TSTP Solution File: LCL088-1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : LCL088-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n019.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 14:34:31 EDT 2022

% Result   : Unsatisfiable 0.58s 0.74s
% Output   : Refutation 0.58s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   30
%            Number of leaves      :    3
% Syntax   : Number of clauses     :   58 (  32 unt;   0 nHn;  58 RR)
%            Number of literals    :   88 (   0 equ;  31 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-1 aty)
%            Number of functors    :   11 (  11 usr;  10 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ( ~ is_a_theorem(u)
    | ~ is_a_theorem(implies__dfg(u,v))
    | is_a_theorem(v) ),
    file('LCL088-1.p',unknown),
    [] ).

cnf(2,axiom,
    is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),implies__dfg(w,x)),implies__dfg(y,implies__dfg(implies__dfg(x,u),implies__dfg(w,u))))),
    file('LCL088-1.p',unknown),
    [] ).

cnf(3,axiom,
    ~ is_a_theorem(implies__dfg(implies__dfg(implies__dfg(a,b),a),a)),
    file('LCL088-1.p',unknown),
    [] ).

cnf(7,plain,
    ( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(w,x)))
    | is_a_theorem(implies__dfg(y,implies__dfg(implies__dfg(x,u),implies__dfg(w,u)))) ),
    inference(res,[status(thm),theory(equality)],[2,1]),
    [iquote('0:Res:2.0,1.1')] ).

cnf(8,plain,
    is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(implies__dfg(implies__dfg(v,w),implies__dfg(x,w)),implies__dfg(w,y)),implies__dfg(z,implies__dfg(w,y))))),
    inference(sor,[status(thm)],[7,2]),
    [iquote('0:SoR:7.0,2.0')] ).

cnf(9,plain,
    is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(implies__dfg(v,implies__dfg(w,x)),y),implies__dfg(implies__dfg(implies__dfg(implies__dfg(z,w),implies__dfg(x1,w)),implies__dfg(w,x)),y)))),
    inference(sor,[status(thm)],[7,8]),
    [iquote('0:SoR:7.0,8.0')] ).

cnf(10,plain,
    ( ~ is_a_theorem(u)
    | is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(v,w),implies__dfg(x,w)),implies__dfg(w,y)),implies__dfg(z,implies__dfg(w,y)))) ),
    inference(res,[status(thm),theory(equality)],[8,1]),
    [iquote('0:Res:8.0,1.1')] ).

cnf(11,plain,
    is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,v),implies__dfg(w,v)),implies__dfg(v,x)),implies__dfg(y,implies__dfg(v,x)))),
    inference(ems,[status(thm)],[10,8]),
    [iquote('0:EmS:10.0,8.0')] ).

cnf(14,plain,
    ( ~ is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),implies__dfg(w,v)),implies__dfg(v,x)))
    | is_a_theorem(implies__dfg(y,implies__dfg(v,x))) ),
    inference(res,[status(thm),theory(equality)],[11,1]),
    [iquote('0:Res:11.0,1.1')] ).

cnf(16,plain,
    is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(v,w),implies__dfg(w,implies__dfg(v,w))))),
    inference(sor,[status(thm)],[14,11]),
    [iquote('0:SoR:14.0,11.0')] ).

cnf(17,plain,
    is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(implies__dfg(v,w),implies__dfg(x,w))))),
    inference(sor,[status(thm)],[14,2]),
    [iquote('0:SoR:14.0,2.0')] ).

cnf(20,plain,
    ( ~ is_a_theorem(u)
    | is_a_theorem(implies__dfg(implies__dfg(v,w),implies__dfg(w,implies__dfg(v,w)))) ),
    inference(res,[status(thm),theory(equality)],[16,1]),
    [iquote('0:Res:16.0,1.1')] ).

cnf(22,plain,
    is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(implies__dfg(implies__dfg(implies__dfg(implies__dfg(v,w),implies__dfg(x,w)),implies__dfg(w,y)),z),x1),implies__dfg(implies__dfg(implies__dfg(x2,implies__dfg(w,y)),z),x1)))),
    inference(sor,[status(thm)],[7,9]),
    [iquote('0:SoR:7.0,9.0')] ).

cnf(23,plain,
    ( ~ is_a_theorem(u)
    | is_a_theorem(implies__dfg(implies__dfg(implies__dfg(v,implies__dfg(w,x)),y),implies__dfg(implies__dfg(implies__dfg(implies__dfg(z,w),implies__dfg(x1,w)),implies__dfg(w,x)),y))) ),
    inference(res,[status(thm),theory(equality)],[9,1]),
    [iquote('0:Res:9.0,1.1')] ).

cnf(26,plain,
    ( ~ is_a_theorem(u)
    | is_a_theorem(implies__dfg(v,implies__dfg(implies__dfg(v,w),implies__dfg(x,w)))) ),
    inference(res,[status(thm),theory(equality)],[17,1]),
    [iquote('0:Res:17.0,1.1')] ).

cnf(27,plain,
    is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(v,implies__dfg(u,v)))),
    inference(ems,[status(thm)],[20,17]),
    [iquote('0:EmS:20.0,17.0')] ).

cnf(33,plain,
    is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(implies__dfg(v,w),v),implies__dfg(w,v)))),
    inference(sor,[status(thm)],[7,27]),
    [iquote('0:SoR:7.0,27.0')] ).

cnf(48,plain,
    is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,implies__dfg(v,w)),x),implies__dfg(implies__dfg(implies__dfg(implies__dfg(y,v),implies__dfg(z,v)),implies__dfg(v,w)),x))),
    inference(ems,[status(thm)],[23,2]),
    [iquote('0:EmS:23.0,2.0')] ).

cnf(52,plain,
    ( ~ is_a_theorem(u)
    | is_a_theorem(implies__dfg(implies__dfg(implies__dfg(v,w),v),implies__dfg(w,v))) ),
    inference(res,[status(thm),theory(equality)],[33,1]),
    [iquote('0:Res:33.0,1.1')] ).

cnf(53,plain,
    is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(u,v),implies__dfg(w,v)))),
    inference(ems,[status(thm)],[26,27]),
    [iquote('0:EmS:26.0,27.0')] ).

cnf(63,plain,
    ( ~ is_a_theorem(u)
    | is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(w,v))) ),
    inference(res,[status(thm),theory(equality)],[53,1]),
    [iquote('0:Res:53.0,1.1')] ).

cnf(67,plain,
    ( ~ is_a_theorem(u)
    | ~ is_a_theorem(implies__dfg(u,v))
    | is_a_theorem(implies__dfg(w,v)) ),
    inference(res,[status(thm),theory(equality)],[63,1]),
    [iquote('0:Res:63.1,1.1')] ).

cnf(71,plain,
    ( ~ is_a_theorem(u)
    | is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(implies__dfg(implies__dfg(v,w),implies__dfg(x,w)),implies__dfg(w,y)),z),x1),implies__dfg(implies__dfg(implies__dfg(x2,implies__dfg(w,y)),z),x1))) ),
    inference(res,[status(thm),theory(equality)],[22,1]),
    [iquote('0:Res:22.0,1.1')] ).

cnf(84,plain,
    is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),u),implies__dfg(v,u))),
    inference(ems,[status(thm)],[52,27]),
    [iquote('0:EmS:52.0,27.0')] ).

cnf(94,plain,
    is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(w,v)))),
    inference(sor,[status(thm)],[14,84]),
    [iquote('0:SoR:14.0,84.0')] ).

cnf(100,plain,
    is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(implies__dfg(v,w),x),implies__dfg(w,x)))),
    inference(sor,[status(thm)],[7,94]),
    [iquote('0:SoR:7.0,94.0')] ).

cnf(103,plain,
    ( ~ is_a_theorem(u)
    | is_a_theorem(implies__dfg(v,implies__dfg(w,v))) ),
    inference(res,[status(thm),theory(equality)],[94,1]),
    [iquote('0:Res:94.0,1.1')] ).

cnf(107,plain,
    is_a_theorem(implies__dfg(u,implies__dfg(v,u))),
    inference(ems,[status(thm)],[103,48]),
    [iquote('0:EmS:103.0,48.0')] ).

cnf(119,plain,
    is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(implies__dfg(v,w),v),implies__dfg(x,v)))),
    inference(sor,[status(thm)],[7,107]),
    [iquote('0:SoR:7.0,107.0')] ).

cnf(155,plain,
    ( ~ is_a_theorem(u)
    | is_a_theorem(implies__dfg(implies__dfg(implies__dfg(v,w),x),implies__dfg(w,x))) ),
    inference(res,[status(thm),theory(equality)],[100,1]),
    [iquote('0:Res:100.0,1.1')] ).

cnf(177,plain,
    is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,v),implies__dfg(w,v)),implies__dfg(v,x)),y),z),implies__dfg(implies__dfg(implies__dfg(x1,implies__dfg(v,x)),y),z))),
    inference(ems,[status(thm)],[71,2]),
    [iquote('0:EmS:71.0,2.0')] ).

cnf(182,plain,
    ( ~ is_a_theorem(u)
    | is_a_theorem(implies__dfg(implies__dfg(implies__dfg(v,w),v),implies__dfg(x,v))) ),
    inference(res,[status(thm),theory(equality)],[119,1]),
    [iquote('0:Res:119.0,1.1')] ).

cnf(244,plain,
    is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),w),implies__dfg(v,w))),
    inference(ems,[status(thm)],[155,48]),
    [iquote('0:EmS:155.0,48.0')] ).

cnf(291,plain,
    ( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),w))
    | is_a_theorem(implies__dfg(x,implies__dfg(v,w))) ),
    inference(sor,[status(thm)],[67,244]),
    [iquote('0:SoR:67.1,244.0')] ).

cnf(367,plain,
    is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),u),implies__dfg(w,u))),
    inference(ems,[status(thm)],[182,244]),
    [iquote('0:EmS:182.0,244.0')] ).

cnf(392,plain,
    is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(v,implies__dfg(v,w)),implies__dfg(x,implies__dfg(v,w))))),
    inference(sor,[status(thm)],[7,367]),
    [iquote('0:SoR:7.0,367.0')] ).

cnf(396,plain,
    ( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),u))
    | is_a_theorem(implies__dfg(w,u)) ),
    inference(res,[status(thm),theory(equality)],[367,1]),
    [iquote('0:Res:367.0,1.1')] ).

cnf(406,plain,
    is_a_theorem(implies__dfg(u,implies__dfg(v,v))),
    inference(sor,[status(thm)],[396,367]),
    [iquote('0:SoR:396.0,367.0')] ).

cnf(431,plain,
    ( ~ is_a_theorem(u)
    | is_a_theorem(implies__dfg(v,v)) ),
    inference(res,[status(thm),theory(equality)],[406,1]),
    [iquote('0:Res:406.0,1.1')] ).

cnf(435,plain,
    is_a_theorem(implies__dfg(u,u)),
    inference(ems,[status(thm)],[431,177]),
    [iquote('0:EmS:431.0,177.0')] ).

cnf(500,plain,
    is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(w,w)))),
    inference(sor,[status(thm)],[291,406]),
    [iquote('0:SoR:291.0,406.0')] ).

cnf(525,plain,
    is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(implies__dfg(v,v),w),implies__dfg(x,w)))),
    inference(sor,[status(thm)],[7,500]),
    [iquote('0:SoR:7.0,500.0')] ).

cnf(596,plain,
    ( ~ is_a_theorem(u)
    | is_a_theorem(implies__dfg(implies__dfg(implies__dfg(v,v),w),implies__dfg(x,w))) ),
    inference(res,[status(thm),theory(equality)],[525,1]),
    [iquote('0:Res:525.0,1.1')] ).

cnf(672,plain,
    is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,u),v),implies__dfg(w,v))),
    inference(ems,[status(thm)],[596,435]),
    [iquote('0:EmS:596.0,435.0')] ).

cnf(1166,plain,
    ( ~ is_a_theorem(u)
    | is_a_theorem(implies__dfg(implies__dfg(v,implies__dfg(v,w)),implies__dfg(x,implies__dfg(v,w)))) ),
    inference(res,[status(thm),theory(equality)],[392,1]),
    [iquote('0:Res:392.0,1.1')] ).

cnf(2163,plain,
    is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(u,v)),implies__dfg(w,implies__dfg(u,v)))),
    inference(ems,[status(thm)],[1166,435]),
    [iquote('0:EmS:1166.0,435.0')] ).

cnf(2252,plain,
    ( ~ is_a_theorem(implies__dfg(u,implies__dfg(u,v)))
    | is_a_theorem(implies__dfg(w,implies__dfg(u,v))) ),
    inference(res,[status(thm),theory(equality)],[2163,1]),
    [iquote('0:Res:2163.0,1.1')] ).

cnf(2281,plain,
    is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(implies__dfg(v,v),w),w))),
    inference(sor,[status(thm)],[2252,672]),
    [iquote('0:SoR:2252.0,672.0')] ).

cnf(2283,plain,
    is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(implies__dfg(v,w),v),v))),
    inference(sor,[status(thm)],[2252,367]),
    [iquote('0:SoR:2252.0,367.0')] ).

cnf(2290,plain,
    ( ~ is_a_theorem(u)
    | is_a_theorem(implies__dfg(v,implies__dfg(implies__dfg(u,w),w))) ),
    inference(sor,[status(thm)],[2252,63]),
    [iquote('0:SoR:2252.0,63.1')] ).

cnf(2362,plain,
    ( ~ is_a_theorem(u)
    | is_a_theorem(implies__dfg(implies__dfg(implies__dfg(v,v),w),w)) ),
    inference(res,[status(thm),theory(equality)],[2281,1]),
    [iquote('0:Res:2281.0,1.1')] ).

cnf(2404,plain,
    ( ~ is_a_theorem(u)
    | ~ is_a_theorem(v)
    | is_a_theorem(implies__dfg(implies__dfg(u,w),w)) ),
    inference(res,[status(thm),theory(equality)],[2290,1]),
    [iquote('0:Res:2290.1,1.1')] ).

cnf(2405,plain,
    ( ~ is_a_theorem(u)
    | is_a_theorem(implies__dfg(implies__dfg(u,v),v)) ),
    inference(con,[status(thm)],[2404]),
    [iquote('0:Con:2404.1')] ).

cnf(2503,plain,
    ( ~ is_a_theorem(u)
    | ~ is_a_theorem(implies__dfg(u,v))
    | is_a_theorem(v) ),
    inference(res,[status(thm),theory(equality)],[2405,1]),
    [iquote('0:Res:2405.1,1.1')] ).

cnf(2658,plain,
    is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,u),v),v)),
    inference(ems,[status(thm)],[2362,435]),
    [iquote('0:EmS:2362.0,435.0')] ).

cnf(2753,plain,
    ( ~ is_a_theorem(implies__dfg(implies__dfg(u,u),v))
    | is_a_theorem(v) ),
    inference(sor,[status(thm)],[2503,2658]),
    [iquote('0:SoR:2503.1,2658.0')] ).

cnf(2769,plain,
    is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),u),u)),
    inference(sor,[status(thm)],[2753,2283]),
    [iquote('0:SoR:2753.0,2283.0')] ).

cnf(2840,plain,
    $false,
    inference(unc,[status(thm)],[2769,3]),
    [iquote('0:UnC:2769.0,3.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : LCL088-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12  % Command  : run_spass %d %s
% 0.14/0.33  % Computer : n019.cluster.edu
% 0.14/0.33  % Model    : x86_64 x86_64
% 0.14/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33  % Memory   : 8042.1875MB
% 0.14/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33  % CPULimit : 300
% 0.14/0.33  % WCLimit  : 600
% 0.14/0.33  % DateTime : Mon Jul  4 12:06:38 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.58/0.74  
% 0.58/0.74  SPASS V 3.9 
% 0.58/0.74  SPASS beiseite: Proof found.
% 0.58/0.74  % SZS status Theorem
% 0.58/0.74  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.58/0.74  SPASS derived 2784 clauses, backtracked 0 clauses, performed 0 splits and kept 449 clauses.
% 0.58/0.74  SPASS allocated 78985 KBytes.
% 0.58/0.74  SPASS spent	0:00:00.37 on the problem.
% 0.58/0.74  		0:00:00.04 for the input.
% 0.58/0.74  		0:00:00.00 for the FLOTTER CNF translation.
% 0.58/0.74  		0:00:00.07 for inferences.
% 0.58/0.74  		0:00:00.00 for the backtracking.
% 0.58/0.74  		0:00:00.23 for the reduction.
% 0.58/0.74  
% 0.58/0.74  
% 0.58/0.74  Here is a proof with depth 28, length 58 :
% 0.58/0.74  % SZS output start Refutation
% See solution above
% 0.58/0.74  Formulae used in the proof : condensed_detachment ic_JLukasiewicz_4 prove_ic_3
% 0.58/0.74  
%------------------------------------------------------------------------------