%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE056+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 12:57:52 PM UTC 2026
% Result : Theorem 0.18s 0.48s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 14 unt; 0 def)
% Number of atoms : 22 ( 21 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 4 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 9 ( 8 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A] : addition(A,zero) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A] : multiplication(zero,A) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,conjecture,
! [X0] :
( domain(X0) = zero
=> X0 = zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
~ ! [X0] :
( domain(X0) = zero
=> X0 = zero ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f22,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f30,plain,
! [X0] : multiplication(zero,X0) = zero,
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f35,plain,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f40,plain,
? [X0] :
( X0 != zero
& domain(X0) = zero ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f41,plain,
( sK0_skl != zero
& domain(sK0_skl) = zero ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X0,sK0_skl)],[f40]) ).
fof(f42,plain,
domain(sK0_skl) = zero,
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f43,plain,
sK0_skl != zero,
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f56,plain,
addition(sK0_skl,multiplication(zero,sK0_skl)) = multiplication(domain(sK0_skl),sK0_skl),
inference(paramodulation,[status(thm)],[f42,f35]) ).
fof(f61,plain,
addition(sK0_skl,zero) = multiplication(domain(sK0_skl),sK0_skl),
inference(forward_demodulation,[status(thm)],[f30,f56]) ).
fof(f62,plain,
sK0_skl = multiplication(domain(sK0_skl),sK0_skl),
inference(forward_demodulation,[status(thm)],[f22,f61]) ).
fof(f63,plain,
sK0_skl = multiplication(zero,sK0_skl),
inference(forward_demodulation,[status(thm)],[f42,f62]) ).
fof(f64,plain,
sK0_skl = zero,
inference(forward_demodulation,[status(thm)],[f30,f63]) ).
fof(f65,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f64,f43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE056+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n004.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sun Sep 20 22:41:36 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.45 % Drodi V4.1.1
% 0.18/0.48 % Refutation found
% 0.18/0.48 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.54 % Elapsed time: 0.089252 seconds
% 0.18/0.54 % CPU time: 0.094802 seconds
% 0.18/0.54 % Total memory used: 2.125 MB
% 0.18/0.54 % Net memory used: 2.125 MB
%------------------------------------------------------------------------------