TSTP Solution File: FLD049-4 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : FLD049-4 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.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 02:28:30 EDT 2022
% Result : Unsatisfiable 0.48s 0.64s
% Output : Refutation 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 15
% Syntax : Number of clauses : 44 ( 17 unt; 10 nHn; 44 RR)
% Number of literals : 91 ( 0 equ; 41 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 : 15 ( 15 usr; 14 con; 0-1 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
defined(a),
file('FLD049-4.p',unknown),
[] ).
cnf(2,axiom,
defined(b),
file('FLD049-4.p',unknown),
[] ).
cnf(3,axiom,
defined(c),
file('FLD049-4.p',unknown),
[] ).
cnf(4,axiom,
defined(d),
file('FLD049-4.p',unknown),
[] ).
cnf(7,axiom,
~ sum__dfg(additive_identity,b,additive_identity),
file('FLD049-4.p',unknown),
[] ).
cnf(8,axiom,
~ sum__dfg(additive_identity,d,additive_identity),
file('FLD049-4.p',unknown),
[] ).
cnf(9,axiom,
product(a,multiplicative_inverse(b),s),
file('FLD049-4.p',unknown),
[] ).
cnf(10,axiom,
product(c,multiplicative_inverse(d),s),
file('FLD049-4.p',unknown),
[] ).
cnf(11,axiom,
product(a,d,k),
file('FLD049-4.p',unknown),
[] ).
cnf(12,axiom,
~ product(b,c,k),
file('FLD049-4.p',unknown),
[] ).
cnf(18,axiom,
( ~ product(u,v,w)
| ~ product(x,v,y)
| ~ product(z,x,u)
| product(z,y,w) ),
file('FLD049-4.p',unknown),
[] ).
cnf(19,axiom,
( ~ product(u,v,w)
| ~ product(x,y,v)
| ~ product(u,x,z)
| product(z,y,w) ),
file('FLD049-4.p',unknown),
[] ).
cnf(20,axiom,
( ~ defined(u)
| product(multiplicative_identity,u,u) ),
file('FLD049-4.p',unknown),
[] ).
cnf(21,axiom,
( ~ defined(u)
| sum__dfg(additive_identity,u,additive_identity)
| product(multiplicative_inverse(u),u,multiplicative_identity) ),
file('FLD049-4.p',unknown),
[] ).
cnf(22,axiom,
( ~ product(u,v,w)
| product(v,u,w) ),
file('FLD049-4.p',unknown),
[] ).
cnf(40,plain,
( ~ product(k,u,v)
| ~ product(d,u,w)
| product(a,w,v) ),
inference(res,[status(thm),theory(equality)],[11,18]),
[iquote('0:Res:11.0,18.0')] ).
cnf(41,plain,
( ~ product(a,u,v)
| ~ product(d,w,u)
| product(k,w,v) ),
inference(res,[status(thm),theory(equality)],[11,19]),
[iquote('0:Res:11.0,19.0')] ).
cnf(48,plain,
( ~ product(u,v,a)
| ~ product(v,d,w)
| product(u,w,k) ),
inference(res,[status(thm),theory(equality)],[11,18]),
[iquote('0:Res:11.0,18.2')] ).
cnf(58,plain,
( ~ product(c,u,v)
| ~ product(multiplicative_inverse(d),w,u)
| product(s,w,v) ),
inference(res,[status(thm),theory(equality)],[10,19]),
[iquote('0:Res:10.0,19.0')] ).
cnf(71,plain,
( ~ product(a,u,v)
| ~ product(multiplicative_inverse(b),w,u)
| product(s,w,v) ),
inference(res,[status(thm),theory(equality)],[9,19]),
[iquote('0:Res:9.0,19.0')] ).
cnf(102,plain,
( ~ defined(u)
| product(u,multiplicative_identity,u) ),
inference(res,[status(thm),theory(equality)],[20,22]),
[iquote('0:Res:20.1,22.0')] ).
cnf(112,plain,
( ~ defined(u)
| sum__dfg(additive_identity,u,additive_identity)
| product(u,multiplicative_inverse(u),multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[21,22]),
[iquote('0:Res:21.2,22.0')] ).
cnf(128,plain,
( ~ defined(a)
| ~ product(d,u,multiplicative_identity)
| product(k,u,a) ),
inference(res,[status(thm),theory(equality)],[102,41]),
[iquote('0:Res:102.1,41.0')] ).
cnf(132,plain,
( ~ product(d,u,multiplicative_identity)
| product(k,u,a) ),
inference(ssi,[status(thm)],[128,1]),
[iquote('0:SSi:128.0,1.0')] ).
cnf(148,plain,
( ~ defined(d)
| sum__dfg(additive_identity,d,additive_identity)
| product(k,multiplicative_inverse(d),a) ),
inference(res,[status(thm),theory(equality)],[112,132]),
[iquote('0:Res:112.2,132.0')] ).
cnf(149,plain,
( sum__dfg(additive_identity,d,additive_identity)
| product(k,multiplicative_inverse(d),a) ),
inference(ssi,[status(thm)],[148,4]),
[iquote('0:SSi:148.0,4.0')] ).
cnf(150,plain,
product(k,multiplicative_inverse(d),a),
inference(mrr,[status(thm)],[149,8]),
[iquote('0:MRR:149.0,8.0')] ).
cnf(208,plain,
( ~ product(d,multiplicative_inverse(d),u)
| product(a,u,a) ),
inference(res,[status(thm),theory(equality)],[150,40]),
[iquote('0:Res:150.0,40.0')] ).
cnf(263,plain,
( ~ defined(d)
| sum__dfg(additive_identity,d,additive_identity)
| product(a,multiplicative_identity,a) ),
inference(res,[status(thm),theory(equality)],[112,208]),
[iquote('0:Res:112.2,208.0')] ).
cnf(266,plain,
( sum__dfg(additive_identity,d,additive_identity)
| product(a,multiplicative_identity,a) ),
inference(ssi,[status(thm)],[263,4]),
[iquote('0:SSi:263.0,4.0')] ).
cnf(267,plain,
product(a,multiplicative_identity,a),
inference(mrr,[status(thm)],[266,8]),
[iquote('0:MRR:266.0,8.0')] ).
cnf(520,plain,
( ~ defined(b)
| ~ product(a,multiplicative_identity,u)
| sum__dfg(additive_identity,b,additive_identity)
| product(s,b,u) ),
inference(res,[status(thm),theory(equality)],[21,71]),
[iquote('0:Res:21.2,71.1')] ).
cnf(529,plain,
( ~ product(a,multiplicative_identity,u)
| sum__dfg(additive_identity,b,additive_identity)
| product(s,b,u) ),
inference(ssi,[status(thm)],[520,2]),
[iquote('0:SSi:520.0,2.0')] ).
cnf(530,plain,
( ~ product(a,multiplicative_identity,u)
| product(s,b,u) ),
inference(mrr,[status(thm)],[529,7]),
[iquote('0:MRR:529.1,7.0')] ).
cnf(591,plain,
( ~ defined(d)
| ~ product(c,multiplicative_identity,u)
| sum__dfg(additive_identity,d,additive_identity)
| product(s,d,u) ),
inference(res,[status(thm),theory(equality)],[21,58]),
[iquote('0:Res:21.2,58.1')] ).
cnf(601,plain,
( ~ product(c,multiplicative_identity,u)
| sum__dfg(additive_identity,d,additive_identity)
| product(s,d,u) ),
inference(ssi,[status(thm)],[591,4]),
[iquote('0:SSi:591.0,4.0')] ).
cnf(602,plain,
( ~ product(c,multiplicative_identity,u)
| product(s,d,u) ),
inference(mrr,[status(thm)],[601,8]),
[iquote('0:MRR:601.1,8.0')] ).
cnf(663,plain,
product(s,b,a),
inference(res,[status(thm),theory(equality)],[267,530]),
[iquote('0:Res:267.0,530.0')] ).
cnf(671,plain,
product(b,s,a),
inference(res,[status(thm),theory(equality)],[663,22]),
[iquote('0:Res:663.0,22.0')] ).
cnf(679,plain,
( ~ product(s,d,u)
| product(b,u,k) ),
inference(res,[status(thm),theory(equality)],[671,48]),
[iquote('0:Res:671.0,48.0')] ).
cnf(827,plain,
( ~ defined(c)
| product(s,d,c) ),
inference(res,[status(thm),theory(equality)],[102,602]),
[iquote('0:Res:102.1,602.0')] ).
cnf(830,plain,
product(s,d,c),
inference(ssi,[status(thm)],[827,3]),
[iquote('0:SSi:827.0,3.0')] ).
cnf(1035,plain,
~ product(s,d,c),
inference(res,[status(thm),theory(equality)],[679,12]),
[iquote('0:Res:679.1,12.0')] ).
cnf(1051,plain,
$false,
inference(mrr,[status(thm)],[1035,830]),
[iquote('0:MRR:1035.0,830.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : FLD049-4 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n017.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 : Mon Jun 6 20:42:46 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.48/0.64
% 0.48/0.64 SPASS V 3.9
% 0.48/0.64 SPASS beiseite: Proof found.
% 0.48/0.64 % SZS status Theorem
% 0.48/0.64 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.48/0.64 SPASS derived 887 clauses, backtracked 0 clauses, performed 1 splits and kept 756 clauses.
% 0.48/0.64 SPASS allocated 76532 KBytes.
% 0.48/0.64 SPASS spent 0:00:00.28 on the problem.
% 0.48/0.64 0:00:00.03 for the input.
% 0.48/0.64 0:00:00.00 for the FLOTTER CNF translation.
% 0.48/0.64 0:00:00.01 for inferences.
% 0.48/0.64 0:00:00.00 for the backtracking.
% 0.48/0.64 0:00:00.20 for the reduction.
% 0.48/0.64
% 0.48/0.64
% 0.48/0.64 Here is a proof with depth 9, length 44 :
% 0.48/0.64 % SZS output start Refutation
% See solution above
% 0.48/0.64 Formulae used in the proof : a_is_defined b_is_defined c_is_defined d_is_defined not_sum_7 not_sum_8 product_9 product_10 product_11 not_product_12 associativity_multiplication_1 associativity_multiplication_2 existence_of_identity_multiplication existence_of_inverse_multiplication commutativity_multiplication
% 0.48/0.64
%------------------------------------------------------------------------------