TSTP Solution File: RNG015-6 by SPASS---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : RNG015-6 : 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 : Mon Jul 18 20:41:13 EDT 2022

% Result   : Unsatisfiable 0.18s 0.49s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    9
% Syntax   : Number of clauses     :   23 (  23 unt;   0 nHn;  23 RR)
%            Number of literals    :   23 (   0 equ;   3 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   7 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ~ equal(multiply(x__dfg,add(y__dfg,additive_inverse(z__dfg))),add(multiply(x__dfg,y__dfg),additive_inverse(multiply(x__dfg,z__dfg)))),
    file('RNG015-6.p',unknown),
    [] ).

cnf(2,axiom,
    equal(add(additive_identity,u),u),
    file('RNG015-6.p',unknown),
    [] ).

cnf(3,axiom,
    equal(add(u,additive_identity),u),
    file('RNG015-6.p',unknown),
    [] ).

cnf(5,axiom,
    equal(multiply(u,additive_identity),additive_identity),
    file('RNG015-6.p',unknown),
    [] ).

cnf(7,axiom,
    equal(add(u,additive_inverse(u)),additive_identity),
    file('RNG015-6.p',unknown),
    [] ).

cnf(8,axiom,
    equal(additive_inverse(additive_inverse(u)),u),
    file('RNG015-6.p',unknown),
    [] ).

cnf(9,axiom,
    equal(multiply(u,add(v,w)),add(multiply(u,v),multiply(u,w))),
    file('RNG015-6.p',unknown),
    [] ).

cnf(11,axiom,
    equal(add(u,v),add(v,u)),
    file('RNG015-6.p',unknown),
    [] ).

cnf(12,axiom,
    equal(add(add(u,v),w),add(u,add(v,w))),
    file('RNG015-6.p',unknown),
    [] ).

cnf(18,plain,
    ~ equal(add(multiply(x__dfg,y__dfg),multiply(x__dfg,additive_inverse(z__dfg))),add(multiply(x__dfg,y__dfg),additive_inverse(multiply(x__dfg,z__dfg)))),
    inference(rew,[status(thm),theory(equality)],[9,1]),
    [iquote('0:Rew:9.0,1.0')] ).

cnf(28,plain,
    equal(additive_inverse(additive_identity),additive_identity),
    inference(spr,[status(thm),theory(equality)],[7,2]),
    [iquote('0:SpR:7.0,2.0')] ).

cnf(65,plain,
    equal(add(u,add(v,additive_inverse(add(u,v)))),additive_identity),
    inference(spr,[status(thm),theory(equality)],[12,7]),
    [iquote('0:SpR:12.0,7.0')] ).

cnf(72,plain,
    equal(add(u,add(additive_inverse(u),v)),add(additive_identity,v)),
    inference(spr,[status(thm),theory(equality)],[7,12]),
    [iquote('0:SpR:7.0,12.0')] ).

cnf(76,plain,
    equal(add(u,add(additive_inverse(u),v)),v),
    inference(rew,[status(thm),theory(equality)],[2,72]),
    [iquote('0:Rew:2.0,72.0')] ).

cnf(121,plain,
    equal(add(u,additive_inverse(add(additive_inverse(v),u))),add(v,additive_identity)),
    inference(spr,[status(thm),theory(equality)],[65,76]),
    [iquote('0:SpR:65.0,76.0')] ).

cnf(137,plain,
    equal(add(u,additive_inverse(add(additive_inverse(v),u))),v),
    inference(rew,[status(thm),theory(equality)],[3,121]),
    [iquote('0:Rew:3.0,121.0')] ).

cnf(186,plain,
    equal(add(u,additive_inverse(add(v,u))),additive_inverse(v)),
    inference(spr,[status(thm),theory(equality)],[8,137]),
    [iquote('0:SpR:8.0,137.0')] ).

cnf(366,plain,
    equal(add(multiply(u,v),multiply(u,additive_inverse(v))),multiply(u,additive_identity)),
    inference(spr,[status(thm),theory(equality)],[7,9]),
    [iquote('0:SpR:7.0,9.0')] ).

cnf(377,plain,
    equal(add(multiply(u,v),multiply(u,additive_inverse(v))),additive_identity),
    inference(rew,[status(thm),theory(equality)],[5,366]),
    [iquote('0:Rew:5.0,366.0')] ).

cnf(672,plain,
    equal(add(multiply(u,additive_inverse(v)),additive_inverse(additive_identity)),additive_inverse(multiply(u,v))),
    inference(spr,[status(thm),theory(equality)],[377,186]),
    [iquote('0:SpR:377.0,186.0')] ).

cnf(700,plain,
    equal(multiply(u,additive_inverse(v)),additive_inverse(multiply(u,v))),
    inference(rew,[status(thm),theory(equality)],[2,672,11,28]),
    [iquote('0:Rew:2.0,672.0,11.0,672.0,28.0,672.0')] ).

cnf(704,plain,
    ~ equal(add(multiply(x__dfg,y__dfg),additive_inverse(multiply(x__dfg,z__dfg))),add(multiply(x__dfg,y__dfg),additive_inverse(multiply(x__dfg,z__dfg)))),
    inference(rew,[status(thm),theory(equality)],[700,18]),
    [iquote('0:Rew:700.0,18.0')] ).

cnf(763,plain,
    $false,
    inference(obv,[status(thm),theory(equality)],[704]),
    [iquote('0:Obv:704.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : RNG015-6 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n017.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % 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 : Mon May 30 13:43:25 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.18/0.49  
% 0.18/0.49  SPASS V 3.9 
% 0.18/0.49  SPASS beiseite: Proof found.
% 0.18/0.49  % SZS status Theorem
% 0.18/0.49  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.18/0.49  SPASS derived 424 clauses, backtracked 0 clauses, performed 0 splits and kept 131 clauses.
% 0.18/0.49  SPASS allocated 64115 KBytes.
% 0.18/0.49  SPASS spent	0:00:00.14 on the problem.
% 0.18/0.49  		0:00:00.04 for the input.
% 0.18/0.49  		0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.49  		0:00:00.01 for inferences.
% 0.18/0.49  		0:00:00.00 for the backtracking.
% 0.18/0.49  		0:00:00.07 for the reduction.
% 0.18/0.49  
% 0.18/0.49  
% 0.18/0.49  Here is a proof with depth 4, length 23 :
% 0.18/0.49  % SZS output start Refutation
% See solution above
% 0.18/0.49  Formulae used in the proof : prove_distributivity left_additive_identity right_additive_identity right_multiplicative_zero right_additive_inverse additive_inverse_additive_inverse distribute1 commutativity_for_addition associativity_for_addition
% 0.18/0.49  
%------------------------------------------------------------------------------