%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU143+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 08:45:09 AM UTC 2026
% Result : Theorem 0.09s 0.49s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 13 unt; 0 def)
% Number of atoms : 34 ( 21 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 27 ( 15 ~; 8 |; 0 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 32 ( 6 sgn 11 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('theBenchmark.p',d1_tarski) ).
fof(d1_xboole_0,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('theBenchmark.p',d1_xboole_0) ).
fof(t28_xboole_1,axiom,
! [A,B] :
( subset(A,B)
=> set_intersection2(A,B) = A ),
file('theBenchmark.p',t28_xboole_1) ).
fof(t7_xboole_1,axiom,
! [A,B] : subset(A,set_union2(A,B)),
file('theBenchmark.p',t7_xboole_1) ).
fof(l1_zfmisc_1,conjecture,
! [A] : singleton(A) != empty_set,
file('theBenchmark.p',l1_zfmisc_1) ).
fof(l1_zfmisc_1_neg,negated_conjecture,
~ ! [A] : singleton(A) != empty_set,
inference(assume_negation,[status(cth)],[l1_zfmisc_1]) ).
cnf(c_73,plain,
( C != A
| in(C,B)
| singleton(A) != B ),
inference(clausify,[status(thm)],[d1_tarski]) ).
cnf(c_76,plain,
( ~ in(B,A)
| empty_set != A ),
inference(clausify,[status(thm)],[d1_xboole_0]) ).
cnf(c_128,plain,
( set_intersection2(A,B) = A
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[t28_xboole_1]) ).
cnf(c_153,plain,
subset(A,set_union2(A,B)),
inference(clausify,[status(thm)],[t7_xboole_1]) ).
fof(nnf_63,plain,
? [A] : singleton(A) = empty_set,
inference(fof_nnf,[status(thm)],[l1_zfmisc_1_neg]) ).
fof(sk_l1_zfmisc_1_neg,plain,
singleton(sK0) = empty_set,
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(A,sK0)],[nnf_63]) ).
cnf(c_158,negated_conjecture,
singleton(sK0) = empty_set,
inference(split_conjunct,[status(thm)],[sk_l1_zfmisc_1_neg]) ).
cnf(c_159,negated_conjecture,
empty_set = singleton(sK0),
inference(copy,[status(thm)],[c_158]) ).
cnf(c_196,plain,
~ in(A,empty_set),
inference(xxres,[status(thm)],[c_76]) ).
cnf(c_1007,plain,
set_intersection2(A,set_union2(A,B)) = A,
inference(resolve,[status(thm)],[c_153,c_128]) ).
cnf(c_1047,plain,
( C != A
| in(C,B)
| B != singleton(A) ),
inference(copy,[status(thm)],[c_73]) ).
cnf(c_1048,negated_conjecture,
( A != sK0
| in(A,empty_set) ),
inference(resolve,[status(thm)],[c_159,c_1047]) ).
cnf(c_1049,negated_conjecture,
( sK0 != A
| in(A,empty_set) ),
inference(copy,[status(thm)],[c_1048]) ).
cnf(c_1045,negated_conjecture,
sK0 != A,
inference(resolve,[status(thm)],[c_196,c_1049]) ).
cnf(c_1050,plain,
A = set_intersection2(A,set_union2(A,B)),
inference(copy,[status(thm)],[c_1007]) ).
cnf(c_1046,plain,
$false,
inference(resolve,[status(thm)],[c_1045,c_1050]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU143+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n008.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 08:40:26 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 3234810 was started by sandbox on n008,
% 0.09/0.37 % Sat Sep 26 08:40:26 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 0.09/0.49
% 0.09/0.49 % SZS status Theorem for theBenchmark
% 0.09/0.49
% 0.09/0.49 % Proof 1 at 0.07 (+ 0.03) seconds.
% 0.09/0.49 % Length of proof is 15.
% 0.09/0.49 % Level of proof is 4.
% 0.09/0.49 % Maximum clause weight is 22.000.
% 0.09/0.49 % Given clauses 94.
% 0.09/0.49
% 0.09/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------