TSTP Solution File: FLD050-4 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : FLD050-4 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 02:28:31 EDT 2022
% Result : Unsatisfiable 3.23s 3.48s
% Output : Refutation 3.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 15
% Syntax : Number of clauses : 36 ( 16 unt; 6 nHn; 36 RR)
% Number of literals : 69 ( 0 equ; 30 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 : 15 ( 15 usr; 14 con; 0-1 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
defined(a),
file('FLD050-4.p',unknown),
[] ).
cnf(2,axiom,
defined(b),
file('FLD050-4.p',unknown),
[] ).
cnf(3,axiom,
defined(c),
file('FLD050-4.p',unknown),
[] ).
cnf(4,axiom,
defined(d),
file('FLD050-4.p',unknown),
[] ).
cnf(7,axiom,
~ sum__dfg(additive_identity,b,additive_identity),
file('FLD050-4.p',unknown),
[] ).
cnf(8,axiom,
~ sum__dfg(additive_identity,d,additive_identity),
file('FLD050-4.p',unknown),
[] ).
cnf(9,axiom,
product(a,multiplicative_inverse(b),s),
file('FLD050-4.p',unknown),
[] ).
cnf(10,axiom,
product(a,d,k),
file('FLD050-4.p',unknown),
[] ).
cnf(11,axiom,
product(b,c,k),
file('FLD050-4.p',unknown),
[] ).
cnf(12,axiom,
~ product(c,multiplicative_inverse(d),s),
file('FLD050-4.p',unknown),
[] ).
cnf(18,axiom,
( ~ product(u,v,w)
| ~ product(x,v,y)
| ~ product(z,x,u)
| product(z,y,w) ),
file('FLD050-4.p',unknown),
[] ).
cnf(19,axiom,
( ~ product(u,v,w)
| ~ product(x,y,v)
| ~ product(u,x,z)
| product(z,y,w) ),
file('FLD050-4.p',unknown),
[] ).
cnf(20,axiom,
( ~ defined(u)
| product(multiplicative_identity,u,u) ),
file('FLD050-4.p',unknown),
[] ).
cnf(21,axiom,
( ~ defined(u)
| sum__dfg(additive_identity,u,additive_identity)
| product(multiplicative_inverse(u),u,multiplicative_identity) ),
file('FLD050-4.p',unknown),
[] ).
cnf(22,axiom,
( ~ product(u,v,w)
| product(v,u,w) ),
file('FLD050-4.p',unknown),
[] ).
cnf(44,plain,
( ~ product(u,c,v)
| ~ product(w,b,u)
| product(w,k,v) ),
inference(res,[status(thm),theory(equality)],[11,18]),
[iquote('0:Res:11.0,18.1')] ).
cnf(54,plain,
( ~ product(a,u,v)
| ~ product(d,w,u)
| product(k,w,v) ),
inference(res,[status(thm),theory(equality)],[10,19]),
[iquote('0:Res:10.0,19.0')] ).
cnf(74,plain,
( ~ product(u,v,a)
| ~ product(v,multiplicative_inverse(b),w)
| product(u,w,s) ),
inference(res,[status(thm),theory(equality)],[9,18]),
[iquote('0:Res:9.0,18.2')] ).
cnf(99,plain,
( ~ defined(u)
| product(u,multiplicative_identity,u) ),
inference(res,[status(thm),theory(equality)],[20,22]),
[iquote('0:Res:20.1,22.0')] ).
cnf(108,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(124,plain,
( ~ defined(a)
| ~ product(d,u,multiplicative_identity)
| product(k,u,a) ),
inference(res,[status(thm),theory(equality)],[99,54]),
[iquote('0:Res:99.1,54.0')] ).
cnf(128,plain,
( ~ product(d,u,multiplicative_identity)
| product(k,u,a) ),
inference(ssi,[status(thm)],[124,1]),
[iquote('0:SSi:124.0,1.0')] ).
cnf(144,plain,
( ~ defined(d)
| sum__dfg(additive_identity,d,additive_identity)
| product(k,multiplicative_inverse(d),a) ),
inference(res,[status(thm),theory(equality)],[108,128]),
[iquote('0:Res:108.2,128.0')] ).
cnf(145,plain,
( sum__dfg(additive_identity,d,additive_identity)
| product(k,multiplicative_inverse(d),a) ),
inference(ssi,[status(thm)],[144,4]),
[iquote('0:SSi:144.0,4.0')] ).
cnf(146,plain,
product(k,multiplicative_inverse(d),a),
inference(mrr,[status(thm)],[145,8]),
[iquote('0:MRR:145.0,8.0')] ).
cnf(147,plain,
product(multiplicative_inverse(d),k,a),
inference(res,[status(thm),theory(equality)],[146,22]),
[iquote('0:Res:146.0,22.0')] ).
cnf(568,plain,
( ~ defined(c)
| ~ product(u,b,multiplicative_identity)
| product(u,k,c) ),
inference(res,[status(thm),theory(equality)],[20,44]),
[iquote('0:Res:20.1,44.0')] ).
cnf(578,plain,
( ~ product(u,b,multiplicative_identity)
| product(u,k,c) ),
inference(ssi,[status(thm)],[568,3]),
[iquote('0:SSi:568.0,3.0')] ).
cnf(674,plain,
( ~ defined(b)
| sum__dfg(additive_identity,b,additive_identity)
| product(multiplicative_inverse(b),k,c) ),
inference(res,[status(thm),theory(equality)],[21,578]),
[iquote('0:Res:21.2,578.0')] ).
cnf(675,plain,
( sum__dfg(additive_identity,b,additive_identity)
| product(multiplicative_inverse(b),k,c) ),
inference(ssi,[status(thm)],[674,2]),
[iquote('0:SSi:674.0,2.0')] ).
cnf(676,plain,
product(multiplicative_inverse(b),k,c),
inference(mrr,[status(thm)],[675,7]),
[iquote('0:MRR:675.0,7.0')] ).
cnf(680,plain,
product(k,multiplicative_inverse(b),c),
inference(res,[status(thm),theory(equality)],[676,22]),
[iquote('0:Res:676.0,22.0')] ).
cnf(925,plain,
( ~ product(u,k,a)
| product(u,c,s) ),
inference(res,[status(thm),theory(equality)],[680,74]),
[iquote('0:Res:680.0,74.1')] ).
cnf(1670,plain,
( ~ product(u,k,a)
| product(c,u,s) ),
inference(res,[status(thm),theory(equality)],[925,22]),
[iquote('0:Res:925.1,22.0')] ).
cnf(7381,plain,
product(c,multiplicative_inverse(d),s),
inference(res,[status(thm),theory(equality)],[147,1670]),
[iquote('0:Res:147.0,1670.0')] ).
cnf(7383,plain,
$false,
inference(mrr,[status(thm)],[7381,12]),
[iquote('0:MRR:7381.0,12.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : FLD050-4 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.00/0.07 % Command : run_spass %d %s
% 0.06/0.25 % Computer : n019.cluster.edu
% 0.06/0.25 % Model : x86_64 x86_64
% 0.06/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.25 % Memory : 8042.1875MB
% 0.06/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.25 % CPULimit : 300
% 0.06/0.25 % WCLimit : 600
% 0.06/0.25 % DateTime : Tue Jun 7 04:21:55 EDT 2022
% 0.06/0.25 % CPUTime :
% 3.23/3.48
% 3.23/3.48 SPASS V 3.9
% 3.23/3.48 SPASS beiseite: Proof found.
% 3.23/3.48 % SZS status Theorem
% 3.23/3.48 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.23/3.48 SPASS derived 4964 clauses, backtracked 0 clauses, performed 2 splits and kept 4152 clauses.
% 3.23/3.48 SPASS allocated 81646 KBytes.
% 3.23/3.48 SPASS spent 0:00:03.18 on the problem.
% 3.23/3.48 0:00:00.02 for the input.
% 3.23/3.48 0:00:00.00 for the FLOTTER CNF translation.
% 3.23/3.48 0:00:00.05 for inferences.
% 3.23/3.48 0:00:00.03 for the backtracking.
% 3.23/3.48 0:00:03.04 for the reduction.
% 3.23/3.48
% 3.23/3.48
% 3.23/3.48 Here is a proof with depth 7, length 36 :
% 3.23/3.48 % SZS output start Refutation
% See solution above
% 3.23/3.48 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
% 3.23/3.48
%------------------------------------------------------------------------------