%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV404+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:32:23 AM UTC 2025
% Result : Theorem 0.11s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SWV404+1 : TPTP v9.0.0. Released v3.3.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n016.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 09:45:32 EDT 2025
% 0.11/0.34 % CPUTime :
% 0.11/0.39 % SZS status Theorem
% 0.11/0.39 % SZS output start Proof
% 0.11/0.39 tff(strictly_less_than_type, type, (
% 0.11/0.39 strictly_less_than: ( $i * $i ) > $o)).
% 0.11/0.39 tff(lookup_slb_type, type, (
% 0.11/0.39 lookup_slb: ( $i * $i ) > $i)).
% 0.11/0.39 tff(findmin_pqp_res_type, type, (
% 0.11/0.39 findmin_pqp_res: $i > $i)).
% 0.11/0.39 tff(tptp_fun_U_2_type, type, (
% 0.11/0.39 tptp_fun_U_2: $i)).
% 0.11/0.39 tff(tptp_fun_V_1_type, type, (
% 0.11/0.39 tptp_fun_V_1: $i)).
% 0.11/0.39 tff(findmin_cpq_res_type, type, (
% 0.11/0.39 findmin_cpq_res: $i > $i)).
% 0.11/0.39 tff(triple_type, type, (
% 0.11/0.39 triple: ( $i * $i * $i ) > $i)).
% 0.11/0.39 tff(tptp_fun_W_0_type, type, (
% 0.11/0.39 tptp_fun_W_0: $i)).
% 0.11/0.39 tff(create_slb_type, type, (
% 0.11/0.39 create_slb: $i)).
% 0.11/0.39 tff(check_cpq_type, type, (
% 0.11/0.39 check_cpq: $i > $o)).
% 0.11/0.39 tff(ok_type, type, (
% 0.11/0.39 ok: $i > $o)).
% 0.11/0.39 tff(removemin_cpq_eff_type, type, (
% 0.11/0.39 removemin_cpq_eff: $i > $i)).
% 0.11/0.39 tff(bad_type, type, (
% 0.11/0.39 bad: $i)).
% 0.11/0.39 tff(update_slb_type, type, (
% 0.11/0.39 update_slb: ( $i * $i ) > $i)).
% 0.11/0.39 tff(findmin_cpq_eff_type, type, (
% 0.11/0.39 findmin_cpq_eff: $i > $i)).
% 0.11/0.39 tff(remove_cpq_type, type, (
% 0.11/0.39 remove_cpq: ( $i * $i ) > $i)).
% 0.11/0.39 tff(contains_slb_type, type, (
% 0.11/0.39 contains_slb: ( $i * $i ) > $o)).
% 0.11/0.39 tff(less_than_type, type, (
% 0.11/0.39 less_than: ( $i * $i ) > $o)).
% 0.11/0.39 tff(1,assumption,(V!1 = create_slb), introduced(assumption)).
% 0.11/0.39 tff(2,plain,
% 0.11/0.39 (create_slb = V!1),
% 0.11/0.39 inference(symmetry,[status(thm)],[1])).
% 0.11/0.39 tff(3,plain,
% 0.11/0.39 (triple(U!2, create_slb, W!0) = triple(U!2, V!1, W!0)),
% 0.11/0.39 inference(monotonicity,[status(thm)],[2])).
% 0.11/0.39 tff(4,plain,
% 0.11/0.39 (check_cpq(triple(U!2, create_slb, W!0)) <=> check_cpq(triple(U!2, V!1, W!0))),
% 0.11/0.39 inference(monotonicity,[status(thm)],[3])).
% 0.11/0.39 tff(5,plain,
% 0.11/0.39 (check_cpq(triple(U!2, V!1, W!0)) <=> check_cpq(triple(U!2, create_slb, W!0))),
% 0.11/0.39 inference(symmetry,[status(thm)],[4])).
% 0.11/0.39 tff(6,plain,
% 0.11/0.39 ((~check_cpq(triple(U!2, V!1, W!0))) <=> (~check_cpq(triple(U!2, create_slb, W!0)))),
% 0.11/0.39 inference(monotonicity,[status(thm)],[5])).
% 0.11/0.39 tff(7,plain,
% 0.11/0.39 ((~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~(check_cpq(removemin_cpq_eff(triple(U, V, W))) & ok(removemin_cpq_eff(triple(U, V, W))))))) <=> (~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~(check_cpq(removemin_cpq_eff(triple(U, V, W))) & ok(removemin_cpq_eff(triple(U, V, W)))))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(8,plain,
% 0.11/0.39 ((~![U: $i, V: $i, W: $i] : ((check_cpq(removemin_cpq_eff(triple(U, V, W))) & ok(removemin_cpq_eff(triple(U, V, W)))) => check_cpq(triple(U, V, W)))) <=> (~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~(check_cpq(removemin_cpq_eff(triple(U, V, W))) & ok(removemin_cpq_eff(triple(U, V, W)))))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(9,axiom,(~![U: $i, V: $i, W: $i] : ((check_cpq(removemin_cpq_eff(triple(U, V, W))) & ok(removemin_cpq_eff(triple(U, V, W)))) => check_cpq(triple(U, V, W)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l40_co')).
% 0.11/0.39 tff(10,plain,
% 0.11/0.39 (~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~(check_cpq(removemin_cpq_eff(triple(U, V, W))) & ok(removemin_cpq_eff(triple(U, V, W))))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.11/0.39 tff(11,plain,
% 0.11/0.39 (~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~(check_cpq(removemin_cpq_eff(triple(U, V, W))) & ok(removemin_cpq_eff(triple(U, V, W))))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[10, 7])).
% 0.11/0.39 tff(12,plain,
% 0.11/0.39 (~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~(check_cpq(removemin_cpq_eff(triple(U, V, W))) & ok(removemin_cpq_eff(triple(U, V, W))))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.11/0.39 tff(13,plain,
% 0.11/0.39 (~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~(check_cpq(removemin_cpq_eff(triple(U, V, W))) & ok(removemin_cpq_eff(triple(U, V, W))))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[12, 7])).
% 0.11/0.39 tff(14,plain,(
% 0.11/0.39 ~(check_cpq(triple(U!2, V!1, W!0)) | (~(check_cpq(removemin_cpq_eff(triple(U!2, V!1, W!0))) & ok(removemin_cpq_eff(triple(U!2, V!1, W!0))))))),
% 0.11/0.39 inference(skolemize,[status(sab)],[13])).
% 0.11/0.39 tff(15,plain,
% 0.11/0.39 (~check_cpq(triple(U!2, V!1, W!0))),
% 0.11/0.39 inference(or_elim,[status(thm)],[14])).
% 0.11/0.39 tff(16,plain,
% 0.11/0.39 (~check_cpq(triple(U!2, create_slb, W!0))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[15, 6])).
% 0.11/0.39 tff(17,plain,
% 0.11/0.39 (^[U: $i, V: $i] : refl(check_cpq(triple(U, create_slb, V)) <=> check_cpq(triple(U, create_slb, V)))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(18,plain,
% 0.11/0.39 (![U: $i, V: $i] : check_cpq(triple(U, create_slb, V)) <=> ![U: $i, V: $i] : check_cpq(triple(U, create_slb, V))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[17])).
% 0.11/0.39 tff(19,plain,
% 0.11/0.39 (![U: $i, V: $i] : check_cpq(triple(U, create_slb, V)) <=> ![U: $i, V: $i] : check_cpq(triple(U, create_slb, V))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(20,axiom,(![U: $i, V: $i] : check_cpq(triple(U, create_slb, V))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax','ax36')).
% 0.11/0.39 tff(21,plain,
% 0.11/0.39 (![U: $i, V: $i] : check_cpq(triple(U, create_slb, V))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.11/0.39 tff(22,plain,(
% 0.11/0.39 ![U: $i, V: $i] : check_cpq(triple(U, create_slb, V))),
% 0.11/0.39 inference(skolemize,[status(sab)],[21])).
% 0.11/0.39 tff(23,plain,
% 0.11/0.39 (![U: $i, V: $i] : check_cpq(triple(U, create_slb, V))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.11/0.39 tff(24,plain,
% 0.11/0.39 ((~![U: $i, V: $i] : check_cpq(triple(U, create_slb, V))) | check_cpq(triple(U!2, create_slb, W!0))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(25,plain,
% 0.11/0.39 (check_cpq(triple(U!2, create_slb, W!0))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.11/0.39 tff(26,plain,
% 0.11/0.39 ($false),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[25, 16])).
% 0.11/0.39 tff(27,plain,(~(V!1 = create_slb)), inference(lemma,lemma(discharge,[]))).
% 0.11/0.39 tff(28,plain,
% 0.11/0.39 (^[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))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(29,plain,
% 0.11/0.39 (![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)))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[28])).
% 0.11/0.39 tff(30,plain,
% 0.11/0.39 (![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)))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(31,plain,
% 0.11/0.39 (![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)))),
% 0.11/0.39 inference(elim_unused_vars,[status(thm)],[])).
% 0.11/0.39 tff(32,plain,
% 0.11/0.39 (^[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))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(33,plain,
% 0.11/0.39 (![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)))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[32])).
% 0.11/0.39 tff(34,plain,
% 0.11/0.39 (![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)))),
% 0.11/0.39 inference(transitivity,[status(thm)],[33, 31])).
% 0.11/0.39 tff(35,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')).
% 0.11/0.39 tff(36,plain,
% 0.11/0.39 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.11/0.39 tff(37,plain,
% 0.11/0.39 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[36, 30])).
% 0.11/0.39 tff(38,plain,(
% 0.11/0.39 ![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.11/0.39 inference(skolemize,[status(sab)],[37])).
% 0.11/0.39 tff(39,plain,
% 0.11/0.39 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[38, 29])).
% 0.11/0.39 tff(40,plain,
% 0.11/0.39 (((~![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)))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(41,plain,
% 0.11/0.39 ((~![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)))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(42,plain,
% 0.11/0.39 ((~![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))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.11/0.39 tff(43,plain,
% 0.11/0.39 ((V!1 = create_slb) | (findmin_cpq_res(triple(U!2, V!1, W!0)) = findmin_pqp_res(U!2))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[42, 39])).
% 0.11/0.39 tff(44,plain,
% 0.11/0.39 (findmin_cpq_res(triple(U!2, V!1, W!0)) = findmin_pqp_res(U!2)),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[43, 27])).
% 0.11/0.39 tff(45,plain,
% 0.11/0.39 (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)))),
% 0.11/0.39 inference(monotonicity,[status(thm)],[44])).
% 0.11/0.39 tff(46,plain,
% 0.11/0.39 (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)))),
% 0.11/0.39 inference(symmetry,[status(thm)],[45])).
% 0.11/0.39 tff(47,plain,
% 0.11/0.39 ((~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))))),
% 0.11/0.39 inference(monotonicity,[status(thm)],[46])).
% 0.11/0.39 tff(48,plain,
% 0.11/0.39 (^[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))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(49,plain,
% 0.11/0.39 (![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)))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[48])).
% 0.11/0.39 tff(50,plain,
% 0.11/0.39 (![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)))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(51,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')).
% 0.11/0.39 tff(52,plain,
% 0.11/0.39 (![U: $i] : (removemin_cpq_eff(U) = remove_cpq(findmin_cpq_eff(U), findmin_cpq_res(U)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.11/0.39 tff(53,plain,(
% 0.11/0.39 ![U: $i] : (removemin_cpq_eff(U) = remove_cpq(findmin_cpq_eff(U), findmin_cpq_res(U)))),
% 0.11/0.39 inference(skolemize,[status(sab)],[52])).
% 0.11/0.39 tff(54,plain,
% 0.11/0.39 (![U: $i] : (removemin_cpq_eff(U) = remove_cpq(findmin_cpq_eff(U), findmin_cpq_res(U)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.11/0.39 tff(55,plain,
% 0.11/0.39 ((~![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))))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(56,plain,
% 0.11/0.39 (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)))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.11/0.39 tff(57,plain,
% 0.11/0.39 (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))),
% 0.11/0.39 inference(symmetry,[status(thm)],[56])).
% 0.11/0.39 tff(58,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)).
% 0.11/0.39 tff(59,plain,
% 0.11/0.39 (triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad) = findmin_cpq_eff(triple(U!2, V!1, W!0))),
% 0.11/0.39 inference(symmetry,[status(thm)],[58])).
% 0.11/0.39 tff(60,plain,
% 0.11/0.39 (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)))),
% 0.11/0.39 inference(monotonicity,[status(thm)],[59])).
% 0.11/0.39 tff(61,plain,
% 0.11/0.39 (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))),
% 0.11/0.39 inference(transitivity,[status(thm)],[60, 57])).
% 0.11/0.39 tff(62,plain,
% 0.11/0.39 (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)))),
% 0.11/0.39 inference(monotonicity,[status(thm)],[61])).
% 0.11/0.39 tff(63,plain,
% 0.11/0.39 (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))))),
% 0.11/0.39 inference(symmetry,[status(thm)],[62])).
% 0.11/0.39 tff(64,plain,
% 0.11/0.39 (check_cpq(removemin_cpq_eff(triple(U!2, V!1, W!0))) & ok(removemin_cpq_eff(triple(U!2, V!1, W!0)))),
% 0.11/0.39 inference(or_elim,[status(thm)],[14])).
% 0.11/0.39 tff(65,plain,
% 0.11/0.39 (ok(removemin_cpq_eff(triple(U!2, V!1, W!0)))),
% 0.11/0.39 inference(and_elim,[status(thm)],[64])).
% 0.11/0.39 tff(66,plain,
% 0.11/0.39 (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))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[65, 63])).
% 0.11/0.39 tff(67,plain,
% 0.11/0.39 (check_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad)) <=> check_cpq(findmin_cpq_eff(triple(U!2, V!1, W!0)))),
% 0.11/0.39 inference(monotonicity,[status(thm)],[59])).
% 0.11/0.39 tff(68,plain,
% 0.11/0.39 (check_cpq(findmin_cpq_eff(triple(U!2, V!1, W!0))) <=> check_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad))),
% 0.11/0.39 inference(symmetry,[status(thm)],[67])).
% 0.11/0.39 tff(69,plain,
% 0.11/0.39 ((~check_cpq(findmin_cpq_eff(triple(U!2, V!1, W!0)))) <=> (~check_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad)))),
% 0.11/0.39 inference(monotonicity,[status(thm)],[68])).
% 0.11/0.39 tff(70,plain,
% 0.11/0.39 (^[U: $i, V: $i, W: $i] : refl((check_cpq(triple(U, V, W)) | (~check_cpq(findmin_cpq_eff(triple(U, V, W))))) <=> (check_cpq(triple(U, V, W)) | (~check_cpq(findmin_cpq_eff(triple(U, V, W))))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(71,plain,
% 0.11/0.39 (![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~check_cpq(findmin_cpq_eff(triple(U, V, W))))) <=> ![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~check_cpq(findmin_cpq_eff(triple(U, V, W)))))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[70])).
% 0.11/0.39 tff(72,plain,
% 0.11/0.39 (![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~check_cpq(findmin_cpq_eff(triple(U, V, W))))) <=> ![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~check_cpq(findmin_cpq_eff(triple(U, V, W)))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(73,plain,
% 0.11/0.39 (^[U: $i, V: $i, W: $i] : rewrite(((~check_cpq(triple(U, V, W))) => (~check_cpq(findmin_cpq_eff(triple(U, V, W))))) <=> (check_cpq(triple(U, V, W)) | (~check_cpq(findmin_cpq_eff(triple(U, V, W))))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(74,plain,
% 0.11/0.39 (![U: $i, V: $i, W: $i] : ((~check_cpq(triple(U, V, W))) => (~check_cpq(findmin_cpq_eff(triple(U, V, W))))) <=> ![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~check_cpq(findmin_cpq_eff(triple(U, V, W)))))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[73])).
% 0.11/0.39 tff(75,axiom,(![U: $i, V: $i, W: $i] : ((~check_cpq(triple(U, V, W))) => (~check_cpq(findmin_cpq_eff(triple(U, V, W)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l40_l34')).
% 0.11/0.39 tff(76,plain,
% 0.11/0.39 (![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~check_cpq(findmin_cpq_eff(triple(U, V, W)))))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.11/0.40 tff(77,plain,
% 0.11/0.40 (![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~check_cpq(findmin_cpq_eff(triple(U, V, W)))))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[76, 72])).
% 0.11/0.40 tff(78,plain,(
% 0.11/0.40 ![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~check_cpq(findmin_cpq_eff(triple(U, V, W)))))),
% 0.11/0.40 inference(skolemize,[status(sab)],[77])).
% 0.11/0.40 tff(79,plain,
% 0.11/0.40 (![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~check_cpq(findmin_cpq_eff(triple(U, V, W)))))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[78, 71])).
% 0.11/0.40 tff(80,plain,
% 0.11/0.40 (((~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~check_cpq(findmin_cpq_eff(triple(U, V, W)))))) | (check_cpq(triple(U!2, V!1, W!0)) | (~check_cpq(findmin_cpq_eff(triple(U!2, V!1, W!0)))))) <=> ((~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~check_cpq(findmin_cpq_eff(triple(U, V, W)))))) | check_cpq(triple(U!2, V!1, W!0)) | (~check_cpq(findmin_cpq_eff(triple(U!2, V!1, W!0)))))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(81,plain,
% 0.11/0.40 ((~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~check_cpq(findmin_cpq_eff(triple(U, V, W)))))) | (check_cpq(triple(U!2, V!1, W!0)) | (~check_cpq(findmin_cpq_eff(triple(U!2, V!1, W!0)))))),
% 0.11/0.40 inference(quant_inst,[status(thm)],[])).
% 0.11/0.40 tff(82,plain,
% 0.11/0.40 ((~![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~check_cpq(findmin_cpq_eff(triple(U, V, W)))))) | check_cpq(triple(U!2, V!1, W!0)) | (~check_cpq(findmin_cpq_eff(triple(U!2, V!1, W!0))))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.11/0.40 tff(83,plain,
% 0.11/0.40 (~check_cpq(findmin_cpq_eff(triple(U!2, V!1, W!0)))),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[82, 79, 15])).
% 0.11/0.40 tff(84,plain,
% 0.11/0.40 (~check_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[83, 69])).
% 0.11/0.40 tff(85,plain,
% 0.11/0.40 (check_cpq(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)))) <=> check_cpq(removemin_cpq_eff(triple(U!2, V!1, W!0)))),
% 0.11/0.40 inference(monotonicity,[status(thm)],[61])).
% 0.11/0.40 tff(86,plain,
% 0.11/0.40 (check_cpq(removemin_cpq_eff(triple(U!2, V!1, W!0))) <=> check_cpq(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))))),
% 0.11/0.40 inference(symmetry,[status(thm)],[85])).
% 0.11/0.40 tff(87,plain,
% 0.11/0.40 (check_cpq(removemin_cpq_eff(triple(U!2, V!1, W!0)))),
% 0.11/0.40 inference(and_elim,[status(thm)],[64])).
% 0.11/0.40 tff(88,plain,
% 0.11/0.40 (check_cpq(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))))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.11/0.40 tff(89,plain,
% 0.11/0.40 (^[U: $i, V: $i, W: $i, X: $i] : refl((check_cpq(triple(U, V, W)) | (~check_cpq(remove_cpq(triple(U, V, W), X))) | (~ok(remove_cpq(triple(U, V, W), X)))) <=> (check_cpq(triple(U, V, W)) | (~check_cpq(remove_cpq(triple(U, V, W), X))) | (~ok(remove_cpq(triple(U, V, W), X)))))),
% 0.11/0.40 inference(bind,[status(th)],[])).
% 0.11/0.40 tff(90,plain,
% 0.11/0.40 (![U: $i, V: $i, W: $i, X: $i] : (check_cpq(triple(U, V, W)) | (~check_cpq(remove_cpq(triple(U, V, W), X))) | (~ok(remove_cpq(triple(U, V, W), X)))) <=> ![U: $i, V: $i, W: $i, X: $i] : (check_cpq(triple(U, V, W)) | (~check_cpq(remove_cpq(triple(U, V, W), X))) | (~ok(remove_cpq(triple(U, V, W), X))))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[89])).
% 0.11/0.40 tff(91,plain,
% 0.11/0.40 (^[U: $i, V: $i, W: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite((check_cpq(remove_cpq(triple(U, V, W), X)) & ok(remove_cpq(triple(U, V, W), X))) <=> (~((~check_cpq(remove_cpq(triple(U, V, W), X))) | (~ok(remove_cpq(triple(U, V, W), X)))))), ((~(check_cpq(remove_cpq(triple(U, V, W), X)) & ok(remove_cpq(triple(U, V, W), X)))) <=> (~(~((~check_cpq(remove_cpq(triple(U, V, W), X))) | (~ok(remove_cpq(triple(U, V, W), X)))))))), rewrite((~(~((~check_cpq(remove_cpq(triple(U, V, W), X))) | (~ok(remove_cpq(triple(U, V, W), X)))))) <=> ((~check_cpq(remove_cpq(triple(U, V, W), X))) | (~ok(remove_cpq(triple(U, V, W), X))))), ((~(check_cpq(remove_cpq(triple(U, V, W), X)) & ok(remove_cpq(triple(U, V, W), X)))) <=> ((~check_cpq(remove_cpq(triple(U, V, W), X))) | (~ok(remove_cpq(triple(U, V, W), X)))))), ((check_cpq(triple(U, V, W)) | (~(check_cpq(remove_cpq(triple(U, V, W), X)) & ok(remove_cpq(triple(U, V, W), X))))) <=> (check_cpq(triple(U, V, W)) | ((~check_cpq(remove_cpq(triple(U, V, W), X))) | (~ok(remove_cpq(triple(U, V, W), X))))))), rewrite((check_cpq(triple(U, V, W)) | ((~check_cpq(remove_cpq(triple(U, V, W), X))) | (~ok(remove_cpq(triple(U, V, W), X))))) <=> (check_cpq(triple(U, V, W)) | (~check_cpq(remove_cpq(triple(U, V, W), X))) | (~ok(remove_cpq(triple(U, V, W), X))))), ((check_cpq(triple(U, V, W)) | (~(check_cpq(remove_cpq(triple(U, V, W), X)) & ok(remove_cpq(triple(U, V, W), X))))) <=> (check_cpq(triple(U, V, W)) | (~check_cpq(remove_cpq(triple(U, V, W), X))) | (~ok(remove_cpq(triple(U, V, W), X))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(92,plain,
% 0.19/0.40 (![U: $i, V: $i, W: $i, X: $i] : (check_cpq(triple(U, V, W)) | (~(check_cpq(remove_cpq(triple(U, V, W), X)) & ok(remove_cpq(triple(U, V, W), X))))) <=> ![U: $i, V: $i, W: $i, X: $i] : (check_cpq(triple(U, V, W)) | (~check_cpq(remove_cpq(triple(U, V, W), X))) | (~ok(remove_cpq(triple(U, V, W), X))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[91])).
% 0.19/0.40 tff(93,plain,
% 0.19/0.40 (![U: $i, V: $i, W: $i, X: $i] : (check_cpq(triple(U, V, W)) | (~(check_cpq(remove_cpq(triple(U, V, W), X)) & ok(remove_cpq(triple(U, V, W), X))))) <=> ![U: $i, V: $i, W: $i, X: $i] : (check_cpq(triple(U, V, W)) | (~(check_cpq(remove_cpq(triple(U, V, W), X)) & ok(remove_cpq(triple(U, V, W), X)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(94,plain,
% 0.19/0.40 (^[U: $i, V: $i, W: $i, X: $i] : rewrite(((check_cpq(remove_cpq(triple(U, V, W), X)) & ok(remove_cpq(triple(U, V, W), X))) => check_cpq(triple(U, V, W))) <=> (check_cpq(triple(U, V, W)) | (~(check_cpq(remove_cpq(triple(U, V, W), X)) & ok(remove_cpq(triple(U, V, W), X))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(95,plain,
% 0.19/0.40 (![U: $i, V: $i, W: $i, X: $i] : ((check_cpq(remove_cpq(triple(U, V, W), X)) & ok(remove_cpq(triple(U, V, W), X))) => check_cpq(triple(U, V, W))) <=> ![U: $i, V: $i, W: $i, X: $i] : (check_cpq(triple(U, V, W)) | (~(check_cpq(remove_cpq(triple(U, V, W), X)) & ok(remove_cpq(triple(U, V, W), X)))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[94])).
% 0.19/0.40 tff(96,axiom,(![U: $i, V: $i, W: $i, X: $i] : ((check_cpq(remove_cpq(triple(U, V, W), X)) & ok(remove_cpq(triple(U, V, W), X))) => check_cpq(triple(U, V, W)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l40_l27')).
% 0.19/0.40 tff(97,plain,
% 0.19/0.40 (![U: $i, V: $i, W: $i, X: $i] : (check_cpq(triple(U, V, W)) | (~(check_cpq(remove_cpq(triple(U, V, W), X)) & ok(remove_cpq(triple(U, V, W), X)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.19/0.40 tff(98,plain,
% 0.19/0.40 (![U: $i, V: $i, W: $i, X: $i] : (check_cpq(triple(U, V, W)) | (~(check_cpq(remove_cpq(triple(U, V, W), X)) & ok(remove_cpq(triple(U, V, W), X)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[97, 93])).
% 0.19/0.40 tff(99,plain,(
% 0.19/0.40 ![U: $i, V: $i, W: $i, X: $i] : (check_cpq(triple(U, V, W)) | (~(check_cpq(remove_cpq(triple(U, V, W), X)) & ok(remove_cpq(triple(U, V, W), X)))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[98])).
% 0.19/0.40 tff(100,plain,
% 0.19/0.40 (![U: $i, V: $i, W: $i, X: $i] : (check_cpq(triple(U, V, W)) | (~check_cpq(remove_cpq(triple(U, V, W), X))) | (~ok(remove_cpq(triple(U, V, W), X))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[99, 92])).
% 0.19/0.40 tff(101,plain,
% 0.19/0.40 (![U: $i, V: $i, W: $i, X: $i] : (check_cpq(triple(U, V, W)) | (~check_cpq(remove_cpq(triple(U, V, W), X))) | (~ok(remove_cpq(triple(U, V, W), X))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[100, 90])).
% 0.19/0.40 tff(102,plain,
% 0.19/0.40 (((~![U: $i, V: $i, W: $i, X: $i] : (check_cpq(triple(U, V, W)) | (~check_cpq(remove_cpq(triple(U, V, W), X))) | (~ok(remove_cpq(triple(U, V, W), X))))) | (check_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad)) | (~check_cpq(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(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] : (check_cpq(triple(U, V, W)) | (~check_cpq(remove_cpq(triple(U, V, W), X))) | (~ok(remove_cpq(triple(U, V, W), X))))) | check_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad)) | (~check_cpq(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(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))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(103,plain,
% 0.19/0.40 ((~![U: $i, V: $i, W: $i, X: $i] : (check_cpq(triple(U, V, W)) | (~check_cpq(remove_cpq(triple(U, V, W), X))) | (~ok(remove_cpq(triple(U, V, W), X))))) | (check_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad)) | (~check_cpq(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(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))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(104,plain,
% 0.19/0.40 ((~![U: $i, V: $i, W: $i, X: $i] : (check_cpq(triple(U, V, W)) | (~check_cpq(remove_cpq(triple(U, V, W), X))) | (~ok(remove_cpq(triple(U, V, W), X))))) | check_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad)) | (~check_cpq(remove_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad), findmin_cpq_res(triple(U!2, V!1, W!0))))) | (~ok(remove_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad), findmin_cpq_res(triple(U!2, V!1, W!0)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.19/0.40 tff(105,plain,
% 0.19/0.40 (check_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad)) | (~check_cpq(remove_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad), findmin_cpq_res(triple(U!2, V!1, W!0))))) | (~ok(remove_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad), findmin_cpq_res(triple(U!2, V!1, W!0)))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[104, 101])).
% 0.19/0.40 tff(106,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[105, 88, 84, 66])).
% 0.19/0.40 tff(107,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,[]))).
% 0.19/0.40 tff(108,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))) <=> ((V = create_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))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(109,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))) <=> ![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)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[108])).
% 0.19/0.40 tff(110,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)))) <=> (~((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)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(111,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))) <=> ![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)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[110])).
% 0.19/0.40 tff(112,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))) <=> ![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)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(113,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(elim_unused_vars,[status(thm)],[])).
% 0.19/0.40 tff(114,plain,
% 0.19/0.40 (^[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))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(115,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[114])).
% 0.19/0.40 tff(116,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(transitivity,[status(thm)],[115, 113])).
% 0.19/0.40 tff(117,axiom,(![U: $i, V: $i, W: $i, X: $i] : (((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U)))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax','ax47')).
% 0.19/0.40 tff(118,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)))),
% 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, 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)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[118, 112])).
% 0.19/0.40 tff(120,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)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[119])).
% 0.19/0.41 tff(121,plain,
% 0.19/0.41 (![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[120, 111])).
% 0.19/0.41 tff(122,plain,
% 0.19/0.41 (![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[121, 109])).
% 0.19/0.41 tff(123,plain,
% 0.19/0.41 (((~![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))) | ((V!1 = create_slb) | contains_slb(V!1, findmin_pqp_res(U!2)) | (findmin_cpq_eff(triple(U!2, V!1, W!0)) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad)))) <=> ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))) | (V!1 = create_slb) | contains_slb(V!1, findmin_pqp_res(U!2)) | (findmin_cpq_eff(triple(U!2, V!1, W!0)) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(124,plain,
% 0.19/0.41 ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))) | ((V!1 = create_slb) | contains_slb(V!1, findmin_pqp_res(U!2)) | (findmin_cpq_eff(triple(U!2, V!1, W!0)) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(125,plain,
% 0.19/0.41 ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))) | (V!1 = create_slb) | contains_slb(V!1, findmin_pqp_res(U!2)) | (findmin_cpq_eff(triple(U!2, V!1, W!0)) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.19/0.41 tff(126,plain,
% 0.19/0.41 ((V!1 = create_slb) | contains_slb(V!1, findmin_pqp_res(U!2)) | (findmin_cpq_eff(triple(U!2, V!1, W!0)) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[125, 122])).
% 0.19/0.41 tff(127,plain,
% 0.19/0.41 (contains_slb(V!1, findmin_pqp_res(U!2)) | (findmin_cpq_eff(triple(U!2, V!1, W!0)) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[126, 27])).
% 0.19/0.41 tff(128,plain,
% 0.19/0.41 (contains_slb(V!1, findmin_pqp_res(U!2))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[127, 107])).
% 0.19/0.41 tff(129,plain,
% 0.19/0.41 (^[U: $i, V: $i, W: $i] : refl(((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~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))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(130,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))))) <=> ![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(quant_intro,[status(thm)],[129])).
% 0.19/0.41 tff(131,plain,
% 0.19/0.41 (^[U: $i, V: $i, W: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & 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)))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(132,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))) <=> ![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(quant_intro,[status(thm)],[131])).
% 0.19/0.41 tff(133,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))) <=> ![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(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(134,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(elim_unused_vars,[status(thm)],[])).
% 0.19/0.41 tff(135,plain,
% 0.19/0.41 (^[U: $i, V: $i, W: $i, X: $i] : trans(monotonicity(rewrite((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & 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(136,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)],[135])).
% 0.19/0.41 tff(137,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)],[136, 134])).
% 0.19/0.41 tff(138,axiom,(![U: $i, V: $i, W: $i, X: $i] : ((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax','ax48')).
% 0.19/0.41 tff(139,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)],[138, 137])).
% 0.19/0.41 tff(140,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)],[139, 133])).
% 0.19/0.41 tff(141,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)],[140])).
% 0.19/0.41 tff(142,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)],[141, 132])).
% 0.19/0.41 tff(143,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)],[142, 130])).
% 0.19/0.41 tff(144,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(145,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(146,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)],[145, 144])).
% 0.19/0.41 tff(147,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)],[146, 143])).
% 0.19/0.41 tff(148,plain,
% 0.19/0.41 ((~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)],[147, 27])).
% 0.19/0.41 tff(149,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)],[148, 128, 107])).
% 0.19/0.41 tff(150,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)],[149, 47])).
% 0.19/0.41 tff(151,plain,
% 0.19/0.41 (^[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))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(152,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[151])).
% 0.19/0.41 tff(153,plain,
% 0.19/0.41 (^[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)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(154,plain,
% 0.19/0.41 (![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)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[153])).
% 0.19/0.41 tff(155,plain,
% 0.19/0.41 (![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))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(156,axiom,(![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+0.ax','stricly_smaller_definition')).
% 0.19/0.41 tff(157,plain,
% 0.19/0.41 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.19/0.41 tff(158,plain,(
% 0.19/0.41 ![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[157])).
% 0.19/0.41 tff(159,plain,
% 0.19/0.41 (![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[158, 154])).
% 0.19/0.41 tff(160,plain,
% 0.19/0.41 (![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[159, 152])).
% 0.19/0.41 tff(161,plain,
% 0.19/0.41 ((~![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)))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(162,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))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[161, 160])).
% 0.19/0.41 tff(163,plain,
% 0.19/0.41 (less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_cpq_res(triple(U!2, V!1, W!0))) <=> less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_pqp_res(U!2))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[44])).
% 0.19/0.42 tff(164,plain,
% 0.19/0.42 (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)))),
% 0.19/0.42 inference(symmetry,[status(thm)],[163])).
% 0.19/0.42 tff(165,plain,
% 0.19/0.42 ((~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))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[164])).
% 0.19/0.42 tff(166,assumption,(findmin_cpq_eff(triple(U!2, V!1, W!0)) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0)), introduced(assumption)).
% 0.19/0.42 tff(167,plain,
% 0.19/0.42 (triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0) = findmin_cpq_eff(triple(U!2, V!1, W!0))),
% 0.19/0.42 inference(symmetry,[status(thm)],[166])).
% 0.19/0.42 tff(168,plain,
% 0.19/0.42 (remove_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0), 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)))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[167])).
% 0.19/0.42 tff(169,plain,
% 0.19/0.42 (remove_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0), findmin_cpq_res(triple(U!2, V!1, W!0))) = removemin_cpq_eff(triple(U!2, V!1, W!0))),
% 0.19/0.42 inference(transitivity,[status(thm)],[168, 57])).
% 0.19/0.42 tff(170,plain,
% 0.19/0.42 (ok(remove_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0), findmin_cpq_res(triple(U!2, V!1, W!0)))) <=> ok(removemin_cpq_eff(triple(U!2, V!1, W!0)))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[169])).
% 0.19/0.42 tff(171,plain,
% 0.19/0.42 (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)), W!0), findmin_cpq_res(triple(U!2, V!1, W!0))))),
% 0.19/0.42 inference(symmetry,[status(thm)],[170])).
% 0.19/0.42 tff(172,plain,
% 0.19/0.42 (ok(remove_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0), findmin_cpq_res(triple(U!2, V!1, W!0))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[65, 171])).
% 0.19/0.42 tff(173,plain,
% 0.19/0.42 (check_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0)) <=> check_cpq(findmin_cpq_eff(triple(U!2, V!1, W!0)))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[167])).
% 0.19/0.42 tff(174,plain,
% 0.19/0.42 (check_cpq(findmin_cpq_eff(triple(U!2, V!1, W!0))) <=> check_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0))),
% 0.19/0.42 inference(symmetry,[status(thm)],[173])).
% 0.19/0.42 tff(175,plain,
% 0.19/0.42 ((~check_cpq(findmin_cpq_eff(triple(U!2, V!1, W!0)))) <=> (~check_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0)))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[174])).
% 0.19/0.42 tff(176,plain,
% 0.19/0.42 (~check_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[83, 175])).
% 0.19/0.42 tff(177,plain,
% 0.19/0.42 (check_cpq(remove_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0), findmin_cpq_res(triple(U!2, V!1, W!0)))) <=> check_cpq(removemin_cpq_eff(triple(U!2, V!1, W!0)))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[169])).
% 0.19/0.42 tff(178,plain,
% 0.19/0.42 (check_cpq(removemin_cpq_eff(triple(U!2, V!1, W!0))) <=> check_cpq(remove_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0), findmin_cpq_res(triple(U!2, V!1, W!0))))),
% 0.19/0.42 inference(symmetry,[status(thm)],[177])).
% 0.19/0.42 tff(179,plain,
% 0.19/0.42 (check_cpq(remove_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0), findmin_cpq_res(triple(U!2, V!1, W!0))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[87, 178])).
% 0.19/0.42 tff(180,plain,
% 0.19/0.42 (((~![U: $i, V: $i, W: $i, X: $i] : (check_cpq(triple(U, V, W)) | (~check_cpq(remove_cpq(triple(U, V, W), X))) | (~ok(remove_cpq(triple(U, V, W), X))))) | (check_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0)) | (~check_cpq(remove_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0), findmin_cpq_res(triple(U!2, V!1, W!0))))) | (~ok(remove_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0), findmin_cpq_res(triple(U!2, V!1, W!0))))))) <=> ((~![U: $i, V: $i, W: $i, X: $i] : (check_cpq(triple(U, V, W)) | (~check_cpq(remove_cpq(triple(U, V, W), X))) | (~ok(remove_cpq(triple(U, V, W), X))))) | check_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0)) | (~check_cpq(remove_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0), findmin_cpq_res(triple(U!2, V!1, W!0))))) | (~ok(remove_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0), findmin_cpq_res(triple(U!2, V!1, W!0))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(181,plain,
% 0.19/0.42 ((~![U: $i, V: $i, W: $i, X: $i] : (check_cpq(triple(U, V, W)) | (~check_cpq(remove_cpq(triple(U, V, W), X))) | (~ok(remove_cpq(triple(U, V, W), X))))) | (check_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0)) | (~check_cpq(remove_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0), findmin_cpq_res(triple(U!2, V!1, W!0))))) | (~ok(remove_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0), findmin_cpq_res(triple(U!2, V!1, W!0))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(182,plain,
% 0.19/0.42 ((~![U: $i, V: $i, W: $i, X: $i] : (check_cpq(triple(U, V, W)) | (~check_cpq(remove_cpq(triple(U, V, W), X))) | (~ok(remove_cpq(triple(U, V, W), X))))) | check_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0)) | (~check_cpq(remove_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0), findmin_cpq_res(triple(U!2, V!1, W!0))))) | (~ok(remove_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0), findmin_cpq_res(triple(U!2, V!1, W!0)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.19/0.42 tff(183,plain,
% 0.19/0.42 (check_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0)) | (~check_cpq(remove_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0), findmin_cpq_res(triple(U!2, V!1, W!0))))) | (~ok(remove_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0), findmin_cpq_res(triple(U!2, V!1, W!0)))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[182, 101])).
% 0.19/0.42 tff(184,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[183, 179, 176, 172])).
% 0.19/0.42 tff(185,plain,(~(findmin_cpq_eff(triple(U!2, V!1, W!0)) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(186,plain,
% 0.19/0.42 (^[U: $i, V: $i, W: $i] : refl(((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), 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)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(187,plain,
% 0.19/0.42 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) <=> ![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[186])).
% 0.19/0.42 tff(188,plain,
% 0.19/0.42 (^[U: $i, V: $i, W: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & 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))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(189,plain,
% 0.19/0.42 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))) <=> ![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[188])).
% 0.19/0.42 tff(190,plain,
% 0.19/0.42 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))) <=> ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(191,plain,
% 0.19/0.42 (![U: $i, V: $i, W: $i, X: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))) <=> ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)))),
% 0.19/0.42 inference(elim_unused_vars,[status(thm)],[])).
% 0.19/0.42 tff(192,plain,
% 0.19/0.42 (^[U: $i, V: $i, W: $i, X: $i] : trans(monotonicity(rewrite((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))) <=> ((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))), (((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))) <=> (((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))))), rewrite((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))) <=> ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)))), (((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))) <=> ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(193,plain,
% 0.19/0.42 (![U: $i, V: $i, W: $i, X: $i] : ((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[192])).
% 0.19/0.42 tff(194,plain,
% 0.19/0.42 (![U: $i, V: $i, W: $i, X: $i] : ((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))) <=> ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)))),
% 0.19/0.42 inference(transitivity,[status(thm)],[193, 191])).
% 0.19/0.42 tff(195,axiom,(![U: $i, V: $i, W: $i, X: $i] : ((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax','ax49')).
% 0.19/0.42 tff(196,plain,
% 0.19/0.42 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.19/0.42 tff(197,plain,
% 0.19/0.42 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[196, 190])).
% 0.19/0.42 tff(198,plain,(
% 0.19/0.42 ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[197])).
% 0.19/0.42 tff(199,plain,
% 0.19/0.42 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[198, 189])).
% 0.19/0.42 tff(200,plain,
% 0.19/0.42 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[199, 187])).
% 0.19/0.42 tff(201,plain,
% 0.19/0.42 (((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))) | ((V!1 = create_slb) | (~contains_slb(V!1, findmin_pqp_res(U!2))) | (findmin_cpq_eff(triple(U!2, V!1, W!0)) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0)) | (~less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_pqp_res(U!2))))) <=> ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))) | (V!1 = create_slb) | (~contains_slb(V!1, findmin_pqp_res(U!2))) | (findmin_cpq_eff(triple(U!2, V!1, W!0)) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0)) | (~less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_pqp_res(U!2))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(202,plain,
% 0.19/0.43 ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), 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))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(203,plain,
% 0.19/0.43 ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), 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)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.19/0.43 tff(204,plain,
% 0.19/0.43 ((V!1 = create_slb) | (~contains_slb(V!1, findmin_pqp_res(U!2))) | (findmin_cpq_eff(triple(U!2, V!1, W!0)) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0)) | (~less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_pqp_res(U!2)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[203, 200])).
% 0.19/0.43 tff(205,plain,
% 0.19/0.43 ((~contains_slb(V!1, findmin_pqp_res(U!2))) | (~less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_pqp_res(U!2)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[204, 27, 185])).
% 0.19/0.43 tff(206,plain,
% 0.19/0.43 (~less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_pqp_res(U!2))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[205, 128])).
% 0.19/0.43 tff(207,plain,
% 0.19/0.43 (~less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_cpq_res(triple(U!2, V!1, W!0)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[206, 165])).
% 0.19/0.43 tff(208,assumption,((~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)))), introduced(assumption)).
% 0.19/0.43 tff(209,assumption,(~less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_cpq_res(triple(U!2, V!1, W!0)))), introduced(assumption)).
% 0.19/0.43 tff(210,plain,
% 0.19/0.43 (^[U: $i, V: $i] : refl((less_than(V, U) | less_than(U, V)) <=> (less_than(V, U) | less_than(U, V)))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(211,plain,
% 0.19/0.43 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[210])).
% 0.19/0.43 tff(212,plain,
% 0.19/0.43 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(213,plain,
% 0.19/0.43 (^[U: $i, V: $i] : rewrite((less_than(U, V) | less_than(V, U)) <=> (less_than(V, U) | less_than(U, V)))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(214,plain,
% 0.19/0.43 (![U: $i, V: $i] : (less_than(U, V) | less_than(V, U)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[213])).
% 0.19/0.43 tff(215,axiom,(![U: $i, V: $i] : (less_than(U, V) | less_than(V, U))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+0.ax','totality')).
% 0.19/0.43 tff(216,plain,
% 0.19/0.43 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[215, 214])).
% 0.19/0.43 tff(217,plain,
% 0.19/0.43 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[216, 212])).
% 0.19/0.43 tff(218,plain,(
% 0.19/0.43 ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.19/0.43 inference(skolemize,[status(sab)],[217])).
% 0.19/0.43 tff(219,plain,
% 0.19/0.43 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[218, 211])).
% 0.19/0.43 tff(220,plain,
% 0.19/0.43 (((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | (less_than(findmin_cpq_res(triple(U!2, V!1, W!0)), lookup_slb(V!1, findmin_pqp_res(U!2))) | less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_cpq_res(triple(U!2, V!1, W!0))))) <=> ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | less_than(findmin_cpq_res(triple(U!2, V!1, W!0)), lookup_slb(V!1, findmin_pqp_res(U!2))) | less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_cpq_res(triple(U!2, V!1, W!0))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(221,plain,
% 0.19/0.43 ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | (less_than(findmin_cpq_res(triple(U!2, V!1, W!0)), lookup_slb(V!1, findmin_pqp_res(U!2))) | less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_cpq_res(triple(U!2, V!1, W!0))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(222,plain,
% 0.19/0.43 ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | less_than(findmin_cpq_res(triple(U!2, V!1, W!0)), lookup_slb(V!1, findmin_pqp_res(U!2))) | less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_cpq_res(triple(U!2, V!1, W!0)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[221, 220])).
% 0.19/0.43 tff(223,plain,
% 0.19/0.43 (less_than(findmin_cpq_res(triple(U!2, V!1, W!0)), lookup_slb(V!1, findmin_pqp_res(U!2)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[222, 219, 209])).
% 0.19/0.43 tff(224,plain,
% 0.19/0.43 ((~((~less_than(findmin_cpq_res(triple(U!2, V!1, W!0)), lookup_slb(V!1, findmin_pqp_res(U!2)))) | less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_cpq_res(triple(U!2, V!1, W!0))))) | (~less_than(findmin_cpq_res(triple(U!2, V!1, W!0)), lookup_slb(V!1, findmin_pqp_res(U!2)))) | less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_cpq_res(triple(U!2, V!1, W!0)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(225,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[224, 223, 209, 208])).
% 0.19/0.43 tff(226,plain,(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)))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(227,plain,
% 0.19/0.43 (~((~less_than(findmin_cpq_res(triple(U!2, V!1, W!0)), lookup_slb(V!1, findmin_pqp_res(U!2)))) | less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_cpq_res(triple(U!2, V!1, W!0))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[226, 207])).
% 0.19/0.43 tff(228,plain,
% 0.19/0.43 ((((~less_than(findmin_cpq_res(triple(U!2, V!1, W!0)), lookup_slb(V!1, findmin_pqp_res(U!2)))) | less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_cpq_res(triple(U!2, V!1, W!0)))) <=> 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)))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(229,plain,
% 0.19/0.43 (strictly_less_than(findmin_cpq_res(triple(U!2, V!1, W!0)), lookup_slb(V!1, findmin_pqp_res(U!2)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[228, 227, 162])).
% 0.19/0.43 tff(230,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[229, 150])).
% 0.19/0.43 % SZS output end Proof
% 0.19/0.43 % E exiting
%------------------------------------------------------------------------------