TSTP Solution File: SWV404+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV404+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 15:11:39 EDT 2022
% Result : Theorem 0.13s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV404+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Sep 4 02:37:34 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.13/0.40 % SZS status Theorem
% 0.13/0.40 % SZS output start Proof
% 0.13/0.40 tff(ok_type, type, (
% 0.13/0.40 ok: $i > $o)).
% 0.13/0.40 tff(remove_cpq_type, type, (
% 0.13/0.40 remove_cpq: ( $i * $i ) > $i)).
% 0.13/0.40 tff(findmin_cpq_res_type, type, (
% 0.13/0.40 findmin_cpq_res: $i > $i)).
% 0.13/0.40 tff(triple_type, type, (
% 0.13/0.40 triple: ( $i * $i * $i ) > $i)).
% 0.13/0.40 tff(tptp_fun_W_0_type, type, (
% 0.13/0.40 tptp_fun_W_0: $i)).
% 0.13/0.40 tff(tptp_fun_V_1_type, type, (
% 0.13/0.40 tptp_fun_V_1: $i)).
% 0.13/0.40 tff(tptp_fun_U_2_type, type, (
% 0.13/0.40 tptp_fun_U_2: $i)).
% 0.13/0.40 tff(update_slb_type, type, (
% 0.13/0.40 update_slb: ( $i * $i ) > $i)).
% 0.13/0.40 tff(findmin_pqp_res_type, type, (
% 0.13/0.40 findmin_pqp_res: $i > $i)).
% 0.13/0.40 tff(removemin_cpq_eff_type, type, (
% 0.13/0.40 removemin_cpq_eff: $i > $i)).
% 0.13/0.40 tff(findmin_cpq_eff_type, type, (
% 0.13/0.40 findmin_cpq_eff: $i > $i)).
% 0.13/0.40 tff(less_than_type, type, (
% 0.13/0.40 less_than: ( $i * $i ) > $o)).
% 0.13/0.40 tff(lookup_slb_type, type, (
% 0.13/0.40 lookup_slb: ( $i * $i ) > $i)).
% 0.13/0.40 tff(create_slb_type, type, (
% 0.13/0.40 create_slb: $i)).
% 0.13/0.40 tff(check_cpq_type, type, (
% 0.13/0.40 check_cpq: $i > $o)).
% 0.13/0.40 tff(strictly_less_than_type, type, (
% 0.13/0.40 strictly_less_than: ( $i * $i ) > $o)).
% 0.13/0.40 tff(bad_type, type, (
% 0.13/0.41 bad: $i)).
% 0.13/0.41 tff(contains_slb_type, type, (
% 0.13/0.41 contains_slb: ( $i * $i ) > $o)).
% 0.13/0.41 tff(1,plain,
% 0.13/0.41 (^[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))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(2,plain,
% 0.13/0.41 (![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)))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.41 tff(3,plain,
% 0.13/0.41 (![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)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(4,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')).
% 0.13/0.41 tff(5,plain,
% 0.13/0.41 (![U: $i] : (removemin_cpq_eff(U) = remove_cpq(findmin_cpq_eff(U), findmin_cpq_res(U)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.13/0.41 tff(6,plain,(
% 0.13/0.41 ![U: $i] : (removemin_cpq_eff(U) = remove_cpq(findmin_cpq_eff(U), findmin_cpq_res(U)))),
% 0.13/0.41 inference(skolemize,[status(sab)],[5])).
% 0.13/0.41 tff(7,plain,
% 0.13/0.41 (![U: $i] : (removemin_cpq_eff(U) = remove_cpq(findmin_cpq_eff(U), findmin_cpq_res(U)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.13/0.41 tff(8,plain,
% 0.13/0.41 ((~![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))))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(9,plain,
% 0.13/0.41 (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)))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.13/0.41 tff(10,plain,
% 0.13/0.41 (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))),
% 0.13/0.41 inference(symmetry,[status(thm)],[9])).
% 0.13/0.41 tff(11,assumption,(V!1 = create_slb), introduced(assumption)).
% 0.13/0.41 tff(12,plain,
% 0.13/0.41 (create_slb = V!1),
% 0.13/0.41 inference(symmetry,[status(thm)],[11])).
% 0.13/0.41 tff(13,plain,
% 0.13/0.41 (triple(U!2, create_slb, W!0) = triple(U!2, V!1, W!0)),
% 0.13/0.41 inference(monotonicity,[status(thm)],[12])).
% 0.13/0.41 tff(14,plain,
% 0.13/0.41 (check_cpq(triple(U!2, create_slb, W!0)) <=> check_cpq(triple(U!2, V!1, W!0))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[13])).
% 0.13/0.41 tff(15,plain,
% 0.13/0.41 (check_cpq(triple(U!2, V!1, W!0)) <=> check_cpq(triple(U!2, create_slb, W!0))),
% 0.13/0.41 inference(symmetry,[status(thm)],[14])).
% 0.13/0.41 tff(16,plain,
% 0.13/0.41 ((~check_cpq(triple(U!2, V!1, W!0))) <=> (~check_cpq(triple(U!2, create_slb, W!0)))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[15])).
% 0.13/0.41 tff(17,plain,
% 0.13/0.41 ((~![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)))))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(18,plain,
% 0.13/0.41 ((~![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)))))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(19,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')).
% 0.13/0.41 tff(20,plain,
% 0.13/0.41 (~![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))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.13/0.41 tff(21,plain,
% 0.13/0.41 (~![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))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[20, 17])).
% 0.13/0.41 tff(22,plain,
% 0.13/0.41 (~![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))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.13/0.41 tff(23,plain,
% 0.13/0.41 (~![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))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[22, 17])).
% 0.13/0.41 tff(24,plain,
% 0.13/0.41 (~![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))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[23, 17])).
% 0.13/0.41 tff(25,plain,
% 0.13/0.41 (~![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))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.13/0.41 tff(26,plain,
% 0.13/0.41 (~![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))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[25, 17])).
% 0.13/0.41 tff(27,plain,(
% 0.13/0.41 ~(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))))))),
% 0.13/0.41 inference(skolemize,[status(sab)],[26])).
% 0.13/0.41 tff(28,plain,
% 0.13/0.41 (~check_cpq(triple(U!2, V!1, W!0))),
% 0.13/0.41 inference(or_elim,[status(thm)],[27])).
% 0.13/0.41 tff(29,plain,
% 0.13/0.41 (~check_cpq(triple(U!2, create_slb, W!0))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[28, 16])).
% 0.13/0.41 tff(30,plain,
% 0.13/0.41 (^[U: $i, V: $i] : refl(check_cpq(triple(U, create_slb, V)) <=> check_cpq(triple(U, create_slb, V)))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(31,plain,
% 0.13/0.41 (![U: $i, V: $i] : check_cpq(triple(U, create_slb, V)) <=> ![U: $i, V: $i] : check_cpq(triple(U, create_slb, V))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[30])).
% 0.13/0.41 tff(32,plain,
% 0.13/0.41 (![U: $i, V: $i] : check_cpq(triple(U, create_slb, V)) <=> ![U: $i, V: $i] : check_cpq(triple(U, create_slb, V))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(33,axiom,(![U: $i, V: $i] : check_cpq(triple(U, create_slb, V))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax','ax36')).
% 0.13/0.41 tff(34,plain,
% 0.13/0.41 (![U: $i, V: $i] : check_cpq(triple(U, create_slb, V))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.13/0.41 tff(35,plain,(
% 0.13/0.41 ![U: $i, V: $i] : check_cpq(triple(U, create_slb, V))),
% 0.13/0.41 inference(skolemize,[status(sab)],[34])).
% 0.13/0.41 tff(36,plain,
% 0.13/0.41 (![U: $i, V: $i] : check_cpq(triple(U, create_slb, V))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.13/0.41 tff(37,plain,
% 0.13/0.41 ((~![U: $i, V: $i] : check_cpq(triple(U, create_slb, V))) | check_cpq(triple(U!2, create_slb, W!0))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(38,plain,
% 0.13/0.41 (check_cpq(triple(U!2, create_slb, W!0))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.13/0.41 tff(39,plain,
% 0.13/0.41 ($false),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[38, 29])).
% 0.13/0.41 tff(40,plain,(~(V!1 = create_slb)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.41 tff(41,plain,
% 0.13/0.41 (^[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))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(42,plain,
% 0.13/0.41 (![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)))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[41])).
% 0.13/0.41 tff(43,plain,
% 0.13/0.41 (![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)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(44,plain,
% 0.13/0.41 (![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)))),
% 0.13/0.41 inference(elim_unused_vars,[status(thm)],[])).
% 0.13/0.41 tff(45,plain,
% 0.13/0.41 (^[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))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(46,plain,
% 0.13/0.41 (![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)))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[45])).
% 0.13/0.41 tff(47,plain,
% 0.13/0.41 (![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)))),
% 0.13/0.41 inference(transitivity,[status(thm)],[46, 44])).
% 0.13/0.41 tff(48,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')).
% 0.13/0.41 tff(49,plain,
% 0.13/0.41 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.13/0.41 tff(50,plain,
% 0.13/0.41 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[49, 43])).
% 0.13/0.41 tff(51,plain,(
% 0.13/0.41 ![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.13/0.41 inference(skolemize,[status(sab)],[50])).
% 0.13/0.41 tff(52,plain,
% 0.13/0.41 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[51, 42])).
% 0.13/0.41 tff(53,plain,
% 0.13/0.41 (((~![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)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(54,plain,
% 0.13/0.41 ((~![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)))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(55,plain,
% 0.13/0.41 ((~![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))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.13/0.41 tff(56,plain,
% 0.13/0.41 ((V!1 = create_slb) | (findmin_cpq_res(triple(U!2, V!1, W!0)) = findmin_pqp_res(U!2))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[55, 52])).
% 0.13/0.41 tff(57,plain,
% 0.13/0.41 (findmin_cpq_res(triple(U!2, V!1, W!0)) = findmin_pqp_res(U!2)),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[56, 40])).
% 0.13/0.41 tff(58,plain,
% 0.13/0.41 (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))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[57])).
% 0.13/0.41 tff(59,assumption,(~less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_cpq_res(triple(U!2, V!1, W!0)))), introduced(assumption)).
% 0.13/0.41 tff(60,plain,
% 0.13/0.41 (^[U: $i, V: $i] : refl((less_than(V, U) | less_than(U, V)) <=> (less_than(V, U) | less_than(U, V)))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(61,plain,
% 0.13/0.41 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[60])).
% 0.13/0.41 tff(62,plain,
% 0.13/0.41 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(63,plain,
% 0.13/0.41 (^[U: $i, V: $i] : rewrite((less_than(U, V) | less_than(V, U)) <=> (less_than(V, U) | less_than(U, V)))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(64,plain,
% 0.13/0.41 (![U: $i, V: $i] : (less_than(U, V) | less_than(V, U)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[63])).
% 0.13/0.41 tff(65,axiom,(![U: $i, V: $i] : (less_than(U, V) | less_than(V, U))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+0.ax','totality')).
% 0.13/0.41 tff(66,plain,
% 0.13/0.41 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.13/0.41 tff(67,plain,
% 0.13/0.41 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.13/0.41 tff(68,plain,(
% 0.13/0.41 ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.13/0.41 inference(skolemize,[status(sab)],[67])).
% 0.13/0.41 tff(69,plain,
% 0.13/0.41 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[68, 61])).
% 0.13/0.41 tff(70,plain,
% 0.13/0.41 (((~![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))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(71,plain,
% 0.13/0.41 ((~![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))))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(72,plain,
% 0.13/0.41 ((~![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)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.13/0.41 tff(73,plain,
% 0.13/0.41 (less_than(findmin_cpq_res(triple(U!2, V!1, W!0)), lookup_slb(V!1, findmin_pqp_res(U!2)))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[72, 69, 59])).
% 0.13/0.41 tff(74,plain,
% 0.13/0.41 (^[U: $i, V: $i] : refl((strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U)))) <=> (strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U)))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(75,plain,
% 0.13/0.41 (![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))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[74])).
% 0.13/0.41 tff(76,plain,
% 0.13/0.41 (^[U: $i, V: $i] : rewrite((strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U)))) <=> (strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U)))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(77,plain,
% 0.13/0.41 (![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))))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[76])).
% 0.13/0.42 tff(78,plain,
% 0.13/0.42 (![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))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(79,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')).
% 0.13/0.42 tff(80,plain,
% 0.13/0.42 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.13/0.42 tff(81,plain,(
% 0.13/0.42 ![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.13/0.42 inference(skolemize,[status(sab)],[80])).
% 0.13/0.42 tff(82,plain,
% 0.13/0.42 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.13/0.42 tff(83,plain,
% 0.13/0.42 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[82, 75])).
% 0.13/0.42 tff(84,plain,
% 0.13/0.42 ((~![U: $i, V: $i] : (strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U))))) | (strictly_less_than(findmin_cpq_res(triple(U!2, V!1, W!0)), lookup_slb(V!1, findmin_pqp_res(U!2))) <=> (~((~less_than(findmin_cpq_res(triple(U!2, V!1, W!0)), lookup_slb(V!1, findmin_pqp_res(U!2)))) | less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_cpq_res(triple(U!2, V!1, W!0))))))),
% 0.13/0.42 inference(quant_inst,[status(thm)],[])).
% 0.13/0.42 tff(85,plain,
% 0.13/0.42 (strictly_less_than(findmin_cpq_res(triple(U!2, V!1, W!0)), lookup_slb(V!1, findmin_pqp_res(U!2))) <=> (~((~less_than(findmin_cpq_res(triple(U!2, V!1, W!0)), lookup_slb(V!1, findmin_pqp_res(U!2)))) | less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_cpq_res(triple(U!2, V!1, W!0)))))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[84, 83])).
% 0.13/0.42 tff(86,plain,
% 0.13/0.42 (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)))),
% 0.13/0.42 inference(monotonicity,[status(thm)],[57])).
% 0.13/0.42 tff(87,plain,
% 0.13/0.42 (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)))),
% 0.13/0.42 inference(symmetry,[status(thm)],[86])).
% 0.13/0.42 tff(88,plain,
% 0.13/0.42 ((~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))))),
% 0.13/0.42 inference(monotonicity,[status(thm)],[87])).
% 0.13/0.42 tff(89,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)).
% 0.13/0.42 tff(90,plain,
% 0.13/0.42 (triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad) = findmin_cpq_eff(triple(U!2, V!1, W!0))),
% 0.13/0.42 inference(symmetry,[status(thm)],[89])).
% 0.13/0.42 tff(91,plain,
% 0.13/0.42 (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)))),
% 0.13/0.42 inference(monotonicity,[status(thm)],[90])).
% 0.13/0.42 tff(92,plain,
% 0.13/0.42 (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))),
% 0.13/0.42 inference(transitivity,[status(thm)],[91, 10])).
% 0.13/0.42 tff(93,plain,
% 0.13/0.42 (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)))),
% 0.13/0.42 inference(monotonicity,[status(thm)],[92])).
% 0.13/0.42 tff(94,plain,
% 0.13/0.42 (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)), bad), findmin_cpq_res(triple(U!2, V!1, W!0))))),
% 0.13/0.42 inference(symmetry,[status(thm)],[93])).
% 0.13/0.42 tff(95,plain,
% 0.13/0.42 (check_cpq(removemin_cpq_eff(triple(U!2, V!1, W!0))) & ok(removemin_cpq_eff(triple(U!2, V!1, W!0)))),
% 0.13/0.42 inference(or_elim,[status(thm)],[27])).
% 0.13/0.42 tff(96,plain,
% 0.13/0.42 (ok(removemin_cpq_eff(triple(U!2, V!1, W!0)))),
% 0.13/0.42 inference(and_elim,[status(thm)],[95])).
% 0.13/0.42 tff(97,plain,
% 0.13/0.42 (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))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[96, 94])).
% 0.13/0.42 tff(98,plain,
% 0.13/0.42 (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)))),
% 0.13/0.42 inference(monotonicity,[status(thm)],[90])).
% 0.13/0.42 tff(99,plain,
% 0.13/0.42 (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)), bad))),
% 0.13/0.42 inference(symmetry,[status(thm)],[98])).
% 0.13/0.42 tff(100,plain,
% 0.13/0.42 ((~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)), bad)))),
% 0.13/0.42 inference(monotonicity,[status(thm)],[99])).
% 0.13/0.42 tff(101,plain,
% 0.13/0.42 (^[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))))))),
% 0.13/0.42 inference(bind,[status(th)],[])).
% 0.13/0.42 tff(102,plain,
% 0.13/0.42 (![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)))))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[101])).
% 0.13/0.42 tff(103,plain,
% 0.13/0.42 (![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)))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(104,plain,
% 0.13/0.42 (^[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))))))),
% 0.13/0.42 inference(bind,[status(th)],[])).
% 0.13/0.42 tff(105,plain,
% 0.13/0.42 (![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)))))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[104])).
% 0.13/0.42 tff(106,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')).
% 0.13/0.42 tff(107,plain,
% 0.13/0.42 (![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~check_cpq(findmin_cpq_eff(triple(U, V, W)))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.13/0.42 tff(108,plain,
% 0.13/0.42 (![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~check_cpq(findmin_cpq_eff(triple(U, V, W)))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[107, 103])).
% 0.13/0.42 tff(109,plain,(
% 0.13/0.42 ![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~check_cpq(findmin_cpq_eff(triple(U, V, W)))))),
% 0.13/0.42 inference(skolemize,[status(sab)],[108])).
% 0.13/0.42 tff(110,plain,
% 0.13/0.42 (![U: $i, V: $i, W: $i] : (check_cpq(triple(U, V, W)) | (~check_cpq(findmin_cpq_eff(triple(U, V, W)))))),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[109, 102])).
% 0.13/0.42 tff(111,plain,
% 0.13/0.42 (((~![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)))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(112,plain,
% 0.13/0.42 ((~![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)))))),
% 0.13/0.42 inference(quant_inst,[status(thm)],[])).
% 0.13/0.42 tff(113,plain,
% 0.20/0.42 ((~![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))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.20/0.42 tff(114,plain,
% 0.20/0.42 (~check_cpq(findmin_cpq_eff(triple(U!2, V!1, W!0)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[113, 110, 28])).
% 0.20/0.42 tff(115,plain,
% 0.20/0.42 (~check_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[114, 100])).
% 0.20/0.42 tff(116,plain,
% 0.20/0.42 (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)))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[92])).
% 0.20/0.42 tff(117,plain,
% 0.20/0.42 (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)), bad), findmin_cpq_res(triple(U!2, V!1, W!0))))),
% 0.20/0.42 inference(symmetry,[status(thm)],[116])).
% 0.20/0.42 tff(118,plain,
% 0.20/0.42 (check_cpq(removemin_cpq_eff(triple(U!2, V!1, W!0)))),
% 0.20/0.42 inference(and_elim,[status(thm)],[95])).
% 0.20/0.42 tff(119,plain,
% 0.20/0.42 (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))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.20/0.42 tff(120,plain,
% 0.20/0.42 (^[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)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(121,plain,
% 0.20/0.42 (![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)))) <=> ![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))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[120])).
% 0.20/0.42 tff(122,plain,
% 0.20/0.42 (^[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))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(123,plain,
% 0.20/0.42 (![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))))) <=> ![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))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[122])).
% 0.20/0.42 tff(124,plain,
% 0.20/0.42 (![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))))) <=> ![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)))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(125,plain,
% 0.20/0.42 (^[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))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(126,plain,
% 0.20/0.42 (![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)))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[125])).
% 0.20/0.42 tff(127,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')).
% 0.20/0.42 tff(128,plain,
% 0.20/0.42 (![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)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.20/0.42 tff(129,plain,
% 0.20/0.42 (![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)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[128, 124])).
% 0.20/0.42 tff(130,plain,(
% 0.20/0.42 ![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)))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[129])).
% 0.20/0.42 tff(131,plain,
% 0.20/0.42 (![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))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[130, 123])).
% 0.20/0.42 tff(132,plain,
% 0.20/0.42 (![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))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[131, 121])).
% 0.20/0.42 tff(133,plain,
% 0.20/0.42 (((~![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)), 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))))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(134,plain,
% 0.20/0.42 ((~![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)), 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))))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(135,plain,
% 0.20/0.42 ((~![U: $i, V: $i, W: $i, X: $i] : (check_cpq(triple(U, V, W)) | (~check_cpq(remove_cpq(triple(U, V, W), X))) | (~ok(remove_cpq(triple(U, V, W), X))))) | check_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad)) | (~check_cpq(remove_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad), findmin_cpq_res(triple(U!2, V!1, W!0))))) | (~ok(remove_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad), findmin_cpq_res(triple(U!2, V!1, W!0)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.20/0.43 tff(136,plain,
% 0.20/0.43 (check_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad)) | (~check_cpq(remove_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad), findmin_cpq_res(triple(U!2, V!1, W!0))))) | (~ok(remove_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad), findmin_cpq_res(triple(U!2, V!1, W!0)))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[135, 132])).
% 0.20/0.43 tff(137,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[136, 119, 115, 97])).
% 0.20/0.43 tff(138,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,[]))).
% 0.20/0.43 tff(139,plain,
% 0.20/0.43 (^[U: $i, V: $i, W: $i] : refl(((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(140,plain,
% 0.20/0.43 (![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[139])).
% 0.20/0.43 tff(141,plain,
% 0.20/0.43 (^[U: $i, V: $i, W: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U)))) <=> (~((V = create_slb) | contains_slb(V, findmin_pqp_res(U))))), ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) <=> (~(~((V = create_slb) | contains_slb(V, findmin_pqp_res(U))))))), rewrite((~(~((V = create_slb) | contains_slb(V, findmin_pqp_res(U))))) <=> ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)))), ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) <=> ((V = create_slb) | contains_slb(V, findmin_pqp_res(U))))), (((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> (((V = create_slb) | contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))))), rewrite((((V = create_slb) | contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))), (((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(142,plain,
% 0.20/0.43 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[141])).
% 0.20/0.43 tff(143,plain,
% 0.20/0.43 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(144,plain,
% 0.20/0.43 (![U: $i, V: $i, W: $i, X: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.20/0.43 inference(elim_unused_vars,[status(thm)],[])).
% 0.20/0.43 tff(145,plain,
% 0.20/0.43 (^[U: $i, V: $i, W: $i, X: $i] : rewrite((((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U)))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(146,plain,
% 0.20/0.43 (![U: $i, V: $i, W: $i, X: $i] : (((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U)))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[145])).
% 0.20/0.43 tff(147,plain,
% 0.20/0.43 (![U: $i, V: $i, W: $i, X: $i] : (((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U)))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[146, 144])).
% 0.20/0.43 tff(148,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')).
% 0.20/0.43 tff(149,plain,
% 0.20/0.43 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.20/0.43 tff(150,plain,
% 0.20/0.43 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[149, 143])).
% 0.20/0.43 tff(151,plain,(
% 0.20/0.43 ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[150])).
% 0.20/0.43 tff(152,plain,
% 0.20/0.43 (![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[151, 142])).
% 0.20/0.43 tff(153,plain,
% 0.20/0.43 (![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[152, 140])).
% 0.20/0.43 tff(154,plain,
% 0.20/0.43 (((~![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))) | ((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)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(155,plain,
% 0.20/0.43 ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))) | ((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)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(156,plain,
% 0.20/0.43 ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))) | (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))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.20/0.43 tff(157,plain,
% 0.20/0.43 ((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)), bad))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[156, 153])).
% 0.20/0.43 tff(158,plain,
% 0.20/0.43 (contains_slb(V!1, findmin_pqp_res(U!2))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[157, 138, 40])).
% 0.20/0.43 tff(159,plain,
% 0.20/0.43 (^[U: $i, V: $i, W: $i] : refl(((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~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))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(160,plain,
% 0.20/0.43 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~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)))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[159])).
% 0.20/0.43 tff(161,plain,
% 0.20/0.43 (^[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)))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(162,plain,
% 0.20/0.43 (![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)))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[161])).
% 0.20/0.43 tff(163,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(164,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.43 inference(elim_unused_vars,[status(thm)],[])).
% 0.20/0.43 tff(165,plain,
% 0.20/0.43 (^[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)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(166,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[165])).
% 0.20/0.43 tff(167,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[166, 164])).
% 0.20/0.43 tff(168,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')).
% 0.20/0.43 tff(169,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.20/0.43 tff(170,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[169, 163])).
% 0.20/0.43 tff(171,plain,(
% 0.20/0.43 ![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)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[170])).
% 0.20/0.43 tff(172,plain,
% 0.20/0.43 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[171, 162])).
% 0.20/0.43 tff(173,plain,
% 0.20/0.43 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~strictly_less_than(findmin_pqp_res(U), lookup_slb(V, findmin_pqp_res(U)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[172, 160])).
% 0.20/0.43 tff(174,plain,
% 0.20/0.43 (((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~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)))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(175,plain,
% 0.20/0.44 ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~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)))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(176,plain,
% 0.20/0.44 ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)) | (~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))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.20/0.44 tff(177,plain,
% 0.20/0.44 ((V!1 = create_slb) | (~contains_slb(V!1, findmin_pqp_res(U!2))) | (findmin_cpq_eff(triple(U!2, V!1, W!0)) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), bad)) | (~strictly_less_than(findmin_pqp_res(U!2), lookup_slb(V!1, findmin_pqp_res(U!2))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[176, 173])).
% 0.20/0.44 tff(178,plain,
% 0.20/0.44 (~strictly_less_than(findmin_pqp_res(U!2), lookup_slb(V!1, findmin_pqp_res(U!2)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[177, 158, 40, 138])).
% 0.20/0.44 tff(179,plain,
% 0.20/0.44 (~strictly_less_than(findmin_cpq_res(triple(U!2, V!1, W!0)), lookup_slb(V!1, findmin_pqp_res(U!2)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[178, 88])).
% 0.20/0.44 tff(180,plain,
% 0.20/0.44 ((~(strictly_less_than(findmin_cpq_res(triple(U!2, V!1, W!0)), lookup_slb(V!1, findmin_pqp_res(U!2))) <=> (~((~less_than(findmin_cpq_res(triple(U!2, V!1, W!0)), lookup_slb(V!1, findmin_pqp_res(U!2)))) | less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_cpq_res(triple(U!2, V!1, W!0))))))) | strictly_less_than(findmin_cpq_res(triple(U!2, V!1, W!0)), lookup_slb(V!1, findmin_pqp_res(U!2))) | ((~less_than(findmin_cpq_res(triple(U!2, V!1, W!0)), lookup_slb(V!1, findmin_pqp_res(U!2)))) | less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_cpq_res(triple(U!2, V!1, W!0))))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(181,plain,
% 0.20/0.44 ((~less_than(findmin_cpq_res(triple(U!2, V!1, W!0)), lookup_slb(V!1, findmin_pqp_res(U!2)))) | less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_cpq_res(triple(U!2, V!1, W!0)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[180, 179, 85])).
% 0.20/0.44 tff(182,plain,
% 0.20/0.44 ((~((~less_than(findmin_cpq_res(triple(U!2, V!1, W!0)), lookup_slb(V!1, findmin_pqp_res(U!2)))) | less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_cpq_res(triple(U!2, V!1, W!0))))) | (~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)))),
% 0.20/0.44 inference(tautology,[status(thm)],[])).
% 0.20/0.44 tff(183,plain,
% 0.20/0.44 ((~less_than(findmin_cpq_res(triple(U!2, V!1, W!0)), lookup_slb(V!1, findmin_pqp_res(U!2)))) | less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_cpq_res(triple(U!2, V!1, W!0)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[182, 181])).
% 0.20/0.44 tff(184,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[183, 73, 59])).
% 0.20/0.44 tff(185,plain,(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,[]))).
% 0.20/0.44 tff(186,plain,
% 0.20/0.44 (less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_pqp_res(U!2))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[185, 58])).
% 0.20/0.44 tff(187,plain,
% 0.20/0.44 (^[U: $i, V: $i, W: $i] : refl(((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) <=> ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(188,plain,
% 0.20/0.44 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) <=> ![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[187])).
% 0.20/0.44 tff(189,plain,
% 0.20/0.44 (^[U: $i, V: $i, W: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))) <=> (~((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))))), ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) <=> (~(~((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))))))), rewrite((~(~((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))))) <=> ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))), ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) <=> ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))))), (((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))) <=> (((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))))), rewrite((((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))) <=> ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))), (((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))) <=> ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(190,plain,
% 0.20/0.44 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))) <=> ![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[189])).
% 0.20/0.44 tff(191,plain,
% 0.20/0.44 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))) <=> ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(192,plain,
% 0.20/0.44 (![U: $i, V: $i, W: $i, X: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))) <=> ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)))),
% 0.20/0.44 inference(elim_unused_vars,[status(thm)],[])).
% 0.20/0.44 tff(193,plain,
% 0.20/0.44 (^[U: $i, V: $i, W: $i, X: $i] : trans(monotonicity(rewrite((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))) <=> ((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))), (((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))) <=> (((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))))), rewrite((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))) <=> ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)))), (((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))) <=> ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(194,plain,
% 0.20/0.44 (![U: $i, V: $i, W: $i, X: $i] : ((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[193])).
% 0.20/0.44 tff(195,plain,
% 0.20/0.44 (![U: $i, V: $i, W: $i, X: $i] : ((((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U))) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W))) <=> ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[194, 192])).
% 0.20/0.44 tff(196,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')).
% 0.20/0.44 tff(197,plain,
% 0.20/0.44 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[196, 195])).
% 0.20/0.44 tff(198,plain,
% 0.20/0.44 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[197, 191])).
% 0.20/0.44 tff(199,plain,(
% 0.20/0.44 ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & contains_slb(V, findmin_pqp_res(U)) & less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U)))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[198])).
% 0.20/0.44 tff(200,plain,
% 0.20/0.44 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[199, 190])).
% 0.20/0.44 tff(201,plain,
% 0.20/0.44 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[200, 188])).
% 0.20/0.44 tff(202,plain,
% 0.20/0.44 (((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))) | ((V!1 = create_slb) | (~contains_slb(V!1, findmin_pqp_res(U!2))) | (findmin_cpq_eff(triple(U!2, V!1, W!0)) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0)) | (~less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_pqp_res(U!2))))) <=> ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))) | (V!1 = create_slb) | (~contains_slb(V!1, findmin_pqp_res(U!2))) | (findmin_cpq_eff(triple(U!2, V!1, W!0)) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0)) | (~less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_pqp_res(U!2))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(203,plain,
% 0.20/0.44 ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))) | ((V!1 = create_slb) | (~contains_slb(V!1, findmin_pqp_res(U!2))) | (findmin_cpq_eff(triple(U!2, V!1, W!0)) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0)) | (~less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_pqp_res(U!2))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(204,plain,
% 0.20/0.44 ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (~contains_slb(V, findmin_pqp_res(U))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), W)) | (~less_than(lookup_slb(V, findmin_pqp_res(U)), findmin_pqp_res(U))))) | (V!1 = create_slb) | (~contains_slb(V!1, findmin_pqp_res(U!2))) | (findmin_cpq_eff(triple(U!2, V!1, W!0)) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0)) | (~less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_pqp_res(U!2)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.20/0.45 tff(205,plain,
% 0.20/0.45 ((V!1 = create_slb) | (~contains_slb(V!1, findmin_pqp_res(U!2))) | (findmin_cpq_eff(triple(U!2, V!1, W!0)) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0)) | (~less_than(lookup_slb(V!1, findmin_pqp_res(U!2)), findmin_pqp_res(U!2)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[204, 201])).
% 0.20/0.45 tff(206,plain,
% 0.20/0.45 ((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)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[205, 40, 158])).
% 0.20/0.45 tff(207,plain,
% 0.20/0.45 (findmin_cpq_eff(triple(U!2, V!1, W!0)) = triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[206, 186])).
% 0.20/0.45 tff(208,plain,
% 0.20/0.45 (triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0) = findmin_cpq_eff(triple(U!2, V!1, W!0))),
% 0.20/0.45 inference(symmetry,[status(thm)],[207])).
% 0.20/0.45 tff(209,plain,
% 0.20/0.45 (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)))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[208])).
% 0.20/0.45 tff(210,plain,
% 0.20/0.45 (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))),
% 0.20/0.45 inference(transitivity,[status(thm)],[209, 10])).
% 0.20/0.45 tff(211,plain,
% 0.20/0.45 (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)))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[210])).
% 0.20/0.45 tff(212,plain,
% 0.20/0.45 (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))))),
% 0.20/0.45 inference(symmetry,[status(thm)],[211])).
% 0.20/0.45 tff(213,plain,
% 0.20/0.45 (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))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[96, 212])).
% 0.20/0.45 tff(214,plain,
% 0.20/0.45 (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)))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[208])).
% 0.20/0.45 tff(215,plain,
% 0.20/0.45 (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))),
% 0.20/0.45 inference(symmetry,[status(thm)],[214])).
% 0.20/0.45 tff(216,plain,
% 0.20/0.45 ((~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)))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[215])).
% 0.20/0.45 tff(217,plain,
% 0.20/0.45 (~check_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[114, 216])).
% 0.20/0.45 tff(218,plain,
% 0.20/0.45 (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)))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[210])).
% 0.20/0.45 tff(219,plain,
% 0.20/0.45 (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))))),
% 0.20/0.45 inference(symmetry,[status(thm)],[218])).
% 0.20/0.45 tff(220,plain,
% 0.20/0.45 (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))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[118, 219])).
% 0.20/0.45 tff(221,plain,
% 0.20/0.45 (((~![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))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(222,plain,
% 0.20/0.45 ((~![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))))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(223,plain,
% 0.20/0.45 ((~![U: $i, V: $i, W: $i, X: $i] : (check_cpq(triple(U, V, W)) | (~check_cpq(remove_cpq(triple(U, V, W), X))) | (~ok(remove_cpq(triple(U, V, W), X))))) | check_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0)) | (~check_cpq(remove_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0), findmin_cpq_res(triple(U!2, V!1, W!0))))) | (~ok(remove_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0), findmin_cpq_res(triple(U!2, V!1, W!0)))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[222, 221])).
% 0.20/0.45 tff(224,plain,
% 0.20/0.45 (check_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0)) | (~check_cpq(remove_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0), findmin_cpq_res(triple(U!2, V!1, W!0))))) | (~ok(remove_cpq(triple(U!2, update_slb(V!1, findmin_pqp_res(U!2)), W!0), findmin_cpq_res(triple(U!2, V!1, W!0)))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[223, 132])).
% 0.20/0.45 tff(225,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[224, 220, 217, 213])).
% 0.20/0.45 % SZS output end Proof
%------------------------------------------------------------------------------