%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWW342+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:36:51 AM UTC 2025
% Result : Theorem 13.93s 14.13s
% Output : Proof 14.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.11 % Problem : SWW342+1 : TPTP v9.0.0. Released v5.2.0.
% 0.01/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n005.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 11:30:20 EDT 2025
% 0.11/0.32 % CPUTime :
% 13.93/14.13 % SZS status Theorem
% 13.93/14.13 % SZS output start Proof
% 13.93/14.13 tff(v_P_type, type, (
% 13.93/14.13 v_P: ( $i * $i ) > $o)).
% 13.93/14.13 tff(tptp_fun_B_s_H_444_type, type, (
% 13.93/14.13 tptp_fun_B_s_H_444: $i)).
% 13.93/14.13 tff(tptp_fun_B_Z_443_type, type, (
% 13.93/14.13 tptp_fun_B_Z_443: $i)).
% 13.93/14.13 tff(tptp_fun_B_s_442_type, type, (
% 13.93/14.13 tptp_fun_B_s_442: $i)).
% 13.93/14.13 tff(c_Natural_Oevaln_type, type, (
% 13.93/14.13 c_Natural_Oevaln: ( $i * $i * $i * $i ) > $o)).
% 13.93/14.13 tff(v_n_type, type, (
% 13.93/14.13 v_n: $i)).
% 13.93/14.13 tff(c_Com_Ocom_OSKIP_type, type, (
% 13.93/14.13 c_Com_Ocom_OSKIP: $i)).
% 13.93/14.13 tff(1,plain,
% 13.93/14.13 ((~![B_Z: $i, B_s: $i] : ((~v_P(B_Z, B_s)) | ![B_s_H: $i] : ((~c_Natural_Oevaln(c_Com_Ocom_OSKIP, B_s, v_n, B_s_H)) | v_P(B_Z, B_s_H)))) <=> (~![B_Z: $i, B_s: $i] : ((~v_P(B_Z, B_s)) | ![B_s_H: $i] : ((~c_Natural_Oevaln(c_Com_Ocom_OSKIP, B_s, v_n, B_s_H)) | v_P(B_Z, B_s_H))))),
% 13.93/14.13 inference(rewrite,[status(thm)],[])).
% 13.93/14.13 tff(2,plain,
% 13.93/14.13 ((~![B_Z: $i, B_s: $i] : (v_P(B_Z, B_s) => ![B_s_H: $i] : (c_Natural_Oevaln(c_Com_Ocom_OSKIP, B_s, v_n, B_s_H) => v_P(B_Z, B_s_H)))) <=> (~![B_Z: $i, B_s: $i] : ((~v_P(B_Z, B_s)) | ![B_s_H: $i] : ((~c_Natural_Oevaln(c_Com_Ocom_OSKIP, B_s, v_n, B_s_H)) | v_P(B_Z, B_s_H))))),
% 13.93/14.13 inference(rewrite,[status(thm)],[])).
% 13.93/14.13 tff(3,axiom,(~![B_Z: $i, B_s: $i] : (v_P(B_Z, B_s) => ![B_s_H: $i] : (c_Natural_Oevaln(c_Com_Ocom_OSKIP, B_s, v_n, B_s_H) => v_P(B_Z, B_s_H)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conj_1')).
% 13.93/14.13 tff(4,plain,
% 13.93/14.13 (~![B_Z: $i, B_s: $i] : ((~v_P(B_Z, B_s)) | ![B_s_H: $i] : ((~c_Natural_Oevaln(c_Com_Ocom_OSKIP, B_s, v_n, B_s_H)) | v_P(B_Z, B_s_H)))),
% 13.93/14.13 inference(modus_ponens,[status(thm)],[3, 2])).
% 13.93/14.13 tff(5,plain,
% 13.93/14.13 (~![B_Z: $i, B_s: $i] : ((~v_P(B_Z, B_s)) | ![B_s_H: $i] : ((~c_Natural_Oevaln(c_Com_Ocom_OSKIP, B_s, v_n, B_s_H)) | v_P(B_Z, B_s_H)))),
% 13.93/14.13 inference(modus_ponens,[status(thm)],[4, 1])).
% 13.93/14.13 tff(6,plain,
% 13.93/14.13 (~![B_Z: $i, B_s: $i] : ((~v_P(B_Z, B_s)) | ![B_s_H: $i] : ((~c_Natural_Oevaln(c_Com_Ocom_OSKIP, B_s, v_n, B_s_H)) | v_P(B_Z, B_s_H)))),
% 13.93/14.13 inference(modus_ponens,[status(thm)],[5, 1])).
% 13.93/14.13 tff(7,plain,
% 13.93/14.13 (~![B_Z: $i, B_s: $i] : ((~v_P(B_Z, B_s)) | ![B_s_H: $i] : ((~c_Natural_Oevaln(c_Com_Ocom_OSKIP, B_s, v_n, B_s_H)) | v_P(B_Z, B_s_H)))),
% 13.93/14.13 inference(modus_ponens,[status(thm)],[6, 1])).
% 13.93/14.13 tff(8,plain,
% 13.93/14.13 (~((~c_Natural_Oevaln(c_Com_Ocom_OSKIP, B_s!442, v_n, B_s_H!444)) | v_P(B_Z!443, B_s_H!444))),
% 13.93/14.13 inference(and_elim,[status(thm)],[7])).
% 13.93/14.13 tff(9,plain,
% 13.93/14.13 (c_Natural_Oevaln(c_Com_Ocom_OSKIP, B_s!442, v_n, B_s_H!444)),
% 13.93/14.13 inference(or_elim,[status(thm)],[8])).
% 13.93/14.13 tff(10,plain,
% 13.93/14.13 (^[V_t: $i, V_n: $i, V_s: $i] : refl(((~c_Natural_Oevaln(c_Com_Ocom_OSKIP, V_s, V_n, V_t)) | (V_t = V_s)) <=> ((~c_Natural_Oevaln(c_Com_Ocom_OSKIP, V_s, V_n, V_t)) | (V_t = V_s)))),
% 13.93/14.13 inference(bind,[status(th)],[])).
% 13.93/14.13 tff(11,plain,
% 13.93/14.13 (![V_t: $i, V_n: $i, V_s: $i] : ((~c_Natural_Oevaln(c_Com_Ocom_OSKIP, V_s, V_n, V_t)) | (V_t = V_s)) <=> ![V_t: $i, V_n: $i, V_s: $i] : ((~c_Natural_Oevaln(c_Com_Ocom_OSKIP, V_s, V_n, V_t)) | (V_t = V_s))),
% 13.93/14.13 inference(quant_intro,[status(thm)],[10])).
% 13.93/14.13 tff(12,plain,
% 13.93/14.13 (![V_t: $i, V_n: $i, V_s: $i] : ((~c_Natural_Oevaln(c_Com_Ocom_OSKIP, V_s, V_n, V_t)) | (V_t = V_s)) <=> ![V_t: $i, V_n: $i, V_s: $i] : ((~c_Natural_Oevaln(c_Com_Ocom_OSKIP, V_s, V_n, V_t)) | (V_t = V_s))),
% 13.93/14.13 inference(rewrite,[status(thm)],[])).
% 13.93/14.13 tff(13,plain,
% 13.93/14.13 (^[V_t: $i, V_n: $i, V_s: $i] : rewrite((c_Natural_Oevaln(c_Com_Ocom_OSKIP, V_s, V_n, V_t) => (V_t = V_s)) <=> ((~c_Natural_Oevaln(c_Com_Ocom_OSKIP, V_s, V_n, V_t)) | (V_t = V_s)))),
% 13.93/14.13 inference(bind,[status(th)],[])).
% 13.93/14.13 tff(14,plain,
% 13.93/14.13 (![V_t: $i, V_n: $i, V_s: $i] : (c_Natural_Oevaln(c_Com_Ocom_OSKIP, V_s, V_n, V_t) => (V_t = V_s)) <=> ![V_t: $i, V_n: $i, V_s: $i] : ((~c_Natural_Oevaln(c_Com_Ocom_OSKIP, V_s, V_n, V_t)) | (V_t = V_s))),
% 13.93/14.13 inference(quant_intro,[status(thm)],[13])).
% 13.93/14.13 tff(15,axiom,(![V_t: $i, V_n: $i, V_s: $i] : (c_Natural_Oevaln(c_Com_Ocom_OSKIP, V_s, V_n, V_t) => (V_t = V_s))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fact_evaln__elim__cases_I1_J')).
% 13.93/14.13 tff(16,plain,
% 13.93/14.13 (![V_t: $i, V_n: $i, V_s: $i] : ((~c_Natural_Oevaln(c_Com_Ocom_OSKIP, V_s, V_n, V_t)) | (V_t = V_s))),
% 13.93/14.13 inference(modus_ponens,[status(thm)],[15, 14])).
% 14.37/14.57 tff(17,plain,
% 14.37/14.57 (![V_t: $i, V_n: $i, V_s: $i] : ((~c_Natural_Oevaln(c_Com_Ocom_OSKIP, V_s, V_n, V_t)) | (V_t = V_s))),
% 14.37/14.57 inference(modus_ponens,[status(thm)],[16, 12])).
% 14.37/14.57 tff(18,plain,(
% 14.37/14.57 ![V_t: $i, V_n: $i, V_s: $i] : ((~c_Natural_Oevaln(c_Com_Ocom_OSKIP, V_s, V_n, V_t)) | (V_t = V_s))),
% 14.37/14.57 inference(skolemize,[status(sab)],[17])).
% 14.37/14.57 tff(19,plain,
% 14.37/14.57 (![V_t: $i, V_n: $i, V_s: $i] : ((~c_Natural_Oevaln(c_Com_Ocom_OSKIP, V_s, V_n, V_t)) | (V_t = V_s))),
% 14.37/14.57 inference(modus_ponens,[status(thm)],[18, 11])).
% 14.37/14.57 tff(20,plain,
% 14.37/14.57 (((~![V_t: $i, V_n: $i, V_s: $i] : ((~c_Natural_Oevaln(c_Com_Ocom_OSKIP, V_s, V_n, V_t)) | (V_t = V_s))) | ((~c_Natural_Oevaln(c_Com_Ocom_OSKIP, B_s!442, v_n, B_s_H!444)) | (B_s_H!444 = B_s!442))) <=> ((~![V_t: $i, V_n: $i, V_s: $i] : ((~c_Natural_Oevaln(c_Com_Ocom_OSKIP, V_s, V_n, V_t)) | (V_t = V_s))) | (~c_Natural_Oevaln(c_Com_Ocom_OSKIP, B_s!442, v_n, B_s_H!444)) | (B_s_H!444 = B_s!442))),
% 14.37/14.57 inference(rewrite,[status(thm)],[])).
% 14.37/14.57 tff(21,plain,
% 14.37/14.57 ((~![V_t: $i, V_n: $i, V_s: $i] : ((~c_Natural_Oevaln(c_Com_Ocom_OSKIP, V_s, V_n, V_t)) | (V_t = V_s))) | ((~c_Natural_Oevaln(c_Com_Ocom_OSKIP, B_s!442, v_n, B_s_H!444)) | (B_s_H!444 = B_s!442))),
% 14.37/14.57 inference(quant_inst,[status(thm)],[])).
% 14.37/14.57 tff(22,plain,
% 14.37/14.57 ((~![V_t: $i, V_n: $i, V_s: $i] : ((~c_Natural_Oevaln(c_Com_Ocom_OSKIP, V_s, V_n, V_t)) | (V_t = V_s))) | (~c_Natural_Oevaln(c_Com_Ocom_OSKIP, B_s!442, v_n, B_s_H!444)) | (B_s_H!444 = B_s!442)),
% 14.37/14.57 inference(modus_ponens,[status(thm)],[21, 20])).
% 14.37/14.57 tff(23,plain,
% 14.37/14.57 (B_s_H!444 = B_s!442),
% 14.37/14.57 inference(unit_resolution,[status(thm)],[22, 19, 9])).
% 14.37/14.57 tff(24,plain,
% 14.37/14.57 (v_P(B_Z!443, B_s_H!444) <=> v_P(B_Z!443, B_s!442)),
% 14.37/14.57 inference(monotonicity,[status(thm)],[23])).
% 14.37/14.57 tff(25,plain,
% 14.37/14.57 (v_P(B_Z!443, B_s!442) <=> v_P(B_Z!443, B_s_H!444)),
% 14.37/14.57 inference(symmetry,[status(thm)],[24])).
% 14.37/14.57 tff(26,plain,
% 14.37/14.57 (v_P(B_Z!443, B_s!442)),
% 14.37/14.57 inference(and_elim,[status(thm)],[7])).
% 14.37/14.57 tff(27,plain,
% 14.37/14.57 (v_P(B_Z!443, B_s_H!444)),
% 14.37/14.57 inference(modus_ponens,[status(thm)],[26, 25])).
% 14.37/14.57 tff(28,plain,
% 14.37/14.57 (~v_P(B_Z!443, B_s_H!444)),
% 14.37/14.57 inference(or_elim,[status(thm)],[8])).
% 14.37/14.57 tff(29,plain,
% 14.37/14.57 ($false),
% 14.37/14.57 inference(unit_resolution,[status(thm)],[28, 27])).
% 14.37/14.57 % SZS output end Proof
% 14.37/14.59 % E exiting
%------------------------------------------------------------------------------