%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU223+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 02:19:46 PM UTC 2026
% Result : Theorem 0.13s 20.45s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 59 ( 10 unt; 5 def)
% Number of atoms : 188 ( 34 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 217 ( 88 ~; 82 |; 29 &)
% ( 7 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 6 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 83 ( 75 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [A,B] :
( relation(A)
=> relation(relation_dom_restriction(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [A,B] :
( ( function(A)
& relation(A) )
=> ( function(relation_dom_restriction(A,B))
& relation(relation_dom_restriction(A,B)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,conjecture,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,relation_dom(relation_dom_restriction(C,A)))
=> apply(relation_dom_restriction(C,A),B) = apply(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
~ ! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,relation_dom(relation_dom_restriction(C,A)))
=> apply(relation_dom_restriction(C,A),B) = apply(C,B) ) ),
inference(negated_conjecture,[status(cth)],[f38]) ).
fof(f40,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( B = relation_dom_restriction(C,A)
<=> ( ! [D] :
( in(D,relation_dom(B))
=> apply(B,D) = apply(C,D) )
& relation_dom(B) = set_intersection2(relation_dom(C),A) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f70,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f71,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f92,plain,
! [A,B] :
( relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f93,plain,
! [A] :
( ! [B] : relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f92]) ).
fof(f94,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f93]) ).
fof(f95,plain,
! [A,B] :
( ( function(relation_dom_restriction(A,B))
& relation(relation_dom_restriction(A,B)) )
| ~ function(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f96,plain,
! [A] :
( ( ! [B] : function(relation_dom_restriction(A,B))
& ! [B] : relation(relation_dom_restriction(A,B)) )
| ~ function(A)
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f95]) ).
fof(f98,plain,
! [X0,X1] :
( function(relation_dom_restriction(X0,X1))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f96]) ).
fof(f132,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f36]) ).
fof(f133,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f134,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f135,plain,
! [B] :
( ~ empty(B)
| ! [A] : ~ in(A,B) ),
inference(miniscoping,[status(thm)],[f134]) ).
fof(f136,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f137,plain,
? [A,B,C] :
( apply(relation_dom_restriction(C,A),B) != apply(C,B)
& in(B,relation_dom(relation_dom_restriction(C,A)))
& function(C)
& relation(C) ),
inference(pre_NNF_transformation,[status(thm)],[f39]) ).
fof(f138,plain,
? [C] :
( ? [A,B] :
( apply(relation_dom_restriction(C,A),B) != apply(C,B)
& in(B,relation_dom(relation_dom_restriction(C,A))) )
& function(C)
& relation(C) ),
inference(miniscoping,[status(thm)],[f137]) ).
fof(f139,plain,
( apply(relation_dom_restriction(sK11_skl,sK12_skl),sK13_skl) != apply(sK11_skl,sK13_skl)
& in(sK13_skl,relation_dom(relation_dom_restriction(sK11_skl,sK12_skl)))
& function(sK11_skl)
& relation(sK11_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl,sK12_skl,sK13_skl]),skolemize(C,sK11_skl),skolemize(A,sK12_skl),skolemize(B,sK13_skl)],[f138]) ).
fof(f140,plain,
relation(sK11_skl),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f141,plain,
function(sK11_skl),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f142,plain,
in(sK13_skl,relation_dom(relation_dom_restriction(sK11_skl,sK12_skl))),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f143,plain,
apply(relation_dom_restriction(sK11_skl,sK12_skl),sK13_skl) != apply(sK11_skl,sK13_skl),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f144,plain,
! [A,B] :
( ! [C] :
( ( B = relation_dom_restriction(C,A)
<=> ( ! [D] :
( apply(B,D) = apply(C,D)
| ~ in(D,relation_dom(B)) )
& relation_dom(B) = set_intersection2(relation_dom(C),A) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f40]) ).
fof(f145,plain,
! [A,B] :
( ! [C] :
( ( ( ? [D] :
( apply(B,D) != apply(C,D)
& in(D,relation_dom(B)) )
| relation_dom(B) != set_intersection2(relation_dom(C),A)
| B = relation_dom_restriction(C,A) )
& ( ( ! [D] :
( apply(B,D) = apply(C,D)
| ~ in(D,relation_dom(B)) )
& relation_dom(B) = set_intersection2(relation_dom(C),A) )
| B != relation_dom_restriction(C,A) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(NNF_transformation,[status(thm)],[f144]) ).
fof(f146,plain,
! [B] :
( ! [C] :
( ( ! [A] :
( ? [D] :
( apply(B,D) != apply(C,D)
& in(D,relation_dom(B)) )
| relation_dom(B) != set_intersection2(relation_dom(C),A)
| B = relation_dom_restriction(C,A) )
& ! [A] :
( ( ! [D] :
( apply(B,D) = apply(C,D)
| ~ in(D,relation_dom(B)) )
& relation_dom(B) = set_intersection2(relation_dom(C),A) )
| B != relation_dom_restriction(C,A) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f145]) ).
fof(f147,plain,
! [B] :
( ! [C] :
( ( ! [A] :
( ( apply(B,sK14_skl(A,C,B)) != apply(C,sK14_skl(A,C,B))
& in(sK14_skl(A,C,B),relation_dom(B)) )
| relation_dom(B) != set_intersection2(relation_dom(C),A)
| B = relation_dom_restriction(C,A) )
& ! [A] :
( ( ! [D] :
( apply(B,D) = apply(C,D)
| ~ in(D,relation_dom(B)) )
& relation_dom(B) = set_intersection2(relation_dom(C),A) )
| B != relation_dom_restriction(C,A) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl]),skolemize(D,sK14_skl(A,C,B))],[f146]) ).
fof(f149,plain,
! [X0,X1,X2,X3] :
( apply(X0,X3) = apply(X1,X3)
| ~ in(X3,relation_dom(X0))
| X0 != relation_dom_restriction(X1,X2)
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f147]) ).
fof(f153,plain,
! [X0,X1,X2] :
( apply(relation_dom_restriction(X0,X1),X2) = apply(X0,X2)
| ~ in(X2,relation_dom(relation_dom_restriction(X0,X1)))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1))
| ~ relation(relation_dom_restriction(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f149]) ).
fof(f154,plain,
~ empty(relation_dom(relation_dom_restriction(sK11_skl,sK12_skl))),
inference(resolution,[status(thm)],[f136,f142]) ).
fof(f158,plain,
element(sK13_skl,relation_dom(relation_dom_restriction(sK11_skl,sK12_skl))),
inference(resolution,[status(thm)],[f133,f142]) ).
fof(f186,plain,
( in(sK13_skl,relation_dom(relation_dom_restriction(sK11_skl,sK12_skl)))
| empty(relation_dom(relation_dom_restriction(sK11_skl,sK12_skl))) ),
inference(resolution,[status(thm)],[f158,f71]) ).
fof(f187,definition,
( sQ4_spl
<=> empty(relation_dom(relation_dom_restriction(sK11_skl,sK12_skl))) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f188,plain,
( ~ sQ4_spl
| empty(relation_dom(relation_dom_restriction(sK11_skl,sK12_skl))) ),
inference(component_clause,[status(thm)],[f187]) ).
fof(f190,definition,
( sQ5_spl
<=> in(sK13_skl,relation_dom(relation_dom_restriction(sK11_skl,sK12_skl))) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f193,plain,
( sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f186,f187,f190]) ).
fof(f194,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f188,f154]) ).
fof(f195,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f194]) ).
fof(f196,plain,
! [X0,X1,X2] :
( apply(relation_dom_restriction(X0,X1),X2) = apply(X0,X2)
| ~ in(X2,relation_dom(relation_dom_restriction(X0,X1)))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f153,f94]) ).
fof(f197,plain,
( ~ in(sK13_skl,relation_dom(relation_dom_restriction(sK11_skl,sK12_skl)))
| ~ function(sK11_skl)
| ~ relation(sK11_skl)
| ~ function(relation_dom_restriction(sK11_skl,sK12_skl)) ),
inference(resolution,[status(thm)],[f196,f143]) ).
fof(f198,definition,
( sQ6_spl
<=> function(relation_dom_restriction(sK11_skl,sK12_skl)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f200,plain,
( sQ6_spl
| ~ function(relation_dom_restriction(sK11_skl,sK12_skl)) ),
inference(component_clause,[status(thm)],[f198]) ).
fof(f201,definition,
( sQ7_spl
<=> relation(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f203,plain,
( sQ7_spl
| ~ relation(sK11_skl) ),
inference(component_clause,[status(thm)],[f201]) ).
fof(f204,definition,
( sQ8_spl
<=> function(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f206,plain,
( sQ8_spl
| ~ function(sK11_skl) ),
inference(component_clause,[status(thm)],[f204]) ).
fof(f207,plain,
( ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f197,f198,f201,f204,f190]) ).
fof(f208,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f206,f141]) ).
fof(f209,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f208]) ).
fof(f210,plain,
( sQ6_spl
| ~ function(sK11_skl)
| ~ relation(sK11_skl) ),
inference(resolution,[status(thm)],[f200,f98]) ).
fof(f211,plain,
( sQ6_spl
| ~ sQ8_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f210,f201,f204,f198]) ).
fof(f212,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f203,f140]) ).
fof(f213,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f212]) ).
fof(f214,plain,
$false,
inference(sat_refutation,[status(thm)],[f193,f195,f207,f209,f211,f213]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU223+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/20.42 % Computer : n026.cluster.edu
% 0.13/20.42 % Model : x86_64 x86_64
% 0.13/20.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/20.42 % Memory : 8046.5625MB
% 0.13/20.42 % OS : Linux 6.8.0-71-generic
% 0.13/20.42 % CPULimit : 300
% 0.13/20.42 % WCLimit : 300
% 0.13/20.42 % DateTime : Mon Sep 21 06:03:12 UTC 2026
% 0.13/20.43 % CPUTime :
% 0.13/20.44 % Drodi V4.1.1
% 0.13/20.45 % Refutation found
% 0.13/20.45 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/20.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/20.55 % Elapsed time: 0.115205 seconds
% 0.18/20.55 % CPU time: 0.098073 seconds
% 0.18/20.55 % Total memory used: 3.268 MB
% 0.18/20.55 % Net memory used: 3.267 MB
%------------------------------------------------------------------------------