%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET751+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 02:10:33 PM UTC 2026
% Result : Theorem 0.18s 5.84s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 32 ( 6 unt; 0 def)
% Number of atoms : 104 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 116 ( 44 ~; 35 |; 31 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 91 ( 76 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [F,A,Y] :
( member(Y,image2(F,A))
<=> ? [X] :
( apply(F,X,Y)
& member(X,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,conjecture,
! [F,A,B,X,Y] :
( ( subset(X,Y)
& subset(Y,A)
& subset(X,A)
& maps(F,A,B) )
=> subset(image2(F,X),image2(F,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ ! [F,A,B,X,Y] :
( ( subset(X,Y)
& subset(Y,A)
& subset(X,A)
& maps(F,A,B) )
=> subset(image2(F,X),image2(F,Y)) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f31,plain,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,B)
| ~ member(X,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f32,plain,
! [A,B] :
( ( ? [X] :
( ~ member(X,B)
& member(X,A) )
| subset(A,B) )
& ( ! [X] :
( member(X,B)
| ~ member(X,A) )
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f31]) ).
fof(f33,plain,
( ! [A,B] :
( ? [X] :
( ~ member(X,B)
& member(X,A) )
| subset(A,B) )
& ! [A,B] :
( ! [X] :
( member(X,B)
| ~ member(X,A) )
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f32]) ).
fof(f34,plain,
( ! [A,B] :
( ( ~ member(sK0_skl(B,A),B)
& member(sK0_skl(B,A),A) )
| subset(A,B) )
& ! [A,B] :
( ! [X] :
( member(X,B)
| ~ member(X,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X,sK0_skl(B,A))],[f33]) ).
fof(f35,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f36,plain,
! [X0,X1] :
( member(sK0_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f37,plain,
! [X0,X1] :
( ~ member(sK0_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f176,plain,
! [F,A,Y] :
( ( ! [X] :
( ~ apply(F,X,Y)
| ~ member(X,A) )
| member(Y,image2(F,A)) )
& ( ? [X] :
( apply(F,X,Y)
& member(X,A) )
| ~ member(Y,image2(F,A)) ) ),
inference(NNF_transformation,[status(thm)],[f22]) ).
fof(f177,plain,
( ! [F,A,Y] :
( ! [X] :
( ~ apply(F,X,Y)
| ~ member(X,A) )
| member(Y,image2(F,A)) )
& ! [F,A,Y] :
( ? [X] :
( apply(F,X,Y)
& member(X,A) )
| ~ member(Y,image2(F,A)) ) ),
inference(miniscoping,[status(thm)],[f176]) ).
fof(f178,plain,
( ! [F,A,Y] :
( ! [X] :
( ~ apply(F,X,Y)
| ~ member(X,A) )
| member(Y,image2(F,A)) )
& ! [F,A,Y] :
( ( apply(F,sK23_skl(Y,A,F),Y)
& member(sK23_skl(Y,A,F),A) )
| ~ member(Y,image2(F,A)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23_skl]),skolemize(X,sK23_skl(Y,A,F))],[f177]) ).
fof(f179,plain,
! [X0,X1,X2] :
( member(sK23_skl(X0,X2,X1),X2)
| ~ member(X0,image2(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f178]) ).
fof(f180,plain,
! [X0,X1,X2] :
( apply(X1,sK23_skl(X0,X2,X1),X0)
| ~ member(X0,image2(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f178]) ).
fof(f181,plain,
! [X0,X1,X2,X3] :
( ~ apply(X1,X3,X0)
| ~ member(X3,X2)
| member(X0,image2(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f178]) ).
fof(f244,plain,
? [F,A,B,X,Y] :
( ~ subset(image2(F,X),image2(F,Y))
& subset(X,Y)
& subset(Y,A)
& subset(X,A)
& maps(F,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f245,plain,
? [F,X,Y] :
( ~ subset(image2(F,X),image2(F,Y))
& subset(X,Y)
& ? [A] :
( subset(Y,A)
& subset(X,A)
& ? [B] : maps(F,A,B) ) ),
inference(miniscoping,[status(thm)],[f244]) ).
fof(f246,plain,
( ~ subset(image2(sK39_skl,sK40_skl),image2(sK39_skl,sK41_skl))
& subset(sK40_skl,sK41_skl)
& subset(sK41_skl,sK42_skl)
& subset(sK40_skl,sK42_skl)
& maps(sK39_skl,sK42_skl,sK43_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39_skl,sK40_skl,sK41_skl,sK42_skl,sK43_skl]),skolemize(F,sK39_skl),skolemize(X,sK40_skl),skolemize(Y,sK41_skl),skolemize(A,sK42_skl),skolemize(B,sK43_skl)],[f245]) ).
fof(f250,plain,
subset(sK40_skl,sK41_skl),
inference(cnf_transformation,[status(thm)],[f246]) ).
fof(f251,plain,
~ subset(image2(sK39_skl,sK40_skl),image2(sK39_skl,sK41_skl)),
inference(cnf_transformation,[status(thm)],[f246]) ).
fof(f272,plain,
~ member(sK0_skl(image2(sK39_skl,sK41_skl),image2(sK39_skl,sK40_skl)),image2(sK39_skl,sK41_skl)),
inference(resolution,[status(thm)],[f37,f251]) ).
fof(f273,plain,
! [X0] :
( ~ apply(sK39_skl,X0,sK0_skl(image2(sK39_skl,sK41_skl),image2(sK39_skl,sK40_skl)))
| ~ member(X0,sK41_skl) ),
inference(resolution,[status(thm)],[f272,f181]) ).
fof(f275,plain,
! [X0] :
( ~ member(sK0_skl(image2(sK39_skl,sK41_skl),image2(sK39_skl,sK40_skl)),image2(sK39_skl,X0))
| ~ member(sK23_skl(sK0_skl(image2(sK39_skl,sK41_skl),image2(sK39_skl,sK40_skl)),X0,sK39_skl),sK41_skl) ),
inference(resolution,[status(thm)],[f273,f180]) ).
fof(f277,plain,
! [X0,X1] :
( ~ member(sK23_skl(sK0_skl(image2(sK39_skl,sK41_skl),image2(sK39_skl,sK40_skl)),X0,sK39_skl),X1)
| ~ subset(X1,sK41_skl)
| ~ member(sK0_skl(image2(sK39_skl,sK41_skl),image2(sK39_skl,sK40_skl)),image2(sK39_skl,X0)) ),
inference(resolution,[status(thm)],[f275,f35]) ).
fof(f313,plain,
! [X0] :
( subset(image2(sK39_skl,sK40_skl),image2(sK39_skl,sK41_skl))
| ~ member(sK23_skl(sK0_skl(image2(sK39_skl,sK41_skl),image2(sK39_skl,sK40_skl)),sK40_skl,sK39_skl),X0)
| ~ subset(X0,sK41_skl) ),
inference(resolution,[status(thm)],[f277,f36]) ).
fof(f316,plain,
! [X0] :
( ~ member(sK23_skl(sK0_skl(image2(sK39_skl,sK41_skl),image2(sK39_skl,sK40_skl)),sK40_skl,sK39_skl),X0)
| ~ subset(X0,sK41_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f313,f251]) ).
fof(f321,plain,
~ member(sK23_skl(sK0_skl(image2(sK39_skl,sK41_skl),image2(sK39_skl,sK40_skl)),sK40_skl,sK39_skl),sK40_skl),
inference(resolution,[status(thm)],[f316,f250]) ).
fof(f541,plain,
! [X0,X1,X2] :
( subset(image2(X1,X2),X0)
| member(sK23_skl(sK0_skl(X0,image2(X1,X2)),X2,X1),X2) ),
inference(resolution,[status(thm)],[f179,f36]) ).
fof(f544,plain,
subset(image2(sK39_skl,sK40_skl),image2(sK39_skl,sK41_skl)),
inference(resolution,[status(thm)],[f541,f321]) ).
fof(f559,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f544,f251]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET751+4 : TPTP v9.3.1. Bugfixed v2.2.1.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/5.39 % Computer : n016.cluster.edu
% 0.14/5.39 % Model : x86_64 x86_64
% 0.14/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/5.39 % Memory : 8046.5625MB
% 0.14/5.39 % OS : Linux 6.8.0-71-generic
% 0.14/5.39 % CPULimit : 300
% 0.14/5.39 % WCLimit : 300
% 0.14/5.39 % DateTime : Mon Sep 21 05:40:58 UTC 2026
% 0.18/5.40 % CPUTime :
% 0.18/5.42 % Drodi V4.1.1
% 0.18/5.84 % Refutation found
% 0.18/5.84 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/5.84 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/5.87 % Elapsed time: 0.458189 seconds
% 0.18/5.87 % CPU time: 3.030049 seconds
% 0.18/5.87 % Total memory used: 113.445 MB
% 0.18/5.87 % Net memory used: 109.538 MB
%------------------------------------------------------------------------------