%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE140+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 : n013.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 12:58:02 PM UTC 2026
% Result : Theorem 63.95s 18.56s
% Output : CNFRefutation 63.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 43 ( 28 unt; 0 def)
% Number of atoms : 62 ( 28 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 34 ( 15 ~; 11 |; 4 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 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 : 75 ( 73 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : addition(A,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] : multiplication(A,one) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A] : multiplication(one,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
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(f15,axiom,
! [A] : strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,conjecture,
! [X0,X1] :
( leq(X0,X1)
=> leq(strong_iteration(X0),strong_iteration(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ ! [X0,X1] :
( leq(X0,X1)
=> leq(strong_iteration(X0),strong_iteration(X1)) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
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(f29,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[status(thm)],[f9]) ).
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(f43,plain,
! [X0,X1] :
( addition(X0,X1) = X1
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f44,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f45,plain,
? [X0,X1] :
( ~ leq(strong_iteration(X0),strong_iteration(X1))
& leq(X0,X1) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f46,plain,
( ~ leq(strong_iteration(sK0_skl),strong_iteration(sK1_skl))
& leq(sK0_skl,sK1_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(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f48,plain,
~ leq(strong_iteration(sK0_skl),strong_iteration(sK1_skl)),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f49,plain,
! [X0] : strong_iteration(X0) = addition(one,multiplication(X0,strong_iteration(X0))),
inference(forward_demodulation,[status(thm)],[f21,f37]) ).
fof(f68,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f24,f22]) ).
fof(f110,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f27,f29]) ).
fof(f149,plain,
addition(sK0_skl,sK1_skl) = sK1_skl,
inference(resolution,[status(thm)],[f43,f47]) ).
fof(f220,plain,
! [X0,X1] : addition(one,addition(multiplication(X0,strong_iteration(X0)),X1)) = addition(strong_iteration(X0),X1),
inference(paramodulation,[status(thm)],[f49,f22]) ).
fof(f227,plain,
! [X0,X1,X2] :
( leq(X0,multiplication(strong_iteration(X2),X1))
| ~ leq(X0,addition(X1,multiplication(X2,X0))) ),
inference(paramodulation,[status(thm)],[f21,f39]) ).
fof(f465,plain,
! [X0,X1] : leq(X0,addition(X0,X1)),
inference(resolution,[status(thm)],[f68,f44]) ).
fof(f1179,plain,
! [X0,X1] : leq(X0,multiplication(addition(one,X1),X0)),
inference(paramodulation,[status(thm)],[f110,f465]) ).
fof(f4806,plain,
! [X0,X1] : addition(one,multiplication(addition(X0,X1),strong_iteration(X0))) = addition(strong_iteration(X0),multiplication(X1,strong_iteration(X0))),
inference(paramodulation,[status(thm)],[f29,f220]) ).
fof(f4829,plain,
! [X0,X1] : addition(one,multiplication(addition(X0,X1),strong_iteration(X0))) = multiplication(addition(one,X1),strong_iteration(X0)),
inference(forward_demodulation,[status(thm)],[f110,f4806]) ).
fof(f29905,plain,
! [X0,X1] :
( leq(strong_iteration(X0),multiplication(strong_iteration(addition(X0,X1)),one))
| ~ leq(strong_iteration(X0),multiplication(addition(one,X1),strong_iteration(X0))) ),
inference(paramodulation,[status(thm)],[f4829,f227]) ).
fof(f30097,plain,
! [X0,X1] :
( leq(strong_iteration(X0),strong_iteration(addition(X0,X1)))
| ~ leq(strong_iteration(X0),multiplication(addition(one,X1),strong_iteration(X0))) ),
inference(forward_demodulation,[status(thm)],[f26,f29905]) ).
fof(f30098,plain,
! [X0,X1] : leq(strong_iteration(X0),strong_iteration(addition(X0,X1))),
inference(forward_subsumption_resolution,[status(thm)],[f30097,f1179]) ).
fof(f31097,plain,
leq(strong_iteration(sK0_skl),strong_iteration(sK1_skl)),
inference(paramodulation,[status(thm)],[f149,f30098]) ).
fof(f31159,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f31097,f48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE140+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/10.42 % Computer : n013.cluster.edu
% 0.14/10.42 % Model : x86_64 x86_64
% 0.14/10.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/10.42 % Memory : 8046.5625MB
% 0.14/10.42 % OS : Linux 6.8.0-71-generic
% 0.14/10.42 % CPULimit : 300
% 0.14/10.42 % WCLimit : 300
% 0.14/10.42 % DateTime : Sun Sep 20 22:45:31 UTC 2026
% 0.14/10.43 % CPUTime :
% 0.14/10.44 % Drodi V4.1.1
% 63.95/18.56 % Refutation found
% 63.95/18.56 % SZS status Theorem for theBenchmark: Theorem is valid
% 63.95/18.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 6.27/18.66 % Elapsed time: 8.221177 seconds
% 6.27/18.66 % CPU time: 65.007761 seconds
% 6.27/18.66 % Total memory used: 452.975 MB
% 6.27/18.66 % Net memory used: 441.322 MB
%------------------------------------------------------------------------------