TSTP Solution File: FLD038-3 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : FLD038-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 02:28:26 EDT 2022
% Result : Unsatisfiable 0.22s 0.43s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 9
% Syntax : Number of clauses : 17 ( 9 unt; 1 nHn; 17 RR)
% Number of literals : 29 ( 0 equ; 17 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('FLD038-3.p',unknown),
[] ).
cnf(2,axiom,
defined(b),
file('FLD038-3.p',unknown),
[] ).
cnf(3,axiom,
~ sum__dfg(additive_identity,a,additive_identity),
file('FLD038-3.p',unknown),
[] ).
cnf(4,axiom,
product(b,multiplicative_inverse(a),multiplicative_identity),
file('FLD038-3.p',unknown),
[] ).
cnf(5,axiom,
~ product(multiplicative_identity,a,b),
file('FLD038-3.p',unknown),
[] ).
cnf(12,axiom,
( ~ product(u,v,w)
| ~ product(x,y,v)
| ~ product(u,x,z)
| product(z,y,w) ),
file('FLD038-3.p',unknown),
[] ).
cnf(13,axiom,
( ~ defined(u)
| product(multiplicative_identity,u,u) ),
file('FLD038-3.p',unknown),
[] ).
cnf(14,axiom,
( ~ defined(u)
| sum__dfg(additive_identity,u,additive_identity)
| product(multiplicative_inverse(u),u,multiplicative_identity) ),
file('FLD038-3.p',unknown),
[] ).
cnf(15,axiom,
( ~ product(u,v,w)
| product(v,u,w) ),
file('FLD038-3.p',unknown),
[] ).
cnf(34,plain,
( ~ product(u,v,b)
| ~ product(u,w,multiplicative_identity)
| ~ product(w,a,v) ),
inference(res,[status(thm),theory(equality)],[12,5]),
[iquote('0:Res:12.3,5.0')] ).
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(63,plain,
( ~ product(b,u,b)
| ~ product(multiplicative_inverse(a),a,u) ),
inference(res,[status(thm),theory(equality)],[4,34]),
[iquote('0:Res:4.0,34.0')] ).
cnf(90,plain,
( ~ defined(u)
| product(u,multiplicative_identity,u) ),
inference(res,[status(thm),theory(equality)],[13,15]),
[iquote('0:Res:13.1,15.0')] ).
cnf(99,plain,
~ product(b,multiplicative_identity,b),
inference(res,[status(thm),theory(equality)],[57,63]),
[iquote('0:Res:57.0,63.1')] ).
cnf(101,plain,
~ defined(b),
inference(res,[status(thm),theory(equality)],[90,99]),
[iquote('0:Res:90.1,99.0')] ).
cnf(102,plain,
$false,
inference(ssi,[status(thm)],[101,2]),
[iquote('0:SSi:101.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : FLD038-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.14 % Command : run_spass %d %s
% 0.15/0.36 % Computer : n020.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Mon Jun 6 22:16:07 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.22/0.43
% 0.22/0.43 SPASS V 3.9
% 0.22/0.43 SPASS beiseite: Proof found.
% 0.22/0.43 % SZS status Theorem
% 0.22/0.43 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.43 SPASS derived 58 clauses, backtracked 0 clauses, performed 0 splits and kept 70 clauses.
% 0.22/0.43 SPASS allocated 75696 KBytes.
% 0.22/0.43 SPASS spent 0:00:00.06 on the problem.
% 0.22/0.43 0:00:00.04 for the input.
% 0.22/0.43 0:00:00.00 for the FLOTTER CNF translation.
% 0.22/0.43 0:00:00.00 for inferences.
% 0.22/0.43 0:00:00.00 for the backtracking.
% 0.22/0.43 0:00:00.00 for the reduction.
% 0.22/0.43
% 0.22/0.43
% 0.22/0.43 Here is a proof with depth 4, length 17 :
% 0.22/0.43 % SZS output start Refutation
% See solution above
% 0.22/0.43 Formulae used in the proof : a_is_defined b_is_defined not_sum_3 product_4 not_product_5 associativity_multiplication_2 existence_of_identity_multiplication existence_of_inverse_multiplication commutativity_multiplication
% 0.22/0.43
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