%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET083+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 08:35:41 AM UTC 2026
% Result : Theorem 0.16s 0.52s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 22 ( 13 unt; 0 def)
% Number of atoms : 39 ( 23 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 30 ( 13 ~; 7 |; 7 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 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 : 21 ( 3 sgn 8 !; 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(singleton_identified_by_element1,conjecture,
! [X,Y] :
( ( member(X,universal_class)
& singleton(X) = singleton(Y) )
=> X = Y ),
file('theBenchmark.p',singleton_identified_by_element1) ).
fof(singleton_identified_by_element1_neg,negated_conjecture,
~ ! [X,Y] :
( ( member(X,universal_class)
& singleton(X) = singleton(Y) )
=> X = Y ),
inference(assume_negation,[status(cth)],[singleton_identified_by_element1]) ).
fof(nnf_42,plain,
? [X,Y] :
( Y != X
& member(X,universal_class)
& singleton(Y) = singleton(X) ),
inference(fof_nnf,[status(thm)],[singleton_identified_by_element1_neg]) ).
fof(sk_singleton_identified_by_element1_neg,plain,
( sK0 != sK1
& member(sK1,universal_class)
& singleton(sK0) = singleton(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X,sK1),skolemize(Y,sK0)],[nnf_42]) ).
cnf(c_64,negated_conjecture,
sK0 != sK1,
inference(split_conjunct,[status(thm)],[sk_singleton_identified_by_element1_neg]) ).
cnf(c_65,negated_conjecture,
member(sK1,universal_class),
inference(split_conjunct,[status(thm)],[sk_singleton_identified_by_element1_neg]) ).
cnf(c_66,negated_conjecture,
singleton(sK0) = singleton(sK1),
inference(split_conjunct,[status(thm)],[sk_singleton_identified_by_element1_neg]) ).
cnf(c_129,plain,
singleton(A) = unordered_pair(A,A),
inference(clausify,[status(thm)],[singleton_set_defn]) ).
cnf(c_131,plain,
( A != C
| ~ member(A,universal_class)
| member(A,unordered_pair(B,C)) ),
inference(clausify,[status(thm)],[unordered_pair_defn]) ).
cnf(c_133,plain,
( A = C
| A = B
| ~ member(A,unordered_pair(B,C)) ),
inference(clausify,[status(thm)],[unordered_pair_defn]) ).
cnf(c_335,negated_conjecture,
unordered_pair(sK0,sK0) = singleton(sK1),
inference(paramod,[status(thm)],[c_129,c_66]) ).
cnf(c_194,negated_conjecture,
unordered_pair(sK0,sK0) = unordered_pair(sK1,sK1),
inference(paramod,[status(thm)],[c_129,c_335]) ).
cnf(c_336,negated_conjecture,
( sK1 != B
| member(sK1,unordered_pair(A,B)) ),
inference(resolve,[status(thm)],[c_131,c_65]) ).
cnf(c_322,plain,
member(sK1,unordered_pair(A,sK1)),
inference(xxres,[status(thm)],[c_336]) ).
cnf(c_337,negated_conjecture,
sK1 != sK0,
inference(copy,[status(thm)],[c_64]) ).
cnf(c_338,negated_conjecture,
( sK1 = A
| ~ member(sK1,unordered_pair(sK0,A)) ),
inference(resolve,[status(thm)],[c_133,c_337]) ).
cnf(c_339,negated_conjecture,
sK1 != sK0,
inference(copy,[status(thm)],[c_64]) ).
cnf(c_340,negated_conjecture,
~ member(sK1,unordered_pair(sK0,sK0)),
inference(resolve,[status(thm)],[c_338,c_339]) ).
cnf(c_341,negated_conjecture,
~ member(sK1,unordered_pair(sK1,sK1)),
inference(paramod,[status(thm)],[c_194,c_340]) ).
cnf(c_334,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_322,c_341]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET083+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n003.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Sat Sep 26 07:05:53 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.44 % Process 2277996 was started by sandbox2 on n003,
% 0.16/0.44 % Sat Sep 26 07:05:53 2026
% 0.16/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.46
% 0.16/0.46 % From the command line: assign(max_seconds, 300).
% 0.16/0.52
% 0.16/0.52 % SZS status Theorem for theBenchmark
% 0.16/0.52
% 0.16/0.52 % Proof 1 at 0.03 (+ 0.02) seconds.
% 0.16/0.52 % Length of proof is 12.
% 0.16/0.52 % Level of proof is 3.
% 0.16/0.52 % Maximum clause weight is 21.000.
% 0.16/0.52 % Given clauses 42.
% 0.16/0.52
% 0.16/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------