%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET882+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 : 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 08:37:13 AM UTC 2026
% Result : Theorem 0.19s 0.47s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 7 unt; 0 def)
% Number of atoms : 37 ( 22 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 39 ( 21 ~; 10 |; 3 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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; 2 con; 0-2 aty)
% Number of variables : 26 ( 0 sgn 10 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('theBenchmark.p',d1_tarski) ).
fof(l39_zfmisc_1,axiom,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = singleton(A)
<=> ( ( A = B
| in(B,C) )
& ~ in(A,C) ) ),
file('theBenchmark.p',l39_zfmisc_1) ).
fof(t23_zfmisc_1,conjecture,
! [A,B] :
( A != B
=> set_difference(unordered_pair(A,B),singleton(B)) = singleton(A) ),
file('theBenchmark.p',t23_zfmisc_1) ).
fof(t23_zfmisc_1_neg,negated_conjecture,
~ ! [A,B] :
( A != B
=> set_difference(unordered_pair(A,B),singleton(B)) = singleton(A) ),
inference(assume_negation,[status(cth)],[t23_zfmisc_1]) ).
cnf(c_10,plain,
( C = A
| ~ in(C,B)
| singleton(A) != B ),
inference(clausify,[status(thm)],[d1_tarski]) ).
cnf(c_11,plain,
( C != A
| in(C,B)
| singleton(A) != B ),
inference(clausify,[status(thm)],[d1_tarski]) ).
cnf(c_16,plain,
( ~ in(B,C)
| in(A,C)
| set_difference(unordered_pair(A,B),C) = singleton(A) ),
inference(clausify,[status(thm)],[l39_zfmisc_1]) ).
fof(nnf_7,plain,
? [A,B] :
( set_difference(unordered_pair(A,B),singleton(B)) != singleton(A)
& B != A ),
inference(fof_nnf,[status(thm)],[t23_zfmisc_1_neg]) ).
fof(sk_t23_zfmisc_1_neg,plain,
( set_difference(unordered_pair(sK1,sK0),singleton(sK0)) != singleton(sK1)
& sK0 != sK1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK1),skolemize(B,sK0)],[nnf_7]) ).
cnf(c_20,negated_conjecture,
sK0 != sK1,
inference(split_conjunct,[status(thm)],[sk_t23_zfmisc_1_neg]) ).
cnf(c_21,negated_conjecture,
set_difference(unordered_pair(sK1,sK0),singleton(sK0)) != singleton(sK1),
inference(split_conjunct,[status(thm)],[sk_t23_zfmisc_1_neg]) ).
cnf(c_24,plain,
( A != B
| in(A,singleton(B)) ),
inference(xxres,[status(thm)],[c_11]) ).
cnf(c_49,plain,
( A = B
| ~ in(A,singleton(B)) ),
inference(xxres,[status(thm)],[c_10]) ).
cnf(c_50,negated_conjecture,
sK1 != sK0,
inference(copy,[status(thm)],[c_20]) ).
cnf(c_35,negated_conjecture,
~ in(sK1,singleton(sK0)),
inference(resolve,[status(thm)],[c_49,c_50]) ).
cnf(c_45,plain,
in(A,singleton(A)),
inference(xxres,[status(thm)],[c_24]) ).
cnf(c_51,negated_conjecture,
( ~ in(sK0,singleton(sK0))
| in(sK1,singleton(sK0)) ),
inference(resolve,[status(thm)],[c_16,c_21]) ).
cnf(c_52,negated_conjecture,
~ in(sK0,singleton(sK0)),
inference(resolve,[status(thm)],[c_51,c_35]) ).
cnf(c_48,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_45,c_52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET882+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n003.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Sat Sep 26 08:25:54 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.45 % Process 2435645 was started by sandbox2 on n003,
% 0.19/0.45 % Sat Sep 26 08:25:54 2026
% 0.19/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.46
% 0.19/0.46 % From the command line: assign(max_seconds, 300).
% 0.19/0.47
% 0.19/0.47 % SZS status Theorem for theBenchmark
% 0.19/0.47
% 0.19/0.47 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.19/0.47 % Length of proof is 12.
% 0.19/0.47 % Level of proof is 4.
% 0.19/0.47 % Maximum clause weight is 14.000.
% 0.19/0.47 % Given clauses 18.
% 0.19/0.47
% 0.19/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------