TSTP Solution File: ALG007-1 by SPASS---3.9

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%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : ALG007-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n032.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 : Thu Jul 14 18:01:56 EDT 2022

% Result   : Unsatisfiable 3.84s 4.02s
% Output   : Refutation 3.84s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    4
% Syntax   : Number of clauses     :   38 (  38 unt;   0 nHn;  38 RR)
%            Number of literals    :   38 (   0 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   7 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(difference(u,difference(v,u)),u),
    file('ALG007-1.p',unknown),
    [] ).

cnf(2,axiom,
    equal(difference(u,difference(u,v)),difference(v,difference(v,u))),
    file('ALG007-1.p',unknown),
    [] ).

cnf(3,axiom,
    equal(difference(difference(u,v),w),difference(difference(u,w),v)),
    file('ALG007-1.p',unknown),
    [] ).

cnf(4,axiom,
    ~ equal(difference(difference(a,c),difference(b,c)),difference(difference(a,b),c)),
    file('ALG007-1.p',unknown),
    [] ).

cnf(5,plain,
    equal(difference(difference(u,v),v),difference(u,v)),
    inference(spr,[status(thm),theory(equality)],[1]),
    [iquote('0:SpR:1.0,1.0')] ).

cnf(21,plain,
    equal(difference(difference(u,v),difference(u,v)),difference(v,difference(v,difference(u,v)))),
    inference(spr,[status(thm),theory(equality)],[5,2]),
    [iquote('0:SpR:5.0,2.0')] ).

cnf(23,plain,
    equal(difference(difference(u,v),difference(u,v)),difference(v,v)),
    inference(rew,[status(thm),theory(equality)],[1,21]),
    [iquote('0:Rew:1.0,21.0')] ).

cnf(25,plain,
    equal(difference(u,difference(difference(v,u),w)),u),
    inference(spr,[status(thm),theory(equality)],[3,1]),
    [iquote('0:SpR:3.0,1.0')] ).

cnf(29,plain,
    equal(difference(difference(difference(u,v),w),x),difference(difference(difference(u,w),x),v)),
    inference(spr,[status(thm),theory(equality)],[3]),
    [iquote('0:SpR:3.0,3.0')] ).

cnf(43,plain,
    equal(difference(difference(u,difference(u,v)),w),difference(difference(v,w),difference(v,u))),
    inference(spr,[status(thm),theory(equality)],[2,3]),
    [iquote('0:SpR:2.0,3.0')] ).

cnf(44,plain,
    equal(difference(difference(u,v),difference(w,u)),difference(u,v)),
    inference(spr,[status(thm),theory(equality)],[1,3]),
    [iquote('0:SpR:1.0,3.0')] ).

cnf(84,plain,
    equal(difference(difference(difference(u,v),w),difference(difference(u,v),w)),difference(v,v)),
    inference(spr,[status(thm),theory(equality)],[25,23]),
    [iquote('0:SpR:25.0,23.0')] ).

cnf(96,plain,
    equal(difference(u,u),difference(v,v)),
    inference(rew,[status(thm),theory(equality)],[23,84]),
    [iquote('0:Rew:23.0,84.0')] ).

cnf(99,plain,
    equal(difference(u,difference(v,v)),u),
    inference(spr,[status(thm),theory(equality)],[96,1]),
    [iquote('0:SpR:96.0,1.0')] ).

cnf(103,plain,
    equal(difference(difference(u,u),v),difference(u,u)),
    inference(spr,[status(thm),theory(equality)],[96,5]),
    [iquote('0:SpR:96.0,5.0')] ).

cnf(158,plain,
    equal(difference(u,difference(u,difference(u,v))),difference(u,v)),
    inference(spr,[status(thm),theory(equality)],[44,2]),
    [iquote('0:SpR:44.0,2.0')] ).

cnf(166,plain,
    equal(difference(difference(difference(u,v),w),difference(x,u)),difference(difference(u,v),w)),
    inference(spr,[status(thm),theory(equality)],[44,3]),
    [iquote('0:SpR:44.0,3.0')] ).

cnf(219,plain,
    equal(difference(difference(u,v),u),difference(u,u)),
    inference(spr,[status(thm),theory(equality)],[103,3]),
    [iquote('0:SpR:103.0,3.0')] ).

cnf(244,plain,
    equal(difference(difference(difference(u,v),w),u),difference(difference(u,u),w)),
    inference(spr,[status(thm),theory(equality)],[219,3]),
    [iquote('0:SpR:219.0,3.0')] ).

cnf(272,plain,
    equal(difference(difference(difference(u,v),w),u),difference(u,u)),
    inference(rew,[status(thm),theory(equality)],[103,244]),
    [iquote('0:Rew:103.0,244.0')] ).

cnf(442,plain,
    equal(difference(difference(difference(u,v),w),x),difference(difference(difference(u,w),v),x)),
    inference(spr,[status(thm),theory(equality)],[29,3]),
    [iquote('0:SpR:29.0,3.0')] ).

cnf(684,plain,
    equal(difference(u,difference(v,difference(v,u))),difference(u,v)),
    inference(spr,[status(thm),theory(equality)],[2,158]),
    [iquote('0:SpR:2.0,158.0')] ).

cnf(703,plain,
    equal(difference(difference(difference(u,v),w),difference(u,u)),difference(u,difference(u,difference(difference(u,v),w)))),
    inference(spr,[status(thm),theory(equality)],[272,2]),
    [iquote('0:SpR:272.0,2.0')] ).

cnf(797,plain,
    equal(difference(u,difference(u,difference(difference(u,v),w))),difference(difference(u,v),w)),
    inference(rew,[status(thm),theory(equality)],[99,703]),
    [iquote('0:Rew:99.0,703.0')] ).

cnf(926,plain,
    equal(difference(difference(u,v),difference(u,w)),difference(difference(w,v),difference(w,u))),
    inference(spr,[status(thm),theory(equality)],[43,3]),
    [iquote('0:SpR:43.0,3.0')] ).

cnf(930,plain,
    equal(difference(difference(u,difference(v,w)),difference(u,w)),difference(w,difference(w,u))),
    inference(spr,[status(thm),theory(equality)],[43,44]),
    [iquote('0:SpR:43.0,44.0')] ).

cnf(957,plain,
    equal(difference(difference(u,v),difference(difference(w,difference(w,u)),v)),difference(difference(u,w),difference(difference(u,w),difference(u,v)))),
    inference(spr,[status(thm),theory(equality)],[43,2]),
    [iquote('0:SpR:43.0,2.0')] ).

cnf(5692,plain,
    equal(difference(u,difference(difference(difference(v,w),x),difference(difference(difference(v,x),w),u))),difference(u,difference(difference(v,w),x))),
    inference(spr,[status(thm),theory(equality)],[442,684]),
    [iquote('0:SpR:442.0,684.0')] ).

cnf(5700,plain,
    equal(difference(u,difference(difference(difference(v,w),x),difference(difference(difference(v,x),w),u))),difference(u,difference(difference(v,x),w))),
    inference(spr,[status(thm),theory(equality)],[442,684]),
    [iquote('0:SpR:442.0,684.0')] ).

cnf(6081,plain,
    equal(difference(u,difference(difference(v,w),x)),difference(u,difference(difference(v,x),w))),
    inference(rew,[status(thm),theory(equality)],[5700,5692]),
    [iquote('0:Rew:5700.0,5692.0')] ).

cnf(8376,plain,
    equal(difference(difference(difference(u,difference(u,v)),w),difference(difference(v,w),u)),difference(u,difference(u,difference(v,w)))),
    inference(spr,[status(thm),theory(equality)],[43,930]),
    [iquote('0:SpR:43.0,930.0')] ).

cnf(8389,plain,
    equal(difference(difference(difference(u,v),difference(u,w)),difference(difference(w,v),u)),difference(u,difference(u,difference(w,v)))),
    inference(spr,[status(thm),theory(equality)],[926,930]),
    [iquote('0:SpR:926.0,930.0')] ).

cnf(8435,plain,
    equal(difference(difference(u,v),difference(u,w)),difference(u,difference(u,difference(w,v)))),
    inference(rew,[status(thm),theory(equality)],[166,8389]),
    [iquote('0:Rew:166.0,8389.0')] ).

cnf(8502,plain,
    equal(difference(difference(u,v),difference(difference(w,difference(w,u)),v)),difference(difference(u,w),difference(u,difference(u,difference(v,w))))),
    inference(rew,[status(thm),theory(equality)],[8435,957]),
    [iquote('0:Rew:8435.0,957.0')] ).

cnf(8741,plain,
    equal(difference(difference(u,difference(u,v)),w),difference(u,difference(u,difference(v,w)))),
    inference(rew,[status(thm),theory(equality)],[166,8376]),
    [iquote('0:Rew:166.0,8376.0')] ).

cnf(9157,plain,
    equal(difference(difference(u,v),difference(w,difference(w,difference(u,v)))),difference(difference(u,w),difference(v,w))),
    inference(rew,[status(thm),theory(equality)],[8741,8502,797,6081,8435]),
    [iquote('0:Rew:8741.0,8502.0,797.0,8502.0,6081.0,8502.0,8435.0,8502.0')] ).

cnf(9158,plain,
    equal(difference(difference(u,v),difference(w,v)),difference(difference(u,w),v)),
    inference(rew,[status(thm),theory(equality)],[684,9157]),
    [iquote('0:Rew:684.0,9157.0')] ).

cnf(9159,plain,
    $false,
    inference(unc,[status(thm)],[9158,4]),
    [iquote('0:UnC:9158.0,4.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : ALG007-1 : TPTP v8.1.0. Released v2.2.0.
% 0.00/0.10  % Command  : run_spass %d %s
% 0.10/0.30  % Computer : n032.cluster.edu
% 0.10/0.30  % Model    : x86_64 x86_64
% 0.10/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30  % Memory   : 8042.1875MB
% 0.10/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30  % CPULimit : 300
% 0.10/0.30  % WCLimit  : 600
% 0.10/0.30  % DateTime : Wed Jun  8 12:52:36 EDT 2022
% 0.10/0.30  % CPUTime  : 
% 3.84/4.02  
% 3.84/4.02  SPASS V 3.9 
% 3.84/4.02  SPASS beiseite: Proof found.
% 3.84/4.02  % SZS status Theorem
% 3.84/4.02  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 3.84/4.02  SPASS derived 7433 clauses, backtracked 0 clauses, performed 0 splits and kept 1114 clauses.
% 3.84/4.02  SPASS allocated 71453 KBytes.
% 3.84/4.02  SPASS spent	0:00:03.67 on the problem.
% 3.84/4.02  		0:00:00.02 for the input.
% 3.84/4.02  		0:00:00.00 for the FLOTTER CNF translation.
% 3.84/4.02  		0:00:00.06 for inferences.
% 3.84/4.02  		0:00:00.00 for the backtracking.
% 3.84/4.02  		0:00:03.56 for the reduction.
% 3.84/4.02  
% 3.84/4.02  
% 3.84/4.02  Here is a proof with depth 7, length 38 :
% 3.84/4.02  % SZS output start Refutation
% See solution above
% 3.84/4.02  Formulae used in the proof : set_difference_1 set_difference_2 set_difference_3_simplified prove_set_difference_3
% 3.84/4.02  
%------------------------------------------------------------------------------