TSTP Solution File: RNG005-2 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : RNG005-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 20:41:10 EDT 2022
% Result : Unsatisfiable 4.80s 5.00s
% Output : Refutation 4.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of clauses : 11 ( 7 unt; 0 nHn; 11 RR)
% Number of literals : 21 ( 0 equ; 15 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(14,axiom,
sum__dfg(additive_inverse(u),u,additive_identity),
file('RNG005-2.p',unknown),
[] ).
cnf(23,axiom,
( ~ product(u,v,w)
| ~ sum__dfg(x,y,u)
| ~ product(y,v,z)
| ~ product(x,v,x1)
| sum__dfg(x1,z,w) ),
file('RNG005-2.p',unknown),
[] ).
cnf(27,axiom,
product(additive_identity,u,additive_identity),
file('RNG005-2.p',unknown),
[] ).
cnf(29,axiom,
product(a,b,d),
file('RNG005-2.p',unknown),
[] ).
cnf(30,axiom,
product(additive_inverse(a),b,c),
file('RNG005-2.p',unknown),
[] ).
cnf(31,axiom,
~ sum__dfg(c,d,additive_identity),
file('RNG005-2.p',unknown),
[] ).
cnf(38,plain,
( ~ sum__dfg(u,v,w)
| ~ product(w,x,additive_identity)
| ~ product(v,x,d)
| ~ product(u,x,c) ),
inference(res,[status(thm),theory(equality)],[23,31]),
[iquote('0:Res:23.4,31.0')] ).
cnf(2834,plain,
( ~ product(additive_identity,u,additive_identity)
| ~ product(v,u,d)
| ~ product(additive_inverse(v),u,c) ),
inference(res,[status(thm),theory(equality)],[14,38]),
[iquote('0:Res:14.0,38.0')] ).
cnf(2875,plain,
( ~ product(u,v,d)
| ~ product(additive_inverse(u),v,c) ),
inference(mrr,[status(thm)],[2834,27]),
[iquote('0:MRR:2834.0,27.0')] ).
cnf(8220,plain,
~ product(a,b,d),
inference(res,[status(thm),theory(equality)],[30,2875]),
[iquote('0:Res:30.0,2875.1')] ).
cnf(8227,plain,
$false,
inference(mrr,[status(thm)],[8220,29]),
[iquote('0:MRR:8220.0,29.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : RNG005-2 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13 % Command : run_spass %d %s
% 0.14/0.34 % Computer : n029.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon May 30 17:54:59 EDT 2022
% 0.14/0.34 % CPUTime :
% 4.80/5.00
% 4.80/5.00 SPASS V 3.9
% 4.80/5.00 SPASS beiseite: Proof found.
% 4.80/5.00 % SZS status Theorem
% 4.80/5.00 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.80/5.00 SPASS derived 8008 clauses, backtracked 0 clauses, performed 0 splits and kept 5299 clauses.
% 4.80/5.00 SPASS allocated 68615 KBytes.
% 4.80/5.00 SPASS spent 0:00:04.60 on the problem.
% 4.80/5.00 0:00:00.03 for the input.
% 4.80/5.00 0:00:00.00 for the FLOTTER CNF translation.
% 4.80/5.00 0:00:00.06 for inferences.
% 4.80/5.00 0:00:00.00 for the backtracking.
% 4.80/5.00 0:00:04.45 for the reduction.
% 4.80/5.00
% 4.80/5.00
% 4.80/5.00 Here is a proof with depth 3, length 11 :
% 4.80/5.00 % SZS output start Refutation
% See solution above
% 4.84/5.00 Formulae used in the proof : left_inverse distributivity3 multiplicative_identity1 a_times_b a_inverse_times_b prove_sum_is_additive_identity
% 4.84/5.00
%------------------------------------------------------------------------------