TSTP Solution File: SEU225+1 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU225+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n025.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 12:36:21 EDT 2023
% Result : Theorem 0.15s 0.34s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of formulae : 72 ( 8 unt; 0 def)
% Number of atoms : 296 ( 62 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 372 ( 148 ~; 152 |; 44 &)
% ( 15 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 8 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 113 (; 105 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [A,B] :
( relation(A)
=> relation(relation_dom_restriction(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,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(f31,axiom,
! [A,B,C] :
( ( relation(C)
& function(C) )
=> ( in(B,relation_dom(relation_dom_restriction(C,A)))
<=> ( in(B,relation_dom(C))
& in(B,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,conjecture,
! [A,B,C] :
( ( relation(C)
& function(C) )
=> ( in(B,A)
=> apply(relation_dom_restriction(C,A),B) = apply(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,negated_conjecture,
~ ! [A,B,C] :
( ( relation(C)
& function(C) )
=> ( in(B,A)
=> apply(relation_dom_restriction(C,A),B) = apply(C,B) ) ),
inference(negated_conjecture,[status(cth)],[f45]) ).
fof(f61,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)],[f7]) ).
fof(f62,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)],[f61]) ).
fof(f63,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)],[f62]) ).
fof(f66,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| ~ function(X0)
| in(X1,relation_dom(X0))
| X2 != apply(X0,X1)
| X2 = empty_set ),
inference(cnf_transformation,[status(esa)],[f63]) ).
fof(f69,plain,
! [A,B] :
( ~ relation(A)
| relation(relation_dom_restriction(A,B)) ),
inference(pre_NNF_transformation,[status(esa)],[f16]) ).
fof(f70,plain,
! [A] :
( ~ relation(A)
| ! [B] : relation(relation_dom_restriction(A,B)) ),
inference(miniscoping,[status(esa)],[f69]) ).
fof(f71,plain,
! [X0,X1] :
( ~ relation(X0)
| relation(relation_dom_restriction(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f70]) ).
fof(f87,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)],[f26]) ).
fof(f88,plain,
! [A] :
( ~ relation(A)
| ~ function(A)
| ( ! [B] : relation(relation_dom_restriction(A,B))
& ! [B] : function(relation_dom_restriction(A,B)) ) ),
inference(miniscoping,[status(esa)],[f87]) ).
fof(f90,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ function(X0)
| function(relation_dom_restriction(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f88]) ).
fof(f100,plain,
! [A,B,C] :
( ~ relation(C)
| ~ function(C)
| ( in(B,relation_dom(relation_dom_restriction(C,A)))
<=> ( in(B,relation_dom(C))
& in(B,A) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f31]) ).
fof(f101,plain,
! [A,B,C] :
( ~ relation(C)
| ~ function(C)
| ( ( ~ in(B,relation_dom(relation_dom_restriction(C,A)))
| ( in(B,relation_dom(C))
& in(B,A) ) )
& ( in(B,relation_dom(relation_dom_restriction(C,A)))
| ~ in(B,relation_dom(C))
| ~ in(B,A) ) ) ),
inference(NNF_transformation,[status(esa)],[f100]) ).
fof(f102,plain,
! [C] :
( ~ relation(C)
| ~ function(C)
| ( ! [A,B] :
( ~ in(B,relation_dom(relation_dom_restriction(C,A)))
| ( in(B,relation_dom(C))
& in(B,A) ) )
& ! [A,B] :
( in(B,relation_dom(relation_dom_restriction(C,A)))
| ~ in(B,relation_dom(C))
| ~ in(B,A) ) ) ),
inference(miniscoping,[status(esa)],[f101]) ).
fof(f103,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| ~ function(X0)
| ~ in(X1,relation_dom(relation_dom_restriction(X0,X2)))
| in(X1,relation_dom(X0)) ),
inference(cnf_transformation,[status(esa)],[f102]) ).
fof(f105,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| ~ function(X0)
| in(X1,relation_dom(relation_dom_restriction(X0,X2)))
| ~ in(X1,relation_dom(X0))
| ~ in(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f102]) ).
fof(f135,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)],[f43]) ).
fof(f136,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)],[f135]) ).
fof(f137,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)],[f136]) ).
fof(f138,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_9(A,C,B),relation_dom(B))
& apply(B,sk0_9(A,C,B)) != apply(C,sk0_9(A,C,B)) ) ) ) ) ),
inference(skolemization,[status(esa)],[f137]) ).
fof(f140,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)],[f138]) ).
fof(f145,plain,
? [A,B,C] :
( relation(C)
& function(C)
& in(B,A)
& apply(relation_dom_restriction(C,A),B) != apply(C,B) ),
inference(pre_NNF_transformation,[status(esa)],[f46]) ).
fof(f146,plain,
? [C] :
( relation(C)
& function(C)
& ? [A,B] :
( in(B,A)
& apply(relation_dom_restriction(C,A),B) != apply(C,B) ) ),
inference(miniscoping,[status(esa)],[f145]) ).
fof(f147,plain,
( relation(sk0_10)
& function(sk0_10)
& in(sk0_12,sk0_11)
& apply(relation_dom_restriction(sk0_10,sk0_11),sk0_12) != apply(sk0_10,sk0_12) ),
inference(skolemization,[status(esa)],[f146]) ).
fof(f148,plain,
relation(sk0_10),
inference(cnf_transformation,[status(esa)],[f147]) ).
fof(f149,plain,
function(sk0_10),
inference(cnf_transformation,[status(esa)],[f147]) ).
fof(f150,plain,
in(sk0_12,sk0_11),
inference(cnf_transformation,[status(esa)],[f147]) ).
fof(f151,plain,
apply(relation_dom_restriction(sk0_10,sk0_11),sk0_12) != apply(sk0_10,sk0_12),
inference(cnf_transformation,[status(esa)],[f147]) ).
fof(f159,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ function(X0)
| in(X1,relation_dom(X0))
| apply(X0,X1) = empty_set ),
inference(destructive_equality_resolution,[status(esa)],[f66]) ).
fof(f162,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)],[f140]) ).
fof(f171,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| ~ function(X0)
| in(X1,relation_dom(X0))
| ~ relation(relation_dom_restriction(X0,X2))
| ~ function(relation_dom_restriction(X0,X2))
| apply(relation_dom_restriction(X0,X2),X1) = empty_set ),
inference(resolution,[status(thm)],[f103,f159]) ).
fof(f172,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| ~ function(X0)
| in(X1,relation_dom(X0))
| ~ function(relation_dom_restriction(X0,X2))
| apply(relation_dom_restriction(X0,X2),X1) = empty_set ),
inference(forward_subsumption_resolution,[status(thm)],[f171,f71]) ).
fof(f178,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| ~ function(X0)
| in(X1,relation_dom(X0))
| apply(relation_dom_restriction(X0,X2),X1) = empty_set ),
inference(forward_subsumption_resolution,[status(thm)],[f172,f90]) ).
fof(f190,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)],[f162,f71]) ).
fof(f191,plain,
( spl0_2
<=> function(relation_dom_restriction(sk0_10,sk0_11)) ),
introduced(split_symbol_definition) ).
fof(f193,plain,
( ~ function(relation_dom_restriction(sk0_10,sk0_11))
| spl0_2 ),
inference(component_clause,[status(thm)],[f191]) ).
fof(f194,plain,
( spl0_3
<=> relation(sk0_10) ),
introduced(split_symbol_definition) ).
fof(f196,plain,
( ~ relation(sk0_10)
| spl0_3 ),
inference(component_clause,[status(thm)],[f194]) ).
fof(f197,plain,
( spl0_4
<=> function(sk0_10) ),
introduced(split_symbol_definition) ).
fof(f199,plain,
( ~ function(sk0_10)
| spl0_4 ),
inference(component_clause,[status(thm)],[f197]) ).
fof(f200,plain,
( spl0_5
<=> in(sk0_12,relation_dom(relation_dom_restriction(sk0_10,sk0_11))) ),
introduced(split_symbol_definition) ).
fof(f202,plain,
( ~ in(sk0_12,relation_dom(relation_dom_restriction(sk0_10,sk0_11)))
| spl0_5 ),
inference(component_clause,[status(thm)],[f200]) ).
fof(f203,plain,
( ~ function(relation_dom_restriction(sk0_10,sk0_11))
| ~ relation(sk0_10)
| ~ function(sk0_10)
| ~ in(sk0_12,relation_dom(relation_dom_restriction(sk0_10,sk0_11))) ),
inference(resolution,[status(thm)],[f190,f151]) ).
fof(f204,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5 ),
inference(split_clause,[status(thm)],[f203,f191,f194,f197,f200]) ).
fof(f205,plain,
( spl0_6
<=> in(sk0_12,relation_dom(sk0_10)) ),
introduced(split_symbol_definition) ).
fof(f207,plain,
( ~ in(sk0_12,relation_dom(sk0_10))
| spl0_6 ),
inference(component_clause,[status(thm)],[f205]) ).
fof(f208,plain,
( spl0_7
<=> in(sk0_12,sk0_11) ),
introduced(split_symbol_definition) ).
fof(f210,plain,
( ~ in(sk0_12,sk0_11)
| spl0_7 ),
inference(component_clause,[status(thm)],[f208]) ).
fof(f211,plain,
( ~ relation(sk0_10)
| ~ function(sk0_10)
| ~ in(sk0_12,relation_dom(sk0_10))
| ~ in(sk0_12,sk0_11)
| spl0_5 ),
inference(resolution,[status(thm)],[f202,f105]) ).
fof(f212,plain,
( ~ spl0_3
| ~ spl0_4
| ~ spl0_6
| ~ spl0_7
| spl0_5 ),
inference(split_clause,[status(thm)],[f211,f194,f197,f205,f208,f200]) ).
fof(f221,plain,
( $false
| spl0_7 ),
inference(forward_subsumption_resolution,[status(thm)],[f210,f150]) ).
fof(f222,plain,
spl0_7,
inference(contradiction_clause,[status(thm)],[f221]) ).
fof(f226,plain,
( spl0_10
<=> apply(sk0_10,sk0_12) = empty_set ),
introduced(split_symbol_definition) ).
fof(f227,plain,
( apply(sk0_10,sk0_12) = empty_set
| ~ spl0_10 ),
inference(component_clause,[status(thm)],[f226]) ).
fof(f229,plain,
( ~ relation(sk0_10)
| ~ function(sk0_10)
| apply(sk0_10,sk0_12) = empty_set
| spl0_6 ),
inference(resolution,[status(thm)],[f207,f159]) ).
fof(f230,plain,
( ~ spl0_3
| ~ spl0_4
| spl0_10
| spl0_6 ),
inference(split_clause,[status(thm)],[f229,f194,f197,f226,f205]) ).
fof(f231,plain,
( $false
| spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f199,f149]) ).
fof(f232,plain,
spl0_4,
inference(contradiction_clause,[status(thm)],[f231]) ).
fof(f233,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[status(thm)],[f196,f148]) ).
fof(f234,plain,
spl0_3,
inference(contradiction_clause,[status(thm)],[f233]) ).
fof(f235,plain,
( ~ relation(sk0_10)
| ~ function(sk0_10)
| spl0_2 ),
inference(resolution,[status(thm)],[f193,f90]) ).
fof(f236,plain,
( ~ spl0_3
| ~ spl0_4
| spl0_2 ),
inference(split_clause,[status(thm)],[f235,f194,f197,f191]) ).
fof(f237,plain,
( apply(relation_dom_restriction(sk0_10,sk0_11),sk0_12) != empty_set
| ~ spl0_10 ),
inference(backward_demodulation,[status(thm)],[f227,f151]) ).
fof(f243,plain,
( ~ relation(sk0_10)
| ~ function(sk0_10)
| in(sk0_12,relation_dom(sk0_10))
| ~ spl0_10 ),
inference(resolution,[status(thm)],[f237,f178]) ).
fof(f244,plain,
( ~ spl0_3
| ~ spl0_4
| spl0_6
| ~ spl0_10 ),
inference(split_clause,[status(thm)],[f243,f194,f197,f205,f226]) ).
fof(f252,plain,
$false,
inference(sat_refutation,[status(thm)],[f204,f212,f222,f230,f232,f234,f236,f244]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : SEU225+1 : TPTP v8.1.2. Released v3.3.0.
% 0.09/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30 % Computer : n025.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Tue May 30 09:27:57 EDT 2023
% 0.09/0.30 % CPUTime :
% 0.09/0.31 % Drodi V3.5.1
% 0.15/0.34 % Refutation found
% 0.15/0.34 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.34 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.36 % Elapsed time: 0.055156 seconds
% 0.15/0.36 % CPU time: 0.064018 seconds
% 0.15/0.36 % Memory used: 11.851 MB
%------------------------------------------------------------------------------