%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET594+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 : n009.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 02:43:32 PM UTC 2026
% Result : Theorem 13.67s 2.43s
% Output : Proof 13.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 32 ( 4 unt; 0 def)
% Number of atoms : 94 ( 5 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 90 ( 28 ~; 41 |; 15 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 63 ( 5 sgn 33 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,conjecture,
! [B,C,D] :
( union(intersection(B,C),intersection(B,D)) = B
=> subset(B,union(C,D)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th53) ).
fof(f8_neg,negated_conjecture,
~ ! [B,C,D] :
( union(intersection(B,C),intersection(B,D)) = B
=> subset(B,union(C,D)) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f8_nnf,plain,
? [B,C,D] :
( ~ subset(B,union(C,D))
& union(intersection(B,C),intersection(B,D)) = B ),
inference(nnf_transformation,[status(thm)],[f8_neg]) ).
fof(f8_sk,plain,
( ~ subset(sk2,union(sk3,sk4))
& union(intersection(sk2,sk3),intersection(sk2,sk4)) = sk2 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3,sk4])],[f8_nnf]) ).
cnf(c21,plain,
union(intersection(sk2,sk3),intersection(sk2,sk4)) = sk2,
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
fof(f1,axiom,
! [B,C,D] :
( member(D,union(B,C))
<=> ( member(D,C)
| member(D,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
fof(f1_nnf,plain,
! [B,C,D] :
( ( ( ~ member(D,C)
& ~ member(D,B) )
| member(D,union(B,C)) )
& ( member(D,C)
| member(D,B)
| ~ member(D,union(B,C)) ) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [D,B,C] :
( ( ( ~ member(D,C)
& ~ member(D,B) )
| member(D,union(B,C)) )
& ( member(D,C)
| member(D,B)
| ~ member(D,union(B,C)) ) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c3,plain,
( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p50,plain,
( member(X0,intersection(sk2,sk4))
| member(X0,intersection(sk2,sk3))
| ~ member(X0,sk2) ),
inference(superposition,[status(thm)],[c21,c3]) ).
fof(f0,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(f0_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)],[f0]) ).
fof(f0_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])],[f0_nnf]) ).
cnf(c1,plain,
( member(sk0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p52,plain,
( subset(sk2,X0)
| member(sk0(sk2,X0),intersection(sk2,sk4))
| member(sk0(sk2,X0),intersection(sk2,sk3)) ),
inference(resolution,[status(thm)],[p50,c1]) ).
fof(f2,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(f2_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)],[f2]) ).
fof(f2_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)],[f2_nnf]) ).
cnf(c7,plain,
( member(X2,X1)
| ~ member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p56,plain,
( member(sk0(sk2,X0),sk4)
| subset(sk2,X0)
| member(sk0(sk2,X0),intersection(sk2,sk3)) ),
inference(resolution,[status(thm)],[p52,c7]) ).
cnf(p60,plain,
( member(sk0(sk2,X0),sk3)
| member(sk0(sk2,X0),sk4)
| subset(sk2,X0) ),
inference(resolution,[status(thm)],[p56,c7]) ).
cnf(c4,plain,
( ~ member(X2,X0)
| member(X2,union(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p62,plain,
( member(sk0(sk2,X0),union(sk4,X1))
| member(sk0(sk2,X0),sk3)
| subset(sk2,X0) ),
inference(resolution,[status(thm)],[p60,c4]) ).
cnf(c2,plain,
( ~ member(sk0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p95,plain,
( subset(sk2,union(sk4,X0))
| member(sk0(sk2,union(sk4,X0)),sk3)
| subset(sk2,union(sk4,X0)) ),
inference(resolution,[status(thm)],[p62,c2]) ).
cnf(p154,plain,
( member(sk0(sk2,union(sk4,X0)),sk3)
| subset(sk2,union(sk4,X0)) ),
inference(factoring,[status(thm)],[p95]) ).
cnf(c5,plain,
( ~ member(X2,X1)
| member(X2,union(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p157,plain,
( member(sk0(sk2,union(sk4,X0)),union(X1,sk3))
| subset(sk2,union(sk4,X0)) ),
inference(resolution,[status(thm)],[p154,c5]) ).
cnf(p162,plain,
( subset(sk2,union(sk3,sk4))
| subset(sk2,union(sk3,sk4)) ),
inference(resolution,[status(thm)],[p157,c2]) ).
cnf(p165,plain,
subset(sk2,union(sk3,sk4)),
inference(factoring,[status(thm)],[p162]) ).
cnf(c22,plain,
~ subset(sk2,union(sk3,sk4)),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p166,plain,
$false,
inference(resolution,[status(thm)],[p165,c22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET594+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n009.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 11:23:14 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 13.67/2.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.67/2.43 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------