TSTP Solution File: FLD029-3 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : FLD029-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n018.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 02:28:23 EDT 2022
% Result : Unsatisfiable 2.73s 2.95s
% Output : Refutation 2.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 13
% Syntax : Number of clauses : 33 ( 14 unt; 2 nHn; 33 RR)
% Number of literals : 64 ( 0 equ; 35 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
defined(a),
file('FLD029-3.p',unknown),
[] ).
cnf(2,axiom,
defined(b),
file('FLD029-3.p',unknown),
[] ).
cnf(4,axiom,
defined(v__dfg),
file('FLD029-3.p',unknown),
[] ).
cnf(5,axiom,
~ sum__dfg(additive_identity,b,additive_identity),
file('FLD029-3.p',unknown),
[] ).
cnf(6,axiom,
product(a,u__dfg,b),
file('FLD029-3.p',unknown),
[] ).
cnf(7,axiom,
product(a,v__dfg,b),
file('FLD029-3.p',unknown),
[] ).
cnf(8,axiom,
~ product(multiplicative_identity,u__dfg,v__dfg),
file('FLD029-3.p',unknown),
[] ).
cnf(15,axiom,
( ~ product(u,v,w)
| ~ product(x,y,v)
| ~ product(u,x,z)
| product(z,y,w) ),
file('FLD029-3.p',unknown),
[] ).
cnf(16,axiom,
( ~ defined(u)
| product(multiplicative_identity,u,u) ),
file('FLD029-3.p',unknown),
[] ).
cnf(17,axiom,
( ~ defined(u)
| sum__dfg(additive_identity,u,additive_identity)
| product(multiplicative_inverse(u),u,multiplicative_identity) ),
file('FLD029-3.p',unknown),
[] ).
cnf(18,axiom,
( ~ product(u,v,w)
| product(v,u,w) ),
file('FLD029-3.p',unknown),
[] ).
cnf(26,axiom,
( ~ defined(u)
| defined(multiplicative_inverse(u))
| sum__dfg(additive_identity,u,additive_identity) ),
file('FLD029-3.p',unknown),
[] ).
cnf(28,axiom,
( ~ defined(u)
| ~ defined(v)
| product(v,u,multiply(v,u)) ),
file('FLD029-3.p',unknown),
[] ).
cnf(41,plain,
( ~ product(u,b,v)
| ~ product(u,a,w)
| product(w,v__dfg,v) ),
inference(res,[status(thm),theory(equality)],[7,15]),
[iquote('0:Res:7.0,15.1')] ).
cnf(54,plain,
( ~ product(u,b,v)
| ~ product(u,a,w)
| product(w,u__dfg,v) ),
inference(res,[status(thm),theory(equality)],[6,15]),
[iquote('0:Res:6.0,15.1')] ).
cnf(63,plain,
( ~ product(u,v,v__dfg)
| ~ product(u,w,multiplicative_identity)
| ~ product(w,u__dfg,v) ),
inference(res,[status(thm),theory(equality)],[15,8]),
[iquote('0:Res:15.3,8.0')] ).
cnf(65,plain,
( ~ defined(b)
| product(multiplicative_inverse(b),b,multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[17,5]),
[iquote('0:Res:17.2,5.0')] ).
cnf(66,plain,
( ~ defined(b)
| defined(multiplicative_inverse(b)) ),
inference(res,[status(thm),theory(equality)],[26,5]),
[iquote('0:Res:26.2,5.0')] ).
cnf(72,plain,
defined(multiplicative_inverse(b)),
inference(mrr,[status(thm)],[66,2]),
[iquote('0:MRR:66.0,2.0')] ).
cnf(73,plain,
product(multiplicative_inverse(b),b,multiplicative_identity),
inference(mrr,[status(thm)],[65,2]),
[iquote('0:MRR:65.0,2.0')] ).
cnf(94,plain,
( ~ defined(u)
| product(u,multiplicative_identity,u) ),
inference(res,[status(thm),theory(equality)],[16,18]),
[iquote('0:Res:16.1,18.0')] ).
cnf(104,plain,
( ~ defined(u)
| ~ defined(v)
| product(u,v,multiply(v,u)) ),
inference(res,[status(thm),theory(equality)],[28,18]),
[iquote('0:Res:28.2,18.0')] ).
cnf(472,plain,
( ~ product(multiplicative_inverse(b),a,u)
| product(u,u__dfg,multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[73,54]),
[iquote('0:Res:73.0,54.0')] ).
cnf(559,plain,
( ~ product(multiplicative_inverse(b),a,u)
| product(u,v__dfg,multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[73,41]),
[iquote('0:Res:73.0,41.0')] ).
cnf(890,plain,
( ~ defined(v__dfg)
| ~ product(v__dfg,u,multiplicative_identity)
| ~ product(u,u__dfg,multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[94,63]),
[iquote('0:Res:94.1,63.0')] ).
cnf(894,plain,
( ~ product(v__dfg,u,multiplicative_identity)
| ~ product(u,u__dfg,multiplicative_identity) ),
inference(ssi,[status(thm)],[890,4]),
[iquote('0:SSi:890.0,4.0')] ).
cnf(6396,plain,
( ~ defined(multiplicative_inverse(b))
| ~ defined(a)
| product(multiply(a,multiplicative_inverse(b)),u__dfg,multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[104,472]),
[iquote('0:Res:104.2,472.0')] ).
cnf(6400,plain,
product(multiply(a,multiplicative_inverse(b)),u__dfg,multiplicative_identity),
inference(ssi,[status(thm)],[6396,1,72]),
[iquote('0:SSi:6396.1,6396.0,1.0,72.0')] ).
cnf(6506,plain,
( ~ defined(multiplicative_inverse(b))
| ~ defined(a)
| product(multiply(a,multiplicative_inverse(b)),v__dfg,multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[104,559]),
[iquote('0:Res:104.2,559.0')] ).
cnf(6510,plain,
product(multiply(a,multiplicative_inverse(b)),v__dfg,multiplicative_identity),
inference(ssi,[status(thm)],[6506,1,72]),
[iquote('0:SSi:6506.1,6506.0,1.0,72.0')] ).
cnf(6598,plain,
product(v__dfg,multiply(a,multiplicative_inverse(b)),multiplicative_identity),
inference(res,[status(thm),theory(equality)],[6510,18]),
[iquote('0:Res:6510.0,18.0')] ).
cnf(6957,plain,
~ product(multiply(a,multiplicative_inverse(b)),u__dfg,multiplicative_identity),
inference(res,[status(thm),theory(equality)],[6598,894]),
[iquote('0:Res:6598.0,894.0')] ).
cnf(6959,plain,
$false,
inference(mrr,[status(thm)],[6957,6400]),
[iquote('0:MRR:6957.0,6400.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : FLD029-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 6 18:41:05 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.73/2.95
% 2.73/2.95 SPASS V 3.9
% 2.73/2.95 SPASS beiseite: Proof found.
% 2.73/2.95 % SZS status Theorem
% 2.73/2.95 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.73/2.95 SPASS derived 5017 clauses, backtracked 0 clauses, performed 3 splits and kept 3680 clauses.
% 2.73/2.95 SPASS allocated 80881 KBytes.
% 2.73/2.95 SPASS spent 0:00:02.57 on the problem.
% 2.73/2.95 0:00:00.04 for the input.
% 2.73/2.95 0:00:00.00 for the FLOTTER CNF translation.
% 2.73/2.95 0:00:00.05 for inferences.
% 2.73/2.95 0:00:00.12 for the backtracking.
% 2.73/2.95 0:00:02.31 for the reduction.
% 2.73/2.95
% 2.73/2.95
% 2.73/2.95 Here is a proof with depth 5, length 33 :
% 2.73/2.95 % SZS output start Refutation
% See solution above
% 2.73/2.95 Formulae used in the proof : a_is_defined b_is_defined v_is_defined not_sum_5 product_6 product_7 not_product_8 associativity_multiplication_2 existence_of_identity_multiplication existence_of_inverse_multiplication commutativity_multiplication well_definedness_of_multiplicative_inverse totality_of_multiplication
% 2.73/2.95
%------------------------------------------------------------------------------