TSTP Solution File: LCL186-3 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : LCL186-3 : TPTP v8.1.0. Released v2.3.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n025.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 14:35:13 EDT 2022

% Result   : Unsatisfiable 167.20s 167.41s
% Output   : Refutation 167.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :    9
% Syntax   : Number of clauses     :   59 (  40 unt;   0 nHn;  59 RR)
%            Number of literals    :   81 (   0 equ;  23 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    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ~ theorem(implies__dfg(not__dfg(p),implies__dfg(p,q))),
    file('LCL186-3.p',unknown),
    [] ).

cnf(2,axiom,
    axiom(implies__dfg(or__dfg(u,u),u)),
    file('LCL186-3.p',unknown),
    [] ).

cnf(3,axiom,
    axiom(implies__dfg(u,or__dfg(v,u))),
    file('LCL186-3.p',unknown),
    [] ).

cnf(4,axiom,
    axiom(implies__dfg(or__dfg(u,v),or__dfg(v,u))),
    file('LCL186-3.p',unknown),
    [] ).

cnf(5,axiom,
    axiom(implies__dfg(or__dfg(u,or__dfg(v,w)),or__dfg(v,or__dfg(u,w)))),
    file('LCL186-3.p',unknown),
    [] ).

cnf(6,axiom,
    axiom(implies__dfg(implies__dfg(u,v),implies__dfg(or__dfg(w,u),or__dfg(w,v)))),
    file('LCL186-3.p',unknown),
    [] ).

cnf(7,axiom,
    equal(or__dfg(not__dfg(u),v),implies__dfg(u,v)),
    file('LCL186-3.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ axiom(u)
    | theorem(u) ),
    file('LCL186-3.p',unknown),
    [] ).

cnf(9,axiom,
    ( ~ theorem(u)
    | ~ theorem(implies__dfg(u,v))
    | theorem(v) ),
    file('LCL186-3.p',unknown),
    [] ).

cnf(16,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(17,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(18,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(21,plain,
    ( ~ theorem(implies__dfg(u,v))
    | theorem(or__dfg(v,not__dfg(u))) ),
    inference(sor,[status(thm)],[18,17]),
    [iquote('0:SoR:18.0,17.0')] ).

cnf(24,plain,
    ( ~ theorem(u)
    | theorem(or__dfg(v,u)) ),
    inference(sor,[status(thm)],[18,3]),
    [iquote('0:SoR:18.0,3.0')] ).

cnf(25,plain,
    ( ~ theorem(or__dfg(u,not__dfg(v)))
    | theorem(implies__dfg(v,u)) ),
    inference(sor,[status(thm)],[18,16]),
    [iquote('0:SoR:18.0,16.0')] ).

cnf(26,plain,
    ( ~ theorem(or__dfg(u,v))
    | theorem(or__dfg(v,u)) ),
    inference(sor,[status(thm)],[18,4]),
    [iquote('0:SoR:18.0,4.0')] ).

cnf(27,plain,
    ( ~ theorem(or__dfg(u,u))
    | theorem(u) ),
    inference(sor,[status(thm)],[18,2]),
    [iquote('0:SoR:18.0,2.0')] ).

cnf(31,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(32,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(35,plain,
    axiom(implies__dfg(implies__dfg(u,or__dfg(v,w)),or__dfg(v,implies__dfg(u,w)))),
    inference(rew,[status(thm),theory(equality)],[7,31]),
    [iquote('0:Rew:7.0,31.0')] ).

cnf(36,plain,
    axiom(implies__dfg(or__dfg(u,implies__dfg(v,w)),implies__dfg(v,or__dfg(u,w)))),
    inference(rew,[status(thm),theory(equality)],[7,32]),
    [iquote('0:Rew:7.0,32.0')] ).

cnf(42,plain,
    ( ~ theorem(implies__dfg(u,v))
    | theorem(implies__dfg(or__dfg(w,u),or__dfg(w,v))) ),
    inference(sor,[status(thm)],[18,6]),
    [iquote('0:SoR:18.0,6.0')] ).

cnf(43,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(45,plain,
    axiom(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(w,u),implies__dfg(w,v)))),
    inference(rew,[status(thm),theory(equality)],[7,43]),
    [iquote('0:Rew:7.0,43.0')] ).

cnf(52,plain,
    ( ~ theorem(implies__dfg(u,or__dfg(v,w)))
    | theorem(or__dfg(v,implies__dfg(u,w))) ),
    inference(sor,[status(thm)],[18,35]),
    [iquote('0:SoR:18.0,35.0')] ).

cnf(63,plain,
    ( ~ theorem(or__dfg(u,implies__dfg(v,w)))
    | theorem(implies__dfg(v,or__dfg(u,w))) ),
    inference(sor,[status(thm)],[18,36]),
    [iquote('0:SoR:18.0,36.0')] ).

cnf(70,plain,
    ( ~ axiom(implies__dfg(u,v))
    | theorem(or__dfg(v,not__dfg(u))) ),
    inference(sor,[status(thm)],[21,8]),
    [iquote('0:SoR:21.0,8.1')] ).

cnf(71,plain,
    ( ~ theorem(implies__dfg(u,v))
    | theorem(implies__dfg(implies__dfg(w,u),implies__dfg(w,v))) ),
    inference(sor,[status(thm)],[18,45]),
    [iquote('0:SoR:18.0,45.0')] ).

cnf(82,plain,
    theorem(or__dfg(or__dfg(u,v),not__dfg(v))),
    inference(sor,[status(thm)],[70,3]),
    [iquote('0:SoR:70.0,3.0')] ).

cnf(86,plain,
    theorem(or__dfg(or__dfg(u,v),not__dfg(or__dfg(v,u)))),
    inference(sor,[status(thm)],[70,4]),
    [iquote('0:SoR:70.0,4.0')] ).

cnf(97,plain,
    theorem(implies__dfg(u,or__dfg(v,u))),
    inference(sor,[status(thm)],[25,82]),
    [iquote('0:SoR:25.0,82.0')] ).

cnf(124,plain,
    theorem(implies__dfg(or__dfg(u,v),or__dfg(v,u))),
    inference(sor,[status(thm)],[25,86]),
    [iquote('0:SoR:25.0,86.0')] ).

cnf(157,plain,
    theorem(or__dfg(u,implies__dfg(v,v))),
    inference(sor,[status(thm)],[52,97]),
    [iquote('0:SoR:52.0,97.0')] ).

cnf(159,plain,
    theorem(implies__dfg(u,u)),
    inference(sor,[status(thm)],[27,157]),
    [iquote('0:SoR:27.0,157.0')] ).

cnf(163,plain,
    theorem(or__dfg(u,not__dfg(u))),
    inference(sor,[status(thm)],[21,159]),
    [iquote('0:SoR:21.0,159.0')] ).

cnf(164,plain,
    theorem(or__dfg(u,implies__dfg(or__dfg(u,v),v))),
    inference(sor,[status(thm)],[52,159]),
    [iquote('0:SoR:52.0,159.0')] ).

cnf(168,plain,
    theorem(implies__dfg(u,not__dfg(not__dfg(u)))),
    inference(spr,[status(thm),theory(equality)],[7,163]),
    [iquote('0:SpR:7.0,163.0')] ).

cnf(170,plain,
    theorem(implies__dfg(or__dfg(u,v),or__dfg(u,not__dfg(not__dfg(v))))),
    inference(sor,[status(thm)],[42,168]),
    [iquote('0:SoR:42.0,168.0')] ).

cnf(176,plain,
    ( ~ theorem(implies__dfg(u,v))
    | theorem(implies__dfg(u,or__dfg(w,v))) ),
    inference(sor,[status(thm)],[63,24]),
    [iquote('0:SoR:63.0,24.1')] ).

cnf(194,plain,
    theorem(implies__dfg(implies__dfg(u,or__dfg(v,w)),implies__dfg(u,or__dfg(w,v)))),
    inference(sor,[status(thm)],[71,124]),
    [iquote('0:SoR:71.0,124.0')] ).

cnf(212,plain,
    theorem(or__dfg(implies__dfg(or__dfg(u,v),v),u)),
    inference(sor,[status(thm)],[26,164]),
    [iquote('0:SoR:26.0,164.0')] ).

cnf(214,plain,
    theorem(or__dfg(not__dfg(u),implies__dfg(implies__dfg(u,v),v))),
    inference(spr,[status(thm),theory(equality)],[7,164]),
    [iquote('0:SpR:7.0,164.0')] ).

cnf(216,plain,
    theorem(implies__dfg(u,implies__dfg(implies__dfg(u,v),v))),
    inference(rew,[status(thm),theory(equality)],[7,214]),
    [iquote('0:Rew:7.0,214.0')] ).

cnf(250,plain,
    ( ~ theorem(u)
    | theorem(implies__dfg(implies__dfg(u,v),v)) ),
    inference(res,[status(thm),theory(equality)],[216,9]),
    [iquote('0:Res:216.0,9.1')] ).

cnf(392,plain,
    theorem(implies__dfg(u,or__dfg(v,or__dfg(w,u)))),
    inference(sor,[status(thm)],[176,97]),
    [iquote('0:SoR:176.0,97.0')] ).

cnf(427,plain,
    theorem(or__dfg(u,implies__dfg(v,or__dfg(w,v)))),
    inference(sor,[status(thm)],[52,392]),
    [iquote('0:SoR:52.0,392.0')] ).

cnf(655,plain,
    ( ~ theorem(u)
    | ~ theorem(implies__dfg(u,v))
    | theorem(v) ),
    inference(res,[status(thm),theory(equality)],[250,9]),
    [iquote('0:Res:250.1,9.1')] ).

cnf(1349,plain,
    ( ~ theorem(or__dfg(u,v))
    | theorem(or__dfg(u,not__dfg(not__dfg(v)))) ),
    inference(res,[status(thm),theory(equality)],[170,9]),
    [iquote('0:Res:170.0,9.1')] ).

cnf(3825,plain,
    theorem(or__dfg(u,not__dfg(not__dfg(implies__dfg(v,or__dfg(w,v)))))),
    inference(sor,[status(thm)],[1349,427]),
    [iquote('0:SoR:1349.0,427.0')] ).

cnf(3882,plain,
    theorem(or__dfg(implies__dfg(or__dfg(u,v),v),not__dfg(not__dfg(u)))),
    inference(sor,[status(thm)],[1349,212]),
    [iquote('0:SoR:1349.0,212.0')] ).

cnf(5574,plain,
    theorem(not__dfg(not__dfg(implies__dfg(u,or__dfg(v,u))))),
    inference(sor,[status(thm)],[27,3825]),
    [iquote('0:SoR:27.0,3825.0')] ).

cnf(5772,plain,
    theorem(implies__dfg(not__dfg(u),implies__dfg(or__dfg(u,v),v))),
    inference(sor,[status(thm)],[25,3882]),
    [iquote('0:SoR:25.0,3882.0')] ).

cnf(5787,plain,
    ( ~ theorem(not__dfg(u))
    | theorem(implies__dfg(or__dfg(u,v),v)) ),
    inference(sor,[status(thm)],[655,5772]),
    [iquote('0:SoR:655.1,5772.0')] ).

cnf(7470,plain,
    theorem(implies__dfg(or__dfg(not__dfg(implies__dfg(u,or__dfg(v,u))),w),w)),
    inference(sor,[status(thm)],[5787,5574]),
    [iquote('0:SoR:5787.0,5574.0')] ).

cnf(7487,plain,
    theorem(implies__dfg(implies__dfg(implies__dfg(u,or__dfg(v,u)),w),w)),
    inference(rew,[status(thm),theory(equality)],[7,7470]),
    [iquote('0:Rew:7.0,7470.0')] ).

cnf(14076,plain,
    ( ~ theorem(implies__dfg(implies__dfg(u,or__dfg(v,u)),w))
    | theorem(w) ),
    inference(sor,[status(thm)],[655,7487]),
    [iquote('0:SoR:655.1,7487.0')] ).

cnf(80794,plain,
    theorem(implies__dfg(u,or__dfg(u,v))),
    inference(sor,[status(thm)],[14076,194]),
    [iquote('0:SoR:14076.0,194.0')] ).

cnf(81227,plain,
    theorem(implies__dfg(not__dfg(u),implies__dfg(u,v))),
    inference(spr,[status(thm),theory(equality)],[7,80794]),
    [iquote('0:SpR:7.0,80794.0')] ).

cnf(81230,plain,
    $false,
    inference(unc,[status(thm)],[81227,1]),
    [iquote('0:UnC:81227.0,1.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : LCL186-3 : TPTP v8.1.0. Released v2.3.0.
% 0.06/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n025.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  : 600
% 0.12/0.33  % DateTime : Sat Jul  2 11:27:09 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 167.20/167.41  
% 167.20/167.41  SPASS V 3.9 
% 167.20/167.41  SPASS beiseite: Proof found.
% 167.20/167.41  % SZS status Theorem
% 167.20/167.41  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 167.20/167.41  SPASS derived 74166 clauses, backtracked 0 clauses, performed 0 splits and kept 28527 clauses.
% 167.20/167.41  SPASS allocated 164782 KBytes.
% 167.20/167.41  SPASS spent	0:2:45.09 on the problem.
% 167.20/167.41  		0:00:00.04 for the input.
% 167.20/167.41  		0:00:00.00 for the FLOTTER CNF translation.
% 167.20/167.41  		0:00:04.92 for inferences.
% 167.20/167.41  		0:00:00.00 for the backtracking.
% 167.20/167.41  		0:2:38.60 for the reduction.
% 167.20/167.41  
% 167.20/167.41  
% 167.20/167.41  Here is a proof with depth 18, length 59 :
% 167.20/167.41  % SZS output start Refutation
% See solution above
% 167.20/167.41  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
% 167.20/167.41  
%------------------------------------------------------------------------------