%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE148+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 12:58:04 PM UTC 2026
% Result : Theorem 1.22s 0.59s
% Output : CNFRefutation 1.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 11
% Syntax : Number of formulae : 53 ( 32 unt; 0 def)
% Number of atoms : 83 ( 62 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 63 ( 33 ~; 20 |; 7 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 65 ( 59 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] : addition(A,zero) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
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(f10,axiom,
! [A] : multiplication(zero,A) = zero,
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(f18,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,conjecture,
! [X0,X1] :
( leq(X0,multiplication(X0,strong_iteration(X1)))
& ( multiplication(X0,X1) = zero
=> leq(multiplication(X0,strong_iteration(X1)),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ ! [X0,X1] :
( leq(X0,multiplication(X0,strong_iteration(X1)))
& ( multiplication(X0,X1) = zero
=> leq(multiplication(X0,strong_iteration(X1)),X0) ) ),
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(f23,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
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(f30,plain,
! [X0] : multiplication(zero,X0) = zero,
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f37,plain,
! [X0] : strong_iteration(X0) = addition(multiplication(X0,strong_iteration(X0)),one),
inference(cnf_transformation,[status(thm)],[f15]) ).
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(X0,multiplication(X0,strong_iteration(X1)))
| ( ~ leq(multiplication(X0,strong_iteration(X1)),X0)
& multiplication(X0,X1) = zero ) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f46,plain,
( ? [X0,X1] : ~ leq(X0,multiplication(X0,strong_iteration(X1)))
| ? [X0,X1] :
( ~ leq(multiplication(X0,strong_iteration(X1)),X0)
& multiplication(X0,X1) = zero ) ),
inference(miniscoping,[status(thm)],[f45]) ).
fof(f47,plain,
( ~ leq(sK2_skl,multiplication(sK2_skl,strong_iteration(sK3_skl)))
| ( ~ leq(multiplication(sK0_skl,strong_iteration(sK1_skl)),sK0_skl)
& multiplication(sK0_skl,sK1_skl) = zero ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl]),skolemize(X0,sK0_skl),skolemize(X1,sK1_skl),skolemize(X0,sK2_skl),skolemize(X1,sK3_skl)],[f46]) ).
fof(f48,plain,
( ~ leq(sK2_skl,multiplication(sK2_skl,strong_iteration(sK3_skl)))
| multiplication(sK0_skl,sK1_skl) = zero ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f49,plain,
( ~ leq(sK2_skl,multiplication(sK2_skl,strong_iteration(sK3_skl)))
| ~ leq(multiplication(sK0_skl,strong_iteration(sK1_skl)),sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f50,plain,
! [X0] : strong_iteration(X0) = addition(one,multiplication(X0,strong_iteration(X0))),
inference(forward_demodulation,[status(thm)],[f21,f37]) ).
fof(f56,plain,
( ~ leq(multiplication(sK0_skl,strong_iteration(sK1_skl)),sK0_skl)
| addition(sK2_skl,multiplication(sK2_skl,strong_iteration(sK3_skl))) != multiplication(sK2_skl,strong_iteration(sK3_skl)) ),
inference(resolution,[status(thm)],[f44,f49]) ).
fof(f57,plain,
( multiplication(sK0_skl,sK1_skl) = zero
| addition(sK2_skl,multiplication(sK2_skl,strong_iteration(sK3_skl))) != multiplication(sK2_skl,strong_iteration(sK3_skl)) ),
inference(resolution,[status(thm)],[f44,f48]) ).
fof(f59,plain,
( addition(multiplication(sK0_skl,strong_iteration(sK1_skl)),sK0_skl) != sK0_skl
| addition(sK2_skl,multiplication(sK2_skl,strong_iteration(sK3_skl))) != multiplication(sK2_skl,strong_iteration(sK3_skl)) ),
inference(resolution,[status(thm)],[f56,f44]) ).
fof(f60,plain,
( addition(sK0_skl,multiplication(sK0_skl,strong_iteration(sK1_skl))) != sK0_skl
| addition(sK2_skl,multiplication(sK2_skl,strong_iteration(sK3_skl))) != multiplication(sK2_skl,strong_iteration(sK3_skl)) ),
inference(forward_demodulation,[status(thm)],[f21,f59]) ).
fof(f190,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f24,f22]) ).
fof(f209,plain,
! [X0] : addition(one,strong_iteration(X0)) = addition(one,multiplication(X0,strong_iteration(X0))),
inference(paramodulation,[status(thm)],[f50,f190]) ).
fof(f230,plain,
! [X0] : addition(one,strong_iteration(X0)) = strong_iteration(X0),
inference(forward_demodulation,[status(thm)],[f50,f209]) ).
fof(f322,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f26,f28]) ).
fof(f344,plain,
( multiplication(sK0_skl,addition(one,strong_iteration(sK1_skl))) != sK0_skl
| addition(sK2_skl,multiplication(sK2_skl,strong_iteration(sK3_skl))) != multiplication(sK2_skl,strong_iteration(sK3_skl)) ),
inference(backward_demodulation,[status(thm)],[f322,f60]) ).
fof(f346,plain,
( multiplication(sK0_skl,sK1_skl) = zero
| multiplication(sK2_skl,addition(one,strong_iteration(sK3_skl))) != multiplication(sK2_skl,strong_iteration(sK3_skl)) ),
inference(backward_demodulation,[status(thm)],[f322,f57]) ).
fof(f364,plain,
( multiplication(sK0_skl,addition(one,strong_iteration(sK1_skl))) != sK0_skl
| multiplication(sK2_skl,addition(one,strong_iteration(sK3_skl))) != multiplication(sK2_skl,strong_iteration(sK3_skl)) ),
inference(forward_demodulation,[status(thm)],[f322,f344]) ).
fof(f365,plain,
( multiplication(sK0_skl,addition(one,strong_iteration(sK1_skl))) != sK0_skl
| multiplication(sK2_skl,strong_iteration(sK3_skl)) != multiplication(sK2_skl,strong_iteration(sK3_skl)) ),
inference(forward_demodulation,[status(thm)],[f230,f364]) ).
fof(f366,plain,
( multiplication(sK0_skl,strong_iteration(sK1_skl)) != sK0_skl
| multiplication(sK2_skl,strong_iteration(sK3_skl)) != multiplication(sK2_skl,strong_iteration(sK3_skl)) ),
inference(forward_demodulation,[status(thm)],[f230,f365]) ).
fof(f367,plain,
multiplication(sK0_skl,strong_iteration(sK1_skl)) != sK0_skl,
inference(trivial_equality_resolution,[status(thm)],[f366]) ).
fof(f370,plain,
( multiplication(sK0_skl,sK1_skl) = zero
| multiplication(sK2_skl,strong_iteration(sK3_skl)) != multiplication(sK2_skl,strong_iteration(sK3_skl)) ),
inference(forward_demodulation,[status(thm)],[f230,f346]) ).
fof(f372,plain,
multiplication(sK0_skl,sK1_skl) = zero,
inference(trivial_equality_resolution,[status(thm)],[f370]) ).
fof(f444,plain,
! [X0] : multiplication(sK0_skl,multiplication(sK1_skl,X0)) = multiplication(zero,X0),
inference(paramodulation,[status(thm)],[f372,f25]) ).
fof(f454,plain,
! [X0] : multiplication(sK0_skl,multiplication(sK1_skl,X0)) = zero,
inference(forward_demodulation,[status(thm)],[f30,f444]) ).
fof(f459,plain,
! [X0,X1] : multiplication(sK0_skl,addition(X0,multiplication(sK1_skl,X1))) = addition(multiplication(sK0_skl,X0),zero),
inference(paramodulation,[status(thm)],[f454,f28]) ).
fof(f475,plain,
! [X0,X1] : multiplication(sK0_skl,addition(X0,multiplication(sK1_skl,X1))) = multiplication(sK0_skl,X0),
inference(forward_demodulation,[status(thm)],[f23,f459]) ).
fof(f667,plain,
multiplication(sK0_skl,strong_iteration(sK1_skl)) = multiplication(sK0_skl,one),
inference(paramodulation,[status(thm)],[f50,f475]) ).
fof(f686,plain,
multiplication(sK0_skl,strong_iteration(sK1_skl)) = sK0_skl,
inference(forward_demodulation,[status(thm)],[f26,f667]) ).
fof(f687,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f686,f367]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE148+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n026.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 20 22:49:09 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.39 % Drodi V4.1.1
% 1.22/0.59 % Refutation found
% 1.22/0.59 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.22/0.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.22/0.62 % Elapsed time: 0.232258 seconds
% 1.22/0.62 % CPU time: 1.555807 seconds
% 1.22/0.62 % Total memory used: 89.975 MB
% 1.22/0.62 % Net memory used: 89.304 MB
%------------------------------------------------------------------------------