%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU045+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 : n009.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 02:19:08 PM UTC 2026
% Result : Theorem 0.15s 5.40s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 46 ( 8 unt; 5 def)
% Number of atoms : 191 ( 31 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 233 ( 88 ~; 87 |; 38 &)
% ( 11 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 5 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 80 ( 70 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f19,axiom,
! [A,B] :
( relation(B)
=> relation(relation_rng_restriction(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ( function(relation_rng_restriction(A,B))
& relation(relation_rng_restriction(A,B)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,conjecture,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,relation_dom(relation_rng_restriction(A,C)))
=> apply(relation_rng_restriction(A,C),B) = apply(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
~ ! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,relation_dom(relation_rng_restriction(A,C)))
=> apply(relation_rng_restriction(A,C),B) = apply(C,B) ) ),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f35,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( B = relation_rng_restriction(A,C)
<=> ( ! [D] :
( in(D,relation_dom(B))
=> apply(B,D) = apply(C,D) )
& ! [D] :
( in(D,relation_dom(B))
<=> ( in(apply(C,D),A)
& in(D,relation_dom(C)) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f79,plain,
! [A,B] :
( relation(relation_rng_restriction(A,B))
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f80,plain,
! [B] :
( ! [A] : relation(relation_rng_restriction(A,B))
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f79]) ).
fof(f81,plain,
! [X0,X1] :
( relation(relation_rng_restriction(X1,X0))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f82,plain,
! [A,B] :
( ( function(relation_rng_restriction(A,B))
& relation(relation_rng_restriction(A,B)) )
| ~ function(B)
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f83,plain,
! [B] :
( ( ! [A] : function(relation_rng_restriction(A,B))
& ! [A] : relation(relation_rng_restriction(A,B)) )
| ~ function(B)
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f82]) ).
fof(f85,plain,
! [X0,X1] :
( function(relation_rng_restriction(X1,X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f83]) ).
fof(f122,plain,
? [A,B,C] :
( apply(relation_rng_restriction(A,C),B) != apply(C,B)
& in(B,relation_dom(relation_rng_restriction(A,C)))
& function(C)
& relation(C) ),
inference(pre_NNF_transformation,[status(thm)],[f34]) ).
fof(f123,plain,
? [C] :
( ? [A,B] :
( apply(relation_rng_restriction(A,C),B) != apply(C,B)
& in(B,relation_dom(relation_rng_restriction(A,C))) )
& function(C)
& relation(C) ),
inference(miniscoping,[status(thm)],[f122]) ).
fof(f124,plain,
( apply(relation_rng_restriction(sK12_skl,sK11_skl),sK13_skl) != apply(sK11_skl,sK13_skl)
& in(sK13_skl,relation_dom(relation_rng_restriction(sK12_skl,sK11_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)],[f123]) ).
fof(f125,plain,
relation(sK11_skl),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f126,plain,
function(sK11_skl),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f127,plain,
in(sK13_skl,relation_dom(relation_rng_restriction(sK12_skl,sK11_skl))),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f128,plain,
apply(relation_rng_restriction(sK12_skl,sK11_skl),sK13_skl) != apply(sK11_skl,sK13_skl),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f129,plain,
! [A,B] :
( ! [C] :
( ( B = relation_rng_restriction(A,C)
<=> ( ! [D] :
( apply(B,D) = apply(C,D)
| ~ in(D,relation_dom(B)) )
& ! [D] :
( in(D,relation_dom(B))
<=> ( in(apply(C,D),A)
& in(D,relation_dom(C)) ) ) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f35]) ).
fof(f130,definition,
! [A,C,D] :
( sP0_prd(D,C,A)
<=> ( in(apply(C,D),A)
& in(D,relation_dom(C)) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f131,plain,
! [A,B] :
( ! [C] :
( ( B = relation_rng_restriction(A,C)
<=> ( ! [D] :
( apply(B,D) = apply(C,D)
| ~ in(D,relation_dom(B)) )
& ! [D] :
( in(D,relation_dom(B))
<=> sP0_prd(D,C,A) ) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(formula_renaming,[status(thm)],[f129,f130]) ).
fof(f132,plain,
! [A,B] :
( ! [C] :
( ( ( ? [D] :
( apply(B,D) != apply(C,D)
& in(D,relation_dom(B)) )
| ? [D] :
( ( sP0_prd(D,C,A)
| in(D,relation_dom(B)) )
& ( ~ sP0_prd(D,C,A)
| ~ in(D,relation_dom(B)) ) )
| B = relation_rng_restriction(A,C) )
& ( ( ! [D] :
( apply(B,D) = apply(C,D)
| ~ in(D,relation_dom(B)) )
& ! [D] :
( ( ~ sP0_prd(D,C,A)
| in(D,relation_dom(B)) )
& ( sP0_prd(D,C,A)
| ~ in(D,relation_dom(B)) ) ) )
| B != relation_rng_restriction(A,C) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(NNF_transformation,[status(thm)],[f131]) ).
fof(f133,plain,
! [B] :
( ! [C] :
( ( ! [A] :
( ? [D] :
( apply(B,D) != apply(C,D)
& in(D,relation_dom(B)) )
| ? [D] :
( ( sP0_prd(D,C,A)
| in(D,relation_dom(B)) )
& ( ~ sP0_prd(D,C,A)
| ~ in(D,relation_dom(B)) ) )
| B = relation_rng_restriction(A,C) )
& ! [A] :
( ( ! [D] :
( apply(B,D) = apply(C,D)
| ~ in(D,relation_dom(B)) )
& ! [D] :
( ~ sP0_prd(D,C,A)
| in(D,relation_dom(B)) )
& ! [D] :
( sP0_prd(D,C,A)
| ~ in(D,relation_dom(B)) ) )
| B != relation_rng_restriction(A,C) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f132]) ).
fof(f134,plain,
! [B] :
( ! [C] :
( ( ! [A] :
( ( apply(B,sK15_skl(A,C,B)) != apply(C,sK15_skl(A,C,B))
& in(sK15_skl(A,C,B),relation_dom(B)) )
| ( ( sP0_prd(sK14_skl(A,C,B),C,A)
| in(sK14_skl(A,C,B),relation_dom(B)) )
& ( ~ sP0_prd(sK14_skl(A,C,B),C,A)
| ~ in(sK14_skl(A,C,B),relation_dom(B)) ) )
| B = relation_rng_restriction(A,C) )
& ! [A] :
( ( ! [D] :
( apply(B,D) = apply(C,D)
| ~ in(D,relation_dom(B)) )
& ! [D] :
( ~ sP0_prd(D,C,A)
| in(D,relation_dom(B)) )
& ! [D] :
( sP0_prd(D,C,A)
| ~ in(D,relation_dom(B)) ) )
| B != relation_rng_restriction(A,C) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl,sK15_skl]),skolemize(D,sK14_skl(A,C,B)),skolemize(D,sK15_skl(A,C,B))],[f133]) ).
fof(f137,plain,
! [X0,X1,X2,X3] :
( apply(X0,X3) = apply(X1,X3)
| ~ in(X3,relation_dom(X0))
| X0 != relation_rng_restriction(X2,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f134]) ).
fof(f149,plain,
! [X0,X1,X2] :
( apply(relation_rng_restriction(X0,X1),X2) = apply(X1,X2)
| ~ in(X2,relation_dom(relation_rng_restriction(X0,X1)))
| ~ function(X1)
| ~ relation(X1)
| ~ function(relation_rng_restriction(X0,X1))
| ~ relation(relation_rng_restriction(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f137]) ).
fof(f194,plain,
! [X0,X1,X2] :
( apply(relation_rng_restriction(X0,X1),X2) = apply(X1,X2)
| ~ in(X2,relation_dom(relation_rng_restriction(X0,X1)))
| ~ function(X1)
| ~ relation(X1)
| ~ function(relation_rng_restriction(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f149,f81]) ).
fof(f195,plain,
( apply(relation_rng_restriction(sK12_skl,sK11_skl),sK13_skl) = apply(sK11_skl,sK13_skl)
| ~ function(sK11_skl)
| ~ relation(sK11_skl)
| ~ function(relation_rng_restriction(sK12_skl,sK11_skl)) ),
inference(resolution,[status(thm)],[f194,f127]) ).
fof(f196,definition,
( sQ8_spl
<=> function(relation_rng_restriction(sK12_skl,sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f198,plain,
( sQ8_spl
| ~ function(relation_rng_restriction(sK12_skl,sK11_skl)) ),
inference(component_clause,[status(thm)],[f196]) ).
fof(f199,definition,
( sQ9_spl
<=> relation(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f201,plain,
( sQ9_spl
| ~ relation(sK11_skl) ),
inference(component_clause,[status(thm)],[f199]) ).
fof(f202,definition,
( sQ10_spl
<=> function(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f204,plain,
( sQ10_spl
| ~ function(sK11_skl) ),
inference(component_clause,[status(thm)],[f202]) ).
fof(f205,definition,
( sQ11_spl
<=> apply(relation_rng_restriction(sK12_skl,sK11_skl),sK13_skl) = apply(sK11_skl,sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f206,plain,
( ~ sQ11_spl
| apply(relation_rng_restriction(sK12_skl,sK11_skl),sK13_skl) = apply(sK11_skl,sK13_skl) ),
inference(component_clause,[status(thm)],[f205]) ).
fof(f208,plain,
( sQ11_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f195,f196,f199,f202,f205]) ).
fof(f209,plain,
( ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f206,f128]) ).
fof(f210,plain,
~ sQ11_spl,
inference(contradiction_clause,[status(thm)],[f209]) ).
fof(f211,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f204,f126]) ).
fof(f212,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f211]) ).
fof(f213,plain,
( sQ8_spl
| ~ function(sK11_skl)
| ~ relation(sK11_skl) ),
inference(resolution,[status(thm)],[f198,f85]) ).
fof(f215,plain,
( sQ8_spl
| ~ sQ10_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f213,f199,f202,f196]) ).
fof(f216,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f201,f125]) ).
fof(f217,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f216]) ).
fof(f218,plain,
$false,
inference(sat_refutation,[status(thm)],[f208,f210,f212,f215,f217]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU045+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/5.38 % Computer : n009.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Mon Sep 21 05:48:18 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.40 % Drodi V4.1.1
% 0.15/5.40 % Refutation found
% 0.15/5.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/5.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/5.43 % Elapsed time: 0.038635 seconds
% 0.15/5.43 % CPU time: 0.080610 seconds
% 0.15/5.43 % Total memory used: 10.282 MB
% 0.15/5.43 % Net memory used: 10.275 MB
%------------------------------------------------------------------------------