%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET917+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 : n015.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 08:37:17 AM UTC 2026
% Result : Theorem 0.20s 0.47s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 9 unt; 0 def)
% Number of atoms : 27 ( 12 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 22 ( 13 ~; 5 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 20 ( 0 sgn 10 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('theBenchmark.p',commutativity_k3_xboole_0) ).
fof(l28_zfmisc_1,axiom,
! [A,B] :
( ~ in(A,B)
=> disjoint(singleton(A),B) ),
file('theBenchmark.p',l28_zfmisc_1) ).
fof(l32_zfmisc_1,axiom,
! [A,B] :
( in(A,B)
=> set_intersection2(B,singleton(A)) = singleton(A) ),
file('theBenchmark.p',l32_zfmisc_1) ).
fof(t58_zfmisc_1,conjecture,
! [A,B] :
( set_intersection2(singleton(A),B) = singleton(A)
| disjoint(singleton(A),B) ),
file('theBenchmark.p',t58_zfmisc_1) ).
fof(t58_zfmisc_1_neg,negated_conjecture,
~ ! [A,B] :
( set_intersection2(singleton(A),B) = singleton(A)
| disjoint(singleton(A),B) ),
inference(assume_negation,[status(cth)],[t58_zfmisc_1]) ).
cnf(c_11,plain,
set_intersection2(A,B) = set_intersection2(B,A),
inference(clausify,[status(thm)],[commutativity_k3_xboole_0]) ).
cnf(c_13,plain,
( disjoint(singleton(A),B)
| in(A,B) ),
inference(clausify,[status(thm)],[l28_zfmisc_1]) ).
cnf(c_14,plain,
( singleton(A) = set_intersection2(B,singleton(A))
| ~ in(A,B) ),
inference(clausify,[status(thm)],[l32_zfmisc_1]) ).
cnf(c_15,plain,
( set_intersection2(B,singleton(A)) = singleton(A)
| ~ in(A,B) ),
inference(copy,[status(thm)],[c_14]) ).
fof(nnf_9,plain,
? [A,B] :
( singleton(A) != set_intersection2(singleton(A),B)
& ~ disjoint(singleton(A),B) ),
inference(fof_nnf,[status(thm)],[t58_zfmisc_1_neg]) ).
fof(sk_t58_zfmisc_1_neg,plain,
( singleton(sK0) != set_intersection2(singleton(sK0),sK1)
& ~ disjoint(singleton(sK0),sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_9]) ).
cnf(c_19,negated_conjecture,
~ disjoint(singleton(sK0),sK1),
inference(split_conjunct,[status(thm)],[sk_t58_zfmisc_1_neg]) ).
cnf(c_20,negated_conjecture,
singleton(sK0) != set_intersection2(singleton(sK0),sK1),
inference(split_conjunct,[status(thm)],[sk_t58_zfmisc_1_neg]) ).
cnf(c_31,negated_conjecture,
singleton(sK0) != set_intersection2(sK1,singleton(sK0)),
inference(paramod,[status(thm)],[c_11,c_20]) ).
cnf(c_21,negated_conjecture,
set_intersection2(sK1,singleton(sK0)) != singleton(sK0),
inference(copy,[status(thm)],[c_31]) ).
cnf(c_26,negated_conjecture,
~ in(sK0,sK1),
inference(resolve,[status(thm)],[c_15,c_21]) ).
cnf(c_32,plain,
disjoint(singleton(sK0),sK1),
inference(resolve,[status(thm)],[c_26,c_13]) ).
cnf(c_30,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_19,c_32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET917+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.44 % Computer : n015.cluster.edu
% 0.20/0.44 % Model : x86_64 x86_64
% 0.20/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.44 % Memory : 8046.5625MB
% 0.20/0.44 % OS : Linux 6.8.0-71-generic
% 0.20/0.44 % CPULimit : 300
% 0.20/0.44 % WCLimit : 300
% 0.20/0.44 % DateTime : Sat Sep 26 08:28:44 UTC 2026
% 0.20/0.45 % CPUTime :
% 0.20/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.20/0.45 % Process 3571878 was started by sandbox2 on n015,
% 0.20/0.45 % Sat Sep 26 08:28:44 2026
% 0.20/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.20/0.46
% 0.20/0.46 % From the command line: assign(max_seconds, 300).
% 0.20/0.47
% 0.20/0.47 % SZS status Theorem for theBenchmark
% 0.20/0.47
% 0.20/0.47 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.20/0.47 % Length of proof is 13.
% 0.20/0.47 % Level of proof is 4.
% 0.20/0.47 % Maximum clause weight is 10.000.
% 0.20/0.47 % Given clauses 13.
% 0.20/0.47
% 0.20/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------