TSTP Solution File: SWW302+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW302+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.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 20:58:15 EDT 2022
% Result : Theorem 4.56s 3.52s
% Output : Proof 4.98s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SWW302+1 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n024.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 : Sun Sep 4 14:22:18 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 4.56/3.52 % SZS status Theorem
% 4.56/3.52 % SZS output start Proof
% 4.56/3.52 tff(v_Q_H_type, type, (
% 4.56/3.52 v_Q_H: ( $i * $i ) > $o)).
% 4.56/3.52 tff(tptp_fun_B_s_H_513_type, type, (
% 4.56/3.52 tptp_fun_B_s_H_513: $i)).
% 4.56/3.52 tff(tptp_fun_B_Z_512_type, type, (
% 4.56/3.52 tptp_fun_B_Z_512: $i)).
% 4.56/3.52 tff(v_Q_type, type, (
% 4.56/3.52 v_Q: ( $i * $i ) > $o)).
% 4.56/3.52 tff(v_P_type, type, (
% 4.56/3.52 v_P: ( $i * $i ) > $o)).
% 4.56/3.52 tff(tptp_fun_B_s_511_type, type, (
% 4.56/3.52 tptp_fun_B_s_511: $i)).
% 4.56/3.52 tff(1,plain,
% 4.56/3.52 ((v_P(B_Z!512, B_s!511) & (![B_Z_H: $i] : ((~v_P(B_Z_H, B_s!511)) | v_Q_H(B_Z_H, B_s_H!513)) & (~v_Q(B_Z!512, B_s_H!513)))) <=> (v_P(B_Z!512, B_s!511) & ![B_Z_H: $i] : ((~v_P(B_Z_H, B_s!511)) | v_Q_H(B_Z_H, B_s_H!513)) & (~v_Q(B_Z!512, B_s_H!513)))),
% 4.56/3.52 inference(rewrite,[status(thm)],[])).
% 4.56/3.52 tff(2,plain,
% 4.56/3.52 ((![B_Z_H: $i] : ((~v_P(B_Z_H, B_s!511)) | v_Q_H(B_Z_H, B_s_H!513)) & (~v_Q(B_Z!512, B_s_H!513))) <=> (![B_Z_H: $i] : ((~v_P(B_Z_H, B_s!511)) | v_Q_H(B_Z_H, B_s_H!513)) & (~v_Q(B_Z!512, B_s_H!513)))),
% 4.56/3.52 inference(rewrite,[status(thm)],[])).
% 4.56/3.52 tff(3,plain,
% 4.56/3.52 ((~(~v_P(B_Z!512, B_s!511))) <=> v_P(B_Z!512, B_s!511)),
% 4.56/3.52 inference(rewrite,[status(thm)],[])).
% 4.56/3.52 tff(4,plain,
% 4.56/3.52 (((~(~v_P(B_Z!512, B_s!511))) & (![B_Z_H: $i] : ((~v_P(B_Z_H, B_s!511)) | v_Q_H(B_Z_H, B_s_H!513)) & (~v_Q(B_Z!512, B_s_H!513)))) <=> (v_P(B_Z!512, B_s!511) & (![B_Z_H: $i] : ((~v_P(B_Z_H, B_s!511)) | v_Q_H(B_Z_H, B_s_H!513)) & (~v_Q(B_Z!512, B_s_H!513))))),
% 4.56/3.52 inference(monotonicity,[status(thm)],[3, 2])).
% 4.56/3.52 tff(5,plain,
% 4.56/3.52 (((~(~v_P(B_Z!512, B_s!511))) & (![B_Z_H: $i] : ((~v_P(B_Z_H, B_s!511)) | v_Q_H(B_Z_H, B_s_H!513)) & (~v_Q(B_Z!512, B_s_H!513)))) <=> (v_P(B_Z!512, B_s!511) & ![B_Z_H: $i] : ((~v_P(B_Z_H, B_s!511)) | v_Q_H(B_Z_H, B_s_H!513)) & (~v_Q(B_Z!512, B_s_H!513)))),
% 4.56/3.52 inference(transitivity,[status(thm)],[4, 1])).
% 4.56/3.52 tff(6,plain,
% 4.56/3.52 ((~![B_Z: $i, B_s: $i] : ((~v_P(B_Z, B_s)) | ![B_s_H: $i] : ((~![B_Z_H: $i] : ((~v_P(B_Z_H, B_s)) | v_Q_H(B_Z_H, B_s_H))) | v_Q(B_Z, B_s_H)))) <=> (~![B_Z: $i, B_s: $i] : ((~v_P(B_Z, B_s)) | ![B_s_H: $i] : ((~![B_Z_H: $i] : ((~v_P(B_Z_H, B_s)) | v_Q_H(B_Z_H, B_s_H))) | v_Q(B_Z, B_s_H))))),
% 4.56/3.52 inference(rewrite,[status(thm)],[])).
% 4.56/3.52 tff(7,plain,
% 4.56/3.52 ((~![B_Z: $i, B_s: $i] : (v_P(B_Z, B_s) => ![B_s_H: $i] : (![B_Z_H: $i] : (v_P(B_Z_H, B_s) => v_Q_H(B_Z_H, B_s_H)) => v_Q(B_Z, B_s_H)))) <=> (~![B_Z: $i, B_s: $i] : ((~v_P(B_Z, B_s)) | ![B_s_H: $i] : ((~![B_Z_H: $i] : ((~v_P(B_Z_H, B_s)) | v_Q_H(B_Z_H, B_s_H))) | v_Q(B_Z, B_s_H))))),
% 4.56/3.52 inference(rewrite,[status(thm)],[])).
% 4.56/3.52 tff(8,axiom,(~![B_Z: $i, B_s: $i] : (v_P(B_Z, B_s) => ![B_s_H: $i] : (![B_Z_H: $i] : (v_P(B_Z_H, B_s) => v_Q_H(B_Z_H, B_s_H)) => v_Q(B_Z, B_s_H)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conj_1')).
% 4.56/3.52 tff(9,plain,
% 4.56/3.52 (~![B_Z: $i, B_s: $i] : ((~v_P(B_Z, B_s)) | ![B_s_H: $i] : ((~![B_Z_H: $i] : ((~v_P(B_Z_H, B_s)) | v_Q_H(B_Z_H, B_s_H))) | v_Q(B_Z, B_s_H)))),
% 4.56/3.52 inference(modus_ponens,[status(thm)],[8, 7])).
% 4.56/3.52 tff(10,plain,
% 4.56/3.52 (~![B_Z: $i, B_s: $i] : ((~v_P(B_Z, B_s)) | ![B_s_H: $i] : ((~![B_Z_H: $i] : ((~v_P(B_Z_H, B_s)) | v_Q_H(B_Z_H, B_s_H))) | v_Q(B_Z, B_s_H)))),
% 4.56/3.52 inference(modus_ponens,[status(thm)],[9, 6])).
% 4.56/3.52 tff(11,plain,
% 4.56/3.52 (~![B_Z: $i, B_s: $i] : ((~v_P(B_Z, B_s)) | ![B_s_H: $i] : ((~![B_Z_H: $i] : ((~v_P(B_Z_H, B_s)) | v_Q_H(B_Z_H, B_s_H))) | v_Q(B_Z, B_s_H)))),
% 4.56/3.52 inference(modus_ponens,[status(thm)],[10, 6])).
% 4.56/3.52 tff(12,plain,
% 4.56/3.52 (~![B_Z: $i, B_s: $i] : ((~v_P(B_Z, B_s)) | ![B_s_H: $i] : ((~![B_Z_H: $i] : ((~v_P(B_Z_H, B_s)) | v_Q_H(B_Z_H, B_s_H))) | v_Q(B_Z, B_s_H)))),
% 4.56/3.52 inference(modus_ponens,[status(thm)],[11, 6])).
% 4.56/3.52 tff(13,plain,
% 4.56/3.52 (~![B_Z: $i, B_s: $i] : ((~v_P(B_Z, B_s)) | ![B_s_H: $i] : ((~![B_Z_H: $i] : ((~v_P(B_Z_H, B_s)) | v_Q_H(B_Z_H, B_s_H))) | v_Q(B_Z, B_s_H)))),
% 4.56/3.52 inference(modus_ponens,[status(thm)],[12, 6])).
% 4.56/3.52 tff(14,plain,
% 4.56/3.52 (~![B_Z: $i, B_s: $i] : ((~v_P(B_Z, B_s)) | ![B_s_H: $i] : ((~![B_Z_H: $i] : ((~v_P(B_Z_H, B_s)) | v_Q_H(B_Z_H, B_s_H))) | v_Q(B_Z, B_s_H)))),
% 4.56/3.52 inference(modus_ponens,[status(thm)],[13, 6])).
% 4.56/3.52 tff(15,plain,
% 4.56/3.52 (~![B_Z: $i, B_s: $i] : ((~v_P(B_Z, B_s)) | ![B_s_H: $i] : ((~![B_Z_H: $i] : ((~v_P(B_Z_H, B_s)) | v_Q_H(B_Z_H, B_s_H))) | v_Q(B_Z, B_s_H)))),
% 4.56/3.52 inference(modus_ponens,[status(thm)],[14, 6])).
% 4.56/3.52 tff(16,plain,
% 4.56/3.52 (~![B_Z: $i, B_s: $i] : ((~v_P(B_Z, B_s)) | ![B_s_H: $i] : ((~![B_Z_H: $i] : ((~v_P(B_Z_H, B_s)) | v_Q_H(B_Z_H, B_s_H))) | v_Q(B_Z, B_s_H)))),
% 4.56/3.52 inference(modus_ponens,[status(thm)],[15, 6])).
% 4.56/3.52 tff(17,plain,
% 4.56/3.52 (~![B_Z: $i, B_s: $i] : ((~v_P(B_Z, B_s)) | ![B_s_H: $i] : ((~![B_Z_H: $i] : ((~v_P(B_Z_H, B_s)) | v_Q_H(B_Z_H, B_s_H))) | v_Q(B_Z, B_s_H)))),
% 4.56/3.52 inference(modus_ponens,[status(thm)],[16, 6])).
% 4.56/3.52 tff(18,plain,
% 4.56/3.52 (~![B_Z: $i, B_s: $i] : ((~v_P(B_Z, B_s)) | ![B_s_H: $i] : ((~![B_Z_H: $i] : ((~v_P(B_Z_H, B_s)) | v_Q_H(B_Z_H, B_s_H))) | v_Q(B_Z, B_s_H)))),
% 4.56/3.52 inference(modus_ponens,[status(thm)],[17, 6])).
% 4.56/3.52 tff(19,plain,
% 4.56/3.52 (v_P(B_Z!512, B_s!511) & ![B_Z_H: $i] : ((~v_P(B_Z_H, B_s!511)) | v_Q_H(B_Z_H, B_s_H!513)) & (~v_Q(B_Z!512, B_s_H!513))),
% 4.56/3.52 inference(modus_ponens,[status(thm)],[18, 5])).
% 4.56/3.52 tff(20,plain,
% 4.56/3.52 (~v_Q(B_Z!512, B_s_H!513)),
% 4.56/3.52 inference(and_elim,[status(thm)],[19])).
% 4.56/3.52 tff(21,plain,
% 4.56/3.52 (^[B_Z: $i, B_s: $i] : refl(((~v_Q_H(B_Z, B_s)) | v_Q(B_Z, B_s)) <=> ((~v_Q_H(B_Z, B_s)) | v_Q(B_Z, B_s)))),
% 4.56/3.52 inference(bind,[status(th)],[])).
% 4.56/3.52 tff(22,plain,
% 4.56/3.52 (![B_Z: $i, B_s: $i] : ((~v_Q_H(B_Z, B_s)) | v_Q(B_Z, B_s)) <=> ![B_Z: $i, B_s: $i] : ((~v_Q_H(B_Z, B_s)) | v_Q(B_Z, B_s))),
% 4.56/3.52 inference(quant_intro,[status(thm)],[21])).
% 4.56/3.52 tff(23,plain,
% 4.56/3.52 (![B_Z: $i, B_s: $i] : ((~v_Q_H(B_Z, B_s)) | v_Q(B_Z, B_s)) <=> ![B_Z: $i, B_s: $i] : ((~v_Q_H(B_Z, B_s)) | v_Q(B_Z, B_s))),
% 4.56/3.52 inference(rewrite,[status(thm)],[])).
% 4.56/3.52 tff(24,plain,
% 4.56/3.52 (^[B_Z: $i, B_s: $i] : rewrite((v_Q_H(B_Z, B_s) => v_Q(B_Z, B_s)) <=> ((~v_Q_H(B_Z, B_s)) | v_Q(B_Z, B_s)))),
% 4.56/3.52 inference(bind,[status(th)],[])).
% 4.56/3.52 tff(25,plain,
% 4.56/3.52 (![B_Z: $i, B_s: $i] : (v_Q_H(B_Z, B_s) => v_Q(B_Z, B_s)) <=> ![B_Z: $i, B_s: $i] : ((~v_Q_H(B_Z, B_s)) | v_Q(B_Z, B_s))),
% 4.56/3.52 inference(quant_intro,[status(thm)],[24])).
% 4.56/3.52 tff(26,axiom,(![B_Z: $i, B_s: $i] : (v_Q_H(B_Z, B_s) => v_Q(B_Z, B_s))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conj_0')).
% 4.56/3.52 tff(27,plain,
% 4.56/3.52 (![B_Z: $i, B_s: $i] : ((~v_Q_H(B_Z, B_s)) | v_Q(B_Z, B_s))),
% 4.56/3.52 inference(modus_ponens,[status(thm)],[26, 25])).
% 4.56/3.52 tff(28,plain,
% 4.56/3.52 (![B_Z: $i, B_s: $i] : ((~v_Q_H(B_Z, B_s)) | v_Q(B_Z, B_s))),
% 4.56/3.52 inference(modus_ponens,[status(thm)],[27, 23])).
% 4.56/3.52 tff(29,plain,(
% 4.56/3.52 ![B_Z: $i, B_s: $i] : ((~v_Q_H(B_Z, B_s)) | v_Q(B_Z, B_s))),
% 4.56/3.52 inference(skolemize,[status(sab)],[28])).
% 4.56/3.52 tff(30,plain,
% 4.56/3.52 (![B_Z: $i, B_s: $i] : ((~v_Q_H(B_Z, B_s)) | v_Q(B_Z, B_s))),
% 4.56/3.52 inference(modus_ponens,[status(thm)],[29, 22])).
% 4.56/3.52 tff(31,plain,
% 4.56/3.52 (((~![B_Z: $i, B_s: $i] : ((~v_Q_H(B_Z, B_s)) | v_Q(B_Z, B_s))) | ((~v_Q_H(B_Z!512, B_s_H!513)) | v_Q(B_Z!512, B_s_H!513))) <=> ((~![B_Z: $i, B_s: $i] : ((~v_Q_H(B_Z, B_s)) | v_Q(B_Z, B_s))) | (~v_Q_H(B_Z!512, B_s_H!513)) | v_Q(B_Z!512, B_s_H!513))),
% 4.56/3.52 inference(rewrite,[status(thm)],[])).
% 4.56/3.52 tff(32,plain,
% 4.56/3.52 ((~![B_Z: $i, B_s: $i] : ((~v_Q_H(B_Z, B_s)) | v_Q(B_Z, B_s))) | ((~v_Q_H(B_Z!512, B_s_H!513)) | v_Q(B_Z!512, B_s_H!513))),
% 4.56/3.52 inference(quant_inst,[status(thm)],[])).
% 4.56/3.52 tff(33,plain,
% 4.56/3.52 ((~![B_Z: $i, B_s: $i] : ((~v_Q_H(B_Z, B_s)) | v_Q(B_Z, B_s))) | (~v_Q_H(B_Z!512, B_s_H!513)) | v_Q(B_Z!512, B_s_H!513)),
% 4.56/3.52 inference(modus_ponens,[status(thm)],[32, 31])).
% 4.56/3.52 tff(34,plain,
% 4.56/3.52 (~v_Q_H(B_Z!512, B_s_H!513)),
% 4.56/3.52 inference(unit_resolution,[status(thm)],[33, 30, 20])).
% 4.56/3.52 tff(35,plain,
% 4.56/3.52 (^[B_Z_H: $i] : refl(((~v_P(B_Z_H, B_s!511)) | v_Q_H(B_Z_H, B_s_H!513)) <=> ((~v_P(B_Z_H, B_s!511)) | v_Q_H(B_Z_H, B_s_H!513)))),
% 4.56/3.52 inference(bind,[status(th)],[])).
% 4.56/3.52 tff(36,plain,
% 4.56/3.52 (![B_Z_H: $i] : ((~v_P(B_Z_H, B_s!511)) | v_Q_H(B_Z_H, B_s_H!513)) <=> ![B_Z_H: $i] : ((~v_P(B_Z_H, B_s!511)) | v_Q_H(B_Z_H, B_s_H!513))),
% 4.56/3.52 inference(quant_intro,[status(thm)],[35])).
% 4.56/3.52 tff(37,plain,
% 4.56/3.52 (![B_Z_H: $i] : ((~v_P(B_Z_H, B_s!511)) | v_Q_H(B_Z_H, B_s_H!513))),
% 4.56/3.52 inference(and_elim,[status(thm)],[19])).
% 4.56/3.52 tff(38,plain,
% 4.56/3.52 (![B_Z_H: $i] : ((~v_P(B_Z_H, B_s!511)) | v_Q_H(B_Z_H, B_s_H!513))),
% 4.56/3.52 inference(modus_ponens,[status(thm)],[37, 36])).
% 4.56/3.52 tff(39,plain,
% 4.56/3.52 (v_P(B_Z!512, B_s!511)),
% 4.56/3.52 inference(and_elim,[status(thm)],[19])).
% 4.56/3.52 tff(40,plain,
% 4.56/3.52 (((~![B_Z_H: $i] : ((~v_P(B_Z_H, B_s!511)) | v_Q_H(B_Z_H, B_s_H!513))) | ((~v_P(B_Z!512, B_s!511)) | v_Q_H(B_Z!512, B_s_H!513))) <=> ((~![B_Z_H: $i] : ((~v_P(B_Z_H, B_s!511)) | v_Q_H(B_Z_H, B_s_H!513))) | (~v_P(B_Z!512, B_s!511)) | v_Q_H(B_Z!512, B_s_H!513))),
% 4.98/3.93 inference(rewrite,[status(thm)],[])).
% 4.98/3.93 tff(41,plain,
% 4.98/3.93 ((~![B_Z_H: $i] : ((~v_P(B_Z_H, B_s!511)) | v_Q_H(B_Z_H, B_s_H!513))) | ((~v_P(B_Z!512, B_s!511)) | v_Q_H(B_Z!512, B_s_H!513))),
% 4.98/3.93 inference(quant_inst,[status(thm)],[])).
% 4.98/3.93 tff(42,plain,
% 4.98/3.93 ((~![B_Z_H: $i] : ((~v_P(B_Z_H, B_s!511)) | v_Q_H(B_Z_H, B_s_H!513))) | (~v_P(B_Z!512, B_s!511)) | v_Q_H(B_Z!512, B_s_H!513)),
% 4.98/3.93 inference(modus_ponens,[status(thm)],[41, 40])).
% 4.98/3.93 tff(43,plain,
% 4.98/3.93 ($false),
% 4.98/3.93 inference(unit_resolution,[status(thm)],[42, 39, 38, 34])).
% 4.98/3.93 % SZS output end Proof
%------------------------------------------------------------------------------