%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET076+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 : n015.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 08:35:38 AM UTC 2026
% Result : Theorem 34.25s 5.32s
% Output : CNFRefutation 34.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 29 ( 11 unt; 0 def)
% Number of atoms : 72 ( 15 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 66 ( 23 ~; 25 |; 13 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 39 ( 0 sgn 25 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subclass_defn,axiom,
! [X,Y] :
( subclass(X,Y)
<=> ! [U] :
( member(U,X)
=> member(U,Y) ) ),
file('theBenchmark.p',subclass_defn) ).
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(unordered_pair_is_subset,conjecture,
! [X,Y,Z] :
( ( member(Y,Z)
& member(X,Z) )
=> subclass(unordered_pair(X,Y),Z) ),
file('theBenchmark.p',unordered_pair_is_subset) ).
fof(unordered_pair_is_subset_neg,negated_conjecture,
~ ! [X,Y,Z] :
( ( member(Y,Z)
& member(X,Z) )
=> subclass(unordered_pair(X,Y),Z) ),
inference(assume_negation,[status(cth)],[unordered_pair_is_subset]) ).
fof(nnf_42,plain,
? [X,Y,Z] :
( ~ subclass(unordered_pair(X,Y),Z)
& member(Y,Z)
& member(X,Z) ),
inference(fof_nnf,[status(thm)],[unordered_pair_is_subset_neg]) ).
fof(sk_unordered_pair_is_subset_neg,plain,
( ~ subclass(unordered_pair(sK0,sK1),sK2)
& member(sK1,sK2)
& member(sK0,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK2,sK1]),skolemize(X,sK0),skolemize(Y,sK1),skolemize(Z,sK2)],[nnf_42]) ).
cnf(c_64,negated_conjecture,
~ subclass(unordered_pair(sK0,sK1),sK2),
inference(split_conjunct,[status(thm)],[sk_unordered_pair_is_subset_neg]) ).
cnf(c_65,negated_conjecture,
member(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_unordered_pair_is_subset_neg]) ).
cnf(c_66,negated_conjecture,
member(sK0,sK2),
inference(split_conjunct,[status(thm)],[sk_unordered_pair_is_subset_neg]) ).
cnf(c_133,plain,
( A = C
| A = B
| ~ member(A,unordered_pair(B,C)) ),
inference(clausify,[status(thm)],[unordered_pair_defn]) ).
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(sK3(X,Y),Y)
& member(sK3(X,Y),X) )
| subclass(X,Y) )
& ( ! [X0] :
( member(X0,Y)
| ~ member(X0,X) )
| ~ subclass(X,Y) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U,sK3(X,Y))],[nnf_1]) ).
fof(sk_subclass_defn,plain,
( ! [VAR_0,VAR_1] :
( ~ member(sK3(VAR_0,VAR_1),VAR_1)
| subclass(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( member(sK3(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_139,plain,
( ~ member(sK3(A,B),B)
| subclass(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subclass_defn]) ).
cnf(c_140,plain,
( member(sK3(A,B),A)
| subclass(A,B) ),
inference(split_conjunct,[status(thm)],[sk_subclass_defn]) ).
cnf(c_428,negated_conjecture,
~ member(sK3(unordered_pair(sK0,sK1),sK2),sK2),
inference(resolve,[status(thm)],[c_139,c_64]) ).
cnf(c_436,plain,
( sK3(unordered_pair(A,B),C) = B
| sK3(unordered_pair(A,B),C) = A
| subclass(unordered_pair(A,B),C) ),
inference(resolve,[status(thm)],[c_140,c_133]) ).
cnf(c_16938,plain,
( ~ member(sK0,sK2)
| sK3(unordered_pair(sK0,sK1),sK2) = sK1
| subclass(unordered_pair(sK0,sK1),sK2) ),
inference(paramod,[status(thm)],[c_436,c_428]) ).
cnf(c_16939,negated_conjecture,
( ~ member(sK0,sK2)
| sK3(unordered_pair(sK0,sK1),sK2) = sK1 ),
inference(resolve,[status(thm)],[c_64,c_16938]) ).
cnf(c_16688,negated_conjecture,
sK3(unordered_pair(sK0,sK1),sK2) = sK1,
inference(resolve,[status(thm)],[c_66,c_16939]) ).
cnf(c_16940,plain,
( ~ member(sK1,sK2)
| sK3(unordered_pair(sK0,sK1),sK2) = sK0
| subclass(unordered_pair(sK0,sK1),sK2) ),
inference(paramod,[status(thm)],[c_436,c_428]) ).
cnf(c_16941,plain,
( ~ member(sK1,sK2)
| sK1 = sK0
| subclass(unordered_pair(sK0,sK1),sK2) ),
inference(paramod,[status(thm)],[c_16688,c_16940]) ).
cnf(c_16942,negated_conjecture,
( ~ member(sK1,sK2)
| sK1 = sK0 ),
inference(resolve,[status(thm)],[c_64,c_16941]) ).
cnf(c_16689,negated_conjecture,
sK1 = sK0,
inference(resolve,[status(thm)],[c_65,c_16942]) ).
cnf(c_16703,negated_conjecture,
~ member(sK3(unordered_pair(sK0,sK0),sK2),sK2),
inference(paramod,[status(thm)],[c_16689,c_428]) ).
cnf(c_16943,negated_conjecture,
sK3(unordered_pair(sK0,sK0),sK2) = sK1,
inference(paramod,[status(thm)],[c_16689,c_16688]) ).
cnf(c_16704,negated_conjecture,
sK3(unordered_pair(sK0,sK0),sK2) = sK0,
inference(paramod,[status(thm)],[c_16689,c_16943]) ).
cnf(c_16944,negated_conjecture,
~ member(sK0,sK2),
inference(paramod,[status(thm)],[c_16704,c_16703]) ).
cnf(c_16937,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_66,c_16944]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET076+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n015.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 26 07:06:43 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.13/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.36 % Process 3393308 was started by sandbox2 on n015,
% 0.13/0.36 % Sat Sep 26 07:06:43 2026
% 0.13/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 34.25/5.32
% 34.25/5.32 % given #500 (F,wt=10): 371 -member(unordered_pair(A,B),complement(universal_class)). [resolve(130,a,113,b)].
% 34.25/5.32
% 34.25/5.32 % SZS status Theorem for theBenchmark
% 34.25/5.32
% 34.25/5.32 % Proof 1 at 3.46 (+ 1.42) seconds.
% 34.25/5.32 % Length of proof is 16.
% 34.25/5.32 % Level of proof is 6.
% 34.25/5.32 % Maximum clause weight is 25.000.
% 34.25/5.32 % Given clauses 903.
% 34.25/5.32
% 34.25/5.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------