%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU096+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 02:19:12 PM UTC 2026
% Result : Theorem 0.08s 0.39s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 25 ( 9 unt; 0 def)
% Number of atoms : 72 ( 7 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 73 ( 26 ~; 21 |; 19 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 24 ( 20 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [A,B] :
( ( finite(B)
& function(A)
& relation(A) )
=> finite(relation_image(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( subset(A,relation_rng(B))
=> relation_image(B,relation_inverse_image(B,A)) = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f53,conjecture,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( ( finite(relation_inverse_image(B,A))
& subset(A,relation_rng(B)) )
=> finite(A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f54,negated_conjecture,
~ ! [A,B] :
( ( function(B)
& relation(B) )
=> ( ( finite(relation_inverse_image(B,A))
& subset(A,relation_rng(B)) )
=> finite(A) ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f104,plain,
! [A,B] :
( finite(relation_image(A,B))
| ~ finite(B)
| ~ function(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f105,plain,
! [X0,X1] :
( finite(relation_image(X0,X1))
| ~ finite(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f240,plain,
! [A,B] :
( relation_image(B,relation_inverse_image(B,A)) = A
| ~ subset(A,relation_rng(B))
| ~ function(B)
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f50]) ).
fof(f241,plain,
! [B] :
( ! [A] :
( relation_image(B,relation_inverse_image(B,A)) = A
| ~ subset(A,relation_rng(B)) )
| ~ function(B)
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f240]) ).
fof(f242,plain,
! [X0,X1] :
( relation_image(X0,relation_inverse_image(X0,X1)) = X1
| ~ subset(X1,relation_rng(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f241]) ).
fof(f248,plain,
? [A,B] :
( ~ finite(A)
& finite(relation_inverse_image(B,A))
& subset(A,relation_rng(B))
& function(B)
& relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f54]) ).
fof(f249,plain,
? [B] :
( ? [A] :
( ~ finite(A)
& finite(relation_inverse_image(B,A))
& subset(A,relation_rng(B)) )
& function(B)
& relation(B) ),
inference(miniscoping,[status(thm)],[f248]) ).
fof(f250,plain,
( ~ finite(sK27_skl)
& finite(relation_inverse_image(sK26_skl,sK27_skl))
& subset(sK27_skl,relation_rng(sK26_skl))
& function(sK26_skl)
& relation(sK26_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26_skl,sK27_skl]),skolemize(B,sK26_skl),skolemize(A,sK27_skl)],[f249]) ).
fof(f251,plain,
relation(sK26_skl),
inference(cnf_transformation,[status(thm)],[f250]) ).
fof(f252,plain,
function(sK26_skl),
inference(cnf_transformation,[status(thm)],[f250]) ).
fof(f253,plain,
subset(sK27_skl,relation_rng(sK26_skl)),
inference(cnf_transformation,[status(thm)],[f250]) ).
fof(f254,plain,
finite(relation_inverse_image(sK26_skl,sK27_skl)),
inference(cnf_transformation,[status(thm)],[f250]) ).
fof(f255,plain,
~ finite(sK27_skl),
inference(cnf_transformation,[status(thm)],[f250]) ).
fof(f281,plain,
( relation_image(sK26_skl,relation_inverse_image(sK26_skl,sK27_skl)) = sK27_skl
| ~ function(sK26_skl)
| ~ relation(sK26_skl) ),
inference(resolution,[status(thm)],[f242,f253]) ).
fof(f283,plain,
( relation_image(sK26_skl,relation_inverse_image(sK26_skl,sK27_skl)) = sK27_skl
| ~ function(sK26_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f281,f251]) ).
fof(f290,plain,
relation_image(sK26_skl,relation_inverse_image(sK26_skl,sK27_skl)) = sK27_skl,
inference(forward_subsumption_resolution,[status(thm)],[f283,f252]) ).
fof(f344,plain,
! [X0] :
( finite(relation_image(sK26_skl,X0))
| ~ finite(X0)
| ~ relation(sK26_skl) ),
inference(resolution,[status(thm)],[f105,f252]) ).
fof(f347,plain,
! [X0] :
( finite(relation_image(sK26_skl,X0))
| ~ finite(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f344,f251]) ).
fof(f350,plain,
finite(relation_image(sK26_skl,relation_inverse_image(sK26_skl,sK27_skl))),
inference(resolution,[status(thm)],[f347,f254]) ).
fof(f351,plain,
finite(sK27_skl),
inference(forward_demodulation,[status(thm)],[f290,f350]) ).
fof(f352,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f351,f255]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU096+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n007.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 05:47:50 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.08/0.39 % Refutation found
% 0.08/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/0.42 % Elapsed time: 0.055311 seconds
% 0.08/0.42 % CPU time: 0.152726 seconds
% 0.08/0.42 % Total memory used: 84.795 MB
% 0.08/0.42 % Net memory used: 84.750 MB
%------------------------------------------------------------------------------