%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU162+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n013.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 02:51:10 PM UTC 2026
% Result : Theorem 4.32s 1.06s
% Output : Proof 4.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 6 unt; 0 def)
% Number of atoms : 66 ( 17 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 61 ( 27 ~; 22 |; 7 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 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; 2 con; 0-2 aty)
% Number of variables : 44 ( 0 sgn 28 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [A,B] :
( disjoint(A,B)
<=> set_difference(A,B) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_xboole_1) ).
fof(f7_nnf,plain,
! [A,B] :
( ( set_difference(A,B) != A
| disjoint(A,B) )
& ( set_difference(A,B) = A
| ~ disjoint(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A,B] :
( ( set_difference(A,B) != A
| disjoint(A,B) )
& ( set_difference(A,B) = A
| ~ disjoint(A,B) ) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c10,plain,
( set_difference(X0,X1) = X0
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
fof(f4,axiom,
! [A,B] :
( ~ in(A,B)
=> disjoint(singleton(A),B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l28_zfmisc_1) ).
fof(f4_nnf,plain,
! [A,B] :
( disjoint(singleton(A),B)
| in(A,B) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B] :
( disjoint(singleton(A),B)
| in(A,B) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( disjoint(singleton(X0),X1)
| in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
fof(f5,axiom,
! [A,B] :
( disjoint(A,B)
=> disjoint(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(f5_nnf,plain,
! [A,B] :
( disjoint(B,A)
| ~ disjoint(A,B) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A,B] :
( disjoint(B,A)
| ~ disjoint(A,B) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p13,plain,
( disjoint(X1,singleton(X0))
| in(X0,X1) ),
inference(resolution,[status(thm)],[c4,c5]) ).
cnf(p16,plain,
( in(X1,X0)
| set_difference(X0,singleton(X1)) = X0 ),
inference(resolution,[status(thm)],[c10,p13]) ).
fof(f6,conjecture,
! [A,B] :
( set_difference(A,singleton(B)) = A
<=> ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_zfmisc_1) ).
fof(f6_neg,negated_conjecture,
~ ! [A,B] :
( set_difference(A,singleton(B)) = A
<=> ~ in(B,A) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f6_nnf,plain,
? [A,B] :
( ( ~ in(B,A)
& set_difference(A,singleton(B)) != A )
| ( in(B,A)
& set_difference(A,singleton(B)) = A ) ),
inference(nnf_transformation,[status(thm)],[f6_neg]) ).
fof(f6_sk,plain,
( ( ~ in(sk1,sk0)
& set_difference(sk0,singleton(sk1)) != sk0 )
| ( in(sk1,sk0)
& set_difference(sk0,singleton(sk1)) = sk0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f6_nnf]) ).
cnf(c8,plain,
( set_difference(sk0,singleton(sk1)) != sk0
| in(sk1,sk0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p17,plain,
( in(sk1,sk0)
| in(sk1,sk0) ),
inference(resolution,[status(thm)],[p16,c8]) ).
cnf(p18,plain,
in(sk1,sk0),
inference(factoring,[status(thm)],[p17]) ).
cnf(c7,plain,
( ~ in(sk1,sk0)
| set_difference(sk0,singleton(sk1)) = sk0 ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p19,plain,
set_difference(sk0,singleton(sk1)) = sk0,
inference(resolution,[status(thm)],[p18,c7]) ).
cnf(c11,plain,
( set_difference(X0,X1) != X0
| disjoint(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p21,plain,
disjoint(sk0,singleton(sk1)),
inference(resolution,[status(thm)],[p19,c11]) ).
cnf(p22,plain,
disjoint(singleton(sk1),sk0),
inference(resolution,[status(thm)],[p21,c5]) ).
fof(f3,axiom,
! [A,B] :
~ ( in(A,B)
& disjoint(singleton(A),B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l25_zfmisc_1) ).
fof(f3_nnf,plain,
! [A,B] :
( ~ in(A,B)
| ~ disjoint(singleton(A),B) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B] :
( ~ in(A,B)
| ~ disjoint(singleton(A),B) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( ~ in(X0,X1)
| ~ disjoint(singleton(X0),X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p23,plain,
~ in(sk1,sk0),
inference(resolution,[status(thm)],[p22,c3]) ).
cnf(p25,plain,
$false,
inference(resolution,[status(thm)],[p23,p18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU162+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n013.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 12:59:21 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.32/1.06 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.32/1.06 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------