TSTP Solution File: SEU214+1 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SEU214+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n028.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 1.73s 0.66s
% Output : CNFRefutation 2.37s
% 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(f15,axiom,
! [A,B] :
( ( relation(A)
& relation(B) )
=> relation(relation_composition(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,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(f36,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(f37,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)],[f36]) ).
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)],[f15]) ).
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)],[f20]) ).
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(f120,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)],[f37]) ).
fof(f121,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)],[f120]) ).
fof(f122,plain,
( relation(sk0_14)
& function(sk0_14)
& relation(sk0_15)
& function(sk0_15)
& in(sk0_16,relation_dom(relation_composition(sk0_15,sk0_14)))
& apply(relation_composition(sk0_15,sk0_14),sk0_16) != apply(sk0_14,apply(sk0_15,sk0_16)) ),
inference(skolemization,[status(esa)],[f121]) ).
fof(f123,plain,
relation(sk0_14),
inference(cnf_transformation,[status(esa)],[f122]) ).
fof(f124,plain,
function(sk0_14),
inference(cnf_transformation,[status(esa)],[f122]) ).
fof(f125,plain,
relation(sk0_15),
inference(cnf_transformation,[status(esa)],[f122]) ).
fof(f126,plain,
function(sk0_15),
inference(cnf_transformation,[status(esa)],[f122]) ).
fof(f127,plain,
in(sk0_16,relation_dom(relation_composition(sk0_15,sk0_14))),
inference(cnf_transformation,[status(esa)],[f122]) ).
fof(f128,plain,
apply(relation_composition(sk0_15,sk0_14),sk0_16) != apply(sk0_14,apply(sk0_15,sk0_16)),
inference(cnf_transformation,[status(esa)],[f122]) ).
fof(f139,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(f143,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(f144,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(f145,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(f148,plain,
( spl0_0
<=> relation(relation_composition(sk0_15,sk0_14)) ),
introduced(split_symbol_definition) ).
fof(f150,plain,
( ~ relation(relation_composition(sk0_15,sk0_14))
| spl0_0 ),
inference(component_clause,[status(thm)],[f148]) ).
fof(f151,plain,
( spl0_1
<=> function(relation_composition(sk0_15,sk0_14)) ),
introduced(split_symbol_definition) ).
fof(f153,plain,
( ~ function(relation_composition(sk0_15,sk0_14))
| spl0_1 ),
inference(component_clause,[status(thm)],[f151]) ).
fof(f154,plain,
( spl0_2
<=> in(ordered_pair(sk0_16,apply(relation_composition(sk0_15,sk0_14),sk0_16)),relation_composition(sk0_15,sk0_14)) ),
introduced(split_symbol_definition) ).
fof(f155,plain,
( in(ordered_pair(sk0_16,apply(relation_composition(sk0_15,sk0_14),sk0_16)),relation_composition(sk0_15,sk0_14))
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f154]) ).
fof(f157,plain,
( ~ relation(relation_composition(sk0_15,sk0_14))
| ~ function(relation_composition(sk0_15,sk0_14))
| in(ordered_pair(sk0_16,apply(relation_composition(sk0_15,sk0_14),sk0_16)),relation_composition(sk0_15,sk0_14)) ),
inference(resolution,[status(thm)],[f139,f127]) ).
fof(f158,plain,
( ~ spl0_0
| ~ spl0_1
| spl0_2 ),
inference(split_clause,[status(thm)],[f157,f148,f151,f154]) ).
fof(f168,plain,
( spl0_5
<=> relation(sk0_14) ),
introduced(split_symbol_definition) ).
fof(f170,plain,
( ~ relation(sk0_14)
| spl0_5 ),
inference(component_clause,[status(thm)],[f168]) ).
fof(f176,plain,
( spl0_7
<=> relation(sk0_15) ),
introduced(split_symbol_definition) ).
fof(f178,plain,
( ~ relation(sk0_15)
| spl0_7 ),
inference(component_clause,[status(thm)],[f176]) ).
fof(f181,plain,
( ~ relation(sk0_15)
| ~ relation(sk0_14)
| spl0_0 ),
inference(resolution,[status(thm)],[f150,f76]) ).
fof(f182,plain,
( ~ spl0_7
| ~ spl0_5
| spl0_0 ),
inference(split_clause,[status(thm)],[f181,f176,f168,f148]) ).
fof(f183,plain,
( $false
| spl0_5 ),
inference(forward_subsumption_resolution,[status(thm)],[f170,f123]) ).
fof(f184,plain,
spl0_5,
inference(contradiction_clause,[status(thm)],[f183]) ).
fof(f185,plain,
( $false
| spl0_7 ),
inference(forward_subsumption_resolution,[status(thm)],[f178,f125]) ).
fof(f186,plain,
spl0_7,
inference(contradiction_clause,[status(thm)],[f185]) ).
fof(f204,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,f143]) ).
fof(f235,plain,
( spl0_17
<=> function(sk0_15) ),
introduced(split_symbol_definition) ).
fof(f237,plain,
( ~ function(sk0_15)
| spl0_17 ),
inference(component_clause,[status(thm)],[f235]) ).
fof(f238,plain,
( spl0_18
<=> function(sk0_14) ),
introduced(split_symbol_definition) ).
fof(f240,plain,
( ~ function(sk0_14)
| spl0_18 ),
inference(component_clause,[status(thm)],[f238]) ).
fof(f241,plain,
( ~ relation(sk0_15)
| ~ function(sk0_15)
| ~ relation(sk0_14)
| ~ function(sk0_14)
| spl0_1 ),
inference(resolution,[status(thm)],[f87,f153]) ).
fof(f242,plain,
( ~ spl0_7
| ~ spl0_17
| ~ spl0_5
| ~ spl0_18
| spl0_1 ),
inference(split_clause,[status(thm)],[f241,f176,f235,f168,f238,f151]) ).
fof(f243,plain,
( $false
| spl0_17 ),
inference(forward_subsumption_resolution,[status(thm)],[f237,f126]) ).
fof(f244,plain,
spl0_17,
inference(contradiction_clause,[status(thm)],[f243]) ).
fof(f245,plain,
( $false
| spl0_18 ),
inference(forward_subsumption_resolution,[status(thm)],[f240,f124]) ).
fof(f246,plain,
spl0_18,
inference(contradiction_clause,[status(thm)],[f245]) ).
fof(f642,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)],[f144,f76]) ).
fof(f643,plain,
( spl0_30
<=> in(ordered_pair(sk0_16,sk0_3(apply(relation_composition(sk0_15,sk0_14),sk0_16),sk0_16,relation_composition(sk0_15,sk0_14),sk0_14,sk0_15)),sk0_15) ),
introduced(split_symbol_definition) ).
fof(f644,plain,
( in(ordered_pair(sk0_16,sk0_3(apply(relation_composition(sk0_15,sk0_14),sk0_16),sk0_16,relation_composition(sk0_15,sk0_14),sk0_14,sk0_15)),sk0_15)
| ~ spl0_30 ),
inference(component_clause,[status(thm)],[f643]) ).
fof(f646,plain,
( ~ relation(sk0_15)
| ~ relation(sk0_14)
| in(ordered_pair(sk0_16,sk0_3(apply(relation_composition(sk0_15,sk0_14),sk0_16),sk0_16,relation_composition(sk0_15,sk0_14),sk0_14,sk0_15)),sk0_15)
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f642,f155]) ).
fof(f647,plain,
( ~ spl0_7
| ~ spl0_5
| spl0_30
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f646,f176,f168,f643,f154]) ).
fof(f648,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)],[f145,f76]) ).
fof(f649,plain,
( spl0_31
<=> in(ordered_pair(sk0_3(apply(relation_composition(sk0_15,sk0_14),sk0_16),sk0_16,relation_composition(sk0_15,sk0_14),sk0_14,sk0_15),apply(relation_composition(sk0_15,sk0_14),sk0_16)),sk0_14) ),
introduced(split_symbol_definition) ).
fof(f650,plain,
( in(ordered_pair(sk0_3(apply(relation_composition(sk0_15,sk0_14),sk0_16),sk0_16,relation_composition(sk0_15,sk0_14),sk0_14,sk0_15),apply(relation_composition(sk0_15,sk0_14),sk0_16)),sk0_14)
| ~ spl0_31 ),
inference(component_clause,[status(thm)],[f649]) ).
fof(f652,plain,
( ~ relation(sk0_15)
| ~ relation(sk0_14)
| in(ordered_pair(sk0_3(apply(relation_composition(sk0_15,sk0_14),sk0_16),sk0_16,relation_composition(sk0_15,sk0_14),sk0_14,sk0_15),apply(relation_composition(sk0_15,sk0_14),sk0_16)),sk0_14)
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f648,f155]) ).
fof(f653,plain,
( ~ spl0_7
| ~ spl0_5
| spl0_31
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f652,f176,f168,f649,f154]) ).
fof(f782,plain,
( spl0_39
<=> sk0_3(apply(relation_composition(sk0_15,sk0_14),sk0_16),sk0_16,relation_composition(sk0_15,sk0_14),sk0_14,sk0_15) = apply(sk0_15,sk0_16) ),
introduced(split_symbol_definition) ).
fof(f783,plain,
( sk0_3(apply(relation_composition(sk0_15,sk0_14),sk0_16),sk0_16,relation_composition(sk0_15,sk0_14),sk0_14,sk0_15) = apply(sk0_15,sk0_16)
| ~ spl0_39 ),
inference(component_clause,[status(thm)],[f782]) ).
fof(f785,plain,
( ~ relation(sk0_15)
| ~ function(sk0_15)
| sk0_3(apply(relation_composition(sk0_15,sk0_14),sk0_16),sk0_16,relation_composition(sk0_15,sk0_14),sk0_14,sk0_15) = apply(sk0_15,sk0_16)
| ~ spl0_30 ),
inference(resolution,[status(thm)],[f644,f204]) ).
fof(f786,plain,
( ~ spl0_7
| ~ spl0_17
| spl0_39
| ~ spl0_30 ),
inference(split_clause,[status(thm)],[f785,f176,f235,f782,f643]) ).
fof(f830,plain,
( in(ordered_pair(apply(sk0_15,sk0_16),apply(relation_composition(sk0_15,sk0_14),sk0_16)),sk0_14)
| ~ spl0_39
| ~ spl0_31 ),
inference(forward_demodulation,[status(thm)],[f783,f650]) ).
fof(f836,plain,
( spl0_48
<=> apply(relation_composition(sk0_15,sk0_14),sk0_16) = apply(sk0_14,apply(sk0_15,sk0_16)) ),
introduced(split_symbol_definition) ).
fof(f837,plain,
( apply(relation_composition(sk0_15,sk0_14),sk0_16) = apply(sk0_14,apply(sk0_15,sk0_16))
| ~ spl0_48 ),
inference(component_clause,[status(thm)],[f836]) ).
fof(f839,plain,
( ~ relation(sk0_14)
| ~ function(sk0_14)
| apply(relation_composition(sk0_15,sk0_14),sk0_16) = apply(sk0_14,apply(sk0_15,sk0_16))
| ~ spl0_39
| ~ spl0_31 ),
inference(resolution,[status(thm)],[f830,f204]) ).
fof(f840,plain,
( ~ spl0_5
| ~ spl0_18
| spl0_48
| ~ spl0_39
| ~ spl0_31 ),
inference(split_clause,[status(thm)],[f839,f168,f238,f836,f782,f649]) ).
fof(f847,plain,
( $false
| ~ spl0_48 ),
inference(forward_subsumption_resolution,[status(thm)],[f837,f128]) ).
fof(f848,plain,
~ spl0_48,
inference(contradiction_clause,[status(thm)],[f847]) ).
fof(f849,plain,
$false,
inference(sat_refutation,[status(thm)],[f158,f182,f184,f186,f242,f244,f246,f647,f653,f786,f840,f848]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SEU214+1 : TPTP v8.1.2. Released v3.3.0.
% 0.04/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Apr 29 20:09:14 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.36 % Drodi V3.6.0
% 1.73/0.66 % Refutation found
% 1.73/0.66 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.73/0.66 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.37/0.69 % Elapsed time: 0.323775 seconds
% 2.37/0.69 % CPU time: 2.390651 seconds
% 2.37/0.69 % Total memory used: 85.842 MB
% 2.37/0.69 % Net memory used: 85.005 MB
%------------------------------------------------------------------------------