TSTP Solution File: LCL025-1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : LCL025-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n017.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 120.59s 120.80s
% Output   : Refutation 120.59s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   43 (  21 unt;   0 nHn;  43 RR)
%            Number of literals    :   69 (   0 equ;  27 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    :    9 (   9 usr;   8 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('LCL025-1.p',unknown),
    [] ).

cnf(2,axiom,
    is_a_theorem(implies__dfg(u,implies__dfg(v,u))),
    file('LCL025-1.p',unknown),
    [] ).

cnf(3,axiom,
    is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,falsehood),falsehood),u)),
    file('LCL025-1.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('LCL025-1.p',unknown),
    [] ).

cnf(5,axiom,
    ~ is_a_theorem(implies__dfg(implies__dfg(a,b),implies__dfg(implies__dfg(b,c),implies__dfg(a,c)))),
    file('LCL025-1.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(19,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(21,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)],[19,4]),
    [iquote('0:SoR:19.0,4.0')] ).

cnf(22,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)],[19,11]),
    [iquote('0:SoR:19.0,11.1')] ).

cnf(23,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)],[19,3]),
    [iquote('0:SoR:19.0,3.0')] ).

cnf(24,plain,
    is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(u,u))),
    inference(sor,[status(thm)],[19,2]),
    [iquote('0:SoR:19.0,2.0')] ).

cnf(26,plain,
    ( ~ is_a_theorem(implies__dfg(u,v))
    | is_a_theorem(implies__dfg(u,u)) ),
    inference(res,[status(thm),theory(equality)],[24,1]),
    [iquote('0:Res:24.0,1.1')] ).

cnf(29,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)],[22,4]),
    [iquote('0:SoR:22.0,4.0')] ).

cnf(31,plain,
    is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(implies__dfg(v,falsehood),falsehood)),implies__dfg(u,v))),
    inference(sor,[status(thm)],[22,3]),
    [iquote('0:SoR:22.0,3.0')] ).

cnf(32,plain,
    is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(u,implies__dfg(w,v)))),
    inference(sor,[status(thm)],[22,2]),
    [iquote('0:SoR:22.0,2.0')] ).

cnf(42,plain,
    is_a_theorem(implies__dfg(u,u)),
    inference(sor,[status(thm)],[26,2]),
    [iquote('0:SoR:26.0,2.0')] ).

cnf(43,plain,
    is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),u),implies__dfg(implies__dfg(u,v),v))),
    inference(sor,[status(thm)],[19,42]),
    [iquote('0:SoR:19.0,42.0')] ).

cnf(48,plain,
    ( ~ is_a_theorem(implies__dfg(u,v))
    | is_a_theorem(implies__dfg(u,implies__dfg(w,v))) ),
    inference(res,[status(thm),theory(equality)],[32,1]),
    [iquote('0:Res:32.0,1.1')] ).

cnf(51,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)],[23,1]),
    [iquote('0:Res:23.0,1.1')] ).

cnf(61,plain,
    ( ~ is_a_theorem(u)
    | is_a_theorem(implies__dfg(v,implies__dfg(w,u))) ),
    inference(sor,[status(thm)],[48,11]),
    [iquote('0:SoR:48.0,11.1')] ).

cnf(63,plain,
    is_a_theorem(implies__dfg(u,implies__dfg(v,implies__dfg(w,u)))),
    inference(sor,[status(thm)],[48,2]),
    [iquote('0:SoR:48.0,2.0')] ).

cnf(64,plain,
    is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(u,implies__dfg(w,u)))),
    inference(sor,[status(thm)],[19,63]),
    [iquote('0:SoR:19.0,63.0')] ).

cnf(78,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)],[21,1]),
    [iquote('0:Res:21.0,1.1')] ).

cnf(98,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)],[31,1]),
    [iquote('0:Res:31.0,1.1')] ).

cnf(155,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)],[29,1]),
    [iquote('0:Res:29.0,1.1')] ).

cnf(167,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)],[43,1]),
    [iquote('0:Res:43.0,1.1')] ).

cnf(174,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)],[51,11]),
    [iquote('0:SoR:51.0,11.1')] ).

cnf(200,plain,
    is_a_theorem(implies__dfg(implies__dfg(u,implies__dfg(implies__dfg(v,u),w)),implies__dfg(u,w))),
    inference(sor,[status(thm)],[78,64]),
    [iquote('0:SoR:78.0,64.0')] ).

cnf(311,plain,
    is_a_theorem(implies__dfg(falsehood,u)),
    inference(sor,[status(thm)],[98,2]),
    [iquote('0:SoR:98.0,2.0')] ).

cnf(316,plain,
    is_a_theorem(implies__dfg(implies__dfg(u,falsehood),implies__dfg(u,v))),
    inference(sor,[status(thm)],[22,311]),
    [iquote('0:SoR:22.0,311.0')] ).

cnf(346,plain,
    ( ~ is_a_theorem(implies__dfg(u,falsehood))
    | is_a_theorem(implies__dfg(u,v)) ),
    inference(res,[status(thm),theory(equality)],[316,1]),
    [iquote('0:Res:316.0,1.1')] ).

cnf(352,plain,
    ( ~ is_a_theorem(u)
    | is_a_theorem(implies__dfg(implies__dfg(u,falsehood),falsehood)) ),
    inference(sor,[status(thm)],[12,174]),
    [iquote('0:SoR:12.0,174.1')] ).

cnf(354,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)],[174,1]),
    [iquote('0:Res:174.1,1.1')] ).

cnf(379,plain,
    ( ~ is_a_theorem(u)
    | is_a_theorem(implies__dfg(implies__dfg(u,falsehood),v)) ),
    inference(sor,[status(thm)],[346,352]),
    [iquote('0:SoR:346.0,352.1')] ).

cnf(659,plain,
    is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(w,u),implies__dfg(w,v)))),
    inference(sor,[status(thm)],[155,2]),
    [iquote('0:SoR:155.0,2.0')] ).

cnf(1123,plain,
    is_a_theorem(implies__dfg(implies__dfg(implies__dfg(u,v),implies__dfg(w,u)),implies__dfg(implies__dfg(u,v),implies__dfg(w,v)))),
    inference(sor,[status(thm)],[19,659]),
    [iquote('0:SoR:19.0,659.0')] ).

cnf(1879,plain,
    ( ~ is_a_theorem(u)
    | ~ is_a_theorem(implies__dfg(u,v))
    | is_a_theorem(v) ),
    inference(sor,[status(thm)],[354,379]),
    [iquote('0:SoR:354.1,379.1')] ).

cnf(10761,plain,
    ( ~ is_a_theorem(u)
    | is_a_theorem(implies__dfg(implies__dfg(implies__dfg(v,u),w),w)) ),
    inference(sor,[status(thm)],[167,61]),
    [iquote('0:SoR:167.0,61.1')] ).

cnf(10860,plain,
    ( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),w))
    | ~ is_a_theorem(v)
    | is_a_theorem(w) ),
    inference(sor,[status(thm)],[1879,10761]),
    [iquote('0:SoR:1879.1,10761.1')] ).

cnf(11579,plain,
    ( ~ is_a_theorem(implies__dfg(implies__dfg(u,v),w))
    | is_a_theorem(implies__dfg(v,w)) ),
    inference(sor,[status(thm)],[10860,200]),
    [iquote('0:SoR:10860.0,200.0')] ).

cnf(69281,plain,
    is_a_theorem(implies__dfg(implies__dfg(u,v),implies__dfg(implies__dfg(v,w),implies__dfg(u,w)))),
    inference(sor,[status(thm)],[11579,1123]),
    [iquote('0:SoR:11579.0,1123.0')] ).

cnf(69284,plain,
    $false,
    inference(unc,[status(thm)],[69281,5]),
    [iquote('0:UnC:69281.0,5.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : LCL025-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.13  % Command  : run_spass %d %s
% 0.12/0.34  % Computer : n017.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Sat Jul  2 16:22:55 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 120.59/120.80  
% 120.59/120.80  SPASS V 3.9 
% 120.59/120.80  SPASS beiseite: Proof found.
% 120.59/120.80  % SZS status Theorem
% 120.59/120.80  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 120.59/120.80  SPASS derived 68855 clauses, backtracked 0 clauses, performed 0 splits and kept 18487 clauses.
% 120.59/120.80  SPASS allocated 157471 KBytes.
% 120.59/120.80  SPASS spent	0:1:58.35 on the problem.
% 120.59/120.80  		0:00:00.04 for the input.
% 120.59/120.80  		0:00:00.00 for the FLOTTER CNF translation.
% 120.59/120.80  		0:00:01.43 for inferences.
% 120.59/120.80  		0:00:00.00 for the backtracking.
% 120.59/120.80  		0:1:56.51 for the reduction.
% 120.59/120.80  
% 120.59/120.80  
% 120.59/120.80  Here is a proof with depth 12, length 43 :
% 120.59/120.80  % SZS output start Refutation
% See solution above
% 120.59/120.80  Formulae used in the proof : condensed_detachment c0_2 c0_5 c0_6 prove_c0_1
% 120.59/120.80  
%------------------------------------------------------------------------------