TSTP Solution File: LCL259-3 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : LCL259-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n020.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  : 600s
% DateTime : Sun Jul 17 14:35:58 EDT 2022

% Result   : Unsatisfiable 234.26s 234.41s
% Output   : Refutation 234.26s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :    9
% Syntax   : Number of clauses     :   69 (  47 unt;   0 nHn;  69 RR)
%            Number of literals    :   94 (   0 equ;  26 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ~ theorem(implies__dfg(implies__dfg(p,implies__dfg(p,q)),implies__dfg(p,q))),
    file('LCL259-3.p',unknown),
    [] ).

cnf(2,axiom,
    axiom(implies__dfg(or__dfg(u,u),u)),
    file('LCL259-3.p',unknown),
    [] ).

cnf(3,axiom,
    axiom(implies__dfg(u,or__dfg(v,u))),
    file('LCL259-3.p',unknown),
    [] ).

cnf(4,axiom,
    axiom(implies__dfg(or__dfg(u,v),or__dfg(v,u))),
    file('LCL259-3.p',unknown),
    [] ).

cnf(5,axiom,
    axiom(implies__dfg(or__dfg(u,or__dfg(v,w)),or__dfg(v,or__dfg(u,w)))),
    file('LCL259-3.p',unknown),
    [] ).

cnf(6,axiom,
    axiom(implies__dfg(implies__dfg(u,v),implies__dfg(or__dfg(w,u),or__dfg(w,v)))),
    file('LCL259-3.p',unknown),
    [] ).

cnf(7,axiom,
    equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)),
    file('LCL259-3.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ axiom(u)
    | theorem(u) ),
    file('LCL259-3.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ theorem(u)
    | ~ theorem(implies__dfg(u,v))
    | theorem(v) ),
    file('LCL259-3.p',unknown),
    [] ).

cnf(15,plain,
    axiom(implies__dfg(or__dfg(u,not__dfg(v)),implies__dfg(v,u))),
    inference(spr,[status(thm),theory(equality)],[7,4]),
    [iquote('0:SpR:7.0,4.0')] ).

cnf(16,plain,
    axiom(implies__dfg(implies__dfg(u,v),or__dfg(v,not__dfg(u)))),
    inference(spr,[status(thm),theory(equality)],[7,4]),
    [iquote('0:SpR:7.0,4.0')] ).

cnf(19,plain,
    ( ~ axiom(implies__dfg(u,v))
    | ~ theorem(u)
    | theorem(v) ),
    inference(res,[status(thm),theory(equality)],[8,9]),
    [iquote('0:Res:8.1,9.1')] ).

cnf(20,plain,
    ( ~ theorem(implies__dfg(u,v))
    | theorem(or__dfg(v,not__dfg(u))) ),
    inference(sor,[status(thm)],[19,16]),
    [iquote('0:SoR:19.0,16.0')] ).

cnf(23,plain,
    ( ~ theorem(or__dfg(u,not__dfg(v)))
    | theorem(implies__dfg(v,u)) ),
    inference(sor,[status(thm)],[19,15]),
    [iquote('0:SoR:19.0,15.0')] ).

cnf(25,plain,
    ( ~ theorem(or__dfg(u,v))
    | theorem(or__dfg(v,u)) ),
    inference(sor,[status(thm)],[19,4]),
    [iquote('0:SoR:19.0,4.0')] ).

cnf(26,plain,
    ( ~ theorem(u)
    | theorem(or__dfg(v,u)) ),
    inference(sor,[status(thm)],[19,3]),
    [iquote('0:SoR:19.0,3.0')] ).

cnf(27,plain,
    ( ~ theorem(or__dfg(u,u))
    | theorem(u) ),
    inference(sor,[status(thm)],[19,2]),
    [iquote('0:SoR:19.0,2.0')] ).

cnf(36,plain,
    axiom(implies__dfg(or__dfg(not__dfg(u),or__dfg(v,w)),or__dfg(v,implies__dfg(u,w)))),
    inference(spr,[status(thm),theory(equality)],[7,5]),
    [iquote('0:SpR:7.0,5.0')] ).

cnf(37,plain,
    axiom(implies__dfg(or__dfg(u,or__dfg(not__dfg(v),w)),implies__dfg(v,or__dfg(u,w)))),
    inference(spr,[status(thm),theory(equality)],[7,5]),
    [iquote('0:SpR:7.0,5.0')] ).

cnf(40,plain,
    axiom(implies__dfg(implies__dfg(u,or__dfg(v,w)),or__dfg(v,implies__dfg(u,w)))),
    inference(rew,[status(thm),theory(equality)],[7,36]),
    [iquote('0:Rew:7.0,36.0')] ).

cnf(41,plain,
    axiom(implies__dfg(or__dfg(u,implies__dfg(v,w)),implies__dfg(v,or__dfg(u,w)))),
    inference(rew,[status(thm),theory(equality)],[7,37]),
    [iquote('0:Rew:7.0,37.0')] ).

cnf(48,plain,
    ( ~ theorem(implies__dfg(u,v))
    | theorem(implies__dfg(or__dfg(w,u),or__dfg(w,v))) ),
    inference(sor,[status(thm)],[19,6]),
    [iquote('0:SoR:19.0,6.0')] ).

cnf(49,plain,
    axiom(implies__dfg(implies__dfg(u,v),implies__dfg(or__dfg(not__dfg(w),u),implies__dfg(w,v)))),
    inference(spr,[status(thm),theory(equality)],[7,6]),
    [iquote('0:SpR:7.0,6.0')] ).

cnf(51,plain,
    axiom(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(w,u),implies__dfg(w,v)))),
    inference(rew,[status(thm),theory(equality)],[7,49]),
    [iquote('0:Rew:7.0,49.0')] ).

cnf(60,plain,
    ( ~ axiom(implies__dfg(u,v))
    | theorem(or__dfg(v,not__dfg(u))) ),
    inference(sor,[status(thm)],[20,8]),
    [iquote('0:SoR:20.0,8.1')] ).

cnf(71,plain,
    theorem(or__dfg(or__dfg(u,v),not__dfg(or__dfg(v,u)))),
    inference(sor,[status(thm)],[60,4]),
    [iquote('0:SoR:60.0,4.0')] ).

cnf(72,plain,
    theorem(or__dfg(or__dfg(u,v),not__dfg(v))),
    inference(sor,[status(thm)],[60,3]),
    [iquote('0:SoR:60.0,3.0')] ).

cnf(73,plain,
    theorem(or__dfg(u,not__dfg(or__dfg(u,u)))),
    inference(sor,[status(thm)],[60,2]),
    [iquote('0:SoR:60.0,2.0')] ).

cnf(76,plain,
    ( ~ theorem(implies__dfg(u,or__dfg(v,w)))
    | theorem(or__dfg(v,implies__dfg(u,w))) ),
    inference(sor,[status(thm)],[19,40]),
    [iquote('0:SoR:19.0,40.0')] ).

cnf(87,plain,
    theorem(implies__dfg(u,or__dfg(v,u))),
    inference(sor,[status(thm)],[23,72]),
    [iquote('0:SoR:23.0,72.0')] ).

cnf(94,plain,
    ( ~ theorem(or__dfg(u,implies__dfg(v,w)))
    | theorem(implies__dfg(v,or__dfg(u,w))) ),
    inference(sor,[status(thm)],[19,41]),
    [iquote('0:SoR:19.0,41.0')] ).

cnf(100,plain,
    theorem(implies__dfg(or__dfg(u,u),u)),
    inference(sor,[status(thm)],[23,73]),
    [iquote('0:SoR:23.0,73.0')] ).

cnf(116,plain,
    ( ~ theorem(implies__dfg(u,v))
    | theorem(implies__dfg(implies__dfg(w,u),implies__dfg(w,v))) ),
    inference(sor,[status(thm)],[19,51]),
    [iquote('0:SoR:19.0,51.0')] ).

cnf(119,plain,
    theorem(implies__dfg(or__dfg(u,v),or__dfg(v,u))),
    inference(sor,[status(thm)],[23,71]),
    [iquote('0:SoR:23.0,71.0')] ).

cnf(174,plain,
    ( ~ axiom(implies__dfg(u,v))
    | theorem(implies__dfg(or__dfg(w,u),or__dfg(w,v))) ),
    inference(sor,[status(thm)],[48,8]),
    [iquote('0:SoR:48.0,8.1')] ).

cnf(190,plain,
    theorem(or__dfg(u,implies__dfg(v,v))),
    inference(sor,[status(thm)],[76,87]),
    [iquote('0:SoR:76.0,87.0')] ).

cnf(192,plain,
    theorem(implies__dfg(u,u)),
    inference(sor,[status(thm)],[27,190]),
    [iquote('0:SoR:27.0,190.0')] ).

cnf(196,plain,
    theorem(or__dfg(u,not__dfg(u))),
    inference(sor,[status(thm)],[20,192]),
    [iquote('0:SoR:20.0,192.0')] ).

cnf(197,plain,
    theorem(or__dfg(u,implies__dfg(or__dfg(u,v),v))),
    inference(sor,[status(thm)],[76,192]),
    [iquote('0:SoR:76.0,192.0')] ).

cnf(201,plain,
    theorem(implies__dfg(u,not__dfg(not__dfg(u)))),
    inference(spr,[status(thm),theory(equality)],[7,196]),
    [iquote('0:SpR:7.0,196.0')] ).

cnf(203,plain,
    theorem(implies__dfg(or__dfg(u,v),or__dfg(u,not__dfg(not__dfg(v))))),
    inference(sor,[status(thm)],[48,201]),
    [iquote('0:SoR:48.0,201.0')] ).

cnf(210,plain,
    ( ~ theorem(implies__dfg(u,v))
    | theorem(implies__dfg(u,or__dfg(w,v))) ),
    inference(sor,[status(thm)],[94,26]),
    [iquote('0:SoR:94.0,26.1')] ).

cnf(232,plain,
    theorem(implies__dfg(implies__dfg(u,or__dfg(v,w)),implies__dfg(u,or__dfg(w,v)))),
    inference(sor,[status(thm)],[116,119]),
    [iquote('0:SoR:116.0,119.0')] ).

cnf(238,plain,
    theorem(implies__dfg(implies__dfg(u,or__dfg(v,v)),implies__dfg(u,v))),
    inference(sor,[status(thm)],[116,100]),
    [iquote('0:SoR:116.0,100.0')] ).

cnf(250,plain,
    theorem(or__dfg(implies__dfg(or__dfg(u,v),v),u)),
    inference(sor,[status(thm)],[25,197]),
    [iquote('0:SoR:25.0,197.0')] ).

cnf(252,plain,
    theorem(or__dfg(not__dfg(u),implies__dfg(implies__dfg(u,v),v))),
    inference(spr,[status(thm),theory(equality)],[7,197]),
    [iquote('0:SpR:7.0,197.0')] ).

cnf(254,plain,
    theorem(implies__dfg(u,implies__dfg(implies__dfg(u,v),v))),
    inference(rew,[status(thm),theory(equality)],[7,252]),
    [iquote('0:Rew:7.0,252.0')] ).

cnf(289,plain,
    ( ~ theorem(u)
    | theorem(implies__dfg(implies__dfg(u,v),v)) ),
    inference(res,[status(thm),theory(equality)],[254,9]),
    [iquote('0:Res:254.0,9.1')] ).

cnf(431,plain,
    theorem(implies__dfg(u,or__dfg(v,or__dfg(w,u)))),
    inference(sor,[status(thm)],[210,87]),
    [iquote('0:SoR:210.0,87.0')] ).

cnf(465,plain,
    theorem(or__dfg(u,implies__dfg(v,or__dfg(w,v)))),
    inference(sor,[status(thm)],[76,431]),
    [iquote('0:SoR:76.0,431.0')] ).

cnf(574,plain,
    theorem(implies__dfg(or__dfg(u,implies__dfg(v,w)),or__dfg(u,implies__dfg(implies__dfg(x,v),implies__dfg(x,w))))),
    inference(sor,[status(thm)],[174,51]),
    [iquote('0:SoR:174.0,51.0')] ).

cnf(690,plain,
    ( ~ theorem(u)
    | ~ theorem(implies__dfg(u,v))
    | theorem(v) ),
    inference(res,[status(thm),theory(equality)],[289,9]),
    [iquote('0:Res:289.1,9.1')] ).

cnf(1374,plain,
    ( ~ theorem(or__dfg(u,v))
    | theorem(or__dfg(u,not__dfg(not__dfg(v)))) ),
    inference(res,[status(thm),theory(equality)],[203,9]),
    [iquote('0:Res:203.0,9.1')] ).

cnf(1524,plain,
    ( ~ theorem(or__dfg(u,implies__dfg(v,w)))
    | theorem(or__dfg(u,implies__dfg(implies__dfg(x,v),implies__dfg(x,w)))) ),
    inference(res,[status(thm),theory(equality)],[574,9]),
    [iquote('0:Res:574.0,9.1')] ).

cnf(1945,plain,
    ( ~ theorem(implies__dfg(u,or__dfg(v,v)))
    | theorem(implies__dfg(u,v)) ),
    inference(sor,[status(thm)],[690,238]),
    [iquote('0:SoR:690.1,238.0')] ).

cnf(3844,plain,
    theorem(or__dfg(u,not__dfg(not__dfg(implies__dfg(v,or__dfg(w,v)))))),
    inference(sor,[status(thm)],[1374,465]),
    [iquote('0:SoR:1374.0,465.0')] ).

cnf(3902,plain,
    theorem(or__dfg(implies__dfg(or__dfg(u,v),v),not__dfg(not__dfg(u)))),
    inference(sor,[status(thm)],[1374,250]),
    [iquote('0:SoR:1374.0,250.0')] ).

cnf(4904,plain,
    theorem(not__dfg(not__dfg(implies__dfg(u,or__dfg(v,u))))),
    inference(sor,[status(thm)],[27,3844]),
    [iquote('0:SoR:27.0,3844.0')] ).

cnf(5112,plain,
    theorem(implies__dfg(not__dfg(u),implies__dfg(or__dfg(u,v),v))),
    inference(sor,[status(thm)],[23,3902]),
    [iquote('0:SoR:23.0,3902.0')] ).

cnf(5115,plain,
    ( ~ theorem(not__dfg(u))
    | theorem(implies__dfg(or__dfg(u,v),v)) ),
    inference(sor,[status(thm)],[690,5112]),
    [iquote('0:SoR:690.1,5112.0')] ).

cnf(6737,plain,
    theorem(implies__dfg(or__dfg(not__dfg(implies__dfg(u,or__dfg(v,u))),w),w)),
    inference(sor,[status(thm)],[5115,4904]),
    [iquote('0:SoR:5115.0,4904.0')] ).

cnf(6754,plain,
    theorem(implies__dfg(implies__dfg(implies__dfg(u,or__dfg(v,u)),w),w)),
    inference(rew,[status(thm),theory(equality)],[7,6737]),
    [iquote('0:Rew:7.0,6737.0')] ).

cnf(11950,plain,
    ( ~ theorem(implies__dfg(implies__dfg(u,or__dfg(v,u)),w))
    | theorem(w) ),
    inference(sor,[status(thm)],[690,6754]),
    [iquote('0:SoR:690.1,6754.0')] ).

cnf(64382,plain,
    theorem(implies__dfg(u,or__dfg(u,v))),
    inference(sor,[status(thm)],[11950,232]),
    [iquote('0:SoR:11950.0,232.0')] ).

cnf(64606,plain,
    theorem(or__dfg(u,implies__dfg(u,v))),
    inference(sor,[status(thm)],[76,64382]),
    [iquote('0:SoR:76.0,64382.0')] ).

cnf(64637,plain,
    theorem(or__dfg(u,implies__dfg(implies__dfg(v,u),implies__dfg(v,w)))),
    inference(sor,[status(thm)],[1524,64606]),
    [iquote('0:SoR:1524.0,64606.0')] ).

cnf(75365,plain,
    theorem(implies__dfg(implies__dfg(u,v),or__dfg(v,implies__dfg(u,w)))),
    inference(sor,[status(thm)],[94,64637]),
    [iquote('0:SoR:94.0,64637.0')] ).

cnf(80333,plain,
    theorem(implies__dfg(implies__dfg(u,implies__dfg(u,v)),implies__dfg(u,v))),
    inference(sor,[status(thm)],[1945,75365]),
    [iquote('0:SoR:1945.0,75365.0')] ).

cnf(80342,plain,
    $false,
    inference(unc,[status(thm)],[80333,1]),
    [iquote('0:UnC:80333.0,1.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : LCL259-3 : TPTP v8.1.0. Released v2.3.0.
% 0.12/0.13  % Command  : run_spass %d %s
% 0.15/0.35  % Computer : n020.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 600
% 0.15/0.35  % DateTime : Sat Jul  2 22:58:00 EDT 2022
% 0.15/0.35  % CPUTime  : 
% 234.26/234.41  
% 234.26/234.41  SPASS V 3.9 
% 234.26/234.41  SPASS beiseite: Proof found.
% 234.26/234.41  % SZS status Theorem
% 234.26/234.41  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 234.26/234.41  SPASS derived 74169 clauses, backtracked 0 clauses, performed 0 splits and kept 28278 clauses.
% 234.26/234.41  SPASS allocated 164594 KBytes.
% 234.26/234.41  SPASS spent	0:3:51.79 on the problem.
% 234.26/234.41  		0:00:00.03 for the input.
% 234.26/234.41  		0:00:00.00 for the FLOTTER CNF translation.
% 234.26/234.41  		0:00:06.63 for inferences.
% 234.26/234.41  		0:00:00.00 for the backtracking.
% 234.26/234.41  		0:3:43.05 for the reduction.
% 234.26/234.41  
% 234.26/234.41  
% 234.26/234.41  Here is a proof with depth 21, length 69 :
% 234.26/234.41  % SZS output start Refutation
% See solution above
% 234.26/234.41  Formulae used in the proof : prove_this axiom_1_2 axiom_1_3 axiom_1_4 axiom_1_5 axiom_1_6 implies_definition rule_1 rule_2
% 234.26/234.41  
%------------------------------------------------------------------------------