TSTP Solution File: SWW342+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW342+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 20:58:22 EDT 2022
% Result : Theorem 6.59s 4.86s
% Output : Proof 6.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWW342+1 : TPTP v8.1.0. Released v5.2.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Sep 4 15:00:29 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 6.59/4.86 % SZS status Theorem
% 6.59/4.86 % SZS output start Proof
% 6.59/4.86 tff(v_P_type, type, (
% 6.59/4.86 v_P: ( $i * $i ) > $o)).
% 6.59/4.86 tff(tptp_fun_B_s_H_444_type, type, (
% 6.59/4.86 tptp_fun_B_s_H_444: $i)).
% 6.59/4.86 tff(tptp_fun_B_Z_443_type, type, (
% 6.59/4.86 tptp_fun_B_Z_443: $i)).
% 6.59/4.86 tff(tptp_fun_B_s_442_type, type, (
% 6.59/4.86 tptp_fun_B_s_442: $i)).
% 6.59/4.86 tff(c_Natural_Oevaln_type, type, (
% 6.59/4.86 c_Natural_Oevaln: ( $i * $i * $i * $i ) > $o)).
% 6.59/4.86 tff(v_n_type, type, (
% 6.59/4.86 v_n: $i)).
% 6.59/4.86 tff(c_Com_Ocom_OSKIP_type, type, (
% 6.59/4.86 c_Com_Ocom_OSKIP: $i)).
% 6.59/4.86 tff(1,plain,
% 6.59/4.86 (((~(~v_P(B_Z!443, B_s!442))) & (~((~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)))) <=> (v_P(B_Z!443, B_s!442) & (~((~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))))),
% 6.59/4.86 inference(rewrite,[status(thm)],[])).
% 6.59/4.86 tff(2,plain,
% 6.59/4.86 ((~![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))))),
% 6.59/4.86 inference(rewrite,[status(thm)],[])).
% 6.59/4.86 tff(3,plain,
% 6.59/4.86 ((~![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))))),
% 6.59/4.86 inference(rewrite,[status(thm)],[])).
% 6.59/4.86 tff(4,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')).
% 6.59/4.86 tff(5,plain,
% 6.59/4.86 (~![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)))),
% 6.59/4.86 inference(modus_ponens,[status(thm)],[4, 3])).
% 6.59/4.86 tff(6,plain,
% 6.59/4.86 (~![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)))),
% 6.59/4.86 inference(modus_ponens,[status(thm)],[5, 2])).
% 6.59/4.86 tff(7,plain,
% 6.59/4.86 (~![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)))),
% 6.59/4.86 inference(modus_ponens,[status(thm)],[6, 2])).
% 6.59/4.86 tff(8,plain,
% 6.59/4.86 (~![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)))),
% 6.59/4.86 inference(modus_ponens,[status(thm)],[7, 2])).
% 6.59/4.86 tff(9,plain,
% 6.59/4.86 (~![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)))),
% 6.59/4.86 inference(modus_ponens,[status(thm)],[8, 2])).
% 6.59/4.86 tff(10,plain,
% 6.59/4.86 (~![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)))),
% 6.59/4.86 inference(modus_ponens,[status(thm)],[9, 2])).
% 6.59/4.86 tff(11,plain,
% 6.59/4.86 (~![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)))),
% 6.59/4.86 inference(modus_ponens,[status(thm)],[10, 2])).
% 6.59/4.86 tff(12,plain,
% 6.59/4.86 (~![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)))),
% 6.59/4.86 inference(modus_ponens,[status(thm)],[11, 2])).
% 6.59/4.86 tff(13,plain,
% 6.59/4.86 (~![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)))),
% 6.59/4.86 inference(modus_ponens,[status(thm)],[12, 2])).
% 6.59/4.86 tff(14,plain,
% 6.59/4.86 (~![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)))),
% 6.59/4.86 inference(modus_ponens,[status(thm)],[13, 2])).
% 6.59/4.86 tff(15,plain,
% 6.59/4.86 (v_P(B_Z!443, B_s!442) & (~((~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)))),
% 6.59/4.86 inference(modus_ponens,[status(thm)],[14, 1])).
% 6.59/4.86 tff(16,plain,
% 6.59/4.86 (~((~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))),
% 6.59/4.86 inference(and_elim,[status(thm)],[15])).
% 6.59/4.86 tff(17,plain,
% 6.59/4.86 (c_Natural_Oevaln(c_Com_Ocom_OSKIP, B_s!442, v_n, B_s_H!444)),
% 6.97/5.27 inference(or_elim,[status(thm)],[16])).
% 6.97/5.27 tff(18,plain,
% 6.97/5.27 (^[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)))),
% 6.97/5.27 inference(bind,[status(th)],[])).
% 6.97/5.27 tff(19,plain,
% 6.97/5.27 (![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))),
% 6.97/5.27 inference(quant_intro,[status(thm)],[18])).
% 6.97/5.27 tff(20,plain,
% 6.97/5.27 (![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))),
% 6.97/5.27 inference(rewrite,[status(thm)],[])).
% 6.97/5.27 tff(21,plain,
% 6.97/5.27 (^[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)))),
% 6.97/5.27 inference(bind,[status(th)],[])).
% 6.97/5.27 tff(22,plain,
% 6.97/5.27 (![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))),
% 6.97/5.27 inference(quant_intro,[status(thm)],[21])).
% 6.97/5.27 tff(23,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')).
% 6.97/5.27 tff(24,plain,
% 6.97/5.27 (![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))),
% 6.97/5.27 inference(modus_ponens,[status(thm)],[23, 22])).
% 6.97/5.27 tff(25,plain,
% 6.97/5.27 (![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))),
% 6.97/5.27 inference(modus_ponens,[status(thm)],[24, 20])).
% 6.97/5.27 tff(26,plain,(
% 6.97/5.27 ![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))),
% 6.97/5.27 inference(skolemize,[status(sab)],[25])).
% 6.97/5.27 tff(27,plain,
% 6.97/5.27 (![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))),
% 6.97/5.27 inference(modus_ponens,[status(thm)],[26, 19])).
% 6.97/5.27 tff(28,plain,
% 6.97/5.27 (((~![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))),
% 6.97/5.27 inference(rewrite,[status(thm)],[])).
% 6.97/5.27 tff(29,plain,
% 6.97/5.27 ((~![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))),
% 6.97/5.27 inference(quant_inst,[status(thm)],[])).
% 6.97/5.27 tff(30,plain,
% 6.97/5.27 ((~![V_t: $i, V_n: $i, V_s: $i] : ((~c_Natural_Oevaln(c_Com_Ocom_OSKIP, V_s, V_n, V_t)) | (V_t = V_s))) | (~c_Natural_Oevaln(c_Com_Ocom_OSKIP, B_s!442, v_n, B_s_H!444)) | (B_s_H!444 = B_s!442)),
% 6.97/5.27 inference(modus_ponens,[status(thm)],[29, 28])).
% 6.97/5.27 tff(31,plain,
% 6.97/5.27 (B_s_H!444 = B_s!442),
% 6.97/5.27 inference(unit_resolution,[status(thm)],[30, 27, 17])).
% 6.97/5.27 tff(32,plain,
% 6.97/5.27 (v_P(B_Z!443, B_s_H!444) <=> v_P(B_Z!443, B_s!442)),
% 6.97/5.27 inference(monotonicity,[status(thm)],[31])).
% 6.97/5.27 tff(33,plain,
% 6.97/5.27 (v_P(B_Z!443, B_s!442) <=> v_P(B_Z!443, B_s_H!444)),
% 6.97/5.27 inference(symmetry,[status(thm)],[32])).
% 6.97/5.27 tff(34,plain,
% 6.97/5.27 (v_P(B_Z!443, B_s!442)),
% 6.97/5.27 inference(and_elim,[status(thm)],[15])).
% 6.97/5.27 tff(35,plain,
% 6.97/5.27 (v_P(B_Z!443, B_s_H!444)),
% 6.97/5.27 inference(modus_ponens,[status(thm)],[34, 33])).
% 6.97/5.27 tff(36,plain,
% 6.97/5.27 (~v_P(B_Z!443, B_s_H!444)),
% 6.97/5.27 inference(or_elim,[status(thm)],[16])).
% 6.97/5.27 tff(37,plain,
% 6.97/5.27 ($false),
% 6.97/5.27 inference(unit_resolution,[status(thm)],[36, 35])).
% 6.97/5.27 % SZS output end Proof
%------------------------------------------------------------------------------