TSTP Solution File: ROB023-1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : ROB023-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n018.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 : Mon Jul 18 20:56:16 EDT 2022

% Result   : Unsatisfiable 0.20s 0.51s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   35 (  35 unt;   0 nHn;  35 RR)
%            Number of literals    :   35 (   0 equ;   3 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    9 (   3 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(add(u,u),u),
    file('ROB023-1.p',unknown),
    [] ).

cnf(2,axiom,
    ~ equal(add(negate(add(a,negate(b))),negate(add(negate(a),negate(b)))),b),
    file('ROB023-1.p',unknown),
    [] ).

cnf(3,axiom,
    equal(add(u,v),add(v,u)),
    file('ROB023-1.p',unknown),
    [] ).

cnf(4,axiom,
    equal(add(add(u,v),w),add(u,add(v,w))),
    file('ROB023-1.p',unknown),
    [] ).

cnf(5,axiom,
    equal(negate(add(negate(add(u,v)),negate(add(u,negate(v))))),u),
    file('ROB023-1.p',unknown),
    [] ).

cnf(14,plain,
    equal(add(u,add(v,w)),add(v,add(w,u))),
    inference(spr,[status(thm),theory(equality)],[4,3]),
    [iquote('0:SpR:4.0,3.0')] ).

cnf(18,plain,
    equal(add(u,add(u,v)),add(u,v)),
    inference(spr,[status(thm),theory(equality)],[1,4]),
    [iquote('0:SpR:1.0,4.0')] ).

cnf(19,plain,
    equal(add(add(u,v),w),add(v,add(u,w))),
    inference(spr,[status(thm),theory(equality)],[3,4]),
    [iquote('0:SpR:3.0,4.0')] ).

cnf(21,plain,
    equal(add(u,add(v,w)),add(v,add(u,w))),
    inference(rew,[status(thm),theory(equality)],[4,19]),
    [iquote('0:Rew:4.0,19.0')] ).

cnf(29,plain,
    equal(add(u,add(v,u)),add(v,u)),
    inference(spr,[status(thm),theory(equality)],[3,18]),
    [iquote('0:SpR:3.0,18.0')] ).

cnf(40,plain,
    equal(negate(add(negate(add(negate(u),u)),negate(negate(u)))),negate(u)),
    inference(spr,[status(thm),theory(equality)],[1,5]),
    [iquote('0:SpR:1.0,5.0')] ).

cnf(41,plain,
    equal(negate(add(negate(add(u,v)),negate(add(negate(v),u)))),u),
    inference(spr,[status(thm),theory(equality)],[3,5]),
    [iquote('0:SpR:3.0,5.0')] ).

cnf(44,plain,
    equal(negate(add(negate(u),negate(add(u,negate(u))))),u),
    inference(spr,[status(thm),theory(equality)],[1,5]),
    [iquote('0:SpR:1.0,5.0')] ).

cnf(49,plain,
    equal(negate(add(negate(negate(u)),negate(add(u,negate(u))))),negate(u)),
    inference(rew,[status(thm),theory(equality)],[3,40]),
    [iquote('0:Rew:3.0,40.0,3.0,40.0')] ).

cnf(72,plain,
    equal(negate(add(negate(add(negate(u),add(u,negate(u)))),u)),negate(u)),
    inference(spr,[status(thm),theory(equality)],[44,5]),
    [iquote('0:SpR:44.0,5.0')] ).

cnf(75,plain,
    equal(negate(add(u,negate(add(add(negate(u),negate(add(u,negate(u)))),u)))),add(negate(u),negate(add(u,negate(u))))),
    inference(spr,[status(thm),theory(equality)],[44]),
    [iquote('0:SpR:44.0,44.0')] ).

cnf(79,plain,
    equal(negate(add(u,negate(add(u,negate(u))))),negate(u)),
    inference(rew,[status(thm),theory(equality)],[3,72,29]),
    [iquote('0:Rew:3.0,72.0,29.0,72.0')] ).

cnf(81,plain,
    equal(negate(add(u,negate(add(negate(u),add(u,negate(add(u,negate(u)))))))),add(negate(u),negate(add(u,negate(u))))),
    inference(rew,[status(thm),theory(equality)],[3,75,4]),
    [iquote('0:Rew:3.0,75.0,4.0,75.0')] ).

cnf(82,plain,
    equal(negate(add(u,negate(add(u,add(negate(u),negate(add(u,negate(u)))))))),add(negate(u),negate(add(u,negate(u))))),
    inference(rew,[status(thm),theory(equality)],[21,81]),
    [iquote('0:Rew:21.0,81.0')] ).

cnf(91,plain,
    equal(negate(add(negate(u),negate(add(add(u,negate(add(u,negate(u)))),negate(u))))),add(u,negate(add(u,negate(u))))),
    inference(spr,[status(thm),theory(equality)],[79,44]),
    [iquote('0:SpR:79.0,44.0')] ).

cnf(104,plain,
    equal(negate(add(negate(u),negate(add(u,add(negate(u),negate(add(u,negate(u)))))))),add(u,negate(add(u,negate(u))))),
    inference(rew,[status(thm),theory(equality)],[3,91,4]),
    [iquote('0:Rew:3.0,91.0,4.0,91.0')] ).

cnf(136,plain,
    equal(add(u,add(v,w)),add(w,add(v,u))),
    inference(spr,[status(thm),theory(equality)],[3,14]),
    [iquote('0:SpR:3.0,14.0')] ).

cnf(478,plain,
    equal(negate(add(negate(u),negate(add(add(negate(u),negate(add(u,negate(u)))),u)))),u),
    inference(spr,[status(thm),theory(equality)],[44,49]),
    [iquote('0:SpR:44.0,49.0')] ).

cnf(484,plain,
    equal(negate(add(negate(u),negate(add(u,add(negate(u),negate(add(u,negate(u)))))))),u),
    inference(rew,[status(thm),theory(equality)],[21,478,3,4]),
    [iquote('0:Rew:21.0,478.0,3.0,478.0,4.0,478.0')] ).

cnf(485,plain,
    equal(add(u,negate(add(u,negate(u)))),u),
    inference(rew,[status(thm),theory(equality)],[104,484]),
    [iquote('0:Rew:104.0,484.0')] ).

cnf(529,plain,
    equal(negate(add(negate(add(u,v)),negate(add(negate(u),v)))),v),
    inference(spr,[status(thm),theory(equality)],[3,41]),
    [iquote('0:SpR:3.0,41.0')] ).

cnf(578,plain,
    equal(add(negate(add(u,negate(u))),add(v,u)),add(v,u)),
    inference(spr,[status(thm),theory(equality)],[485,14]),
    [iquote('0:SpR:485.0,14.0')] ).

cnf(599,plain,
    equal(add(u,add(v,negate(add(u,negate(u))))),add(v,u)),
    inference(rew,[status(thm),theory(equality)],[136,578]),
    [iquote('0:Rew:136.0,578.0')] ).

cnf(600,plain,
    equal(add(negate(u),negate(add(u,negate(u)))),negate(add(u,negate(add(negate(u),u))))),
    inference(rew,[status(thm),theory(equality)],[599,82]),
    [iquote('0:Rew:599.0,82.0')] ).

cnf(616,plain,
    equal(add(negate(u),negate(add(u,negate(u)))),negate(u)),
    inference(rew,[status(thm),theory(equality)],[485,600,3]),
    [iquote('0:Rew:485.0,600.0,3.0,600.0')] ).

cnf(617,plain,
    equal(negate(negate(u)),u),
    inference(rew,[status(thm),theory(equality)],[616,44]),
    [iquote('0:Rew:616.0,44.0')] ).

cnf(826,plain,
    equal(add(negate(add(u,v)),negate(add(negate(u),v))),negate(v)),
    inference(spr,[status(thm),theory(equality)],[529,617]),
    [iquote('0:SpR:529.0,617.0')] ).

cnf(863,plain,
    ~ equal(negate(negate(b)),b),
    inference(rew,[status(thm),theory(equality)],[826,2]),
    [iquote('0:Rew:826.0,2.0')] ).

cnf(864,plain,
    ~ equal(b,b),
    inference(rew,[status(thm),theory(equality)],[617,863]),
    [iquote('0:Rew:617.0,863.0')] ).

cnf(865,plain,
    $false,
    inference(obv,[status(thm),theory(equality)],[864]),
    [iquote('0:Obv:864.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : ROB023-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12  % Command  : run_spass %d %s
% 0.13/0.33  % Computer : n018.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Thu Jun  9 15:10:23 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.20/0.51  
% 0.20/0.51  SPASS V 3.9 
% 0.20/0.51  SPASS beiseite: Proof found.
% 0.20/0.51  % SZS status Theorem
% 0.20/0.51  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.20/0.51  SPASS derived 538 clauses, backtracked 0 clauses, performed 0 splits and kept 143 clauses.
% 0.20/0.51  SPASS allocated 64178 KBytes.
% 0.20/0.51  SPASS spent	0:00:00.16 on the problem.
% 0.20/0.51  		0:00:00.03 for the input.
% 0.20/0.51  		0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.51  		0:00:00.01 for inferences.
% 0.20/0.51  		0:00:00.00 for the backtracking.
% 0.20/0.51  		0:00:00.10 for the reduction.
% 0.20/0.51  
% 0.20/0.51  
% 0.20/0.51  Here is a proof with depth 3, length 35 :
% 0.20/0.51  % SZS output start Refutation
% See solution above
% 0.20/0.51  Formulae used in the proof : x_plus_x_is_x prove_huntingtons_axiom commutativity_of_add associativity_of_add robbins_axiom
% 0.20/0.51  
%------------------------------------------------------------------------------