TSTP Solution File: SEU214+3 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SEU214+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n027.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 20:41:31 EDT 2024
% Result : Theorem 1.71s 0.62s
% Output : CNFRefutation 1.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 17
% Syntax : Number of formulae : 91 ( 12 unt; 0 def)
% Number of atoms : 382 ( 52 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 478 ( 187 ~; 193 |; 60 &)
% ( 23 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 12 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 4 con; 0-5 aty)
% Number of variables : 162 ( 138 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,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(f6,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(f8,axiom,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ! [C] :
( relation(C)
=> ( C = relation_composition(A,B)
<=> ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ? [F] :
( in(ordered_pair(D,F),A)
& in(ordered_pair(F,E),B) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B] :
( ( relation(A)
& relation(B) )
=> relation(relation_composition(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A,B] :
( ( relation(A)
& function(A)
& relation(B)
& function(B) )
=> ( relation(relation_composition(A,B))
& function(relation_composition(A,B)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,conjecture,
! [A,B] :
( ( relation(B)
& function(B) )
=> ! [C] :
( ( relation(C)
& function(C) )
=> ( in(A,relation_dom(relation_composition(C,B)))
=> apply(relation_composition(C,B),A) = apply(B,apply(C,A)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
~ ! [A,B] :
( ( relation(B)
& function(B) )
=> ! [C] :
( ( relation(C)
& function(C) )
=> ( in(A,relation_dom(relation_composition(C,B)))
=> apply(relation_composition(C,B),A) = apply(B,apply(C,A)) ) ) ),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f49,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)],[f5]) ).
fof(f50,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)],[f49]) ).
fof(f51,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)],[f50]) ).
fof(f52,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)],[f51]) ).
fof(f53,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)],[f51]) ).
fof(f56,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)],[f6]) ).
fof(f57,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)],[f56]) ).
fof(f58,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)],[f57]) ).
fof(f59,plain,
! [A] :
( ~ relation(A)
| ( ! [B] :
( B != relation_dom(A)
| ( ! [C] :
( ~ in(C,B)
| in(ordered_pair(C,sk0_0(C,B,A)),A) )
& ! [C] :
( in(C,B)
| ! [D] : ~ in(ordered_pair(C,D),A) ) ) )
& ! [B] :
( B = relation_dom(A)
| ( ( ~ in(sk0_1(B,A),B)
| ! [D] : ~ in(ordered_pair(sk0_1(B,A),D),A) )
& ( in(sk0_1(B,A),B)
| in(ordered_pair(sk0_1(B,A),sk0_2(B,A)),A) ) ) ) ) ),
inference(skolemization,[status(esa)],[f58]) ).
fof(f61,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)],[f59]) ).
fof(f65,plain,
! [A] :
( ~ relation(A)
| ! [B] :
( ~ relation(B)
| ! [C] :
( ~ relation(C)
| ( C = relation_composition(A,B)
<=> ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ? [F] :
( in(ordered_pair(D,F),A)
& in(ordered_pair(F,E),B) ) ) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f8]) ).
fof(f66,plain,
! [A] :
( ~ relation(A)
| ! [B] :
( ~ relation(B)
| ! [C] :
( ~ relation(C)
| ( ( C != relation_composition(A,B)
| ! [D,E] :
( ( ~ in(ordered_pair(D,E),C)
| ? [F] :
( in(ordered_pair(D,F),A)
& in(ordered_pair(F,E),B) ) )
& ( in(ordered_pair(D,E),C)
| ! [F] :
( ~ in(ordered_pair(D,F),A)
| ~ in(ordered_pair(F,E),B) ) ) ) )
& ( C = relation_composition(A,B)
| ? [D,E] :
( ( ~ in(ordered_pair(D,E),C)
| ! [F] :
( ~ in(ordered_pair(D,F),A)
| ~ in(ordered_pair(F,E),B) ) )
& ( in(ordered_pair(D,E),C)
| ? [F] :
( in(ordered_pair(D,F),A)
& in(ordered_pair(F,E),B) ) ) ) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f65]) ).
fof(f67,plain,
! [A] :
( ~ relation(A)
| ! [B] :
( ~ relation(B)
| ! [C] :
( ~ relation(C)
| ( ( C != relation_composition(A,B)
| ( ! [D,E] :
( ~ in(ordered_pair(D,E),C)
| ? [F] :
( in(ordered_pair(D,F),A)
& in(ordered_pair(F,E),B) ) )
& ! [D,E] :
( in(ordered_pair(D,E),C)
| ! [F] :
( ~ in(ordered_pair(D,F),A)
| ~ in(ordered_pair(F,E),B) ) ) ) )
& ( C = relation_composition(A,B)
| ? [D,E] :
( ( ~ in(ordered_pair(D,E),C)
| ! [F] :
( ~ in(ordered_pair(D,F),A)
| ~ in(ordered_pair(F,E),B) ) )
& ( in(ordered_pair(D,E),C)
| ? [F] :
( in(ordered_pair(D,F),A)
& in(ordered_pair(F,E),B) ) ) ) ) ) ) ) ),
inference(miniscoping,[status(esa)],[f66]) ).
fof(f68,plain,
! [A] :
( ~ relation(A)
| ! [B] :
( ~ relation(B)
| ! [C] :
( ~ relation(C)
| ( ( C != relation_composition(A,B)
| ( ! [D,E] :
( ~ in(ordered_pair(D,E),C)
| ( in(ordered_pair(D,sk0_3(E,D,C,B,A)),A)
& in(ordered_pair(sk0_3(E,D,C,B,A),E),B) ) )
& ! [D,E] :
( in(ordered_pair(D,E),C)
| ! [F] :
( ~ in(ordered_pair(D,F),A)
| ~ in(ordered_pair(F,E),B) ) ) ) )
& ( C = relation_composition(A,B)
| ( ( ~ in(ordered_pair(sk0_4(C,B,A),sk0_5(C,B,A)),C)
| ! [F] :
( ~ in(ordered_pair(sk0_4(C,B,A),F),A)
| ~ in(ordered_pair(F,sk0_5(C,B,A)),B) ) )
& ( in(ordered_pair(sk0_4(C,B,A),sk0_5(C,B,A)),C)
| ( in(ordered_pair(sk0_4(C,B,A),sk0_6(C,B,A)),A)
& in(ordered_pair(sk0_6(C,B,A),sk0_5(C,B,A)),B) ) ) ) ) ) ) ) ),
inference(skolemization,[status(esa)],[f67]) ).
fof(f69,plain,
! [X0,X1,X2,X3,X4] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_composition(X0,X1)
| ~ in(ordered_pair(X3,X4),X2)
| in(ordered_pair(X3,sk0_3(X4,X3,X2,X1,X0)),X0) ),
inference(cnf_transformation,[status(esa)],[f68]) ).
fof(f70,plain,
! [X0,X1,X2,X3,X4] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| X2 != relation_composition(X0,X1)
| ~ in(ordered_pair(X3,X4),X2)
| in(ordered_pair(sk0_3(X4,X3,X2,X1,X0),X4),X1) ),
inference(cnf_transformation,[status(esa)],[f68]) ).
fof(f75,plain,
! [A,B] :
( ~ relation(A)
| ~ relation(B)
| relation(relation_composition(A,B)) ),
inference(pre_NNF_transformation,[status(esa)],[f9]) ).
fof(f76,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| relation(relation_composition(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f75]) ).
fof(f85,plain,
! [A,B] :
( ~ relation(A)
| ~ function(A)
| ~ relation(B)
| ~ function(B)
| ( relation(relation_composition(A,B))
& function(relation_composition(A,B)) ) ),
inference(pre_NNF_transformation,[status(esa)],[f13]) ).
fof(f87,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ function(X0)
| ~ relation(X1)
| ~ function(X1)
| function(relation_composition(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f85]) ).
fof(f130,plain,
? [A,B] :
( relation(B)
& function(B)
& ? [C] :
( relation(C)
& function(C)
& in(A,relation_dom(relation_composition(C,B)))
& apply(relation_composition(C,B),A) != apply(B,apply(C,A)) ) ),
inference(pre_NNF_transformation,[status(esa)],[f34]) ).
fof(f131,plain,
? [B] :
( relation(B)
& function(B)
& ? [C] :
( relation(C)
& function(C)
& ? [A] :
( in(A,relation_dom(relation_composition(C,B)))
& apply(relation_composition(C,B),A) != apply(B,apply(C,A)) ) ) ),
inference(miniscoping,[status(esa)],[f130]) ).
fof(f132,plain,
( relation(sk0_16)
& function(sk0_16)
& relation(sk0_17)
& function(sk0_17)
& in(sk0_18,relation_dom(relation_composition(sk0_17,sk0_16)))
& apply(relation_composition(sk0_17,sk0_16),sk0_18) != apply(sk0_16,apply(sk0_17,sk0_18)) ),
inference(skolemization,[status(esa)],[f131]) ).
fof(f133,plain,
relation(sk0_16),
inference(cnf_transformation,[status(esa)],[f132]) ).
fof(f134,plain,
function(sk0_16),
inference(cnf_transformation,[status(esa)],[f132]) ).
fof(f135,plain,
relation(sk0_17),
inference(cnf_transformation,[status(esa)],[f132]) ).
fof(f136,plain,
function(sk0_17),
inference(cnf_transformation,[status(esa)],[f132]) ).
fof(f137,plain,
in(sk0_18,relation_dom(relation_composition(sk0_17,sk0_16))),
inference(cnf_transformation,[status(esa)],[f132]) ).
fof(f138,plain,
apply(relation_composition(sk0_17,sk0_16),sk0_18) != apply(sk0_16,apply(sk0_17,sk0_18)),
inference(cnf_transformation,[status(esa)],[f132]) ).
fof(f159,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)],[f52]) ).
fof(f163,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| in(X1,relation_dom(X0))
| ~ in(ordered_pair(X1,X2),X0) ),
inference(destructive_equality_resolution,[status(esa)],[f61]) ).
fof(f164,plain,
! [X0,X1,X2,X3] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(relation_composition(X0,X1))
| ~ in(ordered_pair(X2,X3),relation_composition(X0,X1))
| in(ordered_pair(X2,sk0_3(X3,X2,relation_composition(X0,X1),X1,X0)),X0) ),
inference(destructive_equality_resolution,[status(esa)],[f69]) ).
fof(f165,plain,
! [X0,X1,X2,X3] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(relation_composition(X0,X1))
| ~ in(ordered_pair(X2,X3),relation_composition(X0,X1))
| in(ordered_pair(sk0_3(X3,X2,relation_composition(X0,X1),X1,X0),X3),X1) ),
inference(destructive_equality_resolution,[status(esa)],[f70]) ).
fof(f168,plain,
( spl0_0
<=> relation(relation_composition(sk0_17,sk0_16)) ),
introduced(split_symbol_definition) ).
fof(f170,plain,
( ~ relation(relation_composition(sk0_17,sk0_16))
| spl0_0 ),
inference(component_clause,[status(thm)],[f168]) ).
fof(f171,plain,
( spl0_1
<=> function(relation_composition(sk0_17,sk0_16)) ),
introduced(split_symbol_definition) ).
fof(f173,plain,
( ~ function(relation_composition(sk0_17,sk0_16))
| spl0_1 ),
inference(component_clause,[status(thm)],[f171]) ).
fof(f174,plain,
( spl0_2
<=> in(ordered_pair(sk0_18,apply(relation_composition(sk0_17,sk0_16),sk0_18)),relation_composition(sk0_17,sk0_16)) ),
introduced(split_symbol_definition) ).
fof(f175,plain,
( in(ordered_pair(sk0_18,apply(relation_composition(sk0_17,sk0_16),sk0_18)),relation_composition(sk0_17,sk0_16))
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f174]) ).
fof(f177,plain,
( ~ relation(relation_composition(sk0_17,sk0_16))
| ~ function(relation_composition(sk0_17,sk0_16))
| in(ordered_pair(sk0_18,apply(relation_composition(sk0_17,sk0_16),sk0_18)),relation_composition(sk0_17,sk0_16)) ),
inference(resolution,[status(thm)],[f159,f137]) ).
fof(f178,plain,
( ~ spl0_0
| ~ spl0_1
| spl0_2 ),
inference(split_clause,[status(thm)],[f177,f168,f171,f174]) ).
fof(f188,plain,
( spl0_5
<=> relation(sk0_16) ),
introduced(split_symbol_definition) ).
fof(f190,plain,
( ~ relation(sk0_16)
| spl0_5 ),
inference(component_clause,[status(thm)],[f188]) ).
fof(f196,plain,
( spl0_7
<=> relation(sk0_17) ),
introduced(split_symbol_definition) ).
fof(f198,plain,
( ~ relation(sk0_17)
| spl0_7 ),
inference(component_clause,[status(thm)],[f196]) ).
fof(f201,plain,
( ~ relation(sk0_17)
| ~ relation(sk0_16)
| spl0_0 ),
inference(resolution,[status(thm)],[f170,f76]) ).
fof(f202,plain,
( ~ spl0_7
| ~ spl0_5
| spl0_0 ),
inference(split_clause,[status(thm)],[f201,f196,f188,f168]) ).
fof(f203,plain,
( $false
| spl0_5 ),
inference(forward_subsumption_resolution,[status(thm)],[f190,f133]) ).
fof(f204,plain,
spl0_5,
inference(contradiction_clause,[status(thm)],[f203]) ).
fof(f205,plain,
( $false
| spl0_7 ),
inference(forward_subsumption_resolution,[status(thm)],[f198,f135]) ).
fof(f206,plain,
spl0_7,
inference(contradiction_clause,[status(thm)],[f205]) ).
fof(f224,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| ~ function(X0)
| X1 = apply(X0,X2)
| ~ in(ordered_pair(X2,X1),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f53,f163]) ).
fof(f255,plain,
( spl0_17
<=> function(sk0_17) ),
introduced(split_symbol_definition) ).
fof(f257,plain,
( ~ function(sk0_17)
| spl0_17 ),
inference(component_clause,[status(thm)],[f255]) ).
fof(f258,plain,
( spl0_18
<=> function(sk0_16) ),
introduced(split_symbol_definition) ).
fof(f260,plain,
( ~ function(sk0_16)
| spl0_18 ),
inference(component_clause,[status(thm)],[f258]) ).
fof(f261,plain,
( ~ relation(sk0_17)
| ~ function(sk0_17)
| ~ relation(sk0_16)
| ~ function(sk0_16)
| spl0_1 ),
inference(resolution,[status(thm)],[f87,f173]) ).
fof(f262,plain,
( ~ spl0_7
| ~ spl0_17
| ~ spl0_5
| ~ spl0_18
| spl0_1 ),
inference(split_clause,[status(thm)],[f261,f196,f255,f188,f258,f171]) ).
fof(f263,plain,
( $false
| spl0_17 ),
inference(forward_subsumption_resolution,[status(thm)],[f257,f136]) ).
fof(f264,plain,
spl0_17,
inference(contradiction_clause,[status(thm)],[f263]) ).
fof(f265,plain,
( $false
| spl0_18 ),
inference(forward_subsumption_resolution,[status(thm)],[f260,f134]) ).
fof(f266,plain,
spl0_18,
inference(contradiction_clause,[status(thm)],[f265]) ).
fof(f658,plain,
! [X0,X1,X2,X3] :
( ~ relation(X0)
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),relation_composition(X0,X1))
| in(ordered_pair(X2,sk0_3(X3,X2,relation_composition(X0,X1),X1,X0)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f164,f76]) ).
fof(f659,plain,
( spl0_30
<=> in(ordered_pair(sk0_18,sk0_3(apply(relation_composition(sk0_17,sk0_16),sk0_18),sk0_18,relation_composition(sk0_17,sk0_16),sk0_16,sk0_17)),sk0_17) ),
introduced(split_symbol_definition) ).
fof(f660,plain,
( in(ordered_pair(sk0_18,sk0_3(apply(relation_composition(sk0_17,sk0_16),sk0_18),sk0_18,relation_composition(sk0_17,sk0_16),sk0_16,sk0_17)),sk0_17)
| ~ spl0_30 ),
inference(component_clause,[status(thm)],[f659]) ).
fof(f662,plain,
( ~ relation(sk0_17)
| ~ relation(sk0_16)
| in(ordered_pair(sk0_18,sk0_3(apply(relation_composition(sk0_17,sk0_16),sk0_18),sk0_18,relation_composition(sk0_17,sk0_16),sk0_16,sk0_17)),sk0_17)
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f658,f175]) ).
fof(f663,plain,
( ~ spl0_7
| ~ spl0_5
| spl0_30
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f662,f196,f188,f659,f174]) ).
fof(f664,plain,
! [X0,X1,X2,X3] :
( ~ relation(X0)
| ~ relation(X1)
| ~ in(ordered_pair(X2,X3),relation_composition(X0,X1))
| in(ordered_pair(sk0_3(X3,X2,relation_composition(X0,X1),X1,X0),X3),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f165,f76]) ).
fof(f665,plain,
( spl0_31
<=> in(ordered_pair(sk0_3(apply(relation_composition(sk0_17,sk0_16),sk0_18),sk0_18,relation_composition(sk0_17,sk0_16),sk0_16,sk0_17),apply(relation_composition(sk0_17,sk0_16),sk0_18)),sk0_16) ),
introduced(split_symbol_definition) ).
fof(f666,plain,
( in(ordered_pair(sk0_3(apply(relation_composition(sk0_17,sk0_16),sk0_18),sk0_18,relation_composition(sk0_17,sk0_16),sk0_16,sk0_17),apply(relation_composition(sk0_17,sk0_16),sk0_18)),sk0_16)
| ~ spl0_31 ),
inference(component_clause,[status(thm)],[f665]) ).
fof(f668,plain,
( ~ relation(sk0_17)
| ~ relation(sk0_16)
| in(ordered_pair(sk0_3(apply(relation_composition(sk0_17,sk0_16),sk0_18),sk0_18,relation_composition(sk0_17,sk0_16),sk0_16,sk0_17),apply(relation_composition(sk0_17,sk0_16),sk0_18)),sk0_16)
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f664,f175]) ).
fof(f669,plain,
( ~ spl0_7
| ~ spl0_5
| spl0_31
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f668,f196,f188,f665,f174]) ).
fof(f798,plain,
( spl0_39
<=> sk0_3(apply(relation_composition(sk0_17,sk0_16),sk0_18),sk0_18,relation_composition(sk0_17,sk0_16),sk0_16,sk0_17) = apply(sk0_17,sk0_18) ),
introduced(split_symbol_definition) ).
fof(f799,plain,
( sk0_3(apply(relation_composition(sk0_17,sk0_16),sk0_18),sk0_18,relation_composition(sk0_17,sk0_16),sk0_16,sk0_17) = apply(sk0_17,sk0_18)
| ~ spl0_39 ),
inference(component_clause,[status(thm)],[f798]) ).
fof(f801,plain,
( ~ relation(sk0_17)
| ~ function(sk0_17)
| sk0_3(apply(relation_composition(sk0_17,sk0_16),sk0_18),sk0_18,relation_composition(sk0_17,sk0_16),sk0_16,sk0_17) = apply(sk0_17,sk0_18)
| ~ spl0_30 ),
inference(resolution,[status(thm)],[f660,f224]) ).
fof(f802,plain,
( ~ spl0_7
| ~ spl0_17
| spl0_39
| ~ spl0_30 ),
inference(split_clause,[status(thm)],[f801,f196,f255,f798,f659]) ).
fof(f846,plain,
( in(ordered_pair(apply(sk0_17,sk0_18),apply(relation_composition(sk0_17,sk0_16),sk0_18)),sk0_16)
| ~ spl0_39
| ~ spl0_31 ),
inference(forward_demodulation,[status(thm)],[f799,f666]) ).
fof(f852,plain,
( spl0_48
<=> apply(relation_composition(sk0_17,sk0_16),sk0_18) = apply(sk0_16,apply(sk0_17,sk0_18)) ),
introduced(split_symbol_definition) ).
fof(f853,plain,
( apply(relation_composition(sk0_17,sk0_16),sk0_18) = apply(sk0_16,apply(sk0_17,sk0_18))
| ~ spl0_48 ),
inference(component_clause,[status(thm)],[f852]) ).
fof(f855,plain,
( ~ relation(sk0_16)
| ~ function(sk0_16)
| apply(relation_composition(sk0_17,sk0_16),sk0_18) = apply(sk0_16,apply(sk0_17,sk0_18))
| ~ spl0_39
| ~ spl0_31 ),
inference(resolution,[status(thm)],[f846,f224]) ).
fof(f856,plain,
( ~ spl0_5
| ~ spl0_18
| spl0_48
| ~ spl0_39
| ~ spl0_31 ),
inference(split_clause,[status(thm)],[f855,f188,f258,f852,f798,f665]) ).
fof(f863,plain,
( $false
| ~ spl0_48 ),
inference(forward_subsumption_resolution,[status(thm)],[f853,f138]) ).
fof(f864,plain,
~ spl0_48,
inference(contradiction_clause,[status(thm)],[f863]) ).
fof(f865,plain,
$false,
inference(sat_refutation,[status(thm)],[f178,f202,f204,f206,f262,f264,f266,f663,f669,f802,f856,f864]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU214+3 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35 % Computer : n027.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Apr 29 20:14:32 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.36 % Drodi V3.6.0
% 1.71/0.62 % Refutation found
% 1.71/0.62 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.71/0.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.71/0.64 % Elapsed time: 0.281925 seconds
% 1.71/0.64 % CPU time: 2.070503 seconds
% 1.71/0.64 % Total memory used: 87.054 MB
% 1.71/0.64 % Net memory used: 86.288 MB
%------------------------------------------------------------------------------