%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET942+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n003.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 02:44:20 PM UTC 2026
% Result : Theorem 6.25s 1.26s
% Output : Proof 6.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 31 ( 4 unt; 0 def)
% Number of atoms : 101 ( 8 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 110 ( 40 ~; 45 |; 19 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 67 ( 0 sgn 25 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] :
( B = union(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( in(D,A)
& in(C,D) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
fof(f2_nnf,plain,
! [A,B] :
( ( ? [C] :
( ( ? [D] :
( in(D,A)
& in(C,D) )
& ~ in(C,B) )
| ( ! [D] :
( ~ in(D,A)
| ~ in(C,D) )
& in(C,B) ) )
| B = union(A) )
& ( ! [C] :
( ( ! [D] :
( ~ in(D,A)
| ~ in(C,D) )
| in(C,B) )
& ( ? [D] :
( in(D,A)
& in(C,D) )
| ~ in(C,B) ) )
| B != union(A) ) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [B,A,C,D] :
( ( ( in(sk3(A,B),A)
& in(sk2(A,B),sk3(A,B))
& ~ in(sk2(A,B),B) )
| ( ( ~ in(D,A)
| ~ in(sk2(A,B),D) )
& in(sk2(A,B),B) )
| B = union(A) )
& ( ( ( ~ in(D,A)
| ~ in(C,D)
| in(C,B) )
& ( ( in(sk1(A,B,C),A)
& in(C,sk1(A,B,C)) )
| ~ in(C,B) ) )
| B != union(A) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1,sk2,sk3])],[f2_nnf]) ).
cnf(c4,plain,
( in(X2,sk1(X0,X1,X2))
| ~ in(X2,X1)
| X1 != union(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p23,plain,
( in(X0,sk1(X1,union(X1),X0))
| ~ in(X0,union(X1)) ),
inference(equality_resolution,[status(thm)],[c4]) ).
fof(f1,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f1_nnf,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B,C] :
( ( ( ~ in(sk0(A,B),B)
& in(sk0(A,B),A) )
| subset(A,B) )
& ( in(C,B)
| ~ in(C,A)
| ~ subset(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f1_nnf]) ).
cnf(c2,plain,
( in(sk0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p24,plain,
( subset(union(X0),X1)
| in(sk0(union(X0),X1),sk1(X0,union(X0),sk0(union(X0),X1))) ),
inference(resolution,[status(thm)],[p23,c2]) ).
cnf(c6,plain,
( ~ in(X3,X0)
| ~ in(X2,X3)
| in(X2,X1)
| X1 != union(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p31,plain,
( ~ in(X2,X1)
| ~ in(X0,X2)
| in(X0,union(X1)) ),
inference(equality_resolution,[status(thm)],[c6]) ).
cnf(p77,plain,
( ~ in(sk1(X0,union(X0),sk0(union(X0),X1)),X2)
| in(sk0(union(X0),X1),union(X2))
| subset(union(X0),X1) ),
inference(resolution,[status(thm)],[p24,p31]) ).
cnf(c5,plain,
( in(sk1(X0,X1,X2),X0)
| ~ in(X2,X1)
| X1 != union(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p25,plain,
( in(sk1(X1,union(X1),X0),X1)
| ~ in(X0,union(X1)) ),
inference(equality_resolution,[status(thm)],[c5]) ).
cnf(p26,plain,
( subset(union(X0),X1)
| in(sk1(X0,union(X0),sk0(union(X0),X1)),X0) ),
inference(resolution,[status(thm)],[p25,c2]) ).
cnf(c1,plain,
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
fof(f6,conjecture,
! [A,B] :
( subset(A,B)
=> subset(union(A),union(B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t95_zfmisc_1) ).
fof(f6_neg,negated_conjecture,
~ ! [A,B] :
( subset(A,B)
=> subset(union(A),union(B)) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f6_nnf,plain,
? [A,B] :
( ~ subset(union(A),union(B))
& subset(A,B) ),
inference(nnf_transformation,[status(thm)],[f6_neg]) ).
fof(f6_sk,plain,
( ~ subset(union(sk6),union(sk7))
& subset(sk6,sk7) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk6,sk7])],[f6_nnf]) ).
cnf(c16,plain,
subset(sk6,sk7),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p20,plain,
( in(X0,sk7)
| ~ in(X0,sk6) ),
inference(resolution,[status(thm)],[c1,c16]) ).
cnf(p28,plain,
( in(sk1(sk6,union(sk6),sk0(union(sk6),X0)),sk7)
| subset(union(sk6),X0) ),
inference(resolution,[status(thm)],[p26,p20]) ).
cnf(p439,plain,
( subset(union(sk6),X0)
| in(sk0(union(sk6),X0),union(sk7))
| subset(union(sk6),X0) ),
inference(resolution,[status(thm)],[p77,p28]) ).
cnf(p441,plain,
( in(sk0(union(sk6),X0),union(sk7))
| subset(union(sk6),X0) ),
inference(factoring,[status(thm)],[p439]) ).
cnf(c3,plain,
( ~ in(sk0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p468,plain,
( subset(union(sk6),union(sk7))
| subset(union(sk6),union(sk7)) ),
inference(resolution,[status(thm)],[p441,c3]) ).
cnf(p479,plain,
subset(union(sk6),union(sk7)),
inference(factoring,[status(thm)],[p468]) ).
cnf(c17,plain,
~ subset(union(sk6),union(sk7)),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p480,plain,
$false,
inference(resolution,[status(thm)],[p479,c17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET942+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n003.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 12:27:51 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 6.25/1.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.25/1.26 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------