TSTP Solution File: SEU223+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU223+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n016.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 0.14s 0.32s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 42 ( 8 unt; 0 def)
% Number of atoms : 155 ( 39 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 188 ( 75 ~; 71 |; 28 &)
% ( 5 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 69 (; 61 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f30,axiom,
! [A,B] :
( relation(A)
=> relation(relation_dom_restriction(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [A,B] :
( ( relation(A)
& function(A) )
=> ( relation(relation_dom_restriction(A,B))
& function(relation_dom_restriction(A,B)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,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/sandbox/benchmark/theBenchmark.p') ).
fof(f37,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)],[f36]) ).
fof(f38,axiom,
! [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/sandbox/benchmark/theBenchmark.p') ).
fof(f98,plain,
! [A,B] :
( ~ relation(A)
| relation(relation_dom_restriction(A,B)) ),
inference(pre_NNF_transformation,[status(esa)],[f30]) ).
fof(f99,plain,
! [A] :
( ~ relation(A)
| ! [B] : relation(relation_dom_restriction(A,B)) ),
inference(miniscoping,[status(esa)],[f98]) ).
fof(f100,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_dom_restriction(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f99]) ).
fof(f104,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)],[f32]) ).
fof(f105,plain,
! [A] :
( ~ relation(A)
| ~ function(A)
| ( ! [B] : relation(relation_dom_restriction(A,B))
& ! [B] : function(relation_dom_restriction(A,B)) ) ),
inference(miniscoping,[status(esa)],[f104]) ).
fof(f107,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ function(X0)
| function(relation_dom_restriction(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f105]) ).
fof(f115,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)],[f37]) ).
fof(f116,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)],[f115]) ).
fof(f117,plain,
( relation(sk0_9)
& function(sk0_9)
& in(sk0_11,relation_dom(relation_dom_restriction(sk0_9,sk0_10)))
& apply(relation_dom_restriction(sk0_9,sk0_10),sk0_11) != apply(sk0_9,sk0_11) ),
inference(skolemization,[status(esa)],[f116]) ).
fof(f118,plain,
relation(sk0_9),
inference(cnf_transformation,[status(esa)],[f117]) ).
fof(f119,plain,
function(sk0_9),
inference(cnf_transformation,[status(esa)],[f117]) ).
fof(f120,plain,
in(sk0_11,relation_dom(relation_dom_restriction(sk0_9,sk0_10))),
inference(cnf_transformation,[status(esa)],[f117]) ).
fof(f121,plain,
apply(relation_dom_restriction(sk0_9,sk0_10),sk0_11) != apply(sk0_9,sk0_11),
inference(cnf_transformation,[status(esa)],[f117]) ).
fof(f122,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)],[f38]) ).
fof(f123,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)],[f122]) ).
fof(f124,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)],[f123]) ).
fof(f125,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_12(A,C,B),relation_dom(B))
& apply(B,sk0_12(A,C,B)) != apply(C,sk0_12(A,C,B)) ) ) ) ) ),
inference(skolemization,[status(esa)],[f124]) ).
fof(f127,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)],[f125]) ).
fof(f131,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)],[f127]) ).
fof(f133,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)],[f131,f100]) ).
fof(f134,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| ~ function(X0)
| ~ in(X1,relation_dom(relation_dom_restriction(X0,X2)))
| apply(relation_dom_restriction(X0,X2),X1) = apply(X0,X1)
| ~ relation(X0)
| ~ function(X0) ),
inference(resolution,[status(thm)],[f133,f107]) ).
fof(f135,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| ~ function(X0)
| ~ in(X1,relation_dom(relation_dom_restriction(X0,X2)))
| apply(relation_dom_restriction(X0,X2),X1) = apply(X0,X1) ),
inference(duplicate_literals_removal,[status(esa)],[f134]) ).
fof(f136,plain,
( spl0_0
<=> relation(sk0_9) ),
introduced(split_symbol_definition) ).
fof(f138,plain,
( ~ relation(sk0_9)
| spl0_0 ),
inference(component_clause,[status(thm)],[f136]) ).
fof(f139,plain,
( spl0_1
<=> function(sk0_9) ),
introduced(split_symbol_definition) ).
fof(f141,plain,
( ~ function(sk0_9)
| spl0_1 ),
inference(component_clause,[status(thm)],[f139]) ).
fof(f142,plain,
( spl0_2
<=> apply(relation_dom_restriction(sk0_9,sk0_10),sk0_11) = apply(sk0_9,sk0_11) ),
introduced(split_symbol_definition) ).
fof(f143,plain,
( apply(relation_dom_restriction(sk0_9,sk0_10),sk0_11) = apply(sk0_9,sk0_11)
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f142]) ).
fof(f145,plain,
( ~ relation(sk0_9)
| ~ function(sk0_9)
| apply(relation_dom_restriction(sk0_9,sk0_10),sk0_11) = apply(sk0_9,sk0_11) ),
inference(resolution,[status(thm)],[f135,f120]) ).
fof(f146,plain,
( ~ spl0_0
| ~ spl0_1
| spl0_2 ),
inference(split_clause,[status(thm)],[f145,f136,f139,f142]) ).
fof(f147,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f141,f119]) ).
fof(f148,plain,
spl0_1,
inference(contradiction_clause,[status(thm)],[f147]) ).
fof(f149,plain,
( $false
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f138,f118]) ).
fof(f150,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f149]) ).
fof(f151,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[status(thm)],[f143,f121]) ).
fof(f152,plain,
~ spl0_2,
inference(contradiction_clause,[status(thm)],[f151]) ).
fof(f153,plain,
$false,
inference(sat_refutation,[status(thm)],[f146,f148,f150,f152]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEU223+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.30 % Computer : n016.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Tue May 30 09:40:14 EDT 2023
% 0.10/0.30 % CPUTime :
% 0.10/0.31 % Drodi V3.5.1
% 0.14/0.32 % Refutation found
% 0.14/0.32 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.54 % Elapsed time: 0.014301 seconds
% 0.14/0.54 % CPU time: 0.011817 seconds
% 0.14/0.54 % Memory used: 3.693 MB
%------------------------------------------------------------------------------