TSTP Solution File: FLD001-3 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : FLD001-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n026.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 02:28:12 EDT 2022
% Result : Unsatisfiable 4.88s 5.09s
% Output : Refutation 4.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of clauses : 32 ( 11 unt; 0 nHn; 32 RR)
% Number of literals : 72 ( 0 equ; 43 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 11 con; 0-0 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
defined(a),
file('FLD001-3.p',unknown),
[] ).
cnf(3,axiom,
sum__dfg(additive_identity,a,b),
file('FLD001-3.p',unknown),
[] ).
cnf(4,axiom,
~ product(multiplicative_identity,a,b),
file('FLD001-3.p',unknown),
[] ).
cnf(5,axiom,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(x,v,y)
| ~ sum__dfg(z,x,u)
| sum__dfg(z,y,w) ),
file('FLD001-3.p',unknown),
[] ).
cnf(6,axiom,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(x,y,v)
| ~ sum__dfg(u,x,z)
| sum__dfg(z,y,w) ),
file('FLD001-3.p',unknown),
[] ).
cnf(7,axiom,
( ~ defined(u)
| sum__dfg(additive_identity,u,u) ),
file('FLD001-3.p',unknown),
[] ).
cnf(9,axiom,
( ~ sum__dfg(u,v,w)
| sum__dfg(v,u,w) ),
file('FLD001-3.p',unknown),
[] ).
cnf(12,axiom,
( ~ defined(u)
| product(multiplicative_identity,u,u) ),
file('FLD001-3.p',unknown),
[] ).
cnf(14,axiom,
( ~ product(u,v,w)
| product(v,u,w) ),
file('FLD001-3.p',unknown),
[] ).
cnf(16,axiom,
( ~ sum__dfg(u,v,w)
| ~ product(x,y,v)
| ~ product(z,y,u)
| ~ sum__dfg(z,x,x1)
| product(x1,y,w) ),
file('FLD001-3.p',unknown),
[] ).
cnf(18,axiom,
defined(additive_identity),
file('FLD001-3.p',unknown),
[] ).
cnf(31,plain,
~ product(a,multiplicative_identity,b),
inference(res,[status(thm),theory(equality)],[14,4]),
[iquote('0:Res:14.1,4.0')] ).
cnf(47,plain,
( ~ defined(u)
| product(u,multiplicative_identity,u) ),
inference(res,[status(thm),theory(equality)],[12,14]),
[iquote('0:Res:12.1,14.0')] ).
cnf(64,plain,
( ~ defined(u)
| ~ sum__dfg(v,w,u)
| ~ sum__dfg(additive_identity,v,x)
| sum__dfg(x,w,u) ),
inference(res,[status(thm),theory(equality)],[7,6]),
[iquote('0:Res:7.1,6.0')] ).
cnf(88,plain,
( ~ defined(u)
| ~ sum__dfg(v,u,w)
| ~ sum__dfg(x,v,additive_identity)
| sum__dfg(x,w,u) ),
inference(res,[status(thm),theory(equality)],[7,5]),
[iquote('0:Res:7.1,5.0')] ).
cnf(241,plain,
( ~ product(u,v,a)
| ~ product(w,v,additive_identity)
| ~ sum__dfg(w,u,x)
| product(x,v,b) ),
inference(res,[status(thm),theory(equality)],[3,16]),
[iquote('0:Res:3.0,16.0')] ).
cnf(456,plain,
( ~ defined(a)
| ~ sum__dfg(u,additive_identity,additive_identity)
| sum__dfg(u,b,a) ),
inference(res,[status(thm),theory(equality)],[3,88]),
[iquote('0:Res:3.0,88.1')] ).
cnf(494,plain,
( ~ sum__dfg(u,additive_identity,additive_identity)
| sum__dfg(u,b,a) ),
inference(ssi,[status(thm)],[456,1]),
[iquote('0:SSi:456.0,1.0')] ).
cnf(584,plain,
( ~ sum__dfg(u,additive_identity,additive_identity)
| sum__dfg(b,u,a) ),
inference(res,[status(thm),theory(equality)],[494,9]),
[iquote('0:Res:494.1,9.0')] ).
cnf(626,plain,
( ~ defined(additive_identity)
| sum__dfg(b,additive_identity,a) ),
inference(res,[status(thm),theory(equality)],[7,584]),
[iquote('0:Res:7.1,584.0')] ).
cnf(632,plain,
sum__dfg(b,additive_identity,a),
inference(ssi,[status(thm)],[626,18]),
[iquote('0:SSi:626.0,18.0')] ).
cnf(643,plain,
sum__dfg(additive_identity,b,a),
inference(res,[status(thm),theory(equality)],[632,9]),
[iquote('0:Res:632.0,9.0')] ).
cnf(646,plain,
( ~ defined(a)
| ~ sum__dfg(additive_identity,b,u)
| sum__dfg(u,additive_identity,a) ),
inference(res,[status(thm),theory(equality)],[632,64]),
[iquote('0:Res:632.0,64.1')] ).
cnf(648,plain,
( ~ sum__dfg(additive_identity,b,u)
| sum__dfg(u,additive_identity,a) ),
inference(ssi,[status(thm)],[646,1]),
[iquote('0:SSi:646.0,1.0')] ).
cnf(722,plain,
sum__dfg(a,additive_identity,a),
inference(res,[status(thm),theory(equality)],[643,648]),
[iquote('0:Res:643.0,648.0')] ).
cnf(735,plain,
sum__dfg(additive_identity,a,a),
inference(res,[status(thm),theory(equality)],[722,9]),
[iquote('0:Res:722.0,9.0')] ).
cnf(792,plain,
( ~ defined(a)
| ~ product(u,multiplicative_identity,additive_identity)
| ~ sum__dfg(u,a,v)
| product(v,multiplicative_identity,b) ),
inference(res,[status(thm),theory(equality)],[47,241]),
[iquote('0:Res:47.1,241.0')] ).
cnf(794,plain,
( ~ product(u,multiplicative_identity,additive_identity)
| ~ sum__dfg(u,a,v)
| product(v,multiplicative_identity,b) ),
inference(ssi,[status(thm)],[792,1]),
[iquote('0:SSi:792.0,1.0')] ).
cnf(4937,plain,
( ~ defined(additive_identity)
| ~ sum__dfg(additive_identity,a,u)
| product(u,multiplicative_identity,b) ),
inference(res,[status(thm),theory(equality)],[47,794]),
[iquote('0:Res:47.1,794.0')] ).
cnf(4938,plain,
( ~ sum__dfg(additive_identity,a,u)
| product(u,multiplicative_identity,b) ),
inference(ssi,[status(thm)],[4937,18]),
[iquote('0:SSi:4937.0,18.0')] ).
cnf(9440,plain,
~ sum__dfg(additive_identity,a,a),
inference(res,[status(thm),theory(equality)],[4938,31]),
[iquote('0:Res:4938.1,31.0')] ).
cnf(9463,plain,
$false,
inference(mrr,[status(thm)],[9440,735]),
[iquote('0:MRR:9440.0,735.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : FLD001-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n026.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jun 6 14:42:15 EDT 2022
% 0.13/0.33 % CPUTime :
% 4.88/5.09
% 4.88/5.09 SPASS V 3.9
% 4.88/5.09 SPASS beiseite: Proof found.
% 4.88/5.09 % SZS status Theorem
% 4.88/5.09 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.88/5.09 SPASS derived 7010 clauses, backtracked 0 clauses, performed 4 splits and kept 4391 clauses.
% 4.88/5.09 SPASS allocated 82739 KBytes.
% 4.88/5.09 SPASS spent 0:00:04.65 on the problem.
% 4.88/5.09 0:00:00.03 for the input.
% 4.88/5.09 0:00:00.00 for the FLOTTER CNF translation.
% 4.88/5.09 0:00:00.07 for inferences.
% 4.88/5.09 0:00:00.12 for the backtracking.
% 4.88/5.09 0:00:04.36 for the reduction.
% 4.88/5.09
% 4.88/5.09
% 4.88/5.09 Here is a proof with depth 7, length 32 :
% 4.88/5.09 % SZS output start Refutation
% See solution above
% 4.88/5.09 Formulae used in the proof : a_is_defined sum_3 not_product_4 associativity_addition_1 associativity_addition_2 existence_of_identity_addition commutativity_addition existence_of_identity_multiplication commutativity_multiplication distributivity_2 well_definedness_of_additive_identity
% 4.88/5.09
%------------------------------------------------------------------------------