TSTP Solution File: COL011-1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : COL011-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n024.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 : Fri Jul 15 00:42:24 EDT 2022

% Result   : Unsatisfiable 29.66s 29.86s
% Output   : Refutation 29.66s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    3
% Syntax   : Number of clauses     :   12 (  12 unt;   0 nHn;  12 RR)
%            Number of literals    :   12 (   0 equ;   5 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(apply(apply(o,u),v),apply(v,apply(u,v))),
    file('COL011-1.p',unknown),
    [] ).

cnf(2,axiom,
    equal(apply(apply(apply(q1,u),v),w),apply(u,apply(w,v))),
    file('COL011-1.p',unknown),
    [] ).

cnf(3,axiom,
    ~ equal(apply(combinator,u),u),
    file('COL011-1.p',unknown),
    [] ).

cnf(6,plain,
    equal(apply(apply(u,v),apply(apply(o,u),v)),apply(apply(o,v),apply(u,v))),
    inference(spr,[status(thm),theory(equality)],[1]),
    [iquote('0:SpR:1.0,1.0')] ).

cnf(9,plain,
    equal(apply(u,apply(apply(v,apply(apply(q1,u),w)),w)),apply(apply(o,v),apply(apply(q1,u),w))),
    inference(spr,[status(thm),theory(equality)],[2,1]),
    [iquote('0:SpR:2.0,1.0')] ).

cnf(672,plain,
    equal(apply(u,apply(v,apply(w,apply(apply(q1,u),w)))),apply(apply(o,apply(q1,v)),apply(apply(q1,u),w))),
    inference(spr,[status(thm),theory(equality)],[2,9]),
    [iquote('0:SpR:2.0,9.0')] ).

cnf(674,plain,
    ~ equal(apply(apply(u,apply(apply(q1,combinator),v)),v),apply(apply(o,u),apply(apply(q1,combinator),v))),
    inference(spl,[status(thm),theory(equality)],[9,3]),
    [iquote('0:SpL:9.0,3.0')] ).

cnf(2616,plain,
    ~ equal(apply(u,apply(v,apply(apply(q1,combinator),v))),apply(apply(o,apply(q1,u)),apply(apply(q1,combinator),v))),
    inference(spl,[status(thm),theory(equality)],[2,674]),
    [iquote('0:SpL:2.0,674.0')] ).

cnf(10442,plain,
    ~ equal(apply(apply(o,apply(q1,u)),apply(apply(q1,combinator),v)),apply(u,apply(apply(o,apply(q1,combinator)),v))),
    inference(spl,[status(thm),theory(equality)],[1,2616]),
    [iquote('0:SpL:1.0,2616.0')] ).

cnf(14307,plain,
    equal(apply(apply(apply(o,apply(q1,u)),apply(apply(q1,v),w)),apply(apply(o,v),apply(u,apply(w,apply(apply(q1,v),w))))),apply(apply(o,apply(u,apply(w,apply(apply(q1,v),w)))),apply(apply(o,apply(q1,u)),apply(apply(q1,v),w)))),
    inference(spr,[status(thm),theory(equality)],[672,6]),
    [iquote('0:SpR:672.0,6.0')] ).

cnf(14602,plain,
    ~ equal(apply(apply(o,apply(q1,u)),apply(apply(o,apply(q1,v)),apply(apply(q1,apply(q1,combinator)),w))),apply(u,apply(apply(o,apply(q1,combinator)),apply(v,apply(w,apply(apply(q1,apply(q1,combinator)),w)))))),
    inference(spl,[status(thm),theory(equality)],[672,10442]),
    [iquote('0:SpL:672.0,10442.0')] ).

cnf(14937,plain,
    $false,
    inference(unc,[status(thm)],[14307,14602]),
    [iquote('0:UnC:14307.0,14602.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : COL011-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12  % Command  : run_spass %d %s
% 0.12/0.34  % Computer : n024.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 : Tue May 31 08:35:36 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 29.66/29.86  
% 29.66/29.86  SPASS V 3.9 
% 29.66/29.86  SPASS beiseite: Proof found.
% 29.66/29.86  % SZS status Theorem
% 29.66/29.86  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 29.66/29.86  SPASS derived 8710 clauses, backtracked 0 clauses, performed 0 splits and kept 3109 clauses.
% 29.66/29.86  SPASS allocated 104795 KBytes.
% 29.66/29.86  SPASS spent	0:0:29.20 on the problem.
% 29.66/29.86  		0:00:00.03 for the input.
% 29.66/29.86  		0:00:00.00 for the FLOTTER CNF translation.
% 29.66/29.86  		0:00:00.22 for inferences.
% 29.66/29.86  		0:00:00.00 for the backtracking.
% 29.66/29.86  		0:0:28.91 for the reduction.
% 29.66/29.86  
% 29.66/29.86  
% 29.66/29.86  Here is a proof with depth 5, length 12 :
% 29.66/29.86  % SZS output start Refutation
% See solution above
% 29.66/29.86  Formulae used in the proof : o_definition q1_definition prove_fixed_point
% 29.66/29.86  
%------------------------------------------------------------------------------