TSTP Solution File: BOO029-1 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : BOO029-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n026.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 23:49:29 EDT 2022

% Result   : Unsatisfiable 0.36s 0.54s
% Output   : Refutation 0.36s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    9
% Syntax   : Number of clauses     :   29 (  29 unt;   0 nHn;  29 RR)
%            Number of literals    :   29 (   0 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(add(u,multiply(v,multiply(u,w))),u),
    file('BOO029-1.p',unknown),
    [] ).

cnf(3,axiom,
    equal(multiply(add(u,v),add(u,inverse(v))),u),
    file('BOO029-1.p',unknown),
    [] ).

cnf(4,axiom,
    equal(multiply(u,add(v,add(u,w))),u),
    file('BOO029-1.p',unknown),
    [] ).

cnf(6,axiom,
    equal(add(multiply(u,v),multiply(u,inverse(v))),u),
    file('BOO029-1.p',unknown),
    [] ).

cnf(7,axiom,
    equal(add(u,v),add(v,u)),
    file('BOO029-1.p',unknown),
    [] ).

cnf(8,axiom,
    equal(multiply(u,v),multiply(v,u)),
    file('BOO029-1.p',unknown),
    [] ).

cnf(9,axiom,
    equal(add(add(u,v),w),add(u,add(v,w))),
    file('BOO029-1.p',unknown),
    [] ).

cnf(10,axiom,
    equal(multiply(multiply(u,v),w),multiply(u,multiply(v,w))),
    file('BOO029-1.p',unknown),
    [] ).

cnf(11,axiom,
    ~ equal(add(a,inverse(a)),add(b,inverse(b))),
    file('BOO029-1.p',unknown),
    [] ).

cnf(29,plain,
    equal(multiply(u,add(v,u)),u),
    inference(spr,[status(thm),theory(equality)],[1,4]),
    [iquote('0:SpR:1.0,4.0')] ).

cnf(40,plain,
    equal(multiply(u,add(u,v)),u),
    inference(spr,[status(thm),theory(equality)],[7,29]),
    [iquote('0:SpR:7.0,29.0')] ).

cnf(76,plain,
    equal(multiply(multiply(u,v),add(w,u)),multiply(u,v)),
    inference(spr,[status(thm),theory(equality)],[6,4]),
    [iquote('0:SpR:6.0,4.0')] ).

cnf(81,plain,
    equal(add(multiply(u,v),multiply(v,inverse(u))),v),
    inference(spr,[status(thm),theory(equality)],[8,6]),
    [iquote('0:SpR:8.0,6.0')] ).

cnf(90,plain,
    equal(multiply(u,multiply(v,add(w,u))),multiply(u,v)),
    inference(rew,[status(thm),theory(equality)],[10,76]),
    [iquote('0:Rew:10.0,76.0')] ).

cnf(378,plain,
    equal(add(u,multiply(add(v,u),inverse(u))),add(v,u)),
    inference(spr,[status(thm),theory(equality)],[29,81]),
    [iquote('0:SpR:29.0,81.0')] ).

cnf(391,plain,
    equal(add(u,multiply(inverse(u),add(v,u))),add(v,u)),
    inference(rew,[status(thm),theory(equality)],[8,378]),
    [iquote('0:Rew:8.0,378.0')] ).

cnf(495,plain,
    equal(add(u,add(v,w)),add(v,add(w,u))),
    inference(spr,[status(thm),theory(equality)],[9,7]),
    [iquote('0:SpR:9.0,7.0')] ).

cnf(685,plain,
    equal(multiply(inverse(u),add(v,u)),multiply(inverse(u),v)),
    inference(spr,[status(thm),theory(equality)],[3,90]),
    [iquote('0:SpR:3.0,90.0')] ).

cnf(695,plain,
    equal(add(u,multiply(inverse(u),v)),add(v,u)),
    inference(rew,[status(thm),theory(equality)],[685,391]),
    [iquote('0:Rew:685.0,391.0')] ).

cnf(753,plain,
    equal(add(add(u,inverse(v)),v),add(v,inverse(v))),
    inference(spr,[status(thm),theory(equality)],[29,695]),
    [iquote('0:SpR:29.0,695.0')] ).

cnf(754,plain,
    equal(add(add(inverse(u),v),u),add(u,inverse(u))),
    inference(spr,[status(thm),theory(equality)],[40,695]),
    [iquote('0:SpR:40.0,695.0')] ).

cnf(763,plain,
    equal(add(u,add(v,inverse(v))),add(v,inverse(v))),
    inference(rew,[status(thm),theory(equality)],[7,753,9]),
    [iquote('0:Rew:7.0,753.0,9.0,753.0')] ).

cnf(764,plain,
    equal(add(inverse(u),add(v,u)),add(u,inverse(u))),
    inference(rew,[status(thm),theory(equality)],[9,754]),
    [iquote('0:Rew:9.0,754.0')] ).

cnf(765,plain,
    equal(add(u,add(inverse(u),v)),add(u,inverse(u))),
    inference(rew,[status(thm),theory(equality)],[495,764]),
    [iquote('0:Rew:495.0,764.0')] ).

cnf(1084,plain,
    equal(multiply(u,add(v,inverse(v))),u),
    inference(spr,[status(thm),theory(equality)],[763,40]),
    [iquote('0:SpR:763.0,40.0')] ).

cnf(1219,plain,
    equal(add(u,inverse(u)),add(add(v,inverse(v)),u)),
    inference(spr,[status(thm),theory(equality)],[1084,695]),
    [iquote('0:SpR:1084.0,695.0')] ).

cnf(1228,plain,
    equal(add(u,inverse(u)),add(v,add(inverse(v),u))),
    inference(rew,[status(thm),theory(equality)],[9,1219]),
    [iquote('0:Rew:9.0,1219.0')] ).

cnf(1229,plain,
    equal(add(u,inverse(u)),add(v,inverse(v))),
    inference(rew,[status(thm),theory(equality)],[765,1228]),
    [iquote('0:Rew:765.0,1228.0')] ).

cnf(1230,plain,
    $false,
    inference(unc,[status(thm)],[1229,11]),
    [iquote('0:UnC:1229.0,11.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : BOO029-1 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12  % Command  : run_spass %d %s
% 0.13/0.33  % Computer : n026.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
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Thu Jun  2 00:25:12 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.36/0.54  
% 0.36/0.54  SPASS V 3.9 
% 0.36/0.54  SPASS beiseite: Proof found.
% 0.36/0.54  % SZS status Theorem
% 0.36/0.54  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.36/0.54  SPASS derived 837 clauses, backtracked 0 clauses, performed 0 splits and kept 219 clauses.
% 0.36/0.54  SPASS allocated 64337 KBytes.
% 0.36/0.54  SPASS spent	0:00:00.17 on the problem.
% 0.36/0.54  		0:00:00.03 for the input.
% 0.36/0.54  		0:00:00.00 for the FLOTTER CNF translation.
% 0.36/0.54  		0:00:00.01 for inferences.
% 0.36/0.54  		0:00:00.00 for the backtracking.
% 0.36/0.54  		0:00:00.11 for the reduction.
% 0.36/0.54  
% 0.36/0.54  
% 0.36/0.54  Here is a proof with depth 5, length 29 :
% 0.36/0.54  % SZS output start Refutation
% See solution above
% 0.36/0.54  Formulae used in the proof : l1 b1 l2 b2 commutativity_of_add commutativity_of_multiply associativity_of_add associativity_of_multiply prove_equal_inverse
% 0.36/0.54  
%------------------------------------------------------------------------------