%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET638+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 : Thu Sep 24 02:10:19 PM UTC 2026
% Result : Theorem 0.14s 5.42s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 26 ( 18 unt; 0 def)
% Number of atoms : 39 ( 20 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 20 ( 7 ~; 2 |; 8 &)
% ( 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 : 36 ( 30 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,C] : subset(intersection(B,C),B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B,C] :
( subset(B,C)
=> intersection(B,C) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B] : union(B,empty_set) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [B,C,D] : intersection(B,union(C,D)) = union(intersection(B,C),intersection(B,D)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [B,C] : intersection(B,C) = intersection(C,B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,conjecture,
! [B,C,D] :
( ( intersection(B,D) = empty_set
& subset(B,union(C,D)) )
=> subset(B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
~ ! [B,C,D] :
( ( intersection(B,D) = empty_set
& subset(B,union(C,D)) )
=> subset(B,C) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f17,plain,
! [X0,X1] : subset(intersection(X0,X1),X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f18,plain,
! [B,C] :
( intersection(B,C) = B
| ~ subset(B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f19,plain,
! [X0,X1] :
( intersection(X0,X1) = X0
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f20,plain,
! [X0] : union(X0,empty_set) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f21,plain,
! [X0,X1,X2] : intersection(X0,union(X1,X2)) = union(intersection(X0,X1),intersection(X0,X2)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f46,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f60,plain,
? [B,C,D] :
( ~ subset(B,C)
& intersection(B,D) = empty_set
& subset(B,union(C,D)) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f61,plain,
? [B,C] :
( ~ subset(B,C)
& ? [D] :
( intersection(B,D) = empty_set
& subset(B,union(C,D)) ) ),
inference(miniscoping,[status(thm)],[f60]) ).
fof(f62,plain,
( ~ subset(sK3_skl,sK4_skl)
& intersection(sK3_skl,sK5_skl) = empty_set
& subset(sK3_skl,union(sK4_skl,sK5_skl)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl,sK5_skl]),skolemize(B,sK3_skl),skolemize(C,sK4_skl),skolemize(D,sK5_skl)],[f61]) ).
fof(f63,plain,
subset(sK3_skl,union(sK4_skl,sK5_skl)),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f64,plain,
intersection(sK3_skl,sK5_skl) = empty_set,
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f65,plain,
~ subset(sK3_skl,sK4_skl),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f70,plain,
intersection(sK3_skl,union(sK4_skl,sK5_skl)) = sK3_skl,
inference(resolution,[status(thm)],[f19,f63]) ).
fof(f92,plain,
! [X0] : intersection(sK3_skl,union(X0,sK5_skl)) = union(intersection(sK3_skl,X0),empty_set),
inference(paramodulation,[status(thm)],[f64,f21]) ).
fof(f99,plain,
! [X0] : intersection(sK3_skl,union(X0,sK5_skl)) = intersection(sK3_skl,X0),
inference(forward_demodulation,[status(thm)],[f20,f92]) ).
fof(f186,plain,
intersection(sK3_skl,sK4_skl) = sK3_skl,
inference(backward_demodulation,[status(thm)],[f99,f70]) ).
fof(f197,plain,
intersection(sK4_skl,sK3_skl) = sK3_skl,
inference(forward_demodulation,[status(thm)],[f46,f186]) ).
fof(f219,plain,
subset(sK3_skl,sK4_skl),
inference(paramodulation,[status(thm)],[f197,f17]) ).
fof(f221,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f219,f65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET638+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/5.38 % Computer : n018.cluster.edu
% 0.12/5.38 % Model : x86_64 x86_64
% 0.12/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.38 % Memory : 8046.5625MB
% 0.12/5.38 % OS : Linux 6.8.0-71-generic
% 0.12/5.38 % CPULimit : 300
% 0.12/5.38 % WCLimit : 300
% 0.12/5.38 % DateTime : Mon Sep 21 05:33:04 UTC 2026
% 0.12/5.38 % CPUTime :
% 0.12/5.39 % Drodi V4.1.1
% 0.14/5.42 % Refutation found
% 0.14/5.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/5.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/5.44 % Elapsed time: 0.047306 seconds
% 0.14/5.44 % CPU time: 0.155686 seconds
% 0.14/5.44 % Total memory used: 70.782 MB
% 0.14/5.44 % Net memory used: 70.562 MB
%------------------------------------------------------------------------------