%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET067+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 08:35:36 AM UTC 2026
% Result : Theorem 12.34s 2.03s
% Output : CNFRefutation 12.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 28 ( 15 unt; 0 def)
% Number of atoms : 60 ( 7 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 57 ( 25 ~; 22 |; 7 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 47 ( 4 sgn 24 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subclass_defn,axiom,
! [X,Y] :
( subclass(X,Y)
<=> ! [U] :
( member(U,X)
=> member(U,Y) ) ),
file('theBenchmark.p',subclass_defn) ).
fof(class_elements_are_sets,axiom,
! [X] : subclass(X,universal_class),
file('theBenchmark.p',class_elements_are_sets) ).
fof(unordered_pair_defn,axiom,
! [U,X,Y] :
( member(U,unordered_pair(X,Y))
<=> ( ( U = Y
| U = X )
& member(U,universal_class) ) ),
file('theBenchmark.p',unordered_pair_defn) ).
fof(pair_contains_other,conjecture,
! [X,Y] : subclass(unordered_pair(X,X),unordered_pair(X,Y)),
file('theBenchmark.p',pair_contains_other) ).
fof(pair_contains_other_neg,negated_conjecture,
~ ! [X,Y] : subclass(unordered_pair(X,X),unordered_pair(X,Y)),
inference(assume_negation,[status(cth)],[pair_contains_other]) ).
fof(nnf_42,plain,
? [X,Y] : ~ subclass(unordered_pair(X,X),unordered_pair(X,Y)),
inference(fof_nnf,[status(thm)],[pair_contains_other_neg]) ).
fof(sk_pair_contains_other_neg,plain,
~ subclass(unordered_pair(sK0,sK0),unordered_pair(sK0,sK1)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X,sK0),skolemize(Y,sK1)],[nnf_42]) ).
cnf(c_64,negated_conjecture,
~ subclass(unordered_pair(sK0,sK0),unordered_pair(sK0,sK1)),
inference(split_conjunct,[status(thm)],[sk_pair_contains_other_neg]) ).
cnf(c_130,plain,
( A != B
| ~ member(A,universal_class)
| member(A,unordered_pair(B,C)) ),
inference(clausify,[status(thm)],[unordered_pair_defn]) ).
cnf(c_131,plain,
( A = C
| A = B
| ~ member(A,unordered_pair(B,C)) ),
inference(clausify,[status(thm)],[unordered_pair_defn]) ).
cnf(c_136,plain,
subclass(A,universal_class),
inference(clausify,[status(thm)],[class_elements_are_sets]) ).
fof(nnf_1,plain,
! [X,Y] :
( ( ? [U] :
( ~ member(U,Y)
& member(U,X) )
| subclass(X,Y) )
& ( ! [X0] :
( member(X0,Y)
| ~ member(X0,X) )
| ~ subclass(X,Y) ) ),
inference(fof_nnf,[status(thm)],[subclass_defn]) ).
fof(sk_subclass_defn_sk,plain,
! [X,Y] :
( ( ( ~ member(sK2(X,Y),Y)
& member(sK2(X,Y),X) )
| subclass(X,Y) )
& ( ! [X0] :
( member(X0,Y)
| ~ member(X0,X) )
| ~ subclass(X,Y) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U,sK2(X,Y))],[nnf_1]) ).
fof(sk_subclass_defn,plain,
( ! [VAR_0,VAR_1] :
( ~ member(sK2(VAR_0,VAR_1),VAR_1)
| subclass(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( member(sK2(VAR_0,VAR_1),VAR_0)
| subclass(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( member(VAR_2,VAR_1)
| ~ member(VAR_2,VAR_0)
| ~ subclass(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_subclass_defn_sk]) ).
cnf(c_137,plain,
( ~ member(sK2(A,B),B)
| subclass(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subclass_defn]) ).
cnf(c_138,plain,
( member(sK2(A,B),A)
| subclass(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subclass_defn]) ).
cnf(c_139,plain,
( member(C,B)
| ~ member(C,A)
| ~ subclass(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subclass_defn]) ).
cnf(c_192,plain,
( A = B
| ~ member(A,unordered_pair(B,B)) ),
inference(factor,[status(thm)],[c_131]) ).
cnf(c_301,plain,
( ~ member(A,universal_class)
| member(A,unordered_pair(A,B)) ),
inference(xxres,[status(thm)],[c_130]) ).
cnf(c_317,negated_conjecture,
~ member(sK2(unordered_pair(sK0,sK0),unordered_pair(sK0,sK1)),unordered_pair(sK0,sK1)),
inference(resolve,[status(thm)],[c_137,c_64]) ).
cnf(c_321,plain,
member(sK2(unordered_pair(sK0,sK0),unordered_pair(sK0,sK1)),unordered_pair(sK0,sK0)),
inference(resolve,[status(thm)],[c_138,c_64]) ).
cnf(c_323,plain,
( member(A,universal_class)
| ~ member(A,B) ),
inference(resolve,[status(thm)],[c_139,c_136]) ).
cnf(c_6176,plain,
member(sK2(unordered_pair(sK0,sK0),unordered_pair(sK0,sK1)),universal_class),
inference(resolve,[status(thm)],[c_321,c_323]) ).
cnf(c_6179,plain,
sK2(unordered_pair(sK0,sK0),unordered_pair(sK0,sK1)) = sK0,
inference(resolve,[status(thm)],[c_321,c_192]) ).
cnf(c_6201,plain,
member(sK0,universal_class),
inference(paramod,[status(thm)],[c_6179,c_6176]) ).
cnf(c_6211,negated_conjecture,
~ member(sK0,unordered_pair(sK0,sK1)),
inference(paramod,[status(thm)],[c_6179,c_317]) ).
cnf(c_6343,plain,
~ member(sK0,universal_class),
inference(resolve,[status(thm)],[c_301,c_6211]) ).
cnf(c_6342,plain,
$false,
inference(resolve,[status(thm)],[c_6201,c_6343]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET067+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n003.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Sat Sep 26 07:03:39 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.43 % Process 2274851 was started by sandbox2 on n003,
% 0.18/0.43 % Sat Sep 26 07:03:39 2026
% 0.18/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.45
% 0.18/0.45 % From the command line: assign(max_seconds, 300).
% 12.34/2.03
% 12.34/2.03 % given #500 (W,wt=16): 2333 -member(unordered_pair(A,null_class),power_class(null_class)). [ur(78,b,1703,a)].
% 12.34/2.03
% 12.34/2.03 % SZS status Theorem for theBenchmark
% 12.34/2.03
% 12.34/2.03 % Proof 1 at 1.24 (+ 0.31) seconds.
% 12.34/2.03 % Length of proof is 21.
% 12.34/2.03 % Level of proof is 5.
% 12.34/2.03 % Maximum clause weight is 26.000.
% 12.34/2.03 % Given clauses 505.
% 12.34/2.03
% 12.34/2.03 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------