%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET908+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 08:37:15 AM UTC 2026
% Result : Theorem 0.17s 0.50s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 11 unt; 0 def)
% Number of atoms : 32 ( 16 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 27 ( 14 ~; 8 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 30 ( 4 sgn 13 !; 2 ?)
% 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(d2_xboole_0,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
| in(D,A) ) ) ),
file('theBenchmark.p',d2_xboole_0) ).
fof(t49_zfmisc_1,conjecture,
! [A,B] : set_union2(singleton(A),B) != empty_set,
file('theBenchmark.p',t49_zfmisc_1) ).
fof(t49_zfmisc_1_neg,negated_conjecture,
~ ! [A,B] : set_union2(singleton(A),B) != empty_set,
inference(assume_negation,[status(cth)],[t49_zfmisc_1]) ).
cnf(c_15,plain,
( C != A
| in(C,B)
| singleton(A) != B ),
inference(clausify,[status(thm)],[d1_tarski]) ).
cnf(c_18,plain,
( ~ in(B,A)
| empty_set != A ),
inference(clausify,[status(thm)],[d1_xboole_0]) ).
cnf(c_21,plain,
( ~ in(D,A)
| in(D,C)
| set_union2(A,B) != C ),
inference(clausify,[status(thm)],[d2_xboole_0]) ).
fof(nnf_11,plain,
? [A,B] : set_union2(singleton(A),B) = empty_set,
inference(fof_nnf,[status(thm)],[t49_zfmisc_1_neg]) ).
fof(sk_t49_zfmisc_1_neg,plain,
set_union2(singleton(sK0),sK1) = empty_set,
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_11]) ).
cnf(c_32,negated_conjecture,
set_union2(singleton(sK0),sK1) = empty_set,
inference(split_conjunct,[status(thm)],[sk_t49_zfmisc_1_neg]) ).
cnf(c_33,negated_conjecture,
empty_set = set_union2(singleton(sK0),sK1),
inference(copy,[status(thm)],[c_32]) ).
cnf(c_42,plain,
( A != B
| in(A,singleton(B)) ),
inference(xxres,[status(thm)],[c_15]) ).
cnf(c_48,plain,
~ in(A,empty_set),
inference(xxres,[status(thm)],[c_18]) ).
cnf(c_219,plain,
in(A,singleton(A)),
inference(xxres,[status(thm)],[c_42]) ).
cnf(c_233,negated_conjecture,
set_union2(singleton(sK0),sK1) = empty_set,
inference(copy,[status(thm)],[c_33]) ).
cnf(c_234,negated_conjecture,
( ~ in(A,singleton(sK0))
| in(A,empty_set) ),
inference(resolve,[status(thm)],[c_21,c_233]) ).
cnf(c_231,negated_conjecture,
~ in(A,singleton(sK0)),
inference(resolve,[status(thm)],[c_234,c_48]) ).
cnf(c_232,plain,
$false,
inference(resolve,[status(thm)],[c_231,c_219]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET908+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.45 % Computer : n003.cluster.edu
% 0.17/0.45 % Model : x86_64 x86_64
% 0.17/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.45 % Memory : 8046.5625MB
% 0.17/0.45 % OS : Linux 6.8.0-71-generic
% 0.17/0.45 % CPULimit : 300
% 0.17/0.45 % WCLimit : 300
% 0.17/0.45 % DateTime : Sat Sep 26 08:26:54 UTC 2026
% 0.17/0.46 % CPUTime :
% 0.17/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.46 % Process 2437663 was started by sandbox2 on n003,
% 0.17/0.46 % Sat Sep 26 08:26:54 2026
% 0.17/0.46 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.47
% 0.17/0.47 % From the command line: assign(max_seconds, 300).
% 0.17/0.50
% 0.17/0.50 % SZS status Theorem for theBenchmark
% 0.17/0.50
% 0.17/0.50 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.17/0.50 % Length of proof is 14.
% 0.17/0.50 % Level of proof is 4.
% 0.17/0.50 % Maximum clause weight is 21.000.
% 0.17/0.50 % Given clauses 32.
% 0.17/0.50
% 0.17/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------