%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET071-7 : 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 : n005.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 08:35:37 AM UTC 2026
% Result : Unsatisfiable 0.13s 5.70s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 37 ( 17 unt; 0 def)
% Number of atoms : 61 ( 32 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 41 ( 17 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 35 ( 2 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_null_unordered_pair_3,axiom,
~ member(y,universal_class),
file('theBenchmark.p',prove_null_unordered_pair_3) ).
cnf(c_33,plain,
~ member(y,universal_class),
inference(clausify,[status(thm)],[prove_null_unordered_pair_3]) ).
fof(prove_null_unordered_pair_2,axiom,
~ member(x,universal_class),
file('theBenchmark.p',prove_null_unordered_pair_2) ).
cnf(c_34,plain,
~ member(x,universal_class),
inference(clausify,[status(thm)],[prove_null_unordered_pair_2]) ).
fof(prove_null_unordered_pair_1,axiom,
unordered_pair(x,y) != null_class,
file('theBenchmark.p',prove_null_unordered_pair_1) ).
cnf(c_35,plain,
unordered_pair(x,y) != null_class,
inference(clausify,[status(thm)],[prove_null_unordered_pair_1]) ).
fof(unordered_pair_equals_singleton1,axiom,
! [VAR_0,VAR_1] :
( unordered_pair(VAR_1,VAR_0) = singleton(VAR_1)
| member(VAR_0,universal_class) ),
file('theBenchmark.p',unordered_pair_equals_singleton1) ).
cnf(c_37,plain,
( unordered_pair(B,A) = singleton(B)
| member(A,universal_class) ),
inference(clausify,[status(thm)],[unordered_pair_equals_singleton1]) ).
fof(regularity1,axiom,
! [VAR_0] :
( member(regular(VAR_0),VAR_0)
| VAR_0 = null_class ),
file('theBenchmark.p',regularity1) ).
cnf(c_75,plain,
( member(regular(A),A)
| A = null_class ),
inference(clausify,[status(thm)],[regularity1]) ).
cnf(c_76,plain,
( member(regular(A),A)
| null_class = A ),
inference(copy,[status(thm)],[c_75]) ).
fof(singleton_set,axiom,
! [VAR_0] : unordered_pair(VAR_0,VAR_0) = singleton(VAR_0),
file('theBenchmark.p',singleton_set) ).
cnf(c_132,plain,
unordered_pair(A,A) = singleton(A),
inference(clausify,[status(thm)],[singleton_set]) ).
cnf(c_133,plain,
singleton(A) = unordered_pair(A,A),
inference(copy,[status(thm)],[c_132]) ).
fof(unordered_pair_member,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_0 = VAR_2
| VAR_0 = VAR_1
| ~ member(VAR_0,unordered_pair(VAR_1,VAR_2)) ),
file('theBenchmark.p',unordered_pair_member) ).
cnf(c_137,plain,
( A = C
| A = B
| ~ member(A,unordered_pair(B,C)) ),
inference(clausify,[status(thm)],[unordered_pair_member]) ).
fof(class_elements_are_sets,axiom,
! [VAR_0] : subclass(VAR_0,universal_class),
file('theBenchmark.p',class_elements_are_sets) ).
cnf(c_141,plain,
subclass(A,universal_class),
inference(clausify,[status(thm)],[class_elements_are_sets]) ).
fof(subclass_members,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(VAR_2,VAR_1)
| ~ member(VAR_2,VAR_0)
| ~ subclass(VAR_0,VAR_1) ),
file('theBenchmark.p',subclass_members) ).
cnf(c_144,plain,
( member(C,B)
| ~ member(C,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_members]) ).
cnf(c_225,plain,
( unordered_pair(B,A) = unordered_pair(B,B)
| member(A,universal_class) ),
inference(paramod,[status(thm)],[c_133,c_37]) ).
cnf(c_227,plain,
( A = B
| ~ member(A,unordered_pair(B,B)) ),
inference(factor,[status(thm)],[c_137]) ).
cnf(c_309,plain,
( member(A,universal_class)
| ~ member(A,B) ),
inference(resolve,[status(thm)],[c_144,c_141]) ).
cnf(c_496,plain,
unordered_pair(A,x) = unordered_pair(A,A),
inference(resolve,[status(thm)],[c_225,c_34]) ).
cnf(c_497,plain,
unordered_pair(A,y) = unordered_pair(A,A),
inference(resolve,[status(thm)],[c_225,c_33]) ).
cnf(c_551,plain,
unordered_pair(x,x) != null_class,
inference(paramod,[status(thm)],[c_497,c_35]) ).
cnf(c_618,plain,
( null_class = A
| member(regular(A),universal_class) ),
inference(resolve,[status(thm)],[c_309,c_76]) ).
cnf(c_1460,plain,
( A = x
| ~ member(A,unordered_pair(x,x)) ),
inference(paramod,[status(thm)],[c_496,c_227]) ).
cnf(c_695,plain,
( x = A
| ~ member(A,unordered_pair(x,x)) ),
inference(copy,[status(thm)],[c_1460]) ).
cnf(c_1461,plain,
( null_class = unordered_pair(x,x)
| x = regular(unordered_pair(x,x)) ),
inference(resolve,[status(thm)],[c_695,c_76]) ).
cnf(c_1462,plain,
( null_class = unordered_pair(x,x)
| regular(unordered_pair(x,x)) = x ),
inference(copy,[status(thm)],[c_1461]) ).
cnf(c_1463,plain,
( unordered_pair(x,x) = null_class
| regular(unordered_pair(x,x)) = x ),
inference(copy,[status(thm)],[c_1462]) ).
cnf(c_1455,plain,
regular(unordered_pair(x,x)) = x,
inference(resolve,[status(thm)],[c_551,c_1463]) ).
cnf(c_1464,plain,
( null_class = unordered_pair(x,x)
| member(x,universal_class) ),
inference(paramod,[status(thm)],[c_1455,c_618]) ).
cnf(c_1465,plain,
( unordered_pair(x,x) = null_class
| member(x,universal_class) ),
inference(copy,[status(thm)],[c_1464]) ).
cnf(c_1466,plain,
unordered_pair(x,x) = null_class,
inference(resolve,[status(thm)],[c_34,c_1465]) ).
cnf(c_1459,plain,
$false,
inference(resolve,[status(thm)],[c_551,c_1466]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET071-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n005.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Sat Sep 26 07:02:07 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.38 % Process 1503062 was started by sandbox on n005,
% 0.10/5.38 % Sat Sep 26 07:02:07 2026
% 0.10/5.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/5.39
% 0.10/5.39 % From the command line: assign(max_seconds, 300).
% 0.13/5.70
% 0.13/5.70 % SZS status Unsatisfiable for theBenchmark
% 0.13/5.70
% 0.13/5.70 % Proof 1 at 0.24 (+ 0.06) seconds.
% 0.13/5.70 % Length of proof is 21.
% 0.13/5.70 % Level of proof is 6.
% 0.13/5.70 % Maximum clause weight is 11.000.
% 0.13/5.70 % Given clauses 243.
% 0.13/5.70
% 0.13/5.70 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------