%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE002+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 : n014.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 12:57:42 PM UTC 2026
% Result : Theorem 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 9 unt; 0 def)
% Number of atoms : 33 ( 13 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 28 ( 14 ~; 6 |; 5 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 30 ( 24 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,conjecture,
! [X0,X1,X2] :
( leq(X0,X1)
=> leq(multiplication(X0,X2),multiplication(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
~ ! [X0,X1,X2] :
( leq(X0,X1)
=> leq(multiplication(X0,X2),multiplication(X1,X2)) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f23,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f26,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f12]) ).
fof(f27,plain,
( ! [A,B] :
( addition(A,B) != B
| leq(A,B) )
& ! [A,B] :
( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(miniscoping,[status(thm)],[f26]) ).
fof(f28,plain,
! [X0,X1] :
( addition(X0,X1) = X1
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f29,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f30,plain,
? [X0,X1,X2] :
( ~ leq(multiplication(X0,X2),multiplication(X1,X2))
& leq(X0,X1) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f31,plain,
? [X0,X1] :
( ? [X2] : ~ leq(multiplication(X0,X2),multiplication(X1,X2))
& leq(X0,X1) ),
inference(miniscoping,[status(thm)],[f30]) ).
fof(f32,plain,
( ~ leq(multiplication(sK0_skl,sK2_skl),multiplication(sK1_skl,sK2_skl))
& leq(sK0_skl,sK1_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(X0,sK0_skl),skolemize(X1,sK1_skl),skolemize(X2,sK2_skl)],[f31]) ).
fof(f33,plain,
leq(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f34,plain,
~ leq(multiplication(sK0_skl,sK2_skl),multiplication(sK1_skl,sK2_skl)),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f35,plain,
addition(sK0_skl,sK1_skl) = sK1_skl,
inference(resolution,[status(thm)],[f28,f33]) ).
fof(f36,plain,
addition(multiplication(sK0_skl,sK2_skl),multiplication(sK1_skl,sK2_skl)) != multiplication(sK1_skl,sK2_skl),
inference(resolution,[status(thm)],[f29,f34]) ).
fof(f38,plain,
multiplication(addition(sK0_skl,sK1_skl),sK2_skl) != multiplication(sK1_skl,sK2_skl),
inference(forward_demodulation,[status(thm)],[f23,f36]) ).
fof(f39,plain,
multiplication(sK1_skl,sK2_skl) != multiplication(sK1_skl,sK2_skl),
inference(forward_demodulation,[status(thm)],[f35,f38]) ).
fof(f40,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE002+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n014.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 20 22:37:35 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 0.13/0.39 % Refutation found
% 0.13/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.43 % Elapsed time: 0.051600 seconds
% 0.13/0.43 % CPU time: 0.147030 seconds
% 0.13/0.43 % Total memory used: 66.561 MB
% 0.13/0.43 % Net memory used: 66.129 MB
%------------------------------------------------------------------------------