%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET082-7 : 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 : n010.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 08:35:41 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.52s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 13 ( 10 unt; 0 def)
% Number of atoms : 18 ( 10 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 10 ( 5 ~; 5 |; 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 8 ( 0 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_singleton_is_null_class_2,axiom,
singleton(x) != null_class,
file('theBenchmark.p',prove_singleton_is_null_class_2) ).
cnf(c_33,plain,
singleton(x) != null_class,
inference(clausify,[status(thm)],[prove_singleton_is_null_class_2]) ).
fof(prove_singleton_is_null_class_1,axiom,
~ member(x,universal_class),
file('theBenchmark.p',prove_singleton_is_null_class_1) ).
cnf(c_34,plain,
~ member(x,universal_class),
inference(clausify,[status(thm)],[prove_singleton_is_null_class_1]) ).
fof(null_unordered_pair,axiom,
! [VAR_0,VAR_1] :
( member(VAR_1,universal_class)
| member(VAR_0,universal_class)
| unordered_pair(VAR_0,VAR_1) = null_class ),
file('theBenchmark.p',null_unordered_pair) ).
cnf(c_47,plain,
( member(B,universal_class)
| member(A,universal_class)
| unordered_pair(A,B) = null_class ),
inference(clausify,[status(thm)],[null_unordered_pair]) ).
fof(singleton_set,axiom,
! [VAR_0] : unordered_pair(VAR_0,VAR_0) = singleton(VAR_0),
file('theBenchmark.p',singleton_set) ).
cnf(c_144,plain,
unordered_pair(A,A) = singleton(A),
inference(clausify,[status(thm)],[singleton_set]) ).
cnf(c_145,plain,
singleton(A) = unordered_pair(A,A),
inference(copy,[status(thm)],[c_144]) ).
cnf(c_191,plain,
( member(A,universal_class)
| unordered_pair(A,A) = null_class ),
inference(factor,[status(thm)],[c_47]) ).
cnf(c_247,plain,
unordered_pair(x,x) != null_class,
inference(paramod,[status(thm)],[c_145,c_33]) ).
cnf(c_432,plain,
unordered_pair(x,x) = null_class,
inference(resolve,[status(thm)],[c_191,c_34]) ).
cnf(c_431,plain,
$false,
inference(resolve,[status(thm)],[c_247,c_432]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET082-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.41 % Computer : n010.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Sat Sep 26 07:04:29 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.42 % Process 2743337 was started by sandbox on n010,
% 0.15/0.42 % Sat Sep 26 07:04:29 2026
% 0.15/0.42 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/0.43
% 0.15/0.43 % From the command line: assign(max_seconds, 300).
% 0.15/0.52
% 0.15/0.52 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.52
% 0.15/0.52 % Proof 1 at 0.06 (+ 0.02) seconds.
% 0.15/0.52 % Length of proof is 8.
% 0.15/0.52 % Level of proof is 3.
% 0.15/0.52 % Maximum clause weight is 11.000.
% 0.15/0.52 % Given clauses 73.
% 0.15/0.52
% 0.15/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------