TSTP Solution File: SEU212+1 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU212+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n004.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 12:36:16 EDT 2023
% Result : Theorem 0.13s 0.36s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 49 ( 5 unt; 0 def)
% Number of atoms : 210 ( 44 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 255 ( 94 ~; 102 |; 37 &)
% ( 15 <=>; 6 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 82 (; 65 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [A] :
( ( relation(A)
& function(A) )
=> ! [B,C] :
( ( in(B,relation_dom(A))
=> ( C = apply(A,B)
<=> in(ordered_pair(B,C),A) ) )
& ( ~ in(B,relation_dom(A))
=> ( C = apply(A,B)
<=> C = empty_set ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f35,conjecture,
! [A,B,C] :
( ( relation(C)
& function(C) )
=> ( in(ordered_pair(A,B),C)
<=> ( in(A,relation_dom(C))
& B = apply(C,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
~ ! [A,B,C] :
( ( relation(C)
& function(C) )
=> ( in(ordered_pair(A,B),C)
<=> ( in(A,relation_dom(C))
& B = apply(C,A) ) ) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f44,plain,
! [A] :
( ~ relation(A)
| ~ function(A)
| ! [B,C] :
( ( ~ in(B,relation_dom(A))
| ( C = apply(A,B)
<=> in(ordered_pair(B,C),A) ) )
& ( in(B,relation_dom(A))
| ( C = apply(A,B)
<=> C = empty_set ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f5]) ).
fof(f45,plain,
! [A] :
( ~ relation(A)
| ~ function(A)
| ! [B,C] :
( ( ~ in(B,relation_dom(A))
| ( ( C != apply(A,B)
| in(ordered_pair(B,C),A) )
& ( C = apply(A,B)
| ~ in(ordered_pair(B,C),A) ) ) )
& ( in(B,relation_dom(A))
| ( ( C != apply(A,B)
| C = empty_set )
& ( C = apply(A,B)
| C != empty_set ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f44]) ).
fof(f46,plain,
! [A] :
( ~ relation(A)
| ~ function(A)
| ( ! [B] :
( ~ in(B,relation_dom(A))
| ( ! [C] :
( C != apply(A,B)
| in(ordered_pair(B,C),A) )
& ! [C] :
( C = apply(A,B)
| ~ in(ordered_pair(B,C),A) ) ) )
& ! [B] :
( in(B,relation_dom(A))
| ( ! [C] :
( C != apply(A,B)
| C = empty_set )
& ! [C] :
( C = apply(A,B)
| C != empty_set ) ) ) ) ),
inference(miniscoping,[status(esa)],[f45]) ).
fof(f47,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| ~ function(X0)
| ~ in(X1,relation_dom(X0))
| X2 != apply(X0,X1)
| in(ordered_pair(X1,X2),X0) ),
inference(cnf_transformation,[status(esa)],[f46]) ).
fof(f48,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| ~ function(X0)
| ~ in(X1,relation_dom(X0))
| X2 = apply(X0,X1)
| ~ in(ordered_pair(X1,X2),X0) ),
inference(cnf_transformation,[status(esa)],[f46]) ).
fof(f51,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(f52,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)],[f51]) ).
fof(f53,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)],[f52]) ).
fof(f54,plain,
! [A] :
( ~ relation(A)
| ( ! [B] :
( B != relation_dom(A)
| ( ! [C] :
( ~ in(C,B)
| in(ordered_pair(C,sk0_0(C,B,A)),A) )
& ! [C] :
( in(C,B)
| ! [D] : ~ in(ordered_pair(C,D),A) ) ) )
& ! [B] :
( B = relation_dom(A)
| ( ( ~ in(sk0_1(B,A),B)
| ! [D] : ~ in(ordered_pair(sk0_1(B,A),D),A) )
& ( in(sk0_1(B,A),B)
| in(ordered_pair(sk0_1(B,A),sk0_2(B,A)),A) ) ) ) ) ),
inference(skolemization,[status(esa)],[f53]) ).
fof(f56,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)],[f54]) ).
fof(f104,plain,
? [A,B,C] :
( relation(C)
& function(C)
& ( in(ordered_pair(A,B),C)
<~> ( in(A,relation_dom(C))
& B = apply(C,A) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f36]) ).
fof(f105,plain,
? [A,B,C] :
( relation(C)
& function(C)
& ( in(ordered_pair(A,B),C)
| ( in(A,relation_dom(C))
& B = apply(C,A) ) )
& ( ~ in(ordered_pair(A,B),C)
| ~ in(A,relation_dom(C))
| B != apply(C,A) ) ),
inference(NNF_transformation,[status(esa)],[f104]) ).
fof(f106,plain,
? [C] :
( relation(C)
& function(C)
& ? [A,B] :
( ( in(ordered_pair(A,B),C)
| ( in(A,relation_dom(C))
& B = apply(C,A) ) )
& ( ~ in(ordered_pair(A,B),C)
| ~ in(A,relation_dom(C))
| B != apply(C,A) ) ) ),
inference(miniscoping,[status(esa)],[f105]) ).
fof(f107,plain,
( relation(sk0_10)
& function(sk0_10)
& ( in(ordered_pair(sk0_11,sk0_12),sk0_10)
| ( in(sk0_11,relation_dom(sk0_10))
& sk0_12 = apply(sk0_10,sk0_11) ) )
& ( ~ in(ordered_pair(sk0_11,sk0_12),sk0_10)
| ~ in(sk0_11,relation_dom(sk0_10))
| sk0_12 != apply(sk0_10,sk0_11) ) ),
inference(skolemization,[status(esa)],[f106]) ).
fof(f108,plain,
relation(sk0_10),
inference(cnf_transformation,[status(esa)],[f107]) ).
fof(f109,plain,
function(sk0_10),
inference(cnf_transformation,[status(esa)],[f107]) ).
fof(f110,plain,
( in(ordered_pair(sk0_11,sk0_12),sk0_10)
| in(sk0_11,relation_dom(sk0_10)) ),
inference(cnf_transformation,[status(esa)],[f107]) ).
fof(f111,plain,
( in(ordered_pair(sk0_11,sk0_12),sk0_10)
| sk0_12 = apply(sk0_10,sk0_11) ),
inference(cnf_transformation,[status(esa)],[f107]) ).
fof(f112,plain,
( ~ in(ordered_pair(sk0_11,sk0_12),sk0_10)
| ~ in(sk0_11,relation_dom(sk0_10))
| sk0_12 != apply(sk0_10,sk0_11) ),
inference(cnf_transformation,[status(esa)],[f107]) ).
fof(f113,plain,
( spl0_0
<=> in(ordered_pair(sk0_11,sk0_12),sk0_10) ),
introduced(split_symbol_definition) ).
fof(f114,plain,
( in(ordered_pair(sk0_11,sk0_12),sk0_10)
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f113]) ).
fof(f116,plain,
( spl0_1
<=> in(sk0_11,relation_dom(sk0_10)) ),
introduced(split_symbol_definition) ).
fof(f119,plain,
( spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f110,f113,f116]) ).
fof(f120,plain,
( spl0_2
<=> sk0_12 = apply(sk0_10,sk0_11) ),
introduced(split_symbol_definition) ).
fof(f121,plain,
( sk0_12 = apply(sk0_10,sk0_11)
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f120]) ).
fof(f123,plain,
( spl0_0
| spl0_2 ),
inference(split_clause,[status(thm)],[f111,f113,f120]) ).
fof(f124,plain,
( ~ spl0_0
| ~ spl0_1
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f112,f113,f116,f120]) ).
fof(f125,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ function(X0)
| ~ in(X1,relation_dom(X0))
| in(ordered_pair(X1,apply(X0,X1)),X0) ),
inference(destructive_equality_resolution,[status(esa)],[f47]) ).
fof(f129,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| in(X1,relation_dom(X0))
| ~ in(ordered_pair(X1,X2),X0) ),
inference(destructive_equality_resolution,[status(esa)],[f56]) ).
fof(f133,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| ~ function(X0)
| X1 = apply(X0,X2)
| ~ in(ordered_pair(X2,X1),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f48,f129]) ).
fof(f152,plain,
( spl0_3
<=> relation(sk0_10) ),
introduced(split_symbol_definition) ).
fof(f154,plain,
( ~ relation(sk0_10)
| spl0_3 ),
inference(component_clause,[status(thm)],[f152]) ).
fof(f155,plain,
( spl0_4
<=> function(sk0_10) ),
introduced(split_symbol_definition) ).
fof(f157,plain,
( ~ function(sk0_10)
| spl0_4 ),
inference(component_clause,[status(thm)],[f155]) ).
fof(f158,plain,
( ~ relation(sk0_10)
| ~ function(sk0_10)
| sk0_12 = apply(sk0_10,sk0_11)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f114,f133]) ).
fof(f159,plain,
( ~ spl0_3
| ~ spl0_4
| spl0_2
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f158,f152,f155,f120,f113]) ).
fof(f160,plain,
( ~ relation(sk0_10)
| in(sk0_11,relation_dom(sk0_10))
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f114,f129]) ).
fof(f161,plain,
( ~ spl0_3
| spl0_1
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f160,f152,f116,f113]) ).
fof(f163,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[status(thm)],[f154,f108]) ).
fof(f164,plain,
spl0_3,
inference(contradiction_clause,[status(thm)],[f163]) ).
fof(f171,plain,
( ~ relation(sk0_10)
| ~ function(sk0_10)
| ~ in(sk0_11,relation_dom(sk0_10))
| in(ordered_pair(sk0_11,sk0_12),sk0_10)
| ~ spl0_2 ),
inference(paramodulation,[status(thm)],[f121,f125]) ).
fof(f172,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_1
| spl0_0
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f171,f152,f155,f116,f113,f120]) ).
fof(f178,plain,
( $false
| spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f157,f109]) ).
fof(f179,plain,
spl0_4,
inference(contradiction_clause,[status(thm)],[f178]) ).
fof(f180,plain,
$false,
inference(sat_refutation,[status(thm)],[f119,f123,f124,f159,f161,f164,f172,f179]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU212+1 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35 % Computer : n004.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue May 30 09:09:22 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.36 % Drodi V3.5.1
% 0.13/0.36 % Refutation found
% 0.13/0.36 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.38 % Elapsed time: 0.023884 seconds
% 0.20/0.38 % CPU time: 0.035979 seconds
% 0.20/0.38 % Memory used: 14.636 MB
%------------------------------------------------------------------------------