%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU148+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n007.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 02:51:06 PM UTC 2026
% Result : Theorem 3.98s 0.97s
% Output : Proof 3.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 28 ( 10 unt; 0 def)
% Number of atoms : 75 ( 48 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 79 ( 32 ~; 28 |; 14 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 39 ( 1 sgn 22 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_zfmisc_1) ).
fof(f4_nnf,plain,
! [A,B] :
( ( ( A != singleton(B)
& A != empty_set )
| subset(A,singleton(B)) )
& ( A = singleton(B)
| A = empty_set
| ~ subset(A,singleton(B)) ) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B] :
( ( ( A != singleton(B)
& A != empty_set )
| subset(A,singleton(B)) )
& ( A = singleton(B)
| A = empty_set
| ~ subset(A,singleton(B)) ) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c9,plain,
( X0 = singleton(X1)
| X0 = empty_set
| ~ subset(X0,singleton(X1)) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
fof(f8,conjecture,
! [A,B] :
( subset(singleton(A),singleton(B))
=> A = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_zfmisc_1) ).
fof(f8_neg,negated_conjecture,
~ ! [A,B] :
( subset(singleton(A),singleton(B))
=> A = B ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f8_nnf,plain,
? [A,B] :
( A != B
& subset(singleton(A),singleton(B)) ),
inference(nnf_transformation,[status(thm)],[f8_neg]) ).
fof(f8_sk,plain,
( sk3 != sk4
& subset(singleton(sk3),singleton(sk4)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3,sk4])],[f8_nnf]) ).
cnf(c15,plain,
subset(singleton(sk3),singleton(sk4)),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p25,plain,
( singleton(sk3) = singleton(sk4)
| singleton(sk3) = empty_set ),
inference(resolution,[status(thm)],[c9,c15]) ).
fof(f1,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox2/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(c2,plain,
( X2 != X0
| in(X2,X1)
| X1 != singleton(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p20,plain,
( X0 != X1
| in(X0,singleton(X1)) ),
inference(equality_resolution,[status(thm)],[c2]) ).
cnf(p22,plain,
in(X0,singleton(X0)),
inference(equality_resolution,[status(thm)],[p20]) ).
cnf(p33,plain,
( in(sk4,singleton(sk3))
| singleton(sk3) = empty_set ),
inference(superposition,[status(thm)],[p25,p22]) ).
cnf(c1,plain,
( X2 = X0
| ~ in(X2,X1)
| X1 != singleton(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p18,plain,
( X0 = X1
| ~ in(X0,singleton(X1)) ),
inference(equality_resolution,[status(thm)],[c1]) ).
cnf(p38,plain,
( sk4 = sk3
| singleton(sk3) = empty_set ),
inference(resolution,[status(thm)],[p33,p18]) ).
fof(f3,axiom,
! [A] : singleton(A) != empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_zfmisc_1) ).
fof(f3_nnf,plain,
! [A] : singleton(A) != empty_set,
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A] : singleton(A) != empty_set,
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c8,plain,
singleton(X0) != empty_set,
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p48,plain,
sk4 = sk3,
inference(resolution,[status(thm)],[p38,c8]) ).
cnf(c16,plain,
sk3 != sk4,
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p49,plain,
sk3 != sk3,
inference(demodulation,[status(thm)],[p48,c16]) ).
cnf(p51,plain,
$false,
inference(equality_resolution,[status(thm)],[p49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU148+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n007.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 12:55:22 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.98/0.97 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.98/0.97 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------