%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET796+4 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:10:38 PM UTC 2026
% Result : Theorem 8.87s 1.66s
% Output : CNFRefutation 8.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 25
% Syntax : Number of formulae : 143 ( 12 unt; 20 def)
% Number of atoms : 845 ( 29 equ)
% Maximal formula atoms : 19 ( 5 avg)
% Number of connectives : 1262 ( 560 ~; 565 |; 99 &)
% ( 29 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 8 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 27 ( 25 usr; 19 prp; 0-4 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-4 aty)
% Number of variables : 370 ( 350 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X,A,B] :
( member(X,unordered_pair(A,B))
<=> ( X = B
| X = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [R,E] :
( order(R,E)
<=> ( ! [X,Y,Z] :
( ( member(Z,E)
& member(Y,E)
& member(X,E) )
=> ( ( apply(R,Y,Z)
& apply(R,X,Y) )
=> apply(R,X,Z) ) )
& ! [X,Y] :
( ( member(Y,E)
& member(X,E) )
=> ( ( apply(R,Y,X)
& apply(R,X,Y) )
=> X = Y ) )
& ! [X] :
( member(X,E)
=> apply(R,X,X) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [R,E,M] :
( lower_bound(M,R,E)
<=> ! [X] :
( member(X,E)
=> apply(R,M,X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [A,X,R,E] :
( greatest_lower_bound(A,X,R,E)
<=> ( ! [M] :
( ( lower_bound(M,R,X)
& member(M,E) )
=> apply(R,M,A) )
& lower_bound(A,R,X)
& member(A,X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,conjecture,
! [R,E,A,B] :
( ( apply(R,A,B)
& member(B,E)
& member(A,E)
& order(R,E) )
=> greatest_lower_bound(A,unordered_pair(A,B),R,E) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
~ ! [R,E,A,B] :
( ( apply(R,A,B)
& member(B,E)
& member(A,E)
& order(R,E) )
=> greatest_lower_bound(A,unordered_pair(A,B),R,E) ),
inference(negated_conjecture,[status(cth)],[f22]) ).
fof(f60,plain,
! [X,A,B] :
( ( ( X != B
& X != A )
| member(X,unordered_pair(A,B)) )
& ( X = B
| X = A
| ~ member(X,unordered_pair(A,B)) ) ),
inference(NNF_transformation,[status(thm)],[f9]) ).
fof(f61,plain,
( ! [X,A,B] :
( ( X != B
& X != A )
| member(X,unordered_pair(A,B)) )
& ! [X,A,B] :
( X = B
| X = A
| ~ member(X,unordered_pair(A,B)) ) ),
inference(miniscoping,[status(thm)],[f60]) ).
fof(f62,plain,
! [X0,X1,X2] :
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f63,plain,
! [X0,X1,X2] :
( X0 != X1
| member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f78,plain,
! [R,E] :
( order(R,E)
<=> ( ! [X,Y,Z] :
( apply(R,X,Z)
| ~ apply(R,Y,Z)
| ~ apply(R,X,Y)
| ~ member(Z,E)
| ~ member(Y,E)
| ~ member(X,E) )
& ! [X,Y] :
( X = Y
| ~ apply(R,Y,X)
| ~ apply(R,X,Y)
| ~ member(Y,E)
| ~ member(X,E) )
& ! [X] :
( apply(R,X,X)
| ~ member(X,E) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f79,definition,
! [R,E] :
( sP0_prd(E,R)
<=> ( ! [X,Y] :
( X = Y
| ~ apply(R,Y,X)
| ~ apply(R,X,Y)
| ~ member(Y,E)
| ~ member(X,E) )
& ! [X] :
( apply(R,X,X)
| ~ member(X,E) ) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f80,plain,
! [R,E] :
( order(R,E)
<=> ( ! [X,Y,Z] :
( apply(R,X,Z)
| ~ apply(R,Y,Z)
| ~ apply(R,X,Y)
| ~ member(Z,E)
| ~ member(Y,E)
| ~ member(X,E) )
& sP0_prd(E,R) ) ),
inference(formula_renaming,[status(thm)],[f78,f79]) ).
fof(f81,plain,
! [R,E] :
( ( ? [X,Y,Z] :
( ~ apply(R,X,Z)
& apply(R,Y,Z)
& apply(R,X,Y)
& member(Z,E)
& member(Y,E)
& member(X,E) )
| ~ sP0_prd(E,R)
| order(R,E) )
& ( ( ! [X,Y,Z] :
( apply(R,X,Z)
| ~ apply(R,Y,Z)
| ~ apply(R,X,Y)
| ~ member(Z,E)
| ~ member(Y,E)
| ~ member(X,E) )
& sP0_prd(E,R) )
| ~ order(R,E) ) ),
inference(NNF_transformation,[status(thm)],[f80]) ).
fof(f82,plain,
( ! [R,E] :
( ? [X,Y,Z] :
( ~ apply(R,X,Z)
& apply(R,Y,Z)
& apply(R,X,Y)
& member(Z,E)
& member(Y,E)
& member(X,E) )
| ~ sP0_prd(E,R)
| order(R,E) )
& ! [R,E] :
( ( ! [X,Y,Z] :
( apply(R,X,Z)
| ~ apply(R,Y,Z)
| ~ apply(R,X,Y)
| ~ member(Z,E)
| ~ member(Y,E)
| ~ member(X,E) )
& sP0_prd(E,R) )
| ~ order(R,E) ) ),
inference(miniscoping,[status(thm)],[f81]) ).
fof(f83,plain,
( ! [R,E] :
( ( ~ apply(R,sK3_skl(E,R),sK5_skl(E,R))
& apply(R,sK4_skl(E,R),sK5_skl(E,R))
& apply(R,sK3_skl(E,R),sK4_skl(E,R))
& member(sK5_skl(E,R),E)
& member(sK4_skl(E,R),E)
& member(sK3_skl(E,R),E) )
| ~ sP0_prd(E,R)
| order(R,E) )
& ! [R,E] :
( ( ! [X,Y,Z] :
( apply(R,X,Z)
| ~ apply(R,Y,Z)
| ~ apply(R,X,Y)
| ~ member(Z,E)
| ~ member(Y,E)
| ~ member(X,E) )
& sP0_prd(E,R) )
| ~ order(R,E) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl,sK5_skl]),skolemize(X,sK3_skl(E,R)),skolemize(Y,sK4_skl(E,R)),skolemize(Z,sK5_skl(E,R))],[f82]) ).
fof(f84,plain,
! [X0,X1] :
( sP0_prd(X1,X0)
| ~ order(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f83]) ).
fof(f85,plain,
! [X0,X1,X2,X3,X4] :
( apply(X0,X2,X4)
| ~ apply(X0,X3,X4)
| ~ apply(X0,X2,X3)
| ~ member(X4,X1)
| ~ member(X3,X1)
| ~ member(X2,X1)
| ~ order(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f83]) ).
fof(f109,plain,
! [R,E,M] :
( lower_bound(M,R,E)
<=> ! [X] :
( apply(R,M,X)
| ~ member(X,E) ) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f110,plain,
! [R,E,M] :
( ( ? [X] :
( ~ apply(R,M,X)
& member(X,E) )
| lower_bound(M,R,E) )
& ( ! [X] :
( apply(R,M,X)
| ~ member(X,E) )
| ~ lower_bound(M,R,E) ) ),
inference(NNF_transformation,[status(thm)],[f109]) ).
fof(f111,plain,
( ! [R,E,M] :
( ? [X] :
( ~ apply(R,M,X)
& member(X,E) )
| lower_bound(M,R,E) )
& ! [R,E,M] :
( ! [X] :
( apply(R,M,X)
| ~ member(X,E) )
| ~ lower_bound(M,R,E) ) ),
inference(miniscoping,[status(thm)],[f110]) ).
fof(f112,plain,
( ! [R,E,M] :
( ( ~ apply(R,M,sK9_skl(M,E,R))
& member(sK9_skl(M,E,R),E) )
| lower_bound(M,R,E) )
& ! [R,E,M] :
( ! [X] :
( apply(R,M,X)
| ~ member(X,E) )
| ~ lower_bound(M,R,E) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl]),skolemize(X,sK9_skl(M,E,R))],[f111]) ).
fof(f113,plain,
! [X0,X1,X2,X3] :
( apply(X1,X0,X3)
| ~ member(X3,X2)
| ~ lower_bound(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f112]) ).
fof(f114,plain,
! [X0,X1,X2] :
( member(sK9_skl(X0,X2,X1),X2)
| lower_bound(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f112]) ).
fof(f115,plain,
! [X0,X1,X2] :
( ~ apply(X1,X0,sK9_skl(X0,X2,X1))
| lower_bound(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f112]) ).
fof(f160,plain,
! [A,X,R,E] :
( greatest_lower_bound(A,X,R,E)
<=> ( ! [M] :
( apply(R,M,A)
| ~ lower_bound(M,R,X)
| ~ member(M,E) )
& lower_bound(A,R,X)
& member(A,X) ) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f161,plain,
! [A,X,R,E] :
( ( ? [M] :
( ~ apply(R,M,A)
& lower_bound(M,R,X)
& member(M,E) )
| ~ lower_bound(A,R,X)
| ~ member(A,X)
| greatest_lower_bound(A,X,R,E) )
& ( ( ! [M] :
( apply(R,M,A)
| ~ lower_bound(M,R,X)
| ~ member(M,E) )
& lower_bound(A,R,X)
& member(A,X) )
| ~ greatest_lower_bound(A,X,R,E) ) ),
inference(NNF_transformation,[status(thm)],[f160]) ).
fof(f162,plain,
( ! [A,X,R,E] :
( ? [M] :
( ~ apply(R,M,A)
& lower_bound(M,R,X)
& member(M,E) )
| ~ lower_bound(A,R,X)
| ~ member(A,X)
| greatest_lower_bound(A,X,R,E) )
& ! [A,X,R,E] :
( ( ! [M] :
( apply(R,M,A)
| ~ lower_bound(M,R,X)
| ~ member(M,E) )
& lower_bound(A,R,X)
& member(A,X) )
| ~ greatest_lower_bound(A,X,R,E) ) ),
inference(miniscoping,[status(thm)],[f161]) ).
fof(f163,plain,
( ! [A,X,R,E] :
( ( ~ apply(R,sK15_skl(E,R,X,A),A)
& lower_bound(sK15_skl(E,R,X,A),R,X)
& member(sK15_skl(E,R,X,A),E) )
| ~ lower_bound(A,R,X)
| ~ member(A,X)
| greatest_lower_bound(A,X,R,E) )
& ! [A,X,R,E] :
( ( ! [M] :
( apply(R,M,A)
| ~ lower_bound(M,R,X)
| ~ member(M,E) )
& lower_bound(A,R,X)
& member(A,X) )
| ~ greatest_lower_bound(A,X,R,E) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15_skl]),skolemize(M,sK15_skl(E,R,X,A))],[f162]) ).
fof(f168,plain,
! [X0,X1,X2,X3] :
( lower_bound(sK15_skl(X3,X2,X1,X0),X2,X1)
| ~ lower_bound(X0,X2,X1)
| ~ member(X0,X1)
| greatest_lower_bound(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f163]) ).
fof(f169,plain,
! [X0,X1,X2,X3] :
( ~ apply(X2,sK15_skl(X3,X2,X1,X0),X0)
| ~ lower_bound(X0,X2,X1)
| ~ member(X0,X1)
| greatest_lower_bound(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f163]) ).
fof(f170,plain,
? [R,E,A,B] :
( ~ greatest_lower_bound(A,unordered_pair(A,B),R,E)
& apply(R,A,B)
& member(B,E)
& member(A,E)
& order(R,E) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f171,plain,
( ~ greatest_lower_bound(sK18_skl,unordered_pair(sK18_skl,sK19_skl),sK16_skl,sK17_skl)
& apply(sK16_skl,sK18_skl,sK19_skl)
& member(sK19_skl,sK17_skl)
& member(sK18_skl,sK17_skl)
& order(sK16_skl,sK17_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16_skl,sK17_skl,sK18_skl,sK19_skl]),skolemize(R,sK16_skl),skolemize(E,sK17_skl),skolemize(A,sK18_skl),skolemize(B,sK19_skl)],[f170]) ).
fof(f172,plain,
order(sK16_skl,sK17_skl),
inference(cnf_transformation,[status(thm)],[f171]) ).
fof(f173,plain,
member(sK18_skl,sK17_skl),
inference(cnf_transformation,[status(thm)],[f171]) ).
fof(f174,plain,
member(sK19_skl,sK17_skl),
inference(cnf_transformation,[status(thm)],[f171]) ).
fof(f175,plain,
apply(sK16_skl,sK18_skl,sK19_skl),
inference(cnf_transformation,[status(thm)],[f171]) ).
fof(f176,plain,
~ greatest_lower_bound(sK18_skl,unordered_pair(sK18_skl,sK19_skl),sK16_skl,sK17_skl),
inference(cnf_transformation,[status(thm)],[f171]) ).
fof(f177,definition,
! [R,E,X] :
( sP1_prd(X,E,R)
<=> ( apply(R,X,X)
| ~ member(X,E) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f178,plain,
! [R,E] :
( sP0_prd(E,R)
<=> ( ! [X,Y] :
( X = Y
| ~ apply(R,Y,X)
| ~ apply(R,X,Y)
| ~ member(Y,E)
| ~ member(X,E) )
& ! [X] : sP1_prd(X,E,R) ) ),
inference(formula_renaming,[status(thm)],[f79,f177]) ).
fof(f179,plain,
! [R,E] :
( ( ? [X,Y] :
( X != Y
& apply(R,Y,X)
& apply(R,X,Y)
& member(Y,E)
& member(X,E) )
| ? [X] : ~ sP1_prd(X,E,R)
| sP0_prd(E,R) )
& ( ( ! [X,Y] :
( X = Y
| ~ apply(R,Y,X)
| ~ apply(R,X,Y)
| ~ member(Y,E)
| ~ member(X,E) )
& ! [X] : sP1_prd(X,E,R) )
| ~ sP0_prd(E,R) ) ),
inference(NNF_transformation,[status(thm)],[f178]) ).
fof(f180,plain,
( ! [R,E] :
( ? [X,Y] :
( X != Y
& apply(R,Y,X)
& apply(R,X,Y)
& member(Y,E)
& member(X,E) )
| ? [X] : ~ sP1_prd(X,E,R)
| sP0_prd(E,R) )
& ! [R,E] :
( ( ! [X,Y] :
( X = Y
| ~ apply(R,Y,X)
| ~ apply(R,X,Y)
| ~ member(Y,E)
| ~ member(X,E) )
& ! [X] : sP1_prd(X,E,R) )
| ~ sP0_prd(E,R) ) ),
inference(miniscoping,[status(thm)],[f179]) ).
fof(f181,plain,
( ! [R,E] :
( ( sK21_skl(E,R) != sK22_skl(E,R)
& apply(R,sK22_skl(E,R),sK21_skl(E,R))
& apply(R,sK21_skl(E,R),sK22_skl(E,R))
& member(sK22_skl(E,R),E)
& member(sK21_skl(E,R),E) )
| ~ sP1_prd(sK20_skl(E,R),E,R)
| sP0_prd(E,R) )
& ! [R,E] :
( ( ! [X,Y] :
( X = Y
| ~ apply(R,Y,X)
| ~ apply(R,X,Y)
| ~ member(Y,E)
| ~ member(X,E) )
& ! [X] : sP1_prd(X,E,R) )
| ~ sP0_prd(E,R) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20_skl,sK21_skl,sK22_skl]),skolemize(X,sK20_skl(E,R)),skolemize(X,sK21_skl(E,R)),skolemize(Y,sK22_skl(E,R))],[f180]) ).
fof(f182,plain,
! [X0,X1,X2] :
( sP1_prd(X2,X0,X1)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f181]) ).
fof(f189,plain,
! [R,E,X] :
( ( ( ~ apply(R,X,X)
& member(X,E) )
| sP1_prd(X,E,R) )
& ( apply(R,X,X)
| ~ member(X,E)
| ~ sP1_prd(X,E,R) ) ),
inference(NNF_transformation,[status(thm)],[f177]) ).
fof(f190,plain,
( ! [R,E,X] :
( ( ~ apply(R,X,X)
& member(X,E) )
| sP1_prd(X,E,R) )
& ! [R,E,X] :
( apply(R,X,X)
| ~ member(X,E)
| ~ sP1_prd(X,E,R) ) ),
inference(miniscoping,[status(thm)],[f189]) ).
fof(f191,plain,
! [X0,X1,X2] :
( apply(X2,X0,X0)
| ~ member(X0,X1)
| ~ sP1_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f195,plain,
! [X0,X1] : member(X0,unordered_pair(X0,X1)),
inference(destructive_equality_resolution,[status(thm)],[f63]) ).
fof(f203,plain,
! [X0,X1] :
( apply(sK16_skl,X1,sK19_skl)
| ~ apply(sK16_skl,X1,sK18_skl)
| ~ member(sK19_skl,X0)
| ~ member(sK18_skl,X0)
| ~ member(X1,X0)
| ~ order(sK16_skl,X0) ),
inference(resolution,[status(thm)],[f175,f85]) ).
fof(f204,plain,
! [X0] :
( apply(sK16_skl,X0,sK19_skl)
| ~ apply(sK16_skl,X0,sK18_skl)
| ~ member(sK19_skl,sK17_skl)
| ~ member(sK18_skl,sK17_skl)
| ~ member(X0,sK17_skl) ),
inference(resolution,[status(thm)],[f203,f172]) ).
fof(f205,definition,
! [X0] :
( sQ0_spl
<=> ( apply(sK16_skl,X0,sK19_skl)
| ~ apply(sK16_skl,X0,sK18_skl)
| ~ member(X0,sK17_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f206,plain,
! [X0] :
( ~ sQ0_spl
| apply(sK16_skl,X0,sK19_skl)
| ~ apply(sK16_skl,X0,sK18_skl)
| ~ member(X0,sK17_skl) ),
inference(component_clause,[status(thm)],[f205]) ).
fof(f208,definition,
( sQ1_spl
<=> member(sK18_skl,sK17_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f210,plain,
( sQ1_spl
| ~ member(sK18_skl,sK17_skl) ),
inference(component_clause,[status(thm)],[f208]) ).
fof(f211,definition,
( sQ2_spl
<=> member(sK19_skl,sK17_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f213,plain,
( sQ2_spl
| ~ member(sK19_skl,sK17_skl) ),
inference(component_clause,[status(thm)],[f211]) ).
fof(f214,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f204,f205,f208,f211]) ).
fof(f215,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f213,f174]) ).
fof(f216,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f215]) ).
fof(f217,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| apply(sK16_skl,X2,sK19_skl)
| ~ apply(sK16_skl,X2,X0)
| ~ member(sK19_skl,X1)
| ~ member(X0,X1)
| ~ member(X2,X1)
| ~ order(sK16_skl,X1)
| ~ apply(sK16_skl,X0,sK18_skl)
| ~ member(X0,sK17_skl) ),
inference(resolution,[status(thm)],[f206,f85]) ).
fof(f228,plain,
! [X0,X1] :
( ~ sQ0_spl
| apply(sK16_skl,X1,sK19_skl)
| ~ apply(sK16_skl,X1,X0)
| ~ member(sK19_skl,sK17_skl)
| ~ member(X0,sK17_skl)
| ~ member(X1,sK17_skl)
| ~ apply(sK16_skl,X0,sK18_skl)
| ~ member(X0,sK17_skl) ),
inference(resolution,[status(thm)],[f217,f172]) ).
fof(f229,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ0_spl
| apply(sK16_skl,X4,sK19_skl)
| ~ apply(sK16_skl,X4,X2)
| ~ member(sK19_skl,X3)
| ~ member(X2,X3)
| ~ member(X4,X3)
| ~ order(sK16_skl,X3)
| ~ apply(sK16_skl,X2,X0)
| ~ member(sK19_skl,X1)
| ~ member(X0,X1)
| ~ member(X2,X1)
| ~ order(sK16_skl,X1)
| ~ apply(sK16_skl,X0,sK18_skl)
| ~ member(X0,sK17_skl) ),
inference(resolution,[status(thm)],[f217,f85]) ).
fof(f230,definition,
! [X0,X1] :
( sQ3_spl
<=> ( apply(sK16_skl,X1,sK19_skl)
| ~ apply(sK16_skl,X1,X0)
| ~ member(X0,sK17_skl)
| ~ member(X1,sK17_skl)
| ~ apply(sK16_skl,X0,sK18_skl)
| ~ member(X0,sK17_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f231,plain,
! [X0,X1] :
( ~ sQ3_spl
| apply(sK16_skl,X1,sK19_skl)
| ~ apply(sK16_skl,X1,X0)
| ~ member(X0,sK17_skl)
| ~ member(X1,sK17_skl)
| ~ apply(sK16_skl,X0,sK18_skl)
| ~ member(X0,sK17_skl) ),
inference(component_clause,[status(thm)],[f230]) ).
fof(f233,plain,
( ~ sQ0_spl
| ~ sQ2_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f228,f230,f211,f205]) ).
fof(f234,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f210,f173]) ).
fof(f235,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f234]) ).
fof(f236,plain,
! [X0,X1] :
( ~ sQ3_spl
| apply(sK16_skl,X1,sK19_skl)
| ~ apply(sK16_skl,X1,X0)
| ~ member(X1,sK17_skl)
| ~ apply(sK16_skl,X0,sK18_skl)
| ~ member(X0,sK17_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f231]) ).
fof(f239,plain,
! [X0,X1,X2,X3] :
( ~ sQ3_spl
| apply(sK16_skl,X3,sK19_skl)
| ~ apply(sK16_skl,X3,X1)
| ~ member(sK19_skl,X2)
| ~ member(X1,X2)
| ~ member(X3,X2)
| ~ order(sK16_skl,X2)
| ~ apply(sK16_skl,X1,X0)
| ~ member(X1,sK17_skl)
| ~ apply(sK16_skl,X0,sK18_skl)
| ~ member(X0,sK17_skl) ),
inference(resolution,[status(thm)],[f236,f85]) ).
fof(f242,plain,
! [X0,X1,X2,X3] :
( ~ sQ0_spl
| apply(sK16_skl,X3,sK19_skl)
| ~ apply(sK16_skl,X3,X2)
| ~ member(sK19_skl,sK17_skl)
| ~ member(X2,sK17_skl)
| ~ member(X3,sK17_skl)
| ~ apply(sK16_skl,X2,X0)
| ~ member(sK19_skl,X1)
| ~ member(X0,X1)
| ~ member(X2,X1)
| ~ order(sK16_skl,X1)
| ~ apply(sK16_skl,X0,sK18_skl)
| ~ member(X0,sK17_skl) ),
inference(resolution,[status(thm)],[f229,f172]) ).
fof(f243,definition,
! [X0,X1,X2,X3] :
( sQ4_spl
<=> ( apply(sK16_skl,X3,sK19_skl)
| ~ apply(sK16_skl,X3,X2)
| ~ member(X2,sK17_skl)
| ~ member(X3,sK17_skl)
| ~ apply(sK16_skl,X2,X0)
| ~ member(sK19_skl,X1)
| ~ member(X0,X1)
| ~ member(X2,X1)
| ~ order(sK16_skl,X1)
| ~ apply(sK16_skl,X0,sK18_skl)
| ~ member(X0,sK17_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f246,plain,
( ~ sQ0_spl
| ~ sQ2_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f242,f243,f211,f205]) ).
fof(f249,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| apply(sK16_skl,X2,sK19_skl)
| ~ apply(sK16_skl,X2,X1)
| ~ member(sK19_skl,sK17_skl)
| ~ member(X1,sK17_skl)
| ~ member(X2,sK17_skl)
| ~ apply(sK16_skl,X1,X0)
| ~ member(X1,sK17_skl)
| ~ apply(sK16_skl,X0,sK18_skl)
| ~ member(X0,sK17_skl) ),
inference(resolution,[status(thm)],[f239,f172]) ).
fof(f250,definition,
! [X0,X1,X2] :
( sQ5_spl
<=> ( apply(sK16_skl,X2,sK19_skl)
| ~ apply(sK16_skl,X2,X1)
| ~ member(X1,sK17_skl)
| ~ member(X2,sK17_skl)
| ~ apply(sK16_skl,X1,X0)
| ~ member(X1,sK17_skl)
| ~ apply(sK16_skl,X0,sK18_skl)
| ~ member(X0,sK17_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f251,plain,
! [X0,X1,X2] :
( ~ sQ5_spl
| apply(sK16_skl,X2,sK19_skl)
| ~ apply(sK16_skl,X2,X1)
| ~ member(X1,sK17_skl)
| ~ member(X2,sK17_skl)
| ~ apply(sK16_skl,X1,X0)
| ~ member(X1,sK17_skl)
| ~ apply(sK16_skl,X0,sK18_skl)
| ~ member(X0,sK17_skl) ),
inference(component_clause,[status(thm)],[f250]) ).
fof(f253,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f249,f250,f211,f230]) ).
fof(f254,plain,
! [X0,X1,X2] :
( ~ sQ5_spl
| apply(sK16_skl,X2,sK19_skl)
| ~ apply(sK16_skl,X2,X1)
| ~ member(X2,sK17_skl)
| ~ apply(sK16_skl,X1,X0)
| ~ member(X1,sK17_skl)
| ~ apply(sK16_skl,X0,sK18_skl)
| ~ member(X0,sK17_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f251]) ).
fof(f260,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ5_spl
| apply(sK16_skl,X4,sK19_skl)
| ~ apply(sK16_skl,X4,X2)
| ~ member(sK19_skl,X3)
| ~ member(X2,X3)
| ~ member(X4,X3)
| ~ order(sK16_skl,X3)
| ~ apply(sK16_skl,X2,X1)
| ~ member(X2,sK17_skl)
| ~ apply(sK16_skl,X1,X0)
| ~ member(X1,sK17_skl)
| ~ apply(sK16_skl,X0,sK18_skl)
| ~ member(X0,sK17_skl) ),
inference(resolution,[status(thm)],[f254,f85]) ).
fof(f262,plain,
! [X0,X1,X2,X3] :
( ~ sQ5_spl
| apply(sK16_skl,X3,sK19_skl)
| ~ apply(sK16_skl,X3,X2)
| ~ member(sK19_skl,sK17_skl)
| ~ member(X2,sK17_skl)
| ~ member(X3,sK17_skl)
| ~ apply(sK16_skl,X2,X1)
| ~ member(X2,sK17_skl)
| ~ apply(sK16_skl,X1,X0)
| ~ member(X1,sK17_skl)
| ~ apply(sK16_skl,X0,sK18_skl)
| ~ member(X0,sK17_skl) ),
inference(resolution,[status(thm)],[f260,f172]) ).
fof(f263,definition,
! [X0,X1,X2,X3] :
( sQ6_spl
<=> ( apply(sK16_skl,X3,sK19_skl)
| ~ apply(sK16_skl,X3,X2)
| ~ member(X2,sK17_skl)
| ~ member(X3,sK17_skl)
| ~ apply(sK16_skl,X2,X1)
| ~ member(X2,sK17_skl)
| ~ apply(sK16_skl,X1,X0)
| ~ member(X1,sK17_skl)
| ~ apply(sK16_skl,X0,sK18_skl)
| ~ member(X0,sK17_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f264,plain,
! [X0,X1,X2,X3] :
( ~ sQ6_spl
| apply(sK16_skl,X3,sK19_skl)
| ~ apply(sK16_skl,X3,X2)
| ~ member(X2,sK17_skl)
| ~ member(X3,sK17_skl)
| ~ apply(sK16_skl,X2,X1)
| ~ member(X2,sK17_skl)
| ~ apply(sK16_skl,X1,X0)
| ~ member(X1,sK17_skl)
| ~ apply(sK16_skl,X0,sK18_skl)
| ~ member(X0,sK17_skl) ),
inference(component_clause,[status(thm)],[f263]) ).
fof(f266,plain,
( ~ sQ5_spl
| ~ sQ2_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f262,f263,f211,f250]) ).
fof(f267,plain,
! [X0,X1,X2,X3] :
( ~ sQ6_spl
| apply(sK16_skl,X3,sK19_skl)
| ~ apply(sK16_skl,X3,X2)
| ~ member(X3,sK17_skl)
| ~ apply(sK16_skl,X2,X1)
| ~ member(X2,sK17_skl)
| ~ apply(sK16_skl,X1,X0)
| ~ member(X1,sK17_skl)
| ~ apply(sK16_skl,X0,sK18_skl)
| ~ member(X0,sK17_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f264]) ).
fof(f268,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ6_spl
| apply(sK16_skl,X5,sK19_skl)
| ~ apply(sK16_skl,X5,X3)
| ~ member(sK19_skl,X4)
| ~ member(X3,X4)
| ~ member(X5,X4)
| ~ order(sK16_skl,X4)
| ~ apply(sK16_skl,X3,X2)
| ~ member(X3,sK17_skl)
| ~ apply(sK16_skl,X2,X1)
| ~ member(X2,sK17_skl)
| ~ apply(sK16_skl,X1,X0)
| ~ member(X1,sK17_skl)
| ~ apply(sK16_skl,X0,sK18_skl)
| ~ member(X0,sK17_skl) ),
inference(resolution,[status(thm)],[f267,f85]) ).
fof(f274,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ6_spl
| apply(sK16_skl,X4,sK19_skl)
| ~ apply(sK16_skl,X4,X3)
| ~ member(sK19_skl,sK17_skl)
| ~ member(X3,sK17_skl)
| ~ member(X4,sK17_skl)
| ~ apply(sK16_skl,X3,X2)
| ~ member(X3,sK17_skl)
| ~ apply(sK16_skl,X2,X1)
| ~ member(X2,sK17_skl)
| ~ apply(sK16_skl,X1,X0)
| ~ member(X1,sK17_skl)
| ~ apply(sK16_skl,X0,sK18_skl)
| ~ member(X0,sK17_skl) ),
inference(resolution,[status(thm)],[f268,f172]) ).
fof(f275,definition,
! [X0,X1,X2,X3,X4] :
( sQ7_spl
<=> ( apply(sK16_skl,X4,sK19_skl)
| ~ apply(sK16_skl,X4,X3)
| ~ member(X3,sK17_skl)
| ~ member(X4,sK17_skl)
| ~ apply(sK16_skl,X3,X2)
| ~ member(X3,sK17_skl)
| ~ apply(sK16_skl,X2,X1)
| ~ member(X2,sK17_skl)
| ~ apply(sK16_skl,X1,X0)
| ~ member(X1,sK17_skl)
| ~ apply(sK16_skl,X0,sK18_skl)
| ~ member(X0,sK17_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f276,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ7_spl
| apply(sK16_skl,X4,sK19_skl)
| ~ apply(sK16_skl,X4,X3)
| ~ member(X3,sK17_skl)
| ~ member(X4,sK17_skl)
| ~ apply(sK16_skl,X3,X2)
| ~ member(X3,sK17_skl)
| ~ apply(sK16_skl,X2,X1)
| ~ member(X2,sK17_skl)
| ~ apply(sK16_skl,X1,X0)
| ~ member(X1,sK17_skl)
| ~ apply(sK16_skl,X0,sK18_skl)
| ~ member(X0,sK17_skl) ),
inference(component_clause,[status(thm)],[f275]) ).
fof(f278,plain,
( ~ sQ6_spl
| ~ sQ2_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f274,f275,f211,f263]) ).
fof(f279,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ7_spl
| apply(sK16_skl,X4,sK19_skl)
| ~ apply(sK16_skl,X4,X3)
| ~ member(X4,sK17_skl)
| ~ apply(sK16_skl,X3,X2)
| ~ member(X3,sK17_skl)
| ~ apply(sK16_skl,X2,X1)
| ~ member(X2,sK17_skl)
| ~ apply(sK16_skl,X1,X0)
| ~ member(X1,sK17_skl)
| ~ apply(sK16_skl,X0,sK18_skl)
| ~ member(X0,sK17_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f276]) ).
fof(f286,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ7_spl
| apply(sK16_skl,X6,sK19_skl)
| ~ apply(sK16_skl,X6,X4)
| ~ member(sK19_skl,X5)
| ~ member(X4,X5)
| ~ member(X6,X5)
| ~ order(sK16_skl,X5)
| ~ apply(sK16_skl,X4,X3)
| ~ member(X4,sK17_skl)
| ~ apply(sK16_skl,X3,X2)
| ~ member(X3,sK17_skl)
| ~ apply(sK16_skl,X2,X1)
| ~ member(X2,sK17_skl)
| ~ apply(sK16_skl,X1,X0)
| ~ member(X1,sK17_skl)
| ~ apply(sK16_skl,X0,sK18_skl)
| ~ member(X0,sK17_skl) ),
inference(resolution,[status(thm)],[f279,f85]) ).
fof(f290,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ7_spl
| apply(sK16_skl,X5,sK19_skl)
| ~ apply(sK16_skl,X5,X4)
| ~ member(sK19_skl,sK17_skl)
| ~ member(X4,sK17_skl)
| ~ member(X5,sK17_skl)
| ~ apply(sK16_skl,X4,X3)
| ~ member(X4,sK17_skl)
| ~ apply(sK16_skl,X3,X2)
| ~ member(X3,sK17_skl)
| ~ apply(sK16_skl,X2,X1)
| ~ member(X2,sK17_skl)
| ~ apply(sK16_skl,X1,X0)
| ~ member(X1,sK17_skl)
| ~ apply(sK16_skl,X0,sK18_skl)
| ~ member(X0,sK17_skl) ),
inference(resolution,[status(thm)],[f286,f172]) ).
fof(f291,definition,
! [X0,X1,X2,X3,X4,X5] :
( sQ8_spl
<=> ( apply(sK16_skl,X5,sK19_skl)
| ~ apply(sK16_skl,X5,X4)
| ~ member(X4,sK17_skl)
| ~ member(X5,sK17_skl)
| ~ apply(sK16_skl,X4,X3)
| ~ member(X4,sK17_skl)
| ~ apply(sK16_skl,X3,X2)
| ~ member(X3,sK17_skl)
| ~ apply(sK16_skl,X2,X1)
| ~ member(X2,sK17_skl)
| ~ apply(sK16_skl,X1,X0)
| ~ member(X1,sK17_skl)
| ~ apply(sK16_skl,X0,sK18_skl)
| ~ member(X0,sK17_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f292,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ8_spl
| apply(sK16_skl,X5,sK19_skl)
| ~ apply(sK16_skl,X5,X4)
| ~ member(X4,sK17_skl)
| ~ member(X5,sK17_skl)
| ~ apply(sK16_skl,X4,X3)
| ~ member(X4,sK17_skl)
| ~ apply(sK16_skl,X3,X2)
| ~ member(X3,sK17_skl)
| ~ apply(sK16_skl,X2,X1)
| ~ member(X2,sK17_skl)
| ~ apply(sK16_skl,X1,X0)
| ~ member(X1,sK17_skl)
| ~ apply(sK16_skl,X0,sK18_skl)
| ~ member(X0,sK17_skl) ),
inference(component_clause,[status(thm)],[f291]) ).
fof(f294,plain,
( ~ sQ7_spl
| ~ sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f290,f291,f211,f275]) ).
fof(f295,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ8_spl
| apply(sK16_skl,X5,sK19_skl)
| ~ apply(sK16_skl,X5,X4)
| ~ member(X5,sK17_skl)
| ~ apply(sK16_skl,X4,X3)
| ~ member(X4,sK17_skl)
| ~ apply(sK16_skl,X3,X2)
| ~ member(X3,sK17_skl)
| ~ apply(sK16_skl,X2,X1)
| ~ member(X2,sK17_skl)
| ~ apply(sK16_skl,X1,X0)
| ~ member(X1,sK17_skl)
| ~ apply(sK16_skl,X0,sK18_skl)
| ~ member(X0,sK17_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f292]) ).
fof(f296,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ8_spl
| apply(sK16_skl,X7,sK19_skl)
| ~ apply(sK16_skl,X7,X5)
| ~ member(sK19_skl,X6)
| ~ member(X5,X6)
| ~ member(X7,X6)
| ~ order(sK16_skl,X6)
| ~ apply(sK16_skl,X5,X4)
| ~ member(X5,sK17_skl)
| ~ apply(sK16_skl,X4,X3)
| ~ member(X4,sK17_skl)
| ~ apply(sK16_skl,X3,X2)
| ~ member(X3,sK17_skl)
| ~ apply(sK16_skl,X2,X1)
| ~ member(X2,sK17_skl)
| ~ apply(sK16_skl,X1,X0)
| ~ member(X1,sK17_skl)
| ~ apply(sK16_skl,X0,sK18_skl)
| ~ member(X0,sK17_skl) ),
inference(resolution,[status(thm)],[f295,f85]) ).
fof(f300,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ8_spl
| apply(sK16_skl,X6,sK19_skl)
| ~ apply(sK16_skl,X6,X5)
| ~ member(sK19_skl,sK17_skl)
| ~ member(X5,sK17_skl)
| ~ member(X6,sK17_skl)
| ~ apply(sK16_skl,X5,X4)
| ~ member(X5,sK17_skl)
| ~ apply(sK16_skl,X4,X3)
| ~ member(X4,sK17_skl)
| ~ apply(sK16_skl,X3,X2)
| ~ member(X3,sK17_skl)
| ~ apply(sK16_skl,X2,X1)
| ~ member(X2,sK17_skl)
| ~ apply(sK16_skl,X1,X0)
| ~ member(X1,sK17_skl)
| ~ apply(sK16_skl,X0,sK18_skl)
| ~ member(X0,sK17_skl) ),
inference(resolution,[status(thm)],[f296,f172]) ).
fof(f301,definition,
! [X0,X1,X2,X3,X4,X5,X6] :
( sQ9_spl
<=> ( apply(sK16_skl,X6,sK19_skl)
| ~ apply(sK16_skl,X6,X5)
| ~ member(X5,sK17_skl)
| ~ member(X6,sK17_skl)
| ~ apply(sK16_skl,X5,X4)
| ~ member(X5,sK17_skl)
| ~ apply(sK16_skl,X4,X3)
| ~ member(X4,sK17_skl)
| ~ apply(sK16_skl,X3,X2)
| ~ member(X3,sK17_skl)
| ~ apply(sK16_skl,X2,X1)
| ~ member(X2,sK17_skl)
| ~ apply(sK16_skl,X1,X0)
| ~ member(X1,sK17_skl)
| ~ apply(sK16_skl,X0,sK18_skl)
| ~ member(X0,sK17_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f304,plain,
( ~ sQ8_spl
| ~ sQ2_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f300,f301,f211,f291]) ).
fof(f467,plain,
( ~ apply(sK16_skl,sK15_skl(sK17_skl,sK16_skl,unordered_pair(sK18_skl,sK19_skl),sK18_skl),sK18_skl)
| ~ lower_bound(sK18_skl,sK16_skl,unordered_pair(sK18_skl,sK19_skl))
| ~ member(sK18_skl,unordered_pair(sK18_skl,sK19_skl)) ),
inference(resolution,[status(thm)],[f169,f176]) ).
fof(f470,definition,
( sQ15_spl
<=> member(sK18_skl,unordered_pair(sK18_skl,sK19_skl)) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f472,plain,
( sQ15_spl
| ~ member(sK18_skl,unordered_pair(sK18_skl,sK19_skl)) ),
inference(component_clause,[status(thm)],[f470]) ).
fof(f473,definition,
( sQ16_spl
<=> lower_bound(sK18_skl,sK16_skl,unordered_pair(sK18_skl,sK19_skl)) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f475,plain,
( sQ16_spl
| ~ lower_bound(sK18_skl,sK16_skl,unordered_pair(sK18_skl,sK19_skl)) ),
inference(component_clause,[status(thm)],[f473]) ).
fof(f476,definition,
( sQ17_spl
<=> apply(sK16_skl,sK15_skl(sK17_skl,sK16_skl,unordered_pair(sK18_skl,sK19_skl),sK18_skl),sK18_skl) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f478,plain,
( sQ17_spl
| ~ apply(sK16_skl,sK15_skl(sK17_skl,sK16_skl,unordered_pair(sK18_skl,sK19_skl),sK18_skl),sK18_skl) ),
inference(component_clause,[status(thm)],[f476]) ).
fof(f479,plain,
( ~ sQ17_spl
| ~ sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f467,f470,f473,f476]) ).
fof(f500,plain,
! [X0] :
( sQ17_spl
| ~ member(sK18_skl,X0)
| ~ lower_bound(sK15_skl(sK17_skl,sK16_skl,unordered_pair(sK18_skl,sK19_skl),sK18_skl),sK16_skl,X0) ),
inference(resolution,[status(thm)],[f478,f113]) ).
fof(f582,plain,
( sQ16_spl
| ~ apply(sK16_skl,sK18_skl,sK9_skl(sK18_skl,unordered_pair(sK18_skl,sK19_skl),sK16_skl)) ),
inference(resolution,[status(thm)],[f475,f115]) ).
fof(f583,plain,
( sQ16_spl
| member(sK9_skl(sK18_skl,unordered_pair(sK18_skl,sK19_skl),sK16_skl),unordered_pair(sK18_skl,sK19_skl)) ),
inference(resolution,[status(thm)],[f475,f114]) ).
fof(f610,definition,
( sQ39_spl
<=> member(sK9_skl(sK18_skl,unordered_pair(sK18_skl,sK19_skl),sK16_skl),sK17_skl) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f612,plain,
( sQ39_spl
| ~ member(sK9_skl(sK18_skl,unordered_pair(sK18_skl,sK19_skl),sK16_skl),sK17_skl) ),
inference(component_clause,[status(thm)],[f610]) ).
fof(f686,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f472,f195]) ).
fof(f687,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f686]) ).
fof(f688,plain,
( sQ16_spl
| ~ apply(sK16_skl,sK18_skl,sK9_skl(sK18_skl,unordered_pair(sK18_skl,sK19_skl),sK16_skl)) ),
inference(resolution,[status(thm)],[f475,f115]) ).
fof(f734,plain,
( sQ16_spl
| sK9_skl(sK18_skl,unordered_pair(sK18_skl,sK19_skl),sK16_skl) = sK19_skl
| sK9_skl(sK18_skl,unordered_pair(sK18_skl,sK19_skl),sK16_skl) = sK18_skl ),
inference(resolution,[status(thm)],[f583,f62]) ).
fof(f735,definition,
( sQ59_spl
<=> sK9_skl(sK18_skl,unordered_pair(sK18_skl,sK19_skl),sK16_skl) = sK18_skl ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f736,plain,
( ~ sQ59_spl
| sK9_skl(sK18_skl,unordered_pair(sK18_skl,sK19_skl),sK16_skl) = sK18_skl ),
inference(component_clause,[status(thm)],[f735]) ).
fof(f738,definition,
( sQ60_spl
<=> sK9_skl(sK18_skl,unordered_pair(sK18_skl,sK19_skl),sK16_skl) = sK19_skl ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f739,plain,
( ~ sQ60_spl
| sK9_skl(sK18_skl,unordered_pair(sK18_skl,sK19_skl),sK16_skl) = sK19_skl ),
inference(component_clause,[status(thm)],[f738]) ).
fof(f741,plain,
( sQ16_spl
| sQ60_spl
| sQ59_spl ),
inference(split_clause,[status(thm)],[f734,f735,f738,f473]) ).
fof(f783,plain,
( sQ16_spl
| ~ sQ59_spl
| ~ apply(sK16_skl,sK18_skl,sK18_skl) ),
inference(backward_demodulation,[status(thm)],[f736,f582]) ).
fof(f785,plain,
( sQ39_spl
| ~ sQ59_spl
| ~ member(sK18_skl,sK17_skl) ),
inference(backward_demodulation,[status(thm)],[f736,f612]) ).
fof(f786,plain,
( sQ39_spl
| ~ sQ59_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f785,f208,f735,f610]) ).
fof(f871,plain,
( sQ17_spl
| ~ lower_bound(sK18_skl,sK16_skl,unordered_pair(sK18_skl,sK19_skl))
| ~ member(sK18_skl,unordered_pair(sK18_skl,sK19_skl))
| greatest_lower_bound(sK18_skl,unordered_pair(sK18_skl,sK19_skl),sK16_skl,sK17_skl)
| ~ member(sK18_skl,unordered_pair(sK18_skl,sK19_skl)) ),
inference(resolution,[status(thm)],[f500,f168]) ).
fof(f875,definition,
( sQ62_spl
<=> greatest_lower_bound(sK18_skl,unordered_pair(sK18_skl,sK19_skl),sK16_skl,sK17_skl) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f876,plain,
( ~ sQ62_spl
| greatest_lower_bound(sK18_skl,unordered_pair(sK18_skl,sK19_skl),sK16_skl,sK17_skl) ),
inference(component_clause,[status(thm)],[f875]) ).
fof(f878,plain,
( sQ17_spl
| ~ sQ16_spl
| sQ62_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f871,f470,f875,f473,f476]) ).
fof(f879,plain,
( ~ sQ62_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f876,f176]) ).
fof(f880,plain,
~ sQ62_spl,
inference(contradiction_clause,[status(thm)],[f879]) ).
fof(f1204,plain,
( sQ16_spl
| ~ sQ60_spl
| ~ apply(sK16_skl,sK18_skl,sK19_skl) ),
inference(backward_demodulation,[status(thm)],[f739,f688]) ).
fof(f1206,plain,
( sQ16_spl
| ~ sQ60_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1204,f175]) ).
fof(f1207,plain,
( sQ16_spl
| ~ sQ60_spl ),
inference(contradiction_clause,[status(thm)],[f1206]) ).
fof(f1236,plain,
! [X0] :
( sQ16_spl
| ~ sQ59_spl
| ~ member(sK18_skl,X0)
| ~ sP1_prd(sK18_skl,X0,sK16_skl) ),
inference(resolution,[status(thm)],[f783,f191]) ).
fof(f1303,plain,
! [X0] :
( sQ16_spl
| ~ sQ59_spl
| ~ sP0_prd(X0,sK16_skl)
| ~ member(sK18_skl,X0) ),
inference(resolution,[status(thm)],[f1236,f182]) ).
fof(f1304,definition,
! [X0] :
( sQ107_spl
<=> ~ member(sK18_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ107_spl])],[split_symbol_definition]) ).
fof(f1305,plain,
! [X0] :
( ~ sQ107_spl
| ~ member(sK18_skl,X0) ),
inference(component_clause,[status(thm)],[f1304]) ).
fof(f1311,plain,
( ~ sQ107_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f173,f1305]) ).
fof(f1325,plain,
~ sQ107_spl,
inference(contradiction_clause,[status(thm)],[f1311]) ).
fof(f1364,plain,
! [X0] :
( sQ16_spl
| ~ sQ59_spl
| ~ order(sK16_skl,X0)
| ~ member(sK18_skl,X0) ),
inference(resolution,[status(thm)],[f1303,f84]) ).
fof(f1368,plain,
( sQ16_spl
| ~ sQ59_spl
| ~ member(sK18_skl,sK17_skl) ),
inference(resolution,[status(thm)],[f1364,f172]) ).
fof(f1369,plain,
( sQ16_spl
| ~ sQ59_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f1368,f208,f735,f473]) ).
fof(f1370,plain,
$false,
inference(sat_refutation,[status(thm)],[f214,f216,f233,f235,f246,f253,f266,f278,f294,f304,f479,f687,f741,f786,f878,f880,f1207,f1325,f1369]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET796+4 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n020.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Mon Sep 21 05:39:32 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 8.87/1.66 % Refutation found
% 8.87/1.66 % SZS status Theorem for theBenchmark: Theorem is valid
% 8.87/1.66 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.63/1.70 % Elapsed time: 1.343056 seconds
% 3.63/1.70 % CPU time: 10.352057 seconds
% 3.63/1.70 % Total memory used: 187.360 MB
% 3.63/1.70 % Net memory used: 172.341 MB
%------------------------------------------------------------------------------