TSTP Solution File: SEU209+1 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SEU209+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n029.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 : Tue Apr 30 20:41:29 EDT 2024
% Result : Theorem 0.18s 0.41s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 45 ( 6 unt; 0 def)
% Number of atoms : 182 ( 18 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 219 ( 82 ~; 84 |; 35 &)
% ( 13 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 2 con; 0-4 aty)
% Number of variables : 120 ( 98 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [A] :
( relation(A)
=> ! [B,C] :
( C = relation_inverse_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E] :
( in(ordered_pair(D,E),A)
& in(E,B) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,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(f32,conjecture,
! [A,B] :
( relation(B)
=> subset(relation_inverse_image(B,A),relation_dom(B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
~ ! [A,B] :
( relation(B)
=> subset(relation_inverse_image(B,A),relation_dom(B)) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f47,plain,
! [A] :
( ~ relation(A)
| ! [B,C] :
( C = relation_inverse_image(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E] :
( in(ordered_pair(D,E),A)
& in(E,B) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f4]) ).
fof(f48,plain,
! [A] :
( ~ relation(A)
| ! [B,C] :
( ( C != relation_inverse_image(A,B)
| ! [D] :
( ( ~ in(D,C)
| ? [E] :
( in(ordered_pair(D,E),A)
& in(E,B) ) )
& ( in(D,C)
| ! [E] :
( ~ in(ordered_pair(D,E),A)
| ~ in(E,B) ) ) ) )
& ( C = relation_inverse_image(A,B)
| ? [D] :
( ( ~ in(D,C)
| ! [E] :
( ~ in(ordered_pair(D,E),A)
| ~ in(E,B) ) )
& ( in(D,C)
| ? [E] :
( in(ordered_pair(D,E),A)
& in(E,B) ) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f47]) ).
fof(f49,plain,
! [A] :
( ~ relation(A)
| ( ! [B,C] :
( C != relation_inverse_image(A,B)
| ( ! [D] :
( ~ in(D,C)
| ? [E] :
( in(ordered_pair(D,E),A)
& in(E,B) ) )
& ! [D] :
( in(D,C)
| ! [E] :
( ~ in(ordered_pair(D,E),A)
| ~ in(E,B) ) ) ) )
& ! [B,C] :
( C = relation_inverse_image(A,B)
| ? [D] :
( ( ~ in(D,C)
| ! [E] :
( ~ in(ordered_pair(D,E),A)
| ~ in(E,B) ) )
& ( in(D,C)
| ? [E] :
( in(ordered_pair(D,E),A)
& in(E,B) ) ) ) ) ) ),
inference(miniscoping,[status(esa)],[f48]) ).
fof(f50,plain,
! [A] :
( ~ relation(A)
| ( ! [B,C] :
( C != relation_inverse_image(A,B)
| ( ! [D] :
( ~ in(D,C)
| ( in(ordered_pair(D,sk0_0(D,C,B,A)),A)
& in(sk0_0(D,C,B,A),B) ) )
& ! [D] :
( in(D,C)
| ! [E] :
( ~ in(ordered_pair(D,E),A)
| ~ in(E,B) ) ) ) )
& ! [B,C] :
( C = relation_inverse_image(A,B)
| ( ( ~ in(sk0_1(C,B,A),C)
| ! [E] :
( ~ in(ordered_pair(sk0_1(C,B,A),E),A)
| ~ in(E,B) ) )
& ( in(sk0_1(C,B,A),C)
| ( in(ordered_pair(sk0_1(C,B,A),sk0_2(C,B,A)),A)
& in(sk0_2(C,B,A),B) ) ) ) ) ) ),
inference(skolemization,[status(esa)],[f49]) ).
fof(f51,plain,
! [X0,X1,X2,X3] :
( ~ relation(X0)
| X1 != relation_inverse_image(X0,X2)
| ~ in(X3,X1)
| in(ordered_pair(X3,sk0_0(X3,X1,X2,X0)),X0) ),
inference(cnf_transformation,[status(esa)],[f50]) ).
fof(f57,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( ~ in(C,A)
| in(C,B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f5]) ).
fof(f58,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)],[f57]) ).
fof(f59,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)],[f58]) ).
fof(f60,plain,
( ! [A,B] :
( ~ subset(A,B)
| ! [C] :
( ~ in(C,A)
| in(C,B) ) )
& ! [A,B] :
( subset(A,B)
| ( in(sk0_3(B,A),A)
& ~ in(sk0_3(B,A),B) ) ) ),
inference(skolemization,[status(esa)],[f59]) ).
fof(f62,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sk0_3(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f60]) ).
fof(f63,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sk0_3(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f60]) ).
fof(f64,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)],[f6]) ).
fof(f65,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)],[f64]) ).
fof(f66,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)],[f65]) ).
fof(f67,plain,
! [A] :
( ~ relation(A)
| ( ! [B] :
( B != relation_dom(A)
| ( ! [C] :
( ~ in(C,B)
| in(ordered_pair(C,sk0_4(C,B,A)),A) )
& ! [C] :
( in(C,B)
| ! [D] : ~ in(ordered_pair(C,D),A) ) ) )
& ! [B] :
( B = relation_dom(A)
| ( ( ~ in(sk0_5(B,A),B)
| ! [D] : ~ in(ordered_pair(sk0_5(B,A),D),A) )
& ( in(sk0_5(B,A),B)
| in(ordered_pair(sk0_5(B,A),sk0_6(B,A)),A) ) ) ) ) ),
inference(skolemization,[status(esa)],[f66]) ).
fof(f69,plain,
! [X0,X1,X2,X3] :
( ~ relation(X0)
| X1 != relation_dom(X0)
| in(X2,X1)
| ~ in(ordered_pair(X2,X3),X0) ),
inference(cnf_transformation,[status(esa)],[f67]) ).
fof(f106,plain,
? [A,B] :
( relation(B)
& ~ subset(relation_inverse_image(B,A),relation_dom(B)) ),
inference(pre_NNF_transformation,[status(esa)],[f33]) ).
fof(f107,plain,
? [B] :
( relation(B)
& ? [A] : ~ subset(relation_inverse_image(B,A),relation_dom(B)) ),
inference(miniscoping,[status(esa)],[f106]) ).
fof(f108,plain,
( relation(sk0_14)
& ~ subset(relation_inverse_image(sk0_14,sk0_15),relation_dom(sk0_14)) ),
inference(skolemization,[status(esa)],[f107]) ).
fof(f109,plain,
relation(sk0_14),
inference(cnf_transformation,[status(esa)],[f108]) ).
fof(f110,plain,
~ subset(relation_inverse_image(sk0_14,sk0_15),relation_dom(sk0_14)),
inference(cnf_transformation,[status(esa)],[f108]) ).
fof(f133,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| ~ in(X1,relation_inverse_image(X0,X2))
| in(ordered_pair(X1,sk0_0(X1,relation_inverse_image(X0,X2),X2,X0)),X0) ),
inference(destructive_equality_resolution,[status(esa)],[f51]) ).
fof(f137,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| in(X1,relation_dom(X0))
| ~ in(ordered_pair(X1,X2),X0) ),
inference(destructive_equality_resolution,[status(esa)],[f69]) ).
fof(f1128,plain,
in(sk0_3(relation_dom(sk0_14),relation_inverse_image(sk0_14,sk0_15)),relation_inverse_image(sk0_14,sk0_15)),
inference(resolution,[status(thm)],[f62,f110]) ).
fof(f1169,plain,
( spl0_12
<=> relation(sk0_14) ),
introduced(split_symbol_definition) ).
fof(f1171,plain,
( ~ relation(sk0_14)
| spl0_12 ),
inference(component_clause,[status(thm)],[f1169]) ).
fof(f1177,plain,
( spl0_14
<=> in(ordered_pair(sk0_3(relation_dom(sk0_14),relation_inverse_image(sk0_14,sk0_15)),sk0_0(sk0_3(relation_dom(sk0_14),relation_inverse_image(sk0_14,sk0_15)),relation_inverse_image(sk0_14,sk0_15),sk0_15,sk0_14)),sk0_14) ),
introduced(split_symbol_definition) ).
fof(f1178,plain,
( in(ordered_pair(sk0_3(relation_dom(sk0_14),relation_inverse_image(sk0_14,sk0_15)),sk0_0(sk0_3(relation_dom(sk0_14),relation_inverse_image(sk0_14,sk0_15)),relation_inverse_image(sk0_14,sk0_15),sk0_15,sk0_14)),sk0_14)
| ~ spl0_14 ),
inference(component_clause,[status(thm)],[f1177]) ).
fof(f1180,plain,
( ~ relation(sk0_14)
| in(ordered_pair(sk0_3(relation_dom(sk0_14),relation_inverse_image(sk0_14,sk0_15)),sk0_0(sk0_3(relation_dom(sk0_14),relation_inverse_image(sk0_14,sk0_15)),relation_inverse_image(sk0_14,sk0_15),sk0_15,sk0_14)),sk0_14) ),
inference(resolution,[status(thm)],[f1128,f133]) ).
fof(f1181,plain,
( ~ spl0_12
| spl0_14 ),
inference(split_clause,[status(thm)],[f1180,f1169,f1177]) ).
fof(f1186,plain,
( $false
| spl0_12 ),
inference(forward_subsumption_resolution,[status(thm)],[f1171,f109]) ).
fof(f1187,plain,
spl0_12,
inference(contradiction_clause,[status(thm)],[f1186]) ).
fof(f1200,plain,
( spl0_17
<=> in(sk0_3(relation_dom(sk0_14),relation_inverse_image(sk0_14,sk0_15)),relation_dom(sk0_14)) ),
introduced(split_symbol_definition) ).
fof(f1201,plain,
( in(sk0_3(relation_dom(sk0_14),relation_inverse_image(sk0_14,sk0_15)),relation_dom(sk0_14))
| ~ spl0_17 ),
inference(component_clause,[status(thm)],[f1200]) ).
fof(f1203,plain,
( ~ relation(sk0_14)
| in(sk0_3(relation_dom(sk0_14),relation_inverse_image(sk0_14,sk0_15)),relation_dom(sk0_14))
| ~ spl0_14 ),
inference(resolution,[status(thm)],[f1178,f137]) ).
fof(f1204,plain,
( ~ spl0_12
| spl0_17
| ~ spl0_14 ),
inference(split_clause,[status(thm)],[f1203,f1169,f1200,f1177]) ).
fof(f1227,plain,
( subset(relation_inverse_image(sk0_14,sk0_15),relation_dom(sk0_14))
| ~ spl0_17 ),
inference(resolution,[status(thm)],[f1201,f63]) ).
fof(f1228,plain,
( $false
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[status(thm)],[f1227,f110]) ).
fof(f1229,plain,
~ spl0_17,
inference(contradiction_clause,[status(thm)],[f1228]) ).
fof(f1230,plain,
$false,
inference(sat_refutation,[status(thm)],[f1181,f1187,f1204,f1229]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU209+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.35 % Computer : n029.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Mon Apr 29 20:07:34 EDT 2024
% 0.12/0.35 % CPUTime :
% 0.12/0.36 % Drodi V3.6.0
% 0.18/0.41 % Refutation found
% 0.18/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.42 % Elapsed time: 0.063559 seconds
% 0.18/0.42 % CPU time: 0.368566 seconds
% 0.18/0.42 % Total memory used: 66.866 MB
% 0.18/0.42 % Net memory used: 66.568 MB
%------------------------------------------------------------------------------