TSTP Solution File: RNG007-4 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : RNG007-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 20:41:11 EDT 2022
% Result : Unsatisfiable 0.18s 0.41s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of clauses : 13 ( 13 unt; 0 nHn; 13 RR)
% Number of literals : 13 ( 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(multiply(u,u),u),
file('RNG007-4.p',unknown),
[] ).
cnf(2,axiom,
~ equal(add(a,a),additive_identity),
file('RNG007-4.p',unknown),
[] ).
cnf(4,axiom,
equal(add(additive_inverse(u),u),additive_identity),
file('RNG007-4.p',unknown),
[] ).
cnf(8,axiom,
equal(additive_inverse(additive_inverse(u)),u),
file('RNG007-4.p',unknown),
[] ).
cnf(12,axiom,
equal(multiply(u,additive_inverse(v)),additive_inverse(multiply(u,v))),
file('RNG007-4.p',unknown),
[] ).
cnf(13,axiom,
equal(multiply(additive_inverse(u),v),additive_inverse(multiply(u,v))),
file('RNG007-4.p',unknown),
[] ).
cnf(15,axiom,
equal(add(u,v),add(v,u)),
file('RNG007-4.p',unknown),
[] ).
cnf(17,plain,
equal(add(u,additive_inverse(u)),additive_identity),
inference(rew,[status(thm),theory(equality)],[15,4]),
[iquote('0:Rew:15.0,4.0')] ).
cnf(43,plain,
equal(additive_inverse(multiply(u,additive_inverse(u))),additive_inverse(u)),
inference(spr,[status(thm),theory(equality)],[13,1]),
[iquote('0:SpR:13.0,1.0')] ).
cnf(48,plain,
equal(additive_inverse(additive_inverse(multiply(u,u))),additive_inverse(u)),
inference(rew,[status(thm),theory(equality)],[12,43]),
[iquote('0:Rew:12.0,43.0')] ).
cnf(49,plain,
equal(additive_inverse(u),u),
inference(rew,[status(thm),theory(equality)],[8,48,1]),
[iquote('0:Rew:8.0,48.0,1.0,48.0')] ).
cnf(52,plain,
equal(add(u,u),additive_identity),
inference(rew,[status(thm),theory(equality)],[49,17]),
[iquote('0:Rew:49.0,17.0')] ).
cnf(55,plain,
$false,
inference(unc,[status(thm)],[52,2]),
[iquote('0:UnC:52.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG007-4 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon May 30 05:03:34 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.41
% 0.18/0.41 SPASS V 3.9
% 0.18/0.41 SPASS beiseite: Proof found.
% 0.18/0.41 % SZS status Theorem
% 0.18/0.41 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.41 SPASS derived 34 clauses, backtracked 0 clauses, performed 0 splits and kept 20 clauses.
% 0.18/0.41 SPASS allocated 63124 KBytes.
% 0.18/0.41 SPASS spent 0:00:00.06 on the problem.
% 0.18/0.41 0:00:00.04 for the input.
% 0.18/0.41 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.41 0:00:00.00 for inferences.
% 0.18/0.41 0:00:00.00 for the backtracking.
% 0.18/0.41 0:00:00.00 for the reduction.
% 0.18/0.41
% 0.18/0.41
% 0.18/0.41 Here is a proof with depth 1, length 13 :
% 0.18/0.41 % SZS output start Refutation
% See solution above
% 0.18/0.41 Formulae used in the proof : boolean_ring prove_inverse left_additive_inverse additive_inverse_additive_inverse multiply_additive_inverse1 multiply_additive_inverse2 commutative_addition
% 0.18/0.41
%------------------------------------------------------------------------------