TSTP Solution File: BOO003-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : BOO003-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n032.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 23:49:21 EDT 2022
% Result : Unsatisfiable 0.36s 0.53s
% Output : Refutation 0.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of clauses : 22 ( 10 unt; 0 nHn; 22 RR)
% Number of literals : 47 ( 0 equ; 30 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 : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ product(x__dfg,x__dfg,x__dfg),
file('BOO003-1.p',unknown),
[] ).
cnf(3,axiom,
product(u,v,multiply(u,v)),
file('BOO003-1.p',unknown),
[] ).
cnf(5,axiom,
( ~ product(u,v,w)
| product(v,u,w) ),
file('BOO003-1.p',unknown),
[] ).
cnf(6,axiom,
sum__dfg(additive_identity,u,u),
file('BOO003-1.p',unknown),
[] ).
cnf(7,axiom,
sum__dfg(u,additive_identity,u),
file('BOO003-1.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('BOO003-1.p',unknown),
[] ).
cnf(16,axiom,
( ~ sum__dfg(u,v,w)
| ~ product(x,y,u)
| ~ sum__dfg(y,v,z)
| ~ sum__dfg(x,v,x1)
| product(x1,z,w) ),
file('BOO003-1.p',unknown),
[] ).
cnf(20,axiom,
product(inverse(u),u,additive_identity),
file('BOO003-1.p',unknown),
[] ).
cnf(23,axiom,
( ~ product(u,v,w)
| ~ product(u,v,x)
| equal(x,w) ),
file('BOO003-1.p',unknown),
[] ).
cnf(27,plain,
( ~ product(u,v,w)
| ~ sum__dfg(w,x,x__dfg)
| ~ sum__dfg(v,x,x__dfg)
| ~ sum__dfg(u,x,x__dfg) ),
inference(res,[status(thm),theory(equality)],[16,1]),
[iquote('0:Res:16.4,1.0')] ).
cnf(33,plain,
product(u,v,multiply(v,u)),
inference(res,[status(thm),theory(equality)],[3,5]),
[iquote('0:Res:3.0,5.0')] ).
cnf(42,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(85,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(483,plain,
( ~ product(additive_identity,u,v)
| ~ product(w,u,additive_identity)
| product(w,u,v) ),
inference(res,[status(thm),theory(equality)],[7,85]),
[iquote('0:Res:7.0,85.0')] ).
cnf(833,plain,
( ~ product(u,v,additive_identity)
| product(u,v,multiply(additive_identity,v)) ),
inference(res,[status(thm),theory(equality)],[3,483]),
[iquote('0:Res:3.0,483.0')] ).
cnf(861,plain,
( ~ product(inverse(u),u,additive_identity)
| equal(multiply(additive_identity,u),additive_identity) ),
inference(res,[status(thm),theory(equality)],[833,42]),
[iquote('0:Res:833.1,42.0')] ).
cnf(870,plain,
equal(multiply(additive_identity,u),additive_identity),
inference(mrr,[status(thm)],[861,20]),
[iquote('0:MRR:861.0,20.0')] ).
cnf(897,plain,
product(u,additive_identity,additive_identity),
inference(spr,[status(thm),theory(equality)],[870,33]),
[iquote('0:SpR:870.0,33.0')] ).
cnf(1032,plain,
( ~ sum__dfg(additive_identity,u,x__dfg)
| ~ sum__dfg(additive_identity,u,x__dfg)
| ~ sum__dfg(v,u,x__dfg) ),
inference(res,[status(thm),theory(equality)],[897,27]),
[iquote('0:Res:897.0,27.0')] ).
cnf(1039,plain,
( ~ sum__dfg(additive_identity,u,x__dfg)
| ~ sum__dfg(v,u,x__dfg) ),
inference(obv,[status(thm),theory(equality)],[1032]),
[iquote('0:Obv:1032.0')] ).
cnf(1040,plain,
~ sum__dfg(additive_identity,u,x__dfg),
inference(con,[status(thm)],[1039]),
[iquote('0:Con:1039.1')] ).
cnf(1041,plain,
$false,
inference(unc,[status(thm)],[1040,6]),
[iquote('0:UnC:1040.0,6.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : BOO003-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.11 % Command : run_spass %d %s
% 0.11/0.31 % Computer : n032.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 600
% 0.11/0.31 % DateTime : Thu Jun 2 00:02:30 EDT 2022
% 0.11/0.31 % CPUTime :
% 0.36/0.53
% 0.36/0.53 SPASS V 3.9
% 0.36/0.53 SPASS beiseite: Proof found.
% 0.36/0.53 % SZS status Theorem
% 0.36/0.53 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.36/0.53 SPASS derived 879 clauses, backtracked 0 clauses, performed 0 splits and kept 367 clauses.
% 0.36/0.53 SPASS allocated 63804 KBytes.
% 0.36/0.53 SPASS spent 0:00:00.21 on the problem.
% 0.36/0.53 0:00:00.03 for the input.
% 0.36/0.53 0:00:00.00 for the FLOTTER CNF translation.
% 0.36/0.53 0:00:00.01 for inferences.
% 0.36/0.53 0:00:00.00 for the backtracking.
% 0.36/0.53 0:00:00.14 for the reduction.
% 0.36/0.53
% 0.36/0.53
% 0.36/0.53 Here is a proof with depth 6, length 22 :
% 0.36/0.53 % SZS output start Refutation
% See solution above
% 0.36/0.53 Formulae used in the proof : prove_both_equalities closure_of_multiplication commutativity_of_multiplication additive_identity1 additive_identity2 distributivity4 distributivity7 multiplicative_inverse1 multiplication_is_well_defined
% 0.36/0.53
%------------------------------------------------------------------------------