%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU147+1 : 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 : n004.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 0.15s 5.49s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 10 unt; 0 def)
% Number of atoms : 94 ( 43 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 100 ( 38 ~; 48 |; 9 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 46 ( 1 sgn 25 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('theBenchmark.p',d1_tarski) ).
fof(d1_zfmisc_1,axiom,
! [A,B] :
( B = powerset(A)
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ),
file('theBenchmark.p',d1_zfmisc_1) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t3_xboole_1,axiom,
! [A] :
( subset(A,empty_set)
=> A = empty_set ),
file('theBenchmark.p',t3_xboole_1) ).
fof(t1_zfmisc_1,conjecture,
powerset(empty_set) = singleton(empty_set),
file('theBenchmark.p',t1_zfmisc_1) ).
fof(t1_zfmisc_1_neg,negated_conjecture,
powerset(empty_set) != singleton(empty_set),
inference(assume_negation,[status(cth)],[t1_zfmisc_1]) ).
cnf(c_14,plain,
( C = A
| ~ in(C,B)
| singleton(A) != B ),
inference(clausify,[status(thm)],[d1_tarski]) ).
cnf(c_15,plain,
( C != A
| in(C,B)
| singleton(A) != B ),
inference(clausify,[status(thm)],[d1_tarski]) ).
fof(nnf_3,plain,
! [A,B] :
( ( ? [C] :
( ( ~ subset(C,A)
| ~ in(C,B) )
& ( subset(C,A)
| in(C,B) ) )
| powerset(A) = B )
& ( ! [X0] :
( ( ~ subset(X0,A)
| in(X0,B) )
& ( subset(X0,A)
| ~ in(X0,B) ) )
| powerset(A) != B ) ),
inference(fof_nnf,[status(thm)],[d1_zfmisc_1]) ).
fof(sk_d1_zfmisc_1_sk,plain,
! [A,B] :
( ( ( ( ~ subset(sK0(A,B),A)
| ~ in(sK0(A,B),B) )
& ( subset(sK0(A,B),A)
| in(sK0(A,B),B) ) )
| powerset(A) = B )
& ( ! [X0] :
( ( ~ subset(X0,A)
| in(X0,B) )
& ( subset(X0,A)
| ~ in(X0,B) ) )
| powerset(A) != B ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(C,sK0(A,B))],[nnf_3]) ).
fof(sk_d1_zfmisc_1,plain,
( ! [VAR_0,VAR_1] :
( ~ subset(sK0(VAR_0,VAR_1),VAR_0)
| ~ in(sK0(VAR_0,VAR_1),VAR_1)
| powerset(VAR_0) = VAR_1 )
& ! [VAR_0,VAR_1] :
( subset(sK0(VAR_0,VAR_1),VAR_0)
| in(sK0(VAR_0,VAR_1),VAR_1)
| powerset(VAR_0) = VAR_1 )
& ! [VAR_0,VAR_1,VAR_2] :
( ~ subset(VAR_2,VAR_0)
| in(VAR_2,VAR_1)
| powerset(VAR_0) != VAR_1 )
& ! [VAR_0,VAR_1,VAR_2] :
( subset(VAR_2,VAR_0)
| ~ in(VAR_2,VAR_1)
| powerset(VAR_0) != VAR_1 ) ),
inference(cnf_transformation,[status(thm)],[sk_d1_zfmisc_1_sk]) ).
cnf(c_20,plain,
( subset(sK0(A,B),A)
| in(sK0(A,B),B)
| powerset(A) = B ),
inference(split_conjunct,[status(thm)],[sk_d1_zfmisc_1]) ).
cnf(c_21,plain,
( ~ subset(sK0(A,B),A)
| ~ in(sK0(A,B),B)
| powerset(A) = B ),
inference(split_conjunct,[status(thm)],[sk_d1_zfmisc_1]) ).
cnf(c_25,plain,
subset(A,A),
inference(clausify,[status(thm)],[reflexivity_r1_tarski]) ).
cnf(c_28,plain,
( empty_set = A
| ~ subset(A,empty_set) ),
inference(clausify,[status(thm)],[t3_xboole_1]) ).
cnf(c_29,negated_conjecture,
powerset(empty_set) != singleton(empty_set),
inference(clausify,[status(thm)],[t1_zfmisc_1_neg]) ).
cnf(c_30,negated_conjecture,
singleton(empty_set) != powerset(empty_set),
inference(copy,[status(thm)],[c_29]) ).
cnf(c_33,plain,
( A != B
| in(A,singleton(B)) ),
inference(xxres,[status(thm)],[c_15]) ).
cnf(c_101,plain,
( in(sK0(empty_set,A),A)
| powerset(empty_set) = A
| empty_set = sK0(empty_set,A) ),
inference(resolve,[status(thm)],[c_28,c_20]) ).
cnf(c_46,plain,
( in(sK0(empty_set,A),A)
| powerset(empty_set) = A
| sK0(empty_set,A) = empty_set ),
inference(copy,[status(thm)],[c_101]) ).
cnf(c_52,plain,
in(A,singleton(A)),
inference(xxres,[status(thm)],[c_33]) ).
cnf(c_87,plain,
( sK0(empty_set,A) = B
| singleton(B) != A
| powerset(empty_set) = A
| sK0(empty_set,A) = empty_set ),
inference(resolve,[status(thm)],[c_46,c_14]) ).
cnf(c_89,plain,
( singleton(empty_set) != A
| powerset(empty_set) = A
| sK0(empty_set,A) = empty_set ),
inference(factor,[status(thm)],[c_87]) ).
cnf(c_102,plain,
( powerset(empty_set) = singleton(empty_set)
| sK0(empty_set,singleton(empty_set)) = empty_set ),
inference(xxres,[status(thm)],[c_89]) ).
cnf(c_103,plain,
( singleton(empty_set) = powerset(empty_set)
| sK0(empty_set,singleton(empty_set)) = empty_set ),
inference(copy,[status(thm)],[c_102]) ).
cnf(c_90,negated_conjecture,
sK0(empty_set,singleton(empty_set)) = empty_set,
inference(resolve,[status(thm)],[c_30,c_103]) ).
cnf(c_104,plain,
( ~ subset(empty_set,empty_set)
| ~ in(sK0(empty_set,singleton(empty_set)),singleton(empty_set))
| powerset(empty_set) = singleton(empty_set) ),
inference(paramod,[status(thm)],[c_90,c_21]) ).
cnf(c_105,plain,
( ~ subset(empty_set,empty_set)
| ~ in(empty_set,singleton(empty_set))
| powerset(empty_set) = singleton(empty_set) ),
inference(paramod,[status(thm)],[c_90,c_104]) ).
cnf(c_106,plain,
( ~ subset(empty_set,empty_set)
| ~ in(empty_set,singleton(empty_set))
| singleton(empty_set) = powerset(empty_set) ),
inference(copy,[status(thm)],[c_105]) ).
cnf(c_107,negated_conjecture,
( ~ subset(empty_set,empty_set)
| ~ in(empty_set,singleton(empty_set)) ),
inference(resolve,[status(thm)],[c_30,c_106]) ).
cnf(c_108,negated_conjecture,
~ subset(empty_set,empty_set),
inference(resolve,[status(thm)],[c_52,c_107]) ).
cnf(c_100,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_25,c_108]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU147+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/5.45 % Computer : n004.cluster.edu
% 0.15/5.45 % Model : x86_64 x86_64
% 0.15/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/5.45 % Memory : 8046.5625MB
% 0.15/5.45 % OS : Linux 6.8.0-71-generic
% 0.15/5.45 % CPULimit : 300
% 0.15/5.45 % WCLimit : 300
% 0.15/5.45 % DateTime : Sat Sep 26 08:40:26 UTC 2026
% 0.15/5.46 % CPUTime :
% 0.15/5.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/5.46 % Process 1269157 was started by sandbox on n004,
% 0.15/5.46 % Sat Sep 26 08:40:26 2026
% 0.15/5.46 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/5.47
% 0.15/5.47 % From the command line: assign(max_seconds, 300).
% 0.15/5.49
% 0.15/5.49 % SZS status Theorem for theBenchmark
% 0.15/5.49
% 0.15/5.49 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.15/5.49 % Length of proof is 20.
% 0.15/5.49 % Level of proof is 6.
% 0.15/5.49 % Maximum clause weight is 18.000.
% 0.15/5.49 % Given clauses 51.
% 0.15/5.49
% 0.15/5.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------