%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV417+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:32:25 AM UTC 2025
% Result : Theorem 0.12s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV417+1 : TPTP v9.0.0. Released v3.3.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n016.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 : Fri Jun 20 09:46:02 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.39 % SZS status Theorem
% 0.12/0.39 % SZS output start Proof
% 0.12/0.39 tff(findmin_pq_res_type, type, (
% 0.12/0.39 findmin_pq_res: ( $i * $i ) > $i)).
% 0.12/0.39 tff(findmin_cpq_res_type, type, (
% 0.12/0.39 findmin_cpq_res: $i > $i)).
% 0.12/0.39 tff(triple_type, type, (
% 0.12/0.39 triple: ( $i * $i * $i ) > $i)).
% 0.12/0.39 tff(tptp_fun_W_3_type, type, (
% 0.12/0.39 tptp_fun_W_3: $i)).
% 0.12/0.39 tff(tptp_fun_V_4_type, type, (
% 0.12/0.39 tptp_fun_V_4: $i)).
% 0.12/0.39 tff(tptp_fun_U_5_type, type, (
% 0.12/0.39 tptp_fun_U_5: $i)).
% 0.12/0.39 tff(i_type, type, (
% 0.12/0.39 i: $i > $i)).
% 0.12/0.39 tff(issmallestelement_pq_type, type, (
% 0.12/0.39 issmallestelement_pq: ( $i * $i ) > $o)).
% 0.12/0.39 tff(contains_pq_type, type, (
% 0.12/0.39 contains_pq: ( $i * $i ) > $o)).
% 0.12/0.39 tff(pi_sharp_find_min_type, type, (
% 0.12/0.39 pi_sharp_find_min: ( $i * $i ) > $o)).
% 0.12/0.39 tff(phi_type, type, (
% 0.12/0.39 phi: $i > $o)).
% 0.12/0.39 tff(findmin_cpq_eff_type, type, (
% 0.12/0.39 findmin_cpq_eff: $i > $i)).
% 0.12/0.39 tff(pi_find_min_type, type, (
% 0.12/0.39 pi_find_min: $i > $o)).
% 0.12/0.39 tff(1,plain,
% 0.12/0.39 (^[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))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(2,plain,
% 0.12/0.39 (![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)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.39 tff(3,plain,
% 0.12/0.39 (^[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)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(4,plain,
% 0.12/0.39 (![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)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.12/0.39 tff(5,plain,
% 0.12/0.39 (![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)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(6,axiom,(![U: $i, V: $i] : (pi_sharp_find_min(U, V) <=> (contains_pq(U, V) & issmallestelement_pq(U, V)))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+4.ax','ax58')).
% 0.12/0.39 tff(7,plain,
% 0.12/0.39 (![U: $i, V: $i] : (pi_sharp_find_min(U, V) <=> (contains_pq(U, V) & issmallestelement_pq(U, V)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.12/0.39 tff(8,plain,(
% 0.12/0.39 ![U: $i, V: $i] : (pi_sharp_find_min(U, V) <=> (contains_pq(U, V) & issmallestelement_pq(U, V)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[7])).
% 0.12/0.39 tff(9,plain,
% 0.12/0.39 (![U: $i, V: $i] : (~(((~contains_pq(U, V)) | (~issmallestelement_pq(U, V))) <=> pi_sharp_find_min(U, V)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.12/0.39 tff(10,plain,
% 0.12/0.39 (![U: $i, V: $i] : (~(((~contains_pq(U, V)) | (~issmallestelement_pq(U, V))) <=> pi_sharp_find_min(U, V)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.12/0.39 tff(11,plain,
% 0.12/0.39 ((~![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)))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(12,plain,
% 0.12/0.39 (~(((~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))))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.12/0.39 tff(13,plain,
% 0.12/0.39 ((![X: $i] : (~(pi_sharp_find_min(i(triple(U!5, V!4, W!3)), X) & (findmin_cpq_res(triple(U!5, V!4, W!3)) = findmin_pq_res(i(triple(U!5, V!4, W!3)), X)))) & phi(findmin_cpq_eff(triple(U!5, V!4, W!3))) & pi_find_min(triple(U!5, V!4, W!3))) <=> (![X: $i] : (~(pi_sharp_find_min(i(triple(U!5, V!4, W!3)), X) & (findmin_cpq_res(triple(U!5, V!4, W!3)) = findmin_pq_res(i(triple(U!5, V!4, W!3)), X)))) & phi(findmin_cpq_eff(triple(U!5, V!4, W!3))) & pi_find_min(triple(U!5, V!4, W!3)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(14,plain,
% 0.12/0.39 ((~![U: $i, V: $i, W: $i] : (?[X: $i] : (pi_sharp_find_min(i(triple(U, V, W)), X) & (findmin_cpq_res(triple(U, V, W)) = findmin_pq_res(i(triple(U, V, W)), X))) | (~phi(findmin_cpq_eff(triple(U, V, W)))) | (~pi_find_min(triple(U, V, W))))) <=> (~![U: $i, V: $i, W: $i] : (?[X: $i] : (pi_sharp_find_min(i(triple(U, V, W)), X) & (findmin_cpq_res(triple(U, V, W)) = findmin_pq_res(i(triple(U, V, W)), X))) | (~phi(findmin_cpq_eff(triple(U, V, W)))) | (~pi_find_min(triple(U, V, W)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(15,plain,
% 0.12/0.39 ((~![U: $i, V: $i, W: $i] : (pi_find_min(triple(U, V, W)) => (phi(findmin_cpq_eff(triple(U, V, W))) => ?[X: $i] : (pi_sharp_find_min(i(triple(U, V, W)), X) & (findmin_cpq_res(triple(U, V, W)) = findmin_pq_res(i(triple(U, V, W)), X)))))) <=> (~![U: $i, V: $i, W: $i] : (?[X: $i] : (pi_sharp_find_min(i(triple(U, V, W)), X) & (findmin_cpq_res(triple(U, V, W)) = findmin_pq_res(i(triple(U, V, W)), X))) | (~phi(findmin_cpq_eff(triple(U, V, W)))) | (~pi_find_min(triple(U, V, W)))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(16,axiom,(~![U: $i, V: $i, W: $i] : (pi_find_min(triple(U, V, W)) => (phi(findmin_cpq_eff(triple(U, V, W))) => ?[X: $i] : (pi_sharp_find_min(i(triple(U, V, W)), X) & (findmin_cpq_res(triple(U, V, W)) = findmin_pq_res(i(triple(U, V, W)), X)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co4')).
% 0.12/0.39 tff(17,plain,
% 0.12/0.39 (~![U: $i, V: $i, W: $i] : (?[X: $i] : (pi_sharp_find_min(i(triple(U, V, W)), X) & (findmin_cpq_res(triple(U, V, W)) = findmin_pq_res(i(triple(U, V, W)), X))) | (~phi(findmin_cpq_eff(triple(U, V, W)))) | (~pi_find_min(triple(U, V, W))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.12/0.39 tff(18,plain,
% 0.12/0.39 (~![U: $i, V: $i, W: $i] : (?[X: $i] : (pi_sharp_find_min(i(triple(U, V, W)), X) & (findmin_cpq_res(triple(U, V, W)) = findmin_pq_res(i(triple(U, V, W)), X))) | (~phi(findmin_cpq_eff(triple(U, V, W)))) | (~pi_find_min(triple(U, V, W))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.12/0.39 tff(19,plain,
% 0.12/0.39 (~![U: $i, V: $i, W: $i] : (?[X: $i] : (pi_sharp_find_min(i(triple(U, V, W)), X) & (findmin_cpq_res(triple(U, V, W)) = findmin_pq_res(i(triple(U, V, W)), X))) | (~phi(findmin_cpq_eff(triple(U, V, W)))) | (~pi_find_min(triple(U, V, W))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.12/0.39 tff(20,plain,
% 0.12/0.39 (~![U: $i, V: $i, W: $i] : (?[X: $i] : (pi_sharp_find_min(i(triple(U, V, W)), X) & (findmin_cpq_res(triple(U, V, W)) = findmin_pq_res(i(triple(U, V, W)), X))) | (~phi(findmin_cpq_eff(triple(U, V, W)))) | (~pi_find_min(triple(U, V, W))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[19, 14])).
% 0.12/0.39 tff(21,plain,
% 0.12/0.39 (![X: $i] : (~(pi_sharp_find_min(i(triple(U!5, V!4, W!3)), X) & (findmin_cpq_res(triple(U!5, V!4, W!3)) = findmin_pq_res(i(triple(U!5, V!4, W!3)), X)))) & phi(findmin_cpq_eff(triple(U!5, V!4, W!3))) & pi_find_min(triple(U!5, V!4, W!3))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.12/0.39 tff(22,plain,
% 0.12/0.39 (phi(findmin_cpq_eff(triple(U!5, V!4, W!3)))),
% 0.12/0.39 inference(and_elim,[status(thm)],[21])).
% 0.12/0.39 tff(23,plain,
% 0.12/0.39 (^[U: $i, V: $i, W: $i] : refl(((~phi(findmin_cpq_eff(triple(U, V, W)))) | pi_sharp_find_min(i(triple(U, V, W)), findmin_cpq_res(triple(U, V, W)))) <=> ((~phi(findmin_cpq_eff(triple(U, V, W)))) | pi_sharp_find_min(i(triple(U, V, W)), findmin_cpq_res(triple(U, V, W)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(24,plain,
% 0.12/0.39 (![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))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[23])).
% 0.12/0.39 tff(25,plain,
% 0.12/0.39 (![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))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(26,plain,
% 0.12/0.39 (^[U: $i, V: $i, W: $i] : rewrite((phi(findmin_cpq_eff(triple(U, V, W))) => pi_sharp_find_min(i(triple(U, V, W)), findmin_cpq_res(triple(U, V, W)))) <=> ((~phi(findmin_cpq_eff(triple(U, V, W)))) | pi_sharp_find_min(i(triple(U, V, W)), findmin_cpq_res(triple(U, V, W)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(27,plain,
% 0.12/0.39 (![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))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[26])).
% 0.12/0.39 tff(28,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/sandbox/benchmark/theBenchmark.p','main4_l7')).
% 0.12/0.39 tff(29,plain,
% 0.12/0.39 (![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))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.12/0.39 tff(30,plain,
% 0.12/0.39 (![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))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.12/0.39 tff(31,plain,(
% 0.12/0.39 ![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))))),
% 0.12/0.39 inference(skolemize,[status(sab)],[30])).
% 0.12/0.39 tff(32,plain,
% 0.12/0.39 (![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))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.12/0.39 tff(33,plain,
% 0.12/0.39 (((~![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))))) | ((~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))))) <=> ((~![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))))) | (~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))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(34,plain,
% 0.12/0.39 ((~![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))))) | ((~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))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(35,plain,
% 0.12/0.39 ((~![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))))) | (~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)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.12/0.40 tff(36,plain,
% 0.12/0.40 (pi_sharp_find_min(i(triple(U!5, V!4, W!3)), findmin_cpq_res(triple(U!5, V!4, W!3)))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[35, 32, 22])).
% 0.12/0.40 tff(37,plain,
% 0.12/0.40 ((((~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))))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(38,plain,
% 0.12/0.40 ((((~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))))))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.12/0.40 tff(39,plain,
% 0.12/0.40 (~((~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)))))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[38, 12])).
% 0.12/0.40 tff(40,plain,
% 0.12/0.40 (((~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))))) | issmallestelement_pq(i(triple(U!5, V!4, W!3)), findmin_cpq_res(triple(U!5, V!4, W!3)))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(41,plain,
% 0.12/0.40 (issmallestelement_pq(i(triple(U!5, V!4, W!3)), findmin_cpq_res(triple(U!5, V!4, W!3)))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.12/0.40 tff(42,plain,
% 0.12/0.40 (((~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)))),
% 0.12/0.40 inference(tautology,[status(thm)],[])).
% 0.12/0.40 tff(43,plain,
% 0.12/0.40 (contains_pq(i(triple(U!5, V!4, W!3)), findmin_cpq_res(triple(U!5, V!4, W!3)))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[42, 39])).
% 0.12/0.40 tff(44,plain,
% 0.12/0.40 (^[U: $i, V: $i] : refl(((findmin_pq_res(U, V) = V) | (~issmallestelement_pq(U, V)) | (~contains_pq(U, V))) <=> ((findmin_pq_res(U, V) = V) | (~issmallestelement_pq(U, V)) | (~contains_pq(U, V))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(45,plain,
% 0.12/0.40 (![U: $i, V: $i] : ((findmin_pq_res(U, V) = V) | (~issmallestelement_pq(U, V)) | (~contains_pq(U, V))) <=> ![U: $i, V: $i] : ((findmin_pq_res(U, V) = V) | (~issmallestelement_pq(U, V)) | (~contains_pq(U, V)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[44])).
% 0.12/0.40 tff(46,plain,
% 0.12/0.40 (^[U: $i, V: $i] : trans(monotonicity(trans(monotonicity(rewrite((contains_pq(U, V) & issmallestelement_pq(U, V)) <=> (~((~contains_pq(U, V)) | (~issmallestelement_pq(U, V))))), ((~(contains_pq(U, V) & issmallestelement_pq(U, V))) <=> (~(~((~contains_pq(U, V)) | (~issmallestelement_pq(U, V))))))), rewrite((~(~((~contains_pq(U, V)) | (~issmallestelement_pq(U, V))))) <=> ((~contains_pq(U, V)) | (~issmallestelement_pq(U, V)))), ((~(contains_pq(U, V) & issmallestelement_pq(U, V))) <=> ((~contains_pq(U, V)) | (~issmallestelement_pq(U, V))))), (((~(contains_pq(U, V) & issmallestelement_pq(U, V))) | (findmin_pq_res(U, V) = V)) <=> (((~contains_pq(U, V)) | (~issmallestelement_pq(U, V))) | (findmin_pq_res(U, V) = V)))), rewrite((((~contains_pq(U, V)) | (~issmallestelement_pq(U, V))) | (findmin_pq_res(U, V) = V)) <=> ((findmin_pq_res(U, V) = V) | (~issmallestelement_pq(U, V)) | (~contains_pq(U, V)))), (((~(contains_pq(U, V) & issmallestelement_pq(U, V))) | (findmin_pq_res(U, V) = V)) <=> ((findmin_pq_res(U, V) = V) | (~issmallestelement_pq(U, V)) | (~contains_pq(U, V)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(47,plain,
% 0.12/0.40 (![U: $i, V: $i] : ((~(contains_pq(U, V) & issmallestelement_pq(U, V))) | (findmin_pq_res(U, V) = V)) <=> ![U: $i, V: $i] : ((findmin_pq_res(U, V) = V) | (~issmallestelement_pq(U, V)) | (~contains_pq(U, V)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[46])).
% 0.12/0.40 tff(48,plain,
% 0.12/0.40 (![U: $i, V: $i] : ((~(contains_pq(U, V) & issmallestelement_pq(U, V))) | (findmin_pq_res(U, V) = V)) <=> ![U: $i, V: $i] : ((~(contains_pq(U, V) & issmallestelement_pq(U, V))) | (findmin_pq_res(U, V) = V))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(49,plain,
% 0.12/0.40 (^[U: $i, V: $i] : rewrite(((contains_pq(U, V) & issmallestelement_pq(U, V)) => (findmin_pq_res(U, V) = V)) <=> ((~(contains_pq(U, V) & issmallestelement_pq(U, V))) | (findmin_pq_res(U, V) = V)))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(50,plain,
% 0.12/0.40 (![U: $i, V: $i] : ((contains_pq(U, V) & issmallestelement_pq(U, V)) => (findmin_pq_res(U, V) = V)) <=> ![U: $i, V: $i] : ((~(contains_pq(U, V) & issmallestelement_pq(U, V))) | (findmin_pq_res(U, V) = V))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[49])).
% 0.12/0.40 tff(51,axiom,(![U: $i, V: $i] : ((contains_pq(U, V) & issmallestelement_pq(U, V)) => (findmin_pq_res(U, V) = V))), file('/export/starexec/sandbox/benchmark/Axioms/SWV007+1.ax','ax14')).
% 0.12/0.40 tff(52,plain,
% 0.12/0.40 (![U: $i, V: $i] : ((~(contains_pq(U, V) & issmallestelement_pq(U, V))) | (findmin_pq_res(U, V) = V))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.12/0.40 tff(53,plain,
% 0.12/0.40 (![U: $i, V: $i] : ((~(contains_pq(U, V) & issmallestelement_pq(U, V))) | (findmin_pq_res(U, V) = V))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.12/0.40 tff(54,plain,(
% 0.12/0.40 ![U: $i, V: $i] : ((~(contains_pq(U, V) & issmallestelement_pq(U, V))) | (findmin_pq_res(U, V) = V))),
% 0.12/0.40 inference(skolemize,[status(sab)],[53])).
% 0.12/0.40 tff(55,plain,
% 0.12/0.40 (![U: $i, V: $i] : ((findmin_pq_res(U, V) = V) | (~issmallestelement_pq(U, V)) | (~contains_pq(U, V)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.12/0.40 tff(56,plain,
% 0.12/0.40 (![U: $i, V: $i] : ((findmin_pq_res(U, V) = V) | (~issmallestelement_pq(U, V)) | (~contains_pq(U, V)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[55, 45])).
% 0.12/0.40 tff(57,plain,
% 0.12/0.40 (((~![U: $i, V: $i] : ((findmin_pq_res(U, V) = V) | (~issmallestelement_pq(U, V)) | (~contains_pq(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)))) | (findmin_pq_res(i(triple(U!5, V!4, W!3)), findmin_cpq_res(triple(U!5, V!4, W!3))) = findmin_cpq_res(triple(U!5, V!4, W!3))))) <=> ((~![U: $i, V: $i] : ((findmin_pq_res(U, V) = V) | (~issmallestelement_pq(U, V)) | (~contains_pq(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)))) | (findmin_pq_res(i(triple(U!5, V!4, W!3)), findmin_cpq_res(triple(U!5, V!4, W!3))) = findmin_cpq_res(triple(U!5, V!4, W!3))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(58,plain,
% 0.12/0.40 (((findmin_pq_res(i(triple(U!5, V!4, W!3)), findmin_cpq_res(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))))) <=> ((~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)))) | (findmin_pq_res(i(triple(U!5, V!4, W!3)), findmin_cpq_res(triple(U!5, V!4, W!3))) = findmin_cpq_res(triple(U!5, V!4, W!3))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(59,plain,
% 0.12/0.40 (((~![U: $i, V: $i] : ((findmin_pq_res(U, V) = V) | (~issmallestelement_pq(U, V)) | (~contains_pq(U, V)))) | ((findmin_pq_res(i(triple(U!5, V!4, W!3)), findmin_cpq_res(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)))))) <=> ((~![U: $i, V: $i] : ((findmin_pq_res(U, V) = V) | (~issmallestelement_pq(U, V)) | (~contains_pq(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)))) | (findmin_pq_res(i(triple(U!5, V!4, W!3)), findmin_cpq_res(triple(U!5, V!4, W!3))) = findmin_cpq_res(triple(U!5, V!4, W!3)))))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[58])).
% 0.12/0.40 tff(60,plain,
% 0.12/0.40 (((~![U: $i, V: $i] : ((findmin_pq_res(U, V) = V) | (~issmallestelement_pq(U, V)) | (~contains_pq(U, V)))) | ((findmin_pq_res(i(triple(U!5, V!4, W!3)), findmin_cpq_res(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)))))) <=> ((~![U: $i, V: $i] : ((findmin_pq_res(U, V) = V) | (~issmallestelement_pq(U, V)) | (~contains_pq(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)))) | (findmin_pq_res(i(triple(U!5, V!4, W!3)), findmin_cpq_res(triple(U!5, V!4, W!3))) = findmin_cpq_res(triple(U!5, V!4, W!3))))),
% 0.12/0.40 inference(transitivity,[status(thm)],[59, 57])).
% 0.12/0.40 tff(61,plain,
% 0.12/0.40 ((~![U: $i, V: $i] : ((findmin_pq_res(U, V) = V) | (~issmallestelement_pq(U, V)) | (~contains_pq(U, V)))) | ((findmin_pq_res(i(triple(U!5, V!4, W!3)), findmin_cpq_res(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)))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(62,plain,
% 0.12/0.40 ((~![U: $i, V: $i] : ((findmin_pq_res(U, V) = V) | (~issmallestelement_pq(U, V)) | (~contains_pq(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)))) | (findmin_pq_res(i(triple(U!5, V!4, W!3)), findmin_cpq_res(triple(U!5, V!4, W!3))) = findmin_cpq_res(triple(U!5, V!4, W!3)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.12/0.40 tff(63,plain,
% 0.12/0.40 (findmin_pq_res(i(triple(U!5, V!4, W!3)), findmin_cpq_res(triple(U!5, V!4, W!3))) = findmin_cpq_res(triple(U!5, V!4, W!3))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[62, 56, 43, 41])).
% 0.12/0.40 tff(64,plain,
% 0.12/0.40 (findmin_cpq_res(triple(U!5, V!4, W!3)) = findmin_pq_res(i(triple(U!5, V!4, W!3)), findmin_cpq_res(triple(U!5, V!4, W!3)))),
% 0.12/0.40 inference(symmetry,[status(thm)],[63])).
% 0.12/0.40 tff(65,plain,
% 0.12/0.40 (^[X: $i] : refl(((~pi_sharp_find_min(i(triple(U!5, V!4, W!3)), X)) | (~(findmin_cpq_res(triple(U!5, V!4, W!3)) = findmin_pq_res(i(triple(U!5, V!4, W!3)), X)))) <=> ((~pi_sharp_find_min(i(triple(U!5, V!4, W!3)), X)) | (~(findmin_cpq_res(triple(U!5, V!4, W!3)) = findmin_pq_res(i(triple(U!5, V!4, W!3)), X)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(66,plain,
% 0.12/0.40 (![X: $i] : ((~pi_sharp_find_min(i(triple(U!5, V!4, W!3)), X)) | (~(findmin_cpq_res(triple(U!5, V!4, W!3)) = findmin_pq_res(i(triple(U!5, V!4, W!3)), X)))) <=> ![X: $i] : ((~pi_sharp_find_min(i(triple(U!5, V!4, W!3)), X)) | (~(findmin_cpq_res(triple(U!5, V!4, W!3)) = findmin_pq_res(i(triple(U!5, V!4, W!3)), X))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[65])).
% 0.12/0.40 tff(67,plain,
% 0.12/0.40 (^[X: $i] : trans(monotonicity(rewrite((pi_sharp_find_min(i(triple(U!5, V!4, W!3)), X) & (findmin_cpq_res(triple(U!5, V!4, W!3)) = findmin_pq_res(i(triple(U!5, V!4, W!3)), X))) <=> (~((~pi_sharp_find_min(i(triple(U!5, V!4, W!3)), X)) | (~(findmin_cpq_res(triple(U!5, V!4, W!3)) = findmin_pq_res(i(triple(U!5, V!4, W!3)), X)))))), ((~(pi_sharp_find_min(i(triple(U!5, V!4, W!3)), X) & (findmin_cpq_res(triple(U!5, V!4, W!3)) = findmin_pq_res(i(triple(U!5, V!4, W!3)), X)))) <=> (~(~((~pi_sharp_find_min(i(triple(U!5, V!4, W!3)), X)) | (~(findmin_cpq_res(triple(U!5, V!4, W!3)) = findmin_pq_res(i(triple(U!5, V!4, W!3)), X)))))))), rewrite((~(~((~pi_sharp_find_min(i(triple(U!5, V!4, W!3)), X)) | (~(findmin_cpq_res(triple(U!5, V!4, W!3)) = findmin_pq_res(i(triple(U!5, V!4, W!3)), X)))))) <=> ((~pi_sharp_find_min(i(triple(U!5, V!4, W!3)), X)) | (~(findmin_cpq_res(triple(U!5, V!4, W!3)) = findmin_pq_res(i(triple(U!5, V!4, W!3)), X))))), ((~(pi_sharp_find_min(i(triple(U!5, V!4, W!3)), X) & (findmin_cpq_res(triple(U!5, V!4, W!3)) = findmin_pq_res(i(triple(U!5, V!4, W!3)), X)))) <=> ((~pi_sharp_find_min(i(triple(U!5, V!4, W!3)), X)) | (~(findmin_cpq_res(triple(U!5, V!4, W!3)) = findmin_pq_res(i(triple(U!5, V!4, W!3)), X))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(68,plain,
% 0.19/0.41 (![X: $i] : (~(pi_sharp_find_min(i(triple(U!5, V!4, W!3)), X) & (findmin_cpq_res(triple(U!5, V!4, W!3)) = findmin_pq_res(i(triple(U!5, V!4, W!3)), X)))) <=> ![X: $i] : ((~pi_sharp_find_min(i(triple(U!5, V!4, W!3)), X)) | (~(findmin_cpq_res(triple(U!5, V!4, W!3)) = findmin_pq_res(i(triple(U!5, V!4, W!3)), X))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[67])).
% 0.19/0.41 tff(69,plain,
% 0.19/0.41 (![X: $i] : (~(pi_sharp_find_min(i(triple(U!5, V!4, W!3)), X) & (findmin_cpq_res(triple(U!5, V!4, W!3)) = findmin_pq_res(i(triple(U!5, V!4, W!3)), X))))),
% 0.19/0.41 inference(and_elim,[status(thm)],[21])).
% 0.19/0.41 tff(70,plain,
% 0.19/0.41 (![X: $i] : ((~pi_sharp_find_min(i(triple(U!5, V!4, W!3)), X)) | (~(findmin_cpq_res(triple(U!5, V!4, W!3)) = findmin_pq_res(i(triple(U!5, V!4, W!3)), X))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.19/0.41 tff(71,plain,
% 0.19/0.41 (![X: $i] : ((~pi_sharp_find_min(i(triple(U!5, V!4, W!3)), X)) | (~(findmin_cpq_res(triple(U!5, V!4, W!3)) = findmin_pq_res(i(triple(U!5, V!4, W!3)), X))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.19/0.41 tff(72,plain,
% 0.19/0.41 (((~![X: $i] : ((~pi_sharp_find_min(i(triple(U!5, V!4, W!3)), X)) | (~(findmin_cpq_res(triple(U!5, V!4, W!3)) = findmin_pq_res(i(triple(U!5, V!4, W!3)), X))))) | ((~pi_sharp_find_min(i(triple(U!5, V!4, W!3)), findmin_cpq_res(triple(U!5, V!4, W!3)))) | (~(findmin_cpq_res(triple(U!5, V!4, W!3)) = findmin_pq_res(i(triple(U!5, V!4, W!3)), findmin_cpq_res(triple(U!5, V!4, W!3))))))) <=> ((~![X: $i] : ((~pi_sharp_find_min(i(triple(U!5, V!4, W!3)), X)) | (~(findmin_cpq_res(triple(U!5, V!4, W!3)) = findmin_pq_res(i(triple(U!5, V!4, W!3)), X))))) | (~pi_sharp_find_min(i(triple(U!5, V!4, W!3)), findmin_cpq_res(triple(U!5, V!4, W!3)))) | (~(findmin_cpq_res(triple(U!5, V!4, W!3)) = findmin_pq_res(i(triple(U!5, V!4, W!3)), findmin_cpq_res(triple(U!5, V!4, W!3))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(73,plain,
% 0.19/0.41 ((~![X: $i] : ((~pi_sharp_find_min(i(triple(U!5, V!4, W!3)), X)) | (~(findmin_cpq_res(triple(U!5, V!4, W!3)) = findmin_pq_res(i(triple(U!5, V!4, W!3)), X))))) | ((~pi_sharp_find_min(i(triple(U!5, V!4, W!3)), findmin_cpq_res(triple(U!5, V!4, W!3)))) | (~(findmin_cpq_res(triple(U!5, V!4, W!3)) = findmin_pq_res(i(triple(U!5, V!4, W!3)), findmin_cpq_res(triple(U!5, V!4, W!3))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(74,plain,
% 0.19/0.41 ((~![X: $i] : ((~pi_sharp_find_min(i(triple(U!5, V!4, W!3)), X)) | (~(findmin_cpq_res(triple(U!5, V!4, W!3)) = findmin_pq_res(i(triple(U!5, V!4, W!3)), X))))) | (~pi_sharp_find_min(i(triple(U!5, V!4, W!3)), findmin_cpq_res(triple(U!5, V!4, W!3)))) | (~(findmin_cpq_res(triple(U!5, V!4, W!3)) = findmin_pq_res(i(triple(U!5, V!4, W!3)), findmin_cpq_res(triple(U!5, V!4, W!3)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.19/0.41 tff(75,plain,
% 0.19/0.41 (~(findmin_cpq_res(triple(U!5, V!4, W!3)) = findmin_pq_res(i(triple(U!5, V!4, W!3)), findmin_cpq_res(triple(U!5, V!4, W!3))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[74, 71, 36])).
% 0.19/0.41 tff(76,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[75, 64])).
% 0.19/0.41 % SZS output end Proof
% 0.19/0.41 % E exiting
%------------------------------------------------------------------------------