%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV112+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 0.16s 0.70s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 48
% Syntax : Number of formulae : 241 ( 17 unt; 37 def)
% Number of atoms : 913 ( 96 equ)
% Maximal formula atoms : 51 ( 3 avg)
% Number of connectives : 1059 ( 387 ~; 433 |; 174 &)
% ( 39 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 41 ( 39 usr; 35 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 19 con; 0-3 aty)
% Number of variables : 236 ( 220 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( X = Y
| gt(Y,X)
| gt(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] : ~ gt(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : leq(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y] :
( gt(Y,X)
=> leq(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y] :
( ( X != Y
& leq(X,Y) )
=> gt(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,Y] :
( leq(X,pred(Y))
<=> gt(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X,Y] :
( leq(X,Y)
<=> gt(succ(Y),X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [X] : plus(n1,X) = succ(X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,axiom,
! [X] : minus(X,n1) = pred(X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,axiom,
! [X] : pred(succ(X)) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f53,conjecture,
( ( ! [I] :
( ( leq(I,minus(pv57,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,pv57)
& leq(n0,H)
& leq(n0,G) )
=> a_select3(id_ds1_filter,G,H) = a_select3(id_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(pv57,minus(n6,n1))
& leq(pv5,minus(n999,n1))
& leq(n0,pv57)
& leq(n0,pv5) )
=> ( ! [Q] :
( ( leq(Q,minus(plus(n1,pv57),n1))
& leq(n0,Q) )
=> ! [R] :
( ( leq(R,minus(n6,n1))
& leq(n0,R) )
=> a_select3(id_ds1_filter,Q,R) = a_select3(id_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/sandbox/benchmark/theBenchmark.p') ).
fof(f54,negated_conjecture,
~ ( ( ! [I] :
( ( leq(I,minus(pv57,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,pv57)
& leq(n0,H)
& leq(n0,G) )
=> a_select3(id_ds1_filter,G,H) = a_select3(id_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(pv57,minus(n6,n1))
& leq(pv5,minus(n999,n1))
& leq(n0,pv57)
& leq(n0,pv5) )
=> ( ! [Q] :
( ( leq(Q,minus(plus(n1,pv57),n1))
& leq(n0,Q) )
=> ! [R] :
( ( leq(R,minus(n6,n1))
& leq(n0,R) )
=> a_select3(id_ds1_filter,Q,R) = a_select3(id_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(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(f127,plain,
! [X0,X1] :
( gt(X1,X0)
| ~ leq(X0,pred(X1)) ),
inference(cnf_transformation,[status(thm)],[f126]) ).
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(f218,plain,
! [X0] : plus(n1,X0) = succ(X0),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f227,plain,
! [X0] : minus(X0,n1) = pred(X0),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f228,plain,
! [X0] : pred(succ(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f261,plain,
( ( ? [Q] :
( ? [R] :
( a_select3(id_ds1_filter,Q,R) != a_select3(id_ds1_filter,R,Q)
& leq(R,minus(n6,n1))
& leq(n0,R) )
& leq(Q,minus(plus(n1,pv57),n1))
& 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(pv57,n1))
| ~ leq(n0,I) )
& ! [G,H] :
( a_select3(id_ds1_filter,G,H) = a_select3(id_ds1_filter,H,G)
| ~ leq(H,minus(n6,n1))
| ~ leq(G,pv57)
| ~ 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(pv57,minus(n6,n1))
& leq(pv5,minus(n999,n1))
& leq(n0,pv57)
& 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,plain,
( ( ? [Q] :
( ? [R] :
( a_select3(id_ds1_filter,Q,R) != a_select3(id_ds1_filter,R,Q)
& leq(R,minus(n6,n1))
& leq(n0,R) )
& leq(Q,minus(plus(n1,pv57),n1))
& leq(n0,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(pv57,n1))
| ~ leq(n0,I) )
& ! [G,H] :
( a_select3(id_ds1_filter,G,H) = a_select3(id_ds1_filter,H,G)
| ~ leq(H,minus(n6,n1))
| ~ leq(G,pv57)
| ~ 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(pv57,minus(n6,n1))
& leq(pv5,minus(n999,n1))
& leq(n0,pv57)
& leq(n0,pv5) ),
inference(formula_renaming,[status(thm)],[f261,f264,f263,f262]) ).
fof(f266,plain,
( ( ( a_select3(id_ds1_filter,sK29_skl,sK30_skl) != a_select3(id_ds1_filter,sK30_skl,sK29_skl)
& leq(sK30_skl,minus(n6,n1))
& leq(n0,sK30_skl)
& leq(sK29_skl,minus(plus(n1,pv57),n1))
& leq(n0,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(pv57,n1))
| ~ leq(n0,I) )
& ! [G,H] :
( a_select3(id_ds1_filter,G,H) = a_select3(id_ds1_filter,H,G)
| ~ leq(H,minus(n6,n1))
| ~ leq(G,pv57)
| ~ 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(pv57,minus(n6,n1))
& leq(pv5,minus(n999,n1))
& leq(n0,pv57)
& 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]),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)],[f265]) ).
fof(f267,plain,
leq(n0,pv5),
inference(cnf_transformation,[status(thm)],[f266]) ).
fof(f269,plain,
leq(pv5,minus(n999,n1)),
inference(cnf_transformation,[status(thm)],[f266]) ).
fof(f271,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)],[f266]) ).
fof(f272,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)],[f266]) ).
fof(f273,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)],[f266]) ).
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(X0,pv57)
| ~ leq(n0,X1)
| ~ leq(n0,X0) ),
inference(cnf_transformation,[status(thm)],[f266]) ).
fof(f275,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(pv57,n1))
| ~ leq(n0,X0) ),
inference(cnf_transformation,[status(thm)],[f266]) ).
fof(f276,plain,
( leq(n0,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)],[f266]) ).
fof(f277,plain,
( leq(sK29_skl,minus(plus(n1,pv57),n1))
| 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)],[f266]) ).
fof(f278,plain,
( leq(n0,sK30_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)],[f266]) ).
fof(f279,plain,
( leq(sK30_skl,minus(n6,n1))
| 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)],[f266]) ).
fof(f280,plain,
( a_select3(id_ds1_filter,sK29_skl,sK30_skl) != a_select3(id_ds1_filter,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)],[f266]) ).
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) )
& ( ( 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(f366,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)],[f365]) ).
fof(f367,plain,
! [X0,X1] :
( leq(n0,X1)
| ~ sP3_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f366]) ).
fof(f368,plain,
! [X0,X1] :
( leq(n0,X0)
| ~ sP3_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f366]) ).
fof(f369,plain,
! [X0,X1] :
( leq(X1,minus(n6,n1))
| ~ sP3_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f366]) ).
fof(f370,plain,
! [X0,X1] :
( leq(X0,minus(n6,n1))
| ~ sP3_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f366]) ).
fof(f371,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)],[f366]) ).
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) )
& ( ( 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(f374,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)],[f373]) ).
fof(f375,plain,
! [X0,X1] :
( leq(n0,X1)
| ~ sP4_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f374]) ).
fof(f376,plain,
! [X0,X1] :
( leq(n0,X0)
| ~ sP4_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f374]) ).
fof(f377,plain,
! [X0,X1] :
( leq(X1,minus(n3,n1))
| ~ sP4_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f374]) ).
fof(f378,plain,
! [X0,X1] :
( leq(X0,minus(n3,n1))
| ~ sP4_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f374]) ).
fof(f379,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)],[f374]) ).
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) )
& ( ( 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(f382,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)],[f381]) ).
fof(f383,plain,
! [X0,X1] :
( leq(n0,X1)
| ~ sP5_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f382]) ).
fof(f384,plain,
! [X0,X1] :
( leq(n0,X0)
| ~ sP5_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f382]) ).
fof(f385,plain,
! [X0,X1] :
( leq(X1,minus(n6,n1))
| ~ sP5_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f382]) ).
fof(f386,plain,
! [X0,X1] :
( leq(X0,minus(n6,n1))
| ~ sP5_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f382]) ).
fof(f387,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)],[f382]) ).
fof(f397,definition,
( sQ0_spl
<=> leq(n0,pv5) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f399,plain,
( sQ0_spl
| ~ leq(n0,pv5) ),
inference(component_clause,[status(thm)],[f397]) ).
fof(f400,definition,
( sQ1_spl
<=> leq(pv5,minus(n999,n1)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f402,plain,
( sQ1_spl
| ~ leq(pv5,minus(n999,n1)) ),
inference(component_clause,[status(thm)],[f400]) ).
fof(f403,definition,
( sQ2_spl
<=> sP3_prd(sK24_skl,sK23_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f404,plain,
( ~ sQ2_spl
| sP3_prd(sK24_skl,sK23_skl) ),
inference(component_clause,[status(thm)],[f403]) ).
fof(f406,definition,
( sQ3_spl
<=> sP4_prd(sK26_skl,sK25_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f407,plain,
( ~ sQ3_spl
| sP4_prd(sK26_skl,sK25_skl) ),
inference(component_clause,[status(thm)],[f406]) ).
fof(f409,definition,
( sQ4_spl
<=> sP5_prd(sK28_skl,sK27_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f410,plain,
( ~ sQ4_spl
| sP5_prd(sK28_skl,sK27_skl) ),
inference(component_clause,[status(thm)],[f409]) ).
fof(f412,definition,
( sQ5_spl
<=> leq(n0,sK29_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f415,plain,
( sQ5_spl
| sQ4_spl
| sQ3_spl
| sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f276,f397,f400,f403,f406,f409,f412]) ).
fof(f416,definition,
( sQ6_spl
<=> leq(sK29_skl,minus(plus(n1,pv57),n1)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f417,plain,
( ~ sQ6_spl
| leq(sK29_skl,minus(plus(n1,pv57),n1)) ),
inference(component_clause,[status(thm)],[f416]) ).
fof(f419,plain,
( sQ6_spl
| sQ4_spl
| sQ3_spl
| sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f277,f397,f400,f403,f406,f409,f416]) ).
fof(f420,definition,
( sQ7_spl
<=> leq(n0,sK30_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f422,plain,
( sQ7_spl
| ~ leq(n0,sK30_skl) ),
inference(component_clause,[status(thm)],[f420]) ).
fof(f423,plain,
( sQ7_spl
| sQ4_spl
| sQ3_spl
| sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f278,f397,f400,f403,f406,f409,f420]) ).
fof(f424,definition,
( sQ8_spl
<=> leq(sK30_skl,minus(n6,n1)) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f425,plain,
( ~ sQ8_spl
| leq(sK30_skl,minus(n6,n1)) ),
inference(component_clause,[status(thm)],[f424]) ).
fof(f427,plain,
( sQ8_spl
| sQ4_spl
| sQ3_spl
| sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f279,f397,f400,f403,f406,f409,f424]) ).
fof(f428,definition,
( sQ9_spl
<=> a_select3(id_ds1_filter,sK29_skl,sK30_skl) = a_select3(id_ds1_filter,sK30_skl,sK29_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f430,plain,
( sQ9_spl
| a_select3(id_ds1_filter,sK29_skl,sK30_skl) != a_select3(id_ds1_filter,sK30_skl,sK29_skl) ),
inference(component_clause,[status(thm)],[f428]) ).
fof(f431,plain,
( ~ sQ9_spl
| sQ4_spl
| sQ3_spl
| sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f280,f397,f400,f403,f406,f409,f428]) ).
fof(f444,plain,
leq(pv5,pred(n999)),
inference(forward_demodulation,[status(thm)],[f227,f269]) ).
fof(f446,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,f271]) ).
fof(f447,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,f446]) ).
fof(f448,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,f272]) ).
fof(f449,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,f448]) ).
fof(f450,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,f273]) ).
fof(f451,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,f450]) ).
fof(f452,plain,
! [X0,X1] :
( a_select3(id_ds1_filter,X0,X1) = a_select3(id_ds1_filter,X1,X0)
| ~ leq(X1,pred(n6))
| ~ leq(X0,pv57)
| ~ leq(n0,X1)
| ~ leq(n0,X0) ),
inference(forward_demodulation,[status(thm)],[f227,f274]) ).
fof(f453,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(pv57))
| ~ leq(n0,X0) ),
inference(forward_demodulation,[status(thm)],[f227,f275]) ).
fof(f454,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(pv57))
| ~ leq(n0,X0) ),
inference(forward_demodulation,[status(thm)],[f227,f453]) ).
fof(f466,plain,
! [X0,X1] :
( leq(X1,pred(n6))
| ~ sP3_prd(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f227,f369]) ).
fof(f467,plain,
! [X0,X1] :
( leq(X0,pred(n6))
| ~ sP3_prd(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f227,f370]) ).
fof(f470,plain,
! [X0,X1] :
( leq(X1,pred(n3))
| ~ sP4_prd(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f227,f377]) ).
fof(f471,plain,
! [X0,X1] :
( leq(X0,pred(n3))
| ~ sP4_prd(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f227,f378]) ).
fof(f474,plain,
! [X0,X1] :
( leq(X1,pred(n6))
| ~ sP5_prd(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f227,f385]) ).
fof(f475,plain,
! [X0,X1] :
( leq(X0,pred(n6))
| ~ sP5_prd(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f227,f386]) ).
fof(f577,plain,
( sQ1_spl
| ~ leq(pv5,pred(n999)) ),
inference(forward_demodulation,[status(thm)],[f227,f402]) ).
fof(f578,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f577,f444]) ).
fof(f579,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f578]) ).
fof(f580,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f399,f267]) ).
fof(f581,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f580]) ).
fof(f663,definition,
( sQ39_spl
<=> leq(n0,n0) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f665,plain,
( sQ39_spl
| ~ leq(n0,n0) ),
inference(component_clause,[status(thm)],[f663]) ).
fof(f688,plain,
( sQ39_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f665,f109]) ).
fof(f689,plain,
sQ39_spl,
inference(contradiction_clause,[status(thm)],[f688]) ).
fof(f690,plain,
( ~ sQ8_spl
| leq(sK30_skl,pred(n6)) ),
inference(forward_demodulation,[status(thm)],[f227,f425]) ).
fof(f691,plain,
( ~ sQ6_spl
| leq(sK29_skl,pred(plus(n1,pv57))) ),
inference(forward_demodulation,[status(thm)],[f227,f417]) ).
fof(f692,plain,
( ~ sQ6_spl
| leq(sK29_skl,pred(succ(pv57))) ),
inference(forward_demodulation,[status(thm)],[f218,f691]) ).
fof(f693,plain,
( ~ sQ6_spl
| leq(sK29_skl,pv57) ),
inference(forward_demodulation,[status(thm)],[f228,f692]) ).
fof(f808,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)],[f371,f404]) ).
fof(f809,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)],[f379,f407]) ).
fof(f810,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)],[f387,f410]) ).
fof(f824,plain,
( sQ9_spl
| ~ leq(sK29_skl,pred(n6))
| ~ leq(n0,sK29_skl)
| ~ leq(sK30_skl,pred(pv57))
| ~ leq(n0,sK30_skl) ),
inference(resolution,[status(thm)],[f454,f430]) ).
fof(f828,definition,
( sQ59_spl
<=> leq(sK30_skl,pred(n6)) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f830,plain,
( sQ59_spl
| ~ leq(sK30_skl,pred(n6)) ),
inference(component_clause,[status(thm)],[f828]) ).
fof(f832,definition,
( sQ60_spl
<=> leq(sK30_skl,pred(pv57)) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f835,definition,
( sQ61_spl
<=> leq(sK29_skl,pred(n6)) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f837,plain,
( sQ61_spl
| ~ leq(sK29_skl,pred(n6)) ),
inference(component_clause,[status(thm)],[f835]) ).
fof(f838,plain,
( sQ9_spl
| ~ sQ61_spl
| ~ sQ5_spl
| ~ sQ60_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f824,f420,f832,f412,f835,f428]) ).
fof(f839,plain,
( sQ59_spl
| ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f830,f690]) ).
fof(f840,plain,
( sQ59_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f839]) ).
fof(f846,plain,
( sQ61_spl
| ~ gt(n6,sK29_skl) ),
inference(resolution,[status(thm)],[f837,f128]) ).
fof(f851,plain,
( sQ61_spl
| sK29_skl = n6
| ~ leq(sK29_skl,n6) ),
inference(resolution,[status(thm)],[f846,f124]) ).
fof(f855,definition,
( sQ62_spl
<=> leq(sK29_skl,n6) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f857,plain,
( sQ62_spl
| ~ leq(sK29_skl,n6) ),
inference(component_clause,[status(thm)],[f855]) ).
fof(f858,definition,
( sQ63_spl
<=> sK29_skl = n6 ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f859,plain,
( ~ sQ63_spl
| sK29_skl = n6 ),
inference(component_clause,[status(thm)],[f858]) ).
fof(f861,plain,
( sQ61_spl
| sQ63_spl
| ~ sQ62_spl ),
inference(split_clause,[status(thm)],[f851,f855,f858,f835]) ).
fof(f862,definition,
( sQ64_spl
<=> gt(sK29_skl,n6) ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f863,plain,
( ~ sQ64_spl
| gt(sK29_skl,n6) ),
inference(component_clause,[status(thm)],[f862]) ).
fof(f866,plain,
( ~ sQ6_spl
| ~ sQ63_spl
| leq(n6,pv57) ),
inference(backward_demodulation,[status(thm)],[f859,f693]) ).
fof(f868,plain,
( ~ sQ64_spl
| ~ sQ63_spl
| gt(n6,n6) ),
inference(forward_demodulation,[status(thm)],[f859,f863]) ).
fof(f869,plain,
( ~ sQ64_spl
| ~ sQ63_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f868,f108]) ).
fof(f870,plain,
( ~ sQ64_spl
| ~ sQ63_spl ),
inference(contradiction_clause,[status(thm)],[f869]) ).
fof(f871,plain,
( sQ62_spl
| ~ gt(n6,sK29_skl) ),
inference(resolution,[status(thm)],[f857,f122]) ).
fof(f882,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)],[f808,f447]) ).
fof(f884,definition,
( sQ65_spl
<=> leq(n0,sK23_skl) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f886,plain,
( sQ65_spl
| ~ leq(n0,sK23_skl) ),
inference(component_clause,[status(thm)],[f884]) ).
fof(f887,definition,
( sQ66_spl
<=> leq(n0,sK24_skl) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f889,plain,
( sQ66_spl
| ~ leq(n0,sK24_skl) ),
inference(component_clause,[status(thm)],[f887]) ).
fof(f890,definition,
( sQ67_spl
<=> leq(sK23_skl,pred(n6)) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f892,plain,
( sQ67_spl
| ~ leq(sK23_skl,pred(n6)) ),
inference(component_clause,[status(thm)],[f890]) ).
fof(f893,definition,
( sQ68_spl
<=> leq(sK24_skl,pred(n6)) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f895,plain,
( sQ68_spl
| ~ leq(sK24_skl,pred(n6)) ),
inference(component_clause,[status(thm)],[f893]) ).
fof(f896,plain,
( ~ sQ2_spl
| ~ sQ68_spl
| ~ sQ67_spl
| ~ sQ66_spl
| ~ sQ65_spl ),
inference(split_clause,[status(thm)],[f882,f884,f887,f890,f893,f403]) ).
fof(f898,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)],[f809,f449]) ).
fof(f900,definition,
( sQ69_spl
<=> leq(n0,sK25_skl) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f902,plain,
( sQ69_spl
| ~ leq(n0,sK25_skl) ),
inference(component_clause,[status(thm)],[f900]) ).
fof(f903,definition,
( sQ70_spl
<=> leq(n0,sK26_skl) ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f905,plain,
( sQ70_spl
| ~ leq(n0,sK26_skl) ),
inference(component_clause,[status(thm)],[f903]) ).
fof(f906,definition,
( sQ71_spl
<=> leq(sK25_skl,pred(n3)) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f908,plain,
( sQ71_spl
| ~ leq(sK25_skl,pred(n3)) ),
inference(component_clause,[status(thm)],[f906]) ).
fof(f909,definition,
( sQ72_spl
<=> leq(sK26_skl,pred(n3)) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f911,plain,
( sQ72_spl
| ~ leq(sK26_skl,pred(n3)) ),
inference(component_clause,[status(thm)],[f909]) ).
fof(f912,plain,
( ~ sQ3_spl
| ~ sQ72_spl
| ~ sQ71_spl
| ~ sQ70_spl
| ~ sQ69_spl ),
inference(split_clause,[status(thm)],[f898,f900,f903,f906,f909,f406]) ).
fof(f914,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)],[f810,f451]) ).
fof(f916,definition,
( sQ73_spl
<=> leq(n0,sK27_skl) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f918,plain,
( sQ73_spl
| ~ leq(n0,sK27_skl) ),
inference(component_clause,[status(thm)],[f916]) ).
fof(f919,definition,
( sQ74_spl
<=> leq(n0,sK28_skl) ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f921,plain,
( sQ74_spl
| ~ leq(n0,sK28_skl) ),
inference(component_clause,[status(thm)],[f919]) ).
fof(f922,definition,
( sQ75_spl
<=> leq(sK27_skl,pred(n6)) ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f924,plain,
( sQ75_spl
| ~ leq(sK27_skl,pred(n6)) ),
inference(component_clause,[status(thm)],[f922]) ).
fof(f925,definition,
( sQ76_spl
<=> leq(sK28_skl,pred(n6)) ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f927,plain,
( sQ76_spl
| ~ leq(sK28_skl,pred(n6)) ),
inference(component_clause,[status(thm)],[f925]) ).
fof(f928,plain,
( ~ sQ4_spl
| ~ sQ76_spl
| ~ sQ75_spl
| ~ sQ74_spl
| ~ sQ73_spl ),
inference(split_clause,[status(thm)],[f914,f916,f919,f922,f925,f409]) ).
fof(f938,plain,
( sQ62_spl
| ~ leq(sK29_skl,pred(n6)) ),
inference(resolution,[status(thm)],[f871,f127]) ).
fof(f940,plain,
( sQ62_spl
| n6 = sK29_skl
| gt(sK29_skl,n6) ),
inference(resolution,[status(thm)],[f871,f104]) ).
fof(f943,plain,
( sQ62_spl
| ~ sQ61_spl ),
inference(split_clause,[status(thm)],[f938,f835,f855]) ).
fof(f945,plain,
( sQ62_spl
| sQ63_spl
| sQ64_spl ),
inference(split_clause,[status(thm)],[f940,f862,f858,f855]) ).
fof(f993,plain,
! [X0] :
( sQ66_spl
| ~ sP3_prd(sK24_skl,X0) ),
inference(resolution,[status(thm)],[f889,f368]) ).
fof(f998,plain,
( ~ sQ2_spl
| sQ66_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f404,f993]) ).
fof(f999,plain,
( ~ sQ2_spl
| sQ66_spl ),
inference(contradiction_clause,[status(thm)],[f998]) ).
fof(f1005,plain,
! [X0] :
( sQ65_spl
| ~ sP3_prd(X0,sK23_skl) ),
inference(resolution,[status(thm)],[f886,f367]) ).
fof(f1018,plain,
! [X0] :
( sQ68_spl
| ~ sP3_prd(sK24_skl,X0) ),
inference(resolution,[status(thm)],[f895,f467]) ).
fof(f1025,plain,
! [X0] :
( sQ67_spl
| ~ sP3_prd(X0,sK23_skl) ),
inference(resolution,[status(thm)],[f892,f466]) ).
fof(f1033,plain,
! [X0] :
( sQ72_spl
| ~ sP4_prd(sK26_skl,X0) ),
inference(resolution,[status(thm)],[f911,f471]) ).
fof(f1039,plain,
( ~ sQ3_spl
| sQ72_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f407,f1033]) ).
fof(f1040,plain,
( ~ sQ3_spl
| sQ72_spl ),
inference(contradiction_clause,[status(thm)],[f1039]) ).
fof(f1042,plain,
! [X0] :
( sQ71_spl
| ~ sP4_prd(X0,sK25_skl) ),
inference(resolution,[status(thm)],[f908,f470]) ).
fof(f1049,plain,
! [X0] :
( sQ70_spl
| ~ sP4_prd(sK26_skl,X0) ),
inference(resolution,[status(thm)],[f905,f376]) ).
fof(f1059,plain,
! [X0] :
( sQ69_spl
| ~ sP4_prd(X0,sK25_skl) ),
inference(resolution,[status(thm)],[f902,f375]) ).
fof(f1068,plain,
! [X0] :
( sQ76_spl
| ~ sP5_prd(sK28_skl,X0) ),
inference(resolution,[status(thm)],[f927,f475]) ).
fof(f1073,plain,
( ~ sQ4_spl
| sQ76_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f410,f1068]) ).
fof(f1074,plain,
( ~ sQ4_spl
| sQ76_spl ),
inference(contradiction_clause,[status(thm)],[f1073]) ).
fof(f1075,plain,
( ~ sQ2_spl
| sQ68_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f404,f1018]) ).
fof(f1076,plain,
( ~ sQ2_spl
| sQ68_spl ),
inference(contradiction_clause,[status(thm)],[f1075]) ).
fof(f1077,plain,
( ~ sQ3_spl
| sQ70_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f407,f1049]) ).
fof(f1078,plain,
( ~ sQ3_spl
| sQ70_spl ),
inference(contradiction_clause,[status(thm)],[f1077]) ).
fof(f1109,plain,
! [X0] :
( sQ75_spl
| ~ sP5_prd(X0,sK27_skl) ),
inference(resolution,[status(thm)],[f924,f474]) ).
fof(f1116,plain,
( ~ sQ4_spl
| sQ75_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f410,f1109]) ).
fof(f1118,plain,
( ~ sQ4_spl
| sQ75_spl ),
inference(contradiction_clause,[status(thm)],[f1116]) ).
fof(f1119,plain,
( ~ sQ2_spl
| sQ65_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f404,f1005]) ).
fof(f1120,plain,
( ~ sQ2_spl
| sQ65_spl ),
inference(contradiction_clause,[status(thm)],[f1119]) ).
fof(f1121,plain,
( ~ sQ3_spl
| sQ71_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f407,f1042]) ).
fof(f1122,plain,
( ~ sQ3_spl
| sQ71_spl ),
inference(contradiction_clause,[status(thm)],[f1121]) ).
fof(f1128,plain,
! [X0] :
( sQ74_spl
| ~ sP5_prd(sK28_skl,X0) ),
inference(resolution,[status(thm)],[f921,f384]) ).
fof(f1138,plain,
( ~ sQ4_spl
| sQ74_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f410,f1128]) ).
fof(f1139,plain,
( ~ sQ4_spl
| sQ74_spl ),
inference(contradiction_clause,[status(thm)],[f1138]) ).
fof(f1140,plain,
( ~ sQ2_spl
| sQ67_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f404,f1025]) ).
fof(f1141,plain,
( ~ sQ2_spl
| sQ67_spl ),
inference(contradiction_clause,[status(thm)],[f1140]) ).
fof(f1149,definition,
( sQ80_spl
<=> leq(n6,pv57) ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f1151,plain,
( sQ80_spl
| ~ leq(n6,pv57) ),
inference(component_clause,[status(thm)],[f1149]) ).
fof(f1165,plain,
( sQ80_spl
| ~ sQ6_spl
| ~ sQ63_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1151,f866]) ).
fof(f1166,plain,
( sQ80_spl
| ~ sQ6_spl
| ~ sQ63_spl ),
inference(contradiction_clause,[status(thm)],[f1165]) ).
fof(f1167,plain,
( sQ9_spl
| ~ leq(sK30_skl,pred(n6))
| ~ leq(sK29_skl,pv57)
| ~ leq(n0,sK30_skl)
| ~ leq(n0,sK29_skl) ),
inference(resolution,[status(thm)],[f430,f452]) ).
fof(f1171,definition,
( sQ84_spl
<=> leq(sK29_skl,pv57) ),
introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition]) ).
fof(f1173,plain,
( sQ84_spl
| ~ leq(sK29_skl,pv57) ),
inference(component_clause,[status(thm)],[f1171]) ).
fof(f1174,plain,
( sQ9_spl
| ~ sQ59_spl
| ~ sQ84_spl
| ~ sQ7_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1167,f412,f420,f1171,f828,f428]) ).
fof(f1178,plain,
( sQ84_spl
| ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1173,f693]) ).
fof(f1179,plain,
( sQ84_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f1178]) ).
fof(f1183,plain,
( ~ sQ3_spl
| sQ69_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f407,f1059]) ).
fof(f1184,plain,
( ~ sQ3_spl
| sQ69_spl ),
inference(contradiction_clause,[status(thm)],[f1183]) ).
fof(f1191,plain,
( sQ7_spl
| ~ gt(succ(sK30_skl),n0) ),
inference(resolution,[status(thm)],[f422,f135]) ).
fof(f1243,plain,
( sQ7_spl
| n0 = succ(sK30_skl)
| ~ leq(n0,succ(sK30_skl)) ),
inference(resolution,[status(thm)],[f1191,f124]) ).
fof(f1244,plain,
( sQ7_spl
| succ(sK30_skl) = n0
| gt(n0,succ(sK30_skl)) ),
inference(resolution,[status(thm)],[f1191,f104]) ).
fof(f1248,definition,
( sQ86_spl
<=> leq(n0,succ(sK30_skl)) ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f1251,definition,
( sQ87_spl
<=> n0 = succ(sK30_skl) ),
introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition]) ).
fof(f1252,plain,
( ~ sQ87_spl
| n0 = succ(sK30_skl) ),
inference(component_clause,[status(thm)],[f1251]) ).
fof(f1254,plain,
( sQ7_spl
| sQ87_spl
| ~ sQ86_spl ),
inference(split_clause,[status(thm)],[f1243,f1248,f1251,f420]) ).
fof(f1255,definition,
( sQ88_spl
<=> gt(n0,succ(sK30_skl)) ),
introduced(definition,[new_symbols(definition,[sQ88_spl])],[split_symbol_definition]) ).
fof(f1256,plain,
( ~ sQ88_spl
| gt(n0,succ(sK30_skl)) ),
inference(component_clause,[status(thm)],[f1255]) ).
fof(f1258,plain,
( sQ7_spl
| sQ87_spl
| sQ88_spl ),
inference(split_clause,[status(thm)],[f1244,f1255,f1251,f420]) ).
fof(f1262,plain,
( ~ sQ88_spl
| ~ sQ87_spl
| gt(n0,n0) ),
inference(forward_demodulation,[status(thm)],[f1252,f1256]) ).
fof(f1263,plain,
( ~ sQ88_spl
| ~ sQ87_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1262,f108]) ).
fof(f1264,plain,
( ~ sQ88_spl
| ~ sQ87_spl ),
inference(contradiction_clause,[status(thm)],[f1263]) ).
fof(f1277,plain,
! [X0] :
( sQ73_spl
| ~ sP5_prd(X0,sK27_skl) ),
inference(resolution,[status(thm)],[f918,f383]) ).
fof(f1286,plain,
( ~ sQ4_spl
| sQ73_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f410,f1277]) ).
fof(f1287,plain,
( ~ sQ4_spl
| sQ73_spl ),
inference(contradiction_clause,[status(thm)],[f1286]) ).
fof(f1288,plain,
$false,
inference(sat_refutation,[status(thm)],[f415,f419,f423,f427,f431,f579,f581,f689,f838,f840,f861,f870,f896,f912,f928,f943,f945,f999,f1040,f1074,f1076,f1078,f1118,f1120,f1122,f1139,f1141,f1166,f1174,f1179,f1184,f1254,f1258,f1264,f1287]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV112+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.44 % Computer : n008.cluster.edu
% 0.16/0.44 % Model : x86_64 x86_64
% 0.16/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.44 % Memory : 8046.5625MB
% 0.16/0.44 % OS : Linux 6.8.0-71-generic
% 0.16/0.44 % CPULimit : 300
% 0.16/0.44 % WCLimit : 300
% 0.16/0.44 % DateTime : Mon Sep 21 08:32:27 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.48 % Drodi V4.1.1
% 0.16/0.70 % Refutation found
% 0.16/0.70 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.70 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.74 % Elapsed time: 0.289243 seconds
% 0.16/0.74 % CPU time: 1.648660 seconds
% 0.16/0.74 % Total memory used: 124.386 MB
% 0.16/0.74 % Net memory used: 122.611 MB
%------------------------------------------------------------------------------