%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU245+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 02:19:53 PM UTC 2026
% Result : Theorem 67.34s 9.01s
% Output : CNFRefutation 53.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 58 ( 22 unt; 0 def)
% Number of atoms : 174 ( 33 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 180 ( 64 ~; 67 |; 37 &)
% ( 6 <=>; 5 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 111 ( 98 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f41,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,axiom,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
& in(D,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f58,axiom,
! [A] :
( relation(A)
=> relation_field(A) = set_union2(relation_dom(A),relation_rng(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f60,axiom,
! [A] :
( relation(A)
=> ! [B] : relation_restriction(A,B) = set_intersection2(A,cartesian_product2(B,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,axiom,
! [A] : relation(identity_relation(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f134,axiom,
! [A,B] : set_union2(A,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f201,conjecture,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_restriction(C,B))
<=> ( in(A,cartesian_product2(B,B))
& in(A,C) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f202,negated_conjecture,
~ ! [A,B,C] :
( relation(C)
=> ( in(A,relation_restriction(C,B))
<=> ( in(A,cartesian_product2(B,B))
& in(A,C) ) ) ),
inference(negated_conjecture,[status(cth)],[f201]) ).
fof(f205,lemma,
! [A,B] : subset(set_intersection2(A,B),A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f283,lemma,
! [A] :
( relation_rng(identity_relation(A)) = A
& relation_dom(identity_relation(A)) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f546,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f41]) ).
fof(f547,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)],[f546]) ).
fof(f548,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)],[f547]) ).
fof(f549,plain,
( ! [A,B] :
( ( ~ in(sK43_skl(B,A),B)
& in(sK43_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,[sK43_skl]),skolemize(C,sK43_skl(B,A))],[f548]) ).
fof(f550,plain,
! [X0,X1,X2] :
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f549]) ).
fof(f562,plain,
! [A,B,C] :
( ( ? [D] :
( ( ( in(D,B)
& in(D,A) )
| in(D,C) )
& ( ~ in(D,B)
| ~ in(D,A)
| ~ in(D,C) ) )
| C = set_intersection2(A,B) )
& ( ! [D] :
( ( ~ in(D,B)
| ~ in(D,A)
| in(D,C) )
& ( ( in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_intersection2(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f43]) ).
fof(f563,plain,
( ! [A,B,C] :
( ? [D] :
( ( ( in(D,B)
& in(D,A) )
| in(D,C) )
& ( ~ in(D,B)
| ~ in(D,A)
| ~ in(D,C) ) )
| C = set_intersection2(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ~ in(D,B)
| ~ in(D,A)
| in(D,C) )
& ! [D] :
( ( in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_intersection2(A,B) ) ),
inference(miniscoping,[status(thm)],[f562]) ).
fof(f564,plain,
( ! [A,B,C] :
( ( ( ( in(sK46_skl(C,B,A),B)
& in(sK46_skl(C,B,A),A) )
| in(sK46_skl(C,B,A),C) )
& ( ~ in(sK46_skl(C,B,A),B)
| ~ in(sK46_skl(C,B,A),A)
| ~ in(sK46_skl(C,B,A),C) ) )
| C = set_intersection2(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ~ in(D,B)
| ~ in(D,A)
| in(D,C) )
& ! [D] :
( ( in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_intersection2(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK46_skl]),skolemize(D,sK46_skl(C,B,A))],[f563]) ).
fof(f566,plain,
! [X0,X1,X2,X3] :
( in(X3,X2)
| ~ in(X3,X0)
| X0 != set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f564]) ).
fof(f567,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| ~ in(X3,X1)
| in(X3,X0)
| X0 != set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f564]) ).
fof(f662,plain,
! [A] :
( relation_field(A) = set_union2(relation_dom(A),relation_rng(A))
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f58]) ).
fof(f663,plain,
! [X0] :
( relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f662]) ).
fof(f674,plain,
! [A] :
( ! [B] : relation_restriction(A,B) = set_intersection2(A,cartesian_product2(B,B))
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f60]) ).
fof(f675,plain,
! [X0,X1] :
( relation_restriction(X0,X1) = set_intersection2(X0,cartesian_product2(X1,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f674]) ).
fof(f751,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[status(thm)],[f96]) ).
fof(f844,plain,
! [A] : set_union2(A,A) = A,
inference(miniscoping,[status(thm)],[f134]) ).
fof(f845,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f844]) ).
fof(f1080,plain,
? [A,B,C] :
( ( in(A,relation_restriction(C,B))
<~> ( in(A,cartesian_product2(B,B))
& in(A,C) ) )
& relation(C) ),
inference(pre_NNF_transformation,[status(thm)],[f202]) ).
fof(f1081,plain,
? [A,B,C] :
( ( ~ in(A,cartesian_product2(B,B))
| ~ in(A,C)
| ~ in(A,relation_restriction(C,B)) )
& ( ( in(A,cartesian_product2(B,B))
& in(A,C) )
| in(A,relation_restriction(C,B)) )
& relation(C) ),
inference(NNF_transformation,[status(thm)],[f1080]) ).
fof(f1082,plain,
? [C] :
( ? [A,B] :
( ( ~ in(A,cartesian_product2(B,B))
| ~ in(A,C)
| ~ in(A,relation_restriction(C,B)) )
& ( ( in(A,cartesian_product2(B,B))
& in(A,C) )
| in(A,relation_restriction(C,B)) ) )
& relation(C) ),
inference(miniscoping,[status(thm)],[f1081]) ).
fof(f1083,plain,
( ( ~ in(sK104_skl,cartesian_product2(sK105_skl,sK105_skl))
| ~ in(sK104_skl,sK103_skl)
| ~ in(sK104_skl,relation_restriction(sK103_skl,sK105_skl)) )
& ( ( in(sK104_skl,cartesian_product2(sK105_skl,sK105_skl))
& in(sK104_skl,sK103_skl) )
| in(sK104_skl,relation_restriction(sK103_skl,sK105_skl)) )
& relation(sK103_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK103_skl,sK104_skl,sK105_skl]),skolemize(C,sK103_skl),skolemize(A,sK104_skl),skolemize(B,sK105_skl)],[f1082]) ).
fof(f1084,plain,
relation(sK103_skl),
inference(cnf_transformation,[status(thm)],[f1083]) ).
fof(f1085,plain,
( in(sK104_skl,sK103_skl)
| in(sK104_skl,relation_restriction(sK103_skl,sK105_skl)) ),
inference(cnf_transformation,[status(thm)],[f1083]) ).
fof(f1086,plain,
( in(sK104_skl,cartesian_product2(sK105_skl,sK105_skl))
| in(sK104_skl,relation_restriction(sK103_skl,sK105_skl)) ),
inference(cnf_transformation,[status(thm)],[f1083]) ).
fof(f1087,plain,
( ~ in(sK104_skl,cartesian_product2(sK105_skl,sK105_skl))
| ~ in(sK104_skl,sK103_skl)
| ~ in(sK104_skl,relation_restriction(sK103_skl,sK105_skl)) ),
inference(cnf_transformation,[status(thm)],[f1083]) ).
fof(f1094,plain,
! [X0,X1] : subset(set_intersection2(X0,X1),X0),
inference(cnf_transformation,[status(thm)],[f205]) ).
fof(f1335,plain,
( ! [A] : relation_rng(identity_relation(A)) = A
& ! [A] : relation_dom(identity_relation(A)) = A ),
inference(miniscoping,[status(thm)],[f283]) ).
fof(f1336,plain,
! [X0] : relation_dom(identity_relation(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f1335]) ).
fof(f1337,plain,
! [X0] : relation_rng(identity_relation(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f1335]) ).
fof(f1452,plain,
! [X0] : relation_restriction(sK103_skl,X0) = set_intersection2(sK103_skl,cartesian_product2(X0,X0)),
inference(resolution,[status(thm)],[f675,f1084]) ).
fof(f5845,plain,
! [X0] : subset(relation_restriction(sK103_skl,X0),sK103_skl),
inference(paramodulation,[status(thm)],[f1452,f1094]) ).
fof(f9542,plain,
! [X0,X1] :
( in(X0,sK103_skl)
| ~ in(X0,relation_restriction(sK103_skl,X1)) ),
inference(resolution,[status(thm)],[f550,f5845]) ).
fof(f10593,plain,
! [X0,X1] :
( in(sK104_skl,cartesian_product2(sK105_skl,sK105_skl))
| in(sK104_skl,X1)
| relation_restriction(sK103_skl,sK105_skl) != set_intersection2(X0,X1) ),
inference(resolution,[status(thm)],[f566,f1086]) ).
fof(f11481,plain,
in(sK104_skl,sK103_skl),
inference(backward_subsumption_resolution,[status(thm)],[f1085,f9542]) ).
fof(f11482,plain,
( ~ in(sK104_skl,cartesian_product2(sK105_skl,sK105_skl))
| ~ in(sK104_skl,relation_restriction(sK103_skl,sK105_skl)) ),
inference(backward_subsumption_resolution,[status(thm)],[f1087,f9542]) ).
fof(f11518,plain,
! [X0,X1] :
( ~ in(sK104_skl,X1)
| in(sK104_skl,X0)
| X0 != set_intersection2(sK103_skl,X1) ),
inference(resolution,[status(thm)],[f11481,f567]) ).
fof(f12515,plain,
( in(sK104_skl,cartesian_product2(sK105_skl,sK105_skl))
| in(sK104_skl,cartesian_product2(sK105_skl,sK105_skl)) ),
inference(resolution,[status(thm)],[f10593,f1452]) ).
fof(f12532,plain,
in(sK104_skl,cartesian_product2(sK105_skl,sK105_skl)),
inference(duplicate_literals_removal,[status(thm)],[f12515]) ).
fof(f12983,plain,
~ in(sK104_skl,relation_restriction(sK103_skl,sK105_skl)),
inference(backward_subsumption_resolution,[status(thm)],[f11482,f12532]) ).
fof(f13346,plain,
! [X0] :
( in(sK104_skl,X0)
| X0 != set_intersection2(sK103_skl,cartesian_product2(sK105_skl,sK105_skl)) ),
inference(resolution,[status(thm)],[f11518,f12532]) ).
fof(f13355,plain,
! [X0] :
( in(sK104_skl,X0)
| X0 != relation_restriction(sK103_skl,sK105_skl) ),
inference(forward_demodulation,[status(thm)],[f1452,f13346]) ).
fof(f16584,plain,
! [X0] : relation_field(identity_relation(X0)) = set_union2(relation_dom(identity_relation(X0)),relation_rng(identity_relation(X0))),
inference(resolution,[status(thm)],[f663,f751]) ).
fof(f16632,plain,
! [X0] : relation_field(identity_relation(X0)) = set_union2(X0,relation_rng(identity_relation(X0))),
inference(forward_demodulation,[status(thm)],[f1336,f16584]) ).
fof(f16633,plain,
! [X0] : relation_field(identity_relation(X0)) = set_union2(X0,X0),
inference(forward_demodulation,[status(thm)],[f1337,f16632]) ).
fof(f16634,plain,
! [X0] : relation_field(identity_relation(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f845,f16633]) ).
fof(f20374,plain,
in(sK104_skl,relation_field(identity_relation(relation_restriction(sK103_skl,sK105_skl)))),
inference(resolution,[status(thm)],[f13355,f16634]) ).
fof(f20387,plain,
in(sK104_skl,relation_restriction(sK103_skl,sK105_skl)),
inference(forward_demodulation,[status(thm)],[f16634,f20374]) ).
fof(f20388,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f20387,f12983]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU245+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n003.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 06:04:46 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.14/0.40 % Drodi V4.1.1
% 67.34/9.01 % Refutation found
% 67.34/9.01 % SZS status Theorem for theBenchmark: Theorem is valid
% 67.34/9.01 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 53.47/9.05 % Elapsed time: 8.677010 seconds
% 53.47/9.05 % CPU time: 68.405843 seconds
% 53.47/9.05 % Total memory used: 433.527 MB
% 53.47/9.05 % Net memory used: 378.486 MB
%------------------------------------------------------------------------------