%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET880+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 08:37:12 AM UTC 2026
% Result : Theorem 0.19s 0.46s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 6 unt; 0 def)
% Number of atoms : 26 ( 18 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 21 ( 10 ~; 4 |; 2 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 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 : 18 ( 0 sgn 9 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('theBenchmark.p',d1_tarski) ).
fof(l36_zfmisc_1,axiom,
! [A,B] :
( set_difference(singleton(A),B) = empty_set
<=> in(A,B) ),
file('theBenchmark.p',l36_zfmisc_1) ).
fof(t21_zfmisc_1,conjecture,
! [A,B] :
( set_difference(singleton(A),singleton(B)) = empty_set
=> A = B ),
file('theBenchmark.p',t21_zfmisc_1) ).
fof(t21_zfmisc_1_neg,negated_conjecture,
~ ! [A,B] :
( set_difference(singleton(A),singleton(B)) = empty_set
=> A = B ),
inference(assume_negation,[status(cth)],[t21_zfmisc_1]) ).
cnf(c_8,plain,
( C = A
| ~ in(C,B)
| singleton(A) != B ),
inference(clausify,[status(thm)],[d1_tarski]) ).
cnf(c_13,plain,
( in(A,B)
| set_difference(singleton(A),B) != empty_set ),
inference(clausify,[status(thm)],[l36_zfmisc_1]) ).
fof(nnf_6,plain,
? [A,B] :
( B != A
& set_difference(singleton(A),singleton(B)) = empty_set ),
inference(fof_nnf,[status(thm)],[t21_zfmisc_1_neg]) ).
fof(sk_t21_zfmisc_1_neg,plain,
( sK1 != sK0
& set_difference(singleton(sK0),singleton(sK1)) = empty_set ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_6]) ).
cnf(c_17,negated_conjecture,
set_difference(singleton(sK0),singleton(sK1)) = empty_set,
inference(split_conjunct,[status(thm)],[sk_t21_zfmisc_1_neg]) ).
cnf(c_18,negated_conjecture,
sK1 != sK0,
inference(split_conjunct,[status(thm)],[sk_t21_zfmisc_1_neg]) ).
cnf(c_26,plain,
in(sK0,singleton(sK1)),
inference(resolve,[status(thm)],[c_17,c_13]) ).
cnf(c_29,plain,
( A = B
| ~ in(A,singleton(B)) ),
inference(xxres,[status(thm)],[c_8]) ).
cnf(c_30,negated_conjecture,
sK0 != sK1,
inference(copy,[status(thm)],[c_18]) ).
cnf(c_31,negated_conjecture,
~ in(sK0,singleton(sK1)),
inference(resolve,[status(thm)],[c_29,c_30]) ).
cnf(c_28,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_26,c_31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET880+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.43 % Computer : n009.cluster.edu
% 0.19/0.43 % Model : x86_64 x86_64
% 0.19/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.43 % Memory : 8046.5625MB
% 0.19/0.43 % OS : Linux 6.8.0-71-generic
% 0.19/0.43 % CPULimit : 300
% 0.19/0.43 % WCLimit : 300
% 0.19/0.43 % DateTime : Sat Sep 26 08:24:14 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.44 % Process 3833430 was started by sandbox2 on n009,
% 0.19/0.44 % Sat Sep 26 08:24:14 2026
% 0.19/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.45
% 0.19/0.45 % From the command line: assign(max_seconds, 300).
% 0.19/0.46
% 0.19/0.46 % SZS status Theorem for theBenchmark
% 0.19/0.46
% 0.19/0.46 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.19/0.46 % Length of proof is 9.
% 0.19/0.46 % Level of proof is 3.
% 0.19/0.46 % Maximum clause weight is 10.000.
% 0.19/0.46 % Given clauses 12.
% 0.19/0.46
% 0.19/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------