%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET637+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n018.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 02:43:41 PM UTC 2026
% Result : Theorem 12.50s 7.18s
% Output : Proof 12.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 50 ( 9 unt; 0 def)
% Number of atoms : 143 ( 15 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 150 ( 57 ~; 59 |; 26 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 93 ( 5 sgn 45 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [B] :
( empty(B)
<=> ! [C] : ~ member(C,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_defn) ).
fof(f7_nnf,plain,
! [B] :
( ( ? [C] : member(C,B)
| empty(B) )
& ( ! [C] : ~ member(C,B)
| ~ empty(B) ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [B,C] :
( ( member(sk2(B),B)
| empty(B) )
& ( ~ member(C,B)
| ~ empty(B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2])],[f7_nnf]) ).
cnf(c18,plain,
( member(sk2(X0),X0)
| empty(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
fof(f0,axiom,
! [B,C,D] :
( member(D,intersection(B,C))
<=> ( member(D,C)
& member(D,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_defn) ).
fof(f0_nnf,plain,
! [B,C,D] :
( ( ~ member(D,C)
| ~ member(D,B)
| member(D,intersection(B,C)) )
& ( ( member(D,C)
& member(D,B) )
| ~ member(D,intersection(B,C)) ) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [D,B,C] :
( ( ~ member(D,C)
| ~ member(D,B)
| member(D,intersection(B,C)) )
& ( ( member(D,C)
& member(D,B) )
| ~ member(D,intersection(B,C)) ) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( member(X2,X0)
| ~ member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p25,plain,
( member(sk2(intersection(X0,X1)),X0)
| empty(intersection(X0,X1)) ),
inference(resolution,[status(thm)],[c18,c0]) ).
fof(f1,axiom,
! [B,C] :
( intersect(B,C)
<=> ? [D] :
( member(D,C)
& member(D,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersect_defn) ).
fof(f1_nnf,plain,
! [B,C] :
( ( ! [D] :
( ~ member(D,C)
| ~ member(D,B) )
| intersect(B,C) )
& ( ? [D] :
( member(D,C)
& member(D,B) )
| ~ intersect(B,C) ) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [B,C,D] :
( ( ~ member(D,C)
| ~ member(D,B)
| intersect(B,C) )
& ( ( member(sk0(B,C),C)
& member(sk0(B,C),B) )
| ~ intersect(B,C) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f1_nnf]) ).
cnf(c5,plain,
( ~ member(X2,X1)
| ~ member(X2,X0)
| intersect(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p56,plain,
( ~ member(sk2(intersection(X0,X1)),X2)
| intersect(X0,X2)
| empty(intersection(X0,X1)) ),
inference(resolution,[status(thm)],[p25,c5]) ).
cnf(c1,plain,
( member(X2,X1)
| ~ member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p26,plain,
( empty(intersection(X0,X1))
| member(sk2(intersection(X0,X1)),X1) ),
inference(resolution,[status(thm)],[c1,c18]) ).
cnf(p452,plain,
( empty(intersection(X0,X1))
| intersect(X0,X1)
| empty(intersection(X0,X1)) ),
inference(resolution,[status(thm)],[p56,p26]) ).
cnf(p1346,plain,
( intersect(X0,X1)
| empty(intersection(X0,X1)) ),
inference(factoring,[status(thm)],[p452]) ).
cnf(c17,plain,
( ~ member(X1,X0)
| ~ empty(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p1347,plain,
( ~ member(X2,intersection(X0,X1))
| intersect(X0,X1) ),
inference(resolution,[status(thm)],[p1346,c17]) ).
fof(f3,axiom,
! [B,C] :
( B = C
<=> ! [D] :
( member(D,B)
<=> member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).
fof(f3_nnf,plain,
! [B,C] :
( ( ? [D] :
( ( member(D,C)
& ~ member(D,B) )
| ( ~ member(D,C)
& member(D,B) ) )
| B = C )
& ( ! [D] :
( ( ~ member(D,C)
| member(D,B) )
& ( member(D,C)
| ~ member(D,B) ) )
| B != C ) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [B,C,D] :
( ( ( member(sk1(B,C),C)
& ~ member(sk1(B,C),B) )
| ( ~ member(sk1(B,C),C)
& member(sk1(B,C),B) )
| B = C )
& ( ( ( ~ member(D,C)
| member(D,B) )
& ( member(D,C)
| ~ member(D,B) ) )
| B != C ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f3_nnf]) ).
cnf(c10,plain,
( member(sk1(X0,X1),X1)
| member(sk1(X0,X1),X0)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
fof(f2,axiom,
! [B] : ~ member(B,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f2_nnf,plain,
! [B] : ~ member(B,empty_set),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [B] : ~ member(B,empty_set),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c6,plain,
~ member(X0,empty_set),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p62,plain,
( member(sk1(X0,empty_set),X0)
| X0 = empty_set ),
inference(resolution,[status(thm)],[c10,c6]) ).
cnf(p1355,plain,
( intersection(X0,X1) = empty_set
| intersect(X0,X1) ),
inference(resolution,[status(thm)],[p1347,p62]) ).
fof(f8,conjecture,
! [B,C] :
( intersect(B,C)
<=> not_equal(intersection(B,C),empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th119) ).
fof(f8_neg,negated_conjecture,
~ ! [B,C] :
( intersect(B,C)
<=> not_equal(intersection(B,C),empty_set) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f8_nnf,plain,
? [B,C] :
( ( not_equal(intersection(B,C),empty_set)
& ~ intersect(B,C) )
| ( ~ not_equal(intersection(B,C),empty_set)
& intersect(B,C) ) ),
inference(nnf_transformation,[status(thm)],[f8_neg]) ).
fof(f8_sk,plain,
( ( not_equal(intersection(sk3,sk4),empty_set)
& ~ intersect(sk3,sk4) )
| ( ~ not_equal(intersection(sk3,sk4),empty_set)
& intersect(sk3,sk4) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3,sk4])],[f8_nnf]) ).
cnf(c20,plain,
( not_equal(intersection(sk3,sk4),empty_set)
| intersect(sk3,sk4) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
fof(f4,axiom,
! [B,C] :
( not_equal(B,C)
<=> B != C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_equal_defn) ).
fof(f4_nnf,plain,
! [B,C] :
( ( B = C
| not_equal(B,C) )
& ( B != C
| ~ not_equal(B,C) ) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [B,C] :
( ( B = C
| not_equal(B,C) )
& ( B != C
| ~ not_equal(B,C) ) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c13,plain,
( X0 != X1
| ~ not_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p29,plain,
( intersection(sk3,sk4) != empty_set
| intersect(sk3,sk4) ),
inference(resolution,[status(thm)],[c20,c13]) ).
cnf(p1414,plain,
( intersect(sk3,sk4)
| intersect(sk3,sk4) ),
inference(resolution,[status(thm)],[p1355,p29]) ).
cnf(p1415,plain,
intersect(sk3,sk4),
inference(factoring,[status(thm)],[p1414]) ).
cnf(c3,plain,
( member(sk0(X0,X1),X0)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p1422,plain,
member(sk0(sk3,sk4),sk3),
inference(resolution,[status(thm)],[p1415,c3]) ).
cnf(c2,plain,
( ~ member(X2,X1)
| ~ member(X2,X0)
| member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p1427,plain,
( ~ member(sk0(sk3,sk4),X0)
| member(sk0(sk3,sk4),intersection(sk3,X0)) ),
inference(resolution,[status(thm)],[p1422,c2]) ).
cnf(c4,plain,
( member(sk0(X0,X1),X1)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p1423,plain,
member(sk0(sk3,sk4),sk4),
inference(resolution,[status(thm)],[p1415,c4]) ).
cnf(p3782,plain,
member(sk0(sk3,sk4),empty_set),
inference(resolution,[status(thm)],[p1427,p1423]) ).
cnf(p3812,plain,
$false,
inference(resolution,[status(thm)],[p3782,c6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET637+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/5.58 % Computer : n018.cluster.edu
% 0.10/5.58 % Model : x86_64 x86_64
% 0.10/5.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.58 % Memory : 8046.5625MB
% 0.10/5.58 % OS : Linux 6.8.0-71-generic
% 0.10/5.58 % CPULimit : 300
% 0.10/5.58 % WCLimit : 300
% 0.10/5.58 % DateTime : Thu Sep 24 11:34:09 UTC 2026
% 0.10/5.59 % CPUTime :
% 0.10/5.59 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 12.50/7.18 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.50/7.18 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------