TSTP Solution File: FLD041-3 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : FLD041-3 : 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 02:28:27 EDT 2022
% Result : Unsatisfiable 4.97s 5.20s
% Output : Refutation 4.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 16
% Syntax : Number of clauses : 34 ( 10 unt; 1 nHn; 34 RR)
% Number of literals : 78 ( 0 equ; 51 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
defined(a),
file('FLD041-3.p',unknown),
[] ).
cnf(2,axiom,
defined(b),
file('FLD041-3.p',unknown),
[] ).
cnf(3,axiom,
~ sum__dfg(additive_identity,a,additive_identity),
file('FLD041-3.p',unknown),
[] ).
cnf(4,axiom,
~ sum__dfg(additive_identity,b,additive_identity),
file('FLD041-3.p',unknown),
[] ).
cnf(5,axiom,
product(a,b,additive_identity),
file('FLD041-3.p',unknown),
[] ).
cnf(8,axiom,
( ~ defined(u)
| sum__dfg(additive_identity,u,u) ),
file('FLD041-3.p',unknown),
[] ).
cnf(10,axiom,
( ~ sum__dfg(u,v,w)
| sum__dfg(v,u,w) ),
file('FLD041-3.p',unknown),
[] ).
cnf(11,axiom,
( ~ product(u,v,w)
| ~ product(x,v,y)
| ~ product(z,x,u)
| product(z,y,w) ),
file('FLD041-3.p',unknown),
[] ).
cnf(12,axiom,
( ~ product(u,v,w)
| ~ product(x,y,v)
| ~ product(u,x,z)
| product(z,y,w) ),
file('FLD041-3.p',unknown),
[] ).
cnf(13,axiom,
( ~ defined(u)
| product(multiplicative_identity,u,u) ),
file('FLD041-3.p',unknown),
[] ).
cnf(14,axiom,
( ~ defined(u)
| sum__dfg(additive_identity,u,additive_identity)
| product(multiplicative_inverse(u),u,multiplicative_identity) ),
file('FLD041-3.p',unknown),
[] ).
cnf(15,axiom,
( ~ product(u,v,w)
| product(v,u,w) ),
file('FLD041-3.p',unknown),
[] ).
cnf(16,axiom,
( ~ product(u,v,w)
| ~ product(x,v,y)
| ~ product(z,v,x1)
| ~ sum__dfg(x,u,z)
| sum__dfg(y,w,x1) ),
file('FLD041-3.p',unknown),
[] ).
cnf(19,axiom,
defined(additive_identity),
file('FLD041-3.p',unknown),
[] ).
cnf(21,axiom,
( ~ defined(u)
| ~ defined(v)
| defined(multiply(v,u)) ),
file('FLD041-3.p',unknown),
[] ).
cnf(25,axiom,
( ~ defined(u)
| ~ defined(v)
| product(v,u,multiply(v,u)) ),
file('FLD041-3.p',unknown),
[] ).
cnf(36,plain,
( ~ product(u,v,b)
| ~ product(a,u,w)
| product(w,v,additive_identity) ),
inference(res,[status(thm),theory(equality)],[5,12]),
[iquote('0:Res:5.0,12.2')] ).
cnf(37,plain,
( ~ product(u,b,v)
| ~ product(w,a,u)
| product(w,additive_identity,v) ),
inference(res,[status(thm),theory(equality)],[5,11]),
[iquote('0:Res:5.0,11.1')] ).
cnf(51,plain,
( ~ sum__dfg(u,v,w)
| ~ product(v,x,b)
| ~ product(u,x,additive_identity)
| ~ product(w,x,additive_identity) ),
inference(res,[status(thm),theory(equality)],[16,4]),
[iquote('0:Res:16.4,4.0')] ).
cnf(52,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(62,plain,
product(multiplicative_inverse(a),a,multiplicative_identity),
inference(mrr,[status(thm)],[52,1]),
[iquote('0:MRR:52.0,1.0')] ).
cnf(89,plain,
( ~ defined(u)
| sum__dfg(u,additive_identity,u) ),
inference(res,[status(thm),theory(equality)],[8,10]),
[iquote('0:Res:8.1,10.0')] ).
cnf(115,plain,
( ~ defined(u)
| ~ defined(v)
| product(u,v,multiply(v,u)) ),
inference(res,[status(thm),theory(equality)],[25,15]),
[iquote('0:Res:25.2,15.0')] ).
cnf(483,plain,
( ~ defined(b)
| ~ product(u,a,multiplicative_identity)
| product(u,additive_identity,b) ),
inference(res,[status(thm),theory(equality)],[13,37]),
[iquote('0:Res:13.1,37.0')] ).
cnf(493,plain,
( ~ product(u,a,multiplicative_identity)
| product(u,additive_identity,b) ),
inference(ssi,[status(thm)],[483,2]),
[iquote('0:SSi:483.0,2.0')] ).
cnf(540,plain,
product(multiplicative_inverse(a),additive_identity,b),
inference(res,[status(thm),theory(equality)],[62,493]),
[iquote('0:Res:62.0,493.0')] ).
cnf(555,plain,
product(additive_identity,multiplicative_inverse(a),b),
inference(res,[status(thm),theory(equality)],[540,15]),
[iquote('0:Res:540.0,15.0')] ).
cnf(563,plain,
( ~ product(a,additive_identity,u)
| product(u,multiplicative_inverse(a),additive_identity) ),
inference(res,[status(thm),theory(equality)],[555,36]),
[iquote('0:Res:555.0,36.0')] ).
cnf(1664,plain,
( ~ defined(u)
| ~ product(additive_identity,v,b)
| ~ product(u,v,additive_identity)
| ~ product(u,v,additive_identity) ),
inference(res,[status(thm),theory(equality)],[89,51]),
[iquote('0:Res:89.1,51.0')] ).
cnf(1667,plain,
( ~ defined(u)
| ~ product(additive_identity,v,b)
| ~ product(u,v,additive_identity) ),
inference(obv,[status(thm),theory(equality)],[1664]),
[iquote('0:Obv:1664.2')] ).
cnf(6286,plain,
( ~ defined(u)
| ~ product(u,multiplicative_inverse(a),additive_identity) ),
inference(res,[status(thm),theory(equality)],[555,1667]),
[iquote('0:Res:555.0,1667.1')] ).
cnf(6835,plain,
( ~ defined(u)
| ~ product(a,additive_identity,u) ),
inference(res,[status(thm),theory(equality)],[563,6286]),
[iquote('0:Res:563.1,6286.1')] ).
cnf(6880,plain,
( ~ defined(a)
| ~ defined(additive_identity)
| ~ defined(multiply(additive_identity,a)) ),
inference(res,[status(thm),theory(equality)],[115,6835]),
[iquote('0:Res:115.2,6835.1')] ).
cnf(6899,plain,
$false,
inference(ssi,[status(thm)],[6880,21,19,1]),
[iquote('0:SSi:6880.2,6880.1,6880.0,21.0,19.0,1.0,19.0,1.2')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.11 % Problem : FLD041-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.05/0.11 % Command : run_spass %d %s
% 0.11/0.32 % Computer : n029.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Tue Jun 7 01:13:05 EDT 2022
% 0.11/0.32 % CPUTime :
% 4.97/5.20
% 4.97/5.20 SPASS V 3.9
% 4.97/5.20 SPASS beiseite: Proof found.
% 4.97/5.20 % SZS status Theorem
% 4.97/5.20 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.97/5.20 SPASS derived 4806 clauses, backtracked 29 clauses, performed 1 splits and kept 3595 clauses.
% 4.97/5.20 SPASS allocated 81237 KBytes.
% 4.97/5.20 SPASS spent 0:00:04.78 on the problem.
% 4.97/5.20 0:00:00.03 for the input.
% 4.97/5.20 0:00:00.00 for the FLOTTER CNF translation.
% 4.97/5.20 0:00:00.09 for inferences.
% 4.97/5.20 0:00:00.02 for the backtracking.
% 4.97/5.20 0:00:04.58 for the reduction.
% 4.97/5.20
% 4.97/5.20
% 4.97/5.20 Here is a proof with depth 7, length 34 :
% 4.97/5.20 % SZS output start Refutation
% See solution above
% 4.97/5.20 Formulae used in the proof : a_is_defined b_is_defined not_sum_3 not_sum_4 product_5 existence_of_identity_addition commutativity_addition associativity_multiplication_1 associativity_multiplication_2 existence_of_identity_multiplication existence_of_inverse_multiplication commutativity_multiplication distributivity_1 well_definedness_of_additive_identity well_definedness_of_multiplication totality_of_multiplication
% 4.97/5.20
%------------------------------------------------------------------------------