%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE151+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 12:58:05 PM UTC 2026
% Result : Theorem 0.14s 5.62s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 33 ( 25 unt; 0 def)
% Number of atoms : 45 ( 23 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 31 ( 19 ~; 8 |; 2 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 50 ( 48 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [A] : addition(A,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] : multiplication(A,one) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A] : strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [A,B,C] :
( leq(C,addition(multiplication(A,C),B))
=> leq(C,multiplication(strong_iteration(A),B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,conjecture,
! [X0,X1] : leq(multiplication(X0,strong_iteration(multiplication(X1,X0))),multiplication(strong_iteration(multiplication(X0,X1)),X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ ! [X0,X1] : leq(multiplication(X0,strong_iteration(multiplication(X1,X0))),multiplication(strong_iteration(multiplication(X0,X1)),X0)),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f24,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f25,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f26,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f28,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f37,plain,
! [X0] : strong_iteration(X0) = addition(multiplication(X0,strong_iteration(X0)),one),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f38,plain,
! [A,B,C] :
( leq(C,multiplication(strong_iteration(A),B))
| ~ leq(C,addition(multiplication(A,C),B)) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f39,plain,
! [X0,X1,X2] :
( leq(X0,multiplication(strong_iteration(X1),X2))
| ~ leq(X0,addition(multiplication(X1,X0),X2)) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f41,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f18]) ).
fof(f42,plain,
( ! [A,B] :
( addition(A,B) != B
| leq(A,B) )
& ! [A,B] :
( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(miniscoping,[status(thm)],[f41]) ).
fof(f44,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f45,plain,
? [X0,X1] : ~ leq(multiplication(X0,strong_iteration(multiplication(X1,X0))),multiplication(strong_iteration(multiplication(X0,X1)),X0)),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f46,plain,
~ leq(multiplication(sK0_skl,strong_iteration(multiplication(sK1_skl,sK0_skl))),multiplication(strong_iteration(multiplication(sK0_skl,sK1_skl)),sK0_skl)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X0,sK0_skl),skolemize(X1,sK1_skl)],[f45]) ).
fof(f47,plain,
~ leq(multiplication(sK0_skl,strong_iteration(multiplication(sK1_skl,sK0_skl))),multiplication(strong_iteration(multiplication(sK0_skl,sK1_skl)),sK0_skl)),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f51,plain,
~ leq(multiplication(sK0_skl,strong_iteration(multiplication(sK1_skl,sK0_skl))),addition(multiplication(multiplication(sK0_skl,sK1_skl),multiplication(sK0_skl,strong_iteration(multiplication(sK1_skl,sK0_skl)))),sK0_skl)),
inference(resolution,[status(thm)],[f39,f47]) ).
fof(f53,plain,
~ leq(multiplication(sK0_skl,strong_iteration(multiplication(sK1_skl,sK0_skl))),addition(multiplication(sK0_skl,multiplication(sK1_skl,multiplication(sK0_skl,strong_iteration(multiplication(sK1_skl,sK0_skl))))),sK0_skl)),
inference(forward_demodulation,[status(thm)],[f25,f51]) ).
fof(f168,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(multiplication(X0,X1),X0),
inference(paramodulation,[status(thm)],[f26,f28]) ).
fof(f176,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X1,X2)) != multiplication(X0,X2)
| leq(multiplication(X0,X1),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f28,f44]) ).
fof(f190,plain,
~ leq(multiplication(sK0_skl,strong_iteration(multiplication(sK1_skl,sK0_skl))),multiplication(sK0_skl,addition(multiplication(sK1_skl,multiplication(sK0_skl,strong_iteration(multiplication(sK1_skl,sK0_skl)))),one))),
inference(backward_demodulation,[status(thm)],[f168,f53]) ).
fof(f243,plain,
multiplication(sK0_skl,addition(strong_iteration(multiplication(sK1_skl,sK0_skl)),addition(multiplication(sK1_skl,multiplication(sK0_skl,strong_iteration(multiplication(sK1_skl,sK0_skl)))),one))) != multiplication(sK0_skl,addition(multiplication(sK1_skl,multiplication(sK0_skl,strong_iteration(multiplication(sK1_skl,sK0_skl)))),one)),
inference(resolution,[status(thm)],[f176,f190]) ).
fof(f922,plain,
! [X0,X1] : strong_iteration(multiplication(X0,X1)) = addition(multiplication(X0,multiplication(X1,strong_iteration(multiplication(X0,X1)))),one),
inference(paramodulation,[status(thm)],[f25,f37]) ).
fof(f943,plain,
multiplication(sK0_skl,addition(strong_iteration(multiplication(sK1_skl,sK0_skl)),addition(multiplication(sK1_skl,multiplication(sK0_skl,strong_iteration(multiplication(sK1_skl,sK0_skl)))),one))) != multiplication(sK0_skl,strong_iteration(multiplication(sK1_skl,sK0_skl))),
inference(backward_demodulation,[status(thm)],[f922,f243]) ).
fof(f957,plain,
multiplication(sK0_skl,addition(strong_iteration(multiplication(sK1_skl,sK0_skl)),strong_iteration(multiplication(sK1_skl,sK0_skl)))) != multiplication(sK0_skl,strong_iteration(multiplication(sK1_skl,sK0_skl))),
inference(forward_demodulation,[status(thm)],[f922,f943]) ).
fof(f958,plain,
multiplication(sK0_skl,strong_iteration(multiplication(sK1_skl,sK0_skl))) != multiplication(sK0_skl,strong_iteration(multiplication(sK1_skl,sK0_skl))),
inference(forward_demodulation,[status(thm)],[f24,f957]) ).
fof(f959,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f958]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE151+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/5.56 % Computer : n016.cluster.edu
% 0.11/5.56 % Model : x86_64 x86_64
% 0.11/5.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.56 % Memory : 8046.5625MB
% 0.11/5.56 % OS : Linux 6.8.0-71-generic
% 0.11/5.56 % CPULimit : 300
% 0.11/5.56 % WCLimit : 300
% 0.11/5.56 % DateTime : Sun Sep 20 22:51:30 UTC 2026
% 0.11/5.56 % CPUTime :
% 0.11/5.57 % Drodi V4.1.1
% 0.14/5.62 % Refutation found
% 0.14/5.62 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/5.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/5.65 % Elapsed time: 0.075097 seconds
% 0.14/5.65 % CPU time: 0.317441 seconds
% 0.14/5.65 % Total memory used: 72.080 MB
% 0.14/5.65 % Net memory used: 71.703 MB
%------------------------------------------------------------------------------