%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV122+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 : n005.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 0.61s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 48
% Syntax : Number of formulae : 182 ( 29 unt; 33 def)
% Number of atoms : 586 ( 94 equ)
% Maximal formula atoms : 30 ( 3 avg)
% Number of connectives : 619 ( 215 ~; 234 |; 116 &)
% ( 35 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 37 ( 35 usr; 33 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 14 con; 0-3 aty)
% Number of variables : 147 ( 127 !; 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(f14,axiom,
! [X,C] :
( leq(n0,X)
=> leq(uniform_int_rnd(C,X),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
succ(tptp_minus_1) = n0,
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,
( ( ! [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) ) )
=> ( ! [K,L] :
( ( leq(L,minus(n6,n1))
& leq(K,minus(n6,n1))
& leq(n0,L)
& leq(n0,K) )
=> a_select3(pminus_ds1_filter,K,L) = a_select3(pminus_ds1_filter,L,K) )
& ! [I,J] :
( ( leq(J,minus(n3,n1))
& leq(I,minus(n3,n1))
& leq(n0,J)
& leq(n0,I) )
=> a_select3(r_ds1_filter,I,J) = a_select3(r_ds1_filter,J,I) )
& ! [G,H] :
( ( leq(H,minus(n6,n1))
& leq(G,minus(n6,n1))
& leq(n0,H)
& leq(n0,G) )
=> a_select3(q_ds1_filter,G,H) = a_select3(q_ds1_filter,H,G) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f54,negated_conjecture,
~ ( ( ! [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) ) )
=> ( ! [K,L] :
( ( leq(L,minus(n6,n1))
& leq(K,minus(n6,n1))
& leq(n0,L)
& leq(n0,K) )
=> a_select3(pminus_ds1_filter,K,L) = a_select3(pminus_ds1_filter,L,K) )
& ! [I,J] :
( ( leq(J,minus(n3,n1))
& leq(I,minus(n3,n1))
& leq(n0,J)
& leq(n0,I) )
=> a_select3(r_ds1_filter,I,J) = a_select3(r_ds1_filter,J,I) )
& ! [G,H] :
( ( leq(H,minus(n6,n1))
& leq(G,minus(n6,n1))
& leq(n0,H)
& leq(n0,G) )
=> a_select3(q_ds1_filter,G,H) = a_select3(q_ds1_filter,H,G) ) ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f61,axiom,
gt(n0,tptp_minus_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f68,axiom,
gt(n1,n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f86,axiom,
! [X] :
( ( leq(X,n0)
& leq(n0,X) )
=> X = n0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f87,axiom,
! [X] :
( ( leq(X,n1)
& leq(n0,X) )
=> ( X = n1
| X = n0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f93,axiom,
succ(n0) = n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,plain,
! [X0,X1] :
( X0 = X1
| gt(X1,X0)
| gt(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f100,plain,
! [X0] : ~ gt(X0,X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f101,plain,
! [X0] : leq(X0,X0),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f113,plain,
! [X,Y] :
( leq(X,Y)
| ~ gt(Y,X) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f114,plain,
! [X0,X1] :
( leq(X1,X0)
| ~ gt(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f115,plain,
! [X,Y] :
( gt(Y,X)
| X = Y
| ~ leq(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f116,plain,
! [X0,X1] :
( gt(X1,X0)
| X0 = X1
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f117,plain,
! [X,Y] :
( ( ~ gt(Y,X)
| leq(X,pred(Y)) )
& ( gt(Y,X)
| ~ leq(X,pred(Y)) ) ),
inference(NNF_transformation,[status(thm)],[f10]) ).
fof(f118,plain,
( ! [X,Y] :
( ~ gt(Y,X)
| leq(X,pred(Y)) )
& ! [X,Y] :
( gt(Y,X)
| ~ leq(X,pred(Y)) ) ),
inference(miniscoping,[status(thm)],[f117]) ).
fof(f119,plain,
! [X0,X1] :
( gt(X1,X0)
| ~ leq(X0,pred(X1)) ),
inference(cnf_transformation,[status(thm)],[f118]) ).
fof(f128,plain,
! [X,C] :
( leq(uniform_int_rnd(C,X),X)
| ~ leq(n0,X) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f129,plain,
! [X] :
( ! [C] : leq(uniform_int_rnd(C,X),X)
| ~ leq(n0,X) ),
inference(miniscoping,[status(thm)],[f128]) ).
fof(f130,plain,
! [X0,X1] :
( leq(uniform_int_rnd(X1,X0),X0)
| ~ leq(n0,X0) ),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f208,plain,
succ(tptp_minus_1) = n0,
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f220,plain,
! [X0] : pred(succ(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f253,plain,
( ( ? [K,L] :
( a_select3(pminus_ds1_filter,K,L) != a_select3(pminus_ds1_filter,L,K)
& leq(L,minus(n6,n1))
& leq(K,minus(n6,n1))
& leq(n0,L)
& leq(n0,K) )
| ? [I,J] :
( a_select3(r_ds1_filter,I,J) != a_select3(r_ds1_filter,J,I)
& leq(J,minus(n3,n1))
& leq(I,minus(n3,n1))
& leq(n0,J)
& leq(n0,I) )
| ? [G,H] :
( a_select3(q_ds1_filter,G,H) != a_select3(q_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) ) ),
inference(pre_NNF_transformation,[status(thm)],[f54]) ).
fof(f254,definition,
( sP3_prd
<=> ( ? [I,J] :
( a_select3(r_ds1_filter,I,J) != a_select3(r_ds1_filter,J,I)
& leq(J,minus(n3,n1))
& leq(I,minus(n3,n1))
& leq(n0,J)
& leq(n0,I) )
| ? [G,H] :
( a_select3(q_ds1_filter,G,H) != a_select3(q_ds1_filter,H,G)
& leq(H,minus(n6,n1))
& leq(G,minus(n6,n1))
& leq(n0,H)
& leq(n0,G) ) ) ),
introduced(definition,[new_symbols(definition,[sP3_prd])],[]) ).
fof(f255,plain,
( ( ? [K,L] :
( a_select3(pminus_ds1_filter,K,L) != a_select3(pminus_ds1_filter,L,K)
& leq(L,minus(n6,n1))
& leq(K,minus(n6,n1))
& leq(n0,L)
& leq(n0,K) )
| sP3_prd )
& ! [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) ) ),
inference(formula_renaming,[status(thm)],[f253,f254]) ).
fof(f256,plain,
( ( ( a_select3(pminus_ds1_filter,sK23_skl,sK24_skl) != a_select3(pminus_ds1_filter,sK24_skl,sK23_skl)
& leq(sK24_skl,minus(n6,n1))
& leq(sK23_skl,minus(n6,n1))
& leq(n0,sK24_skl)
& leq(n0,sK23_skl) )
| sP3_prd )
& ! [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) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23_skl,sK24_skl]),skolemize(K,sK23_skl),skolemize(L,sK24_skl)],[f255]) ).
fof(f257,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)],[f256]) ).
fof(f258,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)],[f256]) ).
fof(f259,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)],[f256]) ).
fof(f260,plain,
( leq(n0,sK23_skl)
| sP3_prd ),
inference(cnf_transformation,[status(thm)],[f256]) ).
fof(f261,plain,
( leq(n0,sK24_skl)
| sP3_prd ),
inference(cnf_transformation,[status(thm)],[f256]) ).
fof(f262,plain,
( leq(sK23_skl,minus(n6,n1))
| sP3_prd ),
inference(cnf_transformation,[status(thm)],[f256]) ).
fof(f263,plain,
( leq(sK24_skl,minus(n6,n1))
| sP3_prd ),
inference(cnf_transformation,[status(thm)],[f256]) ).
fof(f264,plain,
( a_select3(pminus_ds1_filter,sK23_skl,sK24_skl) != a_select3(pminus_ds1_filter,sK24_skl,sK23_skl)
| sP3_prd ),
inference(cnf_transformation,[status(thm)],[f256]) ).
fof(f271,plain,
gt(n0,tptp_minus_1),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f278,plain,
gt(n1,n0),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f299,plain,
! [X] :
( X = n0
| ~ leq(X,n0)
| ~ leq(n0,X) ),
inference(pre_NNF_transformation,[status(thm)],[f86]) ).
fof(f300,plain,
! [X0] :
( X0 = n0
| ~ leq(X0,n0)
| ~ leq(n0,X0) ),
inference(cnf_transformation,[status(thm)],[f299]) ).
fof(f301,plain,
! [X] :
( X = n1
| X = n0
| ~ leq(X,n1)
| ~ leq(n0,X) ),
inference(pre_NNF_transformation,[status(thm)],[f87]) ).
fof(f302,plain,
! [X0] :
( X0 = n1
| X0 = n0
| ~ leq(X0,n1)
| ~ leq(n0,X0) ),
inference(cnf_transformation,[status(thm)],[f301]) ).
fof(f310,plain,
succ(n0) = n1,
inference(cnf_transformation,[status(thm)],[f93]) ).
fof(f341,definition,
! [G,H] :
( sP5_prd(H,G)
<=> ( a_select3(q_ds1_filter,G,H) != a_select3(q_ds1_filter,H,G)
& leq(H,minus(n6,n1))
& leq(G,minus(n6,n1))
& leq(n0,H)
& leq(n0,G) ) ),
introduced(definition,[new_symbols(definition,[sP5_prd])],[]) ).
fof(f342,plain,
( sP3_prd
<=> ( ? [I,J] :
( a_select3(r_ds1_filter,I,J) != a_select3(r_ds1_filter,J,I)
& leq(J,minus(n3,n1))
& leq(I,minus(n3,n1))
& leq(n0,J)
& leq(n0,I) )
| ? [G,H] : sP5_prd(H,G) ) ),
inference(formula_renaming,[status(thm)],[f254,f341]) ).
fof(f343,plain,
( ( ( ! [I,J] :
( a_select3(r_ds1_filter,I,J) = a_select3(r_ds1_filter,J,I)
| ~ leq(J,minus(n3,n1))
| ~ leq(I,minus(n3,n1))
| ~ leq(n0,J)
| ~ leq(n0,I) )
& ! [G,H] : ~ sP5_prd(H,G) )
| sP3_prd )
& ( ? [I,J] :
( a_select3(r_ds1_filter,I,J) != a_select3(r_ds1_filter,J,I)
& leq(J,minus(n3,n1))
& leq(I,minus(n3,n1))
& leq(n0,J)
& leq(n0,I) )
| ? [G,H] : sP5_prd(H,G)
| ~ sP3_prd ) ),
inference(NNF_transformation,[status(thm)],[f342]) ).
fof(f344,plain,
( ( ( ! [I,J] :
( a_select3(r_ds1_filter,I,J) = a_select3(r_ds1_filter,J,I)
| ~ leq(J,minus(n3,n1))
| ~ leq(I,minus(n3,n1))
| ~ leq(n0,J)
| ~ leq(n0,I) )
& ! [G,H] : ~ sP5_prd(H,G) )
| sP3_prd )
& ( ( a_select3(r_ds1_filter,sK31_skl,sK32_skl) != a_select3(r_ds1_filter,sK32_skl,sK31_skl)
& leq(sK32_skl,minus(n3,n1))
& leq(sK31_skl,minus(n3,n1))
& leq(n0,sK32_skl)
& leq(n0,sK31_skl) )
| sP5_prd(sK30_skl,sK29_skl)
| ~ sP3_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29_skl,sK30_skl,sK31_skl,sK32_skl]),skolemize(G,sK29_skl),skolemize(H,sK30_skl),skolemize(I,sK31_skl),skolemize(J,sK32_skl)],[f343]) ).
fof(f345,plain,
( leq(n0,sK31_skl)
| sP5_prd(sK30_skl,sK29_skl)
| ~ sP3_prd ),
inference(cnf_transformation,[status(thm)],[f344]) ).
fof(f346,plain,
( leq(n0,sK32_skl)
| sP5_prd(sK30_skl,sK29_skl)
| ~ sP3_prd ),
inference(cnf_transformation,[status(thm)],[f344]) ).
fof(f347,plain,
( leq(sK31_skl,minus(n3,n1))
| sP5_prd(sK30_skl,sK29_skl)
| ~ sP3_prd ),
inference(cnf_transformation,[status(thm)],[f344]) ).
fof(f348,plain,
( leq(sK32_skl,minus(n3,n1))
| sP5_prd(sK30_skl,sK29_skl)
| ~ sP3_prd ),
inference(cnf_transformation,[status(thm)],[f344]) ).
fof(f349,plain,
( a_select3(r_ds1_filter,sK31_skl,sK32_skl) != a_select3(r_ds1_filter,sK32_skl,sK31_skl)
| sP5_prd(sK30_skl,sK29_skl)
| ~ sP3_prd ),
inference(cnf_transformation,[status(thm)],[f344]) ).
fof(f360,plain,
! [G,H] :
( ( a_select3(q_ds1_filter,G,H) = a_select3(q_ds1_filter,H,G)
| ~ leq(H,minus(n6,n1))
| ~ leq(G,minus(n6,n1))
| ~ leq(n0,H)
| ~ leq(n0,G)
| sP5_prd(H,G) )
& ( ( a_select3(q_ds1_filter,G,H) != a_select3(q_ds1_filter,H,G)
& leq(H,minus(n6,n1))
& leq(G,minus(n6,n1))
& leq(n0,H)
& leq(n0,G) )
| ~ sP5_prd(H,G) ) ),
inference(NNF_transformation,[status(thm)],[f341]) ).
fof(f361,plain,
( ! [G,H] :
( a_select3(q_ds1_filter,G,H) = a_select3(q_ds1_filter,H,G)
| ~ leq(H,minus(n6,n1))
| ~ leq(G,minus(n6,n1))
| ~ leq(n0,H)
| ~ leq(n0,G)
| sP5_prd(H,G) )
& ! [G,H] :
( ( a_select3(q_ds1_filter,G,H) != a_select3(q_ds1_filter,H,G)
& leq(H,minus(n6,n1))
& leq(G,minus(n6,n1))
& leq(n0,H)
& leq(n0,G) )
| ~ sP5_prd(H,G) ) ),
inference(miniscoping,[status(thm)],[f360]) ).
fof(f362,plain,
! [X0,X1] :
( leq(n0,X1)
| ~ sP5_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f361]) ).
fof(f363,plain,
! [X0,X1] :
( leq(n0,X0)
| ~ sP5_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f361]) ).
fof(f364,plain,
! [X0,X1] :
( leq(X1,minus(n6,n1))
| ~ sP5_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f361]) ).
fof(f365,plain,
! [X0,X1] :
( leq(X0,minus(n6,n1))
| ~ sP5_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f361]) ).
fof(f366,plain,
! [X0,X1] :
( a_select3(q_ds1_filter,X1,X0) != a_select3(q_ds1_filter,X0,X1)
| ~ sP5_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f361]) ).
fof(f368,definition,
( sQ0_spl
<=> sP3_prd ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f371,definition,
( sQ1_spl
<=> leq(n0,sK23_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f374,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f260,f368,f371]) ).
fof(f375,definition,
( sQ2_spl
<=> leq(n0,sK24_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f378,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f261,f368,f375]) ).
fof(f379,definition,
( sQ3_spl
<=> leq(sK23_skl,minus(n6,n1)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f382,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f262,f368,f379]) ).
fof(f383,definition,
( sQ4_spl
<=> leq(sK24_skl,minus(n6,n1)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f386,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f263,f368,f383]) ).
fof(f387,definition,
( sQ5_spl
<=> a_select3(pminus_ds1_filter,sK23_skl,sK24_skl) = a_select3(pminus_ds1_filter,sK24_skl,sK23_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f389,plain,
( sQ5_spl
| a_select3(pminus_ds1_filter,sK23_skl,sK24_skl) != a_select3(pminus_ds1_filter,sK24_skl,sK23_skl) ),
inference(component_clause,[status(thm)],[f387]) ).
fof(f390,plain,
( ~ sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f264,f368,f387]) ).
fof(f391,definition,
( sQ6_spl
<=> sP5_prd(sK30_skl,sK29_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f392,plain,
( ~ sQ6_spl
| sP5_prd(sK30_skl,sK29_skl) ),
inference(component_clause,[status(thm)],[f391]) ).
fof(f394,definition,
( sQ7_spl
<=> leq(n0,sK31_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f397,plain,
( sQ7_spl
| sQ6_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f345,f368,f391,f394]) ).
fof(f398,definition,
( sQ8_spl
<=> leq(n0,sK32_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f401,plain,
( sQ8_spl
| sQ6_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f346,f368,f391,f398]) ).
fof(f402,definition,
( sQ9_spl
<=> leq(sK31_skl,minus(n3,n1)) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f405,plain,
( sQ9_spl
| sQ6_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f347,f368,f391,f402]) ).
fof(f406,definition,
( sQ10_spl
<=> leq(sK32_skl,minus(n3,n1)) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f409,plain,
( sQ10_spl
| sQ6_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f348,f368,f391,f406]) ).
fof(f410,definition,
( sQ11_spl
<=> a_select3(r_ds1_filter,sK31_skl,sK32_skl) = a_select3(r_ds1_filter,sK32_skl,sK31_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f412,plain,
( sQ11_spl
| a_select3(r_ds1_filter,sK31_skl,sK32_skl) != a_select3(r_ds1_filter,sK32_skl,sK31_skl) ),
inference(component_clause,[status(thm)],[f410]) ).
fof(f413,plain,
( ~ sQ11_spl
| sQ6_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f349,f368,f391,f410]) ).
fof(f425,plain,
pred(n0) = tptp_minus_1,
inference(paramodulation,[status(thm)],[f208,f220]) ).
fof(f431,plain,
pred(n1) = n0,
inference(paramodulation,[status(thm)],[f310,f220]) ).
fof(f445,plain,
( n0 = n0
| ~ leq(n0,n0) ),
inference(resolution,[status(thm)],[f300,f101]) ).
fof(f446,definition,
( sQ14_spl
<=> leq(n0,n0) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f448,plain,
( sQ14_spl
| ~ leq(n0,n0) ),
inference(component_clause,[status(thm)],[f446]) ).
fof(f449,definition,
( sQ15_spl
<=> n0 = n0 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f464,plain,
( sQ15_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f445,f446,f449]) ).
fof(f465,plain,
( sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f448,f101]) ).
fof(f466,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f465]) ).
fof(f469,plain,
( ~ sQ6_spl
| a_select3(q_ds1_filter,sK29_skl,sK30_skl) != a_select3(q_ds1_filter,sK30_skl,sK29_skl) ),
inference(resolution,[status(thm)],[f366,f392]) ).
fof(f470,plain,
( ~ sQ6_spl
| ~ leq(sK30_skl,minus(n6,n1))
| ~ leq(sK29_skl,minus(n6,n1))
| ~ leq(n0,sK30_skl)
| ~ leq(n0,sK29_skl) ),
inference(resolution,[status(thm)],[f469,f257]) ).
fof(f472,definition,
( sQ19_spl
<=> leq(n0,sK29_skl) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f474,plain,
( sQ19_spl
| ~ leq(n0,sK29_skl) ),
inference(component_clause,[status(thm)],[f472]) ).
fof(f475,definition,
( sQ20_spl
<=> leq(n0,sK30_skl) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f477,plain,
( sQ20_spl
| ~ leq(n0,sK30_skl) ),
inference(component_clause,[status(thm)],[f475]) ).
fof(f478,definition,
( sQ21_spl
<=> leq(sK29_skl,minus(n6,n1)) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f480,plain,
( sQ21_spl
| ~ leq(sK29_skl,minus(n6,n1)) ),
inference(component_clause,[status(thm)],[f478]) ).
fof(f481,definition,
( sQ22_spl
<=> leq(sK30_skl,minus(n6,n1)) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f483,plain,
( sQ22_spl
| ~ leq(sK30_skl,minus(n6,n1)) ),
inference(component_clause,[status(thm)],[f481]) ).
fof(f484,plain,
( ~ sQ6_spl
| ~ sQ22_spl
| ~ sQ21_spl
| ~ sQ20_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f470,f472,f475,f478,f481,f391]) ).
fof(f486,plain,
! [X0] :
( sQ22_spl
| ~ sP5_prd(sK30_skl,X0) ),
inference(resolution,[status(thm)],[f483,f365]) ).
fof(f489,plain,
( ~ sQ6_spl
| sQ22_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f392,f486]) ).
fof(f490,plain,
( ~ sQ6_spl
| sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f489]) ).
fof(f493,plain,
( n1 = n1
| n1 = n0
| ~ leq(n0,n1) ),
inference(resolution,[status(thm)],[f302,f101]) ).
fof(f494,definition,
( sQ23_spl
<=> n0 = n1 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f495,plain,
( ~ sQ23_spl
| n0 = n1 ),
inference(component_clause,[status(thm)],[f494]) ).
fof(f501,definition,
( sQ25_spl
<=> leq(n0,n1) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f503,plain,
( sQ25_spl
| ~ leq(n0,n1) ),
inference(component_clause,[status(thm)],[f501]) ).
fof(f504,definition,
( sQ26_spl
<=> n1 = n1 ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f507,plain,
( sQ26_spl
| sQ23_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f493,f501,f494,f504]) ).
fof(f516,plain,
! [X0] : ~ leq(X0,pred(X0)),
inference(resolution,[status(thm)],[f119,f100]) ).
fof(f517,plain,
( sQ5_spl
| ~ leq(sK24_skl,minus(n6,n1))
| ~ leq(sK23_skl,minus(n6,n1))
| ~ leq(n0,sK24_skl)
| ~ leq(n0,sK23_skl) ),
inference(resolution,[status(thm)],[f389,f259]) ).
fof(f519,plain,
( sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f517,f371,f375,f379,f383,f387]) ).
fof(f534,plain,
( ~ sQ23_spl
| gt(n0,n0) ),
inference(backward_demodulation,[status(thm)],[f495,f278]) ).
fof(f540,plain,
( ~ sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f534,f100]) ).
fof(f541,plain,
~ sQ23_spl,
inference(contradiction_clause,[status(thm)],[f540]) ).
fof(f543,plain,
( sQ25_spl
| ~ gt(n1,n0) ),
inference(resolution,[status(thm)],[f503,f114]) ).
fof(f552,plain,
! [X0] : ~ gt(pred(X0),X0),
inference(resolution,[status(thm)],[f516,f114]) ).
fof(f604,plain,
( sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f543,f278]) ).
fof(f605,plain,
sQ25_spl,
inference(contradiction_clause,[status(thm)],[f604]) ).
fof(f610,plain,
~ gt(n0,n1),
inference(paramodulation,[status(thm)],[f431,f552]) ).
fof(f611,plain,
~ gt(tptp_minus_1,n0),
inference(paramodulation,[status(thm)],[f425,f552]) ).
fof(f636,plain,
! [X0] :
( uniform_int_rnd(X0,n0) = n0
| ~ leq(n0,uniform_int_rnd(X0,n0))
| ~ leq(n0,n0) ),
inference(resolution,[status(thm)],[f130,f300]) ).
fof(f637,definition,
! [X0] :
( sQ31_spl
<=> ( uniform_int_rnd(X0,n0) = n0
| ~ leq(n0,uniform_int_rnd(X0,n0)) ) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f640,plain,
( sQ31_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f636,f446,f637]) ).
fof(f648,plain,
~ leq(n1,pred(n0)),
inference(resolution,[status(thm)],[f610,f119]) ).
fof(f649,plain,
( n1 = n0
| ~ leq(n1,n0) ),
inference(resolution,[status(thm)],[f610,f116]) ).
fof(f651,plain,
( n1 = n0
| gt(n1,n0) ),
inference(resolution,[status(thm)],[f610,f96]) ).
fof(f652,plain,
~ leq(n1,tptp_minus_1),
inference(forward_demodulation,[status(thm)],[f425,f648]) ).
fof(f653,definition,
( sQ32_spl
<=> leq(n1,n0) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f656,plain,
( sQ23_spl
| ~ sQ32_spl ),
inference(split_clause,[status(thm)],[f649,f653,f494]) ).
fof(f657,definition,
( sQ33_spl
<=> gt(n1,n0) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f660,plain,
( sQ23_spl
| sQ33_spl ),
inference(split_clause,[status(thm)],[f651,f657,f494]) ).
fof(f661,plain,
! [X0] :
( ~ leq(n0,n1)
| uniform_int_rnd(X0,n1) = n1
| uniform_int_rnd(X0,n1) = n0
| ~ leq(n0,uniform_int_rnd(X0,n1)) ),
inference(resolution,[status(thm)],[f302,f130]) ).
fof(f668,definition,
! [X0] :
( sQ34_spl
<=> ( uniform_int_rnd(X0,n1) = n1
| uniform_int_rnd(X0,n1) = n0
| ~ leq(n0,uniform_int_rnd(X0,n1)) ) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f671,plain,
( ~ sQ25_spl
| sQ34_spl ),
inference(split_clause,[status(thm)],[f661,f668,f501]) ).
fof(f675,plain,
( sQ11_spl
| ~ leq(sK32_skl,minus(n3,n1))
| ~ leq(sK31_skl,minus(n3,n1))
| ~ leq(n0,sK32_skl)
| ~ leq(n0,sK31_skl) ),
inference(resolution,[status(thm)],[f258,f412]) ).
fof(f677,plain,
( sQ11_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f675,f394,f398,f402,f406,f410]) ).
fof(f682,plain,
( n0 = tptp_minus_1
| ~ leq(n0,tptp_minus_1) ),
inference(resolution,[status(thm)],[f611,f116]) ).
fof(f684,plain,
( n0 = tptp_minus_1
| gt(n0,tptp_minus_1) ),
inference(resolution,[status(thm)],[f611,f96]) ).
fof(f685,definition,
( sQ35_spl
<=> leq(n0,tptp_minus_1) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f688,definition,
( sQ36_spl
<=> n0 = tptp_minus_1 ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f689,plain,
( ~ sQ36_spl
| n0 = tptp_minus_1 ),
inference(component_clause,[status(thm)],[f688]) ).
fof(f691,plain,
( sQ36_spl
| ~ sQ35_spl ),
inference(split_clause,[status(thm)],[f682,f685,f688]) ).
fof(f692,definition,
( sQ37_spl
<=> gt(n0,tptp_minus_1) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f695,plain,
( sQ36_spl
| sQ37_spl ),
inference(split_clause,[status(thm)],[f684,f692,f688]) ).
fof(f702,plain,
( ~ sQ36_spl
| gt(n0,n0) ),
inference(backward_demodulation,[status(thm)],[f689,f271]) ).
fof(f708,plain,
( ~ sQ36_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f702,f100]) ).
fof(f709,plain,
~ sQ36_spl,
inference(contradiction_clause,[status(thm)],[f708]) ).
fof(f823,plain,
( ~ sQ6_spl
| leq(n0,sK30_skl) ),
inference(resolution,[status(thm)],[f363,f392]) ).
fof(f825,plain,
~ gt(tptp_minus_1,n1),
inference(resolution,[status(thm)],[f652,f114]) ).
fof(f835,plain,
( n1 = tptp_minus_1
| ~ leq(n1,tptp_minus_1) ),
inference(resolution,[status(thm)],[f825,f116]) ).
fof(f837,plain,
( n1 = tptp_minus_1
| gt(n1,tptp_minus_1) ),
inference(resolution,[status(thm)],[f825,f96]) ).
fof(f838,definition,
( sQ40_spl
<=> leq(n1,tptp_minus_1) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f841,definition,
( sQ41_spl
<=> n1 = tptp_minus_1 ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f842,plain,
( ~ sQ41_spl
| n1 = tptp_minus_1 ),
inference(component_clause,[status(thm)],[f841]) ).
fof(f844,plain,
( sQ41_spl
| ~ sQ40_spl ),
inference(split_clause,[status(thm)],[f835,f838,f841]) ).
fof(f845,definition,
( sQ42_spl
<=> gt(n1,tptp_minus_1) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f848,plain,
( sQ41_spl
| sQ42_spl ),
inference(split_clause,[status(thm)],[f837,f845,f841]) ).
fof(f850,plain,
( ~ sQ41_spl
| ~ leq(tptp_minus_1,tptp_minus_1) ),
inference(backward_demodulation,[status(thm)],[f842,f652]) ).
fof(f870,plain,
( ~ sQ41_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f850,f101]) ).
fof(f871,plain,
~ sQ41_spl,
inference(contradiction_clause,[status(thm)],[f870]) ).
fof(f909,plain,
( ~ sQ6_spl
| leq(n0,sK29_skl) ),
inference(resolution,[status(thm)],[f362,f392]) ).
fof(f947,plain,
( ~ sQ6_spl
| leq(sK29_skl,minus(n6,n1)) ),
inference(resolution,[status(thm)],[f364,f392]) ).
fof(f948,plain,
( ~ sQ6_spl
| sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f947,f480]) ).
fof(f949,plain,
( ~ sQ6_spl
| sQ21_spl ),
inference(contradiction_clause,[status(thm)],[f948]) ).
fof(f950,plain,
( sQ19_spl
| ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f474,f909]) ).
fof(f951,plain,
( sQ19_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f950]) ).
fof(f952,plain,
( sQ20_spl
| ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f477,f823]) ).
fof(f953,plain,
( sQ20_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f952]) ).
fof(f954,plain,
$false,
inference(sat_refutation,[status(thm)],[f374,f378,f382,f386,f390,f397,f401,f405,f409,f413,f464,f466,f484,f490,f507,f519,f541,f605,f640,f656,f660,f671,f677,f691,f695,f709,f844,f848,f871,f949,f951,f953]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWV122+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n005.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Mon Sep 21 08:32:03 UTC 2026
% 0.17/0.42 % CPUTime :
% 0.17/0.44 % Drodi V4.1.1
% 0.17/0.61 % Refutation found
% 0.17/0.61 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.40/0.63 % Elapsed time: 0.195009 seconds
% 0.40/0.63 % CPU time: 1.205557 seconds
% 0.40/0.63 % Total memory used: 120.059 MB
% 0.40/0.63 % Net memory used: 118.458 MB
%------------------------------------------------------------------------------