%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET024-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:35:22 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.45s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 12 ( 9 unt; 0 def)
% Number of atoms : 17 ( 5 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 13 ( 8 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 11 ( 3 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_membership_of_singleton_set,axiom,
~ member(a,singleton_set(a)),
file('theBenchmark.p',prove_membership_of_singleton_set) ).
cnf(c_64,plain,
~ member(a,singleton_set(a)),
inference(clausify,[status(thm)],[prove_membership_of_singleton_set]) ).
fof(a_little_set,axiom,
little_set(a),
file('theBenchmark.p',a_little_set) ).
cnf(c_65,plain,
little_set(a),
inference(clausify,[status(thm)],[a_little_set]) ).
fof(singleton_set,axiom,
! [VAR_0] : singleton_set(VAR_0) = non_ordered_pair(VAR_0,VAR_0),
file('theBenchmark.p',singleton_set) ).
cnf(c_193,plain,
singleton_set(A) = non_ordered_pair(A,A),
inference(clausify,[status(thm)],[singleton_set]) ).
fof(non_ordered_pair3,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_0 != VAR_2
| ~ little_set(VAR_0)
| member(VAR_0,non_ordered_pair(VAR_1,VAR_2)) ),
file('theBenchmark.p',non_ordered_pair3) ).
cnf(c_195,plain,
( A != C
| ~ little_set(A)
| member(A,non_ordered_pair(B,C)) ),
inference(clausify,[status(thm)],[non_ordered_pair3]) ).
cnf(c_347,plain,
~ member(a,non_ordered_pair(a,a)),
inference(paramod,[status(thm)],[c_193,c_64]) ).
cnf(c_484,plain,
( a != B
| member(a,non_ordered_pair(A,B)) ),
inference(resolve,[status(thm)],[c_195,c_65]) ).
cnf(c_482,plain,
member(a,non_ordered_pair(A,a)),
inference(xxres,[status(thm)],[c_484]) ).
cnf(c_483,plain,
$false,
inference(resolve,[status(thm)],[c_482,c_347]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET024-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n009.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sat Sep 26 06:53:29 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.36 % Process 3606218 was started by sandbox on n009,
% 0.11/0.36 % Sat Sep 26 06:53:29 2026
% 0.11/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.37
% 0.11/0.37 % From the command line: assign(max_seconds, 300).
% 0.11/0.45
% 0.11/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.45
% 0.11/0.45 % Proof 1 at 0.06 (+ 0.01) seconds.
% 0.11/0.45 % Length of proof is 7.
% 0.11/0.45 % Level of proof is 2.
% 0.11/0.45 % Maximum clause weight is 20.000.
% 0.11/0.45 % Given clauses 83.
% 0.11/0.45
% 0.11/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------