TSTP Solution File: SEU223+2 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU223+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n005.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 12:36:20 EDT 2023
% Result : Theorem 0.12s 0.37s
% Output : CNFRefutation 0.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 44 ( 8 unt; 0 def)
% Number of atoms : 157 ( 34 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 187 ( 74 ~; 70 |; 28 &)
% ( 6 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 63 (; 55 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f69,axiom,
! [A,B] :
( relation(A)
=> relation(relation_dom_restriction(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f91,axiom,
! [A,B] :
( ( relation(A)
& function(A) )
=> ( relation(relation_dom_restriction(A,B))
& function(relation_dom_restriction(A,B)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f216,lemma,
! [A,B] :
( ( relation(B)
& function(B) )
=> ! [C] :
( ( relation(C)
& function(C) )
=> ( B = relation_dom_restriction(C,A)
<=> ( relation_dom(B) = set_intersection2(relation_dom(C),A)
& ! [D] :
( in(D,relation_dom(B))
=> apply(B,D) = apply(C,D) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f220,conjecture,
! [A,B,C] :
( ( relation(C)
& function(C) )
=> ( in(B,relation_dom(relation_dom_restriction(C,A)))
=> apply(relation_dom_restriction(C,A),B) = apply(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f221,negated_conjecture,
~ ! [A,B,C] :
( ( relation(C)
& function(C) )
=> ( in(B,relation_dom(relation_dom_restriction(C,A)))
=> apply(relation_dom_restriction(C,A),B) = apply(C,B) ) ),
inference(negated_conjecture,[status(cth)],[f220]) ).
fof(f521,plain,
! [A,B] :
( ~ relation(A)
| relation(relation_dom_restriction(A,B)) ),
inference(pre_NNF_transformation,[status(esa)],[f69]) ).
fof(f522,plain,
! [A] :
( ~ relation(A)
| ! [B] : relation(relation_dom_restriction(A,B)) ),
inference(miniscoping,[status(esa)],[f521]) ).
fof(f523,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_dom_restriction(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f522]) ).
fof(f568,plain,
! [A,B] :
( ~ relation(A)
| ~ function(A)
| ( relation(relation_dom_restriction(A,B))
& function(relation_dom_restriction(A,B)) ) ),
inference(pre_NNF_transformation,[status(esa)],[f91]) ).
fof(f569,plain,
! [A] :
( ~ relation(A)
| ~ function(A)
| ( ! [B] : relation(relation_dom_restriction(A,B))
& ! [B] : function(relation_dom_restriction(A,B)) ) ),
inference(miniscoping,[status(esa)],[f568]) ).
fof(f571,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ function(X0)
| function(relation_dom_restriction(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f569]) ).
fof(f942,plain,
! [A,B] :
( ~ relation(B)
| ~ function(B)
| ! [C] :
( ~ relation(C)
| ~ function(C)
| ( B = relation_dom_restriction(C,A)
<=> ( relation_dom(B) = set_intersection2(relation_dom(C),A)
& ! [D] :
( ~ in(D,relation_dom(B))
| apply(B,D) = apply(C,D) ) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f216]) ).
fof(f943,plain,
! [A,B] :
( ~ relation(B)
| ~ function(B)
| ! [C] :
( ~ relation(C)
| ~ function(C)
| ( ( B != relation_dom_restriction(C,A)
| ( relation_dom(B) = set_intersection2(relation_dom(C),A)
& ! [D] :
( ~ in(D,relation_dom(B))
| apply(B,D) = apply(C,D) ) ) )
& ( B = relation_dom_restriction(C,A)
| relation_dom(B) != set_intersection2(relation_dom(C),A)
| ? [D] :
( in(D,relation_dom(B))
& apply(B,D) != apply(C,D) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f942]) ).
fof(f944,plain,
! [B] :
( ~ relation(B)
| ~ function(B)
| ! [C] :
( ~ relation(C)
| ~ function(C)
| ( ! [A] :
( B != relation_dom_restriction(C,A)
| ( relation_dom(B) = set_intersection2(relation_dom(C),A)
& ! [D] :
( ~ in(D,relation_dom(B))
| apply(B,D) = apply(C,D) ) ) )
& ! [A] :
( B = relation_dom_restriction(C,A)
| relation_dom(B) != set_intersection2(relation_dom(C),A)
| ? [D] :
( in(D,relation_dom(B))
& apply(B,D) != apply(C,D) ) ) ) ) ),
inference(miniscoping,[status(esa)],[f943]) ).
fof(f945,plain,
! [B] :
( ~ relation(B)
| ~ function(B)
| ! [C] :
( ~ relation(C)
| ~ function(C)
| ( ! [A] :
( B != relation_dom_restriction(C,A)
| ( relation_dom(B) = set_intersection2(relation_dom(C),A)
& ! [D] :
( ~ in(D,relation_dom(B))
| apply(B,D) = apply(C,D) ) ) )
& ! [A] :
( B = relation_dom_restriction(C,A)
| relation_dom(B) != set_intersection2(relation_dom(C),A)
| ( in(sk0_78(A,C,B),relation_dom(B))
& apply(B,sk0_78(A,C,B)) != apply(C,sk0_78(A,C,B)) ) ) ) ) ),
inference(skolemization,[status(esa)],[f944]) ).
fof(f947,plain,
! [X0,X1,X2,X3] :
( ~ relation(X0)
| ~ function(X0)
| ~ relation(X1)
| ~ function(X1)
| X0 != relation_dom_restriction(X1,X2)
| ~ in(X3,relation_dom(X0))
| apply(X0,X3) = apply(X1,X3) ),
inference(cnf_transformation,[status(esa)],[f945]) ).
fof(f955,plain,
? [A,B,C] :
( relation(C)
& function(C)
& in(B,relation_dom(relation_dom_restriction(C,A)))
& apply(relation_dom_restriction(C,A),B) != apply(C,B) ),
inference(pre_NNF_transformation,[status(esa)],[f221]) ).
fof(f956,plain,
? [C] :
( relation(C)
& function(C)
& ? [A,B] :
( in(B,relation_dom(relation_dom_restriction(C,A)))
& apply(relation_dom_restriction(C,A),B) != apply(C,B) ) ),
inference(miniscoping,[status(esa)],[f955]) ).
fof(f957,plain,
( relation(sk0_79)
& function(sk0_79)
& in(sk0_81,relation_dom(relation_dom_restriction(sk0_79,sk0_80)))
& apply(relation_dom_restriction(sk0_79,sk0_80),sk0_81) != apply(sk0_79,sk0_81) ),
inference(skolemization,[status(esa)],[f956]) ).
fof(f958,plain,
relation(sk0_79),
inference(cnf_transformation,[status(esa)],[f957]) ).
fof(f959,plain,
function(sk0_79),
inference(cnf_transformation,[status(esa)],[f957]) ).
fof(f960,plain,
in(sk0_81,relation_dom(relation_dom_restriction(sk0_79,sk0_80))),
inference(cnf_transformation,[status(esa)],[f957]) ).
fof(f961,plain,
apply(relation_dom_restriction(sk0_79,sk0_80),sk0_81) != apply(sk0_79,sk0_81),
inference(cnf_transformation,[status(esa)],[f957]) ).
fof(f1110,plain,
! [X0,X1,X2] :
( ~ relation(relation_dom_restriction(X0,X1))
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(X0)
| ~ function(X0)
| ~ in(X2,relation_dom(relation_dom_restriction(X0,X1)))
| apply(relation_dom_restriction(X0,X1),X2) = apply(X0,X2) ),
inference(destructive_equality_resolution,[status(esa)],[f947]) ).
fof(f1117,plain,
( spl0_0
<=> relation(sk0_79) ),
introduced(split_symbol_definition) ).
fof(f1119,plain,
( ~ relation(sk0_79)
| spl0_0 ),
inference(component_clause,[status(thm)],[f1117]) ).
fof(f1125,plain,
( $false
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f1119,f958]) ).
fof(f1126,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f1125]) ).
fof(f1156,plain,
! [X0,X1,X2] :
( ~ function(relation_dom_restriction(X0,X1))
| ~ relation(X0)
| ~ function(X0)
| ~ in(X2,relation_dom(relation_dom_restriction(X0,X1)))
| apply(relation_dom_restriction(X0,X1),X2) = apply(X0,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f1110,f523]) ).
fof(f1157,plain,
( spl0_3
<=> function(relation_dom_restriction(sk0_79,sk0_80)) ),
introduced(split_symbol_definition) ).
fof(f1159,plain,
( ~ function(relation_dom_restriction(sk0_79,sk0_80))
| spl0_3 ),
inference(component_clause,[status(thm)],[f1157]) ).
fof(f1160,plain,
( spl0_4
<=> function(sk0_79) ),
introduced(split_symbol_definition) ).
fof(f1162,plain,
( ~ function(sk0_79)
| spl0_4 ),
inference(component_clause,[status(thm)],[f1160]) ).
fof(f1163,plain,
( spl0_5
<=> in(sk0_81,relation_dom(relation_dom_restriction(sk0_79,sk0_80))) ),
introduced(split_symbol_definition) ).
fof(f1165,plain,
( ~ in(sk0_81,relation_dom(relation_dom_restriction(sk0_79,sk0_80)))
| spl0_5 ),
inference(component_clause,[status(thm)],[f1163]) ).
fof(f1166,plain,
( ~ function(relation_dom_restriction(sk0_79,sk0_80))
| ~ relation(sk0_79)
| ~ function(sk0_79)
| ~ in(sk0_81,relation_dom(relation_dom_restriction(sk0_79,sk0_80))) ),
inference(resolution,[status(thm)],[f1156,f961]) ).
fof(f1167,plain,
( ~ spl0_3
| ~ spl0_0
| ~ spl0_4
| ~ spl0_5 ),
inference(split_clause,[status(thm)],[f1166,f1157,f1117,f1160,f1163]) ).
fof(f1168,plain,
( $false
| spl0_5 ),
inference(forward_subsumption_resolution,[status(thm)],[f1165,f960]) ).
fof(f1169,plain,
spl0_5,
inference(contradiction_clause,[status(thm)],[f1168]) ).
fof(f1170,plain,
( ~ relation(sk0_79)
| ~ function(sk0_79)
| spl0_3 ),
inference(resolution,[status(thm)],[f1159,f571]) ).
fof(f1171,plain,
( ~ spl0_0
| ~ spl0_4
| spl0_3 ),
inference(split_clause,[status(thm)],[f1170,f1117,f1160,f1157]) ).
fof(f1172,plain,
( $false
| spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f1162,f959]) ).
fof(f1173,plain,
spl0_4,
inference(contradiction_clause,[status(thm)],[f1172]) ).
fof(f1174,plain,
$false,
inference(sat_refutation,[status(thm)],[f1126,f1167,f1169,f1171,f1173]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU223+2 : TPTP v8.1.2. Released v3.3.0.
% 0.06/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34 % Computer : n005.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue May 30 09:09:21 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.12/0.36 % Drodi V3.5.1
% 0.12/0.37 % Refutation found
% 0.12/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.34/0.60 % Elapsed time: 0.040341 seconds
% 0.34/0.60 % CPU time: 0.083607 seconds
% 0.34/0.60 % Memory used: 21.233 MB
%------------------------------------------------------------------------------