%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET090+1 : TPTP v9.3.1. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 08:35:43 AM UTC 2026
% Result : Theorem 0.12s 0.47s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 29 ( 15 unt; 0 def)
% Number of atoms : 51 ( 30 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 41 ( 19 ~; 11 |; 7 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 26 ( 3 sgn 9 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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(singleton_set_defn,axiom,
! [X] : singleton(X) = unordered_pair(X,X),
file('theBenchmark.p',singleton_set_defn) ).
fof(member_singleton_singleton,axiom,
! [Y] :
( member(Y,universal_class)
=> singleton(member_of(singleton(Y))) = singleton(Y) ),
file('theBenchmark.p',member_singleton_singleton) ).
fof(member_of_singleton,conjecture,
! [X,U] :
( ( X = singleton(U)
& member(U,universal_class) )
=> member_of(X) = U ),
file('theBenchmark.p',member_of_singleton) ).
fof(member_of_singleton_neg,negated_conjecture,
~ ! [X,U] :
( ( X = singleton(U)
& member(U,universal_class) )
=> member_of(X) = U ),
inference(assume_negation,[status(cth)],[member_of_singleton]) ).
fof(nnf_46,plain,
? [X,U] :
( member_of(X) != U
& singleton(U) = X
& member(U,universal_class) ),
inference(fof_nnf,[status(thm)],[member_of_singleton_neg]) ).
fof(sk_member_of_singleton_neg,plain,
( member_of(sK0) != sK1
& singleton(sK1) = sK0
& member(sK1,universal_class) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK0]),skolemize(X,sK0),skolemize(U,sK1)],[nnf_46]) ).
cnf(c_68,negated_conjecture,
member_of(sK0) != sK1,
inference(split_conjunct,[status(thm)],[sk_member_of_singleton_neg]) ).
cnf(c_69,negated_conjecture,
singleton(sK1) = sK0,
inference(split_conjunct,[status(thm)],[sk_member_of_singleton_neg]) ).
cnf(c_70,negated_conjecture,
sK0 = singleton(sK1),
inference(copy,[status(thm)],[c_69]) ).
cnf(c_71,negated_conjecture,
member(sK1,universal_class),
inference(split_conjunct,[status(thm)],[sk_member_of_singleton_neg]) ).
cnf(c_74,plain,
( singleton(member_of(singleton(A))) = singleton(A)
| ~ member(A,universal_class) ),
inference(clausify,[status(thm)],[member_singleton_singleton]) ).
cnf(c_138,plain,
singleton(A) = unordered_pair(A,A),
inference(clausify,[status(thm)],[singleton_set_defn]) ).
cnf(c_140,plain,
( A != C
| ~ member(A,universal_class)
| member(A,unordered_pair(B,C)) ),
inference(clausify,[status(thm)],[unordered_pair_defn]) ).
cnf(c_142,plain,
( A = C
| A = B
| ~ member(A,unordered_pair(B,C)) ),
inference(clausify,[status(thm)],[unordered_pair_defn]) ).
cnf(c_681,negated_conjecture,
member_of(singleton(sK1)) != sK1,
inference(paramod,[status(thm)],[c_70,c_68]) ).
cnf(c_159,negated_conjecture,
member_of(unordered_pair(sK1,sK1)) != sK1,
inference(paramod,[status(thm)],[c_138,c_681]) ).
cnf(c_682,plain,
( singleton(member_of(unordered_pair(A,A))) = singleton(A)
| ~ member(A,universal_class) ),
inference(paramod,[status(thm)],[c_138,c_74]) ).
cnf(c_683,plain,
( unordered_pair(member_of(unordered_pair(A,A)),member_of(unordered_pair(A,A))) = singleton(A)
| ~ member(A,universal_class) ),
inference(paramod,[status(thm)],[c_138,c_682]) ).
cnf(c_205,plain,
( unordered_pair(member_of(unordered_pair(A,A)),member_of(unordered_pair(A,A))) = unordered_pair(A,A)
| ~ member(A,universal_class) ),
inference(paramod,[status(thm)],[c_138,c_683]) ).
cnf(c_684,negated_conjecture,
( sK1 != B
| member(sK1,unordered_pair(A,B)) ),
inference(resolve,[status(thm)],[c_140,c_71]) ).
cnf(c_353,plain,
member(sK1,unordered_pair(A,sK1)),
inference(xxres,[status(thm)],[c_684]) ).
cnf(c_685,negated_conjecture,
sK1 != member_of(unordered_pair(sK1,sK1)),
inference(copy,[status(thm)],[c_159]) ).
cnf(c_686,negated_conjecture,
( sK1 = A
| ~ member(sK1,unordered_pair(member_of(unordered_pair(sK1,sK1)),A)) ),
inference(resolve,[status(thm)],[c_142,c_685]) ).
cnf(c_687,negated_conjecture,
sK1 != member_of(unordered_pair(sK1,sK1)),
inference(copy,[status(thm)],[c_159]) ).
cnf(c_458,negated_conjecture,
~ member(sK1,unordered_pair(member_of(unordered_pair(sK1,sK1)),member_of(unordered_pair(sK1,sK1)))),
inference(resolve,[status(thm)],[c_686,c_687]) ).
cnf(c_679,plain,
unordered_pair(member_of(unordered_pair(sK1,sK1)),member_of(unordered_pair(sK1,sK1))) = unordered_pair(sK1,sK1),
inference(resolve,[status(thm)],[c_205,c_71]) ).
cnf(c_688,negated_conjecture,
~ member(sK1,unordered_pair(sK1,sK1)),
inference(paramod,[status(thm)],[c_679,c_458]) ).
cnf(c_680,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_353,c_688]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET090+1 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n007.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 07:02:39 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 3073862 was started by sandbox on n007,
% 0.09/0.35 % Sat Sep 26 07:02:39 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.12/0.47
% 0.12/0.47 % SZS status Theorem for theBenchmark
% 0.12/0.47
% 0.12/0.47 % Proof 1 at 0.07 (+ 0.02) seconds.
% 0.12/0.47 % Length of proof is 18.
% 0.12/0.47 % Level of proof is 5.
% 0.12/0.47 % Maximum clause weight is 36.000.
% 0.12/0.47 % Given clauses 100.
% 0.12/0.47
% 0.12/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------