%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET173+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 : n002.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 02:42:43 PM UTC 2026
% Result : Theorem 15.46s 3.05s
% Output : Proof 15.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 10 unt; 0 def)
% Number of atoms : 102 ( 14 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 104 ( 38 ~; 43 |; 18 &)
% ( 4 <=>; 1 =>; 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 82 ( 8 sgn 37 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,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(f1_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)],[f1]) ).
fof(f1_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)],[f1_nnf]) ).
cnf(c5,plain,
( ~ member(X2,X1)
| ~ member(X2,X0)
| member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
fof(f5,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(f5_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)],[f5]) ).
fof(f5_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])],[f5_nnf]) ).
cnf(c12,plain,
( member(sk0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p31,plain,
( subset(X0,X1)
| ~ member(sk0(X0,X1),X2)
| member(sk0(X0,X1),intersection(X0,X2)) ),
inference(resolution,[status(thm)],[c5,c12]) ).
fof(f0,axiom,
! [B,C,D] :
( member(D,union(B,C))
<=> ( member(D,C)
| member(D,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).
fof(f0_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)],[f0]) ).
fof(f0_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)],[f0_nnf]) ).
cnf(c1,plain,
( ~ member(X2,X0)
| member(X2,union(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p26,plain,
( member(sk0(X0,X1),union(X0,X2))
| subset(X0,X1) ),
inference(resolution,[status(thm)],[c12,c1]) ).
cnf(p136,plain,
( subset(X0,X1)
| subset(X0,X1)
| member(sk0(X0,X1),intersection(X0,union(X0,X2))) ),
inference(resolution,[status(thm)],[p31,p26]) ).
cnf(p2275,plain,
( subset(X0,X1)
| member(sk0(X0,X1),intersection(X0,union(X0,X2))) ),
inference(factoring,[status(thm)],[p136]) ).
cnf(c13,plain,
( ~ member(sk0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p2280,plain,
( subset(X0,intersection(X0,union(X0,X1)))
| subset(X0,intersection(X0,union(X0,X1))) ),
inference(resolution,[status(thm)],[p2275,c13]) ).
cnf(p2425,plain,
subset(X0,intersection(X0,union(X0,X1))),
inference(factoring,[status(thm)],[p2280]) ).
cnf(c3,plain,
( member(X2,X0)
| ~ member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p28,plain,
( member(sk0(intersection(X0,X1),X2),X0)
| subset(intersection(X0,X1),X2) ),
inference(resolution,[status(thm)],[c12,c3]) ).
cnf(p88,plain,
( subset(intersection(X0,X1),X0)
| subset(intersection(X0,X1),X0) ),
inference(resolution,[status(thm)],[p28,c13]) ).
cnf(p93,plain,
subset(intersection(X0,X1),X0),
inference(factoring,[status(thm)],[p88]) ).
fof(f2,axiom,
! [B,C] :
( B = C
<=> ( subset(C,B)
& subset(B,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
fof(f2_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)],[f2]) ).
fof(f2_sk,plain,
! [B,C] :
( ( ~ subset(C,B)
| ~ subset(B,C)
| B = C )
& ( ( subset(C,B)
& subset(B,C) )
| B != C ) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c8,plain,
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p95,plain,
( ~ subset(X0,intersection(X0,X1))
| intersection(X0,X1) = X0 ),
inference(resolution,[status(thm)],[p93,c8]) ).
cnf(p2462,plain,
intersection(X0,union(X0,X1)) = X0,
inference(resolution,[status(thm)],[p2425,p95]) ).
fof(f8,conjecture,
! [B,C] : intersection(B,union(B,C)) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_absorbtion_for_intersection) ).
fof(f8_neg,negated_conjecture,
~ ! [B,C] : intersection(B,union(B,C)) = B,
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f8_nnf,plain,
? [B,C] : intersection(B,union(B,C)) != B,
inference(nnf_transformation,[status(thm)],[f8_neg]) ).
fof(f8_sk,plain,
intersection(sk2,union(sk2,sk3)) != sk2,
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3])],[f8_nnf]) ).
cnf(c21,plain,
intersection(sk2,union(sk2,sk3)) != sk2,
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p2463,plain,
sk2 != sk2,
inference(demodulation,[status(thm)],[p2462,c21]) ).
cnf(p2468,plain,
$false,
inference(equality_resolution,[status(thm)],[p2463]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET173+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 : n002.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 10:10:34 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 15.46/3.05 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.46/3.05 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------