TSTP Solution File: FLD009-3 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : FLD009-3 : 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 02:28:15 EDT 2022
% Result : Unsatisfiable 3.15s 3.36s
% Output : Refutation 3.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of clauses : 21 ( 7 unt; 3 nHn; 21 RR)
% Number of literals : 48 ( 0 equ; 31 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
defined(a),
file('FLD009-3.p',unknown),
[] ).
cnf(2,axiom,
defined(b),
file('FLD009-3.p',unknown),
[] ).
cnf(3,axiom,
~ sum__dfg(additive_identity,a,additive_identity),
file('FLD009-3.p',unknown),
[] ).
cnf(4,axiom,
~ product(a,u,b),
file('FLD009-3.p',unknown),
[] ).
cnf(10,axiom,
( ~ product(u,v,w)
| ~ product(x,v,y)
| ~ product(z,x,u)
| product(z,y,w) ),
file('FLD009-3.p',unknown),
[] ).
cnf(12,axiom,
( ~ defined(u)
| product(multiplicative_identity,u,u) ),
file('FLD009-3.p',unknown),
[] ).
cnf(13,axiom,
( ~ defined(u)
| sum__dfg(additive_identity,u,additive_identity)
| product(multiplicative_inverse(u),u,multiplicative_identity) ),
file('FLD009-3.p',unknown),
[] ).
cnf(14,axiom,
( ~ product(u,v,w)
| product(v,u,w) ),
file('FLD009-3.p',unknown),
[] ).
cnf(22,axiom,
( ~ defined(u)
| defined(multiplicative_inverse(u))
| sum__dfg(additive_identity,u,additive_identity) ),
file('FLD009-3.p',unknown),
[] ).
cnf(24,axiom,
( ~ defined(u)
| ~ defined(v)
| product(v,u,multiply(v,u)) ),
file('FLD009-3.p',unknown),
[] ).
cnf(32,plain,
( ~ product(u,v,w)
| ~ product(x,v,b)
| ~ product(a,u,x) ),
inference(res,[status(thm),theory(equality)],[10,4]),
[iquote('0:Res:10.3,4.0')] ).
cnf(36,plain,
( ~ defined(a)
| defined(multiplicative_inverse(a)) ),
inference(res,[status(thm),theory(equality)],[22,3]),
[iquote('0:Res:22.2,3.0')] ).
cnf(42,plain,
defined(multiplicative_inverse(a)),
inference(mrr,[status(thm)],[36,1]),
[iquote('0:MRR:36.0,1.0')] ).
cnf(65,plain,
( ~ defined(u)
| sum__dfg(additive_identity,u,additive_identity)
| product(u,multiplicative_inverse(u),multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[13,14]),
[iquote('0:Res:13.2,14.0')] ).
cnf(356,plain,
( ~ defined(u)
| ~ defined(v)
| ~ product(w,u,b)
| ~ product(a,v,w) ),
inference(res,[status(thm),theory(equality)],[24,32]),
[iquote('0:Res:24.2,32.0')] ).
cnf(7273,plain,
( ~ defined(b)
| ~ defined(b)
| ~ defined(u)
| ~ product(a,u,multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[12,356]),
[iquote('0:Res:12.1,356.2')] ).
cnf(7281,plain,
( ~ defined(b)
| ~ defined(u)
| ~ product(a,u,multiplicative_identity) ),
inference(obv,[status(thm),theory(equality)],[7273]),
[iquote('0:Obv:7273.0')] ).
cnf(7282,plain,
( ~ defined(u)
| ~ product(a,u,multiplicative_identity) ),
inference(ssi,[status(thm)],[7281,2]),
[iquote('0:SSi:7281.0,2.0')] ).
cnf(7286,plain,
( ~ defined(a)
| ~ defined(multiplicative_inverse(a))
| sum__dfg(additive_identity,a,additive_identity) ),
inference(res,[status(thm),theory(equality)],[65,7282]),
[iquote('0:Res:65.2,7282.1')] ).
cnf(7304,plain,
sum__dfg(additive_identity,a,additive_identity),
inference(ssi,[status(thm)],[7286,42,1]),
[iquote('0:SSi:7286.1,7286.0,42.0,1.0')] ).
cnf(7305,plain,
$false,
inference(mrr,[status(thm)],[7304,3]),
[iquote('0:MRR:7304.0,3.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : FLD009-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.06/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jun 7 00:03:50 EDT 2022
% 0.13/0.34 % CPUTime :
% 3.15/3.36
% 3.15/3.36 SPASS V 3.9
% 3.15/3.36 SPASS beiseite: Proof found.
% 3.15/3.36 % SZS status Theorem
% 3.15/3.36 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.15/3.36 SPASS derived 5324 clauses, backtracked 50 clauses, performed 1 splits and kept 3404 clauses.
% 3.15/3.36 SPASS allocated 81418 KBytes.
% 3.15/3.36 SPASS spent 0:00:02.95 on the problem.
% 3.15/3.36 0:00:00.04 for the input.
% 3.15/3.36 0:00:00.00 for the FLOTTER CNF translation.
% 3.15/3.36 0:00:00.06 for inferences.
% 3.15/3.36 0:00:00.06 for the backtracking.
% 3.15/3.36 0:00:02.75 for the reduction.
% 3.15/3.36
% 3.15/3.36
% 3.15/3.36 Here is a proof with depth 4, length 21 :
% 3.15/3.36 % SZS output start Refutation
% See solution above
% 3.15/3.36 Formulae used in the proof : a_is_defined b_is_defined not_sum_3 not_product_4 associativity_multiplication_1 existence_of_identity_multiplication existence_of_inverse_multiplication commutativity_multiplication well_definedness_of_multiplicative_inverse totality_of_multiplication
% 3.15/3.36
%------------------------------------------------------------------------------