%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU217+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 02:19:44 PM UTC 2026
% Result : Theorem 0.12s 0.39s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 48 ( 12 unt; 4 def)
% Number of atoms : 172 ( 56 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 195 ( 71 ~; 74 |; 32 &)
% ( 12 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 73 ( 67 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [A,B] :
( relation(B)
=> ( B = identity_relation(A)
<=> ! [C,D] :
( in(ordered_pair(C,D),B)
<=> ( C = D
& in(C,A) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B,C] :
( ( ~ in(B,relation_dom(A))
=> ( C = apply(A,B)
<=> C = empty_set ) )
& ( in(B,relation_dom(A))
=> ( C = apply(A,B)
<=> in(ordered_pair(B,C),A) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f62,axiom,
! [A] : relation(identity_relation(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f78,axiom,
! [A] :
( function(identity_relation(A))
& relation(identity_relation(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f165,conjecture,
! [A,B] :
( in(B,A)
=> apply(identity_relation(A),B) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f166,negated_conjecture,
~ ! [A,B] :
( in(B,A)
=> apply(identity_relation(A),B) = B ),
inference(negated_conjecture,[status(cth)],[f165]) ).
fof(f206,lemma,
! [A] :
( relation_rng(identity_relation(A)) = A
& relation_dom(identity_relation(A)) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f235,plain,
! [A,B] :
( ( B = identity_relation(A)
<=> ! [C,D] :
( in(ordered_pair(C,D),B)
<=> ( C = D
& in(C,A) ) ) )
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f236,plain,
! [A,B] :
( ( ( ? [C,D] :
( ( ( C = D
& in(C,A) )
| in(ordered_pair(C,D),B) )
& ( C != D
| ~ in(C,A)
| ~ in(ordered_pair(C,D),B) ) )
| B = identity_relation(A) )
& ( ! [C,D] :
( ( C != D
| ~ in(C,A)
| in(ordered_pair(C,D),B) )
& ( ( C = D
& in(C,A) )
| ~ in(ordered_pair(C,D),B) ) )
| B != identity_relation(A) ) )
| ~ relation(B) ),
inference(NNF_transformation,[status(thm)],[f235]) ).
fof(f237,plain,
! [B] :
( ( ! [A] :
( ? [C,D] :
( ( ( C = D
& in(C,A) )
| in(ordered_pair(C,D),B) )
& ( C != D
| ~ in(C,A)
| ~ in(ordered_pair(C,D),B) ) )
| B = identity_relation(A) )
& ! [A] :
( ( ! [C,D] :
( C != D
| ~ in(C,A)
| in(ordered_pair(C,D),B) )
& ! [C,D] :
( ( C = D
& in(C,A) )
| ~ in(ordered_pair(C,D),B) ) )
| B != identity_relation(A) ) )
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f236]) ).
fof(f238,plain,
! [B] :
( ( ! [A] :
( ( ( ( sK0_skl(A,B) = sK1_skl(A,B)
& in(sK0_skl(A,B),A) )
| in(ordered_pair(sK0_skl(A,B),sK1_skl(A,B)),B) )
& ( sK0_skl(A,B) != sK1_skl(A,B)
| ~ in(sK0_skl(A,B),A)
| ~ in(ordered_pair(sK0_skl(A,B),sK1_skl(A,B)),B) ) )
| B = identity_relation(A) )
& ! [A] :
( ( ! [C,D] :
( C != D
| ~ in(C,A)
| in(ordered_pair(C,D),B) )
& ! [C,D] :
( ( C = D
& in(C,A) )
| ~ in(ordered_pair(C,D),B) ) )
| B != identity_relation(A) ) )
| ~ relation(B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(C,sK0_skl(A,B)),skolemize(D,sK1_skl(A,B))],[f237]) ).
fof(f241,plain,
! [X0,X1,X2,X3] :
( X2 != X3
| ~ in(X2,X1)
| in(ordered_pair(X2,X3),X0)
| X0 != identity_relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f238]) ).
fof(f392,plain,
! [A] :
( ! [B,C] :
( ( ( C = apply(A,B)
<=> C = empty_set )
| in(B,relation_dom(A)) )
& ( ( C = apply(A,B)
<=> in(ordered_pair(B,C),A) )
| ~ in(B,relation_dom(A)) ) )
| ~ function(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f393,plain,
! [A] :
( ! [B,C] :
( ( ( ( C != empty_set
| C = apply(A,B) )
& ( C = empty_set
| C != apply(A,B) ) )
| in(B,relation_dom(A)) )
& ( ( ( ~ in(ordered_pair(B,C),A)
| C = apply(A,B) )
& ( in(ordered_pair(B,C),A)
| C != apply(A,B) ) )
| ~ in(B,relation_dom(A)) ) )
| ~ function(A)
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f392]) ).
fof(f394,plain,
! [A] :
( ( ! [B] :
( ( ! [C] :
( C != empty_set
| C = apply(A,B) )
& ! [C] :
( C = empty_set
| C != apply(A,B) ) )
| in(B,relation_dom(A)) )
& ! [B] :
( ( ! [C] :
( ~ in(ordered_pair(B,C),A)
| C = apply(A,B) )
& ! [C] :
( in(ordered_pair(B,C),A)
| C != apply(A,B) ) )
| ~ in(B,relation_dom(A)) ) )
| ~ function(A)
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f393]) ).
fof(f396,plain,
! [X0,X1,X2] :
( ~ in(ordered_pair(X1,X2),X0)
| X2 = apply(X0,X1)
| ~ in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f394]) ).
fof(f483,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f512,plain,
( ! [A] : function(identity_relation(A))
& ! [A] : relation(identity_relation(A)) ),
inference(miniscoping,[status(thm)],[f78]) ).
fof(f514,plain,
! [X0] : function(identity_relation(X0)),
inference(cnf_transformation,[status(thm)],[f512]) ).
fof(f765,plain,
? [A,B] :
( apply(identity_relation(A),B) != B
& in(B,A) ),
inference(pre_NNF_transformation,[status(thm)],[f166]) ).
fof(f766,plain,
( apply(identity_relation(sK66_skl),sK67_skl) != sK67_skl
& in(sK67_skl,sK66_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK66_skl,sK67_skl]),skolemize(A,sK66_skl),skolemize(B,sK67_skl)],[f765]) ).
fof(f767,plain,
in(sK67_skl,sK66_skl),
inference(cnf_transformation,[status(thm)],[f766]) ).
fof(f768,plain,
apply(identity_relation(sK66_skl),sK67_skl) != sK67_skl,
inference(cnf_transformation,[status(thm)],[f766]) ).
fof(f872,plain,
( ! [A] : relation_rng(identity_relation(A)) = A
& ! [A] : relation_dom(identity_relation(A)) = A ),
inference(miniscoping,[status(thm)],[f206]) ).
fof(f873,plain,
! [X0] : relation_dom(identity_relation(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f872]) ).
fof(f943,plain,
! [X0,X1] :
( ~ in(X1,X0)
| in(ordered_pair(X1,X1),identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(destructive_equality_resolution,[status(thm)],[f241]) ).
fof(f1013,plain,
! [X0,X1] :
( ~ in(X0,X1)
| in(ordered_pair(X0,X0),identity_relation(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f943,f483]) ).
fof(f1014,plain,
in(ordered_pair(sK67_skl,sK67_skl),identity_relation(sK66_skl)),
inference(resolution,[status(thm)],[f1013,f767]) ).
fof(f1021,plain,
( sK67_skl = apply(identity_relation(sK66_skl),sK67_skl)
| ~ in(sK67_skl,relation_dom(identity_relation(sK66_skl)))
| ~ function(identity_relation(sK66_skl))
| ~ relation(identity_relation(sK66_skl)) ),
inference(resolution,[status(thm)],[f1014,f396]) ).
fof(f1024,definition,
( sQ0_spl
<=> relation(identity_relation(sK66_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f1026,plain,
( sQ0_spl
| ~ relation(identity_relation(sK66_skl)) ),
inference(component_clause,[status(thm)],[f1024]) ).
fof(f1027,definition,
( sQ1_spl
<=> function(identity_relation(sK66_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f1029,plain,
( sQ1_spl
| ~ function(identity_relation(sK66_skl)) ),
inference(component_clause,[status(thm)],[f1027]) ).
fof(f1030,definition,
( sQ2_spl
<=> in(sK67_skl,relation_dom(identity_relation(sK66_skl))) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f1032,plain,
( sQ2_spl
| ~ in(sK67_skl,relation_dom(identity_relation(sK66_skl))) ),
inference(component_clause,[status(thm)],[f1030]) ).
fof(f1033,definition,
( sQ3_spl
<=> sK67_skl = apply(identity_relation(sK66_skl),sK67_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f1034,plain,
( ~ sQ3_spl
| sK67_skl = apply(identity_relation(sK66_skl),sK67_skl) ),
inference(component_clause,[status(thm)],[f1033]) ).
fof(f1036,plain,
( sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f1021,f1024,f1027,f1030,f1033]) ).
fof(f1037,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1034,f768]) ).
fof(f1038,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f1037]) ).
fof(f1039,plain,
( sQ2_spl
| ~ in(sK67_skl,sK66_skl) ),
inference(forward_demodulation,[status(thm)],[f873,f1032]) ).
fof(f1040,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1039,f767]) ).
fof(f1041,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f1040]) ).
fof(f1042,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1026,f483]) ).
fof(f1043,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f1042]) ).
fof(f1045,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1029,f514]) ).
fof(f1046,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f1045]) ).
fof(f1047,plain,
$false,
inference(sat_refutation,[status(thm)],[f1036,f1038,f1041,f1043,f1046]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU217+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n019.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Mon Sep 21 05:59:05 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 0.12/0.39 % Refutation found
% 0.12/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.42 % Elapsed time: 0.065663 seconds
% 0.12/0.42 % CPU time: 0.173337 seconds
% 0.12/0.42 % Total memory used: 108.540 MB
% 0.12/0.42 % Net memory used: 108.286 MB
%------------------------------------------------------------------------------