%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU119+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n006.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 02:50:59 PM UTC 2026
% Result : Theorem 3.65s 1.07s
% Output : Proof 3.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 47 ( 9 unt; 0 def)
% Number of atoms : 147 ( 35 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 161 ( 61 ~; 63 |; 33 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 76 ( 4 sgn 38 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
& in(D,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f3_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)],[f3]) ).
fof(f3_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])],[f3_nnf]) ).
cnf(c6,plain,
( ~ in(X3,X1)
| ~ in(X3,X0)
| in(X3,X2)
| X2 != set_intersection2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p41,plain,
( ~ in(X0,X2)
| ~ in(X0,X1)
| in(X0,set_intersection2(X1,X2)) ),
inference(equality_resolution,[status(thm)],[c6]) ).
fof(f1,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f1_nnf,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(c4,plain,
( in(X3,X0)
| ~ in(X3,X2)
| X2 != set_intersection2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p34,plain,
( in(X0,X1)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(equality_resolution,[status(thm)],[c4]) ).
fof(f2,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f2_nnf,plain,
! [A] :
( ( ? [B] : in(B,A)
| A = empty_set )
& ( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B] :
( ( in(sk0(A),A)
| A = empty_set )
& ( ~ in(B,A)
| A != empty_set ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f2_nnf]) ).
cnf(c3,plain,
( in(sk0(X0),X0)
| X0 = empty_set ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p42,plain,
( set_intersection2(X0,X1) = empty_set
| in(sk0(set_intersection2(X0,X1)),X0) ),
inference(resolution,[status(thm)],[p34,c3]) ).
fof(f12,conjecture,
! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] :
( in(C,B)
& in(C,A) ) )
& ~ ( ! [C] :
~ ( in(C,B)
& in(C,A) )
& ~ disjoint(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_0) ).
fof(f12_neg,negated_conjecture,
~ ! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] :
( in(C,B)
& in(C,A) ) )
& ~ ( ! [C] :
~ ( in(C,B)
& in(C,A) )
& ~ disjoint(A,B) ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f12_nnf,plain,
? [A,B] :
( ( disjoint(A,B)
& ? [C] :
( in(C,B)
& in(C,A) ) )
| ( ! [C] :
( ~ in(C,B)
| ~ in(C,A) )
& ~ disjoint(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f12_neg]) ).
fof(f12_sk,plain,
! [C] :
( ( disjoint(sk4,sk5)
& in(sk6,sk5)
& in(sk6,sk4) )
| ( ( ~ in(C,sk5)
| ~ in(C,sk4) )
& ~ disjoint(sk4,sk5) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4,sk5,sk6])],[f12_nnf]) ).
cnf(c25,plain,
( in(sk6,sk4)
| ~ in(X2,sk5)
| ~ in(X2,sk4) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p46,plain,
( in(sk6,sk4)
| ~ in(sk0(set_intersection2(sk4,X0)),sk5)
| set_intersection2(sk4,X0) = empty_set ),
inference(resolution,[status(thm)],[p42,c25]) ).
cnf(p55,plain,
( in(sk6,sk4)
| ~ in(sk0(set_intersection2(X0,sk4)),sk5)
| set_intersection2(sk4,X0) = empty_set ),
inference(superposition,[status(thm)],[c1,p46]) ).
cnf(p75,plain,
( set_intersection2(sk4,sk5) = empty_set
| in(sk6,sk4)
| set_intersection2(sk4,sk5) = empty_set ),
inference(resolution,[status(thm)],[p55,p42]) ).
cnf(p76,plain,
( in(sk6,sk4)
| set_intersection2(sk4,sk5) = empty_set ),
inference(factoring,[status(thm)],[p75]) ).
fof(f4,axiom,
! [A,B] :
( disjoint(A,B)
<=> set_intersection2(A,B) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_xboole_0) ).
fof(f4_nnf,plain,
! [A,B] :
( ( set_intersection2(A,B) != empty_set
| disjoint(A,B) )
& ( set_intersection2(A,B) = empty_set
| ~ disjoint(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B] :
( ( set_intersection2(A,B) != empty_set
| disjoint(A,B) )
& ( set_intersection2(A,B) = empty_set
| ~ disjoint(A,B) ) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c14,plain,
( set_intersection2(X0,X1) != empty_set
| disjoint(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p96,plain,
( disjoint(sk4,sk5)
| in(sk6,sk4) ),
inference(resolution,[status(thm)],[p76,c14]) ).
cnf(c22,plain,
( in(sk6,sk4)
| ~ disjoint(sk4,sk5) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p99,plain,
( in(sk6,sk4)
| in(sk6,sk4) ),
inference(resolution,[status(thm)],[p96,c22]) ).
cnf(p101,plain,
in(sk6,sk4),
inference(factoring,[status(thm)],[p99]) ).
cnf(p126,plain,
( ~ in(sk6,X0)
| in(sk6,set_intersection2(sk4,X0)) ),
inference(resolution,[status(thm)],[p41,p101]) ).
cnf(c26,plain,
( in(sk6,sk5)
| ~ in(X2,sk5)
| ~ in(X2,sk4) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p48,plain,
( in(sk6,sk5)
| ~ in(sk0(set_intersection2(sk4,X0)),sk5)
| set_intersection2(sk4,X0) = empty_set ),
inference(resolution,[status(thm)],[p42,c26]) ).
cnf(p73,plain,
( in(sk6,sk5)
| ~ in(sk0(set_intersection2(X0,sk4)),sk5)
| set_intersection2(sk4,X0) = empty_set ),
inference(superposition,[status(thm)],[c1,p48]) ).
cnf(p107,plain,
( set_intersection2(sk4,sk5) = empty_set
| in(sk6,sk5)
| set_intersection2(sk4,sk5) = empty_set ),
inference(resolution,[status(thm)],[p73,p42]) ).
cnf(p108,plain,
( in(sk6,sk5)
| set_intersection2(sk4,sk5) = empty_set ),
inference(factoring,[status(thm)],[p107]) ).
cnf(p111,plain,
( disjoint(sk4,sk5)
| in(sk6,sk5) ),
inference(resolution,[status(thm)],[p108,c14]) ).
cnf(c23,plain,
( in(sk6,sk5)
| ~ disjoint(sk4,sk5) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p114,plain,
( in(sk6,sk5)
| in(sk6,sk5) ),
inference(resolution,[status(thm)],[p111,c23]) ).
cnf(p115,plain,
in(sk6,sk5),
inference(factoring,[status(thm)],[p114]) ).
cnf(p129,plain,
in(sk6,empty_set),
inference(resolution,[status(thm)],[p126,p115]) ).
cnf(c2,plain,
( ~ in(X1,X0)
| X0 != empty_set ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p29,plain,
~ in(X0,empty_set),
inference(equality_resolution,[status(thm)],[c2]) ).
cnf(p131,plain,
$false,
inference(resolution,[status(thm)],[p129,p29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU119+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.35 % Computer : n006.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Thu Sep 24 12:47:41 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.65/1.07 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.65/1.07 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------