%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU148+3 : 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 : n026.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 08:45:10 AM UTC 2026
% Result : Theorem 0.14s 1.20s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 10 unt; 0 def)
% Number of atoms : 41 ( 25 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 34 ( 16 ~; 11 |; 2 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 26 ( 1 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(l1_zfmisc_1,axiom,
! [A] : singleton(A) != empty_set,
file('theBenchmark.p',l1_zfmisc_1) ).
fof(l4_zfmisc_1,axiom,
! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
file('theBenchmark.p',l4_zfmisc_1) ).
fof(t6_zfmisc_1,conjecture,
! [A,B] :
( subset(singleton(A),singleton(B))
=> A = B ),
file('theBenchmark.p',t6_zfmisc_1) ).
fof(t6_zfmisc_1_neg,negated_conjecture,
~ ! [A,B] :
( subset(singleton(A),singleton(B))
=> A = B ),
inference(assume_negation,[status(cth)],[t6_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_15,plain,
singleton(A) != empty_set,
inference(clausify,[status(thm)],[l1_zfmisc_1]) ).
cnf(c_16,plain,
( singleton(B) = A
| empty_set = A
| ~ subset(A,singleton(B)) ),
inference(clausify,[status(thm)],[l4_zfmisc_1]) ).
fof(nnf_8,plain,
? [A,B] :
( B != A
& subset(singleton(A),singleton(B)) ),
inference(fof_nnf,[status(thm)],[t6_zfmisc_1_neg]) ).
fof(sk_t6_zfmisc_1_neg,plain,
( sK1 != sK0
& subset(singleton(sK0),singleton(sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_8]) ).
cnf(c_22,negated_conjecture,
subset(singleton(sK0),singleton(sK1)),
inference(split_conjunct,[status(thm)],[sk_t6_zfmisc_1_neg]) ).
cnf(c_23,negated_conjecture,
sK1 != sK0,
inference(split_conjunct,[status(thm)],[sk_t6_zfmisc_1_neg]) ).
cnf(c_26,plain,
( A != B
| in(A,singleton(B)) ),
inference(xxres,[status(thm)],[c_11]) ).
cnf(c_39,negated_conjecture,
( singleton(sK1) = singleton(sK0)
| empty_set = singleton(sK0) ),
inference(resolve,[status(thm)],[c_22,c_16]) ).
cnf(c_40,negated_conjecture,
( singleton(sK1) = singleton(sK0)
| singleton(sK0) = empty_set ),
inference(copy,[status(thm)],[c_39]) ).
cnf(c_33,negated_conjecture,
singleton(sK1) = singleton(sK0),
inference(resolve,[status(thm)],[c_15,c_40]) ).
cnf(c_41,plain,
( A = B
| ~ in(A,singleton(B)) ),
inference(xxres,[status(thm)],[c_10]) ).
cnf(c_42,negated_conjecture,
sK0 != sK1,
inference(copy,[status(thm)],[c_23]) ).
cnf(c_43,negated_conjecture,
~ in(sK0,singleton(sK1)),
inference(resolve,[status(thm)],[c_41,c_42]) ).
cnf(c_35,negated_conjecture,
~ in(sK0,singleton(sK0)),
inference(paramod,[status(thm)],[c_33,c_43]) ).
cnf(c_37,plain,
in(A,singleton(A)),
inference(xxres,[status(thm)],[c_26]) ).
cnf(c_38,plain,
$false,
inference(resolve,[status(thm)],[c_37,c_35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU148+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/1.18 % Computer : n026.cluster.edu
% 0.11/1.18 % Model : x86_64 x86_64
% 0.11/1.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/1.18 % Memory : 8046.5625MB
% 0.11/1.18 % OS : Linux 6.8.0-71-generic
% 0.11/1.18 % CPULimit : 300
% 0.11/1.18 % WCLimit : 300
% 0.11/1.18 % DateTime : Sat Sep 26 08:43:41 UTC 2026
% 0.11/1.18 % CPUTime :
% 0.11/1.19 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/1.19 % Process 580562 was started by sandbox2 on n026,
% 0.11/1.19 % Sat Sep 26 08:43:41 2026
% 0.11/1.19 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/1.19
% 0.11/1.19 % From the command line: assign(max_seconds, 300).
% 0.14/1.20
% 0.14/1.20 % SZS status Theorem for theBenchmark
% 0.14/1.20
% 0.14/1.20 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.14/1.20 % Length of proof is 15.
% 0.14/1.20 % Level of proof is 4.
% 0.14/1.20 % Maximum clause weight is 11.000.
% 0.14/1.20 % Given clauses 17.
% 0.14/1.20
% 0.14/1.20 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------