%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV117+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 : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:46:41 PM UTC 2026
% Result : Theorem 0.17s 0.76s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 55
% Syntax : Number of formulae : 251 ( 17 unt; 46 def)
% Number of atoms : 905 ( 87 equ)
% Maximal formula atoms : 44 ( 3 avg)
% Number of connectives : 1049 ( 395 ~; 435 |; 149 &)
% ( 46 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 50 ( 48 usr; 44 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 18 con; 0-3 aty)
% Number of variables : 237 ( 221 !; 16 ?)
% 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(f5,axiom,
! [X,Y,Z] :
( ( leq(Y,Z)
& leq(X,Y) )
=> leq(X,Z) ),
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(f30,axiom,
! [X] : plus(n1,X) = succ(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(f40,axiom,
! [X] : pred(succ(X)) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f53,conjecture,
( ( ! [G] :
( ( leq(G,minus(plus(n1,minus(n6,n1)),n1))
& leq(n0,G) )
=> ! [H] :
( ( leq(H,minus(n6,n1))
& leq(n0,H) )
=> 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(pv5,minus(n999,n1))
& leq(n0,pv5) )
=> ( ! [O] :
( ( leq(O,minus(n6,n1))
& leq(n0,O) )
=> ! [P] :
( ( leq(P,minus(n6,n1))
& leq(n0,P) )
=> a_select3(id_ds1_filter,O,P) = a_select3(id_ds1_filter,P,O) ) )
& ! [M,N] :
( ( leq(N,minus(n6,n1))
& leq(M,minus(n6,n1))
& leq(n0,N)
& leq(n0,M) )
=> a_select3(pminus_ds1_filter,M,N) = a_select3(pminus_ds1_filter,N,M) )
& ! [K,L] :
( ( leq(L,minus(n3,n1))
& leq(K,minus(n3,n1))
& leq(n0,L)
& leq(n0,K) )
=> a_select3(r_ds1_filter,K,L) = a_select3(r_ds1_filter,L,K) )
& ! [I,J] :
( ( leq(J,minus(n6,n1))
& leq(I,minus(n6,n1))
& leq(n0,J)
& leq(n0,I) )
=> a_select3(q_ds1_filter,I,J) = a_select3(q_ds1_filter,J,I) )
& leq(pv5,minus(n999,n1))
& leq(n0,pv5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f54,negated_conjecture,
~ ( ( ! [G] :
( ( leq(G,minus(plus(n1,minus(n6,n1)),n1))
& leq(n0,G) )
=> ! [H] :
( ( leq(H,minus(n6,n1))
& leq(n0,H) )
=> 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(pv5,minus(n999,n1))
& leq(n0,pv5) )
=> ( ! [O] :
( ( leq(O,minus(n6,n1))
& leq(n0,O) )
=> ! [P] :
( ( leq(P,minus(n6,n1))
& leq(n0,P) )
=> a_select3(id_ds1_filter,O,P) = a_select3(id_ds1_filter,P,O) ) )
& ! [M,N] :
( ( leq(N,minus(n6,n1))
& leq(M,minus(n6,n1))
& leq(n0,N)
& leq(n0,M) )
=> a_select3(pminus_ds1_filter,M,N) = a_select3(pminus_ds1_filter,N,M) )
& ! [K,L] :
( ( leq(L,minus(n3,n1))
& leq(K,minus(n3,n1))
& leq(n0,L)
& leq(n0,K) )
=> a_select3(r_ds1_filter,K,L) = a_select3(r_ds1_filter,L,K) )
& ! [I,J] :
( ( leq(J,minus(n6,n1))
& leq(I,minus(n6,n1))
& leq(n0,J)
& leq(n0,I) )
=> a_select3(q_ds1_filter,I,J) = a_select3(q_ds1_filter,J,I) )
& 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(f110,plain,
! [X,Y,Z] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f111,plain,
! [X,Z] :
( leq(X,Z)
| ! [Y] :
( ~ leq(Y,Z)
| ~ leq(X,Y) ) ),
inference(miniscoping,[status(thm)],[f110]) ).
fof(f112,plain,
! [X0,X1,X2] :
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f111]) ).
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(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,
( ( ? [O] :
( ? [P] :
( a_select3(id_ds1_filter,O,P) != a_select3(id_ds1_filter,P,O)
& leq(P,minus(n6,n1))
& leq(n0,P) )
& leq(O,minus(n6,n1))
& leq(n0,O) )
| ? [M,N] :
( a_select3(pminus_ds1_filter,M,N) != a_select3(pminus_ds1_filter,N,M)
& leq(N,minus(n6,n1))
& leq(M,minus(n6,n1))
& leq(n0,N)
& leq(n0,M) )
| ? [K,L] :
( a_select3(r_ds1_filter,K,L) != a_select3(r_ds1_filter,L,K)
& leq(L,minus(n3,n1))
& leq(K,minus(n3,n1))
& leq(n0,L)
& leq(n0,K) )
| ? [I,J] :
( a_select3(q_ds1_filter,I,J) != a_select3(q_ds1_filter,J,I)
& leq(J,minus(n6,n1))
& leq(I,minus(n6,n1))
& leq(n0,J)
& leq(n0,I) )
| ~ leq(pv5,minus(n999,n1))
| ~ leq(n0,pv5) )
& ! [G] :
( ! [H] :
( a_select3(id_ds1_filter,G,H) = a_select3(id_ds1_filter,H,G)
| ~ leq(H,minus(n6,n1))
| ~ leq(n0,H) )
| ~ leq(G,minus(plus(n1,minus(n6,n1)),n1))
| ~ 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,
! [I,J] :
( sP3_prd(J,I)
<=> ( a_select3(q_ds1_filter,I,J) != a_select3(q_ds1_filter,J,I)
& leq(J,minus(n6,n1))
& leq(I,minus(n6,n1))
& leq(n0,J)
& leq(n0,I) ) ),
introduced(definition,[new_symbols(definition,[sP3_prd])],[]) ).
fof(f263,definition,
! [K,L] :
( sP4_prd(L,K)
<=> ( a_select3(r_ds1_filter,K,L) != a_select3(r_ds1_filter,L,K)
& leq(L,minus(n3,n1))
& leq(K,minus(n3,n1))
& leq(n0,L)
& leq(n0,K) ) ),
introduced(definition,[new_symbols(definition,[sP4_prd])],[]) ).
fof(f264,definition,
! [M,N] :
( sP5_prd(N,M)
<=> ( a_select3(pminus_ds1_filter,M,N) != a_select3(pminus_ds1_filter,N,M)
& leq(N,minus(n6,n1))
& leq(M,minus(n6,n1))
& leq(n0,N)
& leq(n0,M) ) ),
introduced(definition,[new_symbols(definition,[sP5_prd])],[]) ).
fof(f265,plain,
( ( ? [O] :
( ? [P] :
( a_select3(id_ds1_filter,O,P) != a_select3(id_ds1_filter,P,O)
& leq(P,minus(n6,n1))
& leq(n0,P) )
& leq(O,minus(n6,n1))
& leq(n0,O) )
| ? [M,N] : sP5_prd(N,M)
| ? [K,L] : sP4_prd(L,K)
| ? [I,J] : sP3_prd(J,I)
| ~ leq(pv5,minus(n999,n1))
| ~ leq(n0,pv5) )
& ! [G] :
( ! [H] :
( a_select3(id_ds1_filter,G,H) = a_select3(id_ds1_filter,H,G)
| ~ leq(H,minus(n6,n1))
| ~ leq(n0,H) )
| ~ leq(G,minus(plus(n1,minus(n6,n1)),n1))
| ~ 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,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(n6,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) )
& ! [G] :
( ! [H] :
( a_select3(id_ds1_filter,G,H) = a_select3(id_ds1_filter,H,G)
| ~ leq(H,minus(n6,n1))
| ~ leq(n0,H) )
| ~ leq(G,minus(plus(n1,minus(n6,n1)),n1))
| ~ 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]),skolemize(I,sK23_skl),skolemize(J,sK24_skl),skolemize(K,sK25_skl),skolemize(L,sK26_skl),skolemize(M,sK27_skl),skolemize(N,sK28_skl),skolemize(O,sK29_skl),skolemize(P,sK30_skl)],[f265]) ).
fof(f267,plain,
leq(n0,pv5),
inference(cnf_transformation,[status(thm)],[f266]) ).
fof(f268,plain,
leq(pv5,minus(n999,n1)),
inference(cnf_transformation,[status(thm)],[f266]) ).
fof(f269,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(f270,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(f271,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(f272,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(plus(n1,minus(n6,n1)),n1))
| ~ leq(n0,X0) ),
inference(cnf_transformation,[status(thm)],[f266]) ).
fof(f273,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(f274,plain,
( leq(sK29_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(f275,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(f276,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(f277,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(f362,plain,
! [I,J] :
( ( a_select3(q_ds1_filter,I,J) = a_select3(q_ds1_filter,J,I)
| ~ leq(J,minus(n6,n1))
| ~ leq(I,minus(n6,n1))
| ~ leq(n0,J)
| ~ leq(n0,I)
| sP3_prd(J,I) )
& ( ( a_select3(q_ds1_filter,I,J) != a_select3(q_ds1_filter,J,I)
& leq(J,minus(n6,n1))
& leq(I,minus(n6,n1))
& leq(n0,J)
& leq(n0,I) )
| ~ sP3_prd(J,I) ) ),
inference(NNF_transformation,[status(thm)],[f262]) ).
fof(f363,plain,
( ! [I,J] :
( a_select3(q_ds1_filter,I,J) = a_select3(q_ds1_filter,J,I)
| ~ leq(J,minus(n6,n1))
| ~ leq(I,minus(n6,n1))
| ~ leq(n0,J)
| ~ leq(n0,I)
| sP3_prd(J,I) )
& ! [I,J] :
( ( a_select3(q_ds1_filter,I,J) != a_select3(q_ds1_filter,J,I)
& leq(J,minus(n6,n1))
& leq(I,minus(n6,n1))
& leq(n0,J)
& leq(n0,I) )
| ~ sP3_prd(J,I) ) ),
inference(miniscoping,[status(thm)],[f362]) ).
fof(f364,plain,
! [X0,X1] :
( leq(n0,X1)
| ~ sP3_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f363]) ).
fof(f365,plain,
! [X0,X1] :
( leq(n0,X0)
| ~ sP3_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f363]) ).
fof(f366,plain,
! [X0,X1] :
( leq(X1,minus(n6,n1))
| ~ sP3_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f363]) ).
fof(f367,plain,
! [X0,X1] :
( leq(X0,minus(n6,n1))
| ~ sP3_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f363]) ).
fof(f368,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)],[f363]) ).
fof(f370,plain,
! [K,L] :
( ( a_select3(r_ds1_filter,K,L) = a_select3(r_ds1_filter,L,K)
| ~ leq(L,minus(n3,n1))
| ~ leq(K,minus(n3,n1))
| ~ leq(n0,L)
| ~ leq(n0,K)
| sP4_prd(L,K) )
& ( ( a_select3(r_ds1_filter,K,L) != a_select3(r_ds1_filter,L,K)
& leq(L,minus(n3,n1))
& leq(K,minus(n3,n1))
& leq(n0,L)
& leq(n0,K) )
| ~ sP4_prd(L,K) ) ),
inference(NNF_transformation,[status(thm)],[f263]) ).
fof(f371,plain,
( ! [K,L] :
( a_select3(r_ds1_filter,K,L) = a_select3(r_ds1_filter,L,K)
| ~ leq(L,minus(n3,n1))
| ~ leq(K,minus(n3,n1))
| ~ leq(n0,L)
| ~ leq(n0,K)
| sP4_prd(L,K) )
& ! [K,L] :
( ( a_select3(r_ds1_filter,K,L) != a_select3(r_ds1_filter,L,K)
& leq(L,minus(n3,n1))
& leq(K,minus(n3,n1))
& leq(n0,L)
& leq(n0,K) )
| ~ sP4_prd(L,K) ) ),
inference(miniscoping,[status(thm)],[f370]) ).
fof(f372,plain,
! [X0,X1] :
( leq(n0,X1)
| ~ sP4_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f373,plain,
! [X0,X1] :
( leq(n0,X0)
| ~ sP4_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f374,plain,
! [X0,X1] :
( leq(X1,minus(n3,n1))
| ~ sP4_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f375,plain,
! [X0,X1] :
( leq(X0,minus(n3,n1))
| ~ sP4_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f376,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)],[f371]) ).
fof(f378,plain,
! [M,N] :
( ( a_select3(pminus_ds1_filter,M,N) = a_select3(pminus_ds1_filter,N,M)
| ~ leq(N,minus(n6,n1))
| ~ leq(M,minus(n6,n1))
| ~ leq(n0,N)
| ~ leq(n0,M)
| sP5_prd(N,M) )
& ( ( a_select3(pminus_ds1_filter,M,N) != a_select3(pminus_ds1_filter,N,M)
& leq(N,minus(n6,n1))
& leq(M,minus(n6,n1))
& leq(n0,N)
& leq(n0,M) )
| ~ sP5_prd(N,M) ) ),
inference(NNF_transformation,[status(thm)],[f264]) ).
fof(f379,plain,
( ! [M,N] :
( a_select3(pminus_ds1_filter,M,N) = a_select3(pminus_ds1_filter,N,M)
| ~ leq(N,minus(n6,n1))
| ~ leq(M,minus(n6,n1))
| ~ leq(n0,N)
| ~ leq(n0,M)
| sP5_prd(N,M) )
& ! [M,N] :
( ( a_select3(pminus_ds1_filter,M,N) != a_select3(pminus_ds1_filter,N,M)
& leq(N,minus(n6,n1))
& leq(M,minus(n6,n1))
& leq(n0,N)
& leq(n0,M) )
| ~ sP5_prd(N,M) ) ),
inference(miniscoping,[status(thm)],[f378]) ).
fof(f380,plain,
! [X0,X1] :
( leq(n0,X1)
| ~ sP5_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f379]) ).
fof(f381,plain,
! [X0,X1] :
( leq(n0,X0)
| ~ sP5_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f379]) ).
fof(f382,plain,
! [X0,X1] :
( leq(X1,minus(n6,n1))
| ~ sP5_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f379]) ).
fof(f383,plain,
! [X0,X1] :
( leq(X0,minus(n6,n1))
| ~ sP5_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f379]) ).
fof(f384,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)],[f379]) ).
fof(f394,definition,
( sQ0_spl
<=> leq(n0,pv5) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f396,plain,
( sQ0_spl
| ~ leq(n0,pv5) ),
inference(component_clause,[status(thm)],[f394]) ).
fof(f397,definition,
( sQ1_spl
<=> leq(pv5,minus(n999,n1)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f399,plain,
( sQ1_spl
| ~ leq(pv5,minus(n999,n1)) ),
inference(component_clause,[status(thm)],[f397]) ).
fof(f400,definition,
( sQ2_spl
<=> sP3_prd(sK24_skl,sK23_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f401,plain,
( ~ sQ2_spl
| sP3_prd(sK24_skl,sK23_skl) ),
inference(component_clause,[status(thm)],[f400]) ).
fof(f403,definition,
( sQ3_spl
<=> sP4_prd(sK26_skl,sK25_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f404,plain,
( ~ sQ3_spl
| sP4_prd(sK26_skl,sK25_skl) ),
inference(component_clause,[status(thm)],[f403]) ).
fof(f406,definition,
( sQ4_spl
<=> sP5_prd(sK28_skl,sK27_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f407,plain,
( ~ sQ4_spl
| sP5_prd(sK28_skl,sK27_skl) ),
inference(component_clause,[status(thm)],[f406]) ).
fof(f409,definition,
( sQ5_spl
<=> leq(n0,sK29_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f411,plain,
( sQ5_spl
| ~ leq(n0,sK29_skl) ),
inference(component_clause,[status(thm)],[f409]) ).
fof(f412,plain,
( sQ5_spl
| sQ4_spl
| sQ3_spl
| sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f273,f394,f397,f400,f403,f406,f409]) ).
fof(f413,definition,
( sQ6_spl
<=> leq(sK29_skl,minus(n6,n1)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f414,plain,
( ~ sQ6_spl
| leq(sK29_skl,minus(n6,n1)) ),
inference(component_clause,[status(thm)],[f413]) ).
fof(f416,plain,
( sQ6_spl
| sQ4_spl
| sQ3_spl
| sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f274,f394,f397,f400,f403,f406,f413]) ).
fof(f417,definition,
( sQ7_spl
<=> leq(n0,sK30_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f420,plain,
( sQ7_spl
| sQ4_spl
| sQ3_spl
| sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f275,f394,f397,f400,f403,f406,f417]) ).
fof(f421,definition,
( sQ8_spl
<=> leq(sK30_skl,minus(n6,n1)) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f422,plain,
( ~ sQ8_spl
| leq(sK30_skl,minus(n6,n1)) ),
inference(component_clause,[status(thm)],[f421]) ).
fof(f424,plain,
( sQ8_spl
| sQ4_spl
| sQ3_spl
| sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f276,f394,f397,f400,f403,f406,f421]) ).
fof(f425,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(f427,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)],[f425]) ).
fof(f428,plain,
( ~ sQ9_spl
| sQ4_spl
| sQ3_spl
| sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f277,f394,f397,f400,f403,f406,f425]) ).
fof(f441,plain,
leq(pv5,pred(n999)),
inference(forward_demodulation,[status(thm)],[f227,f268]) ).
fof(f442,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,f269]) ).
fof(f443,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,f442]) ).
fof(f444,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,f270]) ).
fof(f445,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,f444]) ).
fof(f446,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,f271]) ).
fof(f447,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,f446]) ).
fof(f448,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(plus(n1,minus(n6,n1))))
| ~ leq(n0,X0) ),
inference(forward_demodulation,[status(thm)],[f227,f272]) ).
fof(f449,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(succ(minus(n6,n1))))
| ~ leq(n0,X0) ),
inference(forward_demodulation,[status(thm)],[f218,f448]) ).
fof(f450,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(forward_demodulation,[status(thm)],[f228,f449]) ).
fof(f451,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,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(n0,X1)
| ~ leq(X0,pred(n6))
| ~ leq(n0,X0) ),
inference(forward_demodulation,[status(thm)],[f227,f451]) ).
fof(f464,plain,
! [X0,X1] :
( leq(X1,pred(n6))
| ~ sP3_prd(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f227,f366]) ).
fof(f465,plain,
! [X0,X1] :
( leq(X0,pred(n6))
| ~ sP3_prd(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f227,f367]) ).
fof(f468,plain,
! [X0,X1] :
( leq(X1,pred(n3))
| ~ sP4_prd(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f227,f374]) ).
fof(f469,plain,
! [X0,X1] :
( leq(X0,pred(n3))
| ~ sP4_prd(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f227,f375]) ).
fof(f472,plain,
! [X0,X1] :
( leq(X1,pred(n6))
| ~ sP5_prd(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f227,f382]) ).
fof(f473,plain,
! [X0,X1] :
( leq(X0,pred(n6))
| ~ sP5_prd(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f227,f383]) ).
fof(f575,plain,
( sQ1_spl
| ~ leq(pv5,pred(n999)) ),
inference(forward_demodulation,[status(thm)],[f227,f399]) ).
fof(f576,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f575,f441]) ).
fof(f577,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f576]) ).
fof(f578,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f396,f267]) ).
fof(f579,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f578]) ).
fof(f661,definition,
( sQ39_spl
<=> leq(n0,n0) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f663,plain,
( sQ39_spl
| ~ leq(n0,n0) ),
inference(component_clause,[status(thm)],[f661]) ).
fof(f686,plain,
( sQ39_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f663,f109]) ).
fof(f687,plain,
sQ39_spl,
inference(contradiction_clause,[status(thm)],[f686]) ).
fof(f688,plain,
( ~ sQ8_spl
| leq(sK30_skl,pred(n6)) ),
inference(forward_demodulation,[status(thm)],[f227,f422]) ).
fof(f689,plain,
( ~ sQ6_spl
| leq(sK29_skl,pred(n6)) ),
inference(forward_demodulation,[status(thm)],[f227,f414]) ).
fof(f803,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)],[f368,f401]) ).
fof(f804,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)],[f376,f404]) ).
fof(f805,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)],[f384,f407]) ).
fof(f818,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)],[f443,f803]) ).
fof(f820,definition,
( sQ58_spl
<=> leq(n0,sK23_skl) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f822,plain,
( sQ58_spl
| ~ leq(n0,sK23_skl) ),
inference(component_clause,[status(thm)],[f820]) ).
fof(f823,definition,
( sQ59_spl
<=> leq(n0,sK24_skl) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f825,plain,
( sQ59_spl
| ~ leq(n0,sK24_skl) ),
inference(component_clause,[status(thm)],[f823]) ).
fof(f826,definition,
( sQ60_spl
<=> leq(sK23_skl,pred(n6)) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f828,plain,
( sQ60_spl
| ~ leq(sK23_skl,pred(n6)) ),
inference(component_clause,[status(thm)],[f826]) ).
fof(f829,definition,
( sQ61_spl
<=> leq(sK24_skl,pred(n6)) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f831,plain,
( sQ61_spl
| ~ leq(sK24_skl,pred(n6)) ),
inference(component_clause,[status(thm)],[f829]) ).
fof(f832,plain,
( ~ sQ2_spl
| ~ sQ61_spl
| ~ sQ60_spl
| ~ sQ59_spl
| ~ sQ58_spl ),
inference(split_clause,[status(thm)],[f818,f820,f823,f826,f829,f400]) ).
fof(f834,plain,
( sQ9_spl
| ~ leq(sK30_skl,pred(n6))
| ~ leq(n0,sK30_skl)
| ~ leq(sK29_skl,pred(n6))
| ~ leq(n0,sK29_skl) ),
inference(resolution,[status(thm)],[f452,f427]) ).
fof(f836,definition,
( sQ62_spl
<=> leq(sK29_skl,pred(n6)) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f838,plain,
( sQ62_spl
| ~ leq(sK29_skl,pred(n6)) ),
inference(component_clause,[status(thm)],[f836]) ).
fof(f839,definition,
( sQ63_spl
<=> leq(sK30_skl,pred(n6)) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f841,plain,
( sQ63_spl
| ~ leq(sK30_skl,pred(n6)) ),
inference(component_clause,[status(thm)],[f839]) ).
fof(f842,plain,
( sQ9_spl
| ~ sQ63_spl
| ~ sQ7_spl
| ~ sQ62_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f834,f409,f836,f417,f839,f425]) ).
fof(f844,plain,
( sQ63_spl
| ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f841,f688]) ).
fof(f845,plain,
( sQ63_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f844]) ).
fof(f846,plain,
( sQ62_spl
| ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f838,f689]) ).
fof(f847,plain,
( sQ62_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f846]) ).
fof(f866,plain,
! [X0] :
( sQ59_spl
| ~ sP3_prd(sK24_skl,X0) ),
inference(resolution,[status(thm)],[f825,f365]) ).
fof(f871,plain,
( ~ sQ2_spl
| sQ59_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f401,f866]) ).
fof(f872,plain,
( ~ sQ2_spl
| sQ59_spl ),
inference(contradiction_clause,[status(thm)],[f871]) ).
fof(f878,plain,
! [X0] :
( sQ58_spl
| ~ sP3_prd(X0,sK23_skl) ),
inference(resolution,[status(thm)],[f822,f364]) ).
fof(f879,plain,
( sQ58_spl
| ~ gt(sK23_skl,n0) ),
inference(resolution,[status(thm)],[f822,f122]) ).
fof(f890,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)],[f804,f445]) ).
fof(f892,definition,
( sQ64_spl
<=> leq(n0,sK25_skl) ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f894,plain,
( sQ64_spl
| ~ leq(n0,sK25_skl) ),
inference(component_clause,[status(thm)],[f892]) ).
fof(f895,definition,
( sQ65_spl
<=> leq(n0,sK26_skl) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f897,plain,
( sQ65_spl
| ~ leq(n0,sK26_skl) ),
inference(component_clause,[status(thm)],[f895]) ).
fof(f898,definition,
( sQ66_spl
<=> leq(sK25_skl,pred(n3)) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f900,plain,
( sQ66_spl
| ~ leq(sK25_skl,pred(n3)) ),
inference(component_clause,[status(thm)],[f898]) ).
fof(f901,definition,
( sQ67_spl
<=> leq(sK26_skl,pred(n3)) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f903,plain,
( sQ67_spl
| ~ leq(sK26_skl,pred(n3)) ),
inference(component_clause,[status(thm)],[f901]) ).
fof(f904,plain,
( ~ sQ3_spl
| ~ sQ67_spl
| ~ sQ66_spl
| ~ sQ65_spl
| ~ sQ64_spl ),
inference(split_clause,[status(thm)],[f890,f892,f895,f898,f901,f403]) ).
fof(f906,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)],[f805,f447]) ).
fof(f908,definition,
( sQ68_spl
<=> leq(n0,sK27_skl) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f910,plain,
( sQ68_spl
| ~ leq(n0,sK27_skl) ),
inference(component_clause,[status(thm)],[f908]) ).
fof(f911,definition,
( sQ69_spl
<=> leq(n0,sK28_skl) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f913,plain,
( sQ69_spl
| ~ leq(n0,sK28_skl) ),
inference(component_clause,[status(thm)],[f911]) ).
fof(f914,definition,
( sQ70_spl
<=> leq(sK27_skl,pred(n6)) ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f916,plain,
( sQ70_spl
| ~ leq(sK27_skl,pred(n6)) ),
inference(component_clause,[status(thm)],[f914]) ).
fof(f917,definition,
( sQ71_spl
<=> leq(sK28_skl,pred(n6)) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f919,plain,
( sQ71_spl
| ~ leq(sK28_skl,pred(n6)) ),
inference(component_clause,[status(thm)],[f917]) ).
fof(f920,plain,
( ~ sQ4_spl
| ~ sQ71_spl
| ~ sQ70_spl
| ~ sQ69_spl
| ~ sQ68_spl ),
inference(split_clause,[status(thm)],[f906,f908,f911,f914,f917,f406]) ).
fof(f954,plain,
( sQ58_spl
| sK23_skl = n0
| gt(n0,sK23_skl) ),
inference(resolution,[status(thm)],[f879,f104]) ).
fof(f957,definition,
( sQ75_spl
<=> n0 = sK23_skl ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f958,plain,
( ~ sQ75_spl
| n0 = sK23_skl ),
inference(component_clause,[status(thm)],[f957]) ).
fof(f961,definition,
( sQ76_spl
<=> gt(n0,sK23_skl) ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f962,plain,
( ~ sQ76_spl
| gt(n0,sK23_skl) ),
inference(component_clause,[status(thm)],[f961]) ).
fof(f964,plain,
( sQ58_spl
| sQ75_spl
| sQ76_spl ),
inference(split_clause,[status(thm)],[f954,f961,f957,f820]) ).
fof(f966,plain,
( ~ sQ76_spl
| ~ sQ75_spl
| gt(n0,n0) ),
inference(forward_demodulation,[status(thm)],[f958,f962]) ).
fof(f967,plain,
( ~ sQ76_spl
| ~ sQ75_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f966,f108]) ).
fof(f968,plain,
( ~ sQ76_spl
| ~ sQ75_spl ),
inference(contradiction_clause,[status(thm)],[f967]) ).
fof(f1001,plain,
! [X0] :
( sQ65_spl
| ~ sP4_prd(sK26_skl,X0) ),
inference(resolution,[status(thm)],[f897,f373]) ).
fof(f1008,plain,
( ~ sQ3_spl
| sQ65_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f404,f1001]) ).
fof(f1009,plain,
( ~ sQ3_spl
| sQ65_spl ),
inference(contradiction_clause,[status(thm)],[f1008]) ).
fof(f1013,plain,
! [X0] :
( sQ64_spl
| ~ sP4_prd(X0,sK25_skl) ),
inference(resolution,[status(thm)],[f894,f372]) ).
fof(f1036,plain,
( sQ5_spl
| ~ gt(sK29_skl,n0) ),
inference(resolution,[status(thm)],[f411,f122]) ).
fof(f1038,plain,
! [X0] :
( sQ5_spl
| ~ leq(X0,sK29_skl)
| ~ leq(n0,X0) ),
inference(resolution,[status(thm)],[f411,f112]) ).
fof(f1041,plain,
( sQ5_spl
| sK29_skl = n0
| gt(n0,sK29_skl) ),
inference(resolution,[status(thm)],[f1036,f104]) ).
fof(f1044,definition,
( sQ81_spl
<=> n0 = sK29_skl ),
introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition]) ).
fof(f1045,plain,
( ~ sQ81_spl
| n0 = sK29_skl ),
inference(component_clause,[status(thm)],[f1044]) ).
fof(f1048,definition,
( sQ82_spl
<=> gt(n0,sK29_skl) ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f1049,plain,
( ~ sQ82_spl
| gt(n0,sK29_skl) ),
inference(component_clause,[status(thm)],[f1048]) ).
fof(f1051,plain,
( sQ5_spl
| sQ81_spl
| sQ82_spl ),
inference(split_clause,[status(thm)],[f1041,f1048,f1044,f409]) ).
fof(f1056,plain,
( ~ sQ82_spl
| ~ sQ81_spl
| gt(n0,n0) ),
inference(forward_demodulation,[status(thm)],[f1045,f1049]) ).
fof(f1057,plain,
( ~ sQ82_spl
| ~ sQ81_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1056,f108]) ).
fof(f1058,plain,
( ~ sQ82_spl
| ~ sQ81_spl ),
inference(contradiction_clause,[status(thm)],[f1057]) ).
fof(f1087,plain,
! [X0] :
( sQ69_spl
| ~ sP5_prd(sK28_skl,X0) ),
inference(resolution,[status(thm)],[f913,f381]) ).
fof(f1097,plain,
( ~ sQ4_spl
| sQ69_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f407,f1087]) ).
fof(f1098,plain,
( ~ sQ4_spl
| sQ69_spl ),
inference(contradiction_clause,[status(thm)],[f1097]) ).
fof(f1100,plain,
! [X0] :
( sQ68_spl
| ~ sP5_prd(X0,sK27_skl) ),
inference(resolution,[status(thm)],[f910,f380]) ).
fof(f1170,plain,
! [X0] :
( sQ5_spl
| ~ sP3_prd(X0,n0)
| ~ leq(pred(n6),sK29_skl) ),
inference(resolution,[status(thm)],[f1038,f464]) ).
fof(f1171,plain,
! [X0] :
( sQ5_spl
| ~ sP3_prd(n0,X0)
| ~ leq(pred(n6),sK29_skl) ),
inference(resolution,[status(thm)],[f1038,f465]) ).
fof(f1172,plain,
! [X0] :
( sQ5_spl
| ~ sP5_prd(X0,n0)
| ~ leq(pred(n6),sK29_skl) ),
inference(resolution,[status(thm)],[f1038,f472]) ).
fof(f1173,plain,
! [X0] :
( sQ5_spl
| ~ sP5_prd(n0,X0)
| ~ leq(pred(n6),sK29_skl) ),
inference(resolution,[status(thm)],[f1038,f473]) ).
fof(f1174,plain,
! [X0] :
( sQ5_spl
| ~ sP4_prd(n0,X0)
| ~ leq(pred(n3),sK29_skl) ),
inference(resolution,[status(thm)],[f1038,f469]) ).
fof(f1175,plain,
! [X0] :
( sQ5_spl
| ~ sP4_prd(X0,n0)
| ~ leq(pred(n3),sK29_skl) ),
inference(resolution,[status(thm)],[f1038,f468]) ).
fof(f1195,plain,
! [X0] :
( sQ5_spl
| ~ sP5_prd(sK29_skl,X0)
| ~ leq(n0,n0) ),
inference(resolution,[status(thm)],[f1038,f381]) ).
fof(f1196,plain,
! [X0] :
( sQ5_spl
| ~ sP5_prd(X0,sK29_skl)
| ~ leq(n0,n0) ),
inference(resolution,[status(thm)],[f1038,f380]) ).
fof(f1197,plain,
! [X0] :
( sQ5_spl
| ~ sP4_prd(sK29_skl,X0)
| ~ leq(n0,n0) ),
inference(resolution,[status(thm)],[f1038,f373]) ).
fof(f1198,plain,
! [X0] :
( sQ5_spl
| ~ sP4_prd(X0,sK29_skl)
| ~ leq(n0,n0) ),
inference(resolution,[status(thm)],[f1038,f372]) ).
fof(f1199,plain,
! [X0] :
( sQ5_spl
| ~ sP3_prd(sK29_skl,X0)
| ~ leq(n0,n0) ),
inference(resolution,[status(thm)],[f1038,f365]) ).
fof(f1200,plain,
! [X0] :
( sQ5_spl
| ~ sP3_prd(X0,sK29_skl)
| ~ leq(n0,n0) ),
inference(resolution,[status(thm)],[f1038,f364]) ).
fof(f1206,definition,
( sQ85_spl
<=> leq(pred(n6),sK29_skl) ),
introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition]) ).
fof(f1209,definition,
! [X0] :
( sQ86_spl
<=> ~ sP3_prd(X0,n0) ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f1212,plain,
( sQ5_spl
| sQ86_spl
| ~ sQ85_spl ),
inference(split_clause,[status(thm)],[f1170,f1206,f1209,f409]) ).
fof(f1213,definition,
! [X0] :
( sQ87_spl
<=> ~ sP3_prd(n0,X0) ),
introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition]) ).
fof(f1216,plain,
( sQ5_spl
| sQ87_spl
| ~ sQ85_spl ),
inference(split_clause,[status(thm)],[f1171,f1206,f1213,f409]) ).
fof(f1217,definition,
! [X0] :
( sQ88_spl
<=> ~ sP5_prd(X0,n0) ),
introduced(definition,[new_symbols(definition,[sQ88_spl])],[split_symbol_definition]) ).
fof(f1220,plain,
( sQ5_spl
| sQ88_spl
| ~ sQ85_spl ),
inference(split_clause,[status(thm)],[f1172,f1206,f1217,f409]) ).
fof(f1221,definition,
! [X0] :
( sQ89_spl
<=> ~ sP5_prd(n0,X0) ),
introduced(definition,[new_symbols(definition,[sQ89_spl])],[split_symbol_definition]) ).
fof(f1224,plain,
( sQ5_spl
| sQ89_spl
| ~ sQ85_spl ),
inference(split_clause,[status(thm)],[f1173,f1206,f1221,f409]) ).
fof(f1225,definition,
( sQ90_spl
<=> leq(pred(n3),sK29_skl) ),
introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition]) ).
fof(f1228,definition,
! [X0] :
( sQ91_spl
<=> ~ sP4_prd(n0,X0) ),
introduced(definition,[new_symbols(definition,[sQ91_spl])],[split_symbol_definition]) ).
fof(f1231,plain,
( sQ5_spl
| sQ91_spl
| ~ sQ90_spl ),
inference(split_clause,[status(thm)],[f1174,f1225,f1228,f409]) ).
fof(f1232,definition,
! [X0] :
( sQ92_spl
<=> ~ sP4_prd(X0,n0) ),
introduced(definition,[new_symbols(definition,[sQ92_spl])],[split_symbol_definition]) ).
fof(f1235,plain,
( sQ5_spl
| sQ92_spl
| ~ sQ90_spl ),
inference(split_clause,[status(thm)],[f1175,f1225,f1232,f409]) ).
fof(f1237,definition,
! [X0] :
( sQ93_spl
<=> ~ sP5_prd(sK29_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ93_spl])],[split_symbol_definition]) ).
fof(f1240,plain,
( sQ5_spl
| sQ93_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f1195,f661,f1237,f409]) ).
fof(f1241,definition,
! [X0] :
( sQ94_spl
<=> ~ sP5_prd(X0,sK29_skl) ),
introduced(definition,[new_symbols(definition,[sQ94_spl])],[split_symbol_definition]) ).
fof(f1244,plain,
( sQ5_spl
| sQ94_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f1196,f661,f1241,f409]) ).
fof(f1245,definition,
! [X0] :
( sQ95_spl
<=> ~ sP4_prd(sK29_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ95_spl])],[split_symbol_definition]) ).
fof(f1248,plain,
( sQ5_spl
| sQ95_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f1197,f661,f1245,f409]) ).
fof(f1249,definition,
! [X0] :
( sQ96_spl
<=> ~ sP4_prd(X0,sK29_skl) ),
introduced(definition,[new_symbols(definition,[sQ96_spl])],[split_symbol_definition]) ).
fof(f1252,plain,
( sQ5_spl
| sQ96_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f1198,f661,f1249,f409]) ).
fof(f1253,definition,
! [X0] :
( sQ97_spl
<=> ~ sP3_prd(sK29_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ97_spl])],[split_symbol_definition]) ).
fof(f1256,plain,
( sQ5_spl
| sQ97_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f1199,f661,f1253,f409]) ).
fof(f1257,definition,
! [X0] :
( sQ98_spl
<=> ~ sP3_prd(X0,sK29_skl) ),
introduced(definition,[new_symbols(definition,[sQ98_spl])],[split_symbol_definition]) ).
fof(f1260,plain,
( sQ5_spl
| sQ98_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f1200,f661,f1257,f409]) ).
fof(f1266,plain,
! [X0] :
( sQ61_spl
| ~ sP3_prd(sK24_skl,X0) ),
inference(resolution,[status(thm)],[f831,f465]) ).
fof(f1274,plain,
( ~ sQ2_spl
| sQ61_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f401,f1266]) ).
fof(f1276,plain,
( ~ sQ2_spl
| sQ61_spl ),
inference(contradiction_clause,[status(thm)],[f1274]) ).
fof(f1277,plain,
( ~ sQ3_spl
| sQ64_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f404,f1013]) ).
fof(f1278,plain,
( ~ sQ3_spl
| sQ64_spl ),
inference(contradiction_clause,[status(thm)],[f1277]) ).
fof(f1279,plain,
( ~ sQ4_spl
| sQ68_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f407,f1100]) ).
fof(f1280,plain,
( ~ sQ4_spl
| sQ68_spl ),
inference(contradiction_clause,[status(thm)],[f1279]) ).
fof(f1286,plain,
! [X0] :
( sQ67_spl
| ~ sP4_prd(sK26_skl,X0) ),
inference(resolution,[status(thm)],[f903,f469]) ).
fof(f1295,plain,
! [X0] :
( sQ66_spl
| ~ sP4_prd(X0,sK25_skl) ),
inference(resolution,[status(thm)],[f900,f468]) ).
fof(f1305,plain,
! [X0] :
( sQ71_spl
| ~ sP5_prd(sK28_skl,X0) ),
inference(resolution,[status(thm)],[f919,f473]) ).
fof(f1314,plain,
! [X0] :
( sQ70_spl
| ~ sP5_prd(X0,sK27_skl) ),
inference(resolution,[status(thm)],[f916,f472]) ).
fof(f1322,plain,
! [X0] :
( sQ60_spl
| ~ sP3_prd(X0,sK23_skl) ),
inference(resolution,[status(thm)],[f828,f464]) ).
fof(f1331,plain,
( ~ sQ2_spl
| sQ60_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f401,f1322]) ).
fof(f1333,plain,
( ~ sQ2_spl
| sQ60_spl ),
inference(contradiction_clause,[status(thm)],[f1331]) ).
fof(f1334,plain,
( ~ sQ3_spl
| sQ67_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f404,f1286]) ).
fof(f1335,plain,
( ~ sQ3_spl
| sQ67_spl ),
inference(contradiction_clause,[status(thm)],[f1334]) ).
fof(f1336,plain,
( ~ sQ4_spl
| sQ71_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f407,f1305]) ).
fof(f1337,plain,
( ~ sQ4_spl
| sQ71_spl ),
inference(contradiction_clause,[status(thm)],[f1336]) ).
fof(f1338,plain,
( ~ sQ2_spl
| sQ58_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f401,f878]) ).
fof(f1339,plain,
( ~ sQ2_spl
| sQ58_spl ),
inference(contradiction_clause,[status(thm)],[f1338]) ).
fof(f1340,plain,
( ~ sQ3_spl
| sQ66_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f404,f1295]) ).
fof(f1341,plain,
( ~ sQ3_spl
| sQ66_spl ),
inference(contradiction_clause,[status(thm)],[f1340]) ).
fof(f1376,plain,
( ~ sQ4_spl
| sQ70_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f407,f1314]) ).
fof(f1377,plain,
( ~ sQ4_spl
| sQ70_spl ),
inference(contradiction_clause,[status(thm)],[f1376]) ).
fof(f1378,plain,
$false,
inference(sat_refutation,[status(thm)],[f412,f416,f420,f424,f428,f577,f579,f687,f832,f842,f845,f847,f872,f904,f920,f964,f968,f1009,f1051,f1058,f1098,f1212,f1216,f1220,f1224,f1231,f1235,f1240,f1244,f1248,f1252,f1256,f1260,f1276,f1278,f1280,f1333,f1335,f1337,f1339,f1341,f1377]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV117+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.39 % Computer : n020.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Mon Sep 21 08:32:18 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.41 % Drodi V4.1.1
% 0.17/0.76 % Refutation found
% 0.17/0.76 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.76 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.79 % Elapsed time: 0.380767 seconds
% 0.17/0.79 % CPU time: 2.637012 seconds
% 0.17/0.79 % Total memory used: 129.682 MB
% 0.17/0.79 % Net memory used: 127.080 MB
%------------------------------------------------------------------------------