TSTP Solution File: BOO005-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : BOO005-1 : TPTP v8.1.0. Released v1.0.0.
% 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 : Thu Jul 14 23:49:22 EDT 2022
% Result : Unsatisfiable 0.40s 0.57s
% Output : Refutation 0.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of clauses : 17 ( 9 unt; 0 nHn; 17 RR)
% Number of literals : 32 ( 0 equ; 17 neg)
% Maximal clause size : 5 ( 1 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,
~ sum__dfg(x__dfg,multiplicative_identity,multiplicative_identity),
file('BOO005-1.p',unknown),
[] ).
cnf(2,axiom,
sum__dfg(u,v,add(u,v)),
file('BOO005-1.p',unknown),
[] ).
cnf(4,axiom,
( ~ sum__dfg(u,v,w)
| sum__dfg(v,u,w) ),
file('BOO005-1.p',unknown),
[] ).
cnf(8,axiom,
product(multiplicative_identity,u,u),
file('BOO005-1.p',unknown),
[] ).
cnf(9,axiom,
product(u,multiplicative_identity,u),
file('BOO005-1.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('BOO005-1.p',unknown),
[] ).
cnf(18,axiom,
sum__dfg(inverse(u),u,multiplicative_identity),
file('BOO005-1.p',unknown),
[] ).
cnf(22,axiom,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(u,v,x)
| equal(x,w) ),
file('BOO005-1.p',unknown),
[] ).
cnf(25,plain,
~ sum__dfg(multiplicative_identity,x__dfg,multiplicative_identity),
inference(res,[status(thm),theory(equality)],[4,1]),
[iquote('0:Res:4.1,1.0')] ).
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(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(832,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(860,plain,
( ~ sum__dfg(inverse(u),u,multiplicative_identity)
| equal(add(multiplicative_identity,u),multiplicative_identity) ),
inference(res,[status(thm),theory(equality)],[832,43]),
[iquote('0:Res:832.1,43.0')] ).
cnf(869,plain,
equal(add(multiplicative_identity,u),multiplicative_identity),
inference(mrr,[status(thm)],[860,18]),
[iquote('0:MRR:860.0,18.0')] ).
cnf(892,plain,
sum__dfg(multiplicative_identity,u,multiplicative_identity),
inference(spr,[status(thm),theory(equality)],[869,2]),
[iquote('0:SpR:869.0,2.0')] ).
cnf(900,plain,
$false,
inference(unc,[status(thm)],[892,25]),
[iquote('0:UnC:892.0,25.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : BOO005-1 : TPTP v8.1.0. Released v1.0.0.
% 0.13/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jun 1 17:54:25 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.40/0.57
% 0.40/0.57 SPASS V 3.9
% 0.40/0.57 SPASS beiseite: Proof found.
% 0.40/0.57 % SZS status Theorem
% 0.40/0.57 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.40/0.57 SPASS derived 752 clauses, backtracked 0 clauses, performed 0 splits and kept 315 clauses.
% 0.40/0.57 SPASS allocated 63721 KBytes.
% 0.40/0.57 SPASS spent 0:00:00.22 on the problem.
% 0.40/0.57 0:00:00.03 for the input.
% 0.40/0.57 0:00:00.00 for the FLOTTER CNF translation.
% 0.40/0.57 0:00:00.01 for inferences.
% 0.40/0.57 0:00:00.00 for the backtracking.
% 0.40/0.57 0:00:00.15 for the reduction.
% 0.40/0.57
% 0.40/0.57
% 0.40/0.57 Here is a proof with depth 5, length 17 :
% 0.40/0.57 % SZS output start Refutation
% See solution above
% 0.40/0.57 Formulae used in the proof : prove_equations closure_of_addition commutativity_of_addition multiplicative_identity1 multiplicative_identity2 distributivity8 additive_inverse1 addition_is_well_defined
% 0.40/0.57
%------------------------------------------------------------------------------