%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : HAL006+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 : n006.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 150.44s 19.80s
% Output : CNFRefutation 150.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 47 ( 18 unt; 0 def)
% Number of atoms : 121 ( 38 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 117 ( 43 ~; 36 |; 30 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-3 aty)
% Number of variables : 72 ( 58 !; 14 ?)
% 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(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(alpha,a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
morphism(g,b,e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [E] :
( element(E,e)
=> ? [B1,E1,A] :
( apply(g,apply(alpha,A)) = E1
& apply(gamma,apply(f,A)) = E1
& element(A,a)
& subtract(e,apply(g,B1),E) = E1
& element(E1,e)
& element(B1,b) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,conjecture,
! [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,negated_conjecture,
~ ! [E] :
( element(E,e)
=> ? [B1,B2] :
( apply(g,subtract(b,B1,B2)) = E
& element(B2,b)
& element(B1,b) ) ),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f35,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(f36,plain,
! [X0,X1,X2,X3] :
( ~ morphism(X0,X3,X2)
| ~ element(X1,X3)
| element(apply(X0,X1),X2) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f86,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(f87,plain,
! [X0,X1,X2] :
( subtract(X1,X0,subtract(X1,X0,X2)) = X2
| ~ element(X2,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f88,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(f89,plain,
! [X0,X1,X2,X3,X4] :
( ~ element(X4,X1)
| ~ element(X3,X1)
| apply(X0,subtract(X1,X3,X4)) = subtract(X2,apply(X0,X3),apply(X0,X4))
| ~ morphism(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f88]) ).
fof(f90,plain,
morphism(alpha,a,b),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f95,plain,
morphism(g,b,e),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f114,plain,
! [E] :
( ? [B1,E1,A] :
( apply(g,apply(alpha,A)) = E1
& apply(gamma,apply(f,A)) = E1
& element(A,a)
& subtract(e,apply(g,B1),E) = E1
& element(E1,e)
& element(B1,b) )
| ~ element(E,e) ),
inference(pre_NNF_transformation,[status(thm)],[f32]) ).
fof(f115,plain,
! [E] :
( ? [E1,A] :
( apply(g,apply(alpha,A)) = E1
& apply(gamma,apply(f,A)) = E1
& element(A,a)
& ? [B1] :
( subtract(e,apply(g,B1),E) = E1
& element(E1,e)
& element(B1,b) ) )
| ~ element(E,e) ),
inference(miniscoping,[status(thm)],[f114]) ).
fof(f116,plain,
! [E] :
( ( apply(g,apply(alpha,sK11_skl(E))) = sK10_skl(E)
& apply(gamma,apply(f,sK11_skl(E))) = sK10_skl(E)
& element(sK11_skl(E),a)
& subtract(e,apply(g,sK12_skl(E)),E) = sK10_skl(E)
& element(sK10_skl(E),e)
& element(sK12_skl(E),b) )
| ~ element(E,e) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl,sK11_skl,sK12_skl]),skolemize(E1,sK10_skl(E)),skolemize(A,sK11_skl(E)),skolemize(B1,sK12_skl(E))],[f115]) ).
fof(f117,plain,
! [X0] :
( ~ element(X0,e)
| element(sK12_skl(X0),b) ),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f119,plain,
! [X0] :
( ~ element(X0,e)
| subtract(e,apply(g,sK12_skl(X0)),X0) = sK10_skl(X0) ),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f120,plain,
! [X0] :
( ~ element(X0,e)
| element(sK11_skl(X0),a) ),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f122,plain,
! [X0] :
( apply(g,apply(alpha,sK11_skl(X0))) = sK10_skl(X0)
| ~ element(X0,e) ),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f123,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)],[f34]) ).
fof(f124,plain,
( ! [B1,B2] :
( apply(g,subtract(b,B1,B2)) != sK13_skl
| ~ element(B2,b)
| ~ element(B1,b) )
& element(sK13_skl,e) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl]),skolemize(E,sK13_skl)],[f123]) ).
fof(f125,plain,
element(sK13_skl,e),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f126,plain,
! [X0,X1] :
( apply(g,subtract(b,X1,X0)) != sK13_skl
| ~ element(X1,b)
| ~ element(X0,b) ),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f134,plain,
element(sK11_skl(sK13_skl),a),
inference(resolution,[status(thm)],[f125,f120]) ).
fof(f137,plain,
! [X0] :
( ~ element(X0,e)
| sK13_skl = subtract(e,X0,subtract(e,X0,sK13_skl)) ),
inference(resolution,[status(thm)],[f87,f125]) ).
fof(f143,plain,
! [X0] :
( ~ element(X0,b)
| element(apply(g,X0),e) ),
inference(resolution,[status(thm)],[f36,f95]) ).
fof(f169,plain,
! [X0,X1] :
( ~ element(X1,b)
| apply(g,subtract(b,X1,X0)) = subtract(e,apply(g,X1),apply(g,X0))
| ~ element(X0,b) ),
inference(resolution,[status(thm)],[f89,f95]) ).
fof(f216,plain,
! [X0] :
( element(apply(alpha,X0),b)
| ~ element(X0,a) ),
inference(resolution,[status(thm)],[f90,f36]) ).
fof(f221,plain,
subtract(e,apply(g,sK12_skl(sK13_skl)),sK13_skl) = sK10_skl(sK13_skl),
inference(resolution,[status(thm)],[f119,f125]) ).
fof(f241,plain,
element(apply(alpha,sK11_skl(sK13_skl)),b),
inference(resolution,[status(thm)],[f216,f134]) ).
fof(f275,plain,
apply(g,apply(alpha,sK11_skl(sK13_skl))) = sK10_skl(sK13_skl),
inference(resolution,[status(thm)],[f122,f125]) ).
fof(f315,plain,
element(sK12_skl(sK13_skl),b),
inference(resolution,[status(thm)],[f117,f125]) ).
fof(f316,plain,
! [X0] :
( subtract(e,apply(g,sK12_skl(sK13_skl)),apply(g,X0)) = apply(g,subtract(b,sK12_skl(sK13_skl),X0))
| ~ element(X0,b) ),
inference(resolution,[status(thm)],[f315,f169]) ).
fof(f317,plain,
element(apply(g,sK12_skl(sK13_skl)),e),
inference(resolution,[status(thm)],[f315,f143]) ).
fof(f588,plain,
sK13_skl = subtract(e,apply(g,sK12_skl(sK13_skl)),subtract(e,apply(g,sK12_skl(sK13_skl)),sK13_skl)),
inference(resolution,[status(thm)],[f317,f137]) ).
fof(f595,plain,
sK13_skl = subtract(e,apply(g,sK12_skl(sK13_skl)),sK10_skl(sK13_skl)),
inference(forward_demodulation,[status(thm)],[f221,f588]) ).
fof(f1058,plain,
subtract(e,apply(g,sK12_skl(sK13_skl)),apply(g,apply(alpha,sK11_skl(sK13_skl)))) = apply(g,subtract(b,sK12_skl(sK13_skl),apply(alpha,sK11_skl(sK13_skl)))),
inference(resolution,[status(thm)],[f316,f241]) ).
fof(f1060,plain,
subtract(e,apply(g,sK12_skl(sK13_skl)),sK10_skl(sK13_skl)) = apply(g,subtract(b,sK12_skl(sK13_skl),apply(alpha,sK11_skl(sK13_skl)))),
inference(forward_demodulation,[status(thm)],[f275,f1058]) ).
fof(f13284,plain,
apply(g,subtract(b,sK12_skl(sK13_skl),apply(alpha,sK11_skl(sK13_skl)))) = sK13_skl,
inference(forward_demodulation,[status(thm)],[f595,f1060]) ).
fof(f13286,plain,
( sK13_skl != sK13_skl
| ~ element(sK12_skl(sK13_skl),b)
| ~ element(apply(alpha,sK11_skl(sK13_skl)),b) ),
inference(paramodulation,[status(thm)],[f13284,f126]) ).
fof(f13294,plain,
( ~ element(sK12_skl(sK13_skl),b)
| ~ element(apply(alpha,sK11_skl(sK13_skl)),b) ),
inference(trivial_equality_resolution,[status(thm)],[f13286]) ).
fof(f13295,plain,
~ element(sK12_skl(sK13_skl),b),
inference(forward_subsumption_resolution,[status(thm)],[f13294,f241]) ).
fof(f13297,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f13295,f315]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : HAL006+1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.47 % Computer : n006.cluster.edu
% 0.20/0.47 % Model : x86_64 x86_64
% 0.20/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.47 % Memory : 8046.5625MB
% 0.20/0.47 % OS : Linux 6.8.0-71-generic
% 0.20/0.47 % CPULimit : 300
% 0.20/0.47 % WCLimit : 300
% 0.20/0.47 % DateTime : Sun Sep 20 20:44:43 UTC 2026
% 0.20/0.47 % CPUTime :
% 0.20/0.49 % Drodi V4.1.1
% 150.44/19.80 % Refutation found
% 150.44/19.80 % SZS status Theorem for theBenchmark: Theorem is valid
% 150.44/19.80 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 65.69/21.03 % Elapsed time: 20.339200 seconds
% 65.69/21.03 % CPU time: 147.811751 seconds
% 65.69/21.03 % Total memory used: 941.341 MB
% 65.69/21.03 % Net memory used: 843.648 MB
%------------------------------------------------------------------------------