%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET992+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 02:11:06 PM UTC 2026
% Result : Theorem 0.13s 0.42s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 3
% Syntax : Number of formulae : 47 ( 8 unt; 0 def)
% Number of atoms : 223 ( 102 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 270 ( 94 ~; 127 |; 38 &)
% ( 6 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-3 aty)
% Number of variables : 86 ( 72 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,conjecture,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( relation_dom(B) = singleton(A)
=> relation_rng(B) = singleton(apply(B,A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
~ ! [A,B] :
( ( function(B)
& relation(B) )
=> ( relation_dom(B) = singleton(A)
=> relation_rng(B) = singleton(apply(B,A)) ) ),
inference(negated_conjecture,[status(cth)],[f25]) ).
fof(f42,plain,
! [A,B] :
( ( ? [C] :
( ( C = A
| in(C,B) )
& ( C != A
| ~ in(C,B) ) )
| B = singleton(A) )
& ( ! [C] :
( ( C != A
| in(C,B) )
& ( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f43,plain,
( ! [A,B] :
( ? [C] :
( ( C = A
| in(C,B) )
& ( C != A
| ~ in(C,B) ) )
| B = singleton(A) )
& ! [A,B] :
( ( ! [C] :
( C != A
| in(C,B) )
& ! [C] :
( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(miniscoping,[status(thm)],[f42]) ).
fof(f44,plain,
( ! [A,B] :
( ( ( sK0_skl(B,A) = A
| in(sK0_skl(B,A),B) )
& ( sK0_skl(B,A) != A
| ~ in(sK0_skl(B,A),B) ) )
| B = singleton(A) )
& ! [A,B] :
( ( ! [C] :
( C != A
| in(C,B) )
& ! [C] :
( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f43]) ).
fof(f45,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ in(X2,X0)
| X0 != singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f46,plain,
! [X0,X1,X2] :
( X2 != X1
| in(X2,X0)
| X0 != singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f49,plain,
! [A] :
( ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) ) ) )
| ~ function(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f50,plain,
! [A] :
( ! [B] :
( ( ? [C] :
( ( ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) )
| in(C,B) )
& ( ! [D] :
( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
| ~ in(C,B) ) )
| B = relation_rng(A) )
& ( ! [C] :
( ( ! [D] :
( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
| in(C,B) )
& ( ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) )
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f49]) ).
fof(f51,plain,
! [A] :
( ( ! [B] :
( ? [C] :
( ( ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) )
| in(C,B) )
& ( ! [D] :
( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
| ~ in(C,B) ) )
| B = relation_rng(A) )
& ! [B] :
( ( ! [C] :
( ! [D] :
( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
| in(C,B) )
& ! [C] :
( ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) )
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f50]) ).
fof(f52,plain,
! [A] :
( ( ! [B] :
( ( ( ( sK2_skl(B,A) = apply(A,sK3_skl(B,A))
& in(sK3_skl(B,A),relation_dom(A)) )
| in(sK2_skl(B,A),B) )
& ( ! [D] :
( sK2_skl(B,A) != apply(A,D)
| ~ in(D,relation_dom(A)) )
| ~ in(sK2_skl(B,A),B) ) )
| B = relation_rng(A) )
& ! [B] :
( ( ! [C] :
( ! [D] :
( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
| in(C,B) )
& ! [C] :
( ( C = apply(A,sK1_skl(C,B,A))
& in(sK1_skl(C,B,A),relation_dom(A)) )
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl,sK3_skl]),skolemize(D,sK1_skl(C,B,A)),skolemize(C,sK2_skl(B,A)),skolemize(D,sK3_skl(B,A))],[f51]) ).
fof(f56,plain,
! [X0,X1,X2] :
( sK2_skl(X1,X0) != apply(X0,X2)
| ~ in(X2,relation_dom(X0))
| ~ in(sK2_skl(X1,X0),X1)
| X1 = relation_rng(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f57,plain,
! [X0,X1] :
( in(sK3_skl(X1,X0),relation_dom(X0))
| in(sK2_skl(X1,X0),X1)
| X1 = relation_rng(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f58,plain,
! [X0,X1] :
( sK2_skl(X1,X0) = apply(X0,sK3_skl(X1,X0))
| in(sK2_skl(X1,X0),X1)
| X1 = relation_rng(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f104,plain,
? [A,B] :
( relation_rng(B) != singleton(apply(B,A))
& relation_dom(B) = singleton(A)
& function(B)
& relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f105,plain,
? [B] :
( ? [A] :
( relation_rng(B) != singleton(apply(B,A))
& relation_dom(B) = singleton(A) )
& function(B)
& relation(B) ),
inference(miniscoping,[status(thm)],[f104]) ).
fof(f106,plain,
( relation_rng(sK13_skl) != singleton(apply(sK13_skl,sK14_skl))
& relation_dom(sK13_skl) = singleton(sK14_skl)
& function(sK13_skl)
& relation(sK13_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl,sK14_skl]),skolemize(B,sK13_skl),skolemize(A,sK14_skl)],[f105]) ).
fof(f107,plain,
relation(sK13_skl),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f108,plain,
function(sK13_skl),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f109,plain,
relation_dom(sK13_skl) = singleton(sK14_skl),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f110,plain,
relation_rng(sK13_skl) != singleton(apply(sK13_skl,sK14_skl)),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f138,plain,
! [X0,X1] :
( X0 = X1
| ~ in(X0,singleton(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f45]) ).
fof(f139,plain,
! [X0] : in(X0,singleton(X0)),
inference(destructive_equality_resolution,[status(thm)],[f46]) ).
fof(f177,plain,
! [X0] :
( in(sK3_skl(X0,sK13_skl),singleton(sK14_skl))
| in(sK2_skl(X0,sK13_skl),X0)
| X0 = relation_rng(sK13_skl)
| ~ function(sK13_skl)
| ~ relation(sK13_skl) ),
inference(paramodulation,[status(thm)],[f109,f57]) ).
fof(f179,plain,
! [X0] :
( in(sK3_skl(X0,sK13_skl),singleton(sK14_skl))
| in(sK2_skl(X0,sK13_skl),X0)
| X0 = relation_rng(sK13_skl)
| ~ function(sK13_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f177,f107]) ).
fof(f180,plain,
! [X0] :
( sK3_skl(X0,sK13_skl) = sK14_skl
| in(sK2_skl(X0,sK13_skl),X0)
| X0 = relation_rng(sK13_skl)
| ~ function(sK13_skl) ),
inference(resolution,[status(thm)],[f179,f138]) ).
fof(f182,plain,
! [X0] :
( sK3_skl(X0,sK13_skl) = sK14_skl
| in(sK2_skl(X0,sK13_skl),X0)
| X0 = relation_rng(sK13_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f180,f108]) ).
fof(f183,plain,
! [X0] :
( sK2_skl(singleton(X0),sK13_skl) = X0
| sK3_skl(singleton(X0),sK13_skl) = sK14_skl
| singleton(X0) = relation_rng(sK13_skl) ),
inference(resolution,[status(thm)],[f182,f138]) ).
fof(f188,plain,
! [X0] :
( sK2_skl(singleton(X0),sK13_skl) = X0
| singleton(X0) = relation_rng(sK13_skl)
| sK2_skl(singleton(X0),sK13_skl) = apply(sK13_skl,sK14_skl)
| in(sK2_skl(singleton(X0),sK13_skl),singleton(X0))
| singleton(X0) = relation_rng(sK13_skl)
| ~ function(sK13_skl)
| ~ relation(sK13_skl) ),
inference(paramodulation,[status(thm)],[f183,f58]) ).
fof(f194,plain,
! [X0] :
( sK2_skl(singleton(X0),sK13_skl) = X0
| sK2_skl(singleton(X0),sK13_skl) = apply(sK13_skl,sK14_skl)
| in(sK2_skl(singleton(X0),sK13_skl),singleton(X0))
| singleton(X0) = relation_rng(sK13_skl)
| ~ function(sK13_skl)
| ~ relation(sK13_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f188]) ).
fof(f195,plain,
! [X0] :
( sK2_skl(singleton(X0),sK13_skl) = X0
| sK2_skl(singleton(X0),sK13_skl) = apply(sK13_skl,sK14_skl)
| in(sK2_skl(singleton(X0),sK13_skl),singleton(X0))
| singleton(X0) = relation_rng(sK13_skl)
| ~ function(sK13_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f194,f107]) ).
fof(f198,plain,
! [X0] :
( sK2_skl(singleton(X0),sK13_skl) = X0
| apply(sK13_skl,sK14_skl) != X0
| in(sK2_skl(singleton(X0),sK13_skl),singleton(X0))
| singleton(X0) = relation_rng(sK13_skl)
| ~ function(sK13_skl) ),
inference(equality_factoring,[status(thm)],[f195]) ).
fof(f199,plain,
( sK2_skl(singleton(apply(sK13_skl,sK14_skl)),sK13_skl) = apply(sK13_skl,sK14_skl)
| in(sK2_skl(singleton(apply(sK13_skl,sK14_skl)),sK13_skl),singleton(apply(sK13_skl,sK14_skl)))
| singleton(apply(sK13_skl,sK14_skl)) = relation_rng(sK13_skl)
| ~ function(sK13_skl) ),
inference(destructive_equality_resolution,[status(thm)],[f198]) ).
fof(f200,plain,
( sK2_skl(singleton(apply(sK13_skl,sK14_skl)),sK13_skl) = apply(sK13_skl,sK14_skl)
| in(sK2_skl(singleton(apply(sK13_skl,sK14_skl)),sK13_skl),singleton(apply(sK13_skl,sK14_skl)))
| singleton(apply(sK13_skl,sK14_skl)) = relation_rng(sK13_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f199,f108]) ).
fof(f201,plain,
( sK2_skl(singleton(apply(sK13_skl,sK14_skl)),sK13_skl) = apply(sK13_skl,sK14_skl)
| sK2_skl(singleton(apply(sK13_skl,sK14_skl)),sK13_skl) = apply(sK13_skl,sK14_skl)
| singleton(apply(sK13_skl,sK14_skl)) = relation_rng(sK13_skl) ),
inference(resolution,[status(thm)],[f200,f138]) ).
fof(f203,plain,
( sK2_skl(singleton(apply(sK13_skl,sK14_skl)),sK13_skl) = apply(sK13_skl,sK14_skl)
| singleton(apply(sK13_skl,sK14_skl)) = relation_rng(sK13_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f201]) ).
fof(f205,plain,
sK2_skl(singleton(apply(sK13_skl,sK14_skl)),sK13_skl) = apply(sK13_skl,sK14_skl),
inference(forward_subsumption_resolution,[status(thm)],[f203,f110]) ).
fof(f221,plain,
( ~ in(sK14_skl,relation_dom(sK13_skl))
| ~ in(sK2_skl(singleton(apply(sK13_skl,sK14_skl)),sK13_skl),singleton(apply(sK13_skl,sK14_skl)))
| singleton(apply(sK13_skl,sK14_skl)) = relation_rng(sK13_skl)
| ~ function(sK13_skl)
| ~ relation(sK13_skl) ),
inference(resolution,[status(thm)],[f56,f205]) ).
fof(f225,plain,
( ~ in(sK14_skl,relation_dom(sK13_skl))
| ~ in(apply(sK13_skl,sK14_skl),singleton(apply(sK13_skl,sK14_skl)))
| singleton(apply(sK13_skl,sK14_skl)) = relation_rng(sK13_skl)
| ~ function(sK13_skl)
| ~ relation(sK13_skl) ),
inference(forward_demodulation,[status(thm)],[f205,f221]) ).
fof(f226,plain,
( ~ in(sK14_skl,singleton(sK14_skl))
| ~ in(apply(sK13_skl,sK14_skl),singleton(apply(sK13_skl,sK14_skl)))
| singleton(apply(sK13_skl,sK14_skl)) = relation_rng(sK13_skl)
| ~ function(sK13_skl)
| ~ relation(sK13_skl) ),
inference(forward_demodulation,[status(thm)],[f109,f225]) ).
fof(f227,plain,
( ~ in(sK14_skl,singleton(sK14_skl))
| ~ in(apply(sK13_skl,sK14_skl),singleton(apply(sK13_skl,sK14_skl)))
| singleton(apply(sK13_skl,sK14_skl)) = relation_rng(sK13_skl)
| ~ function(sK13_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f226,f107]) ).
fof(f231,plain,
( ~ in(sK14_skl,singleton(sK14_skl))
| singleton(apply(sK13_skl,sK14_skl)) = relation_rng(sK13_skl)
| ~ function(sK13_skl) ),
inference(resolution,[status(thm)],[f227,f139]) ).
fof(f232,plain,
( ~ in(sK14_skl,singleton(sK14_skl))
| singleton(apply(sK13_skl,sK14_skl)) = relation_rng(sK13_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f231,f108]) ).
fof(f235,plain,
~ in(sK14_skl,singleton(sK14_skl)),
inference(resolution,[status(thm)],[f232,f110]) ).
fof(f236,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f235,f139]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET992+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n007.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 05:44:21 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.13/0.42 % Refutation found
% 0.13/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.45 % Elapsed time: 0.078888 seconds
% 0.13/0.45 % CPU time: 0.352796 seconds
% 0.13/0.45 % Total memory used: 108.577 MB
% 0.13/0.45 % Net memory used: 108.057 MB
%------------------------------------------------------------------------------