%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU147+3 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n014.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 : Fri Sep 25 02:51:05 PM UTC 2026
% Result : Theorem 5.43s 1.29s
% Output : Proof 5.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 39 ( 13 unt; 0 def)
% Number of atoms : 111 ( 51 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 114 ( 42 ~; 51 |; 16 &)
% ( 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 : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 55 ( 2 sgn 26 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f1_nnf,plain,
! [A,B] :
( ( ? [C] :
( ( C = A
& ~ in(C,B) )
| ( C != A
& in(C,B) ) )
| B = singleton(A) )
& ( ! [C] :
( ( C != A
| in(C,B) )
& ( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [B,A,C] :
( ( ( sk0(A,B) = A
& ~ in(sk0(A,B),B) )
| ( sk0(A,B) != A
& in(sk0(A,B),B) )
| B = singleton(A) )
& ( ( ( C != A
| in(C,B) )
& ( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f1_nnf]) ).
cnf(c4,plain,
( sk0(X0,X1) = X0
| in(sk0(X0,X1),X1)
| X1 = singleton(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(c3,plain,
( ~ in(sk0(X0,X1),X1)
| in(sk0(X0,X1),X1)
| X1 = singleton(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p36,plain,
( ~ in(X1,X0)
| in(sk0(X1,X0),X0)
| X0 = singleton(X1)
| in(sk0(X1,X0),X0)
| X0 = singleton(X1) ),
inference(superposition,[status(thm)],[c4,c3]) ).
cnf(p132,plain,
( ~ in(X1,X0)
| X0 = singleton(X1)
| in(sk0(X1,X0),X0)
| X0 = singleton(X1) ),
inference(factoring,[status(thm)],[p36]) ).
cnf(p222,plain,
( ~ in(X1,X0)
| in(sk0(X1,X0),X0)
| X0 = singleton(X1) ),
inference(factoring,[status(thm)],[p132]) ).
fof(f2,axiom,
! [A,B] :
( B = powerset(A)
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(f2_nnf,plain,
! [A,B] :
( ( ? [C] :
( ( subset(C,A)
& ~ in(C,B) )
| ( ~ subset(C,A)
& in(C,B) ) )
| B = powerset(A) )
& ( ! [C] :
( ( ~ subset(C,A)
| in(C,B) )
& ( subset(C,A)
| ~ in(C,B) ) )
| B != powerset(A) ) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [B,A,C] :
( ( ( subset(sk1(A,B),A)
& ~ in(sk1(A,B),B) )
| ( ~ subset(sk1(A,B),A)
& in(sk1(A,B),B) )
| B = powerset(A) )
& ( ( ( ~ subset(C,A)
| in(C,B) )
& ( subset(C,A)
| ~ in(C,B) ) )
| B != powerset(A) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f2_nnf]) ).
cnf(c8,plain,
( ~ subset(X2,X0)
| in(X2,X1)
| X1 != powerset(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p30,plain,
( ~ subset(X0,X1)
| in(X0,powerset(X1)) ),
inference(equality_resolution,[status(thm)],[c8]) ).
fof(f6,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f6_nnf,plain,
! [A,B] : subset(A,A),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A] : subset(A,A),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c16,plain,
subset(X0,X0),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p41,plain,
in(X0,powerset(X0)),
inference(resolution,[status(thm)],[p30,c16]) ).
cnf(p224,plain,
( in(sk0(X0,powerset(X0)),powerset(X0))
| powerset(X0) = singleton(X0) ),
inference(resolution,[status(thm)],[p222,p41]) ).
cnf(c7,plain,
( subset(X2,X0)
| ~ in(X2,X1)
| X1 != powerset(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p29,plain,
( subset(X0,X1)
| ~ in(X0,powerset(X1)) ),
inference(equality_resolution,[status(thm)],[c7]) ).
cnf(p242,plain,
( subset(sk0(X0,powerset(X0)),X0)
| powerset(X0) = singleton(X0) ),
inference(resolution,[status(thm)],[p224,p29]) ).
fof(f9,axiom,
! [A] :
( subset(A,empty_set)
=> A = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
fof(f9_nnf,plain,
! [A] :
( A = empty_set
| ~ subset(A,empty_set) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [A] :
( A = empty_set
| ~ subset(A,empty_set) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c22,plain,
( X0 = empty_set
| ~ subset(X0,empty_set) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p248,plain,
( sk0(empty_set,powerset(empty_set)) = empty_set
| powerset(empty_set) = singleton(empty_set) ),
inference(resolution,[status(thm)],[p242,c22]) ).
cnf(c5,plain,
( ~ in(sk0(X0,X1),X1)
| sk0(X0,X1) != X0
| X1 = singleton(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p251,plain,
( ~ in(sk0(empty_set,powerset(empty_set)),powerset(empty_set))
| powerset(empty_set) = singleton(empty_set)
| powerset(empty_set) = singleton(empty_set) ),
inference(resolution,[status(thm)],[p248,c5]) ).
cnf(p377,plain,
( ~ in(sk0(empty_set,powerset(empty_set)),powerset(empty_set))
| powerset(empty_set) = singleton(empty_set) ),
inference(factoring,[status(thm)],[p251]) ).
cnf(p378,plain,
( powerset(empty_set) = singleton(empty_set)
| powerset(empty_set) = singleton(empty_set) ),
inference(resolution,[status(thm)],[p377,p224]) ).
cnf(p379,plain,
powerset(empty_set) = singleton(empty_set),
inference(factoring,[status(thm)],[p378]) ).
fof(f7,conjecture,
powerset(empty_set) = singleton(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_zfmisc_1) ).
fof(f7_neg,negated_conjecture,
powerset(empty_set) != singleton(empty_set),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f7_nnf,plain,
powerset(empty_set) != singleton(empty_set),
inference(nnf_transformation,[status(thm)],[f7_neg]) ).
fof(f7_sk,plain,
powerset(empty_set) != singleton(empty_set),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c17,plain,
powerset(empty_set) != singleton(empty_set),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p380,plain,
singleton(empty_set) != singleton(empty_set),
inference(demodulation,[status(thm)],[p379,c17]) ).
cnf(p458,plain,
$false,
inference(equality_resolution,[status(thm)],[p380]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU147+3 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n014.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 12:56:47 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.43/1.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.43/1.29 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------