%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET910+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 08:37:16 AM UTC 2026
% Result : Theorem 0.08s 0.36s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 12 ( 5 unt; 0 def)
% Number of atoms : 19 ( 9 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 13 ( 6 ~; 2 |; 2 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 12 ( 0 sgn 6 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l30_zfmisc_1,axiom,
! [A,B] :
( set_intersection2(A,singleton(B)) = singleton(B)
=> in(B,A) ),
file('theBenchmark.p',l30_zfmisc_1) ).
fof(t51_zfmisc_1,conjecture,
! [A,B] :
( set_intersection2(A,singleton(B)) = singleton(B)
=> in(B,A) ),
file('theBenchmark.p',t51_zfmisc_1) ).
fof(t51_zfmisc_1_neg,negated_conjecture,
~ ! [A,B] :
( set_intersection2(A,singleton(B)) = singleton(B)
=> in(B,A) ),
inference(assume_negation,[status(cth)],[t51_zfmisc_1]) ).
cnf(c_13,plain,
( in(A,B)
| singleton(A) != set_intersection2(B,singleton(A)) ),
inference(clausify,[status(thm)],[l30_zfmisc_1]) ).
cnf(c_14,plain,
( in(B,A)
| set_intersection2(A,singleton(B)) != singleton(B) ),
inference(copy,[status(thm)],[c_13]) ).
fof(nnf_7,plain,
? [A,B] :
( ~ in(B,A)
& singleton(B) = set_intersection2(A,singleton(B)) ),
inference(fof_nnf,[status(thm)],[t51_zfmisc_1_neg]) ).
fof(sk_t51_zfmisc_1_neg,plain,
( ~ in(sK0,sK1)
& singleton(sK0) = set_intersection2(sK1,singleton(sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK1),skolemize(B,sK0)],[nnf_7]) ).
cnf(c_15,negated_conjecture,
singleton(sK0) = set_intersection2(sK1,singleton(sK0)),
inference(split_conjunct,[status(thm)],[sk_t51_zfmisc_1_neg]) ).
cnf(c_16,negated_conjecture,
set_intersection2(sK1,singleton(sK0)) = singleton(sK0),
inference(copy,[status(thm)],[c_15]) ).
cnf(c_17,negated_conjecture,
~ in(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_t51_zfmisc_1_neg]) ).
cnf(c_21,negated_conjecture,
in(sK0,sK1),
inference(resolve,[status(thm)],[c_14,c_16]) ).
cnf(c_20,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_17,c_21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET910+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n010.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 08:25:47 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 2898101 was started by sandbox on n010,
% 0.08/0.35 % Sat Sep 26 08:25:47 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 0.08/0.36
% 0.08/0.36 % SZS status Theorem for theBenchmark
% 0.08/0.36
% 0.08/0.36 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.08/0.36 % Length of proof is 8.
% 0.08/0.36 % Level of proof is 3.
% 0.08/0.36 % Maximum clause weight is 10.000.
% 0.08/0.36 % Given clauses 7.
% 0.08/0.36
% 0.08/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------