%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV380+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 0.23s 0.42s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.15 % Problem : SWV380+1 : TPTP v9.0.0. Released v3.3.0.
% 0.04/0.15 % Command : run_E %s %d THM
% 0.14/0.37 % Computer : n015.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Fri Jun 20 09:44:56 EDT 2025
% 0.14/0.37 % CPUTime :
% 0.23/0.42 % SZS status Theorem
% 0.23/0.42 % SZS output start Proof
% 0.23/0.42 tff(triple_type, type, (
% 0.23/0.42 triple: ( $i * $i * $i ) > $i)).
% 0.23/0.42 tff(bad_type, type, (
% 0.23/0.42 bad: $i)).
% 0.23/0.42 tff(update_slb_type, type, (
% 0.23/0.42 update_slb: ( $i * $i ) > $i)).
% 0.23/0.42 tff(findmin_pqp_res_type, type, (
% 0.23/0.42 findmin_pqp_res: $i > $i)).
% 0.23/0.42 tff(tptp_fun_U_2_type, type, (
% 0.23/0.42 tptp_fun_U_2: $i)).
% 0.23/0.42 tff(tptp_fun_V_1_type, type, (
% 0.23/0.42 tptp_fun_V_1: $i)).
% 0.23/0.42 tff(findmin_cpq_eff_type, type, (
% 0.23/0.42 findmin_cpq_eff: $i > $i)).
% 0.23/0.42 tff(tptp_fun_W_0_type, type, (
% 0.23/0.42 tptp_fun_W_0: $i)).
% 0.23/0.42 tff(ok_type, type, (
% 0.23/0.42 ok: $i > $o)).
% 0.23/0.42 tff(removemin_cpq_eff_type, type, (
% 0.23/0.42 removemin_cpq_eff: $i > $i)).
% 0.23/0.42 tff(create_slb_type, type, (
% 0.23/0.42 create_slb: $i)).
% 0.23/0.42 tff(less_than_type, type, (
% 0.23/0.42 less_than: ( $i * $i ) > $o)).
% 0.23/0.42 tff(findmin_cpq_res_type, type, (
% 0.23/0.42 findmin_cpq_res: $i > $i)).
% 0.23/0.42 tff(lookup_slb_type, type, (
% 0.23/0.42 lookup_slb: ( $i * $i ) > $i)).
% 0.23/0.42 tff(remove_cpq_type, type, (
% 0.23/0.42 remove_cpq: ( $i * $i ) > $i)).
% 0.23/0.42 tff(contains_slb_type, type, (
% 0.23/0.42 contains_slb: ( $i * $i ) > $o)).
% 0.23/0.42 tff(strictly_less_than_type, type, (
% 0.23/0.42 strictly_less_than: ( $i * $i ) > $o)).
% 0.23/0.42 tff(1,plain,
% 0.23/0.42 ((~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~ok(removemin_cpq_eff(triple(U, V, W)))))) <=> (~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~ok(removemin_cpq_eff(triple(U, V, W))))))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(2,plain,
% 0.23/0.42 ((~![U: $i, V: $i, W: $i] : ((~ok(triple(U, V, W))) => (~ok(removemin_cpq_eff(triple(U, V, W)))))) <=> (~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~ok(removemin_cpq_eff(triple(U, V, W))))))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(3,axiom,(~![U: $i, V: $i, W: $i] : ((~ok(triple(U, V, W))) => (~ok(removemin_cpq_eff(triple(U, V, W)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l16_co')).
% 0.23/0.42 tff(4,plain,
% 0.23/0.42 (~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~ok(removemin_cpq_eff(triple(U, V, W)))))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.23/0.42 tff(5,plain,
% 0.23/0.42 (~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~ok(removemin_cpq_eff(triple(U, V, W)))))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.23/0.42 tff(6,plain,
% 0.23/0.42 (~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~ok(removemin_cpq_eff(triple(U, V, W)))))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.23/0.42 tff(7,plain,
% 0.23/0.42 (~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~ok(removemin_cpq_eff(triple(U, V, W)))))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.23/0.42 tff(8,plain,(
% 0.23/0.42 ~(ok(triple(U!2, V!1, W!0)) | (~ok(removemin_cpq_eff(triple(U!2, V!1, W!0)))))),
% 0.23/0.42 inference(skolemize,[status(sab)],[7])).
% 0.23/0.42 tff(9,plain,
% 0.23/0.42 (~ok(triple(U!2, V!1, W!0))),
% 0.23/0.42 inference(or_elim,[status(thm)],[8])).
% 0.23/0.42 tff(10,plain,
% 0.23/0.42 (^[U: $i, V: $i, W: $i] : refl((ok(triple(U, V, W)) | (W = bad)) <=> (ok(triple(U, V, W)) | (W = bad)))),
% 0.23/0.42 inference(bind,[status(th)],[])).
% 0.23/0.42 tff(11,plain,
% 0.23/0.42 (![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))),
% 0.23/0.42 inference(quant_intro,[status(thm)],[10])).
% 0.23/0.42 tff(12,plain,
% 0.23/0.42 (![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))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(13,plain,
% 0.23/0.42 (^[U: $i, V: $i, W: $i] : rewrite(((~ok(triple(U, V, W))) => (W = bad)) <=> (ok(triple(U, V, W)) | (W = bad)))),
% 0.23/0.42 inference(bind,[status(th)],[])).
% 0.23/0.42 tff(14,plain,
% 0.23/0.42 (![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))),
% 0.23/0.42 inference(quant_intro,[status(thm)],[13])).
% 0.23/0.42 tff(15,axiom,(![U: $i, V: $i, W: $i] : ((~ok(triple(U, V, W))) => (W = bad))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax','ax41')).
% 0.23/0.42 tff(16,plain,
% 0.23/0.42 (![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.23/0.42 tff(17,plain,
% 0.23/0.42 (![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.23/0.42 tff(18,plain,(
% 0.23/0.42 ![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))),
% 0.23/0.42 inference(skolemize,[status(sab)],[17])).
% 0.23/0.42 tff(19,plain,
% 0.23/0.42 (![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.23/0.42 tff(20,plain,
% 0.23/0.42 (((~![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))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(21,plain,
% 0.23/0.42 ((~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))) | (ok(triple(U!2, V!1, W!0)) | (W!0 = bad))),
% 0.23/0.42 inference(quant_inst,[status(thm)],[])).
% 0.23/0.42 tff(22,plain,
% 0.23/0.42 ((~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (W = bad))) | ok(triple(U!2, V!1, W!0)) | (W!0 = bad)),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.23/0.42 tff(23,plain,
% 0.23/0.42 (W!0 = bad),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[22, 19, 9])).
% 0.23/0.42 tff(24,plain,
% 0.23/0.42 (bad = W!0),
% 0.23/0.42 inference(symmetry,[status(thm)],[23])).
% 0.23/0.42 tff(25,assumption,(~(V!1 = create_slb)), introduced(assumption)).
% 0.23/0.42 tff(26,plain,
% 0.23/0.42 (^[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))))),
% 0.23/0.42 inference(bind,[status(th)],[])).
% 0.23/0.42 tff(27,plain,
% 0.23/0.42 (![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)))),
% 0.23/0.42 inference(quant_intro,[status(thm)],[26])).
% 0.23/0.42 tff(28,plain,
% 0.23/0.42 (![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)))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(29,plain,
% 0.23/0.42 (![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)))),
% 0.23/0.42 inference(elim_unused_vars,[status(thm)],[])).
% 0.23/0.42 tff(30,plain,
% 0.23/0.42 (^[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))))),
% 0.23/0.42 inference(bind,[status(th)],[])).
% 0.23/0.42 tff(31,plain,
% 0.23/0.42 (![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)))),
% 0.23/0.42 inference(quant_intro,[status(thm)],[30])).
% 0.23/0.42 tff(32,plain,
% 0.23/0.42 (![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)))),
% 0.23/0.42 inference(transitivity,[status(thm)],[31, 29])).
% 0.23/0.42 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/sandbox2/benchmark/Axioms/SWV007+3.ax','ax51')).
% 0.23/0.42 tff(34,plain,
% 0.23/0.42 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.23/0.42 tff(35,plain,
% 0.23/0.42 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[34, 28])).
% 0.23/0.42 tff(36,plain,(
% 0.23/0.42 ![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.23/0.42 inference(skolemize,[status(sab)],[35])).
% 0.23/0.42 tff(37,plain,
% 0.23/0.42 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[36, 27])).
% 0.23/0.42 tff(38,plain,
% 0.23/0.42 (((~![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)))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(39,plain,
% 0.23/0.42 ((~![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)))),
% 0.23/0.42 inference(quant_inst,[status(thm)],[])).
% 0.23/0.42 tff(40,plain,
% 0.23/0.42 ((~![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))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.23/0.42 tff(41,plain,
% 0.23/0.42 ((V!1 = create_slb) | (findmin_cpq_res(triple(U!2, V!1, W!0)) = findmin_pqp_res(U!2))),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[40, 37])).
% 0.23/0.42 tff(42,plain,
% 0.23/0.42 (findmin_cpq_res(triple(U!2, V!1, W!0)) = findmin_pqp_res(U!2)),
% 0.23/0.42 inference(unit_resolution,[status(thm)],[41, 25])).
% 0.23/0.42 tff(43,plain,
% 0.23/0.42 (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))),
% 0.23/0.42 inference(monotonicity,[status(thm)],[42])).
% 0.23/0.42 tff(44,plain,
% 0.23/0.42 (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)))),
% 0.23/0.42 inference(symmetry,[status(thm)],[43])).
% 0.23/0.42 tff(45,plain,
% 0.23/0.42 ((~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))))),
% 0.23/0.42 inference(monotonicity,[status(thm)],[44])).
% 0.23/0.42 tff(46,plain,
% 0.23/0.42 (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)),
% 0.23/0.42 inference(monotonicity,[status(thm)],[23])).
% 0.23/0.42 tff(47,plain,
% 0.23/0.42 ((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))),
% 0.23/0.42 inference(monotonicity,[status(thm)],[46])).
% 0.23/0.42 tff(48,plain,
% 0.23/0.42 ((findmin_cpq_eff(triple(U!2, V!1, W!0)) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad)) <=> (findmin_cpq_eff(triple(U!2, V!1, W!0)) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0))),
% 0.23/0.42 inference(symmetry,[status(thm)],[47])).
% 0.23/0.42 tff(49,plain,
% 0.23/0.42 ((~(findmin_cpq_eff(triple(U!2, V!1, W!0)) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad))) <=> (~(findmin_cpq_eff(triple(U!2, V!1, W!0)) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0)))),
% 0.23/0.42 inference(monotonicity,[status(thm)],[48])).
% 0.23/0.42 tff(50,plain,
% 0.23/0.42 (^[U: $i] : refl((removemin_cpq_eff(U) = remove_cpq(findmin_cpq_eff(U), findmin_cpq_res(U))) <=> (removemin_cpq_eff(U) = remove_cpq(findmin_cpq_eff(U), findmin_cpq_res(U))))),
% 0.23/0.42 inference(bind,[status(th)],[])).
% 0.23/0.42 tff(51,plain,
% 0.23/0.42 (![U: $i] : (removemin_cpq_eff(U) = remove_cpq(findmin_cpq_eff(U), findmin_cpq_res(U))) <=> ![U: $i] : (removemin_cpq_eff(U) = remove_cpq(findmin_cpq_eff(U), findmin_cpq_res(U)))),
% 0.23/0.42 inference(quant_intro,[status(thm)],[50])).
% 0.23/0.42 tff(52,plain,
% 0.23/0.42 (![U: $i] : (removemin_cpq_eff(U) = remove_cpq(findmin_cpq_eff(U), findmin_cpq_res(U))) <=> ![U: $i] : (removemin_cpq_eff(U) = remove_cpq(findmin_cpq_eff(U), findmin_cpq_res(U)))),
% 0.23/0.42 inference(rewrite,[status(thm)],[])).
% 0.23/0.42 tff(53,axiom,(![U: $i] : (removemin_cpq_eff(U) = remove_cpq(findmin_cpq_eff(U), findmin_cpq_res(U)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax','ax52')).
% 0.23/0.42 tff(54,plain,
% 0.23/0.42 (![U: $i] : (removemin_cpq_eff(U) = remove_cpq(findmin_cpq_eff(U), findmin_cpq_res(U)))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.23/0.42 tff(55,plain,(
% 0.23/0.42 ![U: $i] : (removemin_cpq_eff(U) = remove_cpq(findmin_cpq_eff(U), findmin_cpq_res(U)))),
% 0.23/0.42 inference(skolemize,[status(sab)],[54])).
% 0.23/0.42 tff(56,plain,
% 0.23/0.42 (![U: $i] : (removemin_cpq_eff(U) = remove_cpq(findmin_cpq_eff(U), findmin_cpq_res(U)))),
% 0.23/0.42 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.23/0.42 tff(57,plain,
% 0.23/0.42 ((~![U: $i] : (removemin_cpq_eff(U) = remove_cpq(findmin_cpq_eff(U), findmin_cpq_res(U)))) | (removemin_cpq_eff(triple(U!2, V!1, W!0)) = remove_cpq(findmin_cpq_eff(triple(U!2, V!1, W!0)), findmin_cpq_res(triple(U!2, V!1, W!0))))),
% 0.23/0.43 inference(quant_inst,[status(thm)],[])).
% 0.23/0.43 tff(58,plain,
% 0.23/0.43 (removemin_cpq_eff(triple(U!2, V!1, W!0)) = remove_cpq(findmin_cpq_eff(triple(U!2, V!1, W!0)), findmin_cpq_res(triple(U!2, V!1, W!0)))),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.23/0.43 tff(59,plain,
% 0.23/0.43 (remove_cpq(findmin_cpq_eff(triple(U!2, V!1, W!0)), findmin_cpq_res(triple(U!2, V!1, W!0))) = removemin_cpq_eff(triple(U!2, V!1, W!0))),
% 0.23/0.43 inference(symmetry,[status(thm)],[58])).
% 0.23/0.43 tff(60,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)).
% 0.23/0.43 tff(61,plain,
% 0.23/0.43 (triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad) = findmin_cpq_eff(triple(U!2, V!1, W!0))),
% 0.23/0.43 inference(symmetry,[status(thm)],[60])).
% 0.23/0.43 tff(62,plain,
% 0.23/0.43 (remove_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad), findmin_cpq_res(triple(U!2, V!1, W!0))) = remove_cpq(findmin_cpq_eff(triple(U!2, V!1, W!0)), findmin_cpq_res(triple(U!2, V!1, W!0)))),
% 0.23/0.43 inference(monotonicity,[status(thm)],[61])).
% 0.23/0.43 tff(63,plain,
% 0.23/0.43 (remove_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad), findmin_cpq_res(triple(U!2, V!1, W!0))) = removemin_cpq_eff(triple(U!2, V!1, W!0))),
% 0.23/0.43 inference(transitivity,[status(thm)],[62, 59])).
% 0.23/0.43 tff(64,plain,
% 0.23/0.43 (ok(remove_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad), findmin_cpq_res(triple(U!2, V!1, W!0)))) <=> ok(removemin_cpq_eff(triple(U!2, V!1, W!0)))),
% 0.23/0.43 inference(monotonicity,[status(thm)],[63])).
% 0.23/0.43 tff(65,plain,
% 0.23/0.43 (ok(removemin_cpq_eff(triple(U!2, V!1, W!0))) <=> ok(remove_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad), findmin_cpq_res(triple(U!2, V!1, W!0))))),
% 0.23/0.43 inference(symmetry,[status(thm)],[64])).
% 0.23/0.43 tff(66,plain,
% 0.23/0.43 (ok(removemin_cpq_eff(triple(U!2, V!1, W!0)))),
% 0.23/0.43 inference(or_elim,[status(thm)],[8])).
% 0.23/0.43 tff(67,plain,
% 0.23/0.43 (ok(remove_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad), findmin_cpq_res(triple(U!2, V!1, W!0))))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.23/0.43 tff(68,plain,
% 0.23/0.43 (^[U: $i, V: $i] : refl((~ok(triple(U, V, bad))) <=> (~ok(triple(U, V, bad))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(69,plain,
% 0.23/0.43 (![U: $i, V: $i] : (~ok(triple(U, V, bad))) <=> ![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[68])).
% 0.23/0.43 tff(70,plain,
% 0.23/0.43 (![U: $i, V: $i] : (~ok(triple(U, V, bad))) <=> ![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(71,plain,
% 0.23/0.43 (^[U: $i, V: $i] : rewrite((ok(triple(U, V, bad)) <=> $false) <=> (~ok(triple(U, V, bad))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(72,plain,
% 0.23/0.43 (![U: $i, V: $i] : (ok(triple(U, V, bad)) <=> $false) <=> ![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[71])).
% 0.23/0.43 tff(73,axiom,(![U: $i, V: $i] : (ok(triple(U, V, bad)) <=> $false)), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax','ax40')).
% 0.23/0.43 tff(74,plain,
% 0.23/0.43 (![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.23/0.43 tff(75,plain,
% 0.23/0.43 (![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.23/0.43 tff(76,plain,(
% 0.23/0.43 ![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.23/0.43 inference(skolemize,[status(sab)],[75])).
% 0.23/0.43 tff(77,plain,
% 0.23/0.43 (![U: $i, V: $i] : (~ok(triple(U, V, bad)))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[76, 69])).
% 0.23/0.43 tff(78,plain,
% 0.23/0.43 ((~![U: $i, V: $i] : (~ok(triple(U, V, bad)))) | (~ok(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad)))),
% 0.23/0.43 inference(quant_inst,[status(thm)],[])).
% 0.23/0.43 tff(79,plain,
% 0.23/0.43 (~ok(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad))),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.23/0.43 tff(80,plain,
% 0.23/0.43 (^[U: $i, V: $i, W: $i, X: $i] : refl((ok(triple(U, V, W)) | (~ok(remove_cpq(triple(U, V, W), X)))) <=> (ok(triple(U, V, W)) | (~ok(remove_cpq(triple(U, V, W), X)))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(81,plain,
% 0.23/0.43 (![U: $i, V: $i, W: $i, X: $i] : (ok(triple(U, V, W)) | (~ok(remove_cpq(triple(U, V, W), X)))) <=> ![U: $i, V: $i, W: $i, X: $i] : (ok(triple(U, V, W)) | (~ok(remove_cpq(triple(U, V, W), X))))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[80])).
% 0.23/0.43 tff(82,plain,
% 0.23/0.43 (![U: $i, V: $i, W: $i, X: $i] : (ok(triple(U, V, W)) | (~ok(remove_cpq(triple(U, V, W), X)))) <=> ![U: $i, V: $i, W: $i, X: $i] : (ok(triple(U, V, W)) | (~ok(remove_cpq(triple(U, V, W), X))))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(83,plain,
% 0.23/0.43 (^[U: $i, V: $i, W: $i, X: $i] : rewrite(((~ok(triple(U, V, W))) => (~ok(remove_cpq(triple(U, V, W), X)))) <=> (ok(triple(U, V, W)) | (~ok(remove_cpq(triple(U, V, W), X)))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(84,plain,
% 0.23/0.43 (![U: $i, V: $i, W: $i, X: $i] : ((~ok(triple(U, V, W))) => (~ok(remove_cpq(triple(U, V, W), X)))) <=> ![U: $i, V: $i, W: $i, X: $i] : (ok(triple(U, V, W)) | (~ok(remove_cpq(triple(U, V, W), X))))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[83])).
% 0.23/0.43 tff(85,axiom,(![U: $i, V: $i, W: $i, X: $i] : ((~ok(triple(U, V, W))) => (~ok(remove_cpq(triple(U, V, W), X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l16_l14')).
% 0.23/0.43 tff(86,plain,
% 0.23/0.43 (![U: $i, V: $i, W: $i, X: $i] : (ok(triple(U, V, W)) | (~ok(remove_cpq(triple(U, V, W), X))))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.23/0.43 tff(87,plain,
% 0.23/0.43 (![U: $i, V: $i, W: $i, X: $i] : (ok(triple(U, V, W)) | (~ok(remove_cpq(triple(U, V, W), X))))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.23/0.43 tff(88,plain,(
% 0.23/0.43 ![U: $i, V: $i, W: $i, X: $i] : (ok(triple(U, V, W)) | (~ok(remove_cpq(triple(U, V, W), X))))),
% 0.23/0.43 inference(skolemize,[status(sab)],[87])).
% 0.23/0.43 tff(89,plain,
% 0.23/0.43 (![U: $i, V: $i, W: $i, X: $i] : (ok(triple(U, V, W)) | (~ok(remove_cpq(triple(U, V, W), X))))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[88, 81])).
% 0.23/0.43 tff(90,plain,
% 0.23/0.43 (((~![U: $i, V: $i, W: $i, X: $i] : (ok(triple(U, V, W)) | (~ok(remove_cpq(triple(U, V, W), X))))) | (ok(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad)) | (~ok(remove_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad), findmin_cpq_res(triple(U!2, V!1, W!0))))))) <=> ((~![U: $i, V: $i, W: $i, X: $i] : (ok(triple(U, V, W)) | (~ok(remove_cpq(triple(U, V, W), X))))) | ok(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad)) | (~ok(remove_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad), findmin_cpq_res(triple(U!2, V!1, W!0))))))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(91,plain,
% 0.23/0.43 ((~![U: $i, V: $i, W: $i, X: $i] : (ok(triple(U, V, W)) | (~ok(remove_cpq(triple(U, V, W), X))))) | (ok(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad)) | (~ok(remove_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad), findmin_cpq_res(triple(U!2, V!1, W!0))))))),
% 0.23/0.43 inference(quant_inst,[status(thm)],[])).
% 0.23/0.43 tff(92,plain,
% 0.23/0.43 ((~![U: $i, V: $i, W: $i, X: $i] : (ok(triple(U, V, W)) | (~ok(remove_cpq(triple(U, V, W), X))))) | ok(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad)) | (~ok(remove_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad), findmin_cpq_res(triple(U!2, V!1, W!0)))))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.23/0.43 tff(93,plain,
% 0.23/0.43 (~ok(remove_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad), findmin_cpq_res(triple(U!2, V!1, W!0))))),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[92, 89, 79])).
% 0.23/0.43 tff(94,plain,
% 0.23/0.43 ($false),
% 0.23/0.43 inference(unit_resolution,[status(thm)],[93, 67])).
% 0.23/0.43 tff(95,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,[]))).
% 0.23/0.43 tff(96,plain,
% 0.23/0.43 (~(findmin_cpq_eff(triple(U!2, V!1, W!0)) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0))),
% 0.23/0.43 inference(modus_ponens,[status(thm)],[95, 49])).
% 0.23/0.43 tff(97,plain,
% 0.23/0.43 (^[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))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(98,plain,
% 0.23/0.43 (![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ![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)))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[97])).
% 0.23/0.43 tff(99,plain,
% 0.23/0.43 (^[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)))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(100,plain,
% 0.23/0.43 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ![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)))),
% 0.23/0.43 inference(quant_intro,[status(thm)],[99])).
% 0.23/0.43 tff(101,plain,
% 0.23/0.43 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ![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)))),
% 0.23/0.43 inference(rewrite,[status(thm)],[])).
% 0.23/0.43 tff(102,plain,
% 0.23/0.43 (![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)))),
% 0.23/0.43 inference(elim_unused_vars,[status(thm)],[])).
% 0.23/0.43 tff(103,plain,
% 0.23/0.43 (^[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))))),
% 0.23/0.43 inference(bind,[status(th)],[])).
% 0.23/0.43 tff(104,plain,
% 0.23/0.43 (![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)))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[103])).
% 0.23/0.44 tff(105,plain,
% 0.23/0.44 (![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)))),
% 0.23/0.44 inference(transitivity,[status(thm)],[104, 102])).
% 0.23/0.44 tff(106,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')).
% 0.23/0.44 tff(107,plain,
% 0.23/0.44 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.23/0.44 tff(108,plain,
% 0.23/0.44 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[107, 101])).
% 0.23/0.44 tff(109,plain,(
% 0.23/0.44 ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.23/0.44 inference(skolemize,[status(sab)],[108])).
% 0.23/0.44 tff(110,plain,
% 0.23/0.44 (![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[109, 100])).
% 0.23/0.44 tff(111,plain,
% 0.23/0.44 (![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[110, 98])).
% 0.23/0.44 tff(112,plain,
% 0.23/0.44 (((~![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))) | ((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)))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(113,plain,
% 0.23/0.44 ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))) | ((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)))),
% 0.23/0.44 inference(quant_inst,[status(thm)],[])).
% 0.23/0.44 tff(114,plain,
% 0.23/0.44 ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))) | (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))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.23/0.44 tff(115,plain,
% 0.23/0.44 ((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))),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[114, 111])).
% 0.23/0.44 tff(116,plain,
% 0.23/0.44 (contains_slb(V!1, findmin_pqp_res(U!2))),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[115, 25, 95])).
% 0.23/0.44 tff(117,plain,
% 0.23/0.44 (^[U: $i, V: $i, W: $i] : refl(((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), 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)))))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(118,plain,
% 0.23/0.44 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), 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))))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[117])).
% 0.23/0.44 tff(119,plain,
% 0.23/0.44 (^[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))))))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(120,plain,
% 0.23/0.44 (![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))))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[119])).
% 0.23/0.44 tff(121,plain,
% 0.23/0.44 (![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)))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(122,plain,
% 0.23/0.44 (![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)))),
% 0.23/0.44 inference(elim_unused_vars,[status(thm)],[])).
% 0.23/0.44 tff(123,plain,
% 0.23/0.44 (^[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)))))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(124,plain,
% 0.23/0.44 (![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)))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[123])).
% 0.23/0.44 tff(125,plain,
% 0.23/0.44 (![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)))),
% 0.23/0.44 inference(transitivity,[status(thm)],[124, 122])).
% 0.23/0.44 tff(126,axiom,(![U: $i, V: $i, W: $i, X: $i] : ((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax','ax49')).
% 0.23/0.44 tff(127,plain,
% 0.23/0.44 (![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)))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.23/0.44 tff(128,plain,
% 0.23/0.44 (![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)))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[127, 121])).
% 0.23/0.44 tff(129,plain,(
% 0.23/0.44 ![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)))),
% 0.23/0.44 inference(skolemize,[status(sab)],[128])).
% 0.23/0.44 tff(130,plain,
% 0.23/0.44 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[129, 120])).
% 0.23/0.44 tff(131,plain,
% 0.23/0.44 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[130, 118])).
% 0.23/0.44 tff(132,plain,
% 0.23/0.44 (((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), 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))))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(133,plain,
% 0.23/0.44 ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), 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))))),
% 0.23/0.44 inference(quant_inst,[status(thm)],[])).
% 0.23/0.44 tff(134,plain,
% 0.23/0.44 ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), 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)))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.23/0.44 tff(135,plain,
% 0.23/0.44 ((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)))),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[134, 131])).
% 0.23/0.44 tff(136,plain,
% 0.23/0.44 (~less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_pqp_res(U!2))),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[135, 116, 96, 25])).
% 0.23/0.44 tff(137,plain,
% 0.23/0.44 (~less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_cpq_res(triple(U!2, V!1, W!0)))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[136, 45])).
% 0.23/0.44 tff(138,plain,
% 0.23/0.44 (^[U: $i, V: $i] : refl((less_than(V, U) | less_than(U, V)) <=> (less_than(V, U) | less_than(U, V)))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(139,plain,
% 0.23/0.44 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[138])).
% 0.23/0.44 tff(140,plain,
% 0.23/0.44 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(141,plain,
% 0.23/0.44 (^[U: $i, V: $i] : rewrite((less_than(U, V) | less_than(V, U)) <=> (less_than(V, U) | less_than(U, V)))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(142,plain,
% 0.23/0.44 (![U: $i, V: $i] : (less_than(U, V) | less_than(V, U)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.23/0.44 inference(quant_intro,[status(thm)],[141])).
% 0.23/0.44 tff(143,axiom,(![U: $i, V: $i] : (less_than(U, V) | less_than(V, U))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+0.ax','totality')).
% 0.23/0.44 tff(144,plain,
% 0.23/0.44 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.23/0.44 tff(145,plain,
% 0.23/0.44 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[144, 140])).
% 0.23/0.44 tff(146,plain,(
% 0.23/0.44 ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.23/0.44 inference(skolemize,[status(sab)],[145])).
% 0.23/0.44 tff(147,plain,
% 0.23/0.44 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[146, 139])).
% 0.23/0.44 tff(148,plain,
% 0.23/0.44 (((~![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))))),
% 0.23/0.44 inference(rewrite,[status(thm)],[])).
% 0.23/0.44 tff(149,plain,
% 0.23/0.44 ((~![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))))),
% 0.23/0.44 inference(quant_inst,[status(thm)],[])).
% 0.23/0.44 tff(150,plain,
% 0.23/0.44 ((~![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)))),
% 0.23/0.44 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.23/0.44 tff(151,plain,
% 0.23/0.44 (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)))),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[150, 147])).
% 0.23/0.44 tff(152,plain,
% 0.23/0.44 (less_than(findmin_cpq_res(triple(U!2, V!1, W!0)), lookup_slb(V!1, findmin_pqp_res(U!2)))),
% 0.23/0.44 inference(unit_resolution,[status(thm)],[151, 137])).
% 0.23/0.44 tff(153,plain,
% 0.23/0.44 (^[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))))),
% 0.23/0.44 inference(bind,[status(th)],[])).
% 0.23/0.44 tff(154,plain,
% 0.23/0.45 (![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)))),
% 0.23/0.45 inference(quant_intro,[status(thm)],[153])).
% 0.23/0.45 tff(155,plain,
% 0.23/0.45 (^[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)))))),
% 0.23/0.45 inference(bind,[status(th)],[])).
% 0.23/0.45 tff(156,plain,
% 0.23/0.45 (![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)))),
% 0.23/0.45 inference(quant_intro,[status(thm)],[155])).
% 0.23/0.45 tff(157,plain,
% 0.23/0.45 (![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))))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(158,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')).
% 0.23/0.45 tff(159,plain,
% 0.23/0.45 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.23/0.45 tff(160,plain,(
% 0.23/0.45 ![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.23/0.45 inference(skolemize,[status(sab)],[159])).
% 0.23/0.45 tff(161,plain,
% 0.23/0.45 (![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[160, 156])).
% 0.23/0.45 tff(162,plain,
% 0.23/0.45 (![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[161, 154])).
% 0.23/0.45 tff(163,plain,
% 0.23/0.45 ((~![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)))))),
% 0.23/0.45 inference(quant_inst,[status(thm)],[])).
% 0.23/0.45 tff(164,plain,
% 0.23/0.45 (~(((~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))))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[163, 162])).
% 0.23/0.45 tff(165,plain,
% 0.23/0.45 (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)))),
% 0.23/0.45 inference(monotonicity,[status(thm)],[42])).
% 0.23/0.45 tff(166,plain,
% 0.23/0.45 (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)))),
% 0.23/0.45 inference(symmetry,[status(thm)],[165])).
% 0.23/0.45 tff(167,plain,
% 0.23/0.45 ((~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))))),
% 0.23/0.45 inference(monotonicity,[status(thm)],[166])).
% 0.23/0.45 tff(168,plain,
% 0.23/0.45 (^[U: $i, V: $i, W: $i] : refl(((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), 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))))))),
% 0.23/0.45 inference(bind,[status(th)],[])).
% 0.23/0.45 tff(169,plain,
% 0.23/0.45 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~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)))))),
% 0.23/0.45 inference(quant_intro,[status(thm)],[168])).
% 0.23/0.45 tff(170,plain,
% 0.23/0.45 (^[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)))))))),
% 0.23/0.45 inference(bind,[status(th)],[])).
% 0.23/0.45 tff(171,plain,
% 0.23/0.45 (![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)))))),
% 0.23/0.45 inference(quant_intro,[status(thm)],[170])).
% 0.23/0.45 tff(172,plain,
% 0.23/0.45 (![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)))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(173,plain,
% 0.23/0.45 (![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)))),
% 0.23/0.45 inference(elim_unused_vars,[status(thm)],[])).
% 0.23/0.45 tff(174,plain,
% 0.23/0.45 (^[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)))))),
% 0.23/0.45 inference(bind,[status(th)],[])).
% 0.23/0.45 tff(175,plain,
% 0.23/0.45 (![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)))),
% 0.23/0.45 inference(quant_intro,[status(thm)],[174])).
% 0.23/0.45 tff(176,plain,
% 0.23/0.45 (![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)))),
% 0.23/0.45 inference(transitivity,[status(thm)],[175, 173])).
% 0.23/0.45 tff(177,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')).
% 0.23/0.45 tff(178,plain,
% 0.23/0.45 (![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)))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.23/0.45 tff(179,plain,
% 0.23/0.45 (![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)))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[178, 172])).
% 0.23/0.45 tff(180,plain,(
% 0.23/0.45 ![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)))),
% 0.23/0.45 inference(skolemize,[status(sab)],[179])).
% 0.23/0.45 tff(181,plain,
% 0.23/0.45 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[180, 171])).
% 0.23/0.45 tff(182,plain,
% 0.23/0.45 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[181, 169])).
% 0.23/0.45 tff(183,plain,
% 0.23/0.45 (((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~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)))))),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(184,plain,
% 0.23/0.45 ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~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)))))),
% 0.23/0.45 inference(quant_inst,[status(thm)],[])).
% 0.23/0.45 tff(185,plain,
% 0.23/0.45 ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~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))))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.23/0.45 tff(186,plain,
% 0.23/0.45 ((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))))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[185, 182])).
% 0.23/0.45 tff(187,plain,
% 0.23/0.45 (~strictly_less_than(findmin_pqp_res(U!2), lookup_slb(V!1, findmin_pqp_res(U!2)))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[186, 116, 95, 25])).
% 0.23/0.45 tff(188,plain,
% 0.23/0.45 (~strictly_less_than(findmin_cpq_res(triple(U!2, V!1, W!0)), lookup_slb(V!1, findmin_pqp_res(U!2)))),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[187, 167])).
% 0.23/0.45 tff(189,plain,
% 0.23/0.45 ((((~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)))),
% 0.23/0.45 inference(tautology,[status(thm)],[])).
% 0.23/0.45 tff(190,plain,
% 0.23/0.45 ((~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)))),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[189, 188, 164])).
% 0.23/0.45 tff(191,plain,
% 0.23/0.45 ((~((~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)))),
% 0.23/0.45 inference(tautology,[status(thm)],[])).
% 0.23/0.45 tff(192,plain,
% 0.23/0.45 ($false),
% 0.23/0.45 inference(unit_resolution,[status(thm)],[191, 190, 152, 137])).
% 0.23/0.45 tff(193,plain,(V!1 = create_slb), inference(lemma,lemma(discharge,[]))).
% 0.23/0.45 tff(194,plain,
% 0.23/0.45 (create_slb = V!1),
% 0.23/0.45 inference(symmetry,[status(thm)],[193])).
% 0.23/0.45 tff(195,plain,
% 0.23/0.45 (^[U: $i] : refl((update_slb(create_slb, U) = create_slb) <=> (update_slb(create_slb, U) = create_slb))),
% 0.23/0.45 inference(bind,[status(th)],[])).
% 0.23/0.45 tff(196,plain,
% 0.23/0.45 (![U: $i] : (update_slb(create_slb, U) = create_slb) <=> ![U: $i] : (update_slb(create_slb, U) = create_slb)),
% 0.23/0.45 inference(quant_intro,[status(thm)],[195])).
% 0.23/0.45 tff(197,plain,
% 0.23/0.45 (![U: $i] : (update_slb(create_slb, U) = create_slb) <=> ![U: $i] : (update_slb(create_slb, U) = create_slb)),
% 0.23/0.45 inference(rewrite,[status(thm)],[])).
% 0.23/0.45 tff(198,axiom,(![U: $i] : (update_slb(create_slb, U) = create_slb)), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+2.ax','ax28')).
% 0.23/0.45 tff(199,plain,
% 0.23/0.45 (![U: $i] : (update_slb(create_slb, U) = create_slb)),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.23/0.45 tff(200,plain,(
% 0.23/0.45 ![U: $i] : (update_slb(create_slb, U) = create_slb)),
% 0.23/0.45 inference(skolemize,[status(sab)],[199])).
% 0.23/0.45 tff(201,plain,
% 0.23/0.45 (![U: $i] : (update_slb(create_slb, U) = create_slb)),
% 0.23/0.45 inference(modus_ponens,[status(thm)],[200, 196])).
% 0.23/0.45 tff(202,plain,
% 0.23/0.45 ((~![U: $i] : (update_slb(create_slb, U) = create_slb)) | (update_slb(create_slb, findmin_pqp_res(U!2)) = create_slb)),
% 0.23/0.45 inference(quant_inst,[status(thm)],[])).
% 0.23/0.46 tff(203,plain,
% 0.23/0.46 (update_slb(create_slb, findmin_pqp_res(U!2)) = create_slb),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[202, 201])).
% 0.23/0.46 tff(204,plain,
% 0.23/0.46 (update_slb(V!1, findmin_pqp_res(U!2)) = update_slb(create_slb, findmin_pqp_res(U!2))),
% 0.23/0.46 inference(monotonicity,[status(thm)],[193])).
% 0.23/0.46 tff(205,plain,
% 0.23/0.46 (update_slb(V!1, findmin_pqp_res(U!2)) = V!1),
% 0.23/0.46 inference(transitivity,[status(thm)],[204, 203, 194])).
% 0.23/0.46 tff(206,plain,
% 0.23/0.46 (triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad) = triple(U!2, V!1, W!0)),
% 0.23/0.46 inference(monotonicity,[status(thm)],[205, 24])).
% 0.23/0.46 tff(207,plain,
% 0.23/0.46 (triple(U!2, V!1, W!0) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad)),
% 0.23/0.46 inference(symmetry,[status(thm)],[206])).
% 0.23/0.46 tff(208,plain,
% 0.23/0.46 (triple(U!2, create_slb, bad) = triple(U!2, V!1, W!0)),
% 0.23/0.46 inference(monotonicity,[status(thm)],[194, 24])).
% 0.23/0.46 tff(209,plain,
% 0.23/0.46 (^[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)))),
% 0.23/0.46 inference(bind,[status(th)],[])).
% 0.23/0.46 tff(210,plain,
% 0.23/0.46 (![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))),
% 0.23/0.46 inference(quant_intro,[status(thm)],[209])).
% 0.23/0.46 tff(211,plain,
% 0.23/0.46 (![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))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(212,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')).
% 0.23/0.46 tff(213,plain,
% 0.23/0.46 (![U: $i, V: $i] : (findmin_cpq_eff(triple(U, create_slb, V)) = triple(U, create_slb, bad))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.23/0.46 tff(214,plain,(
% 0.23/0.46 ![U: $i, V: $i] : (findmin_cpq_eff(triple(U, create_slb, V)) = triple(U, create_slb, bad))),
% 0.23/0.46 inference(skolemize,[status(sab)],[213])).
% 0.23/0.46 tff(215,plain,
% 0.23/0.46 (![U: $i, V: $i] : (findmin_cpq_eff(triple(U, create_slb, V)) = triple(U, create_slb, bad))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[214, 210])).
% 0.23/0.46 tff(216,plain,
% 0.23/0.46 ((~![U: $i, V: $i] : (findmin_cpq_eff(triple(U, create_slb, V)) = triple(U, create_slb, bad))) | (findmin_cpq_eff(triple(U!2, create_slb, bad)) = triple(U!2, create_slb, bad))),
% 0.23/0.46 inference(quant_inst,[status(thm)],[])).
% 0.23/0.46 tff(217,plain,
% 0.23/0.46 (findmin_cpq_eff(triple(U!2, create_slb, bad)) = triple(U!2, create_slb, bad)),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[216, 215])).
% 0.23/0.46 tff(218,plain,
% 0.23/0.46 (triple(U!2, V!1, W!0) = triple(U!2, create_slb, bad)),
% 0.23/0.46 inference(symmetry,[status(thm)],[208])).
% 0.23/0.46 tff(219,plain,
% 0.23/0.46 (findmin_cpq_eff(triple(U!2, V!1, W!0)) = findmin_cpq_eff(triple(U!2, create_slb, bad))),
% 0.23/0.46 inference(monotonicity,[status(thm)],[218])).
% 0.23/0.46 tff(220,plain,
% 0.23/0.46 (findmin_cpq_eff(triple(U!2, V!1, W!0)) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad)),
% 0.23/0.46 inference(transitivity,[status(thm)],[219, 217, 208, 207])).
% 0.23/0.46 tff(221,plain,
% 0.23/0.46 ($false),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[95, 220])).
% 0.23/0.46 % SZS output end Proof
% 0.23/0.46 % E exiting
%------------------------------------------------------------------------------