%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV373+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:32:19 AM UTC 2025
% Result : Theorem 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV373+1 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n001.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 09:48:35 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.38 % SZS status Theorem
% 0.19/0.38 % SZS output start Proof
% 0.19/0.38 tff(contains_slb_type, type, (
% 0.19/0.38 contains_slb: ( $i * $i ) > $o)).
% 0.19/0.38 tff(findmin_pqp_res_type, type, (
% 0.19/0.38 findmin_pqp_res: $i > $i)).
% 0.19/0.38 tff(tptp_fun_U_2_type, type, (
% 0.19/0.38 tptp_fun_U_2: $i)).
% 0.19/0.38 tff(tptp_fun_V_1_type, type, (
% 0.19/0.38 tptp_fun_V_1: $i)).
% 0.19/0.38 tff(findmin_cpq_res_type, type, (
% 0.19/0.38 findmin_cpq_res: $i > $i)).
% 0.19/0.38 tff(triple_type, type, (
% 0.19/0.38 triple: ( $i * $i * $i ) > $i)).
% 0.19/0.38 tff(tptp_fun_W_0_type, type, (
% 0.19/0.38 tptp_fun_W_0: $i)).
% 0.19/0.38 tff(create_slb_type, type, (
% 0.19/0.38 create_slb: $i)).
% 0.19/0.38 tff(less_than_type, type, (
% 0.19/0.38 less_than: ( $i * $i ) > $o)).
% 0.19/0.38 tff(lookup_slb_type, type, (
% 0.19/0.38 lookup_slb: ( $i * $i ) > $i)).
% 0.19/0.38 tff(ok_type, type, (
% 0.19/0.38 ok: $i > $o)).
% 0.19/0.38 tff(findmin_cpq_eff_type, type, (
% 0.19/0.38 findmin_cpq_eff: $i > $i)).
% 0.19/0.38 tff(contains_cpq_type, type, (
% 0.19/0.38 contains_cpq: ( $i * $i ) > $o)).
% 0.19/0.38 tff(1,plain,
% 0.19/0.38 ((~![U: $i, V: $i, W: $i] : ((~ok(findmin_cpq_eff(triple(U, V, W)))) | contains_cpq(triple(U, V, W), findmin_cpq_res(triple(U, V, W))))) <=> (~![U: $i, V: $i, W: $i] : ((~ok(findmin_cpq_eff(triple(U, V, W)))) | contains_cpq(triple(U, V, W), findmin_cpq_res(triple(U, V, W)))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(2,plain,
% 0.19/0.38 ((~![U: $i, V: $i, W: $i] : ((~contains_cpq(triple(U, V, W), findmin_cpq_res(triple(U, V, W)))) => (~ok(findmin_cpq_eff(triple(U, V, W)))))) <=> (~![U: $i, V: $i, W: $i] : ((~ok(findmin_cpq_eff(triple(U, V, W)))) | contains_cpq(triple(U, V, W), findmin_cpq_res(triple(U, V, W)))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(3,axiom,(~![U: $i, V: $i, W: $i] : ((~contains_cpq(triple(U, V, W), findmin_cpq_res(triple(U, V, W)))) => (~ok(findmin_cpq_eff(triple(U, V, W)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l9_co')).
% 0.19/0.38 tff(4,plain,
% 0.19/0.38 (~![U: $i, V: $i, W: $i] : ((~ok(findmin_cpq_eff(triple(U, V, W)))) | contains_cpq(triple(U, V, W), findmin_cpq_res(triple(U, V, W))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.19/0.38 tff(5,plain,
% 0.19/0.38 (~![U: $i, V: $i, W: $i] : ((~ok(findmin_cpq_eff(triple(U, V, W)))) | contains_cpq(triple(U, V, W), findmin_cpq_res(triple(U, V, W))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.19/0.38 tff(6,plain,
% 0.19/0.38 (~![U: $i, V: $i, W: $i] : ((~ok(findmin_cpq_eff(triple(U, V, W)))) | contains_cpq(triple(U, V, W), findmin_cpq_res(triple(U, V, W))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.19/0.38 tff(7,plain,
% 0.19/0.38 (~![U: $i, V: $i, W: $i] : ((~ok(findmin_cpq_eff(triple(U, V, W)))) | contains_cpq(triple(U, V, W), findmin_cpq_res(triple(U, V, W))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.19/0.38 tff(8,plain,(
% 0.19/0.38 ~((~ok(findmin_cpq_eff(triple(U!2, V!1, W!0)))) | contains_cpq(triple(U!2, V!1, W!0), findmin_cpq_res(triple(U!2, V!1, W!0))))),
% 0.19/0.38 inference(skolemize,[status(sab)],[7])).
% 0.19/0.38 tff(9,plain,
% 0.19/0.38 (ok(findmin_cpq_eff(triple(U!2, V!1, W!0)))),
% 0.19/0.38 inference(or_elim,[status(thm)],[8])).
% 0.19/0.38 tff(10,plain,
% 0.19/0.38 (^[U: $i, V: $i, W: $i] : refl(((~ok(findmin_cpq_eff(triple(U, V, W)))) | (~((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))))) <=> ((~ok(findmin_cpq_eff(triple(U, V, W)))) | (~((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(11,plain,
% 0.19/0.38 (![U: $i, V: $i, W: $i] : ((~ok(findmin_cpq_eff(triple(U, V, W)))) | (~((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))))) <=> ![U: $i, V: $i, W: $i] : ((~ok(findmin_cpq_eff(triple(U, V, W)))) | (~((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[10])).
% 0.19/0.38 tff(12,plain,
% 0.19/0.38 (^[U: $i, V: $i, W: $i] : rewrite(((~ok(findmin_cpq_eff(triple(U, V, W)))) | ((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) <=> ((~ok(findmin_cpq_eff(triple(U, V, W)))) | (~((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(13,plain,
% 0.19/0.38 (![U: $i, V: $i, W: $i] : ((~ok(findmin_cpq_eff(triple(U, V, W)))) | ((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) <=> ![U: $i, V: $i, W: $i] : ((~ok(findmin_cpq_eff(triple(U, V, W)))) | (~((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[12])).
% 0.19/0.38 tff(14,plain,
% 0.19/0.38 (![U: $i, V: $i, W: $i] : ((~ok(findmin_cpq_eff(triple(U, V, W)))) | ((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) <=> ![U: $i, V: $i, W: $i] : ((~ok(findmin_cpq_eff(triple(U, V, W)))) | ((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(15,plain,
% 0.19/0.38 (^[U: $i, V: $i, W: $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)))), ((ok(findmin_cpq_eff(triple(U, V, W))) => (((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) <=> (ok(findmin_cpq_eff(triple(U, V, W))) => ((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))))), rewrite((ok(findmin_cpq_eff(triple(U, V, W))) => ((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) <=> ((~ok(findmin_cpq_eff(triple(U, V, W)))) | ((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))), ((ok(findmin_cpq_eff(triple(U, V, W))) => (((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) <=> ((~ok(findmin_cpq_eff(triple(U, V, W)))) | ((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(16,plain,
% 0.19/0.38 (![U: $i, V: $i, W: $i] : (ok(findmin_cpq_eff(triple(U, V, W))) => (((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) <=> ![U: $i, V: $i, W: $i] : ((~ok(findmin_cpq_eff(triple(U, V, W)))) | ((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[15])).
% 0.19/0.38 tff(17,axiom,(![U: $i, V: $i, W: $i] : (ok(findmin_cpq_eff(triple(U, V, W))) => (((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l9_l10')).
% 0.19/0.38 tff(18,plain,
% 0.19/0.38 (![U: $i, V: $i, W: $i] : ((~ok(findmin_cpq_eff(triple(U, V, W)))) | ((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.19/0.38 tff(19,plain,
% 0.19/0.38 (![U: $i, V: $i, W: $i] : ((~ok(findmin_cpq_eff(triple(U, V, W)))) | ((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.19/0.38 tff(20,plain,(
% 0.19/0.38 ![U: $i, V: $i, W: $i] : ((~ok(findmin_cpq_eff(triple(U, V, W)))) | ((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))),
% 0.19/0.38 inference(skolemize,[status(sab)],[19])).
% 0.19/0.38 tff(21,plain,
% 0.19/0.38 (![U: $i, V: $i, W: $i] : ((~ok(findmin_cpq_eff(triple(U, V, W)))) | (~((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.19/0.38 tff(22,plain,
% 0.19/0.38 (![U: $i, V: $i, W: $i] : ((~ok(findmin_cpq_eff(triple(U, V, W)))) | (~((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[21, 11])).
% 0.19/0.38 tff(23,plain,
% 0.19/0.38 (((~![U: $i, V: $i, W: $i] : ((~ok(findmin_cpq_eff(triple(U, V, W)))) | (~((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))))) | ((~ok(findmin_cpq_eff(triple(U!2, V!1, W!0)))) | (~((V!1 = create_slb) | (~contains_slb(V!1, findmin_pqp_res(U!2))) | (~less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_pqp_res(U!2))))))) <=> ((~![U: $i, V: $i, W: $i] : ((~ok(findmin_cpq_eff(triple(U, V, W)))) | (~((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))))) | (~ok(findmin_cpq_eff(triple(U!2, V!1, W!0)))) | (~((V!1 = create_slb) | (~contains_slb(V!1, findmin_pqp_res(U!2))) | (~less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_pqp_res(U!2))))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(24,plain,
% 0.19/0.38 ((~![U: $i, V: $i, W: $i] : ((~ok(findmin_cpq_eff(triple(U, V, W)))) | (~((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))))) | ((~ok(findmin_cpq_eff(triple(U!2, V!1, W!0)))) | (~((V!1 = create_slb) | (~contains_slb(V!1, findmin_pqp_res(U!2))) | (~less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_pqp_res(U!2))))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(25,plain,
% 0.19/0.38 ((~![U: $i, V: $i, W: $i] : ((~ok(findmin_cpq_eff(triple(U, V, W)))) | (~((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))))) | (~ok(findmin_cpq_eff(triple(U!2, V!1, W!0)))) | (~((V!1 = create_slb) | (~contains_slb(V!1, findmin_pqp_res(U!2))) | (~less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_pqp_res(U!2)))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.19/0.38 tff(26,plain,
% 0.19/0.38 (~((V!1 = create_slb) | (~contains_slb(V!1, findmin_pqp_res(U!2))) | (~less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_pqp_res(U!2))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[25, 22, 9])).
% 0.19/0.38 tff(27,plain,
% 0.19/0.38 (((V!1 = create_slb) | (~contains_slb(V!1, findmin_pqp_res(U!2))) | (~less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_pqp_res(U!2)))) | (~(V!1 = create_slb))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(28,plain,
% 0.19/0.38 (~(V!1 = create_slb)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.19/0.38 tff(29,plain,
% 0.19/0.38 (^[U: $i, V: $i, W: $i] : refl(((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U))) <=> ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(30,plain,
% 0.19/0.38 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U))) <=> ![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[29])).
% 0.19/0.38 tff(31,plain,
% 0.19/0.38 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U))) <=> ![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(32,plain,
% 0.19/0.38 (![U: $i, V: $i, W: $i, X: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U))) <=> ![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.19/0.38 inference(elim_unused_vars,[status(thm)],[])).
% 0.19/0.38 tff(33,plain,
% 0.19/0.38 (^[U: $i, V: $i, W: $i, X: $i] : rewrite(((~(V = create_slb)) => (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U))) <=> ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(34,plain,
% 0.19/0.38 (![U: $i, V: $i, W: $i, X: $i] : ((~(V = create_slb)) => (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[33])).
% 0.19/0.38 tff(35,plain,
% 0.19/0.38 (![U: $i, V: $i, W: $i, X: $i] : ((~(V = create_slb)) => (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U))) <=> ![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.19/0.38 inference(transitivity,[status(thm)],[34, 32])).
% 0.19/0.38 tff(36,axiom,(![U: $i, V: $i, W: $i, X: $i] : ((~(V = create_slb)) => (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax','ax51')).
% 0.19/0.38 tff(37,plain,
% 0.19/0.38 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.19/0.38 tff(38,plain,
% 0.19/0.38 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[37, 31])).
% 0.19/0.38 tff(39,plain,(
% 0.19/0.38 ![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.19/0.38 inference(skolemize,[status(sab)],[38])).
% 0.19/0.38 tff(40,plain,
% 0.19/0.38 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[39, 30])).
% 0.19/0.38 tff(41,plain,
% 0.19/0.38 (((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))) | ((V!1 = create_slb) | (findmin_cpq_res(triple(U!2, V!1, W!0)) = findmin_pqp_res(U!2)))) <=> ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))) | (V!1 = create_slb) | (findmin_cpq_res(triple(U!2, V!1, W!0)) = findmin_pqp_res(U!2)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(42,plain,
% 0.19/0.38 ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))) | ((V!1 = create_slb) | (findmin_cpq_res(triple(U!2, V!1, W!0)) = findmin_pqp_res(U!2)))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(43,plain,
% 0.19/0.38 ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))) | (V!1 = create_slb) | (findmin_cpq_res(triple(U!2, V!1, W!0)) = findmin_pqp_res(U!2))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.19/0.38 tff(44,plain,
% 0.19/0.38 ((V!1 = create_slb) | (findmin_cpq_res(triple(U!2, V!1, W!0)) = findmin_pqp_res(U!2))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[43, 40])).
% 0.19/0.38 tff(45,plain,
% 0.19/0.38 (findmin_cpq_res(triple(U!2, V!1, W!0)) = findmin_pqp_res(U!2)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[44, 28])).
% 0.19/0.38 tff(46,plain,
% 0.19/0.38 (findmin_pqp_res(U!2) = findmin_cpq_res(triple(U!2, V!1, W!0))),
% 0.19/0.38 inference(symmetry,[status(thm)],[45])).
% 0.19/0.38 tff(47,plain,
% 0.19/0.38 (contains_slb(V!1, findmin_pqp_res(U!2)) <=> contains_slb(V!1, findmin_cpq_res(triple(U!2, V!1, W!0)))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[46])).
% 0.19/0.38 tff(48,plain,
% 0.19/0.38 (contains_slb(V!1, findmin_cpq_res(triple(U!2, V!1, W!0))) <=> contains_slb(V!1, findmin_pqp_res(U!2))),
% 0.19/0.38 inference(symmetry,[status(thm)],[47])).
% 0.19/0.38 tff(49,plain,
% 0.19/0.38 ((~contains_slb(V!1, findmin_cpq_res(triple(U!2, V!1, W!0)))) <=> (~contains_slb(V!1, findmin_pqp_res(U!2)))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[48])).
% 0.19/0.38 tff(50,plain,
% 0.19/0.38 (^[U: $i, V: $i, W: $i, X: $i] : refl((contains_cpq(triple(U, V, W), X) <=> contains_slb(V, X)) <=> (contains_cpq(triple(U, V, W), X) <=> contains_slb(V, X)))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(51,plain,
% 0.19/0.38 (![U: $i, V: $i, W: $i, X: $i] : (contains_cpq(triple(U, V, W), X) <=> contains_slb(V, X)) <=> ![U: $i, V: $i, W: $i, X: $i] : (contains_cpq(triple(U, V, W), X) <=> contains_slb(V, X))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[50])).
% 0.19/0.38 tff(52,plain,
% 0.19/0.38 (![U: $i, V: $i, W: $i, X: $i] : (contains_cpq(triple(U, V, W), X) <=> contains_slb(V, X)) <=> ![U: $i, V: $i, W: $i, X: $i] : (contains_cpq(triple(U, V, W), X) <=> contains_slb(V, X))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(53,axiom,(![U: $i, V: $i, W: $i, X: $i] : (contains_cpq(triple(U, V, W), X) <=> contains_slb(V, X))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax','ax39')).
% 0.19/0.39 tff(54,plain,
% 0.19/0.39 (![U: $i, V: $i, W: $i, X: $i] : (contains_cpq(triple(U, V, W), X) <=> contains_slb(V, X))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.19/0.39 tff(55,plain,(
% 0.19/0.39 ![U: $i, V: $i, W: $i, X: $i] : (contains_cpq(triple(U, V, W), X) <=> contains_slb(V, X))),
% 0.19/0.39 inference(skolemize,[status(sab)],[54])).
% 0.19/0.39 tff(56,plain,
% 0.19/0.39 (![U: $i, V: $i, W: $i, X: $i] : (contains_cpq(triple(U, V, W), X) <=> contains_slb(V, X))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.19/0.39 tff(57,plain,
% 0.19/0.39 ((~![U: $i, V: $i, W: $i, X: $i] : (contains_cpq(triple(U, V, W), X) <=> contains_slb(V, X))) | (contains_cpq(triple(U!2, V!1, W!0), findmin_cpq_res(triple(U!2, V!1, W!0))) <=> contains_slb(V!1, findmin_cpq_res(triple(U!2, V!1, W!0))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(58,plain,
% 0.19/0.39 (contains_cpq(triple(U!2, V!1, W!0), findmin_cpq_res(triple(U!2, V!1, W!0))) <=> contains_slb(V!1, findmin_cpq_res(triple(U!2, V!1, W!0)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.19/0.39 tff(59,plain,
% 0.19/0.39 (~contains_cpq(triple(U!2, V!1, W!0), findmin_cpq_res(triple(U!2, V!1, W!0)))),
% 0.19/0.39 inference(or_elim,[status(thm)],[8])).
% 0.19/0.39 tff(60,plain,
% 0.19/0.39 ((~(contains_cpq(triple(U!2, V!1, W!0), findmin_cpq_res(triple(U!2, V!1, W!0))) <=> contains_slb(V!1, findmin_cpq_res(triple(U!2, V!1, W!0))))) | contains_cpq(triple(U!2, V!1, W!0), findmin_cpq_res(triple(U!2, V!1, W!0))) | (~contains_slb(V!1, findmin_cpq_res(triple(U!2, V!1, W!0))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(61,plain,
% 0.19/0.39 ((~(contains_cpq(triple(U!2, V!1, W!0), findmin_cpq_res(triple(U!2, V!1, W!0))) <=> contains_slb(V!1, findmin_cpq_res(triple(U!2, V!1, W!0))))) | (~contains_slb(V!1, findmin_cpq_res(triple(U!2, V!1, W!0))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.19/0.39 tff(62,plain,
% 0.19/0.39 (~contains_slb(V!1, findmin_cpq_res(triple(U!2, V!1, W!0)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[61, 58])).
% 0.19/0.39 tff(63,plain,
% 0.19/0.39 (~contains_slb(V!1, findmin_pqp_res(U!2))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[62, 49])).
% 0.19/0.39 tff(64,plain,
% 0.19/0.39 (((V!1 = create_slb) | (~contains_slb(V!1, findmin_pqp_res(U!2))) | (~less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_pqp_res(U!2)))) | contains_slb(V!1, findmin_pqp_res(U!2))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(65,plain,
% 0.19/0.39 (contains_slb(V!1, findmin_pqp_res(U!2))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[64, 26])).
% 0.19/0.39 tff(66,plain,
% 0.19/0.39 ($false),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[65, 63])).
% 0.19/0.39 % SZS output end Proof
% 0.19/0.39 % E exiting
%------------------------------------------------------------------------------