%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE142+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 : n009.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 4.01s 0.93s
% Output : CNFRefutation 4.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 52 ( 37 unt; 0 def)
% Number of atoms : 71 ( 44 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 39 ( 20 ~; 15 |; 2 &)
% ( 1 <=>; 1 =>; 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 94 ( 93 !; 1 ?)
% 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(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(f9,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,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] : strong_iteration(strong_iteration(X0)) = strong_iteration(one),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ ! [X0] : strong_iteration(strong_iteration(X0)) = strong_iteration(one),
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(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] : strong_iteration(strong_iteration(X0)) != strong_iteration(one),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f46,plain,
strong_iteration(strong_iteration(sK0_skl)) != strong_iteration(one),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X0,sK0_skl)],[f45]) ).
fof(f47,plain,
strong_iteration(strong_iteration(sK0_skl)) != strong_iteration(one),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f72,plain,
! [X0,X1] :
( addition(X1,X0) = X1
| ~ leq(X0,X1) ),
inference(paramodulation,[status(thm)],[f21,f43]) ).
fof(f84,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f24,f22]) ).
fof(f86,plain,
! [X0,X1,X2] :
( addition(X0,addition(X1,X2)) = X2
| ~ leq(addition(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f22,f43]) ).
fof(f138,plain,
! [X0,X1] : leq(X0,addition(X0,X1)),
inference(resolution,[status(thm)],[f84,f44]) ).
fof(f145,plain,
! [X0,X1] : addition(X0,addition(X1,X0)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f21,f84]) ).
fof(f241,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f27,f29]) ).
fof(f314,plain,
! [X0,X1] :
( addition(X1,X0) = X1
| ~ leq(addition(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f145,f72]) ).
fof(f526,plain,
! [X0] : strong_iteration(X0) = addition(one,multiplication(X0,strong_iteration(X0))),
inference(paramodulation,[status(thm)],[f21,f37]) ).
fof(f571,plain,
! [X0] : addition(one,strong_iteration(X0)) = addition(one,multiplication(X0,strong_iteration(X0))),
inference(paramodulation,[status(thm)],[f526,f84]) ).
fof(f585,plain,
! [X0] : addition(one,strong_iteration(X0)) = strong_iteration(X0),
inference(forward_demodulation,[status(thm)],[f526,f571]) ).
fof(f2511,plain,
! [X0,X1,X2] :
( leq(X0,multiplication(strong_iteration(addition(one,X1)),X2))
| ~ leq(X0,addition(addition(X0,multiplication(X1,X0)),X2)) ),
inference(paramodulation,[status(thm)],[f241,f39]) ).
fof(f2578,plain,
! [X0,X1,X2] :
( leq(X0,multiplication(strong_iteration(addition(one,X1)),X2))
| ~ leq(X0,addition(X0,addition(multiplication(X1,X0),X2))) ),
inference(forward_demodulation,[status(thm)],[f22,f2511]) ).
fof(f2579,plain,
! [X0,X1,X2] : leq(X0,multiplication(strong_iteration(addition(one,X1)),X2)),
inference(forward_subsumption_resolution,[status(thm)],[f2578,f138]) ).
fof(f2849,plain,
! [X0,X1] : leq(X0,strong_iteration(addition(one,X1))),
inference(paramodulation,[status(thm)],[f26,f2579]) ).
fof(f2875,plain,
! [X0,X1] : leq(X0,strong_iteration(strong_iteration(X1))),
inference(paramodulation,[status(thm)],[f585,f2849]) ).
fof(f2898,plain,
! [X0,X1] : addition(strong_iteration(strong_iteration(X0)),X1) = strong_iteration(strong_iteration(X0)),
inference(resolution,[status(thm)],[f2875,f314]) ).
fof(f2994,plain,
! [X0,X1,X2] :
( strong_iteration(strong_iteration(X0)) = X2
| ~ leq(addition(strong_iteration(strong_iteration(X0)),X1),X2) ),
inference(paramodulation,[status(thm)],[f2898,f86]) ).
fof(f3056,plain,
! [X0,X1] :
( strong_iteration(strong_iteration(X0)) = X1
| ~ leq(strong_iteration(strong_iteration(X0)),X1) ),
inference(forward_demodulation,[status(thm)],[f2898,f2994]) ).
fof(f3077,plain,
! [X0,X1] : strong_iteration(strong_iteration(X0)) = strong_iteration(strong_iteration(X1)),
inference(resolution,[status(thm)],[f3056,f2875]) ).
fof(f3078,plain,
! [X0,X1] : strong_iteration(strong_iteration(X0)) = strong_iteration(addition(one,X1)),
inference(resolution,[status(thm)],[f3056,f2849]) ).
fof(f3098,plain,
! [X0] : strong_iteration(strong_iteration(X0)) != strong_iteration(one),
inference(paramodulation,[status(thm)],[f3077,f47]) ).
fof(f3273,plain,
! [X0] : strong_iteration(strong_iteration(X0)) = strong_iteration(one),
inference(paramodulation,[status(thm)],[f23,f3078]) ).
fof(f3306,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f3273,f3098]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE142+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 22:46:12 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 4.01/0.93 % Refutation found
% 4.01/0.93 % SZS status Theorem for theBenchmark: Theorem is valid
% 4.01/0.93 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.01/0.95 % Elapsed time: 0.574877 seconds
% 4.01/0.95 % CPU time: 4.346060 seconds
% 4.01/0.95 % Total memory used: 130.291 MB
% 4.01/0.95 % Net memory used: 128.149 MB
%------------------------------------------------------------------------------