%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : RNG037-2 : TPTP v8.1.0. Released v1.0.0.
% 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 : Mon Jul 18 20:41:17 EDT 2022
% Result : Unsatisfiable 2.59s 2.80s
% Output : Refutation 2.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of clauses : 13 ( 8 unt; 0 nHn; 13 RR)
% Number of literals : 24 ( 0 equ; 16 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 12 con; 0-1 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(13,axiom,
sum__dfg(u,additive_inverse(u),additive_identity),
file('RNG037-2.p',unknown),
[] ).
cnf(16,axiom,
( ~ sum__dfg(u,v,w)
| sum__dfg(v,u,w) ),
file('RNG037-2.p',unknown),
[] ).
cnf(19,axiom,
( ~ product(u,v,w)
| ~ sum__dfg(x,y,v)
| ~ product(u,y,z)
| ~ product(u,x,x1)
| sum__dfg(x1,z,w) ),
file('RNG037-2.p',unknown),
[] ).
cnf(26,axiom,
product(u,additive_identity,additive_identity),
file('RNG037-2.p',unknown),
[] ).
cnf(27,axiom,
product(a,b,d),
file('RNG037-2.p',unknown),
[] ).
cnf(28,axiom,
product(a,additive_inverse(b),c),
file('RNG037-2.p',unknown),
[] ).
cnf(29,axiom,
~ sum__dfg(c,d,additive_identity),
file('RNG037-2.p',unknown),
[] ).
cnf(37,plain,
( ~ sum__dfg(u,v,w)
| ~ product(x,w,additive_identity)
| ~ product(x,v,d)
| ~ product(x,u,c) ),
inference(res,[status(thm),theory(equality)],[19,29]),
[iquote('0:Res:19.4,29.0')] ).
cnf(42,plain,
sum__dfg(additive_inverse(u),u,additive_identity),
inference(res,[status(thm),theory(equality)],[13,16]),
[iquote('0:Res:13.0,16.0')] ).
cnf(2023,plain,
( ~ product(u,additive_identity,additive_identity)
| ~ product(u,v,d)
| ~ product(u,additive_inverse(v),c) ),
inference(res,[status(thm),theory(equality)],[42,37]),
[iquote('0:Res:42.0,37.0')] ).
cnf(2032,plain,
( ~ product(u,v,d)
| ~ product(u,additive_inverse(v),c) ),
inference(mrr,[status(thm)],[2023,26]),
[iquote('0:MRR:2023.0,26.0')] ).
cnf(5018,plain,
~ product(a,b,d),
inference(res,[status(thm),theory(equality)],[28,2032]),
[iquote('0:Res:28.0,2032.1')] ).
cnf(5023,plain,
$false,
inference(mrr,[status(thm)],[5018,27]),
[iquote('0:MRR:5018.0,27.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG037-2 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n026.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 22:16:55 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.59/2.80
% 2.59/2.80 SPASS V 3.9
% 2.59/2.80 SPASS beiseite: Proof found.
% 2.59/2.80 % SZS status Theorem
% 2.59/2.80 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.59/2.80 SPASS derived 4860 clauses, backtracked 0 clauses, performed 0 splits and kept 3539 clauses.
% 2.59/2.80 SPASS allocated 66817 KBytes.
% 2.59/2.80 SPASS spent 0:00:02.44 on the problem.
% 2.59/2.80 0:00:00.04 for the input.
% 2.59/2.80 0:00:00.00 for the FLOTTER CNF translation.
% 2.59/2.80 0:00:00.04 for inferences.
% 2.59/2.80 0:00:00.00 for the backtracking.
% 2.59/2.80 0:00:02.32 for the reduction.
% 2.59/2.80
% 2.59/2.80
% 2.59/2.80 Here is a proof with depth 3, length 13 :
% 2.59/2.80 % SZS output start Refutation
% See solution above
% 2.59/2.80 Formulae used in the proof : additive_inverse2 commutativity_of_addition distributivity1 multiplicative_identity2 a_times_b a_inverse_times_b prove_sum_is_additive_identity
% 2.59/2.80
%------------------------------------------------------------------------------