%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET183+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n015.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 02:42:44 PM UTC 2026
% Result : Theorem 12.51s 2.35s
% Output : Proof 12.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 10 unt; 0 def)
% Number of atoms : 92 ( 14 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 90 ( 33 ~; 35 |; 16 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 59 ( 1 sgn 34 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,axiom,
! [B,C,D] :
( member(D,intersection(B,C))
<=> ( member(D,C)
& member(D,B) ) ),
file('/export/starexec/sandbox2/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(c2,plain,
( ~ member(X2,X1)
| ~ member(X2,X0)
| member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
fof(f2,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(f2_nnf,plain,
! [B,C] :
( ( ? [D] :
( ~ member(D,C)
& member(D,B) )
| subset(B,C) )
& ( ! [D] :
( member(D,C)
| ~ member(D,B) )
| ~ subset(B,C) ) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [B,C,D] :
( ( ( ~ member(sk0(B,C),C)
& member(sk0(B,C),B) )
| subset(B,C) )
& ( member(D,C)
| ~ member(D,B)
| ~ subset(B,C) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f2_nnf]) ).
cnf(c4,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
fof(f7,conjecture,
! [B,C] :
( subset(B,C)
=> intersection(B,C) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_subset_intersection) ).
fof(f7_neg,negated_conjecture,
~ ! [B,C] :
( subset(B,C)
=> intersection(B,C) = B ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f7_nnf,plain,
? [B,C] :
( intersection(B,C) != B
& subset(B,C) ),
inference(nnf_transformation,[status(thm)],[f7_neg]) ).
fof(f7_sk,plain,
( intersection(sk2,sk3) != sk2
& subset(sk2,sk3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3])],[f7_nnf]) ).
cnf(c18,plain,
subset(sk2,sk3),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p24,plain,
( member(X0,sk3)
| ~ member(X0,sk2) ),
inference(resolution,[status(thm)],[c4,c18]) ).
cnf(c5,plain,
( member(sk0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p26,plain,
( subset(sk2,X0)
| member(sk0(sk2,X0),sk3) ),
inference(resolution,[status(thm)],[p24,c5]) ).
cnf(p35,plain,
( subset(sk2,X0)
| ~ member(sk0(sk2,X0),X1)
| member(sk0(sk2,X0),intersection(sk3,X1)) ),
inference(resolution,[status(thm)],[c2,p26]) ).
cnf(p36,plain,
( subset(sk2,X0)
| subset(sk2,X0)
| member(sk0(sk2,X0),intersection(sk2,sk3)) ),
inference(resolution,[status(thm)],[p35,c5]) ).
cnf(p38,plain,
( subset(sk2,X0)
| member(sk0(sk2,X0),intersection(sk2,sk3)) ),
inference(factoring,[status(thm)],[p36]) ).
cnf(c6,plain,
( ~ member(sk0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p39,plain,
( subset(sk2,intersection(sk2,sk3))
| subset(sk2,intersection(sk2,sk3)) ),
inference(resolution,[status(thm)],[p38,c6]) ).
cnf(p42,plain,
subset(sk2,intersection(sk2,sk3)),
inference(factoring,[status(thm)],[p39]) ).
fof(f3,axiom,
! [B,C] :
( B = C
<=> ( subset(C,B)
& subset(B,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
fof(f3_nnf,plain,
! [B,C] :
( ( ~ subset(C,B)
| ~ subset(B,C)
| B = C )
& ( ( subset(C,B)
& subset(B,C) )
| B != C ) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [B,C] :
( ( ~ subset(C,B)
| ~ subset(B,C)
| B = C )
& ( ( subset(C,B)
& subset(B,C) )
| B != C ) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c9,plain,
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
fof(f1,axiom,
! [B,C] : subset(intersection(B,C),B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_is_subset) ).
fof(f1_nnf,plain,
! [B,C] : subset(intersection(B,C),B),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [B,C] : subset(intersection(B,C),B),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c3,plain,
subset(intersection(X0,X1),X0),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p28,plain,
( ~ subset(X0,intersection(X0,X1))
| intersection(X0,X1) = X0 ),
inference(resolution,[status(thm)],[c9,c3]) ).
cnf(p45,plain,
intersection(sk2,sk3) = sk2,
inference(resolution,[status(thm)],[p42,p28]) ).
cnf(c19,plain,
intersection(sk2,sk3) != sk2,
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p46,plain,
sk2 != sk2,
inference(demodulation,[status(thm)],[p45,c19]) ).
cnf(p48,plain,
$false,
inference(equality_resolution,[status(thm)],[p46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET183+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.38 % Computer : n015.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Thu Sep 24 10:13:41 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 12.51/2.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.51/2.35 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------