%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU227+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 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 : Thu Sep 24 02:19:47 PM UTC 2026
% Result : Theorem 0.10s 0.46s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 52 ( 5 unt; 0 def)
% Number of atoms : 265 ( 27 equ)
% Maximal formula atoms : 15 ( 5 avg)
% Number of connectives : 337 ( 124 ~; 136 |; 55 &)
% ( 14 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 2 con; 0-4 aty)
% Number of variables : 193 ( 163 !; 30 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [A] :
( relation(A)
=> ! [B,C] :
( C = relation_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E] :
( in(E,B)
& in(ordered_pair(E,D),A) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,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/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_dom(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,conjecture,
! [A,B] :
( relation(B)
=> ( subset(A,relation_dom(B))
=> subset(A,relation_inverse_image(B,relation_image(B,A))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
~ ! [A,B] :
( relation(B)
=> ( subset(A,relation_dom(B))
=> subset(A,relation_inverse_image(B,relation_image(B,A))) ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f53,plain,
! [A] :
( ! [B,C] :
( C = relation_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E] :
( in(E,B)
& in(ordered_pair(E,D),A) ) ) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f54,plain,
! [A] :
( ! [B,C] :
( ( ? [D] :
( ( ? [E] :
( in(E,B)
& in(ordered_pair(E,D),A) )
| in(D,C) )
& ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(E,D),A) )
| ~ in(D,C) ) )
| C = relation_image(A,B) )
& ( ! [D] :
( ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(E,D),A) )
| in(D,C) )
& ( ? [E] :
( in(E,B)
& in(ordered_pair(E,D),A) )
| ~ in(D,C) ) )
| C != relation_image(A,B) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f53]) ).
fof(f55,plain,
! [A] :
( ( ! [B,C] :
( ? [D] :
( ( ? [E] :
( in(E,B)
& in(ordered_pair(E,D),A) )
| in(D,C) )
& ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(E,D),A) )
| ~ in(D,C) ) )
| C = relation_image(A,B) )
& ! [B,C] :
( ( ! [D] :
( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(E,D),A) )
| in(D,C) )
& ! [D] :
( ? [E] :
( in(E,B)
& in(ordered_pair(E,D),A) )
| ~ in(D,C) ) )
| C != relation_image(A,B) ) )
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f54]) ).
fof(f56,plain,
! [A] :
( ( ! [B,C] :
( ( ( ( in(sK2_skl(C,B,A),B)
& in(ordered_pair(sK2_skl(C,B,A),sK1_skl(C,B,A)),A) )
| in(sK1_skl(C,B,A),C) )
& ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(E,sK1_skl(C,B,A)),A) )
| ~ in(sK1_skl(C,B,A),C) ) )
| C = relation_image(A,B) )
& ! [B,C] :
( ( ! [D] :
( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(E,D),A) )
| in(D,C) )
& ! [D] :
( ( in(sK0_skl(D,C,B,A),B)
& in(ordered_pair(sK0_skl(D,C,B,A),D),A) )
| ~ in(D,C) ) )
| C != relation_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))],[f55]) ).
fof(f59,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(X4,X2)
| ~ in(ordered_pair(X4,X3),X0)
| in(X3,X1)
| X1 != relation_image(X0,X2)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f63,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)],[f7]) ).
fof(f64,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)],[f63]) ).
fof(f65,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)],[f64]) ).
fof(f66,plain,
! [A] :
( ( ! [B,C] :
( ( ( ( in(sK5_skl(C,B,A),B)
& in(ordered_pair(sK4_skl(C,B,A),sK5_skl(C,B,A)),A) )
| in(sK4_skl(C,B,A),C) )
& ( ! [E] :
( ~ in(E,B)
| ~ in(ordered_pair(sK4_skl(C,B,A),E),A) )
| ~ in(sK4_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(sK3_skl(D,C,B,A),B)
& in(ordered_pair(D,sK3_skl(D,C,B,A)),A) )
| ~ in(D,C) ) )
| C != relation_inverse_image(A,B) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl,sK5_skl]),skolemize(E,sK3_skl(D,C,B,A)),skolemize(D,sK4_skl(C,B,A)),skolemize(E,sK5_skl(C,B,A))],[f65]) ).
fof(f69,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(X4,X2)
| ~ in(ordered_pair(X3,X4),X0)
| in(X3,X1)
| X1 != relation_inverse_image(X0,X2)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f73,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f74,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)],[f73]) ).
fof(f75,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)],[f74]) ).
fof(f76,plain,
( ! [A,B] :
( ( ~ in(sK6_skl(B,A),B)
& in(sK6_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,[sK6_skl]),skolemize(C,sK6_skl(B,A))],[f75]) ).
fof(f77,plain,
! [X0,X1,X2] :
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f78,plain,
! [X0,X1] :
( in(sK6_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f79,plain,
! [X0,X1] :
( ~ in(sK6_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f80,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)],[f9]) ).
fof(f81,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)],[f80]) ).
fof(f82,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)],[f81]) ).
fof(f83,plain,
! [A] :
( ( ! [B] :
( ( ( in(ordered_pair(sK8_skl(B,A),sK9_skl(B,A)),A)
| in(sK8_skl(B,A),B) )
& ( ! [D] : ~ in(ordered_pair(sK8_skl(B,A),D),A)
| ~ in(sK8_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,sK7_skl(C,B,A)),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl,sK9_skl]),skolemize(D,sK7_skl(C,B,A)),skolemize(C,sK8_skl(B,A)),skolemize(D,sK9_skl(B,A))],[f82]) ).
fof(f84,plain,
! [X0,X1,X2] :
( in(ordered_pair(X2,sK7_skl(X2,X1,X0)),X0)
| ~ in(X2,X1)
| X1 != relation_dom(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f83]) ).
fof(f139,plain,
? [A,B] :
( ~ subset(A,relation_inverse_image(B,relation_image(B,A)))
& subset(A,relation_dom(B))
& relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f140,plain,
? [B] :
( ? [A] :
( ~ subset(A,relation_inverse_image(B,relation_image(B,A)))
& subset(A,relation_dom(B)) )
& relation(B) ),
inference(miniscoping,[status(thm)],[f139]) ).
fof(f141,plain,
( ~ subset(sK22_skl,relation_inverse_image(sK21_skl,relation_image(sK21_skl,sK22_skl)))
& subset(sK22_skl,relation_dom(sK21_skl))
& relation(sK21_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21_skl,sK22_skl]),skolemize(B,sK21_skl),skolemize(A,sK22_skl)],[f140]) ).
fof(f142,plain,
relation(sK21_skl),
inference(cnf_transformation,[status(thm)],[f141]) ).
fof(f143,plain,
subset(sK22_skl,relation_dom(sK21_skl)),
inference(cnf_transformation,[status(thm)],[f141]) ).
fof(f144,plain,
~ subset(sK22_skl,relation_inverse_image(sK21_skl,relation_image(sK21_skl,sK22_skl))),
inference(cnf_transformation,[status(thm)],[f141]) ).
fof(f169,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| ~ in(ordered_pair(X3,X1),X0)
| in(X1,relation_image(X0,X2))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f59]) ).
fof(f172,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| ~ in(ordered_pair(X1,X3),X0)
| in(X1,relation_inverse_image(X0,X2))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f69]) ).
fof(f173,plain,
! [X0,X1] :
( in(ordered_pair(X1,sK7_skl(X1,relation_dom(X0),X0)),X0)
| ~ in(X1,relation_dom(X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f84]) ).
fof(f251,plain,
! [X0,X1,X2] :
( in(sK6_skl(X1,X0),X2)
| ~ subset(X0,X2)
| subset(X0,X1) ),
inference(resolution,[status(thm)],[f78,f77]) ).
fof(f296,plain,
! [X0] :
( in(ordered_pair(X0,sK7_skl(X0,relation_dom(sK21_skl),sK21_skl)),sK21_skl)
| ~ in(X0,relation_dom(sK21_skl)) ),
inference(resolution,[status(thm)],[f173,f142]) ).
fof(f307,plain,
! [X0,X1] :
( ~ in(sK7_skl(X0,relation_dom(sK21_skl),sK21_skl),X1)
| in(X0,relation_inverse_image(sK21_skl,X1))
| ~ relation(sK21_skl)
| ~ in(X0,relation_dom(sK21_skl)) ),
inference(resolution,[status(thm)],[f296,f172]) ).
fof(f308,plain,
! [X0,X1] :
( ~ in(X0,X1)
| in(sK7_skl(X0,relation_dom(sK21_skl),sK21_skl),relation_image(sK21_skl,X1))
| ~ relation(sK21_skl)
| ~ in(X0,relation_dom(sK21_skl)) ),
inference(resolution,[status(thm)],[f296,f169]) ).
fof(f311,plain,
! [X0,X1] :
( ~ in(sK7_skl(X0,relation_dom(sK21_skl),sK21_skl),X1)
| in(X0,relation_inverse_image(sK21_skl,X1))
| ~ in(X0,relation_dom(sK21_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f307,f142]) ).
fof(f312,plain,
! [X0,X1] :
( ~ in(X0,X1)
| in(sK7_skl(X0,relation_dom(sK21_skl),sK21_skl),relation_image(sK21_skl,X1))
| ~ in(X0,relation_dom(sK21_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f308,f142]) ).
fof(f348,plain,
! [X0,X1] :
( in(X0,relation_inverse_image(sK21_skl,relation_image(sK21_skl,X1)))
| ~ in(X0,relation_dom(sK21_skl))
| ~ in(X0,X1)
| ~ in(X0,relation_dom(sK21_skl)) ),
inference(resolution,[status(thm)],[f312,f311]) ).
fof(f353,plain,
! [X0,X1] :
( in(X0,relation_inverse_image(sK21_skl,relation_image(sK21_skl,X1)))
| ~ in(X0,X1)
| ~ in(X0,relation_dom(sK21_skl)) ),
inference(duplicate_literals_removal,[status(thm)],[f348]) ).
fof(f373,plain,
! [X0] :
( in(sK6_skl(X0,sK22_skl),relation_dom(sK21_skl))
| subset(sK22_skl,X0) ),
inference(resolution,[status(thm)],[f251,f143]) ).
fof(f407,plain,
! [X0,X1] :
( in(sK6_skl(X0,sK22_skl),relation_inverse_image(sK21_skl,relation_image(sK21_skl,X1)))
| ~ in(sK6_skl(X0,sK22_skl),X1)
| subset(sK22_skl,X0) ),
inference(resolution,[status(thm)],[f373,f353]) ).
fof(f677,plain,
! [X0] :
( subset(sK22_skl,X0)
| in(sK6_skl(X0,sK22_skl),relation_inverse_image(sK21_skl,relation_image(sK21_skl,sK22_skl)))
| subset(sK22_skl,X0) ),
inference(resolution,[status(thm)],[f407,f78]) ).
fof(f681,plain,
! [X0] :
( in(sK6_skl(X0,sK22_skl),relation_inverse_image(sK21_skl,relation_image(sK21_skl,sK22_skl)))
| subset(sK22_skl,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f677]) ).
fof(f684,plain,
( subset(sK22_skl,relation_inverse_image(sK21_skl,relation_image(sK21_skl,sK22_skl)))
| subset(sK22_skl,relation_inverse_image(sK21_skl,relation_image(sK21_skl,sK22_skl))) ),
inference(resolution,[status(thm)],[f681,f79]) ).
fof(f690,plain,
subset(sK22_skl,relation_inverse_image(sK21_skl,relation_image(sK21_skl,sK22_skl))),
inference(duplicate_literals_removal,[status(thm)],[f684]) ).
fof(f691,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f690,f144]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU227+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n009.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 06:00:13 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.46 % Refutation found
% 0.10/0.46 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.50 % Elapsed time: 0.120265 seconds
% 0.19/0.50 % CPU time: 0.584509 seconds
% 0.19/0.50 % Total memory used: 109.901 MB
% 0.19/0.50 % Net memory used: 108.797 MB
%------------------------------------------------------------------------------