TSTP Solution File: SEU212+2 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SEU212+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n023.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 20:41:30 EDT 2024
% Result : Theorem 0.14s 0.32s
% Output : CNFRefutation 0.14s
% 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(f27,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(f28,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_dom(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f206,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f207,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)],[f206]) ).
fof(f385,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)],[f27]) ).
fof(f386,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)],[f385]) ).
fof(f387,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)],[f386]) ).
fof(f388,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)],[f387]) ).
fof(f389,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)],[f387]) ).
fof(f392,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)],[f28]) ).
fof(f393,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)],[f392]) ).
fof(f394,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)],[f393]) ).
fof(f395,plain,
! [A] :
( ~ relation(A)
| ( ! [B] :
( B != relation_dom(A)
| ( ! [C] :
( ~ in(C,B)
| in(ordered_pair(C,sk0_34(C,B,A)),A) )
& ! [C] :
( in(C,B)
| ! [D] : ~ in(ordered_pair(C,D),A) ) ) )
& ! [B] :
( B = relation_dom(A)
| ( ( ~ in(sk0_35(B,A),B)
| ! [D] : ~ in(ordered_pair(sk0_35(B,A),D),A) )
& ( in(sk0_35(B,A),B)
| in(ordered_pair(sk0_35(B,A),sk0_36(B,A)),A) ) ) ) ) ),
inference(skolemization,[status(esa)],[f394]) ).
fof(f397,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)],[f395]) ).
fof(f864,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)],[f207]) ).
fof(f865,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)],[f864]) ).
fof(f866,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)],[f865]) ).
fof(f867,plain,
( relation(sk0_69)
& function(sk0_69)
& ( in(ordered_pair(sk0_70,sk0_71),sk0_69)
| ( in(sk0_70,relation_dom(sk0_69))
& sk0_71 = apply(sk0_69,sk0_70) ) )
& ( ~ in(ordered_pair(sk0_70,sk0_71),sk0_69)
| ~ in(sk0_70,relation_dom(sk0_69))
| sk0_71 != apply(sk0_69,sk0_70) ) ),
inference(skolemization,[status(esa)],[f866]) ).
fof(f868,plain,
relation(sk0_69),
inference(cnf_transformation,[status(esa)],[f867]) ).
fof(f869,plain,
function(sk0_69),
inference(cnf_transformation,[status(esa)],[f867]) ).
fof(f870,plain,
( in(ordered_pair(sk0_70,sk0_71),sk0_69)
| in(sk0_70,relation_dom(sk0_69)) ),
inference(cnf_transformation,[status(esa)],[f867]) ).
fof(f871,plain,
( in(ordered_pair(sk0_70,sk0_71),sk0_69)
| sk0_71 = apply(sk0_69,sk0_70) ),
inference(cnf_transformation,[status(esa)],[f867]) ).
fof(f872,plain,
( ~ in(ordered_pair(sk0_70,sk0_71),sk0_69)
| ~ in(sk0_70,relation_dom(sk0_69))
| sk0_71 != apply(sk0_69,sk0_70) ),
inference(cnf_transformation,[status(esa)],[f867]) ).
fof(f907,plain,
( spl0_0
<=> in(ordered_pair(sk0_70,sk0_71),sk0_69) ),
introduced(split_symbol_definition) ).
fof(f908,plain,
( in(ordered_pair(sk0_70,sk0_71),sk0_69)
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f907]) ).
fof(f910,plain,
( spl0_1
<=> in(sk0_70,relation_dom(sk0_69)) ),
introduced(split_symbol_definition) ).
fof(f913,plain,
( spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f870,f907,f910]) ).
fof(f914,plain,
( spl0_2
<=> sk0_71 = apply(sk0_69,sk0_70) ),
introduced(split_symbol_definition) ).
fof(f915,plain,
( sk0_71 = apply(sk0_69,sk0_70)
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f914]) ).
fof(f917,plain,
( spl0_0
| spl0_2 ),
inference(split_clause,[status(thm)],[f871,f907,f914]) ).
fof(f918,plain,
( ~ spl0_0
| ~ spl0_1
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f872,f907,f910,f914]) ).
fof(f957,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)],[f388]) ).
fof(f961,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| in(X1,relation_dom(X0))
| ~ in(ordered_pair(X1,X2),X0) ),
inference(destructive_equality_resolution,[status(esa)],[f397]) ).
fof(f1009,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| ~ function(X0)
| X1 = apply(X0,X2)
| ~ in(ordered_pair(X2,X1),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f389,f961]) ).
fof(f1015,plain,
( spl0_7
<=> relation(sk0_69) ),
introduced(split_symbol_definition) ).
fof(f1017,plain,
( ~ relation(sk0_69)
| spl0_7 ),
inference(component_clause,[status(thm)],[f1015]) ).
fof(f1018,plain,
( spl0_8
<=> function(sk0_69) ),
introduced(split_symbol_definition) ).
fof(f1020,plain,
( ~ function(sk0_69)
| spl0_8 ),
inference(component_clause,[status(thm)],[f1018]) ).
fof(f1021,plain,
( ~ relation(sk0_69)
| ~ function(sk0_69)
| sk0_71 = apply(sk0_69,sk0_70)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f908,f1009]) ).
fof(f1022,plain,
( ~ spl0_7
| ~ spl0_8
| spl0_2
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f1021,f1015,f1018,f914,f907]) ).
fof(f1023,plain,
( ~ relation(sk0_69)
| in(sk0_70,relation_dom(sk0_69))
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f908,f961]) ).
fof(f1024,plain,
( ~ spl0_7
| spl0_1
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f1023,f1015,f910,f907]) ).
fof(f1026,plain,
( $false
| spl0_7 ),
inference(forward_subsumption_resolution,[status(thm)],[f1017,f868]) ).
fof(f1027,plain,
spl0_7,
inference(contradiction_clause,[status(thm)],[f1026]) ).
fof(f1034,plain,
( ~ relation(sk0_69)
| ~ function(sk0_69)
| ~ in(sk0_70,relation_dom(sk0_69))
| in(ordered_pair(sk0_70,sk0_71),sk0_69)
| ~ spl0_2 ),
inference(paramodulation,[status(thm)],[f915,f957]) ).
fof(f1035,plain,
( ~ spl0_7
| ~ spl0_8
| ~ spl0_1
| spl0_0
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f1034,f1015,f1018,f910,f907,f914]) ).
fof(f1036,plain,
( $false
| spl0_8 ),
inference(forward_subsumption_resolution,[status(thm)],[f1020,f869]) ).
fof(f1037,plain,
spl0_8,
inference(contradiction_clause,[status(thm)],[f1036]) ).
fof(f1038,plain,
$false,
inference(sat_refutation,[status(thm)],[f913,f917,f918,f1022,f1024,f1027,f1035,f1037]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.09 % Problem : SEU212+2 : TPTP v8.1.2. Released v3.3.0.
% 0.08/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30 % Computer : n023.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 : Mon Apr 29 20:04:40 EDT 2024
% 0.09/0.30 % CPUTime :
% 0.14/0.32 % Drodi V3.6.0
% 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
% 0.14/0.34 % Elapsed time: 0.031009 seconds
% 0.14/0.34 % CPU time: 0.046650 seconds
% 0.14/0.34 % Total memory used: 18.934 MB
% 0.14/0.34 % Net memory used: 18.878 MB
%------------------------------------------------------------------------------