%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SET046-5 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n012.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 : Tue Jul 19 05:23:08 EDT 2022
% Result : Unsatisfiable 0.19s 0.41s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of clauses : 10 ( 3 unt; 3 nHn; 10 RR)
% Number of literals : 19 ( 0 equ; 9 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ element(u,v)
| ~ element(v,u)
| ~ element(v,a) ),
file('SET046-5.p',unknown),
[] ).
cnf(2,axiom,
( element(u,a)
| element(u,f(u)) ),
file('SET046-5.p',unknown),
[] ).
cnf(3,axiom,
( element(u,a)
| element(f(u),u) ),
file('SET046-5.p',unknown),
[] ).
cnf(4,plain,
( ~ element(f(u),u)
| ~ element(f(u),a)
| element(u,a) ),
inference(res,[status(thm),theory(equality)],[2,1]),
[iquote('0:Res:2.1,1.0')] ).
cnf(6,plain,
( ~ element(f(u),a)
| element(u,a) ),
inference(mrr,[status(thm)],[4,3]),
[iquote('0:MRR:4.0,3.1')] ).
cnf(7,plain,
( element(a,a)
| element(a,a) ),
inference(res,[status(thm),theory(equality)],[3,6]),
[iquote('0:Res:3.1,6.0')] ).
cnf(8,plain,
element(a,a),
inference(obv,[status(thm),theory(equality)],[7]),
[iquote('0:Obv:7.0')] ).
cnf(9,plain,
( ~ element(a,a)
| ~ element(a,a) ),
inference(res,[status(thm),theory(equality)],[8,1]),
[iquote('0:Res:8.0,1.0')] ).
cnf(10,plain,
~ element(a,a),
inference(obv,[status(thm),theory(equality)],[9]),
[iquote('0:Obv:9.0')] ).
cnf(11,plain,
$false,
inference(mrr,[status(thm)],[10,8]),
[iquote('0:MRR:10.0,8.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET046-5 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n012.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 : Sun Jul 10 21:21:28 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.41
% 0.19/0.41 SPASS V 3.9
% 0.19/0.41 SPASS beiseite: Proof found.
% 0.19/0.41 % SZS status Theorem
% 0.19/0.41 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.41 SPASS derived 4 clauses, backtracked 0 clauses, performed 0 splits and kept 6 clauses.
% 0.19/0.41 SPASS allocated 63080 KBytes.
% 0.19/0.41 SPASS spent 0:00:00.06 on the problem.
% 0.19/0.41 0:00:00.03 for the input.
% 0.19/0.41 0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.41 0:00:00.00 for inferences.
% 0.19/0.41 0:00:00.00 for the backtracking.
% 0.19/0.41 0:00:00.00 for the reduction.
% 0.19/0.41
% 0.19/0.41
% 0.19/0.41 Here is a proof with depth 3, length 10 :
% 0.19/0.41 % SZS output start Refutation
% See solution above
% 0.19/0.41 Formulae used in the proof : clause_1 clause_2 clause_3
% 0.19/0.41
%------------------------------------------------------------------------------