%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV115+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 02:46:40 PM UTC 2026
% Result : Theorem 0.62s 0.84s
% Output : CNFRefutation 0.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 58
% Syntax : Number of formulae : 307 ( 17 unt; 46 def)
% Number of atoms : 1104 ( 113 equ)
% Maximal formula atoms : 54 ( 3 avg)
% Number of connectives : 1260 ( 463 ~; 529 |; 191 &)
% ( 48 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 50 ( 48 usr; 43 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 20 con; 0-3 aty)
% Number of variables : 263 ( 243 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( X = Y
| gt(Y,X)
| gt(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] : ~ gt(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : leq(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y] :
( gt(Y,X)
=> leq(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y] :
( ( X != Y
& leq(X,Y) )
=> gt(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,Y] :
( leq(X,pred(Y))
<=> gt(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X,Y] :
( leq(X,Y)
<=> gt(succ(Y),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,axiom,
! [X] : minus(X,n1) = pred(X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f53,conjecture,
( ( ! [I] :
( ( leq(I,minus(n6,n1))
& leq(n0,I) )
=> ! [J] :
( ( leq(J,minus(n6,n1))
& leq(n0,J) )
=> a_select3(id_ds1_filter,I,J) = a_select3(id_ds1_filter,J,I) ) )
& ! [G,H] :
( ( leq(H,minus(n6,n1))
& leq(G,minus(n6,n1))
& leq(n0,H)
& leq(n0,G) )
=> a_select3(pminus_ds1_filter,G,H) = a_select3(pminus_ds1_filter,H,G) )
& ! [E,F] :
( ( leq(F,minus(n6,n1))
& leq(E,minus(n6,n1))
& leq(n0,F)
& leq(n0,E) )
=> a_select3(pminus_ds1_filter,E,F) = a_select3(pminus_ds1_filter,F,E) )
& ! [C,D] :
( ( leq(D,minus(n3,n1))
& leq(C,minus(n3,n1))
& leq(n0,D)
& leq(n0,C) )
=> a_select3(r_ds1_filter,C,D) = a_select3(r_ds1_filter,D,C) )
& ! [A,B] :
( ( leq(B,minus(n6,n1))
& leq(A,minus(n6,n1))
& leq(n0,B)
& leq(n0,A) )
=> a_select3(q_ds1_filter,A,B) = a_select3(q_ds1_filter,B,A) )
& leq(pv5,minus(n999,n1))
& leq(n0,pv5) )
=> ( ! [S] :
( ( leq(S,minus(n6,n1))
& leq(n0,S) )
=> ! [T] :
( ( leq(T,minus(n6,n1))
& leq(n0,T) )
=> a_select3(id_ds1_filter,S,T) = a_select3(id_ds1_filter,T,S) ) )
& ! [Q,R] :
( ( leq(R,minus(n6,n1))
& leq(Q,minus(n6,n1))
& leq(n0,R)
& leq(n0,Q) )
=> a_select3(pminus_ds1_filter,Q,R) = a_select3(pminus_ds1_filter,R,Q) )
& ! [O,P] :
( ( leq(P,minus(n6,n1))
& leq(O,minus(n6,n1))
& leq(n0,P)
& leq(n0,O) )
=> a_select3(pminus_ds1_filter,O,P) = a_select3(pminus_ds1_filter,P,O) )
& ! [M,N] :
( ( leq(N,minus(n3,n1))
& leq(M,minus(n3,n1))
& leq(n0,N)
& leq(n0,M) )
=> a_select3(r_ds1_filter,M,N) = a_select3(r_ds1_filter,N,M) )
& ! [K,L] :
( ( leq(L,minus(n6,n1))
& leq(K,minus(n6,n1))
& leq(n0,L)
& leq(n0,K) )
=> a_select3(q_ds1_filter,K,L) = a_select3(q_ds1_filter,L,K) )
& leq(pv5,minus(n999,n1))
& leq(n0,pv5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f54,negated_conjecture,
~ ( ( ! [I] :
( ( leq(I,minus(n6,n1))
& leq(n0,I) )
=> ! [J] :
( ( leq(J,minus(n6,n1))
& leq(n0,J) )
=> a_select3(id_ds1_filter,I,J) = a_select3(id_ds1_filter,J,I) ) )
& ! [G,H] :
( ( leq(H,minus(n6,n1))
& leq(G,minus(n6,n1))
& leq(n0,H)
& leq(n0,G) )
=> a_select3(pminus_ds1_filter,G,H) = a_select3(pminus_ds1_filter,H,G) )
& ! [E,F] :
( ( leq(F,minus(n6,n1))
& leq(E,minus(n6,n1))
& leq(n0,F)
& leq(n0,E) )
=> a_select3(pminus_ds1_filter,E,F) = a_select3(pminus_ds1_filter,F,E) )
& ! [C,D] :
( ( leq(D,minus(n3,n1))
& leq(C,minus(n3,n1))
& leq(n0,D)
& leq(n0,C) )
=> a_select3(r_ds1_filter,C,D) = a_select3(r_ds1_filter,D,C) )
& ! [A,B] :
( ( leq(B,minus(n6,n1))
& leq(A,minus(n6,n1))
& leq(n0,B)
& leq(n0,A) )
=> a_select3(q_ds1_filter,A,B) = a_select3(q_ds1_filter,B,A) )
& leq(pv5,minus(n999,n1))
& leq(n0,pv5) )
=> ( ! [S] :
( ( leq(S,minus(n6,n1))
& leq(n0,S) )
=> ! [T] :
( ( leq(T,minus(n6,n1))
& leq(n0,T) )
=> a_select3(id_ds1_filter,S,T) = a_select3(id_ds1_filter,T,S) ) )
& ! [Q,R] :
( ( leq(R,minus(n6,n1))
& leq(Q,minus(n6,n1))
& leq(n0,R)
& leq(n0,Q) )
=> a_select3(pminus_ds1_filter,Q,R) = a_select3(pminus_ds1_filter,R,Q) )
& ! [O,P] :
( ( leq(P,minus(n6,n1))
& leq(O,minus(n6,n1))
& leq(n0,P)
& leq(n0,O) )
=> a_select3(pminus_ds1_filter,O,P) = a_select3(pminus_ds1_filter,P,O) )
& ! [M,N] :
( ( leq(N,minus(n3,n1))
& leq(M,minus(n3,n1))
& leq(n0,N)
& leq(n0,M) )
=> a_select3(r_ds1_filter,M,N) = a_select3(r_ds1_filter,N,M) )
& ! [K,L] :
( ( leq(L,minus(n6,n1))
& leq(K,minus(n6,n1))
& leq(n0,L)
& leq(n0,K) )
=> a_select3(q_ds1_filter,K,L) = a_select3(q_ds1_filter,L,K) )
& leq(pv5,minus(n999,n1))
& leq(n0,pv5) ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f73,axiom,
gt(n1,n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f94,axiom,
! [X] :
( ( leq(X,n0)
& leq(n0,X) )
=> X = n0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f101,axiom,
succ(n0) = n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f104,plain,
! [X0,X1] :
( X0 = X1
| gt(X1,X0)
| gt(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f108,plain,
! [X0] : ~ gt(X0,X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f109,plain,
! [X0] : leq(X0,X0),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f121,plain,
! [X,Y] :
( leq(X,Y)
| ~ gt(Y,X) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f122,plain,
! [X0,X1] :
( leq(X1,X0)
| ~ gt(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f123,plain,
! [X,Y] :
( gt(Y,X)
| X = Y
| ~ leq(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f124,plain,
! [X0,X1] :
( gt(X1,X0)
| X0 = X1
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f125,plain,
! [X,Y] :
( ( ~ gt(Y,X)
| leq(X,pred(Y)) )
& ( gt(Y,X)
| ~ leq(X,pred(Y)) ) ),
inference(NNF_transformation,[status(thm)],[f10]) ).
fof(f126,plain,
( ! [X,Y] :
( ~ gt(Y,X)
| leq(X,pred(Y)) )
& ! [X,Y] :
( gt(Y,X)
| ~ leq(X,pred(Y)) ) ),
inference(miniscoping,[status(thm)],[f125]) ).
fof(f128,plain,
! [X0,X1] :
( ~ gt(X1,X0)
| leq(X0,pred(X1)) ),
inference(cnf_transformation,[status(thm)],[f126]) ).
fof(f132,plain,
! [X,Y] :
( ( ~ gt(succ(Y),X)
| leq(X,Y) )
& ( gt(succ(Y),X)
| ~ leq(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f13]) ).
fof(f133,plain,
( ! [X,Y] :
( ~ gt(succ(Y),X)
| leq(X,Y) )
& ! [X,Y] :
( gt(succ(Y),X)
| ~ leq(X,Y) ) ),
inference(miniscoping,[status(thm)],[f132]) ).
fof(f135,plain,
! [X0,X1] :
( ~ gt(succ(X1),X0)
| leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f227,plain,
! [X0] : minus(X0,n1) = pred(X0),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f261,plain,
( ( ? [S] :
( ? [T] :
( a_select3(id_ds1_filter,S,T) != a_select3(id_ds1_filter,T,S)
& leq(T,minus(n6,n1))
& leq(n0,T) )
& leq(S,minus(n6,n1))
& leq(n0,S) )
| ? [Q,R] :
( a_select3(pminus_ds1_filter,Q,R) != a_select3(pminus_ds1_filter,R,Q)
& leq(R,minus(n6,n1))
& leq(Q,minus(n6,n1))
& leq(n0,R)
& leq(n0,Q) )
| ? [O,P] :
( a_select3(pminus_ds1_filter,O,P) != a_select3(pminus_ds1_filter,P,O)
& leq(P,minus(n6,n1))
& leq(O,minus(n6,n1))
& leq(n0,P)
& leq(n0,O) )
| ? [M,N] :
( a_select3(r_ds1_filter,M,N) != a_select3(r_ds1_filter,N,M)
& leq(N,minus(n3,n1))
& leq(M,minus(n3,n1))
& leq(n0,N)
& leq(n0,M) )
| ? [K,L] :
( a_select3(q_ds1_filter,K,L) != a_select3(q_ds1_filter,L,K)
& leq(L,minus(n6,n1))
& leq(K,minus(n6,n1))
& leq(n0,L)
& leq(n0,K) )
| ~ leq(pv5,minus(n999,n1))
| ~ leq(n0,pv5) )
& ! [I] :
( ! [J] :
( a_select3(id_ds1_filter,I,J) = a_select3(id_ds1_filter,J,I)
| ~ leq(J,minus(n6,n1))
| ~ leq(n0,J) )
| ~ leq(I,minus(n6,n1))
| ~ leq(n0,I) )
& ! [G,H] :
( a_select3(pminus_ds1_filter,G,H) = a_select3(pminus_ds1_filter,H,G)
| ~ leq(H,minus(n6,n1))
| ~ leq(G,minus(n6,n1))
| ~ leq(n0,H)
| ~ leq(n0,G) )
& ! [E,F] :
( a_select3(pminus_ds1_filter,E,F) = a_select3(pminus_ds1_filter,F,E)
| ~ leq(F,minus(n6,n1))
| ~ leq(E,minus(n6,n1))
| ~ leq(n0,F)
| ~ leq(n0,E) )
& ! [C,D] :
( a_select3(r_ds1_filter,C,D) = a_select3(r_ds1_filter,D,C)
| ~ leq(D,minus(n3,n1))
| ~ leq(C,minus(n3,n1))
| ~ leq(n0,D)
| ~ leq(n0,C) )
& ! [A,B] :
( a_select3(q_ds1_filter,A,B) = a_select3(q_ds1_filter,B,A)
| ~ leq(B,minus(n6,n1))
| ~ leq(A,minus(n6,n1))
| ~ leq(n0,B)
| ~ leq(n0,A) )
& leq(pv5,minus(n999,n1))
& leq(n0,pv5) ),
inference(pre_NNF_transformation,[status(thm)],[f54]) ).
fof(f262,definition,
! [K,L] :
( sP3_prd(L,K)
<=> ( a_select3(q_ds1_filter,K,L) != a_select3(q_ds1_filter,L,K)
& leq(L,minus(n6,n1))
& leq(K,minus(n6,n1))
& leq(n0,L)
& leq(n0,K) ) ),
introduced(definition,[new_symbols(definition,[sP3_prd])],[]) ).
fof(f263,definition,
! [M,N] :
( sP4_prd(N,M)
<=> ( a_select3(r_ds1_filter,M,N) != a_select3(r_ds1_filter,N,M)
& leq(N,minus(n3,n1))
& leq(M,minus(n3,n1))
& leq(n0,N)
& leq(n0,M) ) ),
introduced(definition,[new_symbols(definition,[sP4_prd])],[]) ).
fof(f264,definition,
! [O,P] :
( sP5_prd(P,O)
<=> ( a_select3(pminus_ds1_filter,O,P) != a_select3(pminus_ds1_filter,P,O)
& leq(P,minus(n6,n1))
& leq(O,minus(n6,n1))
& leq(n0,P)
& leq(n0,O) ) ),
introduced(definition,[new_symbols(definition,[sP5_prd])],[]) ).
fof(f265,definition,
! [Q,R] :
( sP6_prd(R,Q)
<=> ( a_select3(pminus_ds1_filter,Q,R) != a_select3(pminus_ds1_filter,R,Q)
& leq(R,minus(n6,n1))
& leq(Q,minus(n6,n1))
& leq(n0,R)
& leq(n0,Q) ) ),
introduced(definition,[new_symbols(definition,[sP6_prd])],[]) ).
fof(f266,plain,
( ( ? [S] :
( ? [T] :
( a_select3(id_ds1_filter,S,T) != a_select3(id_ds1_filter,T,S)
& leq(T,minus(n6,n1))
& leq(n0,T) )
& leq(S,minus(n6,n1))
& leq(n0,S) )
| ? [Q,R] : sP6_prd(R,Q)
| ? [O,P] : sP5_prd(P,O)
| ? [M,N] : sP4_prd(N,M)
| ? [K,L] : sP3_prd(L,K)
| ~ leq(pv5,minus(n999,n1))
| ~ leq(n0,pv5) )
& ! [I] :
( ! [J] :
( a_select3(id_ds1_filter,I,J) = a_select3(id_ds1_filter,J,I)
| ~ leq(J,minus(n6,n1))
| ~ leq(n0,J) )
| ~ leq(I,minus(n6,n1))
| ~ leq(n0,I) )
& ! [G,H] :
( a_select3(pminus_ds1_filter,G,H) = a_select3(pminus_ds1_filter,H,G)
| ~ leq(H,minus(n6,n1))
| ~ leq(G,minus(n6,n1))
| ~ leq(n0,H)
| ~ leq(n0,G) )
& ! [E,F] :
( a_select3(pminus_ds1_filter,E,F) = a_select3(pminus_ds1_filter,F,E)
| ~ leq(F,minus(n6,n1))
| ~ leq(E,minus(n6,n1))
| ~ leq(n0,F)
| ~ leq(n0,E) )
& ! [C,D] :
( a_select3(r_ds1_filter,C,D) = a_select3(r_ds1_filter,D,C)
| ~ leq(D,minus(n3,n1))
| ~ leq(C,minus(n3,n1))
| ~ leq(n0,D)
| ~ leq(n0,C) )
& ! [A,B] :
( a_select3(q_ds1_filter,A,B) = a_select3(q_ds1_filter,B,A)
| ~ leq(B,minus(n6,n1))
| ~ leq(A,minus(n6,n1))
| ~ leq(n0,B)
| ~ leq(n0,A) )
& leq(pv5,minus(n999,n1))
& leq(n0,pv5) ),
inference(formula_renaming,[status(thm)],[f261,f265,f264,f263,f262]) ).
fof(f267,plain,
( ( ( a_select3(id_ds1_filter,sK31_skl,sK32_skl) != a_select3(id_ds1_filter,sK32_skl,sK31_skl)
& leq(sK32_skl,minus(n6,n1))
& leq(n0,sK32_skl)
& leq(sK31_skl,minus(n6,n1))
& leq(n0,sK31_skl) )
| sP6_prd(sK30_skl,sK29_skl)
| sP5_prd(sK28_skl,sK27_skl)
| sP4_prd(sK26_skl,sK25_skl)
| sP3_prd(sK24_skl,sK23_skl)
| ~ leq(pv5,minus(n999,n1))
| ~ leq(n0,pv5) )
& ! [I] :
( ! [J] :
( a_select3(id_ds1_filter,I,J) = a_select3(id_ds1_filter,J,I)
| ~ leq(J,minus(n6,n1))
| ~ leq(n0,J) )
| ~ leq(I,minus(n6,n1))
| ~ leq(n0,I) )
& ! [G,H] :
( a_select3(pminus_ds1_filter,G,H) = a_select3(pminus_ds1_filter,H,G)
| ~ leq(H,minus(n6,n1))
| ~ leq(G,minus(n6,n1))
| ~ leq(n0,H)
| ~ leq(n0,G) )
& ! [E,F] :
( a_select3(pminus_ds1_filter,E,F) = a_select3(pminus_ds1_filter,F,E)
| ~ leq(F,minus(n6,n1))
| ~ leq(E,minus(n6,n1))
| ~ leq(n0,F)
| ~ leq(n0,E) )
& ! [C,D] :
( a_select3(r_ds1_filter,C,D) = a_select3(r_ds1_filter,D,C)
| ~ leq(D,minus(n3,n1))
| ~ leq(C,minus(n3,n1))
| ~ leq(n0,D)
| ~ leq(n0,C) )
& ! [A,B] :
( a_select3(q_ds1_filter,A,B) = a_select3(q_ds1_filter,B,A)
| ~ leq(B,minus(n6,n1))
| ~ leq(A,minus(n6,n1))
| ~ leq(n0,B)
| ~ leq(n0,A) )
& leq(pv5,minus(n999,n1))
& leq(n0,pv5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23_skl,sK24_skl,sK25_skl,sK26_skl,sK27_skl,sK28_skl,sK29_skl,sK30_skl,sK31_skl,sK32_skl]),skolemize(K,sK23_skl),skolemize(L,sK24_skl),skolemize(M,sK25_skl),skolemize(N,sK26_skl),skolemize(O,sK27_skl),skolemize(P,sK28_skl),skolemize(Q,sK29_skl),skolemize(R,sK30_skl),skolemize(S,sK31_skl),skolemize(T,sK32_skl)],[f266]) ).
fof(f268,plain,
leq(n0,pv5),
inference(cnf_transformation,[status(thm)],[f267]) ).
fof(f269,plain,
leq(pv5,minus(n999,n1)),
inference(cnf_transformation,[status(thm)],[f267]) ).
fof(f270,plain,
! [X0,X1] :
( a_select3(q_ds1_filter,X0,X1) = a_select3(q_ds1_filter,X1,X0)
| ~ leq(X1,minus(n6,n1))
| ~ leq(X0,minus(n6,n1))
| ~ leq(n0,X1)
| ~ leq(n0,X0) ),
inference(cnf_transformation,[status(thm)],[f267]) ).
fof(f271,plain,
! [X0,X1] :
( a_select3(r_ds1_filter,X0,X1) = a_select3(r_ds1_filter,X1,X0)
| ~ leq(X1,minus(n3,n1))
| ~ leq(X0,minus(n3,n1))
| ~ leq(n0,X1)
| ~ leq(n0,X0) ),
inference(cnf_transformation,[status(thm)],[f267]) ).
fof(f272,plain,
! [X0,X1] :
( a_select3(pminus_ds1_filter,X0,X1) = a_select3(pminus_ds1_filter,X1,X0)
| ~ leq(X1,minus(n6,n1))
| ~ leq(X0,minus(n6,n1))
| ~ leq(n0,X1)
| ~ leq(n0,X0) ),
inference(cnf_transformation,[status(thm)],[f267]) ).
fof(f274,plain,
! [X0,X1] :
( a_select3(id_ds1_filter,X0,X1) = a_select3(id_ds1_filter,X1,X0)
| ~ leq(X1,minus(n6,n1))
| ~ leq(n0,X1)
| ~ leq(X0,minus(n6,n1))
| ~ leq(n0,X0) ),
inference(cnf_transformation,[status(thm)],[f267]) ).
fof(f275,plain,
( leq(n0,sK31_skl)
| sP6_prd(sK30_skl,sK29_skl)
| sP5_prd(sK28_skl,sK27_skl)
| sP4_prd(sK26_skl,sK25_skl)
| sP3_prd(sK24_skl,sK23_skl)
| ~ leq(pv5,minus(n999,n1))
| ~ leq(n0,pv5) ),
inference(cnf_transformation,[status(thm)],[f267]) ).
fof(f276,plain,
( leq(sK31_skl,minus(n6,n1))
| sP6_prd(sK30_skl,sK29_skl)
| sP5_prd(sK28_skl,sK27_skl)
| sP4_prd(sK26_skl,sK25_skl)
| sP3_prd(sK24_skl,sK23_skl)
| ~ leq(pv5,minus(n999,n1))
| ~ leq(n0,pv5) ),
inference(cnf_transformation,[status(thm)],[f267]) ).
fof(f277,plain,
( leq(n0,sK32_skl)
| sP6_prd(sK30_skl,sK29_skl)
| sP5_prd(sK28_skl,sK27_skl)
| sP4_prd(sK26_skl,sK25_skl)
| sP3_prd(sK24_skl,sK23_skl)
| ~ leq(pv5,minus(n999,n1))
| ~ leq(n0,pv5) ),
inference(cnf_transformation,[status(thm)],[f267]) ).
fof(f278,plain,
( leq(sK32_skl,minus(n6,n1))
| sP6_prd(sK30_skl,sK29_skl)
| sP5_prd(sK28_skl,sK27_skl)
| sP4_prd(sK26_skl,sK25_skl)
| sP3_prd(sK24_skl,sK23_skl)
| ~ leq(pv5,minus(n999,n1))
| ~ leq(n0,pv5) ),
inference(cnf_transformation,[status(thm)],[f267]) ).
fof(f279,plain,
( a_select3(id_ds1_filter,sK31_skl,sK32_skl) != a_select3(id_ds1_filter,sK32_skl,sK31_skl)
| sP6_prd(sK30_skl,sK29_skl)
| sP5_prd(sK28_skl,sK27_skl)
| sP4_prd(sK26_skl,sK25_skl)
| sP3_prd(sK24_skl,sK23_skl)
| ~ leq(pv5,minus(n999,n1))
| ~ leq(n0,pv5) ),
inference(cnf_transformation,[status(thm)],[f267]) ).
fof(f298,plain,
gt(n1,n0),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f322,plain,
! [X] :
( X = n0
| ~ leq(X,n0)
| ~ leq(n0,X) ),
inference(pre_NNF_transformation,[status(thm)],[f94]) ).
fof(f323,plain,
! [X0] :
( X0 = n0
| ~ leq(X0,n0)
| ~ leq(n0,X0) ),
inference(cnf_transformation,[status(thm)],[f322]) ).
fof(f333,plain,
succ(n0) = n1,
inference(cnf_transformation,[status(thm)],[f101]) ).
fof(f364,plain,
! [K,L] :
( ( a_select3(q_ds1_filter,K,L) = a_select3(q_ds1_filter,L,K)
| ~ leq(L,minus(n6,n1))
| ~ leq(K,minus(n6,n1))
| ~ leq(n0,L)
| ~ leq(n0,K)
| sP3_prd(L,K) )
& ( ( a_select3(q_ds1_filter,K,L) != a_select3(q_ds1_filter,L,K)
& leq(L,minus(n6,n1))
& leq(K,minus(n6,n1))
& leq(n0,L)
& leq(n0,K) )
| ~ sP3_prd(L,K) ) ),
inference(NNF_transformation,[status(thm)],[f262]) ).
fof(f365,plain,
( ! [K,L] :
( a_select3(q_ds1_filter,K,L) = a_select3(q_ds1_filter,L,K)
| ~ leq(L,minus(n6,n1))
| ~ leq(K,minus(n6,n1))
| ~ leq(n0,L)
| ~ leq(n0,K)
| sP3_prd(L,K) )
& ! [K,L] :
( ( a_select3(q_ds1_filter,K,L) != a_select3(q_ds1_filter,L,K)
& leq(L,minus(n6,n1))
& leq(K,minus(n6,n1))
& leq(n0,L)
& leq(n0,K) )
| ~ sP3_prd(L,K) ) ),
inference(miniscoping,[status(thm)],[f364]) ).
fof(f366,plain,
! [X0,X1] :
( leq(n0,X1)
| ~ sP3_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f365]) ).
fof(f367,plain,
! [X0,X1] :
( leq(n0,X0)
| ~ sP3_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f365]) ).
fof(f368,plain,
! [X0,X1] :
( leq(X1,minus(n6,n1))
| ~ sP3_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f365]) ).
fof(f369,plain,
! [X0,X1] :
( leq(X0,minus(n6,n1))
| ~ sP3_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f365]) ).
fof(f370,plain,
! [X0,X1] :
( a_select3(q_ds1_filter,X1,X0) != a_select3(q_ds1_filter,X0,X1)
| ~ sP3_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f365]) ).
fof(f372,plain,
! [M,N] :
( ( a_select3(r_ds1_filter,M,N) = a_select3(r_ds1_filter,N,M)
| ~ leq(N,minus(n3,n1))
| ~ leq(M,minus(n3,n1))
| ~ leq(n0,N)
| ~ leq(n0,M)
| sP4_prd(N,M) )
& ( ( a_select3(r_ds1_filter,M,N) != a_select3(r_ds1_filter,N,M)
& leq(N,minus(n3,n1))
& leq(M,minus(n3,n1))
& leq(n0,N)
& leq(n0,M) )
| ~ sP4_prd(N,M) ) ),
inference(NNF_transformation,[status(thm)],[f263]) ).
fof(f373,plain,
( ! [M,N] :
( a_select3(r_ds1_filter,M,N) = a_select3(r_ds1_filter,N,M)
| ~ leq(N,minus(n3,n1))
| ~ leq(M,minus(n3,n1))
| ~ leq(n0,N)
| ~ leq(n0,M)
| sP4_prd(N,M) )
& ! [M,N] :
( ( a_select3(r_ds1_filter,M,N) != a_select3(r_ds1_filter,N,M)
& leq(N,minus(n3,n1))
& leq(M,minus(n3,n1))
& leq(n0,N)
& leq(n0,M) )
| ~ sP4_prd(N,M) ) ),
inference(miniscoping,[status(thm)],[f372]) ).
fof(f374,plain,
! [X0,X1] :
( leq(n0,X1)
| ~ sP4_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f373]) ).
fof(f375,plain,
! [X0,X1] :
( leq(n0,X0)
| ~ sP4_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f373]) ).
fof(f376,plain,
! [X0,X1] :
( leq(X1,minus(n3,n1))
| ~ sP4_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f373]) ).
fof(f377,plain,
! [X0,X1] :
( leq(X0,minus(n3,n1))
| ~ sP4_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f373]) ).
fof(f378,plain,
! [X0,X1] :
( a_select3(r_ds1_filter,X1,X0) != a_select3(r_ds1_filter,X0,X1)
| ~ sP4_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f373]) ).
fof(f380,plain,
! [O,P] :
( ( a_select3(pminus_ds1_filter,O,P) = a_select3(pminus_ds1_filter,P,O)
| ~ leq(P,minus(n6,n1))
| ~ leq(O,minus(n6,n1))
| ~ leq(n0,P)
| ~ leq(n0,O)
| sP5_prd(P,O) )
& ( ( a_select3(pminus_ds1_filter,O,P) != a_select3(pminus_ds1_filter,P,O)
& leq(P,minus(n6,n1))
& leq(O,minus(n6,n1))
& leq(n0,P)
& leq(n0,O) )
| ~ sP5_prd(P,O) ) ),
inference(NNF_transformation,[status(thm)],[f264]) ).
fof(f381,plain,
( ! [O,P] :
( a_select3(pminus_ds1_filter,O,P) = a_select3(pminus_ds1_filter,P,O)
| ~ leq(P,minus(n6,n1))
| ~ leq(O,minus(n6,n1))
| ~ leq(n0,P)
| ~ leq(n0,O)
| sP5_prd(P,O) )
& ! [O,P] :
( ( a_select3(pminus_ds1_filter,O,P) != a_select3(pminus_ds1_filter,P,O)
& leq(P,minus(n6,n1))
& leq(O,minus(n6,n1))
& leq(n0,P)
& leq(n0,O) )
| ~ sP5_prd(P,O) ) ),
inference(miniscoping,[status(thm)],[f380]) ).
fof(f382,plain,
! [X0,X1] :
( leq(n0,X1)
| ~ sP5_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f381]) ).
fof(f383,plain,
! [X0,X1] :
( leq(n0,X0)
| ~ sP5_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f381]) ).
fof(f384,plain,
! [X0,X1] :
( leq(X1,minus(n6,n1))
| ~ sP5_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f381]) ).
fof(f385,plain,
! [X0,X1] :
( leq(X0,minus(n6,n1))
| ~ sP5_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f381]) ).
fof(f386,plain,
! [X0,X1] :
( a_select3(pminus_ds1_filter,X1,X0) != a_select3(pminus_ds1_filter,X0,X1)
| ~ sP5_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f381]) ).
fof(f388,plain,
! [Q,R] :
( ( a_select3(pminus_ds1_filter,Q,R) = a_select3(pminus_ds1_filter,R,Q)
| ~ leq(R,minus(n6,n1))
| ~ leq(Q,minus(n6,n1))
| ~ leq(n0,R)
| ~ leq(n0,Q)
| sP6_prd(R,Q) )
& ( ( a_select3(pminus_ds1_filter,Q,R) != a_select3(pminus_ds1_filter,R,Q)
& leq(R,minus(n6,n1))
& leq(Q,minus(n6,n1))
& leq(n0,R)
& leq(n0,Q) )
| ~ sP6_prd(R,Q) ) ),
inference(NNF_transformation,[status(thm)],[f265]) ).
fof(f389,plain,
( ! [Q,R] :
( a_select3(pminus_ds1_filter,Q,R) = a_select3(pminus_ds1_filter,R,Q)
| ~ leq(R,minus(n6,n1))
| ~ leq(Q,minus(n6,n1))
| ~ leq(n0,R)
| ~ leq(n0,Q)
| sP6_prd(R,Q) )
& ! [Q,R] :
( ( a_select3(pminus_ds1_filter,Q,R) != a_select3(pminus_ds1_filter,R,Q)
& leq(R,minus(n6,n1))
& leq(Q,minus(n6,n1))
& leq(n0,R)
& leq(n0,Q) )
| ~ sP6_prd(R,Q) ) ),
inference(miniscoping,[status(thm)],[f388]) ).
fof(f390,plain,
! [X0,X1] :
( leq(n0,X1)
| ~ sP6_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f389]) ).
fof(f391,plain,
! [X0,X1] :
( leq(n0,X0)
| ~ sP6_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f389]) ).
fof(f392,plain,
! [X0,X1] :
( leq(X1,minus(n6,n1))
| ~ sP6_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f389]) ).
fof(f393,plain,
! [X0,X1] :
( leq(X0,minus(n6,n1))
| ~ sP6_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f389]) ).
fof(f394,plain,
! [X0,X1] :
( a_select3(pminus_ds1_filter,X1,X0) != a_select3(pminus_ds1_filter,X0,X1)
| ~ sP6_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f389]) ).
fof(f404,definition,
( sQ0_spl
<=> leq(n0,pv5) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f406,plain,
( sQ0_spl
| ~ leq(n0,pv5) ),
inference(component_clause,[status(thm)],[f404]) ).
fof(f407,definition,
( sQ1_spl
<=> leq(pv5,minus(n999,n1)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f409,plain,
( sQ1_spl
| ~ leq(pv5,minus(n999,n1)) ),
inference(component_clause,[status(thm)],[f407]) ).
fof(f410,definition,
( sQ2_spl
<=> sP3_prd(sK24_skl,sK23_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f411,plain,
( ~ sQ2_spl
| sP3_prd(sK24_skl,sK23_skl) ),
inference(component_clause,[status(thm)],[f410]) ).
fof(f413,definition,
( sQ3_spl
<=> sP4_prd(sK26_skl,sK25_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f414,plain,
( ~ sQ3_spl
| sP4_prd(sK26_skl,sK25_skl) ),
inference(component_clause,[status(thm)],[f413]) ).
fof(f416,definition,
( sQ4_spl
<=> sP5_prd(sK28_skl,sK27_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f417,plain,
( ~ sQ4_spl
| sP5_prd(sK28_skl,sK27_skl) ),
inference(component_clause,[status(thm)],[f416]) ).
fof(f419,definition,
( sQ5_spl
<=> sP6_prd(sK30_skl,sK29_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f420,plain,
( ~ sQ5_spl
| sP6_prd(sK30_skl,sK29_skl) ),
inference(component_clause,[status(thm)],[f419]) ).
fof(f422,definition,
( sQ6_spl
<=> leq(n0,sK31_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f424,plain,
( sQ6_spl
| ~ leq(n0,sK31_skl) ),
inference(component_clause,[status(thm)],[f422]) ).
fof(f425,plain,
( sQ6_spl
| sQ5_spl
| sQ4_spl
| sQ3_spl
| sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f275,f404,f407,f410,f413,f416,f419,f422]) ).
fof(f426,definition,
( sQ7_spl
<=> leq(sK31_skl,minus(n6,n1)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f427,plain,
( ~ sQ7_spl
| leq(sK31_skl,minus(n6,n1)) ),
inference(component_clause,[status(thm)],[f426]) ).
fof(f429,plain,
( sQ7_spl
| sQ5_spl
| sQ4_spl
| sQ3_spl
| sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f276,f404,f407,f410,f413,f416,f419,f426]) ).
fof(f430,definition,
( sQ8_spl
<=> leq(n0,sK32_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f433,plain,
( sQ8_spl
| sQ5_spl
| sQ4_spl
| sQ3_spl
| sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f277,f404,f407,f410,f413,f416,f419,f430]) ).
fof(f434,definition,
( sQ9_spl
<=> leq(sK32_skl,minus(n6,n1)) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f435,plain,
( ~ sQ9_spl
| leq(sK32_skl,minus(n6,n1)) ),
inference(component_clause,[status(thm)],[f434]) ).
fof(f436,plain,
( sQ9_spl
| ~ leq(sK32_skl,minus(n6,n1)) ),
inference(component_clause,[status(thm)],[f434]) ).
fof(f437,plain,
( sQ9_spl
| sQ5_spl
| sQ4_spl
| sQ3_spl
| sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f278,f404,f407,f410,f413,f416,f419,f434]) ).
fof(f438,definition,
( sQ10_spl
<=> a_select3(id_ds1_filter,sK31_skl,sK32_skl) = a_select3(id_ds1_filter,sK32_skl,sK31_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f440,plain,
( sQ10_spl
| a_select3(id_ds1_filter,sK31_skl,sK32_skl) != a_select3(id_ds1_filter,sK32_skl,sK31_skl) ),
inference(component_clause,[status(thm)],[f438]) ).
fof(f441,plain,
( ~ sQ10_spl
| sQ5_spl
| sQ4_spl
| sQ3_spl
| sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f279,f404,f407,f410,f413,f416,f419,f438]) ).
fof(f454,plain,
leq(pv5,pred(n999)),
inference(forward_demodulation,[status(thm)],[f227,f269]) ).
fof(f455,plain,
! [X0,X1] :
( a_select3(q_ds1_filter,X0,X1) = a_select3(q_ds1_filter,X1,X0)
| ~ leq(X1,minus(n6,n1))
| ~ leq(X0,pred(n6))
| ~ leq(n0,X1)
| ~ leq(n0,X0) ),
inference(forward_demodulation,[status(thm)],[f227,f270]) ).
fof(f456,plain,
! [X0,X1] :
( a_select3(q_ds1_filter,X0,X1) = a_select3(q_ds1_filter,X1,X0)
| ~ leq(X1,pred(n6))
| ~ leq(X0,pred(n6))
| ~ leq(n0,X1)
| ~ leq(n0,X0) ),
inference(forward_demodulation,[status(thm)],[f227,f455]) ).
fof(f457,plain,
! [X0,X1] :
( a_select3(r_ds1_filter,X0,X1) = a_select3(r_ds1_filter,X1,X0)
| ~ leq(X1,minus(n3,n1))
| ~ leq(X0,pred(n3))
| ~ leq(n0,X1)
| ~ leq(n0,X0) ),
inference(forward_demodulation,[status(thm)],[f227,f271]) ).
fof(f458,plain,
! [X0,X1] :
( a_select3(r_ds1_filter,X0,X1) = a_select3(r_ds1_filter,X1,X0)
| ~ leq(X1,pred(n3))
| ~ leq(X0,pred(n3))
| ~ leq(n0,X1)
| ~ leq(n0,X0) ),
inference(forward_demodulation,[status(thm)],[f227,f457]) ).
fof(f459,plain,
! [X0,X1] :
( a_select3(pminus_ds1_filter,X0,X1) = a_select3(pminus_ds1_filter,X1,X0)
| ~ leq(X1,minus(n6,n1))
| ~ leq(X0,pred(n6))
| ~ leq(n0,X1)
| ~ leq(n0,X0) ),
inference(forward_demodulation,[status(thm)],[f227,f272]) ).
fof(f460,plain,
! [X0,X1] :
( a_select3(pminus_ds1_filter,X0,X1) = a_select3(pminus_ds1_filter,X1,X0)
| ~ leq(X1,pred(n6))
| ~ leq(X0,pred(n6))
| ~ leq(n0,X1)
| ~ leq(n0,X0) ),
inference(forward_demodulation,[status(thm)],[f227,f459]) ).
fof(f463,plain,
! [X0,X1] :
( a_select3(id_ds1_filter,X0,X1) = a_select3(id_ds1_filter,X1,X0)
| ~ leq(X1,minus(n6,n1))
| ~ leq(n0,X1)
| ~ leq(X0,pred(n6))
| ~ leq(n0,X0) ),
inference(forward_demodulation,[status(thm)],[f227,f274]) ).
fof(f464,plain,
! [X0,X1] :
( a_select3(id_ds1_filter,X0,X1) = a_select3(id_ds1_filter,X1,X0)
| ~ leq(X1,pred(n6))
| ~ leq(n0,X1)
| ~ leq(X0,pred(n6))
| ~ leq(n0,X0) ),
inference(forward_demodulation,[status(thm)],[f227,f463]) ).
fof(f476,plain,
! [X0,X1] :
( leq(X1,pred(n6))
| ~ sP3_prd(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f227,f368]) ).
fof(f477,plain,
! [X0,X1] :
( leq(X0,pred(n6))
| ~ sP3_prd(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f227,f369]) ).
fof(f480,plain,
! [X0,X1] :
( leq(X1,pred(n3))
| ~ sP4_prd(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f227,f376]) ).
fof(f481,plain,
! [X0,X1] :
( leq(X0,pred(n3))
| ~ sP4_prd(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f227,f377]) ).
fof(f484,plain,
! [X0,X1] :
( leq(X1,pred(n6))
| ~ sP5_prd(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f227,f384]) ).
fof(f485,plain,
! [X0,X1] :
( leq(X0,pred(n6))
| ~ sP5_prd(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f227,f385]) ).
fof(f488,plain,
! [X0,X1] :
( leq(X1,pred(n6))
| ~ sP6_prd(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f227,f392]) ).
fof(f489,plain,
! [X0,X1] :
( leq(X0,pred(n6))
| ~ sP6_prd(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f227,f393]) ).
fof(f591,plain,
( sQ1_spl
| ~ leq(pv5,pred(n999)) ),
inference(forward_demodulation,[status(thm)],[f227,f409]) ).
fof(f592,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f591,f454]) ).
fof(f593,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f592]) ).
fof(f594,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f406,f268]) ).
fof(f595,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f594]) ).
fof(f677,definition,
( sQ40_spl
<=> leq(n0,n0) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f679,plain,
( sQ40_spl
| ~ leq(n0,n0) ),
inference(component_clause,[status(thm)],[f677]) ).
fof(f698,plain,
( sQ40_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f679,f109]) ).
fof(f699,plain,
sQ40_spl,
inference(contradiction_clause,[status(thm)],[f698]) ).
fof(f700,plain,
( ~ sQ9_spl
| leq(sK32_skl,pred(n6)) ),
inference(forward_demodulation,[status(thm)],[f227,f435]) ).
fof(f701,plain,
( ~ sQ7_spl
| leq(sK31_skl,pred(n6)) ),
inference(forward_demodulation,[status(thm)],[f227,f427]) ).
fof(f817,plain,
( ~ sQ2_spl
| a_select3(q_ds1_filter,sK23_skl,sK24_skl) != a_select3(q_ds1_filter,sK24_skl,sK23_skl) ),
inference(resolution,[status(thm)],[f370,f411]) ).
fof(f818,plain,
( ~ sQ3_spl
| a_select3(r_ds1_filter,sK25_skl,sK26_skl) != a_select3(r_ds1_filter,sK26_skl,sK25_skl) ),
inference(resolution,[status(thm)],[f378,f414]) ).
fof(f819,plain,
( ~ sQ4_spl
| a_select3(pminus_ds1_filter,sK27_skl,sK28_skl) != a_select3(pminus_ds1_filter,sK28_skl,sK27_skl) ),
inference(resolution,[status(thm)],[f386,f417]) ).
fof(f821,plain,
( ~ sQ5_spl
| a_select3(pminus_ds1_filter,sK29_skl,sK30_skl) != a_select3(pminus_ds1_filter,sK30_skl,sK29_skl) ),
inference(resolution,[status(thm)],[f394,f420]) ).
fof(f822,plain,
( ~ sQ2_spl
| ~ leq(sK24_skl,pred(n6))
| ~ leq(sK23_skl,pred(n6))
| ~ leq(n0,sK24_skl)
| ~ leq(n0,sK23_skl) ),
inference(resolution,[status(thm)],[f817,f456]) ).
fof(f824,definition,
( sQ59_spl
<=> leq(n0,sK23_skl) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f826,plain,
( sQ59_spl
| ~ leq(n0,sK23_skl) ),
inference(component_clause,[status(thm)],[f824]) ).
fof(f827,definition,
( sQ60_spl
<=> leq(n0,sK24_skl) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f829,plain,
( sQ60_spl
| ~ leq(n0,sK24_skl) ),
inference(component_clause,[status(thm)],[f827]) ).
fof(f830,definition,
( sQ61_spl
<=> leq(sK23_skl,pred(n6)) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f832,plain,
( sQ61_spl
| ~ leq(sK23_skl,pred(n6)) ),
inference(component_clause,[status(thm)],[f830]) ).
fof(f833,definition,
( sQ62_spl
<=> leq(sK24_skl,pred(n6)) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f835,plain,
( sQ62_spl
| ~ leq(sK24_skl,pred(n6)) ),
inference(component_clause,[status(thm)],[f833]) ).
fof(f836,plain,
( ~ sQ2_spl
| ~ sQ62_spl
| ~ sQ61_spl
| ~ sQ60_spl
| ~ sQ59_spl ),
inference(split_clause,[status(thm)],[f822,f824,f827,f830,f833,f410]) ).
fof(f844,plain,
! [X0] :
( sQ60_spl
| ~ sP3_prd(sK24_skl,X0) ),
inference(resolution,[status(thm)],[f829,f367]) ).
fof(f850,plain,
( ~ sQ2_spl
| sQ60_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f411,f844]) ).
fof(f851,plain,
( ~ sQ2_spl
| sQ60_spl ),
inference(contradiction_clause,[status(thm)],[f850]) ).
fof(f859,plain,
! [X0] :
( sQ59_spl
| ~ sP3_prd(X0,sK23_skl) ),
inference(resolution,[status(thm)],[f826,f366]) ).
fof(f861,plain,
( sQ59_spl
| ~ gt(sK23_skl,n0) ),
inference(resolution,[status(thm)],[f826,f122]) ).
fof(f864,plain,
( sQ10_spl
| ~ leq(sK32_skl,pred(n6))
| ~ leq(n0,sK32_skl)
| ~ leq(sK31_skl,pred(n6))
| ~ leq(n0,sK31_skl) ),
inference(resolution,[status(thm)],[f464,f440]) ).
fof(f866,definition,
( sQ63_spl
<=> leq(sK31_skl,pred(n6)) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f868,plain,
( sQ63_spl
| ~ leq(sK31_skl,pred(n6)) ),
inference(component_clause,[status(thm)],[f866]) ).
fof(f869,definition,
( sQ64_spl
<=> leq(sK32_skl,pred(n6)) ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f870,plain,
( ~ sQ64_spl
| leq(sK32_skl,pred(n6)) ),
inference(component_clause,[status(thm)],[f869]) ).
fof(f871,plain,
( sQ64_spl
| ~ leq(sK32_skl,pred(n6)) ),
inference(component_clause,[status(thm)],[f869]) ).
fof(f872,plain,
( sQ10_spl
| ~ sQ64_spl
| ~ sQ8_spl
| ~ sQ63_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f864,f422,f866,f430,f869,f438]) ).
fof(f874,plain,
( sQ64_spl
| ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f871,f700]) ).
fof(f875,plain,
( sQ64_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f874]) ).
fof(f876,plain,
( sQ63_spl
| ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f868,f701]) ).
fof(f877,plain,
( sQ63_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f876]) ).
fof(f878,plain,
( sQ9_spl
| ~ leq(sK32_skl,pred(n6)) ),
inference(forward_demodulation,[status(thm)],[f227,f436]) ).
fof(f882,plain,
( ~ sQ64_spl
| sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f870,f878]) ).
fof(f883,plain,
( ~ sQ64_spl
| sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f882]) ).
fof(f894,plain,
( ~ sQ3_spl
| ~ leq(sK26_skl,pred(n3))
| ~ leq(sK25_skl,pred(n3))
| ~ leq(n0,sK26_skl)
| ~ leq(n0,sK25_skl) ),
inference(resolution,[status(thm)],[f818,f458]) ).
fof(f896,definition,
( sQ65_spl
<=> leq(n0,sK25_skl) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f898,plain,
( sQ65_spl
| ~ leq(n0,sK25_skl) ),
inference(component_clause,[status(thm)],[f896]) ).
fof(f899,definition,
( sQ66_spl
<=> leq(n0,sK26_skl) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f901,plain,
( sQ66_spl
| ~ leq(n0,sK26_skl) ),
inference(component_clause,[status(thm)],[f899]) ).
fof(f902,definition,
( sQ67_spl
<=> leq(sK25_skl,pred(n3)) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f904,plain,
( sQ67_spl
| ~ leq(sK25_skl,pred(n3)) ),
inference(component_clause,[status(thm)],[f902]) ).
fof(f905,definition,
( sQ68_spl
<=> leq(sK26_skl,pred(n3)) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f907,plain,
( sQ68_spl
| ~ leq(sK26_skl,pred(n3)) ),
inference(component_clause,[status(thm)],[f905]) ).
fof(f908,plain,
( ~ sQ3_spl
| ~ sQ68_spl
| ~ sQ67_spl
| ~ sQ66_spl
| ~ sQ65_spl ),
inference(split_clause,[status(thm)],[f894,f896,f899,f902,f905,f413]) ).
fof(f916,plain,
( sQ9_spl
| ~ gt(n6,sK32_skl) ),
inference(resolution,[status(thm)],[f878,f128]) ).
fof(f920,plain,
( ~ sQ4_spl
| ~ leq(sK28_skl,pred(n6))
| ~ leq(sK27_skl,pred(n6))
| ~ leq(n0,sK28_skl)
| ~ leq(n0,sK27_skl) ),
inference(resolution,[status(thm)],[f819,f460]) ).
fof(f922,definition,
( sQ69_spl
<=> leq(n0,sK27_skl) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f924,plain,
( sQ69_spl
| ~ leq(n0,sK27_skl) ),
inference(component_clause,[status(thm)],[f922]) ).
fof(f925,definition,
( sQ70_spl
<=> leq(n0,sK28_skl) ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f927,plain,
( sQ70_spl
| ~ leq(n0,sK28_skl) ),
inference(component_clause,[status(thm)],[f925]) ).
fof(f928,definition,
( sQ71_spl
<=> leq(sK27_skl,pred(n6)) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f930,plain,
( sQ71_spl
| ~ leq(sK27_skl,pred(n6)) ),
inference(component_clause,[status(thm)],[f928]) ).
fof(f931,definition,
( sQ72_spl
<=> leq(sK28_skl,pred(n6)) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f933,plain,
( sQ72_spl
| ~ leq(sK28_skl,pred(n6)) ),
inference(component_clause,[status(thm)],[f931]) ).
fof(f934,plain,
( ~ sQ4_spl
| ~ sQ72_spl
| ~ sQ71_spl
| ~ sQ70_spl
| ~ sQ69_spl ),
inference(split_clause,[status(thm)],[f920,f922,f925,f928,f931,f416]) ).
fof(f936,plain,
( ~ sQ5_spl
| ~ leq(sK30_skl,pred(n6))
| ~ leq(sK29_skl,pred(n6))
| ~ leq(n0,sK30_skl)
| ~ leq(n0,sK29_skl) ),
inference(resolution,[status(thm)],[f821,f460]) ).
fof(f938,definition,
( sQ73_spl
<=> leq(n0,sK29_skl) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f940,plain,
( sQ73_spl
| ~ leq(n0,sK29_skl) ),
inference(component_clause,[status(thm)],[f938]) ).
fof(f941,definition,
( sQ74_spl
<=> leq(n0,sK30_skl) ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f943,plain,
( sQ74_spl
| ~ leq(n0,sK30_skl) ),
inference(component_clause,[status(thm)],[f941]) ).
fof(f944,definition,
( sQ75_spl
<=> leq(sK29_skl,pred(n6)) ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f946,plain,
( sQ75_spl
| ~ leq(sK29_skl,pred(n6)) ),
inference(component_clause,[status(thm)],[f944]) ).
fof(f947,definition,
( sQ76_spl
<=> leq(sK30_skl,pred(n6)) ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f949,plain,
( sQ76_spl
| ~ leq(sK30_skl,pred(n6)) ),
inference(component_clause,[status(thm)],[f947]) ).
fof(f950,plain,
( ~ sQ5_spl
| ~ sQ76_spl
| ~ sQ75_spl
| ~ sQ74_spl
| ~ sQ73_spl ),
inference(split_clause,[status(thm)],[f936,f938,f941,f944,f947,f419]) ).
fof(f985,plain,
( sQ9_spl
| sK32_skl = n6
| ~ leq(sK32_skl,n6) ),
inference(resolution,[status(thm)],[f916,f124]) ).
fof(f986,plain,
( sQ9_spl
| n6 = sK32_skl
| gt(sK32_skl,n6) ),
inference(resolution,[status(thm)],[f916,f104]) ).
fof(f989,definition,
( sQ80_spl
<=> leq(sK32_skl,n6) ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f991,plain,
( sQ80_spl
| ~ leq(sK32_skl,n6) ),
inference(component_clause,[status(thm)],[f989]) ).
fof(f992,definition,
( sQ81_spl
<=> sK32_skl = n6 ),
introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition]) ).
fof(f993,plain,
( ~ sQ81_spl
| sK32_skl = n6 ),
inference(component_clause,[status(thm)],[f992]) ).
fof(f995,plain,
( sQ9_spl
| sQ81_spl
| ~ sQ80_spl ),
inference(split_clause,[status(thm)],[f985,f989,f992,f434]) ).
fof(f996,definition,
( sQ82_spl
<=> gt(sK32_skl,n6) ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f997,plain,
( ~ sQ82_spl
| gt(sK32_skl,n6) ),
inference(component_clause,[status(thm)],[f996]) ).
fof(f999,plain,
( sQ9_spl
| sQ81_spl
| sQ82_spl ),
inference(split_clause,[status(thm)],[f986,f996,f992,f434]) ).
fof(f1013,plain,
( ~ sQ82_spl
| ~ sQ81_spl
| gt(n6,n6) ),
inference(forward_demodulation,[status(thm)],[f993,f997]) ).
fof(f1014,plain,
( ~ sQ82_spl
| ~ sQ81_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1013,f108]) ).
fof(f1015,plain,
( ~ sQ82_spl
| ~ sQ81_spl ),
inference(contradiction_clause,[status(thm)],[f1014]) ).
fof(f1036,plain,
( sQ6_spl
| ~ gt(sK31_skl,n0) ),
inference(resolution,[status(thm)],[f424,f122]) ).
fof(f1040,plain,
( sQ6_spl
| ~ gt(succ(sK31_skl),n0) ),
inference(resolution,[status(thm)],[f135,f424]) ).
fof(f1041,plain,
( sQ59_spl
| ~ gt(succ(sK23_skl),n0) ),
inference(resolution,[status(thm)],[f135,f826]) ).
fof(f1058,plain,
( sQ6_spl
| sK31_skl = n0
| gt(n0,sK31_skl) ),
inference(resolution,[status(thm)],[f1036,f104]) ).
fof(f1061,definition,
( sQ84_spl
<=> n0 = sK31_skl ),
introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition]) ).
fof(f1062,plain,
( ~ sQ84_spl
| n0 = sK31_skl ),
inference(component_clause,[status(thm)],[f1061]) ).
fof(f1063,plain,
( sQ84_spl
| n0 != sK31_skl ),
inference(component_clause,[status(thm)],[f1061]) ).
fof(f1065,definition,
( sQ85_spl
<=> gt(n0,sK31_skl) ),
introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition]) ).
fof(f1066,plain,
( ~ sQ85_spl
| gt(n0,sK31_skl) ),
inference(component_clause,[status(thm)],[f1065]) ).
fof(f1068,plain,
( sQ6_spl
| sQ84_spl
| sQ85_spl ),
inference(split_clause,[status(thm)],[f1058,f1065,f1061,f422]) ).
fof(f1073,plain,
( ~ sQ85_spl
| ~ sQ84_spl
| gt(n0,n0) ),
inference(forward_demodulation,[status(thm)],[f1062,f1066]) ).
fof(f1074,plain,
( ~ sQ85_spl
| ~ sQ84_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1073,f108]) ).
fof(f1075,plain,
( ~ sQ85_spl
| ~ sQ84_spl ),
inference(contradiction_clause,[status(thm)],[f1074]) ).
fof(f1133,plain,
! [X0] :
( sQ62_spl
| ~ sP3_prd(sK24_skl,X0) ),
inference(resolution,[status(thm)],[f835,f477]) ).
fof(f1146,plain,
( sQ59_spl
| sK23_skl = n0
| gt(n0,sK23_skl) ),
inference(resolution,[status(thm)],[f861,f104]) ).
fof(f1149,definition,
( sQ89_spl
<=> n0 = sK23_skl ),
introduced(definition,[new_symbols(definition,[sQ89_spl])],[split_symbol_definition]) ).
fof(f1150,plain,
( ~ sQ89_spl
| n0 = sK23_skl ),
inference(component_clause,[status(thm)],[f1149]) ).
fof(f1151,plain,
( sQ89_spl
| n0 != sK23_skl ),
inference(component_clause,[status(thm)],[f1149]) ).
fof(f1153,definition,
( sQ90_spl
<=> gt(n0,sK23_skl) ),
introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition]) ).
fof(f1154,plain,
( ~ sQ90_spl
| gt(n0,sK23_skl) ),
inference(component_clause,[status(thm)],[f1153]) ).
fof(f1156,plain,
( sQ59_spl
| sQ89_spl
| sQ90_spl ),
inference(split_clause,[status(thm)],[f1146,f1153,f1149,f824]) ).
fof(f1158,plain,
( ~ sQ90_spl
| ~ sQ89_spl
| gt(n0,n0) ),
inference(forward_demodulation,[status(thm)],[f1150,f1154]) ).
fof(f1159,plain,
( ~ sQ90_spl
| ~ sQ89_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1158,f108]) ).
fof(f1160,plain,
( ~ sQ90_spl
| ~ sQ89_spl ),
inference(contradiction_clause,[status(thm)],[f1159]) ).
fof(f1165,plain,
! [X0] :
( sQ66_spl
| ~ sP4_prd(sK26_skl,X0) ),
inference(resolution,[status(thm)],[f901,f375]) ).
fof(f1174,plain,
( ~ sQ3_spl
| sQ66_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f414,f1165]) ).
fof(f1175,plain,
( ~ sQ3_spl
| sQ66_spl ),
inference(contradiction_clause,[status(thm)],[f1174]) ).
fof(f1181,plain,
! [X0] :
( sQ65_spl
| ~ sP4_prd(X0,sK25_skl) ),
inference(resolution,[status(thm)],[f898,f374]) ).
fof(f1189,plain,
! [X0] :
( sQ68_spl
| ~ sP4_prd(sK26_skl,X0) ),
inference(resolution,[status(thm)],[f907,f481]) ).
fof(f1198,plain,
! [X0] :
( sQ67_spl
| ~ sP4_prd(X0,sK25_skl) ),
inference(resolution,[status(thm)],[f904,f480]) ).
fof(f1199,plain,
( sQ67_spl
| ~ gt(n3,sK25_skl) ),
inference(resolution,[status(thm)],[f904,f128]) ).
fof(f1208,plain,
! [X0] :
( sQ72_spl
| ~ sP5_prd(sK28_skl,X0) ),
inference(resolution,[status(thm)],[f933,f485]) ).
fof(f1216,plain,
( ~ sQ4_spl
| sQ72_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f417,f1208]) ).
fof(f1218,plain,
( ~ sQ4_spl
| sQ72_spl ),
inference(contradiction_clause,[status(thm)],[f1216]) ).
fof(f1221,plain,
! [X0] :
( sQ71_spl
| ~ sP5_prd(X0,sK27_skl) ),
inference(resolution,[status(thm)],[f930,f484]) ).
fof(f1233,plain,
! [X0] :
( sQ70_spl
| ~ sP5_prd(sK28_skl,X0) ),
inference(resolution,[status(thm)],[f927,f383]) ).
fof(f1247,plain,
! [X0] :
( sQ69_spl
| ~ sP5_prd(X0,sK27_skl) ),
inference(resolution,[status(thm)],[f924,f382]) ).
fof(f1262,plain,
! [X0] :
( sQ76_spl
| ~ sP6_prd(sK30_skl,X0) ),
inference(resolution,[status(thm)],[f949,f489]) ).
fof(f1268,plain,
( ~ sQ5_spl
| sQ76_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f420,f1262]) ).
fof(f1270,plain,
( ~ sQ5_spl
| sQ76_spl ),
inference(contradiction_clause,[status(thm)],[f1268]) ).
fof(f1271,plain,
( ~ sQ2_spl
| sQ62_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f411,f1133]) ).
fof(f1272,plain,
( ~ sQ2_spl
| sQ62_spl ),
inference(contradiction_clause,[status(thm)],[f1271]) ).
fof(f1273,plain,
( ~ sQ3_spl
| sQ68_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f414,f1189]) ).
fof(f1274,plain,
( ~ sQ3_spl
| sQ68_spl ),
inference(contradiction_clause,[status(thm)],[f1273]) ).
fof(f1275,plain,
( ~ sQ4_spl
| sQ70_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f417,f1233]) ).
fof(f1276,plain,
( ~ sQ4_spl
| sQ70_spl ),
inference(contradiction_clause,[status(thm)],[f1275]) ).
fof(f1286,plain,
! [X0] :
( sQ75_spl
| ~ sP6_prd(X0,sK29_skl) ),
inference(resolution,[status(thm)],[f946,f488]) ).
fof(f1293,plain,
( ~ sQ5_spl
| sQ75_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f420,f1286]) ).
fof(f1295,plain,
( ~ sQ5_spl
| sQ75_spl ),
inference(contradiction_clause,[status(thm)],[f1293]) ).
fof(f1300,plain,
( sQ89_spl
| ~ leq(sK23_skl,n0)
| ~ leq(n0,sK23_skl) ),
inference(resolution,[status(thm)],[f323,f1151]) ).
fof(f1301,plain,
( sQ84_spl
| ~ leq(sK31_skl,n0)
| ~ leq(n0,sK31_skl) ),
inference(resolution,[status(thm)],[f323,f1063]) ).
fof(f1321,definition,
( sQ96_spl
<=> leq(sK23_skl,n0) ),
introduced(definition,[new_symbols(definition,[sQ96_spl])],[split_symbol_definition]) ).
fof(f1324,plain,
( sQ89_spl
| ~ sQ96_spl
| ~ sQ59_spl ),
inference(split_clause,[status(thm)],[f1300,f824,f1321,f1149]) ).
fof(f1325,definition,
( sQ97_spl
<=> leq(sK31_skl,n0) ),
introduced(definition,[new_symbols(definition,[sQ97_spl])],[split_symbol_definition]) ).
fof(f1328,plain,
( sQ84_spl
| ~ sQ97_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f1301,f422,f1325,f1061]) ).
fof(f1329,plain,
( ~ sQ2_spl
| sQ59_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f411,f859]) ).
fof(f1334,plain,
( sQ59_spl
| ~ sQ89_spl
| ~ gt(succ(n0),n0) ),
inference(backward_demodulation,[status(thm)],[f1150,f1041]) ).
fof(f1369,plain,
( ~ sQ2_spl
| sQ59_spl ),
inference(contradiction_clause,[status(thm)],[f1329]) ).
fof(f1372,plain,
( ~ sQ3_spl
| sQ65_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f414,f1181]) ).
fof(f1373,plain,
( ~ sQ3_spl
| sQ65_spl ),
inference(contradiction_clause,[status(thm)],[f1372]) ).
fof(f1390,plain,
( sQ80_spl
| ~ sQ81_spl
| ~ leq(n6,n6) ),
inference(backward_demodulation,[status(thm)],[f993,f991]) ).
fof(f1392,plain,
( ~ sQ4_spl
| sQ71_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f417,f1221]) ).
fof(f1393,plain,
( ~ sQ4_spl
| sQ71_spl ),
inference(contradiction_clause,[status(thm)],[f1392]) ).
fof(f1394,plain,
( sQ80_spl
| ~ sQ81_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1390,f109]) ).
fof(f1395,plain,
( sQ80_spl
| ~ sQ81_spl ),
inference(contradiction_clause,[status(thm)],[f1394]) ).
fof(f1419,plain,
( sQ6_spl
| ~ sQ84_spl
| ~ gt(succ(n0),n0) ),
inference(backward_demodulation,[status(thm)],[f1062,f1040]) ).
fof(f1431,plain,
( sQ6_spl
| ~ sQ84_spl
| ~ gt(n1,n0) ),
inference(forward_demodulation,[status(thm)],[f333,f1419]) ).
fof(f1432,plain,
( sQ6_spl
| ~ sQ84_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1431,f298]) ).
fof(f1433,plain,
( sQ6_spl
| ~ sQ84_spl ),
inference(contradiction_clause,[status(thm)],[f1432]) ).
fof(f1447,plain,
! [X0] :
( sQ74_spl
| ~ sP6_prd(sK30_skl,X0) ),
inference(resolution,[status(thm)],[f943,f391]) ).
fof(f1460,plain,
( ~ sQ5_spl
| sQ74_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f420,f1447]) ).
fof(f1461,plain,
( ~ sQ5_spl
| sQ74_spl ),
inference(contradiction_clause,[status(thm)],[f1460]) ).
fof(f1468,plain,
! [X0] :
( sQ73_spl
| ~ sP6_prd(X0,sK29_skl) ),
inference(resolution,[status(thm)],[f940,f390]) ).
fof(f1481,plain,
( sQ67_spl
| sK25_skl = n3
| ~ leq(sK25_skl,n3) ),
inference(resolution,[status(thm)],[f1199,f124]) ).
fof(f1482,plain,
( sQ67_spl
| n3 = sK25_skl
| gt(sK25_skl,n3) ),
inference(resolution,[status(thm)],[f1199,f104]) ).
fof(f1485,definition,
( sQ98_spl
<=> leq(sK25_skl,n3) ),
introduced(definition,[new_symbols(definition,[sQ98_spl])],[split_symbol_definition]) ).
fof(f1488,definition,
( sQ99_spl
<=> sK25_skl = n3 ),
introduced(definition,[new_symbols(definition,[sQ99_spl])],[split_symbol_definition]) ).
fof(f1489,plain,
( ~ sQ99_spl
| sK25_skl = n3 ),
inference(component_clause,[status(thm)],[f1488]) ).
fof(f1491,plain,
( sQ67_spl
| sQ99_spl
| ~ sQ98_spl ),
inference(split_clause,[status(thm)],[f1481,f1485,f1488,f902]) ).
fof(f1492,definition,
( sQ100_spl
<=> gt(sK25_skl,n3) ),
introduced(definition,[new_symbols(definition,[sQ100_spl])],[split_symbol_definition]) ).
fof(f1493,plain,
( ~ sQ100_spl
| gt(sK25_skl,n3) ),
inference(component_clause,[status(thm)],[f1492]) ).
fof(f1495,plain,
( sQ67_spl
| sQ99_spl
| sQ100_spl ),
inference(split_clause,[status(thm)],[f1482,f1492,f1488,f902]) ).
fof(f1496,plain,
( ~ sQ100_spl
| ~ sQ99_spl
| gt(n3,n3) ),
inference(forward_demodulation,[status(thm)],[f1489,f1493]) ).
fof(f1497,plain,
( ~ sQ100_spl
| ~ sQ99_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1496,f108]) ).
fof(f1498,plain,
( ~ sQ100_spl
| ~ sQ99_spl ),
inference(contradiction_clause,[status(thm)],[f1497]) ).
fof(f1499,plain,
! [X0] :
( sQ61_spl
| ~ sP3_prd(X0,sK23_skl) ),
inference(resolution,[status(thm)],[f832,f476]) ).
fof(f1510,plain,
( ~ sQ2_spl
| sQ61_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f411,f1499]) ).
fof(f1512,plain,
( ~ sQ2_spl
| sQ61_spl ),
inference(contradiction_clause,[status(thm)],[f1510]) ).
fof(f1513,plain,
( ~ sQ4_spl
| sQ69_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f417,f1247]) ).
fof(f1514,plain,
( ~ sQ4_spl
| sQ69_spl ),
inference(contradiction_clause,[status(thm)],[f1513]) ).
fof(f1515,plain,
( sQ59_spl
| ~ sQ89_spl
| ~ gt(n1,n0) ),
inference(forward_demodulation,[status(thm)],[f333,f1334]) ).
fof(f1516,plain,
( sQ59_spl
| ~ sQ89_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1515,f298]) ).
fof(f1517,plain,
( sQ59_spl
| ~ sQ89_spl ),
inference(contradiction_clause,[status(thm)],[f1516]) ).
fof(f1518,plain,
( ~ sQ5_spl
| sQ73_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f420,f1468]) ).
fof(f1519,plain,
( ~ sQ5_spl
| sQ73_spl ),
inference(contradiction_clause,[status(thm)],[f1518]) ).
fof(f1520,plain,
( ~ sQ3_spl
| sQ67_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f414,f1198]) ).
fof(f1521,plain,
( ~ sQ3_spl
| sQ67_spl ),
inference(contradiction_clause,[status(thm)],[f1520]) ).
fof(f1522,plain,
$false,
inference(sat_refutation,[status(thm)],[f425,f429,f433,f437,f441,f593,f595,f699,f836,f851,f872,f875,f877,f883,f908,f934,f950,f995,f999,f1015,f1068,f1075,f1156,f1160,f1175,f1218,f1270,f1272,f1274,f1276,f1295,f1324,f1328,f1369,f1373,f1393,f1395,f1433,f1461,f1491,f1495,f1498,f1512,f1514,f1517,f1519,f1521]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWV115+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.40 % Computer : n002.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Mon Sep 21 08:34:02 UTC 2026
% 0.15/0.40 % CPUTime :
% 0.15/0.42 % Drodi V4.1.1
% 0.62/0.84 % Refutation found
% 0.62/0.84 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.62/0.84 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.44/0.88 % Elapsed time: 0.455402 seconds
% 1.44/0.88 % CPU time: 3.195337 seconds
% 1.44/0.88 % Total memory used: 134.904 MB
% 1.44/0.88 % Net memory used: 131.292 MB
%------------------------------------------------------------------------------