TSTP Solution File: FLD025-3 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : FLD025-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n027.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 02:28:21 EDT 2022
% Result : Unsatisfiable 0.46s 0.63s
% Output : Refutation 0.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of clauses : 23 ( 9 unt; 0 nHn; 23 RR)
% Number of literals : 45 ( 0 equ; 27 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 11 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
defined(a),
file('FLD025-3.p',unknown),
[] ).
cnf(3,axiom,
defined(c),
file('FLD025-3.p',unknown),
[] ).
cnf(5,axiom,
product(multiplicative_identity,a,b),
file('FLD025-3.p',unknown),
[] ).
cnf(6,axiom,
product(multiplicative_identity,c,d),
file('FLD025-3.p',unknown),
[] ).
cnf(7,axiom,
~ product(d,b,multiply(a,c)),
file('FLD025-3.p',unknown),
[] ).
cnf(13,axiom,
( ~ product(u,v,w)
| ~ product(x,v,y)
| ~ product(z,x,u)
| product(z,y,w) ),
file('FLD025-3.p',unknown),
[] ).
cnf(15,axiom,
( ~ defined(u)
| product(multiplicative_identity,u,u) ),
file('FLD025-3.p',unknown),
[] ).
cnf(17,axiom,
( ~ product(u,v,w)
| product(v,u,w) ),
file('FLD025-3.p',unknown),
[] ).
cnf(24,axiom,
defined(multiplicative_identity),
file('FLD025-3.p',unknown),
[] ).
cnf(27,axiom,
( ~ defined(u)
| ~ defined(v)
| product(v,u,multiply(v,u)) ),
file('FLD025-3.p',unknown),
[] ).
cnf(38,plain,
( ~ product(u,c,v)
| ~ product(w,multiplicative_identity,u)
| product(w,d,v) ),
inference(res,[status(thm),theory(equality)],[6,13]),
[iquote('0:Res:6.0,13.1')] ).
cnf(62,plain,
( ~ product(u,v,b)
| ~ product(w,v,multiply(a,c))
| ~ product(d,u,w) ),
inference(res,[status(thm),theory(equality)],[13,7]),
[iquote('0:Res:13.3,7.0')] ).
cnf(75,plain,
( ~ product(u,a,multiply(a,c))
| ~ product(d,multiplicative_identity,u) ),
inference(res,[status(thm),theory(equality)],[5,62]),
[iquote('0:Res:5.0,62.1')] ).
cnf(95,plain,
( ~ defined(u)
| product(u,multiplicative_identity,u) ),
inference(res,[status(thm),theory(equality)],[15,17]),
[iquote('0:Res:15.1,17.0')] ).
cnf(115,plain,
( ~ defined(u)
| ~ defined(v)
| product(u,v,multiply(v,u)) ),
inference(res,[status(thm),theory(equality)],[27,17]),
[iquote('0:Res:27.2,17.0')] ).
cnf(118,plain,
( ~ defined(c)
| ~ defined(a)
| ~ product(d,multiplicative_identity,c) ),
inference(res,[status(thm),theory(equality)],[115,75]),
[iquote('0:Res:115.2,75.0')] ).
cnf(119,plain,
~ product(d,multiplicative_identity,c),
inference(ssi,[status(thm)],[118,1,3]),
[iquote('0:SSi:118.1,118.0,1.0,3.0')] ).
cnf(655,plain,
( ~ defined(c)
| ~ product(u,multiplicative_identity,multiplicative_identity)
| product(u,d,c) ),
inference(res,[status(thm),theory(equality)],[15,38]),
[iquote('0:Res:15.1,38.0')] ).
cnf(662,plain,
( ~ product(u,multiplicative_identity,multiplicative_identity)
| product(u,d,c) ),
inference(ssi,[status(thm)],[655,3]),
[iquote('0:SSi:655.0,3.0')] ).
cnf(852,plain,
( ~ product(u,multiplicative_identity,multiplicative_identity)
| product(d,u,c) ),
inference(res,[status(thm),theory(equality)],[662,17]),
[iquote('0:Res:662.1,17.0')] ).
cnf(1157,plain,
( ~ defined(multiplicative_identity)
| product(d,multiplicative_identity,c) ),
inference(res,[status(thm),theory(equality)],[95,852]),
[iquote('0:Res:95.1,852.0')] ).
cnf(1160,plain,
product(d,multiplicative_identity,c),
inference(ssi,[status(thm)],[1157,24]),
[iquote('0:SSi:1157.0,24.0')] ).
cnf(1161,plain,
$false,
inference(mrr,[status(thm)],[1160,119]),
[iquote('0:MRR:1160.0,119.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : FLD025-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.08/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n027.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 01:19:10 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.46/0.63
% 0.46/0.63 SPASS V 3.9
% 0.46/0.63 SPASS beiseite: Proof found.
% 0.46/0.63 % SZS status Theorem
% 0.46/0.63 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.46/0.63 SPASS derived 906 clauses, backtracked 0 clauses, performed 2 splits and kept 696 clauses.
% 0.46/0.63 SPASS allocated 76574 KBytes.
% 0.46/0.63 SPASS spent 0:00:00.27 on the problem.
% 0.46/0.63 0:00:00.04 for the input.
% 0.46/0.63 0:00:00.00 for the FLOTTER CNF translation.
% 0.46/0.63 0:00:00.01 for inferences.
% 0.46/0.63 0:00:00.00 for the backtracking.
% 0.46/0.63 0:00:00.19 for the reduction.
% 0.46/0.63
% 0.46/0.63
% 0.46/0.63 Here is a proof with depth 4, length 23 :
% 0.46/0.63 % SZS output start Refutation
% See solution above
% 0.46/0.63 Formulae used in the proof : a_is_defined c_is_defined product_5 product_6 not_product_7 associativity_multiplication_1 existence_of_identity_multiplication commutativity_multiplication well_definedness_of_multiplicative_identity totality_of_multiplication
% 0.46/0.63
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