%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : HAL002+1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 0.30s 0.66s
% Output : CNFRefutation 0.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 32
% Syntax : Number of formulae : 150 ( 5 unt; 21 def)
% Number of atoms : 446 ( 118 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 505 ( 209 ~; 226 |; 31 &)
% ( 23 <=>; 15 =>; 0 <=; 1 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 27 ( 25 usr; 22 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 159 ( 153 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [Morphism,Dom,Cod] :
( morphism(Morphism,Dom,Cod)
=> ( apply(Morphism,zero(Dom)) = zero(Cod)
& ! [El] :
( element(El,Dom)
=> element(apply(Morphism,El),Cod) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [Morphism,Dom,Cod] :
( ( morphism(Morphism,Dom,Cod)
& injection(Morphism) )
=> ! [El1,El2] :
( ( apply(Morphism,El1) = apply(Morphism,El2)
& element(El2,Dom)
& element(El1,Dom) )
=> El1 = El2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [Morphism,Dom,Cod] :
( ( ! [El1,El2] :
( ( apply(Morphism,El1) = apply(Morphism,El2)
& element(El2,Dom)
& element(El1,Dom) )
=> El1 = El2 )
& morphism(Morphism,Dom,Cod) )
=> injection(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(f11,axiom,
! [Dom,El] :
( element(El,Dom)
=> subtract(Dom,El,El) = zero(Dom) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [Dom,El1,El2] :
( ( element(El2,Dom)
& element(El1,Dom) )
=> subtract(Dom,El1,subtract(Dom,El1,El2)) = El2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [Morphism,Dom,Cod] :
( morphism(Morphism,Dom,Cod)
=> ! [El1,El2] :
( ( element(El2,Dom)
& element(El1,Dom) )
=> apply(Morphism,subtract(Dom,El1,El2)) = subtract(Cod,apply(Morphism,El1),apply(Morphism,El2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [Morphism,Dom,Cod] :
( ( morphism(Morphism,Dom,Cod)
& injection_2(Morphism) )
=> ! [El] :
( ( apply(Morphism,El) = zero(Cod)
& element(El,Dom) )
=> El = zero(Dom) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [Morphism,Dom,Cod] :
( ( ! [El] :
( ( apply(Morphism,El) = zero(Cod)
& element(El,Dom) )
=> El = zero(Dom) )
& morphism(Morphism,Dom,Cod) )
=> injection_2(Morphism) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,hypothesis,
morphism(x,any1,any2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,conjecture,
( injection(x)
<=> injection_2(x) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ( injection(x)
<=> injection_2(x) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
! [Morphism,Dom,Cod] :
( ( apply(Morphism,zero(Dom)) = zero(Cod)
& ! [El] :
( element(apply(Morphism,El),Cod)
| ~ element(El,Dom) ) )
| ~ morphism(Morphism,Dom,Cod) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f20,plain,
! [X0,X1,X2,X3] :
( element(apply(X0,X3),X2)
| ~ element(X3,X1)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f21,plain,
! [X0,X1,X2] :
( apply(X0,zero(X1)) = zero(X2)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f22,plain,
! [Morphism,Dom,Cod] :
( ! [El1,El2] :
( El1 = El2
| apply(Morphism,El1) != apply(Morphism,El2)
| ~ element(El2,Dom)
| ~ element(El1,Dom) )
| ~ morphism(Morphism,Dom,Cod)
| ~ injection(Morphism) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f23,plain,
! [Morphism,Dom] :
( ! [El1,El2] :
( El1 = El2
| apply(Morphism,El1) != apply(Morphism,El2)
| ~ element(El2,Dom)
| ~ element(El1,Dom) )
| ! [Cod] : ~ morphism(Morphism,Dom,Cod)
| ~ injection(Morphism) ),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f24,plain,
! [X0,X1,X2,X3,X4] :
( X3 = X4
| apply(X0,X3) != apply(X0,X4)
| ~ element(X4,X1)
| ~ element(X3,X1)
| ~ morphism(X0,X1,X2)
| ~ injection(X0) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f25,plain,
! [Morphism,Dom,Cod] :
( injection(Morphism)
| ? [El1,El2] :
( El1 != El2
& apply(Morphism,El1) = apply(Morphism,El2)
& element(El2,Dom)
& element(El1,Dom) )
| ~ morphism(Morphism,Dom,Cod) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f26,plain,
! [Morphism] :
( injection(Morphism)
| ! [Dom] :
( ? [El1,El2] :
( El1 != El2
& apply(Morphism,El1) = apply(Morphism,El2)
& element(El2,Dom)
& element(El1,Dom) )
| ! [Cod] : ~ morphism(Morphism,Dom,Cod) ) ),
inference(miniscoping,[status(thm)],[f25]) ).
fof(f27,plain,
! [Morphism] :
( injection(Morphism)
| ! [Dom] :
( ( sK0_skl(Dom,Morphism) != sK1_skl(Dom,Morphism)
& apply(Morphism,sK0_skl(Dom,Morphism)) = apply(Morphism,sK1_skl(Dom,Morphism))
& element(sK1_skl(Dom,Morphism),Dom)
& element(sK0_skl(Dom,Morphism),Dom) )
| ! [Cod] : ~ morphism(Morphism,Dom,Cod) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(El1,sK0_skl(Dom,Morphism)),skolemize(El2,sK1_skl(Dom,Morphism))],[f26]) ).
fof(f28,plain,
! [X0,X1,X2] :
( injection(X0)
| element(sK0_skl(X1,X0),X1)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f29,plain,
! [X0,X1,X2] :
( injection(X0)
| element(sK1_skl(X1,X0),X1)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f30,plain,
! [X0,X1,X2] :
( injection(X0)
| apply(X0,sK0_skl(X1,X0)) = apply(X0,sK1_skl(X1,X0))
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f31,plain,
! [X0,X1,X2] :
( injection(X0)
| sK0_skl(X1,X0) != sK1_skl(X1,X0)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f66,plain,
! [Dom,El1,El2] :
( element(subtract(Dom,El1,El2),Dom)
| ~ element(El2,Dom)
| ~ element(El1,Dom) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f67,plain,
! [X0,X1,X2] :
( element(subtract(X1,X0,X2),X1)
| ~ element(X2,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f68,plain,
! [Dom,El] :
( subtract(Dom,El,El) = zero(Dom)
| ~ element(El,Dom) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f69,plain,
! [X0,X1] :
( subtract(X1,X0,X0) = zero(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f70,plain,
! [Dom,El1,El2] :
( subtract(Dom,El1,subtract(Dom,El1,El2)) = El2
| ~ element(El2,Dom)
| ~ element(El1,Dom) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f71,plain,
! [X0,X1,X2] :
( subtract(X1,X0,subtract(X1,X0,X2)) = X2
| ~ element(X2,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f72,plain,
! [Morphism,Dom,Cod] :
( ! [El1,El2] :
( apply(Morphism,subtract(Dom,El1,El2)) = subtract(Cod,apply(Morphism,El1),apply(Morphism,El2))
| ~ element(El2,Dom)
| ~ element(El1,Dom) )
| ~ morphism(Morphism,Dom,Cod) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f73,plain,
! [X0,X1,X2,X3,X4] :
( apply(X0,subtract(X1,X3,X4)) = subtract(X2,apply(X0,X3),apply(X0,X4))
| ~ element(X4,X1)
| ~ element(X3,X1)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f74,plain,
! [Morphism,Dom,Cod] :
( ! [El] :
( El = zero(Dom)
| apply(Morphism,El) != zero(Cod)
| ~ element(El,Dom) )
| ~ morphism(Morphism,Dom,Cod)
| ~ injection_2(Morphism) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f75,plain,
! [X0,X1,X2,X3] :
( X3 = zero(X1)
| apply(X0,X3) != zero(X2)
| ~ element(X3,X1)
| ~ morphism(X0,X1,X2)
| ~ injection_2(X0) ),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f76,plain,
! [Morphism,Dom,Cod] :
( injection_2(Morphism)
| ? [El] :
( El != zero(Dom)
& apply(Morphism,El) = zero(Cod)
& element(El,Dom) )
| ~ morphism(Morphism,Dom,Cod) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f77,plain,
! [Morphism] :
( injection_2(Morphism)
| ! [Dom,Cod] :
( ? [El] :
( El != zero(Dom)
& apply(Morphism,El) = zero(Cod)
& element(El,Dom) )
| ~ morphism(Morphism,Dom,Cod) ) ),
inference(miniscoping,[status(thm)],[f76]) ).
fof(f78,plain,
! [Morphism] :
( injection_2(Morphism)
| ! [Dom,Cod] :
( ( sK8_skl(Cod,Dom,Morphism) != zero(Dom)
& apply(Morphism,sK8_skl(Cod,Dom,Morphism)) = zero(Cod)
& element(sK8_skl(Cod,Dom,Morphism),Dom) )
| ~ morphism(Morphism,Dom,Cod) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl]),skolemize(El,sK8_skl(Cod,Dom,Morphism))],[f77]) ).
fof(f79,plain,
! [X0,X1,X2] :
( injection_2(X0)
| element(sK8_skl(X2,X1,X0),X1)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f80,plain,
! [X0,X1,X2] :
( injection_2(X0)
| apply(X0,sK8_skl(X2,X1,X0)) = zero(X2)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f81,plain,
! [X0,X1,X2] :
( injection_2(X0)
| sK8_skl(X2,X1,X0) != zero(X1)
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f82,plain,
morphism(x,any1,any2),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f83,plain,
( injection(x)
<~> injection_2(x) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f84,plain,
( ( ~ injection_2(x)
| ~ injection(x) )
& ( injection_2(x)
| injection(x) ) ),
inference(NNF_transformation,[status(thm)],[f83]) ).
fof(f85,plain,
( injection_2(x)
| injection(x) ),
inference(cnf_transformation,[status(thm)],[f84]) ).
fof(f86,plain,
( ~ injection_2(x)
| ~ injection(x) ),
inference(cnf_transformation,[status(thm)],[f84]) ).
fof(f92,definition,
( sQ0_spl
<=> injection(x) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f95,definition,
( sQ1_spl
<=> injection_2(x) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f98,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f85,f92,f95]) ).
fof(f99,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f86,f92,f95]) ).
fof(f102,plain,
! [X0] :
( X0 = zero(any1)
| apply(x,X0) != zero(any2)
| ~ element(X0,any1)
| ~ injection_2(x) ),
inference(resolution,[status(thm)],[f82,f75]) ).
fof(f103,plain,
! [X0,X1] :
( X0 = X1
| apply(x,X0) != apply(x,X1)
| ~ element(X1,any1)
| ~ element(X0,any1)
| ~ injection(x) ),
inference(resolution,[status(thm)],[f82,f24]) ).
fof(f104,definition,
! [X0] :
( sQ2_spl
<=> ( X0 = zero(any1)
| apply(x,X0) != zero(any2)
| ~ element(X0,any1) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f105,plain,
! [X0] :
( ~ sQ2_spl
| X0 = zero(any1)
| apply(x,X0) != zero(any2)
| ~ element(X0,any1) ),
inference(component_clause,[status(thm)],[f104]) ).
fof(f107,plain,
( sQ2_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f102,f95,f104]) ).
fof(f108,definition,
! [X0,X1] :
( sQ3_spl
<=> ( X0 = X1
| apply(x,X0) != apply(x,X1)
| ~ element(X1,any1)
| ~ element(X0,any1) ) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f109,plain,
! [X0,X1] :
( ~ sQ3_spl
| X0 = X1
| apply(x,X0) != apply(x,X1)
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(component_clause,[status(thm)],[f108]) ).
fof(f111,plain,
( sQ3_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f103,f92,f108]) ).
fof(f112,plain,
! [X0] :
( element(apply(x,X0),any2)
| ~ element(X0,any1) ),
inference(resolution,[status(thm)],[f20,f82]) ).
fof(f113,plain,
apply(x,zero(any1)) = zero(any2),
inference(resolution,[status(thm)],[f21,f82]) ).
fof(f114,plain,
( injection(x)
| element(sK0_skl(any1,x),any1) ),
inference(resolution,[status(thm)],[f28,f82]) ).
fof(f115,definition,
( sQ4_spl
<=> element(sK0_skl(any1,x),any1) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f116,plain,
( ~ sQ4_spl
| element(sK0_skl(any1,x),any1) ),
inference(component_clause,[status(thm)],[f115]) ).
fof(f118,plain,
( sQ0_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f114,f115,f92]) ).
fof(f120,definition,
( sQ5_spl
<=> apply(x,sK0_skl(any1,x)) = zero(any2) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f122,plain,
( sQ5_spl
| apply(x,sK0_skl(any1,x)) != zero(any2) ),
inference(component_clause,[status(thm)],[f120]) ).
fof(f123,definition,
( sQ6_spl
<=> sK0_skl(any1,x) = zero(any1) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f124,plain,
( ~ sQ6_spl
| sK0_skl(any1,x) = zero(any1) ),
inference(component_clause,[status(thm)],[f123]) ).
fof(f128,plain,
( injection(x)
| element(sK1_skl(any1,x),any1) ),
inference(resolution,[status(thm)],[f29,f82]) ).
fof(f129,definition,
( sQ7_spl
<=> element(sK1_skl(any1,x),any1) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f130,plain,
( ~ sQ7_spl
| element(sK1_skl(any1,x),any1) ),
inference(component_clause,[status(thm)],[f129]) ).
fof(f132,plain,
( sQ0_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f128,f129,f92]) ).
fof(f133,plain,
( injection(x)
| apply(x,sK0_skl(any1,x)) = apply(x,sK1_skl(any1,x)) ),
inference(resolution,[status(thm)],[f30,f82]) ).
fof(f134,definition,
( sQ8_spl
<=> apply(x,sK0_skl(any1,x)) = apply(x,sK1_skl(any1,x)) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f135,plain,
( ~ sQ8_spl
| apply(x,sK0_skl(any1,x)) = apply(x,sK1_skl(any1,x)) ),
inference(component_clause,[status(thm)],[f134]) ).
fof(f137,plain,
( sQ0_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f133,f134,f92]) ).
fof(f138,plain,
( injection(x)
| sK0_skl(any1,x) != sK1_skl(any1,x) ),
inference(resolution,[status(thm)],[f31,f82]) ).
fof(f139,definition,
( sQ9_spl
<=> sK0_skl(any1,x) = sK1_skl(any1,x) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f141,plain,
( sQ9_spl
| sK0_skl(any1,x) != sK1_skl(any1,x) ),
inference(component_clause,[status(thm)],[f139]) ).
fof(f142,plain,
( sQ0_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f138,f139,f92]) ).
fof(f167,plain,
( ~ sQ7_spl
| subtract(any1,sK1_skl(any1,x),sK1_skl(any1,x)) = zero(any1) ),
inference(resolution,[status(thm)],[f130,f69]) ).
fof(f181,plain,
! [X0,X1] :
( apply(x,subtract(any1,X0,X1)) = subtract(any2,apply(x,X0),apply(x,X1))
| ~ element(X1,any1)
| ~ element(X0,any1) ),
inference(resolution,[status(thm)],[f73,f82]) ).
fof(f182,plain,
( injection_2(x)
| element(sK8_skl(any2,any1,x),any1) ),
inference(resolution,[status(thm)],[f79,f82]) ).
fof(f183,definition,
( sQ16_spl
<=> element(sK8_skl(any2,any1,x),any1) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f184,plain,
( ~ sQ16_spl
| element(sK8_skl(any2,any1,x),any1) ),
inference(component_clause,[status(thm)],[f183]) ).
fof(f186,plain,
( sQ1_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f182,f183,f95]) ).
fof(f187,plain,
( injection_2(x)
| apply(x,sK8_skl(any2,any1,x)) = zero(any2) ),
inference(resolution,[status(thm)],[f80,f82]) ).
fof(f188,definition,
( sQ17_spl
<=> apply(x,sK8_skl(any2,any1,x)) = zero(any2) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f189,plain,
( ~ sQ17_spl
| apply(x,sK8_skl(any2,any1,x)) = zero(any2) ),
inference(component_clause,[status(thm)],[f188]) ).
fof(f191,plain,
( sQ1_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f187,f188,f95]) ).
fof(f192,plain,
( injection_2(x)
| sK8_skl(any2,any1,x) != zero(any1) ),
inference(resolution,[status(thm)],[f81,f82]) ).
fof(f193,definition,
( sQ18_spl
<=> sK8_skl(any2,any1,x) = zero(any1) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f196,plain,
( sQ1_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f192,f193,f95]) ).
fof(f202,plain,
( ~ sQ4_spl
| element(apply(x,sK0_skl(any1,x)),any2) ),
inference(resolution,[status(thm)],[f112,f116]) ).
fof(f208,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ16_spl
| sK8_skl(any2,any1,x) = X0
| apply(x,sK8_skl(any2,any1,x)) != apply(x,X0)
| ~ element(X0,any1) ),
inference(resolution,[status(thm)],[f184,f109]) ).
fof(f213,plain,
! [X0] :
( ~ sQ16_spl
| element(subtract(any1,sK8_skl(any2,any1,x),X0),any1)
| ~ element(X0,any1) ),
inference(resolution,[status(thm)],[f184,f67]) ).
fof(f214,plain,
( ~ sQ16_spl
| subtract(any1,sK8_skl(any2,any1,x),sK8_skl(any2,any1,x)) = zero(any1) ),
inference(resolution,[status(thm)],[f184,f69]) ).
fof(f215,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ16_spl
| ~ sQ17_spl
| sK8_skl(any2,any1,x) = X0
| zero(any2) != apply(x,X0)
| ~ element(X0,any1) ),
inference(forward_demodulation,[status(thm)],[f189,f208]) ).
fof(f270,plain,
( ~ sQ16_spl
| element(subtract(any1,sK8_skl(any2,any1,x),sK8_skl(any2,any1,x)),any1) ),
inference(resolution,[status(thm)],[f213,f184]) ).
fof(f271,plain,
( ~ sQ16_spl
| element(zero(any1),any1) ),
inference(forward_demodulation,[status(thm)],[f214,f270]) ).
fof(f275,plain,
( ~ sQ3_spl
| ~ sQ16_spl
| ~ sQ17_spl
| sK8_skl(any2,any1,x) = zero(any1)
| zero(any2) != apply(x,zero(any1)) ),
inference(resolution,[status(thm)],[f271,f215]) ).
fof(f286,definition,
( sQ22_spl
<=> zero(any2) = apply(x,zero(any1)) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f288,plain,
( sQ22_spl
| zero(any2) != apply(x,zero(any1)) ),
inference(component_clause,[status(thm)],[f286]) ).
fof(f289,plain,
( ~ sQ3_spl
| ~ sQ16_spl
| ~ sQ17_spl
| sQ18_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f275,f286,f193,f188,f183,f108]) ).
fof(f293,plain,
( sQ22_spl
| zero(any2) != zero(any2) ),
inference(forward_demodulation,[status(thm)],[f113,f288]) ).
fof(f294,plain,
( sQ22_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f293]) ).
fof(f295,plain,
sQ22_spl,
inference(contradiction_clause,[status(thm)],[f294]) ).
fof(f297,plain,
( sQ5_spl
| ~ sQ6_spl
| apply(x,zero(any1)) != zero(any2) ),
inference(backward_demodulation,[status(thm)],[f124,f122]) ).
fof(f312,plain,
( sQ5_spl
| ~ sQ6_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f297,f286,f123,f120]) ).
fof(f314,plain,
! [X0] :
( ~ sQ7_spl
| apply(x,subtract(any1,sK1_skl(any1,x),X0)) = subtract(any2,apply(x,sK1_skl(any1,x)),apply(x,X0))
| ~ element(X0,any1) ),
inference(resolution,[status(thm)],[f130,f181]) ).
fof(f318,plain,
! [X0] :
( ~ sQ7_spl
| subtract(any1,sK1_skl(any1,x),subtract(any1,sK1_skl(any1,x),X0)) = X0
| ~ element(X0,any1) ),
inference(resolution,[status(thm)],[f130,f71]) ).
fof(f319,plain,
! [X0] :
( ~ sQ7_spl
| element(subtract(any1,sK1_skl(any1,x),X0),any1)
| ~ element(X0,any1) ),
inference(resolution,[status(thm)],[f130,f67]) ).
fof(f321,definition,
( sQ23_spl
<=> apply(x,sK1_skl(any1,x)) = zero(any2) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f323,plain,
( sQ23_spl
| apply(x,sK1_skl(any1,x)) != zero(any2) ),
inference(component_clause,[status(thm)],[f321]) ).
fof(f328,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ8_spl
| apply(x,subtract(any1,sK1_skl(any1,x),X0)) = subtract(any2,apply(x,sK0_skl(any1,x)),apply(x,X0))
| ~ element(X0,any1) ),
inference(forward_demodulation,[status(thm)],[f135,f314]) ).
fof(f331,plain,
( sQ23_spl
| ~ sQ8_spl
| apply(x,sK0_skl(any1,x)) != zero(any2) ),
inference(forward_demodulation,[status(thm)],[f135,f323]) ).
fof(f345,plain,
( sQ23_spl
| ~ sQ8_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f331,f120,f134,f321]) ).
fof(f394,plain,
( ~ sQ4_spl
| subtract(any2,apply(x,sK0_skl(any1,x)),apply(x,sK0_skl(any1,x))) = zero(any2) ),
inference(resolution,[status(thm)],[f202,f69]) ).
fof(f395,plain,
( ~ sQ4_spl
| ~ sQ7_spl
| element(subtract(any1,sK1_skl(any1,x),sK0_skl(any1,x)),any1) ),
inference(resolution,[status(thm)],[f319,f116]) ).
fof(f398,plain,
( ~ sQ4_spl
| ~ sQ7_spl
| subtract(any1,sK1_skl(any1,x),subtract(any1,sK1_skl(any1,x),sK0_skl(any1,x))) = sK0_skl(any1,x) ),
inference(resolution,[status(thm)],[f318,f116]) ).
fof(f399,plain,
( ~ sQ7_spl
| subtract(any1,sK1_skl(any1,x),subtract(any1,sK1_skl(any1,x),sK1_skl(any1,x))) = sK1_skl(any1,x) ),
inference(resolution,[status(thm)],[f318,f130]) ).
fof(f400,plain,
( ~ sQ7_spl
| subtract(any1,sK1_skl(any1,x),zero(any1)) = sK1_skl(any1,x) ),
inference(forward_demodulation,[status(thm)],[f167,f399]) ).
fof(f432,plain,
( ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| apply(x,subtract(any1,sK1_skl(any1,x),sK0_skl(any1,x))) = subtract(any2,apply(x,sK0_skl(any1,x)),apply(x,sK0_skl(any1,x))) ),
inference(resolution,[status(thm)],[f328,f116]) ).
fof(f437,plain,
( ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| apply(x,subtract(any1,sK1_skl(any1,x),sK0_skl(any1,x))) = zero(any2) ),
inference(forward_demodulation,[status(thm)],[f394,f432]) ).
fof(f482,definition,
( sQ26_spl
<=> apply(x,subtract(any1,zero(any1),sK0_skl(any1,x))) = zero(any2) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f484,plain,
( sQ26_spl
| apply(x,subtract(any1,zero(any1),sK0_skl(any1,x))) != zero(any2) ),
inference(component_clause,[status(thm)],[f482]) ).
fof(f485,definition,
( sQ27_spl
<=> subtract(any1,zero(any1),sK0_skl(any1,x)) = zero(any1) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f486,plain,
( ~ sQ27_spl
| subtract(any1,zero(any1),sK0_skl(any1,x)) = zero(any1) ),
inference(component_clause,[status(thm)],[f485]) ).
fof(f490,plain,
( sQ26_spl
| ~ sQ27_spl
| apply(x,zero(any1)) != zero(any2) ),
inference(backward_demodulation,[status(thm)],[f486,f484]) ).
fof(f505,plain,
( sQ26_spl
| ~ sQ27_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f490,f286,f485,f482]) ).
fof(f538,definition,
( sQ28_spl
<=> apply(x,subtract(any1,zero(any1),sK1_skl(any1,x))) = zero(any2) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f540,plain,
( sQ28_spl
| apply(x,subtract(any1,zero(any1),sK1_skl(any1,x))) != zero(any2) ),
inference(component_clause,[status(thm)],[f538]) ).
fof(f541,definition,
( sQ29_spl
<=> subtract(any1,zero(any1),sK1_skl(any1,x)) = zero(any1) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f542,plain,
( ~ sQ29_spl
| subtract(any1,zero(any1),sK1_skl(any1,x)) = zero(any1) ),
inference(component_clause,[status(thm)],[f541]) ).
fof(f546,plain,
( sQ28_spl
| ~ sQ29_spl
| apply(x,zero(any1)) != zero(any2) ),
inference(backward_demodulation,[status(thm)],[f542,f540]) ).
fof(f561,plain,
( sQ28_spl
| ~ sQ29_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f546,f286,f541,f538]) ).
fof(f614,plain,
( ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ7_spl
| subtract(any1,sK1_skl(any1,x),sK0_skl(any1,x)) = zero(any1)
| apply(x,subtract(any1,sK1_skl(any1,x),sK0_skl(any1,x))) != zero(any2) ),
inference(resolution,[status(thm)],[f395,f105]) ).
fof(f627,definition,
( sQ30_spl
<=> apply(x,subtract(any1,sK1_skl(any1,x),sK0_skl(any1,x))) = zero(any2) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f629,plain,
( sQ30_spl
| apply(x,subtract(any1,sK1_skl(any1,x),sK0_skl(any1,x))) != zero(any2) ),
inference(component_clause,[status(thm)],[f627]) ).
fof(f630,definition,
( sQ31_spl
<=> subtract(any1,sK1_skl(any1,x),sK0_skl(any1,x)) = zero(any1) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f631,plain,
( ~ sQ31_spl
| subtract(any1,sK1_skl(any1,x),sK0_skl(any1,x)) = zero(any1) ),
inference(component_clause,[status(thm)],[f630]) ).
fof(f633,plain,
( ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ7_spl
| sQ31_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f614,f627,f630,f129,f115,f104]) ).
fof(f637,plain,
( sQ30_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| zero(any2) != zero(any2) ),
inference(forward_demodulation,[status(thm)],[f437,f629]) ).
fof(f638,plain,
( sQ30_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f637]) ).
fof(f639,plain,
( sQ30_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f638]) ).
fof(f651,plain,
( ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ31_spl
| subtract(any1,sK1_skl(any1,x),zero(any1)) = sK0_skl(any1,x) ),
inference(backward_demodulation,[status(thm)],[f631,f398]) ).
fof(f658,plain,
( ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ31_spl
| sK1_skl(any1,x) = sK0_skl(any1,x) ),
inference(forward_demodulation,[status(thm)],[f400,f651]) ).
fof(f659,plain,
( ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ31_spl
| sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f658,f141]) ).
fof(f660,plain,
( ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ31_spl
| sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f659]) ).
fof(f661,plain,
$false,
inference(sat_refutation,[status(thm)],[f98,f99,f107,f111,f118,f132,f137,f142,f186,f191,f196,f289,f295,f312,f345,f505,f561,f633,f639,f660]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : HAL002+1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.42 % Computer : n008.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Sun Sep 20 20:45:10 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.45 % Drodi V4.1.1
% 0.30/0.66 % Refutation found
% 0.30/0.66 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.30/0.66 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.30/0.68 % Elapsed time: 0.230000 seconds
% 0.30/0.68 % CPU time: 1.497425 seconds
% 0.30/0.68 % Total memory used: 102.424 MB
% 0.30/0.68 % Net memory used: 100.951 MB
%------------------------------------------------------------------------------