TSTP Solution File: SEU262+1 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU262+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed May 31 12:36:30 EDT 2023
% Result : Theorem 1.68s 0.64s
% Output : CNFRefutation 1.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 65 ( 4 unt; 0 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/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(A,C)
& in(B,D) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,conjecture,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
=> ( subset(relation_dom(C),A)
& subset(relation_rng(C),B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ ! [A,B,C] :
( relation_of2_as_subset(C,A,B)
=> ( subset(relation_dom(C),A)
& subset(relation_rng(C),B) ) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f33,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,plain,
! [A,B,C] :
( ~ element(C,powerset(cartesian_product2(A,B)))
| relation(C) ),
inference(pre_NNF_transformation,[status(esa)],[f2]) ).
fof(f42,plain,
! [C] :
( ! [A,B] : ~ element(C,powerset(cartesian_product2(A,B)))
| relation(C) ),
inference(miniscoping,[status(esa)],[f41]) ).
fof(f43,plain,
! [X0,X1,X2] :
( ~ element(X0,powerset(cartesian_product2(X1,X2)))
| relation(X0) ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f45,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( ~ in(C,A)
| in(C,B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f4]) ).
fof(f46,plain,
! [A,B] :
( ( ~ subset(A,B)
| ! [C] :
( ~ in(C,A)
| in(C,B) ) )
& ( subset(A,B)
| ? [C] :
( in(C,A)
& ~ in(C,B) ) ) ),
inference(NNF_transformation,[status(esa)],[f45]) ).
fof(f47,plain,
( ! [A,B] :
( ~ subset(A,B)
| ! [C] :
( ~ in(C,A)
| in(C,B) ) )
& ! [A,B] :
( subset(A,B)
| ? [C] :
( in(C,A)
& ~ in(C,B) ) ) ),
inference(miniscoping,[status(esa)],[f46]) ).
fof(f48,plain,
( ! [A,B] :
( ~ subset(A,B)
| ! [C] :
( ~ in(C,A)
| in(C,B) ) )
& ! [A,B] :
( subset(A,B)
| ( in(sk0_0(B,A),A)
& ~ in(sk0_0(B,A),B) ) ) ),
inference(skolemization,[status(esa)],[f47]) ).
fof(f49,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| ~ in(X2,X0)
| in(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f48]) ).
fof(f50,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sk0_0(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f48]) ).
fof(f51,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sk0_0(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f48]) ).
fof(f52,plain,
! [A] :
( ~ relation(A)
| ! [B] :
( B = relation_dom(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f5]) ).
fof(f53,plain,
! [A] :
( ~ relation(A)
| ! [B] :
( ( B != relation_dom(A)
| ! [C] :
( ( ~ in(C,B)
| ? [D] : in(ordered_pair(C,D),A) )
& ( in(C,B)
| ! [D] : ~ in(ordered_pair(C,D),A) ) ) )
& ( B = relation_dom(A)
| ? [C] :
( ( ~ in(C,B)
| ! [D] : ~ in(ordered_pair(C,D),A) )
& ( in(C,B)
| ? [D] : in(ordered_pair(C,D),A) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f52]) ).
fof(f54,plain,
! [A] :
( ~ relation(A)
| ( ! [B] :
( B != relation_dom(A)
| ( ! [C] :
( ~ in(C,B)
| ? [D] : in(ordered_pair(C,D),A) )
& ! [C] :
( in(C,B)
| ! [D] : ~ in(ordered_pair(C,D),A) ) ) )
& ! [B] :
( B = relation_dom(A)
| ? [C] :
( ( ~ in(C,B)
| ! [D] : ~ in(ordered_pair(C,D),A) )
& ( in(C,B)
| ? [D] : in(ordered_pair(C,D),A) ) ) ) ) ),
inference(miniscoping,[status(esa)],[f53]) ).
fof(f55,plain,
! [A] :
( ~ relation(A)
| ( ! [B] :
( B != relation_dom(A)
| ( ! [C] :
( ~ in(C,B)
| in(ordered_pair(C,sk0_1(C,B,A)),A) )
& ! [C] :
( in(C,B)
| ! [D] : ~ in(ordered_pair(C,D),A) ) ) )
& ! [B] :
( B = relation_dom(A)
| ( ( ~ in(sk0_2(B,A),B)
| ! [D] : ~ in(ordered_pair(sk0_2(B,A),D),A) )
& ( in(sk0_2(B,A),B)
| in(ordered_pair(sk0_2(B,A),sk0_3(B,A)),A) ) ) ) ) ),
inference(skolemization,[status(esa)],[f54]) ).
fof(f56,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| X1 != relation_dom(X0)
| ~ in(X2,X1)
| in(ordered_pair(X2,sk0_1(X2,X1,X0)),X0) ),
inference(cnf_transformation,[status(esa)],[f55]) ).
fof(f60,plain,
! [A] :
( ~ relation(A)
| ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f6]) ).
fof(f61,plain,
! [A] :
( ~ relation(A)
| ! [B] :
( ( B != relation_rng(A)
| ! [C] :
( ( ~ in(C,B)
| ? [D] : in(ordered_pair(D,C),A) )
& ( in(C,B)
| ! [D] : ~ in(ordered_pair(D,C),A) ) ) )
& ( B = relation_rng(A)
| ? [C] :
( ( ~ in(C,B)
| ! [D] : ~ in(ordered_pair(D,C),A) )
& ( in(C,B)
| ? [D] : in(ordered_pair(D,C),A) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f60]) ).
fof(f62,plain,
! [A] :
( ~ relation(A)
| ( ! [B] :
( B != relation_rng(A)
| ( ! [C] :
( ~ in(C,B)
| ? [D] : in(ordered_pair(D,C),A) )
& ! [C] :
( in(C,B)
| ! [D] : ~ in(ordered_pair(D,C),A) ) ) )
& ! [B] :
( B = relation_rng(A)
| ? [C] :
( ( ~ in(C,B)
| ! [D] : ~ in(ordered_pair(D,C),A) )
& ( in(C,B)
| ? [D] : in(ordered_pair(D,C),A) ) ) ) ) ),
inference(miniscoping,[status(esa)],[f61]) ).
fof(f63,plain,
! [A] :
( ~ relation(A)
| ( ! [B] :
( B != relation_rng(A)
| ( ! [C] :
( ~ in(C,B)
| in(ordered_pair(sk0_4(C,B,A),C),A) )
& ! [C] :
( in(C,B)
| ! [D] : ~ in(ordered_pair(D,C),A) ) ) )
& ! [B] :
( B = relation_rng(A)
| ( ( ~ in(sk0_5(B,A),B)
| ! [D] : ~ in(ordered_pair(D,sk0_5(B,A)),A) )
& ( in(sk0_5(B,A),B)
| in(ordered_pair(sk0_6(B,A),sk0_5(B,A)),A) ) ) ) ) ),
inference(skolemization,[status(esa)],[f62]) ).
fof(f64,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| X1 != relation_rng(X0)
| ~ in(X2,X1)
| in(ordered_pair(sk0_4(X2,X1,X0),X2),X0) ),
inference(cnf_transformation,[status(esa)],[f63]) ).
fof(f69,plain,
! [A,B,C] :
( ~ relation_of2_as_subset(C,A,B)
| element(C,powerset(cartesian_product2(A,B))) ),
inference(pre_NNF_transformation,[status(esa)],[f18]) ).
fof(f70,plain,
! [X0,X1,X2] :
( ~ relation_of2_as_subset(X0,X1,X2)
| element(X0,powerset(cartesian_product2(X1,X2))) ),
inference(cnf_transformation,[status(esa)],[f69]) ).
fof(f89,plain,
! [A,B,C,D] :
( ( ~ in(ordered_pair(A,B),cartesian_product2(C,D))
| ( in(A,C)
& in(B,D) ) )
& ( in(ordered_pair(A,B),cartesian_product2(C,D))
| ~ in(A,C)
| ~ in(B,D) ) ),
inference(NNF_transformation,[status(esa)],[f28]) ).
fof(f90,plain,
( ! [A,B,C,D] :
( ~ in(ordered_pair(A,B),cartesian_product2(C,D))
| ( in(A,C)
& in(B,D) ) )
& ! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
| ~ in(A,C)
| ~ in(B,D) ) ),
inference(miniscoping,[status(esa)],[f89]) ).
fof(f91,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f90]) ).
fof(f92,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(cnf_transformation,[status(esa)],[f90]) ).
fof(f94,plain,
? [A,B,C] :
( relation_of2_as_subset(C,A,B)
& ( ~ subset(relation_dom(C),A)
| ~ subset(relation_rng(C),B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f30]) ).
fof(f95,plain,
( relation_of2_as_subset(sk0_14,sk0_12,sk0_13)
& ( ~ subset(relation_dom(sk0_14),sk0_12)
| ~ subset(relation_rng(sk0_14),sk0_13) ) ),
inference(skolemization,[status(esa)],[f94]) ).
fof(f96,plain,
relation_of2_as_subset(sk0_14,sk0_12,sk0_13),
inference(cnf_transformation,[status(esa)],[f95]) ).
fof(f97,plain,
( ~ subset(relation_dom(sk0_14),sk0_12)
| ~ subset(relation_rng(sk0_14),sk0_13) ),
inference(cnf_transformation,[status(esa)],[f95]) ).
fof(f102,plain,
! [A,B] :
( ( ~ element(A,powerset(B))
| subset(A,B) )
& ( element(A,powerset(B))
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(esa)],[f33]) ).
fof(f103,plain,
( ! [A,B] :
( ~ element(A,powerset(B))
| subset(A,B) )
& ! [A,B] :
( element(A,powerset(B))
| ~ subset(A,B) ) ),
inference(miniscoping,[status(esa)],[f102]) ).
fof(f104,plain,
! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f103]) ).
fof(f120,plain,
( spl0_0
<=> subset(relation_dom(sk0_14),sk0_12) ),
introduced(split_symbol_definition) ).
fof(f123,plain,
( spl0_1
<=> subset(relation_rng(sk0_14),sk0_13) ),
introduced(split_symbol_definition) ).
fof(f126,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f97,f120,f123]) ).
fof(f127,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| in(ordered_pair(X1,sk0_1(X1,relation_dom(X0),X0)),X0) ),
inference(destructive_equality_resolution,[status(esa)],[f56]) ).
fof(f129,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ in(X1,relation_rng(X0))
| in(ordered_pair(sk0_4(X1,relation_rng(X0),X0),X1),X0) ),
inference(destructive_equality_resolution,[status(esa)],[f64]) ).
fof(f132,plain,
! [X0,X1,X2] :
( relation(X0)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(resolution,[status(thm)],[f43,f70]) ).
fof(f135,plain,
! [X0,X1,X2] :
( subset(X0,cartesian_product2(X1,X2))
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(resolution,[status(thm)],[f104,f70]) ).
fof(f137,plain,
! [X0,X1,X2,X3] :
( ~ relation_of2_as_subset(X0,X1,X2)
| ~ in(X3,X0)
| in(X3,cartesian_product2(X1,X2)) ),
inference(resolution,[status(thm)],[f135,f49]) ).
fof(f645,plain,
! [X0,X1,X2,X3,X4] :
( in(X0,X1)
| ~ relation_of2_as_subset(X2,X1,X3)
| ~ in(ordered_pair(X0,X4),X2) ),
inference(resolution,[status(thm)],[f91,f137]) ).
fof(f654,plain,
! [X0,X1,X2,X3,X4] :
( in(X0,X1)
| ~ relation_of2_as_subset(X2,X3,X1)
| ~ in(ordered_pair(X4,X0),X2) ),
inference(resolution,[status(thm)],[f92,f137]) ).
fof(f710,plain,
! [X0,X1,X2,X3] :
( in(X0,X1)
| ~ relation_of2_as_subset(X2,X1,X3)
| ~ relation(X2)
| ~ in(X0,relation_dom(X2)) ),
inference(resolution,[status(thm)],[f645,f127]) ).
fof(f711,plain,
! [X0,X1,X2,X3] :
( in(X0,X1)
| ~ relation_of2_as_subset(X2,X1,X3)
| ~ in(X0,relation_dom(X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f710,f132]) ).
fof(f717,plain,
! [X0] :
( in(X0,sk0_12)
| ~ in(X0,relation_dom(sk0_14)) ),
inference(resolution,[status(thm)],[f711,f96]) ).
fof(f741,plain,
! [X0] :
( in(sk0_0(X0,relation_dom(sk0_14)),sk0_12)
| subset(relation_dom(sk0_14),X0) ),
inference(resolution,[status(thm)],[f717,f50]) ).
fof(f742,plain,
( subset(relation_dom(sk0_14),sk0_12)
| subset(relation_dom(sk0_14),sk0_12) ),
inference(resolution,[status(thm)],[f741,f51]) ).
fof(f743,plain,
spl0_0,
inference(split_clause,[status(thm)],[f742,f120]) ).
fof(f772,plain,
! [X0,X1,X2,X3] :
( in(X0,X1)
| ~ relation_of2_as_subset(X2,X3,X1)
| ~ relation(X2)
| ~ in(X0,relation_rng(X2)) ),
inference(resolution,[status(thm)],[f654,f129]) ).
fof(f773,plain,
! [X0,X1,X2,X3] :
( in(X0,X1)
| ~ relation_of2_as_subset(X2,X3,X1)
| ~ in(X0,relation_rng(X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f772,f132]) ).
fof(f783,plain,
! [X0] :
( in(X0,sk0_13)
| ~ in(X0,relation_rng(sk0_14)) ),
inference(resolution,[status(thm)],[f773,f96]) ).
fof(f807,plain,
! [X0] :
( in(sk0_0(X0,relation_rng(sk0_14)),sk0_13)
| subset(relation_rng(sk0_14),X0) ),
inference(resolution,[status(thm)],[f783,f50]) ).
fof(f808,plain,
( subset(relation_rng(sk0_14),sk0_13)
| subset(relation_rng(sk0_14),sk0_13) ),
inference(resolution,[status(thm)],[f807,f51]) ).
fof(f809,plain,
spl0_1,
inference(split_clause,[status(thm)],[f808,f123]) ).
fof(f819,plain,
$false,
inference(sat_refutation,[status(thm)],[f126,f743,f809]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU262+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.32 % Computer : n018.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Tue May 30 09:26:25 EDT 2023
% 0.10/0.32 % CPUTime :
% 0.10/0.33 % Drodi V3.5.1
% 1.68/0.64 % Refutation found
% 1.68/0.64 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.68/0.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.88/0.66 % Elapsed time: 0.334656 seconds
% 1.88/0.66 % CPU time: 1.945192 seconds
% 1.88/0.66 % Memory used: 74.684 MB
%------------------------------------------------------------------------------