%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU263+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 : n018.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 0.08s 0.56s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 54 ( 8 unt; 0 def)
% Number of atoms : 127 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 132 ( 59 ~; 44 |; 16 &)
% ( 3 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 132 ( 124 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] :
( element(C,powerset(cartesian_product2(A,B)))
=> relation(C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B,C] :
( relation_of2(C,A,B)
<=> subset(C,cartesian_product2(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,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(f13,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
<=> relation_of2(C,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A,B,C,D] :
( ( subset(C,D)
& subset(A,B) )
=> subset(cartesian_product2(A,C),cartesian_product2(B,D)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [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(f17,conjecture,
! [A,B,C,D] :
( relation_of2_as_subset(D,C,A)
=> ( subset(relation_rng(D),B)
=> relation_of2_as_subset(D,C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [A,B,C,D] :
( relation_of2_as_subset(D,C,A)
=> ( subset(relation_rng(D),B)
=> relation_of2_as_subset(D,C,B) ) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,axiom,
! [A,B,C] :
( ( subset(B,C)
& subset(A,B) )
=> subset(A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [A] :
( relation(A)
=> subset(A,cartesian_product2(relation_dom(A),relation_rng(A))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,plain,
! [A,B,C] :
( relation(C)
| ~ element(C,powerset(cartesian_product2(A,B))) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f23,plain,
! [C] :
( relation(C)
| ! [A,B] : ~ element(C,powerset(cartesian_product2(A,B))) ),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f24,plain,
! [X0,X1,X2] :
( relation(X0)
| ~ element(X0,powerset(cartesian_product2(X1,X2))) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f25,plain,
! [A,B,C] :
( ( ~ subset(C,cartesian_product2(A,B))
| relation_of2(C,A,B) )
& ( subset(C,cartesian_product2(A,B))
| ~ relation_of2(C,A,B) ) ),
inference(NNF_transformation,[status(thm)],[f2]) ).
fof(f26,plain,
( ! [A,B,C] :
( ~ subset(C,cartesian_product2(A,B))
| relation_of2(C,A,B) )
& ! [A,B,C] :
( subset(C,cartesian_product2(A,B))
| ~ relation_of2(C,A,B) ) ),
inference(miniscoping,[status(thm)],[f25]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ~ subset(X0,cartesian_product2(X1,X2))
| relation_of2(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f29,plain,
! [A,B,C] :
( element(C,powerset(cartesian_product2(A,B)))
| ~ relation_of2_as_subset(C,A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f30,plain,
! [X0,X1,X2] :
( element(X0,powerset(cartesian_product2(X1,X2)))
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f37,plain,
! [A,B,C] :
( ( ~ relation_of2(C,A,B)
| relation_of2_as_subset(C,A,B) )
& ( relation_of2(C,A,B)
| ~ relation_of2_as_subset(C,A,B) ) ),
inference(NNF_transformation,[status(thm)],[f13]) ).
fof(f38,plain,
( ! [A,B,C] :
( ~ relation_of2(C,A,B)
| relation_of2_as_subset(C,A,B) )
& ! [A,B,C] :
( relation_of2(C,A,B)
| ~ relation_of2_as_subset(C,A,B) ) ),
inference(miniscoping,[status(thm)],[f37]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ~ relation_of2(X0,X1,X2)
| relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f43,plain,
! [A,B,C,D] :
( subset(cartesian_product2(A,C),cartesian_product2(B,D))
| ~ subset(C,D)
| ~ subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f44,plain,
! [X0,X1,X2,X3] :
( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f45,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)],[f16]) ).
fof(f46,plain,
! [X0,X1,X2] :
( subset(relation_dom(X0),X1)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f48,plain,
? [A,B,C,D] :
( ~ relation_of2_as_subset(D,C,B)
& subset(relation_rng(D),B)
& relation_of2_as_subset(D,C,A) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f49,plain,
? [C,D] :
( ? [B] :
( ~ relation_of2_as_subset(D,C,B)
& subset(relation_rng(D),B) )
& ? [A] : relation_of2_as_subset(D,C,A) ),
inference(miniscoping,[status(thm)],[f48]) ).
fof(f50,plain,
( ~ relation_of2_as_subset(sK4_skl,sK3_skl,sK6_skl)
& subset(relation_rng(sK4_skl),sK6_skl)
& relation_of2_as_subset(sK4_skl,sK3_skl,sK5_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl,sK5_skl,sK6_skl]),skolemize(C,sK3_skl),skolemize(D,sK4_skl),skolemize(A,sK5_skl),skolemize(B,sK6_skl)],[f49]) ).
fof(f51,plain,
relation_of2_as_subset(sK4_skl,sK3_skl,sK5_skl),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f52,plain,
subset(relation_rng(sK4_skl),sK6_skl),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f53,plain,
~ relation_of2_as_subset(sK4_skl,sK3_skl,sK6_skl),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f54,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f55,plain,
! [A,C] :
( subset(A,C)
| ! [B] :
( ~ subset(B,C)
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f54]) ).
fof(f56,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f57,plain,
! [A] :
( subset(A,cartesian_product2(relation_dom(A),relation_rng(A)))
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f58,plain,
! [X0] :
( subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0)))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f59,plain,
! [A,B] :
( ( ~ subset(A,B)
| element(A,powerset(B)) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(NNF_transformation,[status(thm)],[f21]) ).
fof(f60,plain,
( ! [A,B] :
( ~ subset(A,B)
| element(A,powerset(B)) )
& ! [A,B] :
( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(miniscoping,[status(thm)],[f59]) ).
fof(f61,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f62,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f63,plain,
~ relation_of2(sK4_skl,sK3_skl,sK6_skl),
inference(resolution,[status(thm)],[f40,f53]) ).
fof(f65,plain,
~ subset(sK4_skl,cartesian_product2(sK3_skl,sK6_skl)),
inference(resolution,[status(thm)],[f63,f28]) ).
fof(f67,plain,
! [X0] :
( ~ subset(X0,cartesian_product2(sK3_skl,sK6_skl))
| ~ subset(sK4_skl,X0) ),
inference(resolution,[status(thm)],[f65,f56]) ).
fof(f72,plain,
! [X0,X1,X2] :
( ~ relation_of2_as_subset(X0,X1,X2)
| subset(X0,cartesian_product2(X1,X2)) ),
inference(resolution,[status(thm)],[f61,f30]) ).
fof(f74,plain,
( ~ subset(cartesian_product2(relation_dom(sK4_skl),relation_rng(sK4_skl)),cartesian_product2(sK3_skl,sK6_skl))
| ~ relation(sK4_skl) ),
inference(resolution,[status(thm)],[f58,f67]) ).
fof(f87,plain,
! [X0,X1] :
( ~ element(sK4_skl,powerset(cartesian_product2(X0,X1)))
| ~ subset(cartesian_product2(relation_dom(sK4_skl),relation_rng(sK4_skl)),cartesian_product2(sK3_skl,sK6_skl)) ),
inference(resolution,[status(thm)],[f74,f24]) ).
fof(f95,plain,
subset(sK4_skl,cartesian_product2(sK3_skl,sK5_skl)),
inference(resolution,[status(thm)],[f72,f51]) ).
fof(f111,plain,
! [X0,X1] :
( ~ subset(sK4_skl,cartesian_product2(X0,X1))
| ~ subset(cartesian_product2(relation_dom(sK4_skl),relation_rng(sK4_skl)),cartesian_product2(sK3_skl,sK6_skl)) ),
inference(resolution,[status(thm)],[f87,f62]) ).
fof(f154,plain,
! [X0,X1] :
( ~ subset(relation_rng(sK4_skl),sK6_skl)
| ~ subset(relation_dom(sK4_skl),sK3_skl)
| ~ subset(sK4_skl,cartesian_product2(X0,X1)) ),
inference(resolution,[status(thm)],[f111,f44]) ).
fof(f157,plain,
! [X0,X1] :
( ~ subset(relation_dom(sK4_skl),sK3_skl)
| ~ subset(sK4_skl,cartesian_product2(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f154,f52]) ).
fof(f159,plain,
! [X0,X1,X2] :
( ~ relation_of2_as_subset(sK4_skl,sK3_skl,X2)
| ~ subset(sK4_skl,cartesian_product2(X0,X1)) ),
inference(resolution,[status(thm)],[f157,f46]) ).
fof(f163,plain,
! [X0,X1] : ~ subset(sK4_skl,cartesian_product2(X0,X1)),
inference(resolution,[status(thm)],[f159,f51]) ).
fof(f166,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f95,f163]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU263+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.52 % Computer : n018.cluster.edu
% 0.08/0.52 % Model : x86_64 x86_64
% 0.08/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.52 % Memory : 8046.5625MB
% 0.08/0.52 % OS : Linux 6.8.0-71-generic
% 0.08/0.52 % CPULimit : 300
% 0.08/0.52 % WCLimit : 300
% 0.08/0.52 % DateTime : Mon Sep 21 06:06:44 UTC 2026
% 0.08/0.53 % CPUTime :
% 0.08/0.54 % Drodi V4.1.1
% 0.08/0.56 % Refutation found
% 0.08/0.56 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.59 % Elapsed time: 0.051309 seconds
% 0.15/0.59 % CPU time: 0.172435 seconds
% 0.15/0.59 % Total memory used: 53.843 MB
% 0.15/0.59 % Net memory used: 53.433 MB
%------------------------------------------------------------------------------