%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU130+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 : 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 02:51:01 PM UTC 2026
% Result : Theorem 13.28s 2.35s
% Output : Proof 13.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 10 unt; 0 def)
% Number of atoms : 113 ( 20 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 121 ( 44 ~; 46 |; 24 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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; 2 con; 0-3 aty)
% Number of variables : 68 ( 1 sgn 37 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
& in(D,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f4_nnf,plain,
! [A,B,C] :
( ( ? [D] :
( ( in(D,B)
& in(D,A)
& ~ in(D,C) )
| ( ( ~ in(D,B)
| ~ in(D,A) )
& in(D,C) ) )
| C = set_intersection2(A,B) )
& ( ! [D] :
( ( ~ in(D,B)
| ~ in(D,A)
| in(D,C) )
& ( ( in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_intersection2(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [C,A,B,D] :
( ( ( in(sk1(A,B,C),B)
& in(sk1(A,B,C),A)
& ~ in(sk1(A,B,C),C) )
| ( ( ~ in(sk1(A,B,C),B)
| ~ in(sk1(A,B,C),A) )
& in(sk1(A,B,C),C) )
| C = set_intersection2(A,B) )
& ( ( ( ~ in(D,B)
| ~ in(D,A)
| in(D,C) )
& ( ( in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_intersection2(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f4_nnf]) ).
cnf(c10,plain,
( ~ in(X3,X1)
| ~ in(X3,X0)
| in(X3,X2)
| X2 != set_intersection2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p60,plain,
( ~ in(X0,X2)
| ~ in(X0,X1)
| in(X0,set_intersection2(X1,X2)) ),
inference(equality_resolution,[status(thm)],[c10]) ).
fof(f3,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f3_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)],[f3]) ).
fof(f3_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])],[f3_nnf]) ).
cnf(c6,plain,
( in(sk0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p126,plain,
( subset(X0,X1)
| ~ in(sk0(X0,X1),X2)
| in(sk0(X0,X1),set_intersection2(X0,X2)) ),
inference(resolution,[status(thm)],[p60,c6]) ).
cnf(c5,plain,
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
fof(f13,conjecture,
! [A,B] :
( subset(A,B)
=> set_intersection2(A,B) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
fof(f13_neg,negated_conjecture,
~ ! [A,B] :
( subset(A,B)
=> set_intersection2(A,B) = A ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f13_nnf,plain,
? [A,B] :
( set_intersection2(A,B) != A
& subset(A,B) ),
inference(nnf_transformation,[status(thm)],[f13_neg]) ).
fof(f13_sk,plain,
( set_intersection2(sk4,sk5) != sk4
& subset(sk4,sk5) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4,sk5])],[f13_nnf]) ).
cnf(c25,plain,
subset(sk4,sk5),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(p44,plain,
( in(X0,sk5)
| ~ in(X0,sk4) ),
inference(resolution,[status(thm)],[c5,c25]) ).
cnf(p49,plain,
( subset(sk4,X0)
| in(sk0(sk4,X0),sk5) ),
inference(resolution,[status(thm)],[p44,c6]) ).
cnf(p936,plain,
( subset(sk4,X0)
| subset(sk4,X0)
| in(sk0(sk4,X0),set_intersection2(sk4,sk5)) ),
inference(resolution,[status(thm)],[p126,p49]) ).
cnf(p968,plain,
( subset(sk4,X0)
| in(sk0(sk4,X0),set_intersection2(sk4,sk5)) ),
inference(factoring,[status(thm)],[p936]) ).
cnf(c7,plain,
( ~ in(sk0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p971,plain,
( subset(sk4,set_intersection2(sk4,sk5))
| subset(sk4,set_intersection2(sk4,sk5)) ),
inference(resolution,[status(thm)],[p968,c7]) ).
cnf(p1007,plain,
subset(sk4,set_intersection2(sk4,sk5)),
inference(factoring,[status(thm)],[p971]) ).
fof(f2,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f2_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)],[f2]) ).
fof(f2_sk,plain,
! [A,B] :
( ( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c4,plain,
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
fof(f12,axiom,
! [A,B] : subset(set_intersection2(A,B),A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_xboole_1) ).
fof(f12_nnf,plain,
! [A,B] : subset(set_intersection2(A,B),A),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [A,B] : subset(set_intersection2(A,B),A),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c24,plain,
subset(set_intersection2(X0,X1),X0),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p41,plain,
( ~ subset(X0,set_intersection2(X0,X1))
| set_intersection2(X0,X1) = X0 ),
inference(resolution,[status(thm)],[c4,c24]) ).
cnf(p1010,plain,
set_intersection2(sk4,sk5) = sk4,
inference(resolution,[status(thm)],[p1007,p41]) ).
cnf(c26,plain,
set_intersection2(sk4,sk5) != sk4,
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(p1011,plain,
sk4 != sk4,
inference(demodulation,[status(thm)],[p1010,c26]) ).
cnf(p1016,plain,
$false,
inference(equality_resolution,[status(thm)],[p1011]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU130+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.35 % Computer : n003.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % 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 12:53:21 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 13.28/2.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.28/2.35 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------