%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE137+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 : n001.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 12:58:01 PM UTC 2026
% Result : Theorem 0.09s 0.36s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 27 ( 19 unt; 0 def)
% Number of atoms : 39 ( 17 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 28 ( 16 ~; 8 |; 2 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 38 ( 37 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : addition(A,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] : multiplication(A,one) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A] : multiplication(one,A) = A,
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] : leq(X0,strong_iteration(one)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ ! [X0] : leq(X0,strong_iteration(one)),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f22,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f24,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f26,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f27,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[status(thm)],[f7]) ).
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] : ~ leq(X0,strong_iteration(one)),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f46,plain,
~ leq(sK0_skl,strong_iteration(one)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X0,sK0_skl)],[f45]) ).
fof(f47,plain,
~ leq(sK0_skl,strong_iteration(one)),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f56,plain,
! [X0,X1] :
( leq(X0,strong_iteration(X1))
| ~ leq(X0,addition(multiplication(X1,X0),one)) ),
inference(paramodulation,[status(thm)],[f26,f39]) ).
fof(f57,plain,
~ leq(sK0_skl,addition(multiplication(one,sK0_skl),one)),
inference(resolution,[status(thm)],[f56,f47]) ).
fof(f59,plain,
~ leq(sK0_skl,addition(sK0_skl,one)),
inference(forward_demodulation,[status(thm)],[f27,f57]) ).
fof(f60,plain,
addition(sK0_skl,addition(sK0_skl,one)) != addition(sK0_skl,one),
inference(resolution,[status(thm)],[f59,f44]) ).
fof(f195,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f24,f22]) ).
fof(f208,plain,
addition(sK0_skl,one) != addition(sK0_skl,one),
inference(backward_demodulation,[status(thm)],[f195,f60]) ).
fof(f216,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f208]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE137+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n001.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Sun Sep 20 22:51:12 UTC 2026
% 0.09/0.34 % CPUTime :
% 0.09/0.35 % Drodi V4.1.1
% 0.09/0.36 % Refutation found
% 0.09/0.36 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.41 % Elapsed time: 0.055034 seconds
% 0.13/0.41 % CPU time: 0.095883 seconds
% 0.13/0.41 % Total memory used: 13.483 MB
% 0.13/0.41 % Net memory used: 13.459 MB
%------------------------------------------------------------------------------