > $o)).
% 0.19/0.38 tff(create_slb_type, type, (
% 0.19/0.38 create_slb: $i)).
% 0.19/0.38 tff(less_than_type, type, (
% 0.19/0.38 less_than: ( $i * $i ) > $o)).
% 0.19/0.38 tff(findmin_cpq_res_type, type, (
% 0.19/0.38 findmin_cpq_res: $i > $i)).
% 0.19/0.38 tff(lookup_slb_type, type, (
% 0.19/0.38 lookup_slb: ( $i * $i ) > $i)).
% 0.19/0.38 tff(contains_slb_type, type, (
% 0.19/0.38 contains_slb: ( $i * $i ) > $o)).
% 0.19/0.38 tff(strictly_less_than_type, type, (
% 0.19/0.38 strictly_less_than: ( $i * $i ) > $o)).
% 0.19/0.38 tff(1,plain,
% 0.19/0.38 ((~![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))))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(2,plain,
% 0.19/0.38 ((~![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))))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 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/sandbox/benchmark/theBenchmark.p','l15_co')).
% 0.19/0.38 tff(4,plain,
% 0.19/0.38 (~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~ok(findmin_cpq_eff(triple(U, V, W)))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.19/0.38 tff(5,plain,
% 0.19/0.38 (~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~ok(findmin_cpq_eff(triple(U, V, W)))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.19/0.38 tff(6,plain,
% 0.19/0.38 (~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~ok(findmin_cpq_eff(triple(U, V, W)))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.19/0.38 tff(7,plain,
% 0.19/0.38 (~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~ok(findmin_cpq_eff(triple(U, V, W)))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.19/0.38 tff(8,plain,(
% 0.19/0.38 ~(ok(triple(U!2, V!1, W!0)) | (~ok(findmin_cpq_eff(triple(U!2, V!1, W!0)))))),
% 0.19/0.38 inference(skolemize,[status(sab)],[7])).
% 0.19/0.38 tff(9,plain,
% 0.19/0.38 (~ok(triple(U!2, V!1, W!0))),
% 0.19/0.38 inference(or_elim,[status(thm)],[8])).
% 0.19/0.38 tff(10,plain,
% 0.19/0.38 (^[U: $i, V: $i, W: $i] : refl((ok(triple(U, V, W)) | (W = bad)) <=> (ok(triple(U, V, W)) | (W = bad)))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(11,plain,
% 0.19/0.38 (![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))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[10])).
% 0.19/0.38 tff(12,plain,
% 0.19/0.38 (![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))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(13,plain,
% 0.19/0.38 (^[U: $i, V: $i, W: $i] : rewrite(((~ok(triple(U, V, W))) => (W = bad)) <=> (ok(triple(U, V, W)) | (W = bad)))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(14,plain,
% 0.19/0.38 (![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))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[13])).
% 0.19/0.38 tff(15,axiom,(![U: $i, V: $i, W: $i] : ((~ok(triple(U, V, W))) => (W = bad))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax','ax41')).
% 0.19/0.38 tff(16,plain,
% 0.19/0.38 (![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.19/0.38 tff(17,plain,
% 0.19/0.38 (![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.19/0.38 tff(18,plain,(
% 0.19/0.38 ![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))),
% 0.19/0.38 inference(skolemize,[status(sab)],[17])).
% 0.19/0.38 tff(19,plain,
% 0.19/0.38 (![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.19/0.38 tff(20,plain,
% 0.19/0.38 (((~![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))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(21,plain,
% 0.19/0.38 ((~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))) | (ok(triple(U!2, V!1, W!0)) | (W!0 = bad))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(22,plain,
% 0.19/0.38 ((~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))) | ok(triple(U!2, V!1, W!0)) | (W!0 = bad)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.19/0.38 tff(23,plain,
% 0.19/0.38 (W!0 = bad),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[22, 19, 9])).
% 0.19/0.38 tff(24,plain,
% 0.19/0.38 (bad = W!0),
% 0.19/0.38 inference(symmetry,[status(thm)],[23])).
% 0.19/0.38 tff(25,assumption,(~(V!1 = create_slb)), introduced(assumption)).
% 0.19/0.38 tff(26,plain,
% 0.19/0.38 (^[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))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(27,plain,
% 0.19/0.38 (![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)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[26])).
% 0.19/0.38 tff(28,plain,
% 0.19/0.38 (![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)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(29,plain,
% 0.19/0.38 (![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)))),
% 0.19/0.38 inference(elim_unused_vars,[status(thm)],[])).
% 0.19/0.38 tff(30,plain,
% 0.19/0.38 (^[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))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(31,plain,
% 0.19/0.38 (![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)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[30])).
% 0.19/0.38 tff(32,plain,
% 0.19/0.38 (![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)))),
% 0.19/0.38 inference(transitivity,[status(thm)],[31, 29])).
% 0.19/0.38 tff(33,axiom,(![U: $i, V: $i, W: $i, X: $i] : ((~(V = create_slb)) => (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax','ax51')).
% 0.19/0.38 tff(34,plain,
% 0.19/0.38 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.19/0.38 tff(35,plain,
% 0.19/0.38 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[34, 28])).
% 0.19/0.38 tff(36,plain,(
% 0.19/0.38 ![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.19/0.38 inference(skolemize,[status(sab)],[35])).
% 0.19/0.38 tff(37,plain,
% 0.19/0.38 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[36, 27])).
% 0.19/0.38 tff(38,plain,
% 0.19/0.38 (((~![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)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(39,plain,
% 0.19/0.38 ((~![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)))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(40,plain,
% 0.19/0.38 ((~![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))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.19/0.38 tff(41,plain,
% 0.19/0.38 ((V!1 = create_slb) | (findmin_cpq_res(triple(U!2, V!1, W!0)) = findmin_pqp_res(U!2))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[40, 37])).
% 0.19/0.38 tff(42,plain,
% 0.19/0.38 (findmin_cpq_res(triple(U!2, V!1, W!0)) = findmin_pqp_res(U!2)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[41, 25])).
% 0.19/0.38 tff(43,plain,
% 0.19/0.38 (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))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[42])).
% 0.19/0.39 tff(44,plain,
% 0.19/0.39 (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)))),
% 0.19/0.39 inference(symmetry,[status(thm)],[43])).
% 0.19/0.39 tff(45,plain,
% 0.19/0.39 ((~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))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[44])).
% 0.19/0.39 tff(46,plain,
% 0.19/0.39 (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)),
% 0.19/0.39 inference(monotonicity,[status(thm)],[23])).
% 0.19/0.39 tff(47,plain,
% 0.19/0.39 ((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))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[46])).
% 0.19/0.39 tff(48,plain,
% 0.19/0.39 ((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))),
% 0.19/0.39 inference(symmetry,[status(thm)],[47])).
% 0.19/0.39 tff(49,plain,
% 0.19/0.39 ((~(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)))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[48])).
% 0.19/0.39 tff(50,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)).
% 0.19/0.39 tff(51,plain,
% 0.19/0.39 (triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad) = findmin_cpq_eff(triple(U!2, V!1, W!0))),
% 0.19/0.39 inference(symmetry,[status(thm)],[50])).
% 0.19/0.39 tff(52,plain,
% 0.19/0.39 (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)))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[51])).
% 0.19/0.39 tff(53,plain,
% 0.19/0.39 (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))),
% 0.19/0.39 inference(symmetry,[status(thm)],[52])).
% 0.19/0.39 tff(54,plain,
% 0.19/0.39 (ok(findmin_cpq_eff(triple(U!2, V!1, W!0)))),
% 0.19/0.39 inference(or_elim,[status(thm)],[8])).
% 0.19/0.39 tff(55,plain,
% 0.19/0.39 (ok(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.19/0.39 tff(56,plain,
% 0.19/0.39 (^[U: $i, V: $i] : refl((~ok(triple(U, V, bad))) <=> (~ok(triple(U, V, bad))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(57,plain,
% 0.19/0.39 (![U: $i, V: $i] : (~ok(triple(U, V, bad))) <=> ![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[56])).
% 0.19/0.39 tff(58,plain,
% 0.19/0.39 (![U: $i, V: $i] : (~ok(triple(U, V, bad))) <=> ![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(59,plain,
% 0.19/0.39 (^[U: $i, V: $i] : rewrite((ok(triple(U, V, bad)) <=> $false) <=> (~ok(triple(U, V, bad))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(60,plain,
% 0.19/0.39 (![U: $i, V: $i] : (ok(triple(U, V, bad)) <=> $false) <=> ![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[59])).
% 0.19/0.39 tff(61,axiom,(![U: $i, V: $i] : (ok(triple(U, V, bad)) <=> $false)), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax','ax40')).
% 0.19/0.39 tff(62,plain,
% 0.19/0.39 (![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.19/0.39 tff(63,plain,
% 0.19/0.39 (![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.19/0.39 tff(64,plain,(
% 0.19/0.39 ![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[63])).
% 0.19/0.39 tff(65,plain,
% 0.19/0.39 (![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[64, 57])).
% 0.19/0.39 tff(66,plain,
% 0.19/0.39 ((~![U: $i, V: $i] : (~ok(triple(U, V, bad)))) | (~ok(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(67,plain,
% 0.19/0.39 (~ok(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.19/0.39 tff(68,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[67, 55])).
% 0.19/0.39 tff(69,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,[]))).
% 0.19/0.39 tff(70,plain,
% 0.19/0.39 (~(findmin_cpq_eff(triple(U!2, V!1, W!0)) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[69, 49])).
% 0.19/0.39 tff(71,plain,
% 0.19/0.39 (^[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))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(72,plain,
% 0.19/0.39 (![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))) <=> ![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)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[71])).
% 0.19/0.39 tff(73,plain,
% 0.19/0.39 (^[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)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(74,plain,
% 0.19/0.39 (![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))) <=> ![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)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[73])).
% 0.19/0.39 tff(75,plain,
% 0.19/0.39 (![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))) <=> ![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)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(76,plain,
% 0.19/0.39 (![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)))),
% 0.19/0.39 inference(elim_unused_vars,[status(thm)],[])).
% 0.19/0.39 tff(77,plain,
% 0.19/0.39 (^[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))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(78,plain,
% 0.19/0.39 (![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)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[77])).
% 0.19/0.39 tff(79,plain,
% 0.19/0.39 (![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)))),
% 0.19/0.39 inference(transitivity,[status(thm)],[78, 76])).
% 0.19/0.39 tff(80,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/sandbox/benchmark/Axioms/SWV007+3.ax','ax47')).
% 0.19/0.39 tff(81,plain,
% 0.19/0.39 (![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)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.19/0.39 tff(82,plain,
% 0.19/0.39 (![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)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[81, 75])).
% 0.19/0.39 tff(83,plain,(
% 0.19/0.39 ![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)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[82])).
% 0.19/0.39 tff(84,plain,
% 0.19/0.39 (![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)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[83, 74])).
% 0.19/0.39 tff(85,plain,
% 0.19/0.39 (![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)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[84, 72])).
% 0.19/0.39 tff(86,plain,
% 0.19/0.39 (((~![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)))) | ((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)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(87,plain,
% 0.19/0.39 ((~![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)))) | ((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)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(88,plain,
% 0.19/0.39 ((~![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)))) | (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))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.19/0.39 tff(89,plain,
% 0.19/0.39 ((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))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[88, 85])).
% 0.19/0.39 tff(90,plain,
% 0.19/0.39 (contains_slb(V!1, findmin_pqp_res(U!2))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[89, 25, 69])).
% 0.19/0.39 tff(91,plain,
% 0.19/0.39 (^[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)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(92,plain,
% 0.19/0.39 (![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)), 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))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[91])).
% 0.19/0.39 tff(93,plain,
% 0.19/0.39 (^[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))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(94,plain,
% 0.19/0.39 (![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))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[93])).
% 0.19/0.39 tff(95,plain,
% 0.19/0.39 (![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)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(96,plain,
% 0.19/0.39 (![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)))),
% 0.19/0.39 inference(elim_unused_vars,[status(thm)],[])).
% 0.19/0.39 tff(97,plain,
% 0.19/0.39 (^[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)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(98,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[97])).
% 0.19/0.40 tff(99,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(transitivity,[status(thm)],[98, 96])).
% 0.19/0.40 tff(100,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/sandbox/benchmark/Axioms/SWV007+3.ax','ax49')).
% 0.19/0.40 tff(101,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.19/0.40 tff(102,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[101, 95])).
% 0.19/0.40 tff(103,plain,(
% 0.19/0.40 ![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)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[102])).
% 0.19/0.40 tff(104,plain,
% 0.19/0.40 (![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))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[103, 94])).
% 0.19/0.40 tff(105,plain,
% 0.19/0.40 (![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))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[104, 92])).
% 0.19/0.40 tff(106,plain,
% 0.19/0.40 (((~![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))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(107,plain,
% 0.19/0.40 ((~![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))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(108,plain,
% 0.19/0.40 ((~![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)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.19/0.40 tff(109,plain,
% 0.19/0.40 ((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)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[108, 105])).
% 0.19/0.40 tff(110,plain,
% 0.19/0.40 (~less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_pqp_res(U!2))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[109, 90, 70, 25])).
% 0.19/0.40 tff(111,plain,
% 0.19/0.40 (~less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_cpq_res(triple(U!2, V!1, W!0)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[110, 45])).
% 0.19/0.40 tff(112,plain,
% 0.19/0.40 (^[U: $i, V: $i] : refl((less_than(V, U) | less_than(U, V)) <=> (less_than(V, U) | less_than(U, V)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(113,plain,
% 0.19/0.40 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[112])).
% 0.19/0.40 tff(114,plain,
% 0.19/0.40 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(115,plain,
% 0.19/0.40 (^[U: $i, V: $i] : rewrite((less_than(U, V) | less_than(V, U)) <=> (less_than(V, U) | less_than(U, V)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(116,plain,
% 0.19/0.40 (![U: $i, V: $i] : (less_than(U, V) | less_than(V, U)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[115])).
% 0.19/0.40 tff(117,axiom,(![U: $i, V: $i] : (less_than(U, V) | less_than(V, U))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax','totality')).
% 0.19/0.40 tff(118,plain,
% 0.19/0.40 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.19/0.40 tff(119,plain,
% 0.19/0.40 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[118, 114])).
% 0.19/0.40 tff(120,plain,(
% 0.19/0.40 ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.19/0.40 inference(skolemize,[status(sab)],[119])).
% 0.19/0.40 tff(121,plain,
% 0.19/0.40 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[120, 113])).
% 0.19/0.40 tff(122,plain,
% 0.19/0.40 (((~![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))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(123,plain,
% 0.19/0.40 ((~![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))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(124,plain,
% 0.19/0.40 ((~![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)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.19/0.40 tff(125,plain,
% 0.19/0.40 (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)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[124, 121])).
% 0.19/0.40 tff(126,plain,
% 0.19/0.40 (less_than(findmin_cpq_res(triple(U!2, V!1, W!0)), lookup_slb(V!1, findmin_pqp_res(U!2)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[125, 111])).
% 0.19/0.40 tff(127,plain,
% 0.19/0.40 (^[U: $i, V: $i] : refl((~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V))) <=> (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(128,plain,
% 0.19/0.40 (![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V))) <=> ![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[127])).
% 0.19/0.40 tff(129,plain,
% 0.19/0.40 (^[U: $i, V: $i] : trans(trans(monotonicity(rewrite((less_than(U, V) & (~less_than(V, U))) <=> (~((~less_than(U, V)) | less_than(V, U)))), ((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)))))), rewrite((strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U)))) <=> (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))), ((strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U)))) <=> (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V))))), rewrite((~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V))) <=> (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))), ((strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U)))) <=> (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(130,plain,
% 0.19/0.40 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U)))) <=> ![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[129])).
% 0.19/0.40 tff(131,plain,
% 0.19/0.40 (![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))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(132,axiom,(![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax','stricly_smaller_definition')).
% 0.19/0.40 tff(133,plain,
% 0.19/0.40 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.19/0.40 tff(134,plain,(
% 0.19/0.40 ![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[133])).
% 0.19/0.40 tff(135,plain,
% 0.19/0.40 (![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[134, 130])).
% 0.19/0.40 tff(136,plain,
% 0.19/0.40 (![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[135, 128])).
% 0.19/0.40 tff(137,plain,
% 0.19/0.40 ((~![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_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)))) <=> strictly_less_than(findmin_cpq_res(triple(U!2, V!1, W!0)), lookup_slb(V!1, findmin_pqp_res(U!2)))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(138,plain,
% 0.19/0.40 (~(((~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))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[137, 136])).
% 0.19/0.40 tff(139,plain,
% 0.19/0.40 (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)))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[42])).
% 0.19/0.40 tff(140,plain,
% 0.19/0.40 (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)))),
% 0.19/0.40 inference(symmetry,[status(thm)],[139])).
% 0.19/0.40 tff(141,plain,
% 0.19/0.40 ((~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))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[140])).
% 0.19/0.40 tff(142,plain,
% 0.19/0.40 (^[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))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(143,plain,
% 0.19/0.40 (![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)))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[142])).
% 0.19/0.40 tff(144,plain,
% 0.19/0.40 (^[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)))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(145,plain,
% 0.19/0.40 (![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)))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[144])).
% 0.19/0.40 tff(146,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(147,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(elim_unused_vars,[status(thm)],[])).
% 0.19/0.40 tff(148,plain,
% 0.19/0.40 (^[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)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(149,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[148])).
% 0.19/0.41 tff(150,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(transitivity,[status(thm)],[149, 147])).
% 0.19/0.41 tff(151,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/sandbox/benchmark/Axioms/SWV007+3.ax','ax48')).
% 0.19/0.41 tff(152,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.19/0.41 tff(153,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[152, 146])).
% 0.19/0.41 tff(154,plain,(
% 0.19/0.41 ![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)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[153])).
% 0.19/0.41 tff(155,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)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[154, 145])).
% 0.19/0.41 tff(156,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)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[155, 143])).
% 0.19/0.41 tff(157,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)) | (~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)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(158,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)) | (~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)))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(159,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)) | (~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))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.19/0.41 tff(160,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)) | (~strictly_less_than(findmin_pqp_res(U!2), lookup_slb(V!1, findmin_pqp_res(U!2))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[159, 156])).
% 0.19/0.41 tff(161,plain,
% 0.19/0.41 (~strictly_less_than(findmin_pqp_res(U!2), lookup_slb(V!1, findmin_pqp_res(U!2)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[160, 90, 69, 25])).
% 0.19/0.41 tff(162,plain,
% 0.19/0.41 (~strictly_less_than(findmin_cpq_res(triple(U!2, V!1, W!0)), lookup_slb(V!1, findmin_pqp_res(U!2)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[161, 141])).
% 0.19/0.41 tff(163,plain,
% 0.19/0.41 ((((~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)))) | strictly_less_than(findmin_cpq_res(triple(U!2, V!1, W!0)), lookup_slb(V!1, findmin_pqp_res(U!2)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(164,plain,
% 0.19/0.41 ((~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)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[163, 162, 138])).
% 0.19/0.41 tff(165,plain,
% 0.19/0.41 ((~((~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)))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(166,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[165, 164, 126, 111])).
% 0.19/0.41 tff(167,plain,(V!1 = create_slb), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(168,plain,
% 0.19/0.41 (create_slb = V!1),
% 0.19/0.41 inference(symmetry,[status(thm)],[167])).
% 0.19/0.41 tff(169,plain,
% 0.19/0.41 (^[U: $i] : refl((update_slb(create_slb, U) = create_slb) <=> (update_slb(create_slb, U) = create_slb))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(170,plain,
% 0.19/0.41 (![U: $i] : (update_slb(create_slb, U) = create_slb) <=> ![U: $i] : (update_slb(create_slb, U) = create_slb)),
% 0.19/0.41 inference(quant_intro,[status(thm)],[169])).
% 0.19/0.41 tff(171,plain,
% 0.19/0.41 (![U: $i] : (update_slb(create_slb, U) = create_slb) <=> ![U: $i] : (update_slb(create_slb, U) = create_slb)),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(172,axiom,(![U: $i] : (update_slb(create_slb, U) = create_slb)), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+2.ax','ax28')).
% 0.19/0.41 tff(173,plain,
% 0.19/0.41 (![U: $i] : (update_slb(create_slb, U) = create_slb)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.19/0.41 tff(174,plain,(
% 0.19/0.41 ![U: $i] : (update_slb(create_slb, U) = create_slb)),
% 0.19/0.41 inference(skolemize,[status(sab)],[173])).
% 0.19/0.41 tff(175,plain,
% 0.19/0.41 (![U: $i] : (update_slb(create_slb, U) = create_slb)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[174, 170])).
% 0.19/0.41 tff(176,plain,
% 0.19/0.41 ((~![U: $i] : (update_slb(create_slb, U) = create_slb)) | (update_slb(create_slb, findmin_pqp_res(U!2)) = create_slb)),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(177,plain,
% 0.19/0.41 (update_slb(create_slb, findmin_pqp_res(U!2)) = create_slb),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[176, 175])).
% 0.19/0.41 tff(178,plain,
% 0.19/0.41 (update_slb(V!1, findmin_pqp_res(U!2)) = update_slb(create_slb, findmin_pqp_res(U!2))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[167])).
% 0.19/0.41 tff(179,plain,
% 0.19/0.41 (update_slb(V!1, findmin_pqp_res(U!2)) = V!1),
% 0.19/0.41 inference(transitivity,[status(thm)],[178, 177, 168])).
% 0.19/0.41 tff(180,plain,
% 0.19/0.41 (triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad) = triple(U!2, V!1, W!0)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[179, 24])).
% 0.19/0.41 tff(181,plain,
% 0.19/0.41 (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(symmetry,[status(thm)],[180])).
% 0.19/0.41 tff(182,plain,
% 0.19/0.41 (triple(U!2, create_slb, bad) = triple(U!2, V!1, W!0)),
% 0.19/0.41 inference(monotonicity,[status(thm)],[168, 24])).
% 0.19/0.41 tff(183,plain,
% 0.19/0.41 (^[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)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(184,plain,
% 0.19/0.41 (![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))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[183])).
% 0.19/0.41 tff(185,plain,
% 0.19/0.41 (![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))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(186,axiom,(![U: $i, V: $i] : (findmin_cpq_eff(triple(U, create_slb, V)) = triple(U, create_slb, bad))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax','ax46')).
% 0.19/0.41 tff(187,plain,
% 0.19/0.41 (![U: $i, V: $i] : (findmin_cpq_eff(triple(U, create_slb, V)) = triple(U, create_slb, bad))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.19/0.41 tff(188,plain,(
% 0.19/0.41 ![U: $i, V: $i] : (findmin_cpq_eff(triple(U, create_slb, V)) = triple(U, create_slb, bad))),
% 0.19/0.41 inference(skolemize,[status(sab)],[187])).
% 0.19/0.41 tff(189,plain,
% 0.19/0.41 (![U: $i, V: $i] : (findmin_cpq_eff(triple(U, create_slb, V)) = triple(U, create_slb, bad))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[188, 184])).
% 0.19/0.41 tff(190,plain,
% 0.19/0.41 ((~![U: $i, V: $i] : (findmin_cpq_eff(triple(U, create_slb, V)) = triple(U, create_slb, bad))) | (findmin_cpq_eff(triple(U!2, create_slb, bad)) = triple(U!2, create_slb, bad))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(191,plain,
% 0.19/0.42 (findmin_cpq_eff(triple(U!2, create_slb, bad)) = triple(U!2, create_slb, bad)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[190, 189])).
% 0.19/0.42 tff(192,plain,
% 0.19/0.42 (triple(U!2, V!1, W!0) = triple(U!2, create_slb, bad)),
% 0.19/0.42 inference(symmetry,[status(thm)],[182])).
% 0.19/0.42 tff(193,plain,
% 0.19/0.42 (findmin_cpq_eff(triple(U!2, V!1, W!0)) = findmin_cpq_eff(triple(U!2, create_slb, bad))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[192])).
% 0.19/0.42 tff(194,plain,
% 0.19/0.42 (findmin_cpq_eff(triple(U!2, V!1, W!0)) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad)),
% 0.19/0.42 inference(transitivity,[status(thm)],[193, 191, 182, 181])).
% 0.19/0.42 tff(195,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[69, 194])).
% 0.19/0.42 % SZS output end Proof
% 0.19/0.42 % E exiting
%------------------------------------------------------------------------------