%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : HAL003+3 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/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 12:45:12 PM UTC 2026
% Result : Theorem 0.11s 0.43s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 38 ( 8 unt; 3 def)
% Number of atoms : 107 ( 9 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 124 ( 55 ~; 50 |; 12 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 54 ( 47 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [Morphism,Dom,Cod] :
( ( ! [ElCod] :
( element(ElCod,Cod)
=> ? [ElDom] :
( apply(Morphism,ElDom) = ElCod
& element(ElDom,Dom) ) )
& morphism(Morphism,Dom,Cod) )
=> surjection(Morphism) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [Dom,El1,El2] :
( ( element(El2,Dom)
& element(El1,Dom) )
=> element(subtract(Dom,El1,El2),Dom) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
morphism(g,b,e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,axiom,
! [E] :
( element(E,e)
=> ? [B1,B2] :
( apply(g,subtract(b,B1,B2)) = E
& element(B2,b)
& element(B1,b) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,conjecture,
surjection(g),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
~ surjection(g),
inference(negated_conjecture,[status(cth)],[f34]) ).
fof(f53,plain,
! [Morphism,Dom,Cod] :
( surjection(Morphism)
| ? [ElCod] :
( ! [ElDom] :
( apply(Morphism,ElDom) != ElCod
| ~ element(ElDom,Dom) )
& element(ElCod,Cod) )
| ~ morphism(Morphism,Dom,Cod) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f54,plain,
! [Morphism] :
( surjection(Morphism)
| ! [Dom,Cod] :
( ? [ElCod] :
( ! [ElDom] :
( apply(Morphism,ElDom) != ElCod
| ~ element(ElDom,Dom) )
& element(ElCod,Cod) )
| ~ morphism(Morphism,Dom,Cod) ) ),
inference(miniscoping,[status(thm)],[f53]) ).
fof(f55,plain,
! [Morphism] :
( surjection(Morphism)
| ! [Dom,Cod] :
( ( ! [ElDom] :
( apply(Morphism,ElDom) != sK3_skl(Cod,Dom,Morphism)
| ~ element(ElDom,Dom) )
& element(sK3_skl(Cod,Dom,Morphism),Cod) )
| ~ morphism(Morphism,Dom,Cod) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(ElCod,sK3_skl(Cod,Dom,Morphism))],[f54]) ).
fof(f56,plain,
! [X0,X1,X2] :
( surjection(X0)
| element(sK3_skl(X2,X1,X0),X2)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f57,plain,
! [X0,X1,X2,X3] :
( surjection(X0)
| apply(X0,X3) != sK3_skl(X2,X1,X0)
| ~ element(X3,X1)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f83,plain,
! [Dom,El1,El2] :
( element(subtract(Dom,El1,El2),Dom)
| ~ element(El2,Dom)
| ~ element(El1,Dom) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f84,plain,
! [X0,X1,X2] :
( element(subtract(X1,X0,X2),X1)
| ~ element(X2,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f83]) ).
fof(f96,plain,
morphism(g,b,e),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f124,plain,
! [E] :
( ? [B1,B2] :
( apply(g,subtract(b,B1,B2)) = E
& element(B2,b)
& element(B1,b) )
| ~ element(E,e) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f125,plain,
! [E] :
( ( apply(g,subtract(b,sK13_skl(E),sK14_skl(E))) = E
& element(sK14_skl(E),b)
& element(sK13_skl(E),b) )
| ~ element(E,e) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl,sK14_skl]),skolemize(B1,sK13_skl(E)),skolemize(B2,sK14_skl(E))],[f124]) ).
fof(f126,plain,
! [X0] :
( element(sK13_skl(X0),b)
| ~ element(X0,e) ),
inference(cnf_transformation,[status(thm)],[f125]) ).
fof(f127,plain,
! [X0] :
( element(sK14_skl(X0),b)
| ~ element(X0,e) ),
inference(cnf_transformation,[status(thm)],[f125]) ).
fof(f128,plain,
! [X0] :
( apply(g,subtract(b,sK13_skl(X0),sK14_skl(X0))) = X0
| ~ element(X0,e) ),
inference(cnf_transformation,[status(thm)],[f125]) ).
fof(f129,plain,
~ surjection(g),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f147,plain,
! [X0,X1] :
( surjection(g)
| ~ element(subtract(b,sK13_skl(sK3_skl(X0,X1,g)),sK14_skl(sK3_skl(X0,X1,g))),X1)
| ~ morphism(g,X1,X0)
| ~ element(sK3_skl(X0,X1,g),e) ),
inference(resolution,[status(thm)],[f128,f57]) ).
fof(f151,definition,
! [X0,X1] :
( sQ0_spl
<=> ( ~ element(subtract(b,sK13_skl(sK3_skl(X0,X1,g)),sK14_skl(sK3_skl(X0,X1,g))),X1)
| ~ morphism(g,X1,X0)
| ~ element(sK3_skl(X0,X1,g),e) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f152,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ element(subtract(b,sK13_skl(sK3_skl(X0,X1,g)),sK14_skl(sK3_skl(X0,X1,g))),X1)
| ~ morphism(g,X1,X0)
| ~ element(sK3_skl(X0,X1,g),e) ),
inference(component_clause,[status(thm)],[f151]) ).
fof(f154,definition,
( sQ1_spl
<=> surjection(g) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f155,plain,
( ~ sQ1_spl
| surjection(g) ),
inference(component_clause,[status(thm)],[f154]) ).
fof(f157,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f147,f151,f154]) ).
fof(f188,plain,
! [X0] :
( ~ sQ0_spl
| ~ element(sK14_skl(sK3_skl(X0,b,g)),b)
| ~ element(sK13_skl(sK3_skl(X0,b,g)),b)
| ~ morphism(g,b,X0)
| ~ element(sK3_skl(X0,b,g),e) ),
inference(resolution,[status(thm)],[f152,f84]) ).
fof(f189,plain,
! [X0] :
( ~ sQ0_spl
| ~ element(sK14_skl(sK3_skl(X0,b,g)),b)
| ~ morphism(g,b,X0)
| ~ element(sK3_skl(X0,b,g),e) ),
inference(forward_subsumption_resolution,[status(thm)],[f188,f126]) ).
fof(f190,plain,
! [X0] :
( ~ sQ0_spl
| ~ morphism(g,b,X0)
| ~ element(sK3_skl(X0,b,g),e) ),
inference(forward_subsumption_resolution,[status(thm)],[f189,f127]) ).
fof(f191,plain,
( ~ sQ0_spl
| surjection(g)
| ~ morphism(g,b,e)
| ~ morphism(g,b,e) ),
inference(resolution,[status(thm)],[f190,f56]) ).
fof(f192,definition,
( sQ4_spl
<=> morphism(g,b,e) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f194,plain,
( sQ4_spl
| ~ morphism(g,b,e) ),
inference(component_clause,[status(thm)],[f192]) ).
fof(f195,plain,
( ~ sQ0_spl
| sQ1_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f191,f192,f154,f151]) ).
fof(f196,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f155,f129]) ).
fof(f197,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f196]) ).
fof(f198,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f194,f96]) ).
fof(f199,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f198]) ).
fof(f200,plain,
$false,
inference(sat_refutation,[status(thm)],[f157,f195,f197,f199]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HAL003+3 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.39 % Computer : n009.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 20 20:44:28 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.40 % Drodi V4.1.1
% 0.11/0.43 % Refutation found
% 0.11/0.43 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.46 % Elapsed time: 0.067818 seconds
% 0.11/0.46 % CPU time: 0.190373 seconds
% 0.11/0.46 % Total memory used: 83.442 MB
% 0.11/0.46 % Net memory used: 83.315 MB
%------------------------------------------------------------------------------