%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU146+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n020.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 17.94s 3.20s
% Output : Proof 17.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 8
% Syntax : Number of formulae : 57 ( 12 unt; 0 def)
% Number of atoms : 146 ( 60 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 132 ( 43 ~; 67 |; 15 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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; 3 con; 0-2 aty)
% Number of variables : 63 ( 3 sgn 42 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f13,axiom,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).
fof(f13_nnf,plain,
! [A,B] :
( ( ~ subset(A,B)
| set_difference(A,B) = empty_set )
& ( subset(A,B)
| set_difference(A,B) != empty_set ) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [A,B] :
( ( ~ subset(A,B)
| set_difference(A,B) = empty_set )
& ( subset(A,B)
| set_difference(A,B) != empty_set ) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c22,plain,
( ~ subset(X0,X1)
| set_difference(X0,X1) = empty_set ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
fof(f8,conjecture,
! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4_zfmisc_1) ).
fof(f8_neg,negated_conjecture,
~ ! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f8_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)],[f8_neg]) ).
fof(f8_sk,plain,
( ( ( sk0 = singleton(sk1)
| sk0 = empty_set )
& ~ subset(sk0,singleton(sk1)) )
| ( sk0 != singleton(sk1)
& sk0 != empty_set
& subset(sk0,singleton(sk1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f8_nnf]) ).
cnf(c12,plain,
( sk0 = singleton(sk1)
| sk0 = empty_set
| subset(sk0,singleton(sk1)) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p47,plain,
( sk0 = singleton(sk1)
| sk0 = empty_set
| set_difference(sk0,singleton(sk1)) = empty_set ),
inference(resolution,[status(thm)],[c22,c12]) ).
fof(f7,axiom,
! [A,B,C] :
( subset(A,B)
=> ( subset(A,set_difference(B,singleton(C)))
| in(C,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_zfmisc_1) ).
fof(f7_nnf,plain,
! [A,B,C] :
( subset(A,set_difference(B,singleton(C)))
| in(C,A)
| ~ subset(A,B) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A,B,C] :
( subset(A,set_difference(B,singleton(C)))
| in(C,A)
| ~ subset(A,B) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c10,plain,
( subset(X0,set_difference(X1,singleton(X2)))
| in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
fof(f11,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f11_nnf,plain,
! [A,B] : subset(A,A),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [A] : subset(A,A),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c19,plain,
subset(X0,X0),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p37,plain,
( subset(X1,set_difference(X1,singleton(X0)))
| in(X0,X1) ),
inference(resolution,[status(thm)],[c10,c19]) ).
cnf(p64,plain,
( subset(sk0,empty_set)
| in(sk1,sk0)
| sk0 = singleton(sk1)
| sk0 = empty_set ),
inference(superposition,[status(thm)],[p47,p37]) ).
fof(f6,axiom,
! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_zfmisc_1) ).
fof(f6_nnf,plain,
! [A,B] :
( ( ~ in(A,B)
| subset(singleton(A),B) )
& ( in(A,B)
| ~ subset(singleton(A),B) ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A,B] :
( ( ~ in(A,B)
| subset(singleton(A),B) )
& ( in(A,B)
| ~ subset(singleton(A),B) ) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c8,plain,
( in(X0,X1)
| ~ subset(singleton(X0),X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p32,plain,
in(X0,singleton(X0)),
inference(resolution,[status(thm)],[c8,c19]) ).
cnf(p80,plain,
( in(sk1,sk0)
| subset(sk0,empty_set)
| in(sk1,sk0)
| sk0 = empty_set ),
inference(superposition,[status(thm)],[p64,p32]) ).
cnf(p83,plain,
( subset(sk0,empty_set)
| in(sk1,sk0)
| sk0 = empty_set ),
inference(factoring,[status(thm)],[p80]) ).
fof(f14,axiom,
! [A] :
( subset(A,empty_set)
=> A = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
fof(f14_nnf,plain,
! [A] :
( A = empty_set
| ~ subset(A,empty_set) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [A] :
( A = empty_set
| ~ subset(A,empty_set) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c23,plain,
( X0 = empty_set
| ~ subset(X0,empty_set) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(p85,plain,
( sk0 = empty_set
| in(sk1,sk0)
| sk0 = empty_set ),
inference(resolution,[status(thm)],[p83,c23]) ).
cnf(p89,plain,
( in(sk1,sk0)
| sk0 = empty_set ),
inference(factoring,[status(thm)],[p85]) ).
cnf(c9,plain,
( ~ in(X0,X1)
| subset(singleton(X0),X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p96,plain,
( subset(singleton(sk1),sk0)
| sk0 = empty_set ),
inference(resolution,[status(thm)],[p89,c9]) ).
fof(f1,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f1_nnf,plain,
! [A,B] :
( ( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B] :
( ( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c3,plain,
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p29,plain,
( sk0 = singleton(sk1)
| sk0 = empty_set
| ~ subset(singleton(sk1),sk0)
| sk0 = singleton(sk1) ),
inference(resolution,[status(thm)],[c3,c12]) ).
cnf(p30,plain,
( sk0 = empty_set
| ~ subset(singleton(sk1),sk0)
| sk0 = singleton(sk1) ),
inference(factoring,[status(thm)],[p29]) ).
cnf(p98,plain,
( sk0 = empty_set
| sk0 = singleton(sk1)
| sk0 = empty_set ),
inference(resolution,[status(thm)],[p96,p30]) ).
cnf(p107,plain,
( sk0 = singleton(sk1)
| sk0 = empty_set ),
inference(factoring,[status(thm)],[p98]) ).
cnf(c1,plain,
( subset(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p112,plain,
( subset(sk0,singleton(sk1))
| sk0 = empty_set ),
inference(resolution,[status(thm)],[p107,c1]) ).
cnf(c15,plain,
( ~ subset(sk0,singleton(sk1))
| sk0 != singleton(sk1) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p111,plain,
( ~ subset(sk0,singleton(sk1))
| sk0 = empty_set ),
inference(resolution,[status(thm)],[p107,c15]) ).
cnf(p121,plain,
( sk0 = empty_set
| sk0 = empty_set ),
inference(resolution,[status(thm)],[p112,p111]) ).
cnf(p122,plain,
sk0 = empty_set,
inference(factoring,[status(thm)],[p121]) ).
cnf(c13,plain,
( ~ subset(sk0,singleton(sk1))
| sk0 != empty_set ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p123,plain,
( ~ subset(empty_set,singleton(sk1))
| empty_set != empty_set ),
inference(demodulation,[status(thm)],[p122,c13]) ).
cnf(p126,plain,
~ subset(empty_set,singleton(sk1)),
inference(equality_resolution,[status(thm)],[p123]) ).
fof(f12,axiom,
! [A] : subset(empty_set,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(f12_nnf,plain,
! [A] : subset(empty_set,A),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [A] : subset(empty_set,A),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c20,plain,
subset(empty_set,X0),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p127,plain,
$false,
inference(resolution,[status(thm)],[p126,c20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU146+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.37 % Computer : n020.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Thu Sep 24 12:57:18 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 17.94/3.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.94/3.20 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------