TSTP Solution File: LCL026-1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : LCL026-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n012.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 14:34:07 EDT 2022

% Result   : Unsatisfiable 65.20s 65.39s
% Output   : Refutation 66.42s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   67 (  36 unt;   0 nHn;  67 RR)
%            Number of literals    :  103 (   0 equ;  37 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-1 aty)
%            Number of functors    :    8 (   8 usr;   7 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('LCL026-1.p',unknown),
    [] ).

cnf(2,axiom,
    is_a_theorem(implies__dfg(u,implies__dfg(v,u))),
    file('LCL026-1.p',unknown),
    [] ).

cnf(3,axiom,
    is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,falsehood),falsehood),u)),
    file('LCL026-1.p',unknown),
    [] ).

cnf(4,axiom,
    is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(implies__dfg(u,v),implies__dfg(u,w)))),
    file('LCL026-1.p',unknown),
    [] ).

cnf(5,axiom,
    ~ is_a_theorem(implies__dfg(implies__dfg(implies__dfg(a,b),a),a)),
    file('LCL026-1.p',unknown),
    [] ).

cnf(11,plain,
    ( ~ is_a_theorem(u)
    | is_a_theorem(implies__dfg(v,u)) ),
    inference(res,[status(thm),theory(equality)],[2,1]),
    [iquote('0:Res:2.0,1.1')] ).

cnf(12,plain,
    ( ~ is_a_theorem(implies__dfg(implies__dfg(u,falsehood),falsehood))
    | is_a_theorem(u) ),
    inference(res,[status(thm),theory(equality)],[3,1]),
    [iquote('0:Res:3.0,1.1')] ).

cnf(13,plain,
    ( ~ is_a_theorem(implies__dfg(u,implies__dfg(v,w)))
    | is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(u,w))) ),
    inference(res,[status(thm),theory(equality)],[4,1]),
    [iquote('0:Res:4.0,1.1')] ).

cnf(19,plain,
    ( ~ is_a_theorem(implies__dfg(u,v))
    | is_a_theorem(implies__dfg(implies__dfg(w,u),implies__dfg(w,v))) ),
    inference(sor,[status(thm)],[13,11]),
    [iquote('0:SoR:13.0,11.1')] ).

cnf(20,plain,
    is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(u,v)),implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(u,w)))),
    inference(sor,[status(thm)],[13,4]),
    [iquote('0:SoR:13.0,4.0')] ).

cnf(21,plain,
    is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,v),falsehood),falsehood),u),implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,v),falsehood),falsehood),v))),
    inference(sor,[status(thm)],[13,3]),
    [iquote('0:SoR:13.0,3.0')] ).

cnf(22,plain,
    is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(u,u))),
    inference(sor,[status(thm)],[13,2]),
    [iquote('0:SoR:13.0,2.0')] ).

cnf(24,plain,
    ( ~ is_a_theorem(implies__dfg(u,v))
    | is_a_theorem(implies__dfg(u,u)) ),
    inference(res,[status(thm),theory(equality)],[22,1]),
    [iquote('0:Res:22.0,1.1')] ).

cnf(30,plain,
    is_a_theorem(implies__dfg(u,u)),
    inference(sor,[status(thm)],[24,2]),
    [iquote('0:SoR:24.0,2.0')] ).

cnf(31,plain,
    is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),u),implies__dfg(implies__dfg(u,v),v))),
    inference(sor,[status(thm)],[13,30]),
    [iquote('0:SoR:13.0,30.0')] ).

cnf(35,plain,
    is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(v,implies__dfg(w,x))),implies__dfg(u,implies__dfg(implies__dfg(v,w),implies__dfg(v,x))))),
    inference(sor,[status(thm)],[19,4]),
    [iquote('0:SoR:19.0,4.0')] ).

cnf(36,plain,
    is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(implies__dfg(v,falsehood),falsehood)),implies__dfg(u,v))),
    inference(sor,[status(thm)],[19,3]),
    [iquote('0:SoR:19.0,3.0')] ).

cnf(38,plain,
    is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(u,implies__dfg(w,v)))),
    inference(sor,[status(thm)],[19,2]),
    [iquote('0:SoR:19.0,2.0')] ).

cnf(40,plain,
    is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(u,implies__dfg(v,implies__dfg(x,w))))),
    inference(sor,[status(thm)],[19,38]),
    [iquote('0:SoR:19.0,38.0')] ).

cnf(41,plain,
    ( ~ is_a_theorem(implies__dfg(u,v))
    | is_a_theorem(implies__dfg(u,implies__dfg(w,v))) ),
    inference(res,[status(thm),theory(equality)],[38,1]),
    [iquote('0:Res:38.0,1.1')] ).

cnf(45,plain,
    ( ~ is_a_theorem(u)
    | is_a_theorem(implies__dfg(v,implies__dfg(w,u))) ),
    inference(sor,[status(thm)],[41,11]),
    [iquote('0:SoR:41.0,11.1')] ).

cnf(52,plain,
    is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(w,u)))),
    inference(sor,[status(thm)],[41,2]),
    [iquote('0:SoR:41.0,2.0')] ).

cnf(53,plain,
    is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(u,implies__dfg(w,u)))),
    inference(sor,[status(thm)],[13,52]),
    [iquote('0:SoR:13.0,52.0')] ).

cnf(60,plain,
    ( ~ is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,v),falsehood),falsehood),u))
    | is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,v),falsehood),falsehood),v)) ),
    inference(res,[status(thm),theory(equality)],[21,1]),
    [iquote('0:Res:21.0,1.1')] ).

cnf(81,plain,
    ( ~ is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(u,v)))
    | is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(v,w)),implies__dfg(u,w))) ),
    inference(res,[status(thm),theory(equality)],[20,1]),
    [iquote('0:Res:20.0,1.1')] ).

cnf(98,plain,
    is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(v,implies__dfg(implies__dfg(w,falsehood),falsehood))),implies__dfg(u,implies__dfg(v,w)))),
    inference(sor,[status(thm)],[19,36]),
    [iquote('0:SoR:19.0,36.0')] ).

cnf(99,plain,
    ( ~ is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(v,falsehood),falsehood)))
    | is_a_theorem(implies__dfg(u,v)) ),
    inference(res,[status(thm),theory(equality)],[36,1]),
    [iquote('0:Res:36.0,1.1')] ).

cnf(136,plain,
    ( ~ is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(w,x))))
    | is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(v,w),implies__dfg(v,x)))) ),
    inference(res,[status(thm),theory(equality)],[35,1]),
    [iquote('0:Res:35.0,1.1')] ).

cnf(152,plain,
    ( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),u))
    | is_a_theorem(implies__dfg(implies__dfg(u,v),v)) ),
    inference(res,[status(thm),theory(equality)],[31,1]),
    [iquote('0:Res:31.0,1.1')] ).

cnf(155,plain,
    ( ~ is_a_theorem(u)
    | is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,v),falsehood),falsehood),v)) ),
    inference(sor,[status(thm)],[60,11]),
    [iquote('0:SoR:60.0,11.1')] ).

cnf(178,plain,
    ( ~ is_a_theorem(u)
    | is_a_theorem(implies__dfg(implies__dfg(v,implies__dfg(u,w)),implies__dfg(v,w))) ),
    inference(sor,[status(thm)],[81,45]),
    [iquote('0:SoR:81.0,45.1')] ).

cnf(180,plain,
    is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(implies__dfg(v,u),w)),implies__dfg(u,w))),
    inference(sor,[status(thm)],[81,53]),
    [iquote('0:SoR:81.0,53.0')] ).

cnf(289,plain,
    is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,falsehood),u),u)),
    inference(sor,[status(thm)],[99,31]),
    [iquote('0:SoR:99.0,31.0')] ).

cnf(296,plain,
    is_a_theorem(implies__dfg(falsehood,u)),
    inference(sor,[status(thm)],[99,2]),
    [iquote('0:SoR:99.0,2.0')] ).

cnf(301,plain,
    is_a_theorem(implies__dfg(implies__dfg(falsehood,u),implies__dfg(falsehood,v))),
    inference(sor,[status(thm)],[13,296]),
    [iquote('0:SoR:13.0,296.0')] ).

cnf(305,plain,
    is_a_theorem(implies__dfg(implies__dfg(u,falsehood),implies__dfg(u,v))),
    inference(sor,[status(thm)],[19,296]),
    [iquote('0:SoR:19.0,296.0')] ).

cnf(308,plain,
    is_a_theorem(implies__dfg(implies__dfg(falsehood,u),implies__dfg(v,implies__dfg(falsehood,w)))),
    inference(sor,[status(thm)],[41,301]),
    [iquote('0:SoR:41.0,301.0')] ).

cnf(323,plain,
    is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(implies__dfg(v,falsehood),v)),implies__dfg(u,v))),
    inference(sor,[status(thm)],[19,289]),
    [iquote('0:SoR:19.0,289.0')] ).

cnf(333,plain,
    ( ~ is_a_theorem(u)
    | is_a_theorem(implies__dfg(implies__dfg(u,falsehood),falsehood)) ),
    inference(sor,[status(thm)],[12,155]),
    [iquote('0:SoR:12.0,155.1')] ).

cnf(334,plain,
    ( ~ is_a_theorem(u)
    | ~ is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),falsehood),falsehood))
    | is_a_theorem(v) ),
    inference(res,[status(thm),theory(equality)],[155,1]),
    [iquote('0:Res:155.1,1.1')] ).

cnf(337,plain,
    is_a_theorem(implies__dfg(implies__dfg(u,falsehood),implies__dfg(v,implies__dfg(u,w)))),
    inference(sor,[status(thm)],[41,305]),
    [iquote('0:SoR:41.0,305.0')] ).

cnf(339,plain,
    ( ~ is_a_theorem(implies__dfg(u,falsehood))
    | is_a_theorem(implies__dfg(u,v)) ),
    inference(res,[status(thm),theory(equality)],[305,1]),
    [iquote('0:Res:305.0,1.1')] ).

cnf(367,plain,
    ( ~ is_a_theorem(u)
    | is_a_theorem(implies__dfg(implies__dfg(u,falsehood),v)) ),
    inference(sor,[status(thm)],[339,333]),
    [iquote('0:SoR:339.0,333.1')] ).

cnf(391,plain,
    ( ~ is_a_theorem(implies__dfg(falsehood,u))
    | is_a_theorem(implies__dfg(v,implies__dfg(falsehood,w))) ),
    inference(res,[status(thm),theory(equality)],[308,1]),
    [iquote('0:Res:308.0,1.1')] ).

cnf(392,plain,
    is_a_theorem(implies__dfg(u,implies__dfg(falsehood,v))),
    inference(ssi,[status(thm)],[391,296]),
    [iquote('0:SSi:391.0,296.0')] ).

cnf(395,plain,
    is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(falsehood,w)))),
    inference(sor,[status(thm)],[41,392]),
    [iquote('0:SoR:41.0,392.0')] ).

cnf(404,plain,
    ( ~ is_a_theorem(implies__dfg(u,implies__dfg(v,w)))
    | is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(x,w)))) ),
    inference(res,[status(thm),theory(equality)],[40,1]),
    [iquote('0:Res:40.0,1.1')] ).

cnf(535,plain,
    ( ~ is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(implies__dfg(w,falsehood),falsehood))))
    | is_a_theorem(implies__dfg(u,implies__dfg(v,w))) ),
    inference(res,[status(thm),theory(equality)],[98,1]),
    [iquote('0:Res:98.0,1.1')] ).

cnf(584,plain,
    is_a_theorem(implies__dfg(implies__dfg(u,falsehood),implies__dfg(implies__dfg(v,u),implies__dfg(v,w)))),
    inference(sor,[status(thm)],[136,337]),
    [iquote('0:SoR:136.0,337.0')] ).

cnf(624,plain,
    is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(v,falsehood),implies__dfg(v,w)))),
    inference(sor,[status(thm)],[136,395]),
    [iquote('0:SoR:136.0,395.0')] ).

cnf(1009,plain,
    ( ~ is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(v,falsehood),v)))
    | is_a_theorem(implies__dfg(u,v)) ),
    inference(res,[status(thm),theory(equality)],[323,1]),
    [iquote('0:Res:323.0,1.1')] ).

cnf(1833,plain,
    ( ~ is_a_theorem(u)
    | ~ is_a_theorem(implies__dfg(u,v))
    | is_a_theorem(v) ),
    inference(sor,[status(thm)],[334,367]),
    [iquote('0:SoR:334.1,367.1')] ).

cnf(3480,plain,
    is_a_theorem(implies__dfg(implies__dfg(u,falsehood),implies__dfg(implies__dfg(implies__dfg(v,falsehood),u),v))),
    inference(sor,[status(thm)],[535,584]),
    [iquote('0:SoR:535.0,584.0')] ).

cnf(3951,plain,
    is_a_theorem(implies__dfg(implies__dfg(u,falsehood),implies__dfg(implies__dfg(implies__dfg(v,falsehood),u),implies__dfg(w,v)))),
    inference(sor,[status(thm)],[404,3480]),
    [iquote('0:SoR:404.0,3480.0')] ).

cnf(10719,plain,
    ( ~ is_a_theorem(u)
    | is_a_theorem(implies__dfg(implies__dfg(implies__dfg(v,u),w),w)) ),
    inference(sor,[status(thm)],[152,45]),
    [iquote('0:SoR:152.0,45.1')] ).

cnf(10796,plain,
    is_a_theorem(implies__dfg(implies__dfg(implies__dfg(implies__dfg(u,falsehood),implies__dfg(u,v)),w),w)),
    inference(sor,[status(thm)],[152,624]),
    [iquote('0:SoR:152.0,624.0')] ).

cnf(10837,plain,
    ( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),w))
    | ~ is_a_theorem(v)
    | is_a_theorem(w) ),
    inference(sor,[status(thm)],[1833,10719]),
    [iquote('0:SoR:1833.1,10719.1')] ).

cnf(11222,plain,
    ( ~ is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,falsehood),implies__dfg(u,v)),w))
    | is_a_theorem(w) ),
    inference(sor,[status(thm)],[1833,10796]),
    [iquote('0:SoR:1833.1,10796.0')] ).

cnf(11448,plain,
    ( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),w))
    | is_a_theorem(implies__dfg(v,w)) ),
    inference(sor,[status(thm)],[10837,180]),
    [iquote('0:SoR:10837.0,180.0')] ).

cnf(11837,plain,
    is_a_theorem(implies__dfg(u,implies__dfg(implies__dfg(u,v),v))),
    inference(sor,[status(thm)],[11448,31]),
    [iquote('0:SoR:11448.0,31.0')] ).

cnf(11926,plain,
    is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(u,implies__dfg(implies__dfg(v,w),w)))),
    inference(sor,[status(thm)],[19,11837]),
    [iquote('0:SoR:19.0,11837.0')] ).

cnf(15287,plain,
    is_a_theorem(implies__dfg(implies__dfg(u,falsehood),implies__dfg(implies__dfg(implies__dfg(u,v),w),w))),
    inference(sor,[status(thm)],[11222,11926]),
    [iquote('0:SoR:11222.0,11926.0')] ).

cnf(16692,plain,
    ( ~ is_a_theorem(u)
    | is_a_theorem(implies__dfg(implies__dfg(implies__dfg(v,falsehood),implies__dfg(u,v)),v)) ),
    inference(sor,[status(thm)],[1009,178]),
    [iquote('0:SoR:1009.0,178.1')] ).

cnf(16757,plain,
    ( ~ is_a_theorem(implies__dfg(implies__dfg(u,falsehood),implies__dfg(v,u)))
    | ~ is_a_theorem(v)
    | is_a_theorem(u) ),
    inference(sor,[status(thm)],[1833,16692]),
    [iquote('0:SoR:1833.1,16692.1')] ).

cnf(51008,plain,
    ( ~ is_a_theorem(implies__dfg(implies__dfg(u,falsehood),implies__dfg(v,u)))
    | is_a_theorem(implies__dfg(v,u)) ),
    inference(sor,[status(thm)],[16757,3951]),
    [iquote('0:SoR:16757.0,3951.0')] ).

cnf(51668,plain,
    is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),u),u)),
    inference(sor,[status(thm)],[51008,15287]),
    [iquote('0:SoR:51008.0,15287.0')] ).

cnf(51864,plain,
    $false,
    inference(unc,[status(thm)],[51668,5]),
    [iquote('0:UnC:51668.0,5.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.07  % Problem  : LCL026-1 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.07  % Command  : run_spass %d %s
% 0.07/0.25  % Computer : n012.cluster.edu
% 0.07/0.25  % Model    : x86_64 x86_64
% 0.07/0.25  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25  % Memory   : 8042.1875MB
% 0.07/0.25  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25  % CPULimit : 300
% 0.07/0.25  % WCLimit  : 600
% 0.07/0.25  % DateTime : Sun Jul  3 06:02:46 EDT 2022
% 0.07/0.25  % CPUTime  : 
% 65.20/65.39  
% 65.20/65.39  SPASS V 3.9 
% 65.20/65.39  SPASS beiseite: Proof found.
% 65.20/65.39  % SZS status Theorem
% 65.20/65.39  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 65.20/65.39  SPASS derived 51568 clauses, backtracked 0 clauses, performed 0 splits and kept 14401 clauses.
% 65.20/65.39  SPASS allocated 138229 KBytes.
% 65.20/65.39  SPASS spent	0:01:05.09 on the problem.
% 65.20/65.39  		0:00:00.02 for the input.
% 65.20/65.39  		0:00:00.00 for the FLOTTER CNF translation.
% 65.20/65.39  		0:00:01.01 for inferences.
% 65.20/65.39  		0:00:00.00 for the backtracking.
% 65.20/65.39  		0:01:03.81 for the reduction.
% 65.20/65.39  
% 65.20/65.39  
% 65.20/65.39  Here is a proof with depth 15, length 67 :
% 65.20/65.39  % SZS output start Refutation
% See solution above
% 66.42/66.61  Formulae used in the proof : condensed_detachment c0_2 c0_5 c0_6 prove_c0_3
% 66.42/66.61  
%------------------------------------------------------------------------------