%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET024-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 08:35:23 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.40s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 12 ( 10 unt; 0 def)
% Number of atoms : 14 ( 3 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 5 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 8 ( 2 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_set_in_its_singleton_2,axiom,
~ member(x,singleton(x)),
file('theBenchmark.p',prove_set_in_its_singleton_2) ).
cnf(c_33,plain,
~ member(x,singleton(x)),
inference(clausify,[status(thm)],[prove_set_in_its_singleton_2]) ).
fof(prove_set_in_its_singleton_1,axiom,
member(x,universal_class),
file('theBenchmark.p',prove_set_in_its_singleton_1) ).
cnf(c_34,plain,
member(x,universal_class),
inference(clausify,[status(thm)],[prove_set_in_its_singleton_1]) ).
fof(singleton_set,axiom,
! [VAR_0] : unordered_pair(VAR_0,VAR_0) = singleton(VAR_0),
file('theBenchmark.p',singleton_set) ).
cnf(c_140,plain,
unordered_pair(A,A) = singleton(A),
inference(clausify,[status(thm)],[singleton_set]) ).
cnf(c_141,plain,
singleton(A) = unordered_pair(A,A),
inference(copy,[status(thm)],[c_140]) ).
fof(unordered_pair3,axiom,
! [VAR_0,VAR_1] :
( member(VAR_0,unordered_pair(VAR_1,VAR_0))
| ~ member(VAR_0,universal_class) ),
file('theBenchmark.p',unordered_pair3) ).
cnf(c_143,plain,
( member(A,unordered_pair(B,A))
| ~ member(A,universal_class) ),
inference(clausify,[status(thm)],[unordered_pair3]) ).
cnf(c_410,plain,
~ member(x,unordered_pair(x,x)),
inference(paramod,[status(thm)],[c_141,c_33]) ).
cnf(c_442,plain,
member(x,unordered_pair(A,x)),
inference(resolve,[status(thm)],[c_143,c_34]) ).
cnf(c_443,plain,
$false,
inference(resolve,[status(thm)],[c_442,c_410]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET024-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n018.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 06:56:07 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 3985321 was started by sandbox on n018,
% 0.08/0.36 % Sat Sep 26 06:56:07 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.37
% 0.12/0.37 % From the command line: assign(max_seconds, 300).
% 0.12/0.40
% 0.12/0.40 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.40
% 0.12/0.40 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.12/0.40 % Length of proof is 8.
% 0.12/0.40 % Level of proof is 3.
% 0.12/0.40 % Maximum clause weight is 18.000.
% 0.12/0.40 % Given clauses 94.
% 0.12/0.40
% 0.12/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------