%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET008+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 : n001.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 02:41:26 PM UTC 2026
% Result : Theorem 18.10s 2.90s
% Output : Proof 18.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 42 ( 19 unt; 0 def)
% Number of atoms : 105 ( 19 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 109 ( 46 ~; 38 |; 20 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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; 3 con; 0-2 aty)
% Number of variables : 84 ( 9 sgn 46 !; 4 ?)
% 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(sk1(B),B)
| empty(B) )
& ( ~ member(C,B)
| ~ empty(B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f7_nnf]) ).
cnf(c16,plain,
( member(sk1(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(p27,plain,
( member(sk1(intersection(X0,X1)),X0)
| empty(intersection(X0,X1)) ),
inference(resolution,[status(thm)],[c16,c0]) ).
fof(f1,axiom,
! [B,C,D] :
( member(D,difference(B,C))
<=> ( ~ member(D,C)
& member(D,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).
fof(f1_nnf,plain,
! [B,C,D] :
( ( member(D,C)
| ~ member(D,B)
| member(D,difference(B,C)) )
& ( ( ~ member(D,C)
& member(D,B) )
| ~ member(D,difference(B,C)) ) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [D,B,C] :
( ( member(D,C)
| ~ member(D,B)
| member(D,difference(B,C)) )
& ( ( ~ member(D,C)
& member(D,B) )
| ~ member(D,difference(B,C)) ) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c4,plain,
( ~ member(X2,X1)
| ~ member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p54,plain,
( ~ member(sk1(intersection(difference(X0,X1),X2)),X1)
| empty(intersection(difference(X0,X1),X2)) ),
inference(resolution,[status(thm)],[p27,c4]) ).
cnf(c1,plain,
( member(X2,X1)
| ~ member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p28,plain,
( member(sk1(intersection(X0,X1)),X1)
| empty(intersection(X0,X1)) ),
inference(resolution,[status(thm)],[c16,c1]) ).
cnf(p371,plain,
( empty(intersection(X0,difference(X1,X0)))
| empty(intersection(X0,difference(X1,X0))) ),
inference(resolution,[status(thm)],[p54,p28]) ).
cnf(p372,plain,
empty(intersection(X0,difference(X1,X0))),
inference(factoring,[status(thm)],[p371]) ).
cnf(c15,plain,
( ~ member(X1,X0)
| ~ empty(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p373,plain,
~ member(X0,intersection(X1,difference(X2,X1))),
inference(resolution,[status(thm)],[p372,c15]) ).
fof(f8,axiom,
! [B,C] :
( B = C
<=> ! [D] :
( member(D,B)
<=> member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).
fof(f8_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)],[f8]) ).
fof(f8_sk,plain,
! [B,C,D] :
( ( ( member(sk2(B,C),C)
& ~ member(sk2(B,C),B) )
| ( ~ member(sk2(B,C),C)
& member(sk2(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,[sk2])],[f8_nnf]) ).
cnf(c20,plain,
( member(sk2(X0,X1),X1)
| member(sk2(X0,X1),X0)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f8_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(p67,plain,
( member(sk2(X0,empty_set),X0)
| X0 = empty_set ),
inference(resolution,[status(thm)],[c20,c6]) ).
cnf(p384,plain,
intersection(X0,difference(X1,X0)) = empty_set,
inference(resolution,[status(thm)],[p373,p67]) ).
fof(f4,axiom,
! [B,C] : intersection(B,C) = intersection(C,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(f4_nnf,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c10,plain,
intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
fof(f9,conjecture,
! [B,C] : intersection(difference(B,C),C) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_intersection_difference_empty_set) ).
fof(f9_neg,negated_conjecture,
~ ! [B,C] : intersection(difference(B,C),C) = empty_set,
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f9_nnf,plain,
? [B,C] : intersection(difference(B,C),C) != empty_set,
inference(nnf_transformation,[status(thm)],[f9_neg]) ).
fof(f9_sk,plain,
intersection(difference(sk3,sk4),sk4) != empty_set,
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3,sk4])],[f9_nnf]) ).
cnf(c23,plain,
intersection(difference(sk3,sk4),sk4) != empty_set,
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p24,plain,
intersection(sk4,difference(sk3,sk4)) != empty_set,
inference(superposition,[status(thm)],[c10,c23]) ).
cnf(p385,plain,
empty_set != empty_set,
inference(demodulation,[status(thm)],[p384,p24]) ).
cnf(p386,plain,
$false,
inference(equality_resolution,[status(thm)],[p385]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET008+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 09:09:52 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 18.10/2.90 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.10/2.90 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------