%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU062+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 02:19:10 PM UTC 2026
% Result : Theorem 0.15s 0.39s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 49 ( 8 unt; 3 def)
% Number of atoms : 128 ( 24 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 133 ( 54 ~; 45 |; 20 &)
% ( 7 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 4 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 65 ( 58 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [A,B] :
( relation(B)
=> ( in(A,relation_rng(B))
<=> relation_inverse_image(B,singleton(A)) != empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,conjecture,
! [A,B] :
( relation(B)
=> ( ! [C] :
~ ( relation_inverse_image(B,singleton(C)) = empty_set
& in(C,A) )
=> subset(A,relation_rng(B)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
~ ! [A,B] :
( relation(B)
=> ( ! [C] :
~ ( relation_inverse_image(B,singleton(C)) = empty_set
& in(C,A) )
=> subset(A,relation_rng(B)) ) ),
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f33,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,B)
| ~ in(C,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f47,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f46]) ).
fof(f48,plain,
( ! [A,B] :
( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f47]) ).
fof(f49,plain,
( ! [A,B] :
( ( ~ in(sK0_skl(B,A),B)
& in(sK0_skl(B,A),A) )
| subset(A,B) )
& ! [A,B] :
( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f48]) ).
fof(f50,plain,
! [X0,X1,X2] :
( in(X2,X1)
| ~ in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f51,plain,
! [X0,X1] :
( in(sK0_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f52,plain,
! [X0,X1] :
( ~ in(sK0_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f80,plain,
( function(sK6_skl)
& empty(sK6_skl)
& relation(sK6_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(A,sK6_skl)],[f18]) ).
fof(f82,plain,
empty(sK6_skl),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f101,plain,
! [A,B] :
( ( in(A,relation_rng(B))
<=> relation_inverse_image(B,singleton(A)) != empty_set )
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f102,plain,
! [A,B] :
( ( ( relation_inverse_image(B,singleton(A)) = empty_set
| in(A,relation_rng(B)) )
& ( relation_inverse_image(B,singleton(A)) != empty_set
| ~ in(A,relation_rng(B)) ) )
| ~ relation(B) ),
inference(NNF_transformation,[status(thm)],[f101]) ).
fof(f103,plain,
! [B] :
( ( ! [A] :
( relation_inverse_image(B,singleton(A)) = empty_set
| in(A,relation_rng(B)) )
& ! [A] :
( relation_inverse_image(B,singleton(A)) != empty_set
| ~ in(A,relation_rng(B)) ) )
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f102]) ).
fof(f105,plain,
! [X0,X1] :
( relation_inverse_image(X0,singleton(X1)) = empty_set
| in(X1,relation_rng(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f106,plain,
? [A,B] :
( ~ subset(A,relation_rng(B))
& ! [C] :
( relation_inverse_image(B,singleton(C)) != empty_set
| ~ in(C,A) )
& relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f107,plain,
? [B] :
( ? [A] :
( ~ subset(A,relation_rng(B))
& ! [C] :
( relation_inverse_image(B,singleton(C)) != empty_set
| ~ in(C,A) ) )
& relation(B) ),
inference(miniscoping,[status(thm)],[f106]) ).
fof(f108,plain,
( ~ subset(sK13_skl,relation_rng(sK12_skl))
& ! [C] :
( relation_inverse_image(sK12_skl,singleton(C)) != empty_set
| ~ in(C,sK13_skl) )
& relation(sK12_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12_skl,sK13_skl]),skolemize(B,sK12_skl),skolemize(A,sK13_skl)],[f107]) ).
fof(f109,plain,
relation(sK12_skl),
inference(cnf_transformation,[status(thm)],[f108]) ).
fof(f110,plain,
! [X0] :
( relation_inverse_image(sK12_skl,singleton(X0)) != empty_set
| ~ in(X0,sK13_skl) ),
inference(cnf_transformation,[status(thm)],[f108]) ).
fof(f111,plain,
~ subset(sK13_skl,relation_rng(sK12_skl)),
inference(cnf_transformation,[status(thm)],[f108]) ).
fof(f126,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f127,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f126]) ).
fof(f135,plain,
in(sK0_skl(relation_rng(sK12_skl),sK13_skl),sK13_skl),
inference(resolution,[status(thm)],[f51,f111]) ).
fof(f136,plain,
! [X0] :
( in(sK0_skl(relation_rng(sK12_skl),sK13_skl),X0)
| ~ subset(sK13_skl,X0) ),
inference(resolution,[status(thm)],[f135,f50]) ).
fof(f138,plain,
! [X0] :
( in(sK0_skl(X0,sK13_skl),sK13_skl)
| in(sK0_skl(relation_rng(sK12_skl),sK13_skl),X0) ),
inference(resolution,[status(thm)],[f136,f51]) ).
fof(f142,plain,
sK6_skl = empty_set,
inference(resolution,[status(thm)],[f127,f82]) ).
fof(f150,plain,
! [X0] :
( relation_inverse_image(sK12_skl,singleton(X0)) != sK6_skl
| ~ in(X0,sK13_skl) ),
inference(backward_demodulation,[status(thm)],[f142,f110]) ).
fof(f166,plain,
! [X0] :
( in(sK0_skl(relation_rng(sK12_skl),sK13_skl),X0)
| relation_inverse_image(sK12_skl,singleton(sK0_skl(X0,sK13_skl))) != sK6_skl ),
inference(resolution,[status(thm)],[f150,f138]) ).
fof(f200,plain,
! [X0,X1] :
( relation_inverse_image(X0,singleton(X1)) = sK6_skl
| in(X1,relation_rng(X0))
| ~ relation(X0) ),
inference(forward_demodulation,[status(thm)],[f142,f105]) ).
fof(f201,plain,
! [X0,X1] :
( subset(X1,relation_rng(X0))
| relation_inverse_image(X0,singleton(sK0_skl(relation_rng(X0),X1))) = sK6_skl
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f200,f52]) ).
fof(f233,plain,
( subset(sK13_skl,relation_rng(sK12_skl))
| relation_inverse_image(sK12_skl,singleton(sK0_skl(relation_rng(sK12_skl),sK13_skl))) != sK6_skl ),
inference(resolution,[status(thm)],[f166,f52]) ).
fof(f240,definition,
( sQ7_spl
<=> relation_inverse_image(sK12_skl,singleton(sK0_skl(relation_rng(sK12_skl),sK13_skl))) = sK6_skl ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f243,definition,
( sQ8_spl
<=> subset(sK13_skl,relation_rng(sK12_skl)) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f244,plain,
( ~ sQ8_spl
| subset(sK13_skl,relation_rng(sK12_skl)) ),
inference(component_clause,[status(thm)],[f243]) ).
fof(f246,plain,
( sQ8_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f233,f240,f243]) ).
fof(f268,plain,
( relation_inverse_image(sK12_skl,singleton(sK0_skl(relation_rng(sK12_skl),sK13_skl))) = sK6_skl
| ~ relation(sK12_skl) ),
inference(resolution,[status(thm)],[f201,f111]) ).
fof(f273,definition,
( sQ10_spl
<=> relation(sK12_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f275,plain,
( sQ10_spl
| ~ relation(sK12_skl) ),
inference(component_clause,[status(thm)],[f273]) ).
fof(f276,plain,
( sQ7_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f268,f273,f240]) ).
fof(f281,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f275,f109]) ).
fof(f282,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f281]) ).
fof(f283,plain,
( ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f244,f111]) ).
fof(f284,plain,
~ sQ8_spl,
inference(contradiction_clause,[status(thm)],[f283]) ).
fof(f285,plain,
$false,
inference(sat_refutation,[status(thm)],[f246,f276,f282,f284]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU062+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n016.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 05:53:07 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.15/0.38 % Drodi V4.1.1
% 0.15/0.39 % Refutation found
% 0.15/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.43 % Elapsed time: 0.047408 seconds
% 0.15/0.43 % CPU time: 0.096604 seconds
% 0.15/0.43 % Total memory used: 10.365 MB
% 0.15/0.43 % Net memory used: 10.341 MB
%------------------------------------------------------------------------------