TSTP Solution File: SWV372+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV372+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.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 15:11:31 EDT 2022
% Result : Theorem 0.17s 0.39s
% Output : Proof 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV372+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.32 % Computer : n003.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Sun Sep 4 02:43:56 EDT 2022
% 0.17/0.32 % CPUTime :
% 0.17/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.17/0.33 Usage: tptp [options] [-file:]file
% 0.17/0.33 -h, -? prints this message.
% 0.17/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.17/0.33 -m, -model generate model.
% 0.17/0.33 -p, -proof generate proof.
% 0.17/0.33 -c, -core generate unsat core of named formulas.
% 0.17/0.33 -st, -statistics display statistics.
% 0.17/0.33 -t:timeout set timeout (in second).
% 0.17/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.17/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.17/0.33 -<param>:<value> configuration parameter and value.
% 0.17/0.33 -o:<output-file> file to place output in.
% 0.17/0.39 % SZS status Theorem
% 0.17/0.39 % SZS output start Proof
% 0.17/0.39 tff(triple_type, type, (
% 0.17/0.39 triple: ( $i * $i * $i ) > $i)).
% 0.17/0.39 tff(bad_type, type, (
% 0.17/0.39 bad: $i)).
% 0.17/0.39 tff(update_slb_type, type, (
% 0.17/0.39 update_slb: ( $i * $i ) > $i)).
% 0.17/0.39 tff(findmin_pqp_res_type, type, (
% 0.17/0.39 findmin_pqp_res: $i > $i)).
% 0.17/0.39 tff(tptp_fun_U_5_type, type, (
% 0.17/0.39 tptp_fun_U_5: $i)).
% 0.17/0.39 tff(tptp_fun_V_4_type, type, (
% 0.17/0.39 tptp_fun_V_4: $i)).
% 0.17/0.39 tff(findmin_cpq_eff_type, type, (
% 0.17/0.39 findmin_cpq_eff: $i > $i)).
% 0.17/0.39 tff(tptp_fun_W_3_type, type, (
% 0.17/0.39 tptp_fun_W_3: $i)).
% 0.17/0.39 tff(create_slb_type, type, (
% 0.17/0.39 create_slb: $i)).
% 0.17/0.39 tff(contains_slb_type, type, (
% 0.17/0.39 contains_slb: ( $i * $i ) > $o)).
% 0.17/0.39 tff(findmin_cpq_res_type, type, (
% 0.17/0.39 findmin_cpq_res: $i > $i)).
% 0.17/0.39 tff(contains_cpq_type, type, (
% 0.17/0.39 contains_cpq: ( $i * $i ) > $o)).
% 0.17/0.39 tff(contains_pq_type, type, (
% 0.17/0.39 contains_pq: ( $i * $i ) > $o)).
% 0.17/0.39 tff(i_type, type, (
% 0.17/0.39 i: $i > $i)).
% 0.17/0.39 tff(phi_type, type, (
% 0.17/0.39 phi: $i > $o)).
% 0.17/0.39 tff(ok_type, type, (
% 0.17/0.39 ok: $i > $o)).
% 0.17/0.39 tff(1,assumption,(~(V!4 = create_slb)), introduced(assumption)).
% 0.17/0.39 tff(2,plain,
% 0.17/0.39 (^[U: $i, V: $i, W: $i] : refl(((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U))) <=> ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U))))),
% 0.17/0.39 inference(bind,[status(th)],[])).
% 0.17/0.39 tff(3,plain,
% 0.17/0.39 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U))) <=> ![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.17/0.39 inference(quant_intro,[status(thm)],[2])).
% 0.17/0.39 tff(4,plain,
% 0.17/0.39 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U))) <=> ![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.17/0.39 inference(rewrite,[status(thm)],[])).
% 0.17/0.39 tff(5,plain,
% 0.17/0.39 (![U: $i, V: $i, W: $i, X: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U))) <=> ![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.17/0.39 inference(elim_unused_vars,[status(thm)],[])).
% 0.17/0.39 tff(6,plain,
% 0.17/0.39 (^[U: $i, V: $i, W: $i, X: $i] : rewrite(((~(V = create_slb)) => (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U))) <=> ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U))))),
% 0.17/0.39 inference(bind,[status(th)],[])).
% 0.17/0.39 tff(7,plain,
% 0.17/0.39 (![U: $i, V: $i, W: $i, X: $i] : ((~(V = create_slb)) => (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U))) <=> ![U: $i, V: $i, W: $i, X: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.17/0.39 inference(quant_intro,[status(thm)],[6])).
% 0.17/0.39 tff(8,plain,
% 0.17/0.39 (![U: $i, V: $i, W: $i, X: $i] : ((~(V = create_slb)) => (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U))) <=> ![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.17/0.39 inference(transitivity,[status(thm)],[7, 5])).
% 0.17/0.39 tff(9,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')).
% 0.17/0.39 tff(10,plain,
% 0.17/0.39 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.17/0.39 tff(11,plain,
% 0.17/0.39 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[10, 4])).
% 0.17/0.39 tff(12,plain,(
% 0.17/0.39 ![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.17/0.39 inference(skolemize,[status(sab)],[11])).
% 0.17/0.39 tff(13,plain,
% 0.17/0.39 (![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))),
% 0.17/0.39 inference(modus_ponens,[status(thm)],[12, 3])).
% 0.17/0.39 tff(14,plain,
% 0.17/0.39 (((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))) | ((V!4 = create_slb) | (findmin_cpq_res(triple(U!5, V!4, W!3)) = findmin_pqp_res(U!5)))) <=> ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))) | (V!4 = create_slb) | (findmin_cpq_res(triple(U!5, V!4, W!3)) = findmin_pqp_res(U!5)))),
% 0.17/0.40 inference(rewrite,[status(thm)],[])).
% 0.17/0.40 tff(15,plain,
% 0.17/0.40 ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))) | ((V!4 = create_slb) | (findmin_cpq_res(triple(U!5, V!4, W!3)) = findmin_pqp_res(U!5)))),
% 0.17/0.40 inference(quant_inst,[status(thm)],[])).
% 0.17/0.40 tff(16,plain,
% 0.17/0.40 ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | (findmin_cpq_res(triple(U, V, W)) = findmin_pqp_res(U)))) | (V!4 = create_slb) | (findmin_cpq_res(triple(U!5, V!4, W!3)) = findmin_pqp_res(U!5))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.17/0.40 tff(17,plain,
% 0.17/0.40 ((V!4 = create_slb) | (findmin_cpq_res(triple(U!5, V!4, W!3)) = findmin_pqp_res(U!5))),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[16, 13])).
% 0.17/0.40 tff(18,plain,
% 0.17/0.40 (findmin_cpq_res(triple(U!5, V!4, W!3)) = findmin_pqp_res(U!5)),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[17, 1])).
% 0.17/0.40 tff(19,plain,
% 0.17/0.40 (findmin_pqp_res(U!5) = findmin_cpq_res(triple(U!5, V!4, W!3))),
% 0.17/0.40 inference(symmetry,[status(thm)],[18])).
% 0.17/0.40 tff(20,plain,
% 0.17/0.40 (contains_slb(V!4, findmin_pqp_res(U!5)) <=> contains_slb(V!4, findmin_cpq_res(triple(U!5, V!4, W!3)))),
% 0.17/0.40 inference(monotonicity,[status(thm)],[19])).
% 0.17/0.40 tff(21,plain,
% 0.17/0.40 (contains_slb(V!4, findmin_cpq_res(triple(U!5, V!4, W!3))) <=> contains_slb(V!4, findmin_pqp_res(U!5))),
% 0.17/0.40 inference(symmetry,[status(thm)],[20])).
% 0.17/0.40 tff(22,plain,
% 0.17/0.40 ((~contains_slb(V!4, findmin_cpq_res(triple(U!5, V!4, W!3)))) <=> (~contains_slb(V!4, findmin_pqp_res(U!5)))),
% 0.17/0.40 inference(monotonicity,[status(thm)],[21])).
% 0.17/0.40 tff(23,plain,
% 0.17/0.40 (^[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)))),
% 0.17/0.40 inference(bind,[status(th)],[])).
% 0.17/0.40 tff(24,plain,
% 0.17/0.40 (![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))),
% 0.17/0.40 inference(quant_intro,[status(thm)],[23])).
% 0.17/0.40 tff(25,plain,
% 0.17/0.40 (![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))),
% 0.17/0.40 inference(rewrite,[status(thm)],[])).
% 0.17/0.40 tff(26,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')).
% 0.17/0.40 tff(27,plain,
% 0.17/0.40 (![U: $i, V: $i, W: $i, X: $i] : (contains_cpq(triple(U, V, W), X) <=> contains_slb(V, X))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.17/0.40 tff(28,plain,(
% 0.17/0.40 ![U: $i, V: $i, W: $i, X: $i] : (contains_cpq(triple(U, V, W), X) <=> contains_slb(V, X))),
% 0.17/0.40 inference(skolemize,[status(sab)],[27])).
% 0.17/0.40 tff(29,plain,
% 0.17/0.40 (![U: $i, V: $i, W: $i, X: $i] : (contains_cpq(triple(U, V, W), X) <=> contains_slb(V, X))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.17/0.40 tff(30,plain,
% 0.17/0.40 ((~![U: $i, V: $i, W: $i, X: $i] : (contains_cpq(triple(U, V, W), X) <=> contains_slb(V, X))) | (contains_cpq(triple(U!5, V!4, W!3), findmin_cpq_res(triple(U!5, V!4, W!3))) <=> contains_slb(V!4, findmin_cpq_res(triple(U!5, V!4, W!3))))),
% 0.17/0.40 inference(quant_inst,[status(thm)],[])).
% 0.17/0.40 tff(31,plain,
% 0.17/0.40 (contains_cpq(triple(U!5, V!4, W!3), findmin_cpq_res(triple(U!5, V!4, W!3))) <=> contains_slb(V!4, findmin_cpq_res(triple(U!5, V!4, W!3)))),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.17/0.40 tff(32,plain,
% 0.17/0.40 (^[U: $i, V: $i, W: $i, X: $i] : refl((contains_cpq(triple(U, V, W), X) <=> contains_pq(i(triple(U, V, W)), X)) <=> (contains_cpq(triple(U, V, W), X) <=> contains_pq(i(triple(U, V, W)), X)))),
% 0.17/0.40 inference(bind,[status(th)],[])).
% 0.17/0.40 tff(33,plain,
% 0.17/0.40 (![U: $i, V: $i, W: $i, X: $i] : (contains_cpq(triple(U, V, W), X) <=> contains_pq(i(triple(U, V, W)), X)) <=> ![U: $i, V: $i, W: $i, X: $i] : (contains_cpq(triple(U, V, W), X) <=> contains_pq(i(triple(U, V, W)), X))),
% 0.17/0.40 inference(quant_intro,[status(thm)],[32])).
% 0.17/0.40 tff(34,plain,
% 0.17/0.40 (![U: $i, V: $i, W: $i, X: $i] : (contains_cpq(triple(U, V, W), X) <=> contains_pq(i(triple(U, V, W)), X)) <=> ![U: $i, V: $i, W: $i, X: $i] : (contains_cpq(triple(U, V, W), X) <=> contains_pq(i(triple(U, V, W)), X))),
% 0.17/0.40 inference(rewrite,[status(thm)],[])).
% 0.17/0.40 tff(35,axiom,(![U: $i, V: $i, W: $i, X: $i] : (contains_cpq(triple(U, V, W), X) <=> contains_pq(i(triple(U, V, W)), X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l8_li56')).
% 0.17/0.40 tff(36,plain,
% 0.17/0.40 (![U: $i, V: $i, W: $i, X: $i] : (contains_cpq(triple(U, V, W), X) <=> contains_pq(i(triple(U, V, W)), X))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.17/0.40 tff(37,plain,(
% 0.17/0.40 ![U: $i, V: $i, W: $i, X: $i] : (contains_cpq(triple(U, V, W), X) <=> contains_pq(i(triple(U, V, W)), X))),
% 0.17/0.40 inference(skolemize,[status(sab)],[36])).
% 0.17/0.40 tff(38,plain,
% 0.17/0.40 (![U: $i, V: $i, W: $i, X: $i] : (contains_cpq(triple(U, V, W), X) <=> contains_pq(i(triple(U, V, W)), X))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.17/0.40 tff(39,plain,
% 0.17/0.40 ((~![U: $i, V: $i, W: $i, X: $i] : (contains_cpq(triple(U, V, W), X) <=> contains_pq(i(triple(U, V, W)), X))) | (contains_cpq(triple(U!5, V!4, W!3), findmin_cpq_res(triple(U!5, V!4, W!3))) <=> contains_pq(i(triple(U!5, V!4, W!3)), findmin_cpq_res(triple(U!5, V!4, W!3))))),
% 0.17/0.40 inference(quant_inst,[status(thm)],[])).
% 0.17/0.40 tff(40,plain,
% 0.17/0.40 (contains_cpq(triple(U!5, V!4, W!3), findmin_cpq_res(triple(U!5, V!4, W!3))) <=> contains_pq(i(triple(U!5, V!4, W!3)), findmin_cpq_res(triple(U!5, V!4, W!3)))),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.17/0.40 tff(41,plain,
% 0.17/0.40 ((~![U: $i, V: $i, W: $i] : ((~phi(findmin_cpq_eff(triple(U, V, W)))) | contains_pq(i(triple(U, V, W)), findmin_cpq_res(triple(U, V, W))))) <=> (~![U: $i, V: $i, W: $i] : ((~phi(findmin_cpq_eff(triple(U, V, W)))) | contains_pq(i(triple(U, V, W)), findmin_cpq_res(triple(U, V, W)))))),
% 0.17/0.40 inference(rewrite,[status(thm)],[])).
% 0.17/0.40 tff(42,plain,
% 0.17/0.40 ((~![U: $i, V: $i, W: $i] : (phi(findmin_cpq_eff(triple(U, V, W))) => contains_pq(i(triple(U, V, W)), findmin_cpq_res(triple(U, V, W))))) <=> (~![U: $i, V: $i, W: $i] : ((~phi(findmin_cpq_eff(triple(U, V, W)))) | contains_pq(i(triple(U, V, W)), findmin_cpq_res(triple(U, V, W)))))),
% 0.17/0.40 inference(rewrite,[status(thm)],[])).
% 0.17/0.40 tff(43,axiom,(~![U: $i, V: $i, W: $i] : (phi(findmin_cpq_eff(triple(U, V, W))) => contains_pq(i(triple(U, V, W)), findmin_cpq_res(triple(U, V, W))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l8_co')).
% 0.17/0.40 tff(44,plain,
% 0.17/0.40 (~![U: $i, V: $i, W: $i] : ((~phi(findmin_cpq_eff(triple(U, V, W)))) | contains_pq(i(triple(U, V, W)), findmin_cpq_res(triple(U, V, W))))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.17/0.40 tff(45,plain,
% 0.17/0.40 (~![U: $i, V: $i, W: $i] : ((~phi(findmin_cpq_eff(triple(U, V, W)))) | contains_pq(i(triple(U, V, W)), findmin_cpq_res(triple(U, V, W))))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[44, 41])).
% 0.17/0.40 tff(46,plain,
% 0.17/0.40 (~![U: $i, V: $i, W: $i] : ((~phi(findmin_cpq_eff(triple(U, V, W)))) | contains_pq(i(triple(U, V, W)), findmin_cpq_res(triple(U, V, W))))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.17/0.40 tff(47,plain,
% 0.17/0.40 (~![U: $i, V: $i, W: $i] : ((~phi(findmin_cpq_eff(triple(U, V, W)))) | contains_pq(i(triple(U, V, W)), findmin_cpq_res(triple(U, V, W))))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[46, 41])).
% 0.17/0.40 tff(48,plain,
% 0.17/0.40 (~![U: $i, V: $i, W: $i] : ((~phi(findmin_cpq_eff(triple(U, V, W)))) | contains_pq(i(triple(U, V, W)), findmin_cpq_res(triple(U, V, W))))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[47, 41])).
% 0.17/0.40 tff(49,plain,
% 0.17/0.40 (~![U: $i, V: $i, W: $i] : ((~phi(findmin_cpq_eff(triple(U, V, W)))) | contains_pq(i(triple(U, V, W)), findmin_cpq_res(triple(U, V, W))))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[48, 41])).
% 0.17/0.40 tff(50,plain,
% 0.17/0.40 (~![U: $i, V: $i, W: $i] : ((~phi(findmin_cpq_eff(triple(U, V, W)))) | contains_pq(i(triple(U, V, W)), findmin_cpq_res(triple(U, V, W))))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[49, 41])).
% 0.17/0.40 tff(51,plain,(
% 0.17/0.40 ~((~phi(findmin_cpq_eff(triple(U!5, V!4, W!3)))) | contains_pq(i(triple(U!5, V!4, W!3)), findmin_cpq_res(triple(U!5, V!4, W!3))))),
% 0.17/0.40 inference(skolemize,[status(sab)],[50])).
% 0.17/0.40 tff(52,plain,
% 0.17/0.40 (~contains_pq(i(triple(U!5, V!4, W!3)), findmin_cpq_res(triple(U!5, V!4, W!3)))),
% 0.17/0.40 inference(or_elim,[status(thm)],[51])).
% 0.17/0.40 tff(53,plain,
% 0.17/0.40 ((~(contains_cpq(triple(U!5, V!4, W!3), findmin_cpq_res(triple(U!5, V!4, W!3))) <=> contains_pq(i(triple(U!5, V!4, W!3)), findmin_cpq_res(triple(U!5, V!4, W!3))))) | (~contains_cpq(triple(U!5, V!4, W!3), findmin_cpq_res(triple(U!5, V!4, W!3)))) | contains_pq(i(triple(U!5, V!4, W!3)), findmin_cpq_res(triple(U!5, V!4, W!3)))),
% 0.17/0.40 inference(tautology,[status(thm)],[])).
% 0.17/0.40 tff(54,plain,
% 0.17/0.40 ((~(contains_cpq(triple(U!5, V!4, W!3), findmin_cpq_res(triple(U!5, V!4, W!3))) <=> contains_pq(i(triple(U!5, V!4, W!3)), findmin_cpq_res(triple(U!5, V!4, W!3))))) | (~contains_cpq(triple(U!5, V!4, W!3), findmin_cpq_res(triple(U!5, V!4, W!3))))),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.17/0.40 tff(55,plain,
% 0.17/0.40 (~contains_cpq(triple(U!5, V!4, W!3), findmin_cpq_res(triple(U!5, V!4, W!3)))),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[54, 40])).
% 0.17/0.40 tff(56,plain,
% 0.17/0.40 ((~(contains_cpq(triple(U!5, V!4, W!3), findmin_cpq_res(triple(U!5, V!4, W!3))) <=> contains_slb(V!4, findmin_cpq_res(triple(U!5, V!4, W!3))))) | contains_cpq(triple(U!5, V!4, W!3), findmin_cpq_res(triple(U!5, V!4, W!3))) | (~contains_slb(V!4, findmin_cpq_res(triple(U!5, V!4, W!3))))),
% 0.17/0.40 inference(tautology,[status(thm)],[])).
% 0.17/0.40 tff(57,plain,
% 0.17/0.40 ((~(contains_cpq(triple(U!5, V!4, W!3), findmin_cpq_res(triple(U!5, V!4, W!3))) <=> contains_slb(V!4, findmin_cpq_res(triple(U!5, V!4, W!3))))) | (~contains_slb(V!4, findmin_cpq_res(triple(U!5, V!4, W!3))))),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.17/0.40 tff(58,plain,
% 0.17/0.40 (~contains_slb(V!4, findmin_cpq_res(triple(U!5, V!4, W!3)))),
% 0.17/0.40 inference(unit_resolution,[status(thm)],[57, 31])).
% 0.17/0.40 tff(59,plain,
% 0.17/0.40 (~contains_slb(V!4, findmin_pqp_res(U!5))),
% 0.17/0.40 inference(modus_ponens,[status(thm)],[58, 22])).
% 0.17/0.40 tff(60,assumption,(findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad)), introduced(assumption)).
% 0.17/0.40 tff(61,plain,
% 0.17/0.40 (triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad) = findmin_cpq_eff(triple(U!5, V!4, W!3))),
% 0.17/0.40 inference(symmetry,[status(thm)],[60])).
% 0.17/0.40 tff(62,plain,
% 0.17/0.40 (ok(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad)) <=> ok(findmin_cpq_eff(triple(U!5, V!4, W!3)))),
% 0.17/0.40 inference(monotonicity,[status(thm)],[61])).
% 0.17/0.40 tff(63,plain,
% 0.17/0.40 (ok(findmin_cpq_eff(triple(U!5, V!4, W!3))) <=> ok(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad))),
% 0.17/0.40 inference(symmetry,[status(thm)],[62])).
% 0.17/0.40 tff(64,plain,
% 0.17/0.40 ((~ok(findmin_cpq_eff(triple(U!5, V!4, W!3)))) <=> (~ok(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad)))),
% 0.17/0.40 inference(monotonicity,[status(thm)],[63])).
% 0.17/0.40 tff(65,plain,
% 0.17/0.40 (^[U: $i, V: $i, W: $i] : refl(((~ok(findmin_cpq_eff(triple(U, V, W)))) | contains_cpq(triple(U, V, W), findmin_cpq_res(triple(U, V, W)))) <=> ((~ok(findmin_cpq_eff(triple(U, V, W)))) | contains_cpq(triple(U, V, W), findmin_cpq_res(triple(U, V, W)))))),
% 0.17/0.40 inference(bind,[status(th)],[])).
% 0.17/0.40 tff(66,plain,
% 0.17/0.40 (![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))))),
% 0.17/0.40 inference(quant_intro,[status(thm)],[65])).
% 0.17/0.40 tff(67,plain,
% 0.17/0.40 (![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))))),
% 0.17/0.40 inference(rewrite,[status(thm)],[])).
% 0.17/0.40 tff(68,plain,
% 0.17/0.40 (^[U: $i, V: $i, W: $i] : rewrite(((~contains_cpq(triple(U, V, W), findmin_cpq_res(triple(U, V, W)))) => (~ok(findmin_cpq_eff(triple(U, V, W))))) <=> ((~ok(findmin_cpq_eff(triple(U, V, W)))) | contains_cpq(triple(U, V, W), findmin_cpq_res(triple(U, V, W)))))),
% 0.17/0.40 inference(bind,[status(th)],[])).
% 0.17/0.40 tff(69,plain,
% 0.17/0.40 (![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))))),
% 0.17/0.41 inference(quant_intro,[status(thm)],[68])).
% 0.17/0.41 tff(70,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','l8_l9')).
% 0.17/0.41 tff(71,plain,
% 0.17/0.41 (![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))))),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.17/0.41 tff(72,plain,
% 0.17/0.41 (![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))))),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.17/0.41 tff(73,plain,(
% 0.17/0.41 ![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))))),
% 0.17/0.41 inference(skolemize,[status(sab)],[72])).
% 0.17/0.41 tff(74,plain,
% 0.17/0.41 (![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))))),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.17/0.41 tff(75,plain,
% 0.17/0.41 (((~![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))))) | ((~ok(findmin_cpq_eff(triple(U!5, V!4, W!3)))) | contains_cpq(triple(U!5, V!4, W!3), findmin_cpq_res(triple(U!5, V!4, W!3))))) <=> ((~![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))))) | (~ok(findmin_cpq_eff(triple(U!5, V!4, W!3)))) | contains_cpq(triple(U!5, V!4, W!3), findmin_cpq_res(triple(U!5, V!4, W!3))))),
% 0.17/0.41 inference(rewrite,[status(thm)],[])).
% 0.17/0.41 tff(76,plain,
% 0.17/0.41 ((~![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))))) | ((~ok(findmin_cpq_eff(triple(U!5, V!4, W!3)))) | contains_cpq(triple(U!5, V!4, W!3), findmin_cpq_res(triple(U!5, V!4, W!3))))),
% 0.17/0.41 inference(quant_inst,[status(thm)],[])).
% 0.17/0.41 tff(77,plain,
% 0.17/0.41 ((~![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))))) | (~ok(findmin_cpq_eff(triple(U!5, V!4, W!3)))) | contains_cpq(triple(U!5, V!4, W!3), findmin_cpq_res(triple(U!5, V!4, W!3)))),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.17/0.41 tff(78,plain,
% 0.17/0.41 ((~ok(findmin_cpq_eff(triple(U!5, V!4, W!3)))) | contains_cpq(triple(U!5, V!4, W!3), findmin_cpq_res(triple(U!5, V!4, W!3)))),
% 0.17/0.41 inference(unit_resolution,[status(thm)],[77, 74])).
% 0.17/0.41 tff(79,plain,
% 0.17/0.41 (~ok(findmin_cpq_eff(triple(U!5, V!4, W!3)))),
% 0.17/0.41 inference(unit_resolution,[status(thm)],[78, 55])).
% 0.17/0.41 tff(80,plain,
% 0.17/0.41 (~ok(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad))),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[79, 64])).
% 0.17/0.41 tff(81,plain,
% 0.17/0.41 (phi(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad)) <=> phi(findmin_cpq_eff(triple(U!5, V!4, W!3)))),
% 0.17/0.41 inference(monotonicity,[status(thm)],[61])).
% 0.17/0.41 tff(82,plain,
% 0.17/0.41 (phi(findmin_cpq_eff(triple(U!5, V!4, W!3))) <=> phi(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad))),
% 0.17/0.41 inference(symmetry,[status(thm)],[81])).
% 0.17/0.41 tff(83,plain,
% 0.17/0.41 (phi(findmin_cpq_eff(triple(U!5, V!4, W!3)))),
% 0.17/0.41 inference(or_elim,[status(thm)],[51])).
% 0.17/0.41 tff(84,plain,
% 0.17/0.41 (phi(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad))),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.17/0.41 tff(85,plain,
% 0.17/0.41 (^[U: $i, V: $i, W: $i] : refl((ok(triple(U, V, W)) | (~phi(triple(U, V, W)))) <=> (ok(triple(U, V, W)) | (~phi(triple(U, V, W)))))),
% 0.17/0.41 inference(bind,[status(th)],[])).
% 0.17/0.41 tff(86,plain,
% 0.17/0.41 (![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~phi(triple(U, V, W)))) <=> ![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~phi(triple(U, V, W))))),
% 0.17/0.41 inference(quant_intro,[status(thm)],[85])).
% 0.17/0.41 tff(87,plain,
% 0.17/0.41 (![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~phi(triple(U, V, W)))) <=> ![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~phi(triple(U, V, W))))),
% 0.17/0.41 inference(rewrite,[status(thm)],[])).
% 0.17/0.41 tff(88,plain,
% 0.17/0.41 (^[U: $i, V: $i, W: $i] : rewrite(((~ok(triple(U, V, W))) => (~phi(triple(U, V, W)))) <=> (ok(triple(U, V, W)) | (~phi(triple(U, V, W)))))),
% 0.17/0.41 inference(bind,[status(th)],[])).
% 0.17/0.41 tff(89,plain,
% 0.17/0.41 (![U: $i, V: $i, W: $i] : ((~ok(triple(U, V, W))) => (~phi(triple(U, V, W)))) <=> ![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~phi(triple(U, V, W))))),
% 0.17/0.41 inference(quant_intro,[status(thm)],[88])).
% 0.17/0.41 tff(90,axiom,(![U: $i, V: $i, W: $i] : ((~ok(triple(U, V, W))) => (~phi(triple(U, V, W))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l8_lX')).
% 0.17/0.41 tff(91,plain,
% 0.17/0.41 (![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~phi(triple(U, V, W))))),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.17/0.41 tff(92,plain,
% 0.17/0.41 (![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~phi(triple(U, V, W))))),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[91, 87])).
% 0.17/0.41 tff(93,plain,(
% 0.17/0.41 ![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~phi(triple(U, V, W))))),
% 0.17/0.41 inference(skolemize,[status(sab)],[92])).
% 0.17/0.41 tff(94,plain,
% 0.17/0.41 (![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~phi(triple(U, V, W))))),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[93, 86])).
% 0.17/0.41 tff(95,plain,
% 0.17/0.41 (((~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~phi(triple(U, V, W))))) | (ok(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad)) | (~phi(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad))))) <=> ((~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~phi(triple(U, V, W))))) | ok(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad)) | (~phi(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad))))),
% 0.17/0.41 inference(rewrite,[status(thm)],[])).
% 0.17/0.41 tff(96,plain,
% 0.17/0.41 ((~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~phi(triple(U, V, W))))) | (ok(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad)) | (~phi(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad))))),
% 0.17/0.41 inference(quant_inst,[status(thm)],[])).
% 0.17/0.41 tff(97,plain,
% 0.17/0.41 ((~![U: $i, V: $i, W: $i] : (ok(triple(U, V, W)) | (~phi(triple(U, V, W))))) | ok(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad)) | (~phi(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad)))),
% 0.17/0.41 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.17/0.41 tff(98,plain,
% 0.17/0.41 (ok(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad)) | (~phi(triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad)))),
% 0.17/0.41 inference(unit_resolution,[status(thm)],[97, 94])).
% 0.17/0.41 tff(99,plain,
% 0.17/0.41 ($false),
% 0.17/0.41 inference(unit_resolution,[status(thm)],[98, 84, 80])).
% 0.17/0.41 tff(100,plain,(~(findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad))), inference(lemma,lemma(discharge,[]))).
% 0.17/0.41 tff(101,plain,
% 0.17/0.41 (^[U: $i, V: $i, W: $i] : refl(((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ((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))))),
% 0.17/0.41 inference(bind,[status(th)],[])).
% 0.17/0.41 tff(102,plain,
% 0.17/0.41 (![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ![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)))),
% 0.17/0.41 inference(quant_intro,[status(thm)],[101])).
% 0.17/0.41 tff(103,plain,
% 0.17/0.41 (^[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)))))),
% 0.17/0.41 inference(bind,[status(th)],[])).
% 0.17/0.41 tff(104,plain,
% 0.17/0.41 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ![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)))),
% 0.17/0.41 inference(quant_intro,[status(thm)],[103])).
% 0.17/0.41 tff(105,plain,
% 0.17/0.41 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad))) <=> ![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)))),
% 0.17/0.41 inference(rewrite,[status(thm)],[])).
% 0.17/0.41 tff(106,plain,
% 0.17/0.41 (![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)))),
% 0.17/0.41 inference(elim_unused_vars,[status(thm)],[])).
% 0.17/0.41 tff(107,plain,
% 0.17/0.41 (^[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))))),
% 0.17/0.41 inference(bind,[status(th)],[])).
% 0.17/0.41 tff(108,plain,
% 0.17/0.41 (![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)))),
% 0.17/0.41 inference(quant_intro,[status(thm)],[107])).
% 0.17/0.41 tff(109,plain,
% 0.17/0.41 (![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)))),
% 0.17/0.41 inference(transitivity,[status(thm)],[108, 106])).
% 0.17/0.41 tff(110,axiom,(![U: $i, V: $i, W: $i, X: $i] : (((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U)))) => (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax','ax47')).
% 0.17/0.41 tff(111,plain,
% 0.17/0.41 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.17/0.42 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.17/0.42 tff(112,plain,
% 0.17/0.42 (![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.17/0.42 inference(modus_ponens,[status(thm)],[111, 105])).
% 0.17/0.42 tff(113,plain,(
% 0.17/0.42 ![U: $i, V: $i, W: $i] : ((~((~(V = create_slb)) & (~contains_slb(V, findmin_pqp_res(U))))) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.17/0.42 inference(skolemize,[status(sab)],[112])).
% 0.17/0.42 tff(114,plain,
% 0.17/0.42 (![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.17/0.42 inference(modus_ponens,[status(thm)],[113, 104])).
% 0.17/0.42 tff(115,plain,
% 0.17/0.42 (![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))),
% 0.17/0.42 inference(modus_ponens,[status(thm)],[114, 102])).
% 0.17/0.42 tff(116,plain,
% 0.17/0.42 (((~![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))) | ((V!4 = create_slb) | contains_slb(V!4, findmin_pqp_res(U!5)) | (findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), 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!4 = create_slb) | contains_slb(V!4, findmin_pqp_res(U!5)) | (findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad)))),
% 0.17/0.42 inference(rewrite,[status(thm)],[])).
% 0.17/0.42 tff(117,plain,
% 0.17/0.42 ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))) | ((V!4 = create_slb) | contains_slb(V!4, findmin_pqp_res(U!5)) | (findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad)))),
% 0.17/0.42 inference(quant_inst,[status(thm)],[])).
% 0.17/0.42 tff(118,plain,
% 0.17/0.42 ((~![U: $i, V: $i, W: $i] : ((V = create_slb) | contains_slb(V, findmin_pqp_res(U)) | (findmin_cpq_eff(triple(U, V, W)) = triple(U, update_slb(V, findmin_pqp_res(U)), bad)))) | (V!4 = create_slb) | contains_slb(V!4, findmin_pqp_res(U!5)) | (findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad))),
% 0.17/0.42 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.17/0.42 tff(119,plain,
% 0.17/0.42 ((V!4 = create_slb) | contains_slb(V!4, findmin_pqp_res(U!5)) | (findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad))),
% 0.17/0.42 inference(unit_resolution,[status(thm)],[118, 115])).
% 0.17/0.42 tff(120,plain,
% 0.17/0.42 (contains_slb(V!4, findmin_pqp_res(U!5))),
% 0.17/0.42 inference(unit_resolution,[status(thm)],[119, 1, 100])).
% 0.17/0.42 tff(121,plain,
% 0.17/0.42 ($false),
% 0.17/0.42 inference(unit_resolution,[status(thm)],[120, 59])).
% 0.17/0.42 tff(122,plain,(V!4 = create_slb), inference(lemma,lemma(discharge,[]))).
% 0.17/0.42 tff(123,plain,
% 0.17/0.42 (create_slb = V!4),
% 0.17/0.42 inference(symmetry,[status(thm)],[122])).
% 0.17/0.42 tff(124,plain,
% 0.17/0.42 (^[U: $i] : refl((update_slb(create_slb, U) = create_slb) <=> (update_slb(create_slb, U) = create_slb))),
% 0.17/0.42 inference(bind,[status(th)],[])).
% 0.17/0.42 tff(125,plain,
% 0.17/0.42 (![U: $i] : (update_slb(create_slb, U) = create_slb) <=> ![U: $i] : (update_slb(create_slb, U) = create_slb)),
% 0.17/0.42 inference(quant_intro,[status(thm)],[124])).
% 0.17/0.42 tff(126,plain,
% 0.17/0.42 (![U: $i] : (update_slb(create_slb, U) = create_slb) <=> ![U: $i] : (update_slb(create_slb, U) = create_slb)),
% 0.17/0.42 inference(rewrite,[status(thm)],[])).
% 0.17/0.42 tff(127,axiom,(![U: $i] : (update_slb(create_slb, U) = create_slb)), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+2.ax','ax28')).
% 0.17/0.42 tff(128,plain,
% 0.17/0.42 (![U: $i] : (update_slb(create_slb, U) = create_slb)),
% 0.17/0.42 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.17/0.42 tff(129,plain,(
% 0.17/0.42 ![U: $i] : (update_slb(create_slb, U) = create_slb)),
% 0.17/0.42 inference(skolemize,[status(sab)],[128])).
% 0.17/0.42 tff(130,plain,
% 0.17/0.42 (![U: $i] : (update_slb(create_slb, U) = create_slb)),
% 0.17/0.42 inference(modus_ponens,[status(thm)],[129, 125])).
% 0.17/0.42 tff(131,plain,
% 0.17/0.42 ((~![U: $i] : (update_slb(create_slb, U) = create_slb)) | (update_slb(create_slb, findmin_pqp_res(U!5)) = create_slb)),
% 0.17/0.42 inference(quant_inst,[status(thm)],[])).
% 0.17/0.42 tff(132,plain,
% 0.17/0.42 (update_slb(create_slb, findmin_pqp_res(U!5)) = create_slb),
% 0.17/0.42 inference(unit_resolution,[status(thm)],[131, 130])).
% 0.17/0.42 tff(133,plain,
% 0.17/0.42 (update_slb(V!4, findmin_pqp_res(U!5)) = update_slb(create_slb, findmin_pqp_res(U!5))),
% 0.17/0.42 inference(monotonicity,[status(thm)],[122])).
% 0.17/0.42 tff(134,plain,
% 0.17/0.42 (update_slb(V!4, findmin_pqp_res(U!5)) = V!4),
% 0.17/0.42 inference(transitivity,[status(thm)],[133, 132, 123])).
% 0.17/0.42 tff(135,plain,
% 0.17/0.42 (triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad) = triple(U!5, V!4, bad)),
% 0.17/0.42 inference(monotonicity,[status(thm)],[134])).
% 0.17/0.42 tff(136,plain,
% 0.17/0.42 (triple(U!5, V!4, bad) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad)),
% 0.17/0.42 inference(symmetry,[status(thm)],[135])).
% 0.17/0.42 tff(137,plain,
% 0.17/0.42 (triple(U!5, V!4, bad) = triple(U!5, create_slb, bad)),
% 0.17/0.42 inference(monotonicity,[status(thm)],[122])).
% 0.17/0.42 tff(138,plain,
% 0.17/0.42 (triple(U!5, create_slb, bad) = triple(U!5, V!4, bad)),
% 0.17/0.42 inference(symmetry,[status(thm)],[137])).
% 0.17/0.42 tff(139,plain,
% 0.17/0.42 (^[U: $i, V: $i] : refl((findmin_cpq_eff(triple(U, create_slb, V)) = triple(U, create_slb, bad)) <=> (findmin_cpq_eff(triple(U, create_slb, V)) = triple(U, create_slb, bad)))),
% 0.17/0.42 inference(bind,[status(th)],[])).
% 0.17/0.42 tff(140,plain,
% 0.17/0.42 (![U: $i, V: $i] : (findmin_cpq_eff(triple(U, create_slb, V)) = triple(U, create_slb, bad)) <=> ![U: $i, V: $i] : (findmin_cpq_eff(triple(U, create_slb, V)) = triple(U, create_slb, bad))),
% 0.17/0.42 inference(quant_intro,[status(thm)],[139])).
% 0.17/0.42 tff(141,plain,
% 0.17/0.42 (![U: $i, V: $i] : (findmin_cpq_eff(triple(U, create_slb, V)) = triple(U, create_slb, bad)) <=> ![U: $i, V: $i] : (findmin_cpq_eff(triple(U, create_slb, V)) = triple(U, create_slb, bad))),
% 0.17/0.42 inference(rewrite,[status(thm)],[])).
% 0.17/0.42 tff(142,axiom,(![U: $i, V: $i] : (findmin_cpq_eff(triple(U, create_slb, V)) = triple(U, create_slb, bad))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax','ax46')).
% 0.17/0.42 tff(143,plain,
% 0.17/0.42 (![U: $i, V: $i] : (findmin_cpq_eff(triple(U, create_slb, V)) = triple(U, create_slb, bad))),
% 0.17/0.42 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.17/0.42 tff(144,plain,(
% 0.17/0.42 ![U: $i, V: $i] : (findmin_cpq_eff(triple(U, create_slb, V)) = triple(U, create_slb, bad))),
% 0.17/0.42 inference(skolemize,[status(sab)],[143])).
% 0.17/0.42 tff(145,plain,
% 0.17/0.42 (![U: $i, V: $i] : (findmin_cpq_eff(triple(U, create_slb, V)) = triple(U, create_slb, bad))),
% 0.17/0.42 inference(modus_ponens,[status(thm)],[144, 140])).
% 0.17/0.42 tff(146,plain,
% 0.17/0.42 ((~![U: $i, V: $i] : (findmin_cpq_eff(triple(U, create_slb, V)) = triple(U, create_slb, bad))) | (findmin_cpq_eff(triple(U!5, create_slb, W!3)) = triple(U!5, create_slb, bad))),
% 0.17/0.42 inference(quant_inst,[status(thm)],[])).
% 0.17/0.42 tff(147,plain,
% 0.17/0.42 (findmin_cpq_eff(triple(U!5, create_slb, W!3)) = triple(U!5, create_slb, bad)),
% 0.17/0.42 inference(unit_resolution,[status(thm)],[146, 145])).
% 0.17/0.42 tff(148,plain,
% 0.17/0.42 (triple(U!5, create_slb, W!3) = triple(U!5, V!4, W!3)),
% 0.17/0.42 inference(monotonicity,[status(thm)],[123])).
% 0.17/0.42 tff(149,plain,
% 0.17/0.42 (triple(U!5, V!4, W!3) = triple(U!5, create_slb, W!3)),
% 0.17/0.42 inference(symmetry,[status(thm)],[148])).
% 0.17/0.42 tff(150,plain,
% 0.17/0.42 (findmin_cpq_eff(triple(U!5, V!4, W!3)) = findmin_cpq_eff(triple(U!5, create_slb, W!3))),
% 0.17/0.42 inference(monotonicity,[status(thm)],[149])).
% 0.17/0.42 tff(151,plain,
% 0.17/0.42 (findmin_cpq_eff(triple(U!5, V!4, W!3)) = triple(U!5, update_slb(V!4, findmin_pqp_res(U!5)), bad)),
% 0.17/0.42 inference(transitivity,[status(thm)],[150, 147, 138, 136])).
% 0.17/0.42 tff(152,plain,
% 0.17/0.42 ($false),
% 0.17/0.42 inference(unit_resolution,[status(thm)],[100, 151])).
% 0.17/0.42 % SZS output end Proof
%------------------------------------------------------------------------------