TSTP Solution File: FLD033-3 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : FLD033-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 : Sat Jul 16 02:28:24 EDT 2022
% Result : Unsatisfiable 0.19s 0.57s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of clauses : 17 ( 8 unt; 4 nHn; 17 RR)
% Number of literals : 32 ( 0 equ; 14 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 10 con; 0-1 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
defined(a),
file('FLD033-3.p',unknown),
[] ).
cnf(3,axiom,
~ sum__dfg(additive_identity,a,additive_identity),
file('FLD033-3.p',unknown),
[] ).
cnf(4,axiom,
product(m,a,a),
file('FLD033-3.p',unknown),
[] ).
cnf(5,axiom,
~ product(multiplicative_identity,m,multiplicative_identity),
file('FLD033-3.p',unknown),
[] ).
cnf(11,axiom,
( ~ product(u,v,w)
| ~ product(x,v,y)
| ~ product(z,x,u)
| product(z,y,w) ),
file('FLD033-3.p',unknown),
[] ).
cnf(14,axiom,
( ~ defined(u)
| sum__dfg(additive_identity,u,additive_identity)
| product(multiplicative_inverse(u),u,multiplicative_identity) ),
file('FLD033-3.p',unknown),
[] ).
cnf(15,axiom,
( ~ product(u,v,w)
| product(v,u,w) ),
file('FLD033-3.p',unknown),
[] ).
cnf(33,plain,
( ~ product(a,u,v)
| ~ product(a,u,w)
| product(m,w,v) ),
inference(res,[status(thm),theory(equality)],[4,11]),
[iquote('0:Res:4.0,11.0')] ).
cnf(45,plain,
~ product(m,multiplicative_identity,multiplicative_identity),
inference(res,[status(thm),theory(equality)],[15,5]),
[iquote('0:Res:15.1,5.0')] ).
cnf(49,plain,
( ~ defined(a)
| product(multiplicative_inverse(a),a,multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[14,3]),
[iquote('0:Res:14.2,3.0')] ).
cnf(57,plain,
product(multiplicative_inverse(a),a,multiplicative_identity),
inference(mrr,[status(thm)],[49,1]),
[iquote('0:MRR:49.0,1.0')] ).
cnf(89,plain,
product(a,multiplicative_inverse(a),multiplicative_identity),
inference(res,[status(thm),theory(equality)],[57,15]),
[iquote('0:Res:57.0,15.0')] ).
cnf(101,plain,
( ~ defined(u)
| sum__dfg(additive_identity,u,additive_identity)
| product(u,multiplicative_inverse(u),multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[14,15]),
[iquote('0:Res:14.2,15.0')] ).
cnf(407,plain,
( ~ product(a,multiplicative_inverse(a),u)
| product(m,u,multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[89,33]),
[iquote('0:Res:89.0,33.0')] ).
cnf(750,plain,
( ~ defined(a)
| sum__dfg(additive_identity,a,additive_identity)
| product(m,multiplicative_identity,multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[101,407]),
[iquote('0:Res:101.2,407.0')] ).
cnf(756,plain,
( sum__dfg(additive_identity,a,additive_identity)
| product(m,multiplicative_identity,multiplicative_identity) ),
inference(ssi,[status(thm)],[750,1]),
[iquote('0:SSi:750.0,1.0')] ).
cnf(757,plain,
$false,
inference(mrr,[status(thm)],[756,3,45]),
[iquote('0:MRR:756.0,756.1,3.0,45.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : FLD033-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.10/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n024.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 7 02:40:50 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.57
% 0.19/0.57 SPASS V 3.9
% 0.19/0.57 SPASS beiseite: Proof found.
% 0.19/0.57 % SZS status Theorem
% 0.19/0.57 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.57 SPASS derived 668 clauses, backtracked 0 clauses, performed 1 splits and kept 521 clauses.
% 0.19/0.57 SPASS allocated 76244 KBytes.
% 0.19/0.57 SPASS spent 0:00:00.22 on the problem.
% 0.19/0.57 0:00:00.04 for the input.
% 0.19/0.57 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.57 0:00:00.01 for inferences.
% 0.19/0.57 0:00:00.00 for the backtracking.
% 0.19/0.57 0:00:00.14 for the reduction.
% 0.19/0.57
% 0.19/0.57
% 0.19/0.57 Here is a proof with depth 4, length 17 :
% 0.19/0.57 % SZS output start Refutation
% See solution above
% 0.19/0.57 Formulae used in the proof : a_is_defined not_sum_3 product_4 not_product_5 associativity_multiplication_1 existence_of_inverse_multiplication commutativity_multiplication
% 0.19/0.57
%------------------------------------------------------------------------------