TSTP Solution File: BOO009-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : BOO009-1 : TPTP v8.1.0. Released v1.0.0.
% 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 : Thu Jul 14 23:49:24 EDT 2022
% Result : Unsatisfiable 0.66s 0.82s
% Output : Refutation 0.66s
% 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,
~ product(x__dfg,add(x__dfg,y__dfg),x__dfg),
file('BOO009-1.p',unknown),
[] ).
cnf(2,axiom,
sum__dfg(u,v,add(u,v)),
file('BOO009-1.p',unknown),
[] ).
cnf(3,axiom,
product(u,v,multiply(u,v)),
file('BOO009-1.p',unknown),
[] ).
cnf(6,axiom,
sum__dfg(additive_identity,u,u),
file('BOO009-1.p',unknown),
[] ).
cnf(7,axiom,
sum__dfg(u,additive_identity,u),
file('BOO009-1.p',unknown),
[] ).
cnf(13,axiom,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(x,y,z)
| ~ product(y,x1,v)
| ~ product(x,x1,u)
| product(z,x1,w) ),
file('BOO009-1.p',unknown),
[] ).
cnf(14,axiom,
( ~ sum__dfg(u,v,w)
| ~ product(x,y,v)
| ~ sum__dfg(u,y,z)
| ~ sum__dfg(u,x,x1)
| product(x1,z,w) ),
file('BOO009-1.p',unknown),
[] ).
cnf(20,axiom,
product(inverse(u),u,additive_identity),
file('BOO009-1.p',unknown),
[] ).
cnf(23,axiom,
( ~ product(u,v,w)
| ~ product(u,v,x)
| equal(x,w) ),
file('BOO009-1.p',unknown),
[] ).
cnf(43,plain,
( ~ product(inverse(u),u,v)
| equal(v,additive_identity) ),
inference(res,[status(thm),theory(equality)],[20,23]),
[iquote('0:Res:20.0,23.0')] ).
cnf(80,plain,
( ~ sum__dfg(u,v,w)
| ~ product(v,x,y)
| ~ product(u,x,additive_identity)
| product(w,x,y) ),
inference(res,[status(thm),theory(equality)],[6,13]),
[iquote('0:Res:6.0,13.0')] ).
cnf(164,plain,
( ~ product(u,v,additive_identity)
| ~ sum__dfg(w,v,x)
| ~ sum__dfg(w,u,y)
| product(y,x,w) ),
inference(res,[status(thm),theory(equality)],[7,14]),
[iquote('0:Res:7.0,14.0')] ).
cnf(481,plain,
( ~ product(additive_identity,u,v)
| ~ product(w,u,additive_identity)
| product(w,u,v) ),
inference(res,[status(thm),theory(equality)],[7,80]),
[iquote('0:Res:7.0,80.0')] ).
cnf(832,plain,
( ~ product(u,v,additive_identity)
| product(u,v,multiply(additive_identity,v)) ),
inference(res,[status(thm),theory(equality)],[3,481]),
[iquote('0:Res:3.0,481.0')] ).
cnf(860,plain,
( ~ product(inverse(u),u,additive_identity)
| equal(multiply(additive_identity,u),additive_identity) ),
inference(res,[status(thm),theory(equality)],[832,43]),
[iquote('0:Res:832.1,43.0')] ).
cnf(869,plain,
equal(multiply(additive_identity,u),additive_identity),
inference(mrr,[status(thm)],[860,20]),
[iquote('0:MRR:860.0,20.0')] ).
cnf(892,plain,
product(additive_identity,u,additive_identity),
inference(spr,[status(thm),theory(equality)],[869,3]),
[iquote('0:SpR:869.0,3.0')] ).
cnf(931,plain,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(u,additive_identity,x)
| product(x,w,u) ),
inference(res,[status(thm),theory(equality)],[892,164]),
[iquote('0:Res:892.0,164.0')] ).
cnf(1932,plain,
( ~ sum__dfg(u,additive_identity,v)
| product(v,add(u,w),u) ),
inference(res,[status(thm),theory(equality)],[2,931]),
[iquote('0:Res:2.0,931.0')] ).
cnf(2157,plain,
~ sum__dfg(x__dfg,additive_identity,x__dfg),
inference(res,[status(thm),theory(equality)],[1932,1]),
[iquote('0:Res:1932.1,1.0')] ).
cnf(2184,plain,
$false,
inference(mrr,[status(thm)],[2157,7]),
[iquote('0:MRR:2157.0,7.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : BOO009-1 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.13/0.35 % Computer : n029.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Wed Jun 1 21:31:46 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.66/0.82
% 0.66/0.82 SPASS V 3.9
% 0.66/0.82 SPASS beiseite: Proof found.
% 0.66/0.82 % SZS status Theorem
% 0.66/0.82 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.66/0.82 SPASS derived 1778 clauses, backtracked 0 clauses, performed 0 splits and kept 617 clauses.
% 0.66/0.82 SPASS allocated 64514 KBytes.
% 0.66/0.82 SPASS spent 0:00:00.46 on the problem.
% 0.66/0.82 0:00:00.04 for the input.
% 0.66/0.82 0:00:00.00 for the FLOTTER CNF translation.
% 0.66/0.82 0:00:00.03 for inferences.
% 0.66/0.82 0:00:00.00 for the backtracking.
% 0.66/0.82 0:00:00.37 for the reduction.
% 0.66/0.82
% 0.66/0.82
% 0.66/0.82 Here is a proof with depth 8, length 21 :
% 0.66/0.82 % SZS output start Refutation
% See solution above
% 0.66/0.82 Formulae used in the proof : prove_equations closure_of_addition closure_of_multiplication additive_identity1 additive_identity2 distributivity4 distributivity5 multiplicative_inverse1 multiplication_is_well_defined
% 0.66/0.82
%------------------------------------------------------------------------------