%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV221+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 : n001.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 02:46:55 PM UTC 2026
% Result : Theorem 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 10 unt; 4 def)
% Number of atoms : 235 ( 46 equ)
% Maximal formula atoms : 47 ( 8 avg)
% Number of connectives : 290 ( 84 ~; 74 |; 102 &)
% ( 4 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 13 con; 0-3 aty)
% Number of variables : 56 ( 54 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f53,conjecture,
( ( ! [K] :
( ( leq(K,pred(pv57))
& leq(n0,K) )
=> ! [L] :
( ( leq(L,n5)
& leq(n0,L) )
=> a_select3(id_ds1_filter,K,L) = a_select3(id_ds1_filter,L,K) ) )
& ! [I,J] :
( ( leq(J,n5)
& leq(I,n5)
& leq(n0,J)
& leq(n0,I) )
=> ( gt(pv57,I)
=> a_select3(id_ds1_filter,I,J) = a_select3(id_ds1_filter,J,I) ) )
& ! [G,H] :
( ( leq(H,n5)
& leq(G,n5)
& leq(n0,H)
& leq(n0,G) )
=> ( ( gt(pv58,H)
& G = pv57 )
=> a_select3(id_ds1_filter,G,H) = a_select3(id_ds1_filter,H,G) ) )
& ! [E,F] :
( ( leq(F,n5)
& leq(E,n5)
& leq(n0,F)
& leq(n0,E) )
=> a_select3(pminus_ds1_filter,E,F) = a_select3(pminus_ds1_filter,F,E) )
& ! [C,D] :
( ( leq(D,n2)
& leq(C,n2)
& leq(n0,D)
& leq(n0,C) )
=> a_select3(r_ds1_filter,C,D) = a_select3(r_ds1_filter,D,C) )
& ! [A,B] :
( ( leq(B,n5)
& leq(A,n5)
& leq(n0,B)
& leq(n0,A) )
=> a_select3(q_ds1_filter,A,B) = a_select3(q_ds1_filter,B,A) )
& gt(pv58,pv57)
& leq(pv58,n5)
& leq(pv57,n5)
& leq(pv5,n998)
& leq(n0,pv57)
& leq(n0,pv5) )
=> ! [M] :
( ( leq(M,pred(pv57))
& leq(n0,M) )
=> ! [N] :
( ( leq(N,n5)
& leq(n0,N) )
=> ( ( pv57 != M
& ~ ( N = M
& pv57 = N ) )
=> a_select3(id_ds1_filter,M,N) = a_select3(id_ds1_filter,N,M) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f54,negated_conjecture,
~ ( ( ! [K] :
( ( leq(K,pred(pv57))
& leq(n0,K) )
=> ! [L] :
( ( leq(L,n5)
& leq(n0,L) )
=> a_select3(id_ds1_filter,K,L) = a_select3(id_ds1_filter,L,K) ) )
& ! [I,J] :
( ( leq(J,n5)
& leq(I,n5)
& leq(n0,J)
& leq(n0,I) )
=> ( gt(pv57,I)
=> a_select3(id_ds1_filter,I,J) = a_select3(id_ds1_filter,J,I) ) )
& ! [G,H] :
( ( leq(H,n5)
& leq(G,n5)
& leq(n0,H)
& leq(n0,G) )
=> ( ( gt(pv58,H)
& G = pv57 )
=> a_select3(id_ds1_filter,G,H) = a_select3(id_ds1_filter,H,G) ) )
& ! [E,F] :
( ( leq(F,n5)
& leq(E,n5)
& leq(n0,F)
& leq(n0,E) )
=> a_select3(pminus_ds1_filter,E,F) = a_select3(pminus_ds1_filter,F,E) )
& ! [C,D] :
( ( leq(D,n2)
& leq(C,n2)
& leq(n0,D)
& leq(n0,C) )
=> a_select3(r_ds1_filter,C,D) = a_select3(r_ds1_filter,D,C) )
& ! [A,B] :
( ( leq(B,n5)
& leq(A,n5)
& leq(n0,B)
& leq(n0,A) )
=> a_select3(q_ds1_filter,A,B) = a_select3(q_ds1_filter,B,A) )
& gt(pv58,pv57)
& leq(pv58,n5)
& leq(pv57,n5)
& leq(pv5,n998)
& leq(n0,pv57)
& leq(n0,pv5) )
=> ! [M] :
( ( leq(M,pred(pv57))
& leq(n0,M) )
=> ! [N] :
( ( leq(N,n5)
& leq(n0,N) )
=> ( ( pv57 != M
& ~ ( N = M
& pv57 = N ) )
=> a_select3(id_ds1_filter,M,N) = a_select3(id_ds1_filter,N,M) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f251,plain,
( ? [M] :
( ? [N] :
( a_select3(id_ds1_filter,M,N) != a_select3(id_ds1_filter,N,M)
& pv57 != M
& ( N != M
| pv57 != N )
& leq(N,n5)
& leq(n0,N) )
& leq(M,pred(pv57))
& leq(n0,M) )
& ! [K] :
( ! [L] :
( a_select3(id_ds1_filter,K,L) = a_select3(id_ds1_filter,L,K)
| ~ leq(L,n5)
| ~ leq(n0,L) )
| ~ leq(K,pred(pv57))
| ~ leq(n0,K) )
& ! [I,J] :
( a_select3(id_ds1_filter,I,J) = a_select3(id_ds1_filter,J,I)
| ~ gt(pv57,I)
| ~ leq(J,n5)
| ~ leq(I,n5)
| ~ leq(n0,J)
| ~ leq(n0,I) )
& ! [G,H] :
( a_select3(id_ds1_filter,G,H) = a_select3(id_ds1_filter,H,G)
| ~ gt(pv58,H)
| G != pv57
| ~ leq(H,n5)
| ~ leq(G,n5)
| ~ leq(n0,H)
| ~ leq(n0,G) )
& ! [E,F] :
( a_select3(pminus_ds1_filter,E,F) = a_select3(pminus_ds1_filter,F,E)
| ~ leq(F,n5)
| ~ leq(E,n5)
| ~ leq(n0,F)
| ~ leq(n0,E) )
& ! [C,D] :
( a_select3(r_ds1_filter,C,D) = a_select3(r_ds1_filter,D,C)
| ~ leq(D,n2)
| ~ leq(C,n2)
| ~ leq(n0,D)
| ~ leq(n0,C) )
& ! [A,B] :
( a_select3(q_ds1_filter,A,B) = a_select3(q_ds1_filter,B,A)
| ~ leq(B,n5)
| ~ leq(A,n5)
| ~ leq(n0,B)
| ~ leq(n0,A) )
& gt(pv58,pv57)
& leq(pv58,n5)
& leq(pv57,n5)
& leq(pv5,n998)
& leq(n0,pv57)
& leq(n0,pv5) ),
inference(pre_NNF_transformation,[status(thm)],[f54]) ).
fof(f252,plain,
( a_select3(id_ds1_filter,sK23_skl,sK24_skl) != a_select3(id_ds1_filter,sK24_skl,sK23_skl)
& pv57 != sK23_skl
& ( sK24_skl != sK23_skl
| pv57 != sK24_skl )
& leq(sK24_skl,n5)
& leq(n0,sK24_skl)
& leq(sK23_skl,pred(pv57))
& leq(n0,sK23_skl)
& ! [K] :
( ! [L] :
( a_select3(id_ds1_filter,K,L) = a_select3(id_ds1_filter,L,K)
| ~ leq(L,n5)
| ~ leq(n0,L) )
| ~ leq(K,pred(pv57))
| ~ leq(n0,K) )
& ! [I,J] :
( a_select3(id_ds1_filter,I,J) = a_select3(id_ds1_filter,J,I)
| ~ gt(pv57,I)
| ~ leq(J,n5)
| ~ leq(I,n5)
| ~ leq(n0,J)
| ~ leq(n0,I) )
& ! [G,H] :
( a_select3(id_ds1_filter,G,H) = a_select3(id_ds1_filter,H,G)
| ~ gt(pv58,H)
| G != pv57
| ~ leq(H,n5)
| ~ leq(G,n5)
| ~ leq(n0,H)
| ~ leq(n0,G) )
& ! [E,F] :
( a_select3(pminus_ds1_filter,E,F) = a_select3(pminus_ds1_filter,F,E)
| ~ leq(F,n5)
| ~ leq(E,n5)
| ~ leq(n0,F)
| ~ leq(n0,E) )
& ! [C,D] :
( a_select3(r_ds1_filter,C,D) = a_select3(r_ds1_filter,D,C)
| ~ leq(D,n2)
| ~ leq(C,n2)
| ~ leq(n0,D)
| ~ leq(n0,C) )
& ! [A,B] :
( a_select3(q_ds1_filter,A,B) = a_select3(q_ds1_filter,B,A)
| ~ leq(B,n5)
| ~ leq(A,n5)
| ~ leq(n0,B)
| ~ leq(n0,A) )
& gt(pv58,pv57)
& leq(pv58,n5)
& leq(pv57,n5)
& leq(pv5,n998)
& leq(n0,pv57)
& leq(n0,pv5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23_skl,sK24_skl]),skolemize(M,sK23_skl),skolemize(N,sK24_skl)],[f251]) ).
fof(f264,plain,
! [X0,X1] :
( a_select3(id_ds1_filter,X0,X1) = a_select3(id_ds1_filter,X1,X0)
| ~ leq(X1,n5)
| ~ leq(n0,X1)
| ~ leq(X0,pred(pv57))
| ~ leq(n0,X0) ),
inference(cnf_transformation,[status(thm)],[f252]) ).
fof(f265,plain,
leq(n0,sK23_skl),
inference(cnf_transformation,[status(thm)],[f252]) ).
fof(f266,plain,
leq(sK23_skl,pred(pv57)),
inference(cnf_transformation,[status(thm)],[f252]) ).
fof(f267,plain,
leq(n0,sK24_skl),
inference(cnf_transformation,[status(thm)],[f252]) ).
fof(f268,plain,
leq(sK24_skl,n5),
inference(cnf_transformation,[status(thm)],[f252]) ).
fof(f271,plain,
a_select3(id_ds1_filter,sK23_skl,sK24_skl) != a_select3(id_ds1_filter,sK24_skl,sK23_skl),
inference(cnf_transformation,[status(thm)],[f252]) ).
fof(f373,plain,
( ~ leq(sK24_skl,n5)
| ~ leq(n0,sK24_skl)
| ~ leq(sK23_skl,pred(pv57))
| ~ leq(n0,sK23_skl) ),
inference(resolution,[status(thm)],[f264,f271]) ).
fof(f375,definition,
( sQ2_spl
<=> leq(n0,sK23_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f377,plain,
( sQ2_spl
| ~ leq(n0,sK23_skl) ),
inference(component_clause,[status(thm)],[f375]) ).
fof(f378,definition,
( sQ3_spl
<=> leq(sK23_skl,pred(pv57)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f380,plain,
( sQ3_spl
| ~ leq(sK23_skl,pred(pv57)) ),
inference(component_clause,[status(thm)],[f378]) ).
fof(f381,definition,
( sQ4_spl
<=> leq(n0,sK24_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f383,plain,
( sQ4_spl
| ~ leq(n0,sK24_skl) ),
inference(component_clause,[status(thm)],[f381]) ).
fof(f384,definition,
( sQ5_spl
<=> leq(sK24_skl,n5) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f386,plain,
( sQ5_spl
| ~ leq(sK24_skl,n5) ),
inference(component_clause,[status(thm)],[f384]) ).
fof(f387,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f373,f375,f378,f381,f384]) ).
fof(f395,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f377,f265]) ).
fof(f396,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f395]) ).
fof(f397,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f383,f267]) ).
fof(f398,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f397]) ).
fof(f399,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f380,f266]) ).
fof(f400,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f399]) ).
fof(f401,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f386,f268]) ).
fof(f402,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f401]) ).
fof(f403,plain,
$false,
inference(sat_refutation,[status(thm)],[f387,f396,f398,f400,f402]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV221+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n001.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Mon Sep 21 08:40:35 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.38 % Refutation found
% 0.12/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.41 % Elapsed time: 0.055880 seconds
% 0.12/0.41 % CPU time: 0.162009 seconds
% 0.12/0.41 % Total memory used: 92.607 MB
% 0.12/0.41 % Net memory used: 92.436 MB
%------------------------------------------------------------------------------