%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU211+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 26.93s 3.92s
% Output : CNFRefutation 27.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of formulae : 38 ( 5 unt; 0 def)
% Number of atoms : 160 ( 11 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 204 ( 82 ~; 81 |; 29 &)
% ( 6 <=>; 6 =>; 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 : 9 ( 9 usr; 3 con; 0-4 aty)
% Number of variables : 123 ( 107 !; 16 ?)
% 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/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,conjecture,
! [A,B,C] :
( relation(C)
=> ( subset(A,B)
=> subset(relation_inverse_image(C,A),relation_inverse_image(C,B)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
~ ! [A,B,C] :
( relation(C)
=> ( subset(A,B)
=> subset(relation_inverse_image(C,A),relation_inverse_image(C,B)) ) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f43,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(f44,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)],[f43]) ).
fof(f45,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)],[f44]) ).
fof(f46,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))],[f45]) ).
fof(f47,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)],[f46]) ).
fof(f48,plain,
! [X0,X1,X2,X3] :
( in(sK0_skl(X3,X1,X2,X0),X2)
| ~ in(X3,X1)
| X1 != relation_inverse_image(X0,X2)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f49,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)],[f46]) ).
fof(f53,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f54,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)],[f53]) ).
fof(f55,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)],[f54]) ).
fof(f56,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))],[f55]) ).
fof(f57,plain,
! [X0,X1,X2] :
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f58,plain,
! [X0,X1] :
( in(sK3_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f59,plain,
! [X0,X1] :
( ~ in(sK3_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f89,plain,
? [A,B,C] :
( ~ subset(relation_inverse_image(C,A),relation_inverse_image(C,B))
& subset(A,B)
& relation(C) ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f90,plain,
? [C] :
( ? [A,B] :
( ~ subset(relation_inverse_image(C,A),relation_inverse_image(C,B))
& subset(A,B) )
& relation(C) ),
inference(miniscoping,[status(thm)],[f89]) ).
fof(f91,plain,
( ~ subset(relation_inverse_image(sK11_skl,sK12_skl),relation_inverse_image(sK11_skl,sK13_skl))
& subset(sK12_skl,sK13_skl)
& relation(sK11_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl,sK12_skl,sK13_skl]),skolemize(C,sK11_skl),skolemize(A,sK12_skl),skolemize(B,sK13_skl)],[f90]) ).
fof(f92,plain,
relation(sK11_skl),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f93,plain,
subset(sK12_skl,sK13_skl),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f94,plain,
~ subset(relation_inverse_image(sK11_skl,sK12_skl),relation_inverse_image(sK11_skl,sK13_skl)),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f117,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)],[f47]) ).
fof(f118,plain,
! [X0,X1,X2] :
( in(sK0_skl(X1,relation_inverse_image(X0,X2),X2,X0),X2)
| ~ in(X1,relation_inverse_image(X0,X2))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f48]) ).
fof(f119,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)],[f49]) ).
fof(f120,plain,
! [X0] :
( in(X0,sK13_skl)
| ~ in(X0,sK12_skl) ),
inference(resolution,[status(thm)],[f57,f93]) ).
fof(f171,plain,
! [X0,X1,X2,X3] :
( ~ in(X1,relation_inverse_image(X0,X3))
| ~ relation(X0)
| ~ in(sK0_skl(X1,relation_inverse_image(X0,X3),X3,X0),X2)
| in(X1,relation_inverse_image(X0,X2))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f119,f117]) ).
fof(f173,plain,
! [X0,X1,X2,X3] :
( ~ in(X1,relation_inverse_image(X0,X3))
| ~ in(sK0_skl(X1,relation_inverse_image(X0,X3),X3,X0),X2)
| in(X1,relation_inverse_image(X0,X2))
| ~ relation(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f171]) ).
fof(f1812,plain,
! [X0,X1,X2] :
( ~ in(sK0_skl(X1,relation_inverse_image(X0,X2),X2,X0),sK12_skl)
| ~ in(X1,relation_inverse_image(X0,X2))
| in(X1,relation_inverse_image(X0,sK13_skl))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f173,f120]) ).
fof(f2122,plain,
! [X0,X1] :
( ~ in(X1,relation_inverse_image(X0,sK12_skl))
| ~ relation(X0)
| ~ in(X1,relation_inverse_image(X0,sK12_skl))
| in(X1,relation_inverse_image(X0,sK13_skl))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f1812,f118]) ).
fof(f2123,plain,
! [X0,X1] :
( ~ in(X1,relation_inverse_image(X0,sK12_skl))
| in(X1,relation_inverse_image(X0,sK13_skl))
| ~ relation(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f2122]) ).
fof(f3235,plain,
! [X0,X1] :
( subset(X1,relation_inverse_image(X0,sK13_skl))
| ~ in(sK3_skl(relation_inverse_image(X0,sK13_skl),X1),relation_inverse_image(X0,sK12_skl))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f2123,f59]) ).
fof(f5960,plain,
! [X0] :
( subset(relation_inverse_image(X0,sK12_skl),relation_inverse_image(X0,sK13_skl))
| subset(relation_inverse_image(X0,sK12_skl),relation_inverse_image(X0,sK13_skl))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f3235,f58]) ).
fof(f5966,plain,
! [X0] :
( subset(relation_inverse_image(X0,sK12_skl),relation_inverse_image(X0,sK13_skl))
| ~ relation(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f5960]) ).
fof(f5967,plain,
~ relation(sK11_skl),
inference(resolution,[status(thm)],[f5966,f94]) ).
fof(f5972,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f5967,f92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU211+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n014.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 05:58:19 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 26.93/3.92 % Refutation found
% 26.93/3.92 % SZS status Theorem for theBenchmark: Theorem is valid
% 26.93/3.92 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 27.70/3.99 % Elapsed time: 3.612601 seconds
% 27.70/3.99 % CPU time: 28.143805 seconds
% 27.70/3.99 % Total memory used: 242.225 MB
% 27.70/3.99 % Net memory used: 214.540 MB
%------------------------------------------------------------------------------