%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV381+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 05:32:20 AM UTC 2025
% Result : Theorem 0.16s 0.36s
% Output : Proof 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SWV381+1 : TPTP v9.0.0. Released v3.3.0.
% 0.00/0.10 % Command : run_E %s %d THM
% 0.10/0.30 % Computer : n014.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Fri Jun 20 09:44:39 EDT 2025
% 0.10/0.31 % CPUTime :
% 0.16/0.36 % SZS status Theorem
% 0.16/0.36 % SZS output start Proof
% 0.16/0.36 tff(contains_cpq_type, type, (
% 0.16/0.36 contains_cpq: ( $i * $i ) > $o)).
% 0.16/0.36 tff(tptp_fun_W_0_type, type, (
% 0.16/0.36 tptp_fun_W_0: ( $i * $i ) > $i)).
% 0.16/0.36 tff(i_type, type, (
% 0.16/0.36 i: $i > $i)).
% 0.16/0.36 tff(triple_type, type, (
% 0.16/0.36 triple: ( $i * $i * $i ) > $i)).
% 0.16/0.36 tff(tptp_fun_W_3_type, type, (
% 0.16/0.36 tptp_fun_W_3: $i)).
% 0.16/0.36 tff(tptp_fun_V_4_type, type, (
% 0.16/0.36 tptp_fun_V_4: $i)).
% 0.16/0.36 tff(tptp_fun_U_5_type, type, (
% 0.16/0.36 tptp_fun_U_5: $i)).
% 0.16/0.36 tff(findmin_cpq_res_type, type, (
% 0.16/0.36 findmin_cpq_res: $i > $i)).
% 0.16/0.36 tff(contains_pq_type, type, (
% 0.16/0.36 contains_pq: ( $i * $i ) > $o)).
% 0.16/0.36 tff(less_than_type, type, (
% 0.16/0.36 less_than: ( $i * $i ) > $o)).
% 0.16/0.36 tff(issmallestelement_pq_type, type, (
% 0.16/0.36 issmallestelement_pq: ( $i * $i ) > $o)).
% 0.16/0.36 tff(phi_type, type, (
% 0.16/0.36 phi: $i > $o)).
% 0.16/0.36 tff(findmin_cpq_eff_type, type, (
% 0.16/0.36 findmin_cpq_eff: $i > $i)).
% 0.16/0.36 tff(strictly_less_than_type, type, (
% 0.16/0.36 strictly_less_than: ( $i * $i ) > $o)).
% 0.16/0.36 tff(1,plain,
% 0.16/0.36 (^[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)))),
% 0.16/0.36 inference(bind,[status(th)],[])).
% 0.16/0.36 tff(2,plain,
% 0.16/0.36 (![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))),
% 0.16/0.36 inference(quant_intro,[status(thm)],[1])).
% 0.16/0.36 tff(3,plain,
% 0.16/0.36 (![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))),
% 0.16/0.36 inference(rewrite,[status(thm)],[])).
% 0.16/0.36 tff(4,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/sandbox2/benchmark/theBenchmark.p','l17_li56')).
% 0.16/0.36 tff(5,plain,
% 0.16/0.36 (![U: $i, V: $i, W: $i, X: $i] : (contains_cpq(triple(U, V, W), X) <=> contains_pq(i(triple(U, V, W)), X))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.16/0.36 tff(6,plain,(
% 0.16/0.36 ![U: $i, V: $i, W: $i, X: $i] : (contains_cpq(triple(U, V, W), X) <=> contains_pq(i(triple(U, V, W)), X))),
% 0.16/0.36 inference(skolemize,[status(sab)],[5])).
% 0.16/0.36 tff(7,plain,
% 0.16/0.36 (![U: $i, V: $i, W: $i, X: $i] : (contains_cpq(triple(U, V, W), X) <=> contains_pq(i(triple(U, V, W)), X))),
% 0.16/0.36 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.16/0.36 tff(8,plain,
% 0.16/0.36 ((~![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), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3)))) <=> contains_pq(i(triple(U!5, V!4, W!3)), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3)))))),
% 0.16/0.36 inference(quant_inst,[status(thm)],[])).
% 0.16/0.36 tff(9,plain,
% 0.16/0.36 (contains_cpq(triple(U!5, V!4, W!3), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3)))) <=> contains_pq(i(triple(U!5, V!4, W!3)), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))))),
% 0.16/0.36 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.16/0.36 tff(10,plain,
% 0.16/0.36 (^[U: $i, V: $i] : refl((~((~((~issmallestelement_pq(U, V)) | ![W: $i] : ((~contains_pq(U, W)) | less_than(V, W)))) | (~(issmallestelement_pq(U, V) | (~((~contains_pq(U, tptp_fun_W_0(V, U))) | less_than(V, tptp_fun_W_0(V, U)))))))) <=> (~((~((~issmallestelement_pq(U, V)) | ![W: $i] : ((~contains_pq(U, W)) | less_than(V, W)))) | (~(issmallestelement_pq(U, V) | (~((~contains_pq(U, tptp_fun_W_0(V, U))) | less_than(V, tptp_fun_W_0(V, U)))))))))),
% 0.16/0.36 inference(bind,[status(th)],[])).
% 0.16/0.36 tff(11,plain,
% 0.16/0.36 (![U: $i, V: $i] : (~((~((~issmallestelement_pq(U, V)) | ![W: $i] : ((~contains_pq(U, W)) | less_than(V, W)))) | (~(issmallestelement_pq(U, V) | (~((~contains_pq(U, tptp_fun_W_0(V, U))) | less_than(V, tptp_fun_W_0(V, U)))))))) <=> ![U: $i, V: $i] : (~((~((~issmallestelement_pq(U, V)) | ![W: $i] : ((~contains_pq(U, W)) | less_than(V, W)))) | (~(issmallestelement_pq(U, V) | (~((~contains_pq(U, tptp_fun_W_0(V, U))) | less_than(V, tptp_fun_W_0(V, U))))))))),
% 0.16/0.36 inference(quant_intro,[status(thm)],[10])).
% 0.16/0.36 tff(12,plain,
% 0.16/0.36 (^[U: $i, V: $i] : rewrite((~((~((~issmallestelement_pq(U, V)) | ![W: $i] : ((~contains_pq(U, W)) | less_than(V, W)))) | (~(issmallestelement_pq(U, V) | (~((~contains_pq(U, tptp_fun_W_0(V, U))) | less_than(V, tptp_fun_W_0(V, U)))))))) <=> (~((~((~issmallestelement_pq(U, V)) | ![W: $i] : ((~contains_pq(U, W)) | less_than(V, W)))) | (~(issmallestelement_pq(U, V) | (~((~contains_pq(U, tptp_fun_W_0(V, U))) | less_than(V, tptp_fun_W_0(V, U)))))))))),
% 0.16/0.36 inference(bind,[status(th)],[])).
% 0.16/0.36 tff(13,plain,
% 0.16/0.36 (![U: $i, V: $i] : (~((~((~issmallestelement_pq(U, V)) | ![W: $i] : ((~contains_pq(U, W)) | less_than(V, W)))) | (~(issmallestelement_pq(U, V) | (~((~contains_pq(U, tptp_fun_W_0(V, U))) | less_than(V, tptp_fun_W_0(V, U)))))))) <=> ![U: $i, V: $i] : (~((~((~issmallestelement_pq(U, V)) | ![W: $i] : ((~contains_pq(U, W)) | less_than(V, W)))) | (~(issmallestelement_pq(U, V) | (~((~contains_pq(U, tptp_fun_W_0(V, U))) | less_than(V, tptp_fun_W_0(V, U))))))))),
% 0.16/0.36 inference(quant_intro,[status(thm)],[12])).
% 0.16/0.36 tff(14,plain,
% 0.16/0.36 (![U: $i, V: $i] : (~((~((~issmallestelement_pq(U, V)) | ![W: $i] : ((~contains_pq(U, W)) | less_than(V, W)))) | (~(issmallestelement_pq(U, V) | (~((~contains_pq(U, tptp_fun_W_0(V, U))) | less_than(V, tptp_fun_W_0(V, U)))))))) <=> ![U: $i, V: $i] : (~((~((~issmallestelement_pq(U, V)) | ![W: $i] : ((~contains_pq(U, W)) | less_than(V, W)))) | (~(issmallestelement_pq(U, V) | (~((~contains_pq(U, tptp_fun_W_0(V, U))) | less_than(V, tptp_fun_W_0(V, U))))))))),
% 0.16/0.36 inference(transitivity,[status(thm)],[13, 11])).
% 0.16/0.36 tff(15,plain,
% 0.16/0.36 (^[U: $i, V: $i] : trans(monotonicity(rewrite(((~issmallestelement_pq(U, V)) | ![W: $i] : ((~contains_pq(U, W)) | less_than(V, W))) <=> ((~issmallestelement_pq(U, V)) | ![W: $i] : ((~contains_pq(U, W)) | less_than(V, W)))), rewrite((issmallestelement_pq(U, V) | (~((~contains_pq(U, tptp_fun_W_0(V, U))) | less_than(V, tptp_fun_W_0(V, U))))) <=> (issmallestelement_pq(U, V) | (~((~contains_pq(U, tptp_fun_W_0(V, U))) | less_than(V, tptp_fun_W_0(V, U)))))), ((((~issmallestelement_pq(U, V)) | ![W: $i] : ((~contains_pq(U, W)) | less_than(V, W))) & (issmallestelement_pq(U, V) | (~((~contains_pq(U, tptp_fun_W_0(V, U))) | less_than(V, tptp_fun_W_0(V, U)))))) <=> (((~issmallestelement_pq(U, V)) | ![W: $i] : ((~contains_pq(U, W)) | less_than(V, W))) & (issmallestelement_pq(U, V) | (~((~contains_pq(U, tptp_fun_W_0(V, U))) | less_than(V, tptp_fun_W_0(V, U)))))))), rewrite((((~issmallestelement_pq(U, V)) | ![W: $i] : ((~contains_pq(U, W)) | less_than(V, W))) & (issmallestelement_pq(U, V) | (~((~contains_pq(U, tptp_fun_W_0(V, U))) | less_than(V, tptp_fun_W_0(V, U)))))) <=> (~((~((~issmallestelement_pq(U, V)) | ![W: $i] : ((~contains_pq(U, W)) | less_than(V, W)))) | (~(issmallestelement_pq(U, V) | (~((~contains_pq(U, tptp_fun_W_0(V, U))) | less_than(V, tptp_fun_W_0(V, U))))))))), ((((~issmallestelement_pq(U, V)) | ![W: $i] : ((~contains_pq(U, W)) | less_than(V, W))) & (issmallestelement_pq(U, V) | (~((~contains_pq(U, tptp_fun_W_0(V, U))) | less_than(V, tptp_fun_W_0(V, U)))))) <=> (~((~((~issmallestelement_pq(U, V)) | ![W: $i] : ((~contains_pq(U, W)) | less_than(V, W)))) | (~(issmallestelement_pq(U, V) | (~((~contains_pq(U, tptp_fun_W_0(V, U))) | less_than(V, tptp_fun_W_0(V, U))))))))))),
% 0.16/0.36 inference(bind,[status(th)],[])).
% 0.16/0.36 tff(16,plain,
% 0.16/0.36 (![U: $i, V: $i] : (((~issmallestelement_pq(U, V)) | ![W: $i] : ((~contains_pq(U, W)) | less_than(V, W))) & (issmallestelement_pq(U, V) | (~((~contains_pq(U, tptp_fun_W_0(V, U))) | less_than(V, tptp_fun_W_0(V, U)))))) <=> ![U: $i, V: $i] : (~((~((~issmallestelement_pq(U, V)) | ![W: $i] : ((~contains_pq(U, W)) | less_than(V, W)))) | (~(issmallestelement_pq(U, V) | (~((~contains_pq(U, tptp_fun_W_0(V, U))) | less_than(V, tptp_fun_W_0(V, U))))))))),
% 0.16/0.36 inference(quant_intro,[status(thm)],[15])).
% 0.16/0.36 tff(17,plain,
% 0.16/0.36 (![U: $i, V: $i] : (issmallestelement_pq(U, V) <=> ![W: $i] : ((~contains_pq(U, W)) | less_than(V, W))) <=> ![U: $i, V: $i] : (issmallestelement_pq(U, V) <=> ![W: $i] : ((~contains_pq(U, W)) | less_than(V, W)))),
% 0.16/0.37 inference(rewrite,[status(thm)],[])).
% 0.16/0.37 tff(18,plain,
% 0.16/0.37 (^[U: $i, V: $i] : rewrite((issmallestelement_pq(U, V) <=> ![W: $i] : (contains_pq(U, W) => less_than(V, W))) <=> (issmallestelement_pq(U, V) <=> ![W: $i] : ((~contains_pq(U, W)) | less_than(V, W))))),
% 0.16/0.37 inference(bind,[status(th)],[])).
% 0.16/0.37 tff(19,plain,
% 0.16/0.37 (![U: $i, V: $i] : (issmallestelement_pq(U, V) <=> ![W: $i] : (contains_pq(U, W) => less_than(V, W))) <=> ![U: $i, V: $i] : (issmallestelement_pq(U, V) <=> ![W: $i] : ((~contains_pq(U, W)) | less_than(V, W)))),
% 0.16/0.37 inference(quant_intro,[status(thm)],[18])).
% 0.16/0.37 tff(20,axiom,(![U: $i, V: $i] : (issmallestelement_pq(U, V) <=> ![W: $i] : (contains_pq(U, W) => less_than(V, W)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+1.ax','ax10')).
% 0.16/0.37 tff(21,plain,
% 0.16/0.37 (![U: $i, V: $i] : (issmallestelement_pq(U, V) <=> ![W: $i] : ((~contains_pq(U, W)) | less_than(V, W)))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.16/0.37 tff(22,plain,
% 0.16/0.37 (![U: $i, V: $i] : (issmallestelement_pq(U, V) <=> ![W: $i] : ((~contains_pq(U, W)) | less_than(V, W)))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.16/0.37 tff(23,plain,(
% 0.16/0.37 ![U: $i, V: $i] : (((~issmallestelement_pq(U, V)) | ![W: $i] : ((~contains_pq(U, W)) | less_than(V, W))) & (issmallestelement_pq(U, V) | (~((~contains_pq(U, tptp_fun_W_0(V, U))) | less_than(V, tptp_fun_W_0(V, U))))))),
% 0.16/0.37 inference(skolemize,[status(sab)],[22])).
% 0.16/0.37 tff(24,plain,
% 0.16/0.37 (![U: $i, V: $i] : (~((~((~issmallestelement_pq(U, V)) | ![W: $i] : ((~contains_pq(U, W)) | less_than(V, W)))) | (~(issmallestelement_pq(U, V) | (~((~contains_pq(U, tptp_fun_W_0(V, U))) | less_than(V, tptp_fun_W_0(V, U))))))))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.16/0.37 tff(25,plain,
% 0.16/0.37 (![U: $i, V: $i] : (~((~((~issmallestelement_pq(U, V)) | ![W: $i] : ((~contains_pq(U, W)) | less_than(V, W)))) | (~(issmallestelement_pq(U, V) | (~((~contains_pq(U, tptp_fun_W_0(V, U))) | less_than(V, tptp_fun_W_0(V, U))))))))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[24, 14])).
% 0.16/0.37 tff(26,plain,
% 0.16/0.37 ((~![U: $i, V: $i] : (~((~((~issmallestelement_pq(U, V)) | ![W: $i] : ((~contains_pq(U, W)) | less_than(V, W)))) | (~(issmallestelement_pq(U, V) | (~((~contains_pq(U, tptp_fun_W_0(V, U))) | less_than(V, tptp_fun_W_0(V, U))))))))) | (~((~((~issmallestelement_pq(i(triple(U!5, V!4, W!3)), findmin_cpq_res(triple(U!5, V!4, W!3)))) | ![W: $i] : ((~contains_pq(i(triple(U!5, V!4, W!3)), W)) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), W)))) | (~(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)), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))))))))))),
% 0.16/0.37 inference(quant_inst,[status(thm)],[])).
% 0.16/0.37 tff(27,plain,
% 0.16/0.37 (~((~((~issmallestelement_pq(i(triple(U!5, V!4, W!3)), findmin_cpq_res(triple(U!5, V!4, W!3)))) | ![W: $i] : ((~contains_pq(i(triple(U!5, V!4, W!3)), W)) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), W)))) | (~(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)), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3)))))))))),
% 0.16/0.37 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.16/0.37 tff(28,plain,
% 0.16/0.37 (((~((~issmallestelement_pq(i(triple(U!5, V!4, W!3)), findmin_cpq_res(triple(U!5, V!4, W!3)))) | ![W: $i] : ((~contains_pq(i(triple(U!5, V!4, W!3)), W)) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), W)))) | (~(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)), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(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)), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3)))))))),
% 0.16/0.37 inference(tautology,[status(thm)],[])).
% 0.16/0.37 tff(29,plain,
% 0.16/0.37 (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)), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))))))),
% 0.16/0.37 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.16/0.37 tff(30,plain,
% 0.16/0.37 ((~![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)))))),
% 0.16/0.37 inference(rewrite,[status(thm)],[])).
% 0.16/0.37 tff(31,plain,
% 0.16/0.37 ((~![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)))))),
% 0.16/0.37 inference(rewrite,[status(thm)],[])).
% 0.16/0.37 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','l17_co')).
% 0.16/0.37 tff(33,plain,
% 0.16/0.37 (~![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))))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.16/0.37 tff(34,plain,
% 0.16/0.37 (~![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))))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[33, 30])).
% 0.16/0.37 tff(35,plain,
% 0.16/0.37 (~![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))))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.16/0.37 tff(36,plain,
% 0.16/0.37 (~![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))))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[35, 30])).
% 0.16/0.37 tff(37,plain,(
% 0.16/0.37 ~((~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))))),
% 0.16/0.37 inference(skolemize,[status(sab)],[36])).
% 0.16/0.37 tff(38,plain,
% 0.16/0.37 (~issmallestelement_pq(i(triple(U!5, V!4, W!3)), findmin_cpq_res(triple(U!5, V!4, W!3)))),
% 0.16/0.37 inference(or_elim,[status(thm)],[37])).
% 0.16/0.37 tff(39,plain,
% 0.16/0.37 ((~(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)), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(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)), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))))))),
% 0.16/0.37 inference(tautology,[status(thm)],[])).
% 0.16/0.37 tff(40,plain,
% 0.16/0.37 ((~(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)), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3)))))))) | (~((~contains_pq(i(triple(U!5, V!4, W!3)), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))))))),
% 0.16/0.37 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.16/0.37 tff(41,plain,
% 0.16/0.37 (~((~contains_pq(i(triple(U!5, V!4, W!3)), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3)))))),
% 0.16/0.37 inference(unit_resolution,[status(thm)],[40, 29])).
% 0.16/0.37 tff(42,plain,
% 0.16/0.37 (((~contains_pq(i(triple(U!5, V!4, W!3)), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))))) | contains_pq(i(triple(U!5, V!4, W!3)), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))))),
% 0.16/0.37 inference(tautology,[status(thm)],[])).
% 0.16/0.37 tff(43,plain,
% 0.16/0.37 (contains_pq(i(triple(U!5, V!4, W!3)), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))))),
% 0.16/0.37 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.16/0.37 tff(44,plain,
% 0.16/0.37 ((~(contains_cpq(triple(U!5, V!4, W!3), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3)))) <=> contains_pq(i(triple(U!5, V!4, W!3)), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3)))))) | contains_cpq(triple(U!5, V!4, W!3), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3)))) | (~contains_pq(i(triple(U!5, V!4, W!3)), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3)))))),
% 0.16/0.37 inference(tautology,[status(thm)],[])).
% 0.16/0.37 tff(45,plain,
% 0.16/0.37 ((~(contains_cpq(triple(U!5, V!4, W!3), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3)))) <=> contains_pq(i(triple(U!5, V!4, W!3)), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3)))))) | contains_cpq(triple(U!5, V!4, W!3), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))))),
% 0.16/0.37 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.16/0.37 tff(46,plain,
% 0.16/0.37 (contains_cpq(triple(U!5, V!4, W!3), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))))),
% 0.16/0.37 inference(unit_resolution,[status(thm)],[45, 9])).
% 0.16/0.37 tff(47,plain,
% 0.16/0.37 (^[U: $i, V: $i] : refl((~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V))) <=> (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V))))),
% 0.16/0.37 inference(bind,[status(th)],[])).
% 0.16/0.37 tff(48,plain,
% 0.16/0.37 (![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V))) <=> ![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))),
% 0.16/0.37 inference(quant_intro,[status(thm)],[47])).
% 0.16/0.37 tff(49,plain,
% 0.16/0.37 (^[U: $i, V: $i] : trans(trans(monotonicity(rewrite((less_than(U, V) & (~less_than(V, U))) <=> (~((~less_than(U, V)) | less_than(V, U)))), ((strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U)))) <=> (strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U)))))), rewrite((strictly_less_than(U, V) <=> (~((~less_than(U, V)) | less_than(V, U)))) <=> (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))), ((strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U)))) <=> (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V))))), rewrite((~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V))) <=> (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))), ((strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U)))) <=> (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))))),
% 0.16/0.37 inference(bind,[status(th)],[])).
% 0.16/0.37 tff(50,plain,
% 0.16/0.37 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U)))) <=> ![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))),
% 0.16/0.37 inference(quant_intro,[status(thm)],[49])).
% 0.16/0.37 tff(51,plain,
% 0.16/0.37 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U)))) <=> ![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.16/0.37 inference(rewrite,[status(thm)],[])).
% 0.16/0.37 tff(52,axiom,(![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+0.ax','stricly_smaller_definition')).
% 0.16/0.37 tff(53,plain,
% 0.16/0.37 (![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.16/0.37 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.16/0.37 tff(54,plain,(
% 0.16/0.37 ![U: $i, V: $i] : (strictly_less_than(U, V) <=> (less_than(U, V) & (~less_than(V, U))))),
% 0.16/0.37 inference(skolemize,[status(sab)],[53])).
% 0.16/0.37 tff(55,plain,
% 0.16/0.37 (![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.16/0.38 tff(56,plain,
% 0.16/0.38 (![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[55, 48])).
% 0.16/0.38 tff(57,plain,
% 0.16/0.38 ((~![U: $i, V: $i] : (~(((~less_than(U, V)) | less_than(V, U)) <=> strictly_less_than(U, V)))) | (~(((~less_than(tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))), findmin_cpq_res(triple(U!5, V!4, W!3)))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))))) <=> strictly_less_than(tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))), findmin_cpq_res(triple(U!5, V!4, W!3)))))),
% 0.16/0.38 inference(quant_inst,[status(thm)],[])).
% 0.16/0.38 tff(58,plain,
% 0.16/0.38 (~(((~less_than(tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))), findmin_cpq_res(triple(U!5, V!4, W!3)))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))))) <=> strictly_less_than(tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))), findmin_cpq_res(triple(U!5, V!4, W!3))))),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.16/0.38 tff(59,plain,
% 0.16/0.38 (((~contains_pq(i(triple(U!5, V!4, W!3)), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))))) | (~less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3)))))),
% 0.16/0.38 inference(tautology,[status(thm)],[])).
% 0.16/0.38 tff(60,plain,
% 0.16/0.38 (~less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))))),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[59, 41])).
% 0.16/0.38 tff(61,plain,
% 0.16/0.38 (^[U: $i, V: $i] : refl((less_than(V, U) | less_than(U, V)) <=> (less_than(V, U) | less_than(U, V)))),
% 0.16/0.38 inference(bind,[status(th)],[])).
% 0.16/0.38 tff(62,plain,
% 0.16/0.38 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.16/0.38 inference(quant_intro,[status(thm)],[61])).
% 0.16/0.38 tff(63,plain,
% 0.16/0.38 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.16/0.38 inference(rewrite,[status(thm)],[])).
% 0.16/0.38 tff(64,plain,
% 0.16/0.38 (^[U: $i, V: $i] : rewrite((less_than(U, V) | less_than(V, U)) <=> (less_than(V, U) | less_than(U, V)))),
% 0.16/0.38 inference(bind,[status(th)],[])).
% 0.16/0.38 tff(65,plain,
% 0.16/0.38 (![U: $i, V: $i] : (less_than(U, V) | less_than(V, U)) <=> ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.16/0.38 inference(quant_intro,[status(thm)],[64])).
% 0.16/0.38 tff(66,axiom,(![U: $i, V: $i] : (less_than(U, V) | less_than(V, U))), file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+0.ax','totality')).
% 0.16/0.38 tff(67,plain,
% 0.16/0.38 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.16/0.38 tff(68,plain,
% 0.16/0.38 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.16/0.38 tff(69,plain,(
% 0.16/0.38 ![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.16/0.38 inference(skolemize,[status(sab)],[68])).
% 0.16/0.38 tff(70,plain,
% 0.16/0.38 (![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[69, 62])).
% 0.16/0.38 tff(71,plain,
% 0.16/0.38 (((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | (less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3)))) | less_than(tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))), findmin_cpq_res(triple(U!5, V!4, W!3))))) <=> ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3)))) | less_than(tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))), findmin_cpq_res(triple(U!5, V!4, W!3))))),
% 0.16/0.38 inference(rewrite,[status(thm)],[])).
% 0.16/0.38 tff(72,plain,
% 0.16/0.38 ((less_than(tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))), findmin_cpq_res(triple(U!5, V!4, W!3))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))))) <=> (less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3)))) | less_than(tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))), findmin_cpq_res(triple(U!5, V!4, W!3))))),
% 0.16/0.38 inference(rewrite,[status(thm)],[])).
% 0.16/0.38 tff(73,plain,
% 0.16/0.38 (((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | (less_than(tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))), findmin_cpq_res(triple(U!5, V!4, W!3))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3)))))) <=> ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | (less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3)))) | less_than(tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))), findmin_cpq_res(triple(U!5, V!4, W!3)))))),
% 0.16/0.38 inference(monotonicity,[status(thm)],[72])).
% 0.16/0.38 tff(74,plain,
% 0.16/0.38 (((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | (less_than(tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))), findmin_cpq_res(triple(U!5, V!4, W!3))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3)))))) <=> ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3)))) | less_than(tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))), findmin_cpq_res(triple(U!5, V!4, W!3))))),
% 0.16/0.38 inference(transitivity,[status(thm)],[73, 71])).
% 0.16/0.38 tff(75,plain,
% 0.16/0.38 ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | (less_than(tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))), findmin_cpq_res(triple(U!5, V!4, W!3))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3)))))),
% 0.16/0.38 inference(quant_inst,[status(thm)],[])).
% 0.16/0.38 tff(76,plain,
% 0.16/0.38 ((~![U: $i, V: $i] : (less_than(V, U) | less_than(U, V))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3)))) | less_than(tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))), findmin_cpq_res(triple(U!5, V!4, W!3)))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.16/0.38 tff(77,plain,
% 0.16/0.38 (less_than(tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))), findmin_cpq_res(triple(U!5, V!4, W!3)))),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[76, 70, 60])).
% 0.16/0.38 tff(78,plain,
% 0.16/0.38 ((~((~less_than(tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))), findmin_cpq_res(triple(U!5, V!4, W!3)))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3)))))) | (~less_than(tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))), findmin_cpq_res(triple(U!5, V!4, W!3)))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))))),
% 0.16/0.38 inference(tautology,[status(thm)],[])).
% 0.16/0.38 tff(79,plain,
% 0.16/0.38 ((~((~less_than(tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))), findmin_cpq_res(triple(U!5, V!4, W!3)))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3)))))) | (~less_than(tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))), findmin_cpq_res(triple(U!5, V!4, W!3))))),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[78, 60])).
% 0.16/0.38 tff(80,plain,
% 0.16/0.38 (~((~less_than(tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))), findmin_cpq_res(triple(U!5, V!4, W!3)))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3)))))),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[79, 77])).
% 0.16/0.38 tff(81,plain,
% 0.16/0.38 ((((~less_than(tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))), findmin_cpq_res(triple(U!5, V!4, W!3)))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))))) <=> strictly_less_than(tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))), findmin_cpq_res(triple(U!5, V!4, W!3)))) | ((~less_than(tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))), findmin_cpq_res(triple(U!5, V!4, W!3)))) | less_than(findmin_cpq_res(triple(U!5, V!4, W!3)), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))))) | strictly_less_than(tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))), findmin_cpq_res(triple(U!5, V!4, W!3)))),
% 0.16/0.38 inference(tautology,[status(thm)],[])).
% 0.16/0.38 tff(82,plain,
% 0.16/0.38 (strictly_less_than(tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))), findmin_cpq_res(triple(U!5, V!4, W!3)))),
% 0.16/0.38 inference(unit_resolution,[status(thm)],[81, 80, 58])).
% 0.16/0.38 tff(83,plain,
% 0.16/0.38 (phi(findmin_cpq_eff(triple(U!5, V!4, W!3)))),
% 0.16/0.38 inference(or_elim,[status(thm)],[37])).
% 0.16/0.38 tff(84,plain,
% 0.16/0.38 (^[U: $i, V: $i, W: $i] : refl(((~phi(findmin_cpq_eff(triple(U, V, W)))) | ![X: $i] : ((~contains_cpq(triple(U, V, W), X)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))))) <=> ((~phi(findmin_cpq_eff(triple(U, V, W)))) | ![X: $i] : ((~contains_cpq(triple(U, V, W), X)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))))))),
% 0.16/0.38 inference(bind,[status(th)],[])).
% 0.16/0.38 tff(85,plain,
% 0.16/0.38 (![U: $i, V: $i, W: $i] : ((~phi(findmin_cpq_eff(triple(U, V, W)))) | ![X: $i] : ((~contains_cpq(triple(U, V, W), X)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))))) <=> ![U: $i, V: $i, W: $i] : ((~phi(findmin_cpq_eff(triple(U, V, W)))) | ![X: $i] : ((~contains_cpq(triple(U, V, W), X)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))))),
% 0.16/0.38 inference(quant_intro,[status(thm)],[84])).
% 0.16/0.38 tff(86,plain,
% 0.16/0.38 (^[U: $i, V: $i, W: $i] : rewrite(((~phi(findmin_cpq_eff(triple(U, V, W)))) | ![X: $i] : ((~contains_cpq(triple(U, V, W), X)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))))) <=> ((~phi(findmin_cpq_eff(triple(U, V, W)))) | ![X: $i] : ((~contains_cpq(triple(U, V, W), X)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))))))),
% 0.16/0.38 inference(bind,[status(th)],[])).
% 0.16/0.38 tff(87,plain,
% 0.16/0.38 (![U: $i, V: $i, W: $i] : ((~phi(findmin_cpq_eff(triple(U, V, W)))) | ![X: $i] : ((~contains_cpq(triple(U, V, W), X)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))))) <=> ![U: $i, V: $i, W: $i] : ((~phi(findmin_cpq_eff(triple(U, V, W)))) | ![X: $i] : ((~contains_cpq(triple(U, V, W), X)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))))),
% 0.16/0.38 inference(quant_intro,[status(thm)],[86])).
% 0.16/0.38 tff(88,plain,
% 0.16/0.38 (![U: $i, V: $i, W: $i] : ((~phi(findmin_cpq_eff(triple(U, V, W)))) | ![X: $i] : ((~contains_cpq(triple(U, V, W), X)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))))) <=> ![U: $i, V: $i, W: $i] : ((~phi(findmin_cpq_eff(triple(U, V, W)))) | ![X: $i] : ((~contains_cpq(triple(U, V, W), X)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))))),
% 0.16/0.38 inference(transitivity,[status(thm)],[87, 85])).
% 0.16/0.38 tff(89,plain,
% 0.16/0.38 (^[U: $i, V: $i, W: $i] : rewrite(((~phi(findmin_cpq_eff(triple(U, V, W)))) | ![X: $i] : (~(contains_cpq(triple(U, V, W), X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))))) <=> ((~phi(findmin_cpq_eff(triple(U, V, W)))) | ![X: $i] : ((~contains_cpq(triple(U, V, W), X)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))))))),
% 0.16/0.38 inference(bind,[status(th)],[])).
% 0.16/0.38 tff(90,plain,
% 0.16/0.38 (![U: $i, V: $i, W: $i] : ((~phi(findmin_cpq_eff(triple(U, V, W)))) | ![X: $i] : (~(contains_cpq(triple(U, V, W), X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))))) <=> ![U: $i, V: $i, W: $i] : ((~phi(findmin_cpq_eff(triple(U, V, W)))) | ![X: $i] : ((~contains_cpq(triple(U, V, W), X)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))))),
% 0.16/0.38 inference(quant_intro,[status(thm)],[89])).
% 0.16/0.38 tff(91,plain,
% 0.16/0.38 (![U: $i, V: $i, W: $i] : ((~phi(findmin_cpq_eff(triple(U, V, W)))) | (~?[X: $i] : (contains_cpq(triple(U, V, W), X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))))) <=> ![U: $i, V: $i, W: $i] : ((~phi(findmin_cpq_eff(triple(U, V, W)))) | (~?[X: $i] : (contains_cpq(triple(U, V, W), X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))))),
% 0.16/0.38 inference(rewrite,[status(thm)],[])).
% 0.16/0.38 tff(92,plain,
% 0.16/0.38 (^[U: $i, V: $i, W: $i] : rewrite((?[X: $i] : (contains_cpq(triple(U, V, W), X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))) => (~phi(findmin_cpq_eff(triple(U, V, W))))) <=> ((~phi(findmin_cpq_eff(triple(U, V, W)))) | (~?[X: $i] : (contains_cpq(triple(U, V, W), X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))))))),
% 0.16/0.38 inference(bind,[status(th)],[])).
% 0.16/0.38 tff(93,plain,
% 0.16/0.38 (![U: $i, V: $i, W: $i] : (?[X: $i] : (contains_cpq(triple(U, V, W), X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))) => (~phi(findmin_cpq_eff(triple(U, V, W))))) <=> ![U: $i, V: $i, W: $i] : ((~phi(findmin_cpq_eff(triple(U, V, W)))) | (~?[X: $i] : (contains_cpq(triple(U, V, W), X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))))),
% 0.16/0.38 inference(quant_intro,[status(thm)],[92])).
% 0.16/0.38 tff(94,axiom,(![U: $i, V: $i, W: $i] : (?[X: $i] : (contains_cpq(triple(U, V, W), X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W)))) => (~phi(findmin_cpq_eff(triple(U, V, W)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','l17_l18')).
% 0.16/0.38 tff(95,plain,
% 0.16/0.38 (![U: $i, V: $i, W: $i] : ((~phi(findmin_cpq_eff(triple(U, V, W)))) | (~?[X: $i] : (contains_cpq(triple(U, V, W), X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.16/0.38 tff(96,plain,
% 0.16/0.38 (![U: $i, V: $i, W: $i] : ((~phi(findmin_cpq_eff(triple(U, V, W)))) | (~?[X: $i] : (contains_cpq(triple(U, V, W), X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.16/0.38 tff(97,plain,(
% 0.16/0.38 ![U: $i, V: $i, W: $i] : ((~phi(findmin_cpq_eff(triple(U, V, W)))) | ![X: $i] : (~(contains_cpq(triple(U, V, W), X) & strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))))),
% 0.16/0.38 inference(skolemize,[status(sab)],[96])).
% 0.16/0.38 tff(98,plain,
% 0.16/0.38 (![U: $i, V: $i, W: $i] : ((~phi(findmin_cpq_eff(triple(U, V, W)))) | ![X: $i] : ((~contains_cpq(triple(U, V, W), X)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))))),
% 0.16/0.38 inference(modus_ponens,[status(thm)],[97, 90])).
% 0.16/0.38 tff(99,plain,
% 0.16/0.39 (![U: $i, V: $i, W: $i] : ((~phi(findmin_cpq_eff(triple(U, V, W)))) | ![X: $i] : ((~contains_cpq(triple(U, V, W), X)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[98, 88])).
% 0.16/0.39 tff(100,plain,
% 0.16/0.39 (((~![U: $i, V: $i, W: $i] : ((~phi(findmin_cpq_eff(triple(U, V, W)))) | ![X: $i] : ((~contains_cpq(triple(U, V, W), X)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))))) | ((~phi(findmin_cpq_eff(triple(U!5, V!4, W!3)))) | ![X: $i] : ((~contains_cpq(triple(U!5, V!4, W!3), X)) | (~strictly_less_than(X, findmin_cpq_res(triple(U!5, V!4, W!3))))))) <=> ((~![U: $i, V: $i, W: $i] : ((~phi(findmin_cpq_eff(triple(U, V, W)))) | ![X: $i] : ((~contains_cpq(triple(U, V, W), X)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))))) | (~phi(findmin_cpq_eff(triple(U!5, V!4, W!3)))) | ![X: $i] : ((~contains_cpq(triple(U!5, V!4, W!3), X)) | (~strictly_less_than(X, findmin_cpq_res(triple(U!5, V!4, W!3))))))),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(101,plain,
% 0.16/0.39 ((~![U: $i, V: $i, W: $i] : ((~phi(findmin_cpq_eff(triple(U, V, W)))) | ![X: $i] : ((~contains_cpq(triple(U, V, W), X)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))))) | ((~phi(findmin_cpq_eff(triple(U!5, V!4, W!3)))) | ![X: $i] : ((~contains_cpq(triple(U!5, V!4, W!3), X)) | (~strictly_less_than(X, findmin_cpq_res(triple(U!5, V!4, W!3))))))),
% 0.16/0.39 inference(quant_inst,[status(thm)],[])).
% 0.16/0.39 tff(102,plain,
% 0.16/0.39 ((~![U: $i, V: $i, W: $i] : ((~phi(findmin_cpq_eff(triple(U, V, W)))) | ![X: $i] : ((~contains_cpq(triple(U, V, W), X)) | (~strictly_less_than(X, findmin_cpq_res(triple(U, V, W))))))) | (~phi(findmin_cpq_eff(triple(U!5, V!4, W!3)))) | ![X: $i] : ((~contains_cpq(triple(U!5, V!4, W!3), X)) | (~strictly_less_than(X, findmin_cpq_res(triple(U!5, V!4, W!3)))))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.16/0.39 tff(103,plain,
% 0.16/0.39 (![X: $i] : ((~contains_cpq(triple(U!5, V!4, W!3), X)) | (~strictly_less_than(X, findmin_cpq_res(triple(U!5, V!4, W!3)))))),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[102, 99, 83])).
% 0.16/0.39 tff(104,plain,
% 0.16/0.39 (((~![X: $i] : ((~contains_cpq(triple(U!5, V!4, W!3), X)) | (~strictly_less_than(X, findmin_cpq_res(triple(U!5, V!4, W!3)))))) | ((~contains_cpq(triple(U!5, V!4, W!3), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))))) | (~strictly_less_than(tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))), findmin_cpq_res(triple(U!5, V!4, W!3)))))) <=> ((~![X: $i] : ((~contains_cpq(triple(U!5, V!4, W!3), X)) | (~strictly_less_than(X, findmin_cpq_res(triple(U!5, V!4, W!3)))))) | (~contains_cpq(triple(U!5, V!4, W!3), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))))) | (~strictly_less_than(tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))), findmin_cpq_res(triple(U!5, V!4, W!3)))))),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(105,plain,
% 0.16/0.39 ((~![X: $i] : ((~contains_cpq(triple(U!5, V!4, W!3), X)) | (~strictly_less_than(X, findmin_cpq_res(triple(U!5, V!4, W!3)))))) | ((~contains_cpq(triple(U!5, V!4, W!3), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))))) | (~strictly_less_than(tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))), findmin_cpq_res(triple(U!5, V!4, W!3)))))),
% 0.16/0.39 inference(quant_inst,[status(thm)],[])).
% 0.16/0.39 tff(106,plain,
% 0.16/0.39 ((~![X: $i] : ((~contains_cpq(triple(U!5, V!4, W!3), X)) | (~strictly_less_than(X, findmin_cpq_res(triple(U!5, V!4, W!3)))))) | (~contains_cpq(triple(U!5, V!4, W!3), tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))))) | (~strictly_less_than(tptp_fun_W_0(findmin_cpq_res(triple(U!5, V!4, W!3)), i(triple(U!5, V!4, W!3))), findmin_cpq_res(triple(U!5, V!4, W!3))))),
% 0.16/0.39 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.16/0.39 tff(107,plain,
% 0.16/0.39 ($false),
% 0.16/0.39 inference(unit_resolution,[status(thm)],[106, 103, 82, 46])).
% 0.16/0.39 % SZS output end Proof
% 0.16/0.39 % E exiting
%------------------------------------------------------------------------------