TSTP Solution File: BOO010-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : BOO010-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 : Thu Jul 14 23:49:24 EDT 2022
% Result : Unsatisfiable 0.65s 0.82s
% Output : Refutation 0.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of clauses : 21 ( 10 unt; 0 nHn; 21 RR)
% Number of literals : 45 ( 0 equ; 26 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; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ sum__dfg(x__dfg,multiply(x__dfg,y__dfg),x__dfg),
file('BOO010-1.p',unknown),
[] ).
cnf(2,axiom,
sum__dfg(u,v,add(u,v)),
file('BOO010-1.p',unknown),
[] ).
cnf(3,axiom,
product(u,v,multiply(u,v)),
file('BOO010-1.p',unknown),
[] ).
cnf(8,axiom,
product(multiplicative_identity,u,u),
file('BOO010-1.p',unknown),
[] ).
cnf(9,axiom,
product(u,multiplicative_identity,u),
file('BOO010-1.p',unknown),
[] ).
cnf(10,axiom,
( ~ product(u,v,w)
| ~ sum__dfg(x,y,v)
| ~ product(u,y,z)
| ~ product(u,x,x1)
| sum__dfg(x1,z,w) ),
file('BOO010-1.p',unknown),
[] ).
cnf(17,axiom,
( ~ product(u,v,w)
| ~ product(x,y,z)
| ~ sum__dfg(y,x1,v)
| ~ sum__dfg(x,x1,u)
| sum__dfg(z,x1,w) ),
file('BOO010-1.p',unknown),
[] ).
cnf(18,axiom,
sum__dfg(inverse(u),u,multiplicative_identity),
file('BOO010-1.p',unknown),
[] ).
cnf(22,axiom,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(u,v,x)
| equal(x,w) ),
file('BOO010-1.p',unknown),
[] ).
cnf(43,plain,
( ~ sum__dfg(inverse(u),u,v)
| equal(v,multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[18,22]),
[iquote('0:Res:18.0,22.0')] ).
cnf(80,plain,
( ~ product(u,v,w)
| ~ sum__dfg(v,x,y)
| ~ sum__dfg(u,x,multiplicative_identity)
| sum__dfg(w,x,y) ),
inference(res,[status(thm),theory(equality)],[8,17]),
[iquote('0:Res:8.0,17.0')] ).
cnf(164,plain,
( ~ sum__dfg(u,v,multiplicative_identity)
| ~ product(w,v,x)
| ~ product(w,u,y)
| sum__dfg(y,x,w) ),
inference(res,[status(thm),theory(equality)],[9,10]),
[iquote('0:Res:9.0,10.0')] ).
cnf(481,plain,
( ~ sum__dfg(multiplicative_identity,u,v)
| ~ sum__dfg(w,u,multiplicative_identity)
| sum__dfg(w,u,v) ),
inference(res,[status(thm),theory(equality)],[9,80]),
[iquote('0:Res:9.0,80.0')] ).
cnf(896,plain,
( ~ sum__dfg(u,v,multiplicative_identity)
| sum__dfg(u,v,add(multiplicative_identity,v)) ),
inference(res,[status(thm),theory(equality)],[2,481]),
[iquote('0:Res:2.0,481.0')] ).
cnf(927,plain,
( ~ sum__dfg(inverse(u),u,multiplicative_identity)
| equal(add(multiplicative_identity,u),multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[896,43]),
[iquote('0:Res:896.1,43.0')] ).
cnf(937,plain,
equal(add(multiplicative_identity,u),multiplicative_identity),
inference(mrr,[status(thm)],[927,18]),
[iquote('0:MRR:927.0,18.0')] ).
cnf(960,plain,
sum__dfg(multiplicative_identity,u,multiplicative_identity),
inference(spr,[status(thm),theory(equality)],[937,2]),
[iquote('0:SpR:937.0,2.0')] ).
cnf(1001,plain,
( ~ product(u,v,w)
| ~ product(u,multiplicative_identity,x)
| sum__dfg(x,w,u) ),
inference(res,[status(thm),theory(equality)],[960,164]),
[iquote('0:Res:960.0,164.0')] ).
cnf(1972,plain,
( ~ product(u,multiplicative_identity,v)
| sum__dfg(v,multiply(u,w),u) ),
inference(res,[status(thm),theory(equality)],[3,1001]),
[iquote('0:Res:3.0,1001.0')] ).
cnf(2203,plain,
~ product(x__dfg,multiplicative_identity,x__dfg),
inference(res,[status(thm),theory(equality)],[1972,1]),
[iquote('0:Res:1972.1,1.0')] ).
cnf(2230,plain,
$false,
inference(mrr,[status(thm)],[2203,9]),
[iquote('0:MRR:2203.0,9.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : BOO010-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n028.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jun 1 19:34:52 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.65/0.82
% 0.65/0.82 SPASS V 3.9
% 0.65/0.82 SPASS beiseite: Proof found.
% 0.65/0.82 % SZS status Theorem
% 0.65/0.82 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.65/0.82 SPASS derived 1833 clauses, backtracked 0 clauses, performed 0 splits and kept 625 clauses.
% 0.65/0.82 SPASS allocated 64534 KBytes.
% 0.65/0.82 SPASS spent 0:00:00.47 on the problem.
% 0.65/0.82 0:00:00.03 for the input.
% 0.65/0.82 0:00:00.00 for the FLOTTER CNF translation.
% 0.65/0.82 0:00:00.03 for inferences.
% 0.65/0.82 0:00:00.00 for the backtracking.
% 0.65/0.82 0:00:00.38 for the reduction.
% 0.65/0.82
% 0.65/0.82
% 0.65/0.82 Here is a proof with depth 8, length 21 :
% 0.65/0.82 % SZS output start Refutation
% See solution above
% 0.65/0.83 Formulae used in the proof : prove_equations closure_of_addition closure_of_multiplication multiplicative_identity1 multiplicative_identity2 distributivity1 distributivity8 additive_inverse1 addition_is_well_defined
% 0.65/0.83
%------------------------------------------------------------------------------