%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : BOO012-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n024.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 23:49:25 EDT 2022
% Result : Unsatisfiable 45.88s 46.13s
% Output : Refutation 45.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of clauses : 25 ( 12 unt; 0 nHn; 25 RR)
% Number of literals : 46 ( 0 equ; 24 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ equal(inverse(inverse(x__dfg)),x__dfg),
file('BOO012-1.p',unknown),
[] ).
cnf(2,axiom,
sum__dfg(u,v,add(u,v)),
file('BOO012-1.p',unknown),
[] ).
cnf(4,axiom,
( ~ sum__dfg(u,v,w)
| sum__dfg(v,u,w) ),
file('BOO012-1.p',unknown),
[] ).
cnf(6,axiom,
sum__dfg(additive_identity,u,u),
file('BOO012-1.p',unknown),
[] ).
cnf(8,axiom,
product(multiplicative_identity,u,u),
file('BOO012-1.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('BOO012-1.p',unknown),
[] ).
cnf(18,axiom,
sum__dfg(inverse(u),u,multiplicative_identity),
file('BOO012-1.p',unknown),
[] ).
cnf(19,axiom,
sum__dfg(u,inverse(u),multiplicative_identity),
file('BOO012-1.p',unknown),
[] ).
cnf(20,axiom,
product(inverse(u),u,additive_identity),
file('BOO012-1.p',unknown),
[] ).
cnf(21,axiom,
product(u,inverse(u),additive_identity),
file('BOO012-1.p',unknown),
[] ).
cnf(22,axiom,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(u,v,x)
| equal(x,w) ),
file('BOO012-1.p',unknown),
[] ).
cnf(24,plain,
( ~ sum__dfg(u,v,x__dfg)
| ~ sum__dfg(u,v,inverse(inverse(x__dfg))) ),
inference(res,[status(thm),theory(equality)],[22,1]),
[iquote('0:Res:22.2,1.0')] ).
cnf(38,plain,
sum__dfg(u,v,add(v,u)),
inference(res,[status(thm),theory(equality)],[2,4]),
[iquote('0:Res:2.0,4.0')] ).
cnf(59,plain,
( ~ sum__dfg(additive_identity,u,v)
| equal(v,u) ),
inference(res,[status(thm),theory(equality)],[6,22]),
[iquote('0:Res:6.0,22.0')] ).
cnf(84,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(234,plain,
~ sum__dfg(additive_identity,inverse(inverse(x__dfg)),x__dfg),
inference(res,[status(thm),theory(equality)],[6,24]),
[iquote('0:Res:6.0,24.1')] ).
cnf(403,plain,
( ~ sum__dfg(u,v,w)
| ~ sum__dfg(inverse(u),v,multiplicative_identity)
| sum__dfg(additive_identity,v,w) ),
inference(res,[status(thm),theory(equality)],[20,84]),
[iquote('0:Res:20.0,84.0')] ).
cnf(404,plain,
( ~ sum__dfg(inverse(u),v,w)
| ~ sum__dfg(u,v,multiplicative_identity)
| sum__dfg(additive_identity,v,w) ),
inference(res,[status(thm),theory(equality)],[21,84]),
[iquote('0:Res:21.0,84.0')] ).
cnf(3838,plain,
( ~ sum__dfg(u,inverse(inverse(u)),v)
| sum__dfg(additive_identity,inverse(inverse(u)),v) ),
inference(res,[status(thm),theory(equality)],[19,403]),
[iquote('0:Res:19.0,403.1')] ).
cnf(3931,plain,
( ~ sum__dfg(u,v,multiplicative_identity)
| sum__dfg(additive_identity,v,add(inverse(u),v)) ),
inference(res,[status(thm),theory(equality)],[2,404]),
[iquote('0:Res:2.0,404.0')] ).
cnf(7660,plain,
( ~ sum__dfg(u,v,multiplicative_identity)
| equal(add(inverse(u),v),v) ),
inference(res,[status(thm),theory(equality)],[3931,59]),
[iquote('0:Res:3931.1,59.0')] ).
cnf(7741,plain,
( ~ sum__dfg(u,v,multiplicative_identity)
| sum__dfg(v,inverse(u),v) ),
inference(spr,[status(thm),theory(equality)],[7660,38]),
[iquote('0:SpR:7660.1,38.0')] ).
cnf(48144,plain,
( ~ sum__dfg(inverse(u),u,multiplicative_identity)
| sum__dfg(additive_identity,inverse(inverse(u)),u) ),
inference(res,[status(thm),theory(equality)],[7741,3838]),
[iquote('0:Res:7741.1,3838.0')] ).
cnf(48156,plain,
sum__dfg(additive_identity,inverse(inverse(u)),u),
inference(mrr,[status(thm)],[48144,18]),
[iquote('0:MRR:48144.0,18.0')] ).
cnf(48157,plain,
$false,
inference(unc,[status(thm)],[48156,234]),
[iquote('0:UnC:48156.0,234.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : BOO012-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n024.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 15:16:21 EDT 2022
% 0.13/0.34 % CPUTime :
% 45.88/46.13
% 45.88/46.13 SPASS V 3.9
% 45.88/46.13 SPASS beiseite: Proof found.
% 45.88/46.13 % SZS status Theorem
% 45.88/46.13 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 45.88/46.13 SPASS derived 38213 clauses, backtracked 0 clauses, performed 0 splits and kept 10332 clauses.
% 45.88/46.13 SPASS allocated 90414 KBytes.
% 45.88/46.13 SPASS spent 0:0:45.29 on the problem.
% 45.88/46.13 0:00:00.03 for the input.
% 45.88/46.13 0:00:00.00 for the FLOTTER CNF translation.
% 45.88/46.13 0:00:00.37 for inferences.
% 45.88/46.13 0:00:00.00 for the backtracking.
% 45.88/46.13 0:0:44.75 for the reduction.
% 45.88/46.13
% 45.88/46.13
% 45.88/46.13 Here is a proof with depth 6, length 25 :
% 45.88/46.13 % SZS output start Refutation
% See solution above
% 45.88/46.13 Formulae used in the proof : prove_inverse_is_an_involution closure_of_addition commutativity_of_addition additive_identity1 multiplicative_identity1 distributivity8 additive_inverse1 additive_inverse2 multiplicative_inverse1 multiplicative_inverse2 addition_is_well_defined
% 45.88/46.13
%------------------------------------------------------------------------------