%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU209+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 02:19:41 PM UTC 2026
% Result : Theorem 0.11s 0.40s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 35 ( 7 unt; 0 def)
% Number of atoms : 159 ( 18 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 196 ( 72 ~; 74 |; 35 &)
% ( 10 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 2 con; 0-4 aty)
% Number of variables : 120 ( 98 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [A] :
( relation(A)
=> ! [B,C] :
( C = relation_inverse_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E] :
( in(E,B)
& in(ordered_pair(D,E),A) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_dom(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,conjecture,
! [A,B] :
( relation(B)
=> subset(relation_inverse_image(B,A),relation_dom(B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
~ ! [A,B] :
( relation(B)
=> subset(relation_inverse_image(B,A),relation_dom(B)) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f47,plain,
! [A] :
( ! [B,C] :
( C = relation_inverse_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E] :
( in(E,B)
& in(ordered_pair(D,E),A) ) ) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f48,plain,
! [A] :
( ! [B,C] :
( ( ? [D] :
( ( ? [E] :
( in(E,B)
& in(ordered_pair(D,E),A) )
| in(D,C) )
& ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(D,E),A) )
| ~ in(D,C) ) )
| C = relation_inverse_image(A,B) )
& ( ! [D] :
( ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(D,E),A) )
| in(D,C) )
& ( ? [E] :
( in(E,B)
& in(ordered_pair(D,E),A) )
| ~ in(D,C) ) )
| C != relation_inverse_image(A,B) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f47]) ).
fof(f49,plain,
! [A] :
( ( ! [B,C] :
( ? [D] :
( ( ? [E] :
( in(E,B)
& in(ordered_pair(D,E),A) )
| in(D,C) )
& ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(D,E),A) )
| ~ in(D,C) ) )
| C = relation_inverse_image(A,B) )
& ! [B,C] :
( ( ! [D] :
( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(D,E),A) )
| in(D,C) )
& ! [D] :
( ? [E] :
( in(E,B)
& in(ordered_pair(D,E),A) )
| ~ in(D,C) ) )
| C != relation_inverse_image(A,B) ) )
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f48]) ).
fof(f50,plain,
! [A] :
( ( ! [B,C] :
( ( ( ( in(sK2_skl(C,B,A),B)
& in(ordered_pair(sK1_skl(C,B,A),sK2_skl(C,B,A)),A) )
| in(sK1_skl(C,B,A),C) )
& ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(sK1_skl(C,B,A),E),A) )
| ~ in(sK1_skl(C,B,A),C) ) )
| C = relation_inverse_image(A,B) )
& ! [B,C] :
( ( ! [D] :
( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(D,E),A) )
| in(D,C) )
& ! [D] :
( ( in(sK0_skl(D,C,B,A),B)
& in(ordered_pair(D,sK0_skl(D,C,B,A)),A) )
| ~ in(D,C) ) )
| C != relation_inverse_image(A,B) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(E,sK0_skl(D,C,B,A)),skolemize(D,sK1_skl(C,B,A)),skolemize(E,sK2_skl(C,B,A))],[f49]) ).
fof(f51,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(X3,sK0_skl(X3,X1,X2,X0)),X0)
| ~ in(X3,X1)
| X1 != relation_inverse_image(X0,X2)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f57,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f58,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f57]) ).
fof(f59,plain,
( ! [A,B] :
( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f58]) ).
fof(f60,plain,
( ! [A,B] :
( ( ~ in(sK3_skl(B,A),B)
& in(sK3_skl(B,A),A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(C,sK3_skl(B,A))],[f59]) ).
fof(f62,plain,
! [X0,X1] :
( in(sK3_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f63,plain,
! [X0,X1] :
( ~ in(sK3_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f64,plain,
! [A] :
( ! [B] :
( B = relation_dom(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f65,plain,
! [A] :
( ! [B] :
( ( ? [C] :
( ( ? [D] : in(ordered_pair(C,D),A)
| in(C,B) )
& ( ! [D] : ~ in(ordered_pair(C,D),A)
| ~ in(C,B) ) )
| B = relation_dom(A) )
& ( ! [C] :
( ( ! [D] : ~ in(ordered_pair(C,D),A)
| in(C,B) )
& ( ? [D] : in(ordered_pair(C,D),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f64]) ).
fof(f66,plain,
! [A] :
( ( ! [B] :
( ? [C] :
( ( ? [D] : in(ordered_pair(C,D),A)
| in(C,B) )
& ( ! [D] : ~ in(ordered_pair(C,D),A)
| ~ in(C,B) ) )
| B = relation_dom(A) )
& ! [B] :
( ( ! [C] :
( ! [D] : ~ in(ordered_pair(C,D),A)
| in(C,B) )
& ! [C] :
( ? [D] : in(ordered_pair(C,D),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f65]) ).
fof(f67,plain,
! [A] :
( ( ! [B] :
( ( ( in(ordered_pair(sK5_skl(B,A),sK6_skl(B,A)),A)
| in(sK5_skl(B,A),B) )
& ( ! [D] : ~ in(ordered_pair(sK5_skl(B,A),D),A)
| ~ in(sK5_skl(B,A),B) ) )
| B = relation_dom(A) )
& ! [B] :
( ( ! [C] :
( ! [D] : ~ in(ordered_pair(C,D),A)
| in(C,B) )
& ! [C] :
( in(ordered_pair(C,sK4_skl(C,B,A)),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl,sK6_skl]),skolemize(D,sK4_skl(C,B,A)),skolemize(C,sK5_skl(B,A)),skolemize(D,sK6_skl(B,A))],[f66]) ).
fof(f69,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X2,X3),X0)
| in(X2,X1)
| X1 != relation_dom(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f106,plain,
? [A,B] :
( ~ subset(relation_inverse_image(B,A),relation_dom(B))
& relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f107,plain,
? [B] :
( ? [A] : ~ subset(relation_inverse_image(B,A),relation_dom(B))
& relation(B) ),
inference(miniscoping,[status(thm)],[f106]) ).
fof(f108,plain,
( ~ subset(relation_inverse_image(sK14_skl,sK15_skl),relation_dom(sK14_skl))
& relation(sK14_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl,sK15_skl]),skolemize(B,sK14_skl),skolemize(A,sK15_skl)],[f107]) ).
fof(f109,plain,
relation(sK14_skl),
inference(cnf_transformation,[status(thm)],[f108]) ).
fof(f110,plain,
~ subset(relation_inverse_image(sK14_skl,sK15_skl),relation_dom(sK14_skl)),
inference(cnf_transformation,[status(thm)],[f108]) ).
fof(f133,plain,
! [X0,X1,X2] :
( in(ordered_pair(X1,sK0_skl(X1,relation_inverse_image(X0,X2),X2,X0)),X0)
| ~ in(X1,relation_inverse_image(X0,X2))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f51]) ).
fof(f137,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X1,X2),X0)
| in(X1,relation_dom(X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f69]) ).
fof(f201,plain,
in(sK3_skl(relation_dom(sK14_skl),relation_inverse_image(sK14_skl,sK15_skl)),relation_inverse_image(sK14_skl,sK15_skl)),
inference(resolution,[status(thm)],[f62,f110]) ).
fof(f203,plain,
( in(ordered_pair(sK3_skl(relation_dom(sK14_skl),relation_inverse_image(sK14_skl,sK15_skl)),sK0_skl(sK3_skl(relation_dom(sK14_skl),relation_inverse_image(sK14_skl,sK15_skl)),relation_inverse_image(sK14_skl,sK15_skl),sK15_skl,sK14_skl)),sK14_skl)
| ~ relation(sK14_skl) ),
inference(resolution,[status(thm)],[f201,f133]) ).
fof(f207,plain,
in(ordered_pair(sK3_skl(relation_dom(sK14_skl),relation_inverse_image(sK14_skl,sK15_skl)),sK0_skl(sK3_skl(relation_dom(sK14_skl),relation_inverse_image(sK14_skl,sK15_skl)),relation_inverse_image(sK14_skl,sK15_skl),sK15_skl,sK14_skl)),sK14_skl),
inference(forward_subsumption_resolution,[status(thm)],[f203,f109]) ).
fof(f295,plain,
( in(sK3_skl(relation_dom(sK14_skl),relation_inverse_image(sK14_skl,sK15_skl)),relation_dom(sK14_skl))
| ~ relation(sK14_skl) ),
inference(resolution,[status(thm)],[f207,f137]) ).
fof(f299,plain,
in(sK3_skl(relation_dom(sK14_skl),relation_inverse_image(sK14_skl,sK15_skl)),relation_dom(sK14_skl)),
inference(forward_subsumption_resolution,[status(thm)],[f295,f109]) ).
fof(f339,plain,
subset(relation_inverse_image(sK14_skl,sK15_skl),relation_dom(sK14_skl)),
inference(resolution,[status(thm)],[f299,f63]) ).
fof(f343,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f339,f110]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU209+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n017.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 05:53:28 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.39 % Drodi V4.1.1
% 0.11/0.40 % Refutation found
% 0.11/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.44 % Elapsed time: 0.059369 seconds
% 0.15/0.44 % CPU time: 0.129341 seconds
% 0.15/0.44 % Total memory used: 16.900 MB
% 0.15/0.44 % Net memory used: 16.772 MB
%------------------------------------------------------------------------------