%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV371+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:32:19 AM UTC 2025
% Result : Theorem 0.14s 0.42s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.14 % Problem : SWV371+1 : TPTP v9.0.0. Released v3.3.0.
% 0.14/0.14 % Command : run_E %s %d THM
% 0.14/0.37 % Computer : n015.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Fri Jun 20 09:44:41 EDT 2025
% 0.14/0.37 % CPUTime :
% 0.14/0.42 % SZS status Theorem
% 0.14/0.42 % SZS output start Proof
% 0.14/0.42 tff(pi_sharp_find_min_type, type, (
% 0.14/0.42 pi_sharp_find_min: ( $i * $i ) > $o)).
% 0.14/0.42 tff(findmin_cpq_res_type, type, (
% 0.14/0.42 findmin_cpq_res: $i > $i)).
% 0.14/0.42 tff(triple_type, type, (
% 0.14/0.42 triple: ( $i * $i * $i ) > $i)).
% 0.14/0.42 tff(tptp_fun_W_3_type, type, (
% 0.14/0.42 tptp_fun_W_3: $i)).
% 0.14/0.42 tff(tptp_fun_V_4_type, type, (
% 0.14/0.42 tptp_fun_V_4: $i)).
% 0.14/0.42 tff(tptp_fun_U_5_type, type, (
% 0.14/0.42 tptp_fun_U_5: $i)).
% 0.14/0.42 tff(i_type, type, (
% 0.14/0.42 i: $i > $i)).
% 0.14/0.42 tff(issmallestelement_pq_type, type, (
% 0.14/0.42 issmallestelement_pq: ( $i * $i ) > $o)).
% 0.14/0.42 tff(contains_pq_type, type, (
% 0.14/0.42 contains_pq: ( $i * $i ) > $o)).
% 0.14/0.42 tff(phi_type, type, (
% 0.14/0.42 phi: $i > $o)).
% 0.14/0.42 tff(findmin_cpq_eff_type, type, (
% 0.14/0.42 findmin_cpq_eff: $i > $i)).
% 0.14/0.42 tff(1,plain,
% 0.14/0.42 ((~![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)))))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(2,plain,
% 0.14/0.42 ((~![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)))))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 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')).
% 0.14/0.42 tff(4,plain,
% 0.14/0.42 (~![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))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.14/0.42 tff(5,plain,
% 0.14/0.42 (~![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))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.14/0.42 tff(6,plain,
% 0.14/0.42 (~![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))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.14/0.42 tff(7,plain,
% 0.14/0.42 (~![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))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.14/0.42 tff(8,plain,(
% 0.14/0.42 ~((~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))))),
% 0.14/0.42 inference(skolemize,[status(sab)],[7])).
% 0.14/0.42 tff(9,plain,
% 0.14/0.42 (phi(findmin_cpq_eff(triple(U!5, V!4, W!3)))),
% 0.14/0.42 inference(or_elim,[status(thm)],[8])).
% 0.14/0.42 tff(10,plain,
% 0.14/0.42 (^[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)))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(11,plain,
% 0.14/0.42 (![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))))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[10])).
% 0.14/0.42 tff(12,plain,
% 0.14/0.42 (![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))))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(13,plain,
% 0.14/0.42 (^[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)))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.43 tff(14,plain,
% 0.14/0.43 (![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))))),
% 0.14/0.43 inference(quant_intro,[status(thm)],[13])).
% 0.14/0.43 tff(15,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')).
% 0.14/0.43 tff(16,plain,
% 0.14/0.43 (![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))))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.14/0.43 tff(17,plain,
% 0.14/0.43 (![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))))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.14/0.43 tff(18,plain,(
% 0.14/0.43 ![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))))),
% 0.14/0.43 inference(skolemize,[status(sab)],[17])).
% 0.14/0.43 tff(19,plain,
% 0.14/0.43 (![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))))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.14/0.43 tff(20,plain,
% 0.14/0.43 (((~![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))))),
% 0.14/0.43 inference(rewrite,[status(thm)],[])).
% 0.14/0.43 tff(21,plain,
% 0.14/0.43 ((~![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))))),
% 0.14/0.43 inference(quant_inst,[status(thm)],[])).
% 0.14/0.43 tff(22,plain,
% 0.14/0.43 ((~![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)))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.14/0.43 tff(23,plain,
% 0.14/0.43 (contains_pq(i(triple(U!5, V!4, W!3)), findmin_cpq_res(triple(U!5, V!4, W!3)))),
% 0.14/0.43 inference(unit_resolution,[status(thm)],[22, 19, 9])).
% 0.14/0.43 tff(24,plain,
% 0.14/0.43 (^[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)))))),
% 0.14/0.43 inference(bind,[status(th)],[])).
% 0.14/0.43 tff(25,plain,
% 0.14/0.43 (![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))))),
% 0.14/0.43 inference(quant_intro,[status(thm)],[24])).
% 0.14/0.43 tff(26,plain,
% 0.14/0.43 (![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))))),
% 0.14/0.43 inference(rewrite,[status(thm)],[])).
% 0.14/0.43 tff(27,plain,
% 0.14/0.43 (^[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)))))),
% 0.14/0.43 inference(bind,[status(th)],[])).
% 0.14/0.43 tff(28,plain,
% 0.14/0.43 (![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))))),
% 0.14/0.43 inference(quant_intro,[status(thm)],[27])).
% 0.14/0.43 tff(29,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')).
% 0.14/0.43 tff(30,plain,
% 0.14/0.43 (![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))))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.14/0.43 tff(31,plain,
% 0.14/0.43 (![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))))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.14/0.43 tff(32,plain,(
% 0.14/0.43 ![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))))),
% 0.14/0.43 inference(skolemize,[status(sab)],[31])).
% 0.14/0.43 tff(33,plain,
% 0.14/0.43 (![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))))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.14/0.43 tff(34,plain,
% 0.14/0.43 (((~![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))))),
% 0.14/0.43 inference(rewrite,[status(thm)],[])).
% 0.14/0.43 tff(35,plain,
% 0.14/0.43 ((~![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))))),
% 0.14/0.43 inference(quant_inst,[status(thm)],[])).
% 0.14/0.43 tff(36,plain,
% 0.14/0.43 ((~![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)))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.14/0.43 tff(37,plain,
% 0.14/0.43 (issmallestelement_pq(i(triple(U!5, V!4, W!3)), findmin_cpq_res(triple(U!5, V!4, W!3)))),
% 0.14/0.43 inference(unit_resolution,[status(thm)],[36, 33, 9])).
% 0.14/0.43 tff(38,plain,
% 0.14/0.43 ((~((~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))))),
% 0.14/0.43 inference(tautology,[status(thm)],[])).
% 0.14/0.43 tff(39,plain,
% 0.14/0.43 (~((~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)))))),
% 0.14/0.43 inference(unit_resolution,[status(thm)],[38, 37, 23])).
% 0.14/0.43 tff(40,plain,
% 0.14/0.43 (~pi_sharp_find_min(i(triple(U!5, V!4, W!3)), findmin_cpq_res(triple(U!5, V!4, W!3)))),
% 0.14/0.43 inference(or_elim,[status(thm)],[8])).
% 0.14/0.43 tff(41,plain,
% 0.14/0.43 ((((~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))))) | pi_sharp_find_min(i(triple(U!5, V!4, W!3)), findmin_cpq_res(triple(U!5, V!4, W!3)))),
% 0.14/0.43 inference(tautology,[status(thm)],[])).
% 0.14/0.43 tff(42,plain,
% 0.14/0.43 (((~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)))),
% 0.14/0.43 inference(unit_resolution,[status(thm)],[41, 40, 39])).
% 0.14/0.43 tff(43,plain,
% 0.14/0.43 (^[U: $i, V: $i] : refl((~(((~contains_pq(U, V)) | (~issmallestelement_pq(U, V))) <=> pi_sharp_find_min(U, V))) <=> (~(((~contains_pq(U, V)) | (~issmallestelement_pq(U, V))) <=> pi_sharp_find_min(U, V))))),
% 0.14/0.43 inference(bind,[status(th)],[])).
% 0.14/0.43 tff(44,plain,
% 0.14/0.43 (![U: $i, V: $i] : (~(((~contains_pq(U, V)) | (~issmallestelement_pq(U, V))) <=> pi_sharp_find_min(U, V))) <=> ![U: $i, V: $i] : (~(((~contains_pq(U, V)) | (~issmallestelement_pq(U, V))) <=> pi_sharp_find_min(U, V)))),
% 0.14/0.43 inference(quant_intro,[status(thm)],[43])).
% 0.14/0.43 tff(45,plain,
% 0.14/0.43 (^[U: $i, V: $i] : trans(trans(monotonicity(rewrite((contains_pq(U, V) & issmallestelement_pq(U, V)) <=> (~((~contains_pq(U, V)) | (~issmallestelement_pq(U, V))))), ((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))))))), rewrite((pi_sharp_find_min(U, V) <=> (~((~contains_pq(U, V)) | (~issmallestelement_pq(U, V))))) <=> (~(((~contains_pq(U, V)) | (~issmallestelement_pq(U, V))) <=> pi_sharp_find_min(U, V)))), ((pi_sharp_find_min(U, V) <=> (contains_pq(U, V) & issmallestelement_pq(U, V))) <=> (~(((~contains_pq(U, V)) | (~issmallestelement_pq(U, V))) <=> pi_sharp_find_min(U, V))))), rewrite((~(((~contains_pq(U, V)) | (~issmallestelement_pq(U, V))) <=> pi_sharp_find_min(U, V))) <=> (~(((~contains_pq(U, V)) | (~issmallestelement_pq(U, V))) <=> pi_sharp_find_min(U, V)))), ((pi_sharp_find_min(U, V) <=> (contains_pq(U, V) & issmallestelement_pq(U, V))) <=> (~(((~contains_pq(U, V)) | (~issmallestelement_pq(U, V))) <=> pi_sharp_find_min(U, V)))))),
% 0.14/0.43 inference(bind,[status(th)],[])).
% 0.14/0.43 tff(46,plain,
% 0.14/0.43 (![U: $i, V: $i] : (pi_sharp_find_min(U, V) <=> (contains_pq(U, V) & issmallestelement_pq(U, V))) <=> ![U: $i, V: $i] : (~(((~contains_pq(U, V)) | (~issmallestelement_pq(U, V))) <=> pi_sharp_find_min(U, V)))),
% 0.14/0.43 inference(quant_intro,[status(thm)],[45])).
% 0.14/0.43 tff(47,plain,
% 0.14/0.43 (![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)))),
% 0.14/0.43 inference(rewrite,[status(thm)],[])).
% 0.14/0.43 tff(48,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')).
% 0.14/0.43 tff(49,plain,
% 0.14/0.43 (![U: $i, V: $i] : (pi_sharp_find_min(U, V) <=> (contains_pq(U, V) & issmallestelement_pq(U, V)))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.14/0.43 tff(50,plain,(
% 0.14/0.43 ![U: $i, V: $i] : (pi_sharp_find_min(U, V) <=> (contains_pq(U, V) & issmallestelement_pq(U, V)))),
% 0.14/0.43 inference(skolemize,[status(sab)],[49])).
% 0.14/0.43 tff(51,plain,
% 0.14/0.43 (![U: $i, V: $i] : (~(((~contains_pq(U, V)) | (~issmallestelement_pq(U, V))) <=> pi_sharp_find_min(U, V)))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.14/0.43 tff(52,plain,
% 0.14/0.43 (![U: $i, V: $i] : (~(((~contains_pq(U, V)) | (~issmallestelement_pq(U, V))) <=> pi_sharp_find_min(U, V)))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.14/0.43 tff(53,plain,
% 0.14/0.43 ((~![U: $i, V: $i] : (~(((~contains_pq(U, V)) | (~issmallestelement_pq(U, V))) <=> pi_sharp_find_min(U, V)))) | (~(((~contains_pq(i(triple(U!5, V!4, W!3)), findmin_cpq_res(triple(U!5, V!4, W!3)))) | (~issmallestelement_pq(i(triple(U!5, V!4, W!3)), findmin_cpq_res(triple(U!5, V!4, W!3))))) <=> pi_sharp_find_min(i(triple(U!5, V!4, W!3)), findmin_cpq_res(triple(U!5, V!4, W!3)))))),
% 0.14/0.44 inference(quant_inst,[status(thm)],[])).
% 0.14/0.44 tff(54,plain,
% 0.14/0.44 ($false),
% 0.14/0.44 inference(unit_resolution,[status(thm)],[53, 52, 42])).
% 0.14/0.44 % SZS output end Proof
% 0.14/0.44 % E exiting
%------------------------------------------------------------------------------