TSTP Solution File: SEU225+1 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% 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 : n002.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 20:41:35 EDT 2024
% Result : Theorem 0.21s 0.37s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 15
% Syntax : Number of formulae : 77 ( 9 unt; 0 def)
% Number of atoms : 295 ( 62 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 359 ( 141 ~; 144 |; 44 &)
% ( 17 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 10 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 101 ( 93 !; 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/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [A,B] :
( relation(A)
=> relation(relation_dom_restriction(A,B)) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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(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(f205,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(f206,plain,
( spl0_6
<=> function(relation_dom_restriction(sk0_10,sk0_11)) ),
introduced(split_symbol_definition) ).
fof(f208,plain,
( ~ function(relation_dom_restriction(sk0_10,sk0_11))
| spl0_6 ),
inference(component_clause,[status(thm)],[f206]) ).
fof(f209,plain,
( spl0_7
<=> relation(sk0_10) ),
introduced(split_symbol_definition) ).
fof(f211,plain,
( ~ relation(sk0_10)
| spl0_7 ),
inference(component_clause,[status(thm)],[f209]) ).
fof(f212,plain,
( spl0_8
<=> function(sk0_10) ),
introduced(split_symbol_definition) ).
fof(f214,plain,
( ~ function(sk0_10)
| spl0_8 ),
inference(component_clause,[status(thm)],[f212]) ).
fof(f215,plain,
( spl0_9
<=> in(sk0_12,relation_dom(relation_dom_restriction(sk0_10,sk0_11))) ),
introduced(split_symbol_definition) ).
fof(f217,plain,
( ~ in(sk0_12,relation_dom(relation_dom_restriction(sk0_10,sk0_11)))
| spl0_9 ),
inference(component_clause,[status(thm)],[f215]) ).
fof(f218,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)],[f205,f151]) ).
fof(f219,plain,
( ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9 ),
inference(split_clause,[status(thm)],[f218,f206,f209,f212,f215]) ).
fof(f220,plain,
( spl0_10
<=> in(sk0_12,relation_dom(sk0_10)) ),
introduced(split_symbol_definition) ).
fof(f222,plain,
( ~ in(sk0_12,relation_dom(sk0_10))
| spl0_10 ),
inference(component_clause,[status(thm)],[f220]) ).
fof(f223,plain,
( spl0_11
<=> in(sk0_12,sk0_11) ),
introduced(split_symbol_definition) ).
fof(f225,plain,
( ~ in(sk0_12,sk0_11)
| spl0_11 ),
inference(component_clause,[status(thm)],[f223]) ).
fof(f226,plain,
( ~ relation(sk0_10)
| ~ function(sk0_10)
| ~ in(sk0_12,relation_dom(sk0_10))
| ~ in(sk0_12,sk0_11)
| spl0_9 ),
inference(resolution,[status(thm)],[f217,f105]) ).
fof(f227,plain,
( ~ spl0_7
| ~ spl0_8
| ~ spl0_10
| ~ spl0_11
| spl0_9 ),
inference(split_clause,[status(thm)],[f226,f209,f212,f220,f223,f215]) ).
fof(f228,plain,
( spl0_12
<=> relation(relation_dom_restriction(sk0_10,sk0_11)) ),
introduced(split_symbol_definition) ).
fof(f230,plain,
( ~ relation(relation_dom_restriction(sk0_10,sk0_11))
| spl0_12 ),
inference(component_clause,[status(thm)],[f228]) ).
fof(f231,plain,
( spl0_13
<=> apply(relation_dom_restriction(sk0_10,sk0_11),sk0_12) = empty_set ),
introduced(split_symbol_definition) ).
fof(f232,plain,
( apply(relation_dom_restriction(sk0_10,sk0_11),sk0_12) = empty_set
| ~ spl0_13 ),
inference(component_clause,[status(thm)],[f231]) ).
fof(f234,plain,
( ~ relation(relation_dom_restriction(sk0_10,sk0_11))
| ~ function(relation_dom_restriction(sk0_10,sk0_11))
| apply(relation_dom_restriction(sk0_10,sk0_11),sk0_12) = empty_set
| spl0_9 ),
inference(resolution,[status(thm)],[f217,f159]) ).
fof(f235,plain,
( ~ spl0_12
| ~ spl0_6
| spl0_13
| spl0_9 ),
inference(split_clause,[status(thm)],[f234,f228,f206,f231,f215]) ).
fof(f236,plain,
( $false
| spl0_11 ),
inference(forward_subsumption_resolution,[status(thm)],[f225,f150]) ).
fof(f237,plain,
spl0_11,
inference(contradiction_clause,[status(thm)],[f236]) ).
fof(f238,plain,
( ~ relation(sk0_10)
| spl0_12 ),
inference(resolution,[status(thm)],[f230,f71]) ).
fof(f239,plain,
( $false
| spl0_12 ),
inference(forward_subsumption_resolution,[status(thm)],[f238,f148]) ).
fof(f240,plain,
spl0_12,
inference(contradiction_clause,[status(thm)],[f239]) ).
fof(f241,plain,
( spl0_14
<=> apply(sk0_10,sk0_12) = empty_set ),
introduced(split_symbol_definition) ).
fof(f242,plain,
( apply(sk0_10,sk0_12) = empty_set
| ~ spl0_14 ),
inference(component_clause,[status(thm)],[f241]) ).
fof(f244,plain,
( ~ relation(sk0_10)
| ~ function(sk0_10)
| apply(sk0_10,sk0_12) = empty_set
| spl0_10 ),
inference(resolution,[status(thm)],[f222,f159]) ).
fof(f245,plain,
( ~ spl0_7
| ~ spl0_8
| spl0_14
| spl0_10 ),
inference(split_clause,[status(thm)],[f244,f209,f212,f241,f220]) ).
fof(f246,plain,
( $false
| spl0_8 ),
inference(forward_subsumption_resolution,[status(thm)],[f214,f149]) ).
fof(f247,plain,
spl0_8,
inference(contradiction_clause,[status(thm)],[f246]) ).
fof(f248,plain,
( $false
| spl0_7 ),
inference(forward_subsumption_resolution,[status(thm)],[f211,f148]) ).
fof(f249,plain,
spl0_7,
inference(contradiction_clause,[status(thm)],[f248]) ).
fof(f250,plain,
( ~ relation(sk0_10)
| ~ function(sk0_10)
| spl0_6 ),
inference(resolution,[status(thm)],[f208,f90]) ).
fof(f251,plain,
( ~ spl0_7
| ~ spl0_8
| spl0_6 ),
inference(split_clause,[status(thm)],[f250,f209,f212,f206]) ).
fof(f253,plain,
( apply(relation_dom_restriction(sk0_10,sk0_11),sk0_12) != empty_set
| ~ spl0_14 ),
inference(backward_demodulation,[status(thm)],[f242,f151]) ).
fof(f281,plain,
( $false
| ~ spl0_14
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[status(thm)],[f232,f253]) ).
fof(f282,plain,
( ~ spl0_14
| ~ spl0_13 ),
inference(contradiction_clause,[status(thm)],[f281]) ).
fof(f283,plain,
$false,
inference(sat_refutation,[status(thm)],[f219,f227,f235,f237,f240,f245,f247,f249,f251,f282]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SEU225+1 : TPTP v8.1.2. Released v3.3.0.
% 0.04/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.15/0.35 % Computer : n002.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon Apr 29 20:07:54 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.36 % Drodi V3.6.0
% 0.21/0.37 % Refutation found
% 0.21/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.21/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/0.39 % Elapsed time: 0.031640 seconds
% 0.21/0.39 % CPU time: 0.112518 seconds
% 0.21/0.39 % Total memory used: 24.183 MB
% 0.21/0.39 % Net memory used: 24.046 MB
%------------------------------------------------------------------------------