TSTP Solution File: FLD002-3 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : FLD002-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 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 : Sat Jul 16 02:28:13 EDT 2022
% Result : Unsatisfiable 6.64s 6.85s
% Output : Refutation 6.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of clauses : 30 ( 11 unt; 0 nHn; 30 RR)
% Number of literals : 66 ( 0 equ; 43 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 11 con; 0-0 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
defined(a),
file('FLD002-3.p',unknown),
[] ).
cnf(2,axiom,
defined(b),
file('FLD002-3.p',unknown),
[] ).
cnf(3,axiom,
product(multiplicative_identity,a,b),
file('FLD002-3.p',unknown),
[] ).
cnf(4,axiom,
~ sum__dfg(additive_identity,a,b),
file('FLD002-3.p',unknown),
[] ).
cnf(7,axiom,
( ~ defined(u)
| sum__dfg(additive_identity,u,u) ),
file('FLD002-3.p',unknown),
[] ).
cnf(10,axiom,
( ~ product(u,v,w)
| ~ product(x,v,y)
| ~ product(z,x,u)
| product(z,y,w) ),
file('FLD002-3.p',unknown),
[] ).
cnf(11,axiom,
( ~ product(u,v,w)
| ~ product(x,y,v)
| ~ product(u,x,z)
| product(z,y,w) ),
file('FLD002-3.p',unknown),
[] ).
cnf(12,axiom,
( ~ defined(u)
| product(multiplicative_identity,u,u) ),
file('FLD002-3.p',unknown),
[] ).
cnf(14,axiom,
( ~ product(u,v,w)
| product(v,u,w) ),
file('FLD002-3.p',unknown),
[] ).
cnf(15,axiom,
( ~ product(u,v,w)
| ~ product(x,v,y)
| ~ product(z,v,x1)
| ~ sum__dfg(x,u,z)
| sum__dfg(y,w,x1) ),
file('FLD002-3.p',unknown),
[] ).
cnf(18,axiom,
defined(additive_identity),
file('FLD002-3.p',unknown),
[] ).
cnf(21,axiom,
defined(multiplicative_identity),
file('FLD002-3.p',unknown),
[] ).
cnf(35,plain,
( ~ sum__dfg(u,v,w)
| ~ product(v,x,a)
| ~ product(u,x,additive_identity)
| ~ product(w,x,b) ),
inference(res,[status(thm),theory(equality)],[15,4]),
[iquote('0:Res:15.4,4.0')] ).
cnf(45,plain,
( ~ defined(u)
| product(u,multiplicative_identity,u) ),
inference(res,[status(thm),theory(equality)],[12,14]),
[iquote('0:Res:12.1,14.0')] ).
cnf(64,plain,
( ~ product(u,v,a)
| ~ product(multiplicative_identity,u,w)
| product(w,v,b) ),
inference(res,[status(thm),theory(equality)],[3,11]),
[iquote('0:Res:3.0,11.0')] ).
cnf(74,plain,
( ~ defined(a)
| ~ product(multiplicative_identity,a,u)
| product(u,multiplicative_identity,b) ),
inference(res,[status(thm),theory(equality)],[45,64]),
[iquote('0:Res:45.1,64.0')] ).
cnf(76,plain,
( ~ product(multiplicative_identity,a,u)
| product(u,multiplicative_identity,b) ),
inference(ssi,[status(thm)],[74,1]),
[iquote('0:SSi:74.0,1.0')] ).
cnf(85,plain,
( ~ defined(u)
| ~ product(v,u,w)
| ~ product(x,v,multiplicative_identity)
| product(x,w,u) ),
inference(res,[status(thm),theory(equality)],[12,10]),
[iquote('0:Res:12.1,10.0')] ).
cnf(98,plain,
product(b,multiplicative_identity,b),
inference(res,[status(thm),theory(equality)],[3,76]),
[iquote('0:Res:3.0,76.0')] ).
cnf(410,plain,
( ~ defined(a)
| ~ product(u,multiplicative_identity,multiplicative_identity)
| product(u,b,a) ),
inference(res,[status(thm),theory(equality)],[3,85]),
[iquote('0:Res:3.0,85.1')] ).
cnf(435,plain,
( ~ product(u,multiplicative_identity,multiplicative_identity)
| product(u,b,a) ),
inference(ssi,[status(thm)],[410,1]),
[iquote('0:SSi:410.0,1.0')] ).
cnf(515,plain,
( ~ product(u,multiplicative_identity,multiplicative_identity)
| product(b,u,a) ),
inference(res,[status(thm),theory(equality)],[435,14]),
[iquote('0:Res:435.1,14.0')] ).
cnf(675,plain,
( ~ defined(multiplicative_identity)
| product(b,multiplicative_identity,a) ),
inference(res,[status(thm),theory(equality)],[12,515]),
[iquote('0:Res:12.1,515.0')] ).
cnf(678,plain,
product(b,multiplicative_identity,a),
inference(ssi,[status(thm)],[675,21]),
[iquote('0:SSi:675.0,21.0')] ).
cnf(854,plain,
( ~ defined(u)
| ~ product(u,v,a)
| ~ product(additive_identity,v,additive_identity)
| ~ product(u,v,b) ),
inference(res,[status(thm),theory(equality)],[7,35]),
[iquote('0:Res:7.1,35.0')] ).
cnf(11698,plain,
( ~ defined(b)
| ~ product(additive_identity,multiplicative_identity,additive_identity)
| ~ product(b,multiplicative_identity,b) ),
inference(res,[status(thm),theory(equality)],[678,854]),
[iquote('0:Res:678.0,854.1')] ).
cnf(11727,plain,
( ~ product(additive_identity,multiplicative_identity,additive_identity)
| ~ product(b,multiplicative_identity,b) ),
inference(ssi,[status(thm)],[11698,2]),
[iquote('0:SSi:11698.0,2.0')] ).
cnf(11728,plain,
~ product(additive_identity,multiplicative_identity,additive_identity),
inference(mrr,[status(thm)],[11727,98]),
[iquote('0:MRR:11727.1,98.0')] ).
cnf(11762,plain,
~ defined(additive_identity),
inference(res,[status(thm),theory(equality)],[45,11728]),
[iquote('0:Res:45.1,11728.0')] ).
cnf(11763,plain,
$false,
inference(ssi,[status(thm)],[11762,18]),
[iquote('0:SSi:11762.0,18.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.13 % Problem : FLD002-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.09/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n029.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jun 6 12:41:19 EDT 2022
% 0.13/0.35 % CPUTime :
% 6.64/6.85
% 6.64/6.85 SPASS V 3.9
% 6.64/6.85 SPASS beiseite: Proof found.
% 6.64/6.85 % SZS status Theorem
% 6.64/6.85 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.64/6.85 SPASS derived 8358 clauses, backtracked 149 clauses, performed 9 splits and kept 5740 clauses.
% 6.64/6.85 SPASS allocated 84184 KBytes.
% 6.64/6.85 SPASS spent 0:00:06.31 on the problem.
% 6.64/6.85 0:00:00.03 for the input.
% 6.64/6.85 0:00:00.00 for the FLOTTER CNF translation.
% 6.64/6.85 0:00:00.08 for inferences.
% 6.64/6.85 0:00:00.30 for the backtracking.
% 6.64/6.85 0:00:05.82 for the reduction.
% 6.64/6.85
% 6.64/6.85
% 6.64/6.85 Here is a proof with depth 6, length 30 :
% 6.64/6.85 % SZS output start Refutation
% See solution above
% 6.64/6.85 Formulae used in the proof : a_is_defined b_is_defined product_3 not_sum_4 existence_of_identity_addition associativity_multiplication_1 associativity_multiplication_2 existence_of_identity_multiplication commutativity_multiplication distributivity_1 well_definedness_of_additive_identity well_definedness_of_multiplicative_identity
% 6.64/6.85
%------------------------------------------------------------------------------