TSTP Solution File: SWV371+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV371+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n011.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 0.12s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV371+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Sep 4 02:40:44 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.12/0.40 % SZS status Theorem
% 0.12/0.40 % SZS output start Proof
% 0.12/0.40 tff(issmallestelement_pq_type, type, (
% 0.12/0.40 issmallestelement_pq: ( $i * $i ) > $o)).
% 0.12/0.40 tff(findmin_cpq_res_type, type, (
% 0.12/0.40 findmin_cpq_res: $i > $i)).
% 0.12/0.40 tff(triple_type, type, (
% 0.12/0.40 triple: ( $i * $i * $i ) > $i)).
% 0.12/0.40 tff(tptp_fun_W_3_type, type, (
% 0.12/0.40 tptp_fun_W_3: $i)).
% 0.12/0.40 tff(tptp_fun_V_4_type, type, (
% 0.12/0.40 tptp_fun_V_4: $i)).
% 0.12/0.40 tff(tptp_fun_U_5_type, type, (
% 0.12/0.40 tptp_fun_U_5: $i)).
% 0.12/0.40 tff(i_type, type, (
% 0.12/0.40 i: $i > $i)).
% 0.12/0.40 tff(contains_pq_type, type, (
% 0.12/0.40 contains_pq: ( $i * $i ) > $o)).
% 0.12/0.40 tff(pi_sharp_find_min_type, type, (
% 0.12/0.40 pi_sharp_find_min: ( $i * $i ) > $o)).
% 0.12/0.40 tff(phi_type, type, (
% 0.12/0.40 phi: $i > $o)).
% 0.12/0.40 tff(findmin_cpq_eff_type, type, (
% 0.12/0.40 findmin_cpq_eff: $i > $i)).
% 0.12/0.40 tff(1,plain,
% 0.12/0.40 ((~![U: $i, V: $i, W: $i] : ((~phi(findmin_cpq_eff(triple(U, V, W)))) | pi_sharp_find_min(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)))) | pi_sharp_find_min(i(triple(U, V, W)), findmin_cpq_res(triple(U, V, W)))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(2,plain,
% 0.12/0.40 ((~![U: $i, V: $i, W: $i] : (phi(findmin_cpq_eff(triple(U, V, W))) => pi_sharp_find_min(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)))) | pi_sharp_find_min(i(triple(U, V, W)), findmin_cpq_res(triple(U, V, W)))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(3,axiom,(~![U: $i, V: $i, W: $i] : (phi(findmin_cpq_eff(triple(U, V, W))) => pi_sharp_find_min(i(triple(U, V, W)), findmin_cpq_res(triple(U, V, W))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l7_co')).
% 0.12/0.40 tff(4,plain,
% 0.12/0.40 (~![U: $i, V: $i, W: $i] : ((~phi(findmin_cpq_eff(triple(U, V, W)))) | pi_sharp_find_min(i(triple(U, V, W)), findmin_cpq_res(triple(U, V, W))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.12/0.40 tff(5,plain,
% 0.12/0.40 (~![U: $i, V: $i, W: $i] : ((~phi(findmin_cpq_eff(triple(U, V, W)))) | pi_sharp_find_min(i(triple(U, V, W)), findmin_cpq_res(triple(U, V, W))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.12/0.41 tff(6,plain,
% 0.12/0.41 (~![U: $i, V: $i, W: $i] : ((~phi(findmin_cpq_eff(triple(U, V, W)))) | pi_sharp_find_min(i(triple(U, V, W)), findmin_cpq_res(triple(U, V, W))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.12/0.41 tff(7,plain,
% 0.12/0.41 (~![U: $i, V: $i, W: $i] : ((~phi(findmin_cpq_eff(triple(U, V, W)))) | pi_sharp_find_min(i(triple(U, V, W)), findmin_cpq_res(triple(U, V, W))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.12/0.41 tff(8,plain,
% 0.12/0.41 (~![U: $i, V: $i, W: $i] : ((~phi(findmin_cpq_eff(triple(U, V, W)))) | pi_sharp_find_min(i(triple(U, V, W)), findmin_cpq_res(triple(U, V, W))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.12/0.41 tff(9,plain,
% 0.12/0.41 (~![U: $i, V: $i, W: $i] : ((~phi(findmin_cpq_eff(triple(U, V, W)))) | pi_sharp_find_min(i(triple(U, V, W)), findmin_cpq_res(triple(U, V, W))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.12/0.41 tff(10,plain,
% 0.12/0.41 (~![U: $i, V: $i, W: $i] : ((~phi(findmin_cpq_eff(triple(U, V, W)))) | pi_sharp_find_min(i(triple(U, V, W)), findmin_cpq_res(triple(U, V, W))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.12/0.41 tff(11,plain,(
% 0.12/0.41 ~((~phi(findmin_cpq_eff(triple(U!5, V!4, W!3)))) | pi_sharp_find_min(i(triple(U!5, V!4, W!3)), findmin_cpq_res(triple(U!5, V!4, W!3))))),
% 0.12/0.41 inference(skolemize,[status(sab)],[10])).
% 0.12/0.41 tff(12,plain,
% 0.12/0.41 (phi(findmin_cpq_eff(triple(U!5, V!4, W!3)))),
% 0.12/0.41 inference(or_elim,[status(thm)],[11])).
% 0.12/0.41 tff(13,plain,
% 0.12/0.41 (^[U: $i, V: $i, W: $i] : refl(((~phi(findmin_cpq_eff(triple(U, V, W)))) | contains_pq(i(triple(U, V, W)), findmin_cpq_res(triple(U, V, W)))) <=> ((~phi(findmin_cpq_eff(triple(U, V, W)))) | contains_pq(i(triple(U, V, W)), findmin_cpq_res(triple(U, V, W)))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(14,plain,
% 0.12/0.41 (![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))))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[13])).
% 0.12/0.41 tff(15,plain,
% 0.12/0.41 (![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))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(16,plain,
% 0.12/0.41 (^[U: $i, V: $i, W: $i] : rewrite((phi(findmin_cpq_eff(triple(U, V, W))) => contains_pq(i(triple(U, V, W)), findmin_cpq_res(triple(U, V, W)))) <=> ((~phi(findmin_cpq_eff(triple(U, V, W)))) | contains_pq(i(triple(U, V, W)), findmin_cpq_res(triple(U, V, W)))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(17,plain,
% 0.12/0.41 (![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))))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[16])).
% 0.12/0.41 tff(18,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/sandbox2/benchmark/theBenchmark.p','l7_l8')).
% 0.12/0.41 tff(19,plain,
% 0.12/0.41 (![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))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.12/0.41 tff(20,plain,
% 0.12/0.41 (![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))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.12/0.41 tff(21,plain,(
% 0.12/0.41 ![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))))),
% 0.12/0.41 inference(skolemize,[status(sab)],[20])).
% 0.12/0.41 tff(22,plain,
% 0.12/0.41 (![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))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.12/0.41 tff(23,plain,
% 0.12/0.41 (((~![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))))) | ((~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))))) <=> ((~![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))))) | (~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))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(24,plain,
% 0.12/0.41 ((~![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))))) | ((~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))))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(25,plain,
% 0.12/0.41 ((~![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))))) | (~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)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.12/0.41 tff(26,plain,
% 0.12/0.41 (contains_pq(i(triple(U!5, V!4, W!3)), findmin_cpq_res(triple(U!5, V!4, W!3)))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[25, 22, 12])).
% 0.12/0.41 tff(27,plain,
% 0.12/0.41 (^[U: $i, V: $i, W: $i] : refl(((~phi(findmin_cpq_eff(triple(U, V, W)))) | issmallestelement_pq(i(triple(U, V, W)), findmin_cpq_res(triple(U, V, W)))) <=> ((~phi(findmin_cpq_eff(triple(U, V, W)))) | issmallestelement_pq(i(triple(U, V, W)), findmin_cpq_res(triple(U, V, W)))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(28,plain,
% 0.12/0.41 (![U: $i, V: $i, W: $i] : ((~phi(findmin_cpq_eff(triple(U, V, W)))) | issmallestelement_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)))) | issmallestelement_pq(i(triple(U, V, W)), findmin_cpq_res(triple(U, V, W))))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[27])).
% 0.12/0.41 tff(29,plain,
% 0.12/0.41 (![U: $i, V: $i, W: $i] : ((~phi(findmin_cpq_eff(triple(U, V, W)))) | issmallestelement_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)))) | issmallestelement_pq(i(triple(U, V, W)), findmin_cpq_res(triple(U, V, W))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(30,plain,
% 0.12/0.41 (^[U: $i, V: $i, W: $i] : rewrite((phi(findmin_cpq_eff(triple(U, V, W))) => issmallestelement_pq(i(triple(U, V, W)), findmin_cpq_res(triple(U, V, W)))) <=> ((~phi(findmin_cpq_eff(triple(U, V, W)))) | issmallestelement_pq(i(triple(U, V, W)), findmin_cpq_res(triple(U, V, W)))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(31,plain,
% 0.12/0.41 (![U: $i, V: $i, W: $i] : (phi(findmin_cpq_eff(triple(U, V, W))) => issmallestelement_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)))) | issmallestelement_pq(i(triple(U, V, W)), findmin_cpq_res(triple(U, V, W))))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[30])).
% 0.12/0.41 tff(32,axiom,(![U: $i, V: $i, W: $i] : (phi(findmin_cpq_eff(triple(U, V, W))) => issmallestelement_pq(i(triple(U, V, W)), findmin_cpq_res(triple(U, V, W))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l7_lX')).
% 0.12/0.41 tff(33,plain,
% 0.12/0.41 (![U: $i, V: $i, W: $i] : ((~phi(findmin_cpq_eff(triple(U, V, W)))) | issmallestelement_pq(i(triple(U, V, W)), findmin_cpq_res(triple(U, V, W))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.12/0.41 tff(34,plain,
% 0.12/0.41 (![U: $i, V: $i, W: $i] : ((~phi(findmin_cpq_eff(triple(U, V, W)))) | issmallestelement_pq(i(triple(U, V, W)), findmin_cpq_res(triple(U, V, W))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.12/0.41 tff(35,plain,(
% 0.12/0.41 ![U: $i, V: $i, W: $i] : ((~phi(findmin_cpq_eff(triple(U, V, W)))) | issmallestelement_pq(i(triple(U, V, W)), findmin_cpq_res(triple(U, V, W))))),
% 0.12/0.41 inference(skolemize,[status(sab)],[34])).
% 0.12/0.41 tff(36,plain,
% 0.12/0.41 (![U: $i, V: $i, W: $i] : ((~phi(findmin_cpq_eff(triple(U, V, W)))) | issmallestelement_pq(i(triple(U, V, W)), findmin_cpq_res(triple(U, V, W))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.12/0.41 tff(37,plain,
% 0.12/0.41 (((~![U: $i, V: $i, W: $i] : ((~phi(findmin_cpq_eff(triple(U, V, W)))) | issmallestelement_pq(i(triple(U, V, W)), findmin_cpq_res(triple(U, V, W))))) | ((~phi(findmin_cpq_eff(triple(U!5, V!4, W!3)))) | issmallestelement_pq(i(triple(U!5, V!4, W!3)), findmin_cpq_res(triple(U!5, V!4, W!3))))) <=> ((~![U: $i, V: $i, W: $i] : ((~phi(findmin_cpq_eff(triple(U, V, W)))) | issmallestelement_pq(i(triple(U, V, W)), findmin_cpq_res(triple(U, V, W))))) | (~phi(findmin_cpq_eff(triple(U!5, V!4, W!3)))) | issmallestelement_pq(i(triple(U!5, V!4, W!3)), findmin_cpq_res(triple(U!5, V!4, W!3))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(38,plain,
% 0.12/0.41 ((~![U: $i, V: $i, W: $i] : ((~phi(findmin_cpq_eff(triple(U, V, W)))) | issmallestelement_pq(i(triple(U, V, W)), findmin_cpq_res(triple(U, V, W))))) | ((~phi(findmin_cpq_eff(triple(U!5, V!4, W!3)))) | issmallestelement_pq(i(triple(U!5, V!4, W!3)), findmin_cpq_res(triple(U!5, V!4, W!3))))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(39,plain,
% 0.12/0.41 ((~![U: $i, V: $i, W: $i] : ((~phi(findmin_cpq_eff(triple(U, V, W)))) | issmallestelement_pq(i(triple(U, V, W)), findmin_cpq_res(triple(U, V, W))))) | (~phi(findmin_cpq_eff(triple(U!5, V!4, W!3)))) | issmallestelement_pq(i(triple(U!5, V!4, W!3)), findmin_cpq_res(triple(U!5, V!4, W!3)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.12/0.41 tff(40,plain,
% 0.12/0.41 (issmallestelement_pq(i(triple(U!5, V!4, W!3)), findmin_cpq_res(triple(U!5, V!4, W!3)))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[39, 36, 12])).
% 0.12/0.41 tff(41,plain,
% 0.12/0.41 ((~((~contains_pq(i(triple(U!5, V!4, W!3)), findmin_cpq_res(triple(U!5, V!4, W!3)))) | (~issmallestelement_pq(i(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)))) | (~issmallestelement_pq(i(triple(U!5, V!4, W!3)), findmin_cpq_res(triple(U!5, V!4, W!3))))),
% 0.12/0.41 inference(tautology,[status(thm)],[])).
% 0.12/0.41 tff(42,plain,
% 0.12/0.41 (~((~contains_pq(i(triple(U!5, V!4, W!3)), findmin_cpq_res(triple(U!5, V!4, W!3)))) | (~issmallestelement_pq(i(triple(U!5, V!4, W!3)), findmin_cpq_res(triple(U!5, V!4, W!3)))))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[41, 40, 26])).
% 0.12/0.41 tff(43,plain,
% 0.12/0.41 (~pi_sharp_find_min(i(triple(U!5, V!4, W!3)), findmin_cpq_res(triple(U!5, V!4, W!3)))),
% 0.12/0.41 inference(or_elim,[status(thm)],[11])).
% 0.12/0.41 tff(44,plain,
% 0.12/0.41 ((~(pi_sharp_find_min(i(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)))) | (~issmallestelement_pq(i(triple(U!5, V!4, W!3)), findmin_cpq_res(triple(U!5, V!4, W!3)))))))) | pi_sharp_find_min(i(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)))) | (~issmallestelement_pq(i(triple(U!5, V!4, W!3)), findmin_cpq_res(triple(U!5, V!4, W!3)))))),
% 0.12/0.41 inference(tautology,[status(thm)],[])).
% 0.12/0.41 tff(45,plain,
% 0.12/0.41 (~(pi_sharp_find_min(i(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)))) | (~issmallestelement_pq(i(triple(U!5, V!4, W!3)), findmin_cpq_res(triple(U!5, V!4, W!3)))))))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[44, 43, 42])).
% 0.12/0.41 tff(46,plain,
% 0.12/0.41 (^[U: $i, V: $i] : refl((pi_sharp_find_min(U, V) <=> (~((~contains_pq(U, V)) | (~issmallestelement_pq(U, V))))) <=> (pi_sharp_find_min(U, V) <=> (~((~contains_pq(U, V)) | (~issmallestelement_pq(U, V))))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(47,plain,
% 0.12/0.41 (![U: $i, V: $i] : (pi_sharp_find_min(U, V) <=> (~((~contains_pq(U, V)) | (~issmallestelement_pq(U, V))))) <=> ![U: $i, V: $i] : (pi_sharp_find_min(U, V) <=> (~((~contains_pq(U, V)) | (~issmallestelement_pq(U, V)))))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[46])).
% 0.12/0.41 tff(48,plain,
% 0.12/0.41 (^[U: $i, V: $i] : rewrite((pi_sharp_find_min(U, V) <=> (contains_pq(U, V) & issmallestelement_pq(U, V))) <=> (pi_sharp_find_min(U, V) <=> (~((~contains_pq(U, V)) | (~issmallestelement_pq(U, V))))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(49,plain,
% 0.12/0.41 (![U: $i, V: $i] : (pi_sharp_find_min(U, V) <=> (contains_pq(U, V) & issmallestelement_pq(U, V))) <=> ![U: $i, V: $i] : (pi_sharp_find_min(U, V) <=> (~((~contains_pq(U, V)) | (~issmallestelement_pq(U, V)))))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[48])).
% 0.12/0.41 tff(50,plain,
% 0.12/0.41 (![U: $i, V: $i] : (pi_sharp_find_min(U, V) <=> (contains_pq(U, V) & issmallestelement_pq(U, V))) <=> ![U: $i, V: $i] : (pi_sharp_find_min(U, V) <=> (contains_pq(U, V) & issmallestelement_pq(U, V)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(51,axiom,(![U: $i, V: $i] : (pi_sharp_find_min(U, V) <=> (contains_pq(U, V) & issmallestelement_pq(U, V)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+4.ax','ax58')).
% 0.12/0.41 tff(52,plain,
% 0.12/0.41 (![U: $i, V: $i] : (pi_sharp_find_min(U, V) <=> (contains_pq(U, V) & issmallestelement_pq(U, V)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.12/0.41 tff(53,plain,(
% 0.12/0.41 ![U: $i, V: $i] : (pi_sharp_find_min(U, V) <=> (contains_pq(U, V) & issmallestelement_pq(U, V)))),
% 0.12/0.41 inference(skolemize,[status(sab)],[52])).
% 0.12/0.41 tff(54,plain,
% 0.12/0.41 (![U: $i, V: $i] : (pi_sharp_find_min(U, V) <=> (~((~contains_pq(U, V)) | (~issmallestelement_pq(U, V)))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.12/0.41 tff(55,plain,
% 0.12/0.41 (![U: $i, V: $i] : (pi_sharp_find_min(U, V) <=> (~((~contains_pq(U, V)) | (~issmallestelement_pq(U, V)))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.12/0.41 tff(56,plain,
% 0.12/0.41 ((~![U: $i, V: $i] : (pi_sharp_find_min(U, V) <=> (~((~contains_pq(U, V)) | (~issmallestelement_pq(U, V)))))) | (pi_sharp_find_min(i(triple(U!5, V!4, W!3)), findmin_cpq_res(triple(U!5, V!4, W!3))) <=> (~((~contains_pq(i(triple(U!5, V!4, W!3)), findmin_cpq_res(triple(U!5, V!4, W!3)))) | (~issmallestelement_pq(i(triple(U!5, V!4, W!3)), findmin_cpq_res(triple(U!5, V!4, W!3)))))))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(57,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[56, 55, 45])).
% 0.19/0.42 % SZS output end Proof
%------------------------------------------------------------------------------