%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU262+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 : n006.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 02:19:56 PM UTC 2026
% Result : Theorem 0.06s 0.64s
% Output : CNFRefutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 65 ( 4 unt; 2 def)
% Number of atoms : 235 ( 18 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 278 ( 108 ~; 114 |; 35 &)
% ( 14 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 3 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 3 con; 0-3 aty)
% Number of variables : 208 ( 187 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B,C] :
( element(C,powerset(cartesian_product2(A,B)))
=> relation(C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,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(f6,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
=> element(C,powerset(cartesian_product2(A,B))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(B,D)
& in(A,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,conjecture,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
=> ( subset(relation_rng(C),B)
& subset(relation_dom(C),A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ ! [A,B,C] :
( relation_of2_as_subset(C,A,B)
=> ( subset(relation_rng(C),B)
& subset(relation_dom(C),A) ) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f33,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,plain,
! [A,B,C] :
( relation(C)
| ~ element(C,powerset(cartesian_product2(A,B))) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f42,plain,
! [C] :
( relation(C)
| ! [A,B] : ~ element(C,powerset(cartesian_product2(A,B))) ),
inference(miniscoping,[status(thm)],[f41]) ).
fof(f43,plain,
! [X0,X1,X2] :
( relation(X0)
| ~ element(X0,powerset(cartesian_product2(X1,X2))) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f45,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f46,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)],[f45]) ).
fof(f47,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)],[f46]) ).
fof(f48,plain,
( ! [A,B] :
( ( ~ in(sK0_skl(B,A),B)
& in(sK0_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,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f47]) ).
fof(f49,plain,
! [X0,X1,X2] :
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f50,plain,
! [X0,X1] :
( in(sK0_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f51,plain,
! [X0,X1] :
( ~ in(sK0_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f52,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)],[f5]) ).
fof(f53,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)],[f52]) ).
fof(f54,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)],[f53]) ).
fof(f55,plain,
! [A] :
( ( ! [B] :
( ( ( in(ordered_pair(sK2_skl(B,A),sK3_skl(B,A)),A)
| in(sK2_skl(B,A),B) )
& ( ! [D] : ~ in(ordered_pair(sK2_skl(B,A),D),A)
| ~ in(sK2_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,sK1_skl(C,B,A)),A)
| ~ in(C,B) ) )
| B != relation_dom(A) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl,sK3_skl]),skolemize(D,sK1_skl(C,B,A)),skolemize(C,sK2_skl(B,A)),skolemize(D,sK3_skl(B,A))],[f54]) ).
fof(f56,plain,
! [X0,X1,X2] :
( in(ordered_pair(X2,sK1_skl(X2,X1,X0)),X0)
| ~ in(X2,X1)
| X1 != relation_dom(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f60,plain,
! [A] :
( ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) )
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f61,plain,
! [A] :
( ! [B] :
( ( ? [C] :
( ( ? [D] : in(ordered_pair(D,C),A)
| in(C,B) )
& ( ! [D] : ~ in(ordered_pair(D,C),A)
| ~ in(C,B) ) )
| B = relation_rng(A) )
& ( ! [C] :
( ( ! [D] : ~ in(ordered_pair(D,C),A)
| in(C,B) )
& ( ? [D] : in(ordered_pair(D,C),A)
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f60]) ).
fof(f62,plain,
! [A] :
( ( ! [B] :
( ? [C] :
( ( ? [D] : in(ordered_pair(D,C),A)
| in(C,B) )
& ( ! [D] : ~ in(ordered_pair(D,C),A)
| ~ in(C,B) ) )
| B = relation_rng(A) )
& ! [B] :
( ( ! [C] :
( ! [D] : ~ in(ordered_pair(D,C),A)
| in(C,B) )
& ! [C] :
( ? [D] : in(ordered_pair(D,C),A)
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f61]) ).
fof(f63,plain,
! [A] :
( ( ! [B] :
( ( ( in(ordered_pair(sK6_skl(B,A),sK5_skl(B,A)),A)
| in(sK5_skl(B,A),B) )
& ( ! [D] : ~ in(ordered_pair(D,sK5_skl(B,A)),A)
| ~ in(sK5_skl(B,A),B) ) )
| B = relation_rng(A) )
& ! [B] :
( ( ! [C] :
( ! [D] : ~ in(ordered_pair(D,C),A)
| in(C,B) )
& ! [C] :
( in(ordered_pair(sK4_skl(C,B,A),C),A)
| ~ in(C,B) ) )
| B != relation_rng(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))],[f62]) ).
fof(f64,plain,
! [X0,X1,X2] :
( in(ordered_pair(sK4_skl(X2,X1,X0),X2),X0)
| ~ in(X2,X1)
| X1 != relation_rng(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f69,plain,
! [A,B,C] :
( element(C,powerset(cartesian_product2(A,B)))
| ~ relation_of2_as_subset(C,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f70,plain,
! [X0,X1,X2] :
( element(X0,powerset(cartesian_product2(X1,X2)))
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f89,plain,
! [A,B,C,D] :
( ( ~ in(B,D)
| ~ in(A,C)
| in(ordered_pair(A,B),cartesian_product2(C,D)) )
& ( ( in(B,D)
& in(A,C) )
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ) ),
inference(NNF_transformation,[status(thm)],[f28]) ).
fof(f90,plain,
( ! [A,B,C,D] :
( ~ in(B,D)
| ~ in(A,C)
| in(ordered_pair(A,B),cartesian_product2(C,D)) )
& ! [A,B,C,D] :
( ( in(B,D)
& in(A,C) )
| ~ in(ordered_pair(A,B),cartesian_product2(C,D)) ) ),
inference(miniscoping,[status(thm)],[f89]) ).
fof(f91,plain,
! [X0,X1,X2,X3] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f90]) ).
fof(f92,plain,
! [X0,X1,X2,X3] :
( in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f90]) ).
fof(f94,plain,
? [A,B,C] :
( ( ~ subset(relation_rng(C),B)
| ~ subset(relation_dom(C),A) )
& relation_of2_as_subset(C,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f95,plain,
( ( ~ subset(relation_rng(sK14_skl),sK13_skl)
| ~ subset(relation_dom(sK14_skl),sK12_skl) )
& relation_of2_as_subset(sK14_skl,sK12_skl,sK13_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12_skl,sK13_skl,sK14_skl]),skolemize(A,sK12_skl),skolemize(B,sK13_skl),skolemize(C,sK14_skl)],[f94]) ).
fof(f96,plain,
relation_of2_as_subset(sK14_skl,sK12_skl,sK13_skl),
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f97,plain,
( ~ subset(relation_rng(sK14_skl),sK13_skl)
| ~ subset(relation_dom(sK14_skl),sK12_skl) ),
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f102,plain,
! [A,B] :
( ( ~ subset(A,B)
| element(A,powerset(B)) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(NNF_transformation,[status(thm)],[f33]) ).
fof(f103,plain,
( ! [A,B] :
( ~ subset(A,B)
| element(A,powerset(B)) )
& ! [A,B] :
( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(miniscoping,[status(thm)],[f102]) ).
fof(f104,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f120,definition,
( sQ0_spl
<=> subset(relation_dom(sK14_skl),sK12_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f123,definition,
( sQ1_spl
<=> subset(relation_rng(sK14_skl),sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f126,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f97,f120,f123]) ).
fof(f127,plain,
! [X0,X1] :
( in(ordered_pair(X1,sK1_skl(X1,relation_dom(X0),X0)),X0)
| ~ in(X1,relation_dom(X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f56]) ).
fof(f129,plain,
! [X0,X1] :
( in(ordered_pair(sK4_skl(X1,relation_rng(X0),X0),X1),X0)
| ~ in(X1,relation_rng(X0))
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f64]) ).
fof(f137,plain,
! [X0,X1,X2] :
( ~ relation_of2_as_subset(X0,X1,X2)
| relation(X0) ),
inference(resolution,[status(thm)],[f43,f70]) ).
fof(f143,plain,
! [X0,X1,X2] :
( ~ relation_of2_as_subset(X0,X1,X2)
| subset(X0,cartesian_product2(X1,X2)) ),
inference(resolution,[status(thm)],[f104,f70]) ).
fof(f159,plain,
! [X0,X1,X2,X3] :
( in(X3,cartesian_product2(X1,X2))
| ~ in(X3,X0)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(resolution,[status(thm)],[f143,f49]) ).
fof(f452,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(ordered_pair(X0,X4),X2)
| ~ relation_of2_as_subset(X2,X1,X3)
| in(X0,X1) ),
inference(resolution,[status(thm)],[f91,f159]) ).
fof(f460,plain,
! [X0,X1,X2,X3] :
( ~ in(X0,relation_dom(X2))
| ~ relation(X2)
| ~ relation_of2_as_subset(X2,X1,X3)
| in(X0,X1) ),
inference(resolution,[status(thm)],[f452,f127]) ).
fof(f467,plain,
! [X0,X1,X2,X3] :
( ~ in(X0,relation_dom(X2))
| ~ relation_of2_as_subset(X2,X1,X3)
| in(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f460,f137]) ).
fof(f469,plain,
! [X0] :
( ~ in(X0,relation_dom(sK14_skl))
| in(X0,sK12_skl) ),
inference(resolution,[status(thm)],[f467,f96]) ).
fof(f477,plain,
! [X0] :
( subset(relation_dom(sK14_skl),X0)
| in(sK0_skl(X0,relation_dom(sK14_skl)),sK12_skl) ),
inference(resolution,[status(thm)],[f469,f50]) ).
fof(f509,plain,
( subset(relation_dom(sK14_skl),sK12_skl)
| subset(relation_dom(sK14_skl),sK12_skl) ),
inference(resolution,[status(thm)],[f477,f51]) ).
fof(f512,plain,
sQ0_spl,
inference(split_clause,[status(thm)],[f509,f120]) ).
fof(f642,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(ordered_pair(X4,X0),X2)
| ~ relation_of2_as_subset(X2,X3,X1)
| in(X0,X1) ),
inference(resolution,[status(thm)],[f92,f159]) ).
fof(f745,plain,
! [X0,X1,X2,X3] :
( ~ in(X0,relation_rng(X2))
| ~ relation(X2)
| ~ relation_of2_as_subset(X2,X3,X1)
| in(X0,X1) ),
inference(resolution,[status(thm)],[f642,f129]) ).
fof(f752,plain,
! [X0,X1,X2,X3] :
( ~ in(X0,relation_rng(X2))
| ~ relation_of2_as_subset(X2,X3,X1)
| in(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f745,f137]) ).
fof(f756,plain,
! [X0] :
( ~ in(X0,relation_rng(sK14_skl))
| in(X0,sK13_skl) ),
inference(resolution,[status(thm)],[f752,f96]) ).
fof(f771,plain,
! [X0] :
( subset(relation_rng(sK14_skl),X0)
| in(sK0_skl(X0,relation_rng(sK14_skl)),sK13_skl) ),
inference(resolution,[status(thm)],[f756,f50]) ).
fof(f841,plain,
( subset(relation_rng(sK14_skl),sK13_skl)
| subset(relation_rng(sK14_skl),sK13_skl) ),
inference(resolution,[status(thm)],[f771,f51]) ).
fof(f844,plain,
sQ1_spl,
inference(split_clause,[status(thm)],[f841,f123]) ).
fof(f852,plain,
$false,
inference(sat_refutation,[status(thm)],[f126,f512,f844]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU262+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.41 % Computer : n006.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Mon Sep 21 06:04:27 UTC 2026
% 0.06/0.42 % CPUTime :
% 0.06/0.43 % Drodi V4.1.1
% 0.06/0.64 % Refutation found
% 0.06/0.64 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.06/0.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.06/0.69 % Elapsed time: 0.253634 seconds
% 0.06/0.69 % CPU time: 1.564857 seconds
% 0.06/0.69 % Total memory used: 119.783 MB
% 0.06/0.69 % Net memory used: 117.096 MB
%------------------------------------------------------------------------------