%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET638+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 02:43:41 PM UTC 2026
% Result : Theorem 15.18s 2.39s
% Output : Proof 15.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 21 unt; 0 def)
% Number of atoms : 41 ( 20 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 19 ( 7 ~; 3 |; 6 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 48 ( 2 sgn 33 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,conjecture,
! [B,C,D] :
( ( intersection(B,D) = empty_set
& subset(B,union(C,D)) )
=> subset(B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th120) ).
fof(f14_neg,negated_conjecture,
~ ! [B,C,D] :
( ( intersection(B,D) = empty_set
& subset(B,union(C,D)) )
=> subset(B,C) ),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f14_nnf,plain,
? [B,C,D] :
( ~ subset(B,C)
& intersection(B,D) = empty_set
& subset(B,union(C,D)) ),
inference(nnf_transformation,[status(thm)],[f14_neg]) ).
fof(f14_sk,plain,
( ~ subset(sk3,sk4)
& intersection(sk3,sk5) = empty_set
& subset(sk3,union(sk4,sk5)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk3,sk4,sk5])],[f14_nnf]) ).
cnf(c29,plain,
intersection(sk3,sk5) = empty_set,
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
fof(f3,axiom,
! [B,C,D] : intersection(B,union(C,D)) = union(intersection(B,C),intersection(B,D)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_distributes_over_union) ).
fof(f3_nnf,plain,
! [B,C,D] : intersection(B,union(C,D)) = union(intersection(B,C),intersection(B,D)),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [B,C,D] : intersection(B,union(C,D)) = union(intersection(B,C),intersection(B,D)),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
intersection(X0,union(X1,X2)) = union(intersection(X0,X1),intersection(X0,X2)),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p38,plain,
intersection(sk3,union(X0,sk5)) = intersection(sk3,X0),
inference(superposition,[status(thm)],[c29,c3]) ).
cnf(c28,plain,
subset(sk3,union(sk4,sk5)),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
fof(f1,axiom,
! [B,C] :
( subset(B,C)
=> intersection(B,C) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_intersection) ).
fof(f1_nnf,plain,
! [B,C] :
( intersection(B,C) = B
| ~ subset(B,C) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [B,C] :
( intersection(B,C) = B
| ~ subset(B,C) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( intersection(X0,X1) = X0
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p33,plain,
intersection(sk3,union(sk4,sk5)) = sk3,
inference(resolution,[status(thm)],[c28,c1]) ).
cnf(p39,plain,
intersection(sk3,sk4) = sk3,
inference(demodulation,[status(thm)],[p38,p33]) ).
fof(f10,axiom,
! [B,C] : intersection(B,C) = intersection(C,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(f10_nnf,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c18,plain,
intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
fof(f0,axiom,
! [B,C] : subset(intersection(B,C),B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_is_subset) ).
fof(f0_nnf,plain,
! [B,C] : subset(intersection(B,C),B),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [B,C] : subset(intersection(B,C),B),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
subset(intersection(X0,X1),X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p62,plain,
subset(intersection(X0,X1),X1),
inference(superposition,[status(thm)],[c18,c0]) ).
cnf(p66,plain,
subset(sk3,sk4),
inference(superposition,[status(thm)],[p39,p62]) ).
cnf(c30,plain,
~ subset(sk3,sk4),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(p68,plain,
$false,
inference(resolution,[status(thm)],[p66,c30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET638+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n009.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 11:32:14 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 15.18/2.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.18/2.39 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------