%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE142+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 : n004.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 1.36s 0.64s
% Output : CNFRefutation 1.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of formulae : 56 ( 35 unt; 0 def)
% Number of atoms : 81 ( 31 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 59 ( 34 ~; 19 |; 4 &)
% ( 1 <=>; 1 =>; 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 : 85 ( 82 !; 3 ?)
% 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(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(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(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] :
( leq(strong_iteration(one),strong_iteration(strong_iteration(X0)))
& leq(strong_iteration(strong_iteration(X0)),strong_iteration(one)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ ! [X0] :
( leq(strong_iteration(one),strong_iteration(strong_iteration(X0)))
& leq(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(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(f28,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[status(thm)],[f8]) ).
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] :
( ~ leq(strong_iteration(one),strong_iteration(strong_iteration(X0)))
| ~ leq(strong_iteration(strong_iteration(X0)),strong_iteration(one)) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f46,plain,
( ? [X0] : ~ leq(strong_iteration(one),strong_iteration(strong_iteration(X0)))
| ? [X0] : ~ leq(strong_iteration(strong_iteration(X0)),strong_iteration(one)) ),
inference(miniscoping,[status(thm)],[f45]) ).
fof(f47,plain,
( ~ leq(strong_iteration(one),strong_iteration(strong_iteration(sK1_skl)))
| ~ leq(strong_iteration(strong_iteration(sK0_skl)),strong_iteration(one)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X0,sK0_skl),skolemize(X0,sK1_skl)],[f46]) ).
fof(f48,plain,
( ~ leq(strong_iteration(one),strong_iteration(strong_iteration(sK1_skl)))
| ~ leq(strong_iteration(strong_iteration(sK0_skl)),strong_iteration(one)) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f60,plain,
! [X0] : leq(X0,X0),
inference(resolution,[status(thm)],[f24,f44]) ).
fof(f100,plain,
! [X0,X1] : addition(multiplication(X0,strong_iteration(X0)),addition(one,X1)) = addition(strong_iteration(X0),X1),
inference(paramodulation,[status(thm)],[f37,f22]) ).
fof(f107,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f24,f22]) ).
fof(f136,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(multiplication(X0,X1),X0),
inference(paramodulation,[status(thm)],[f26,f28]) ).
fof(f158,plain,
! [X0,X1,X2] :
( addition(X0,multiplication(strong_iteration(X1),X2)) = multiplication(strong_iteration(X1),X2)
| ~ leq(X0,addition(multiplication(X1,X0),X2)) ),
inference(resolution,[status(thm)],[f39,f43]) ).
fof(f159,plain,
! [X0,X1] :
( leq(X0,strong_iteration(X1))
| ~ leq(X0,addition(multiplication(X1,X0),one)) ),
inference(paramodulation,[status(thm)],[f26,f39]) ).
fof(f226,plain,
! [X0,X1] : leq(X0,addition(X0,X1)),
inference(resolution,[status(thm)],[f107,f44]) ).
fof(f275,plain,
! [X0,X1] : leq(X0,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f21,f226]) ).
fof(f283,plain,
! [X0,X1,X2] : leq(X0,addition(X1,addition(X2,X0))),
inference(paramodulation,[status(thm)],[f22,f275]) ).
fof(f303,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(multiplication(X0,X1),X1),
inference(paramodulation,[status(thm)],[f27,f29]) ).
fof(f365,plain,
! [X0,X1] : leq(one,addition(X0,strong_iteration(X1))),
inference(paramodulation,[status(thm)],[f37,f283]) ).
fof(f454,plain,
! [X0] : addition(multiplication(X0,strong_iteration(X0)),one) = addition(strong_iteration(X0),one),
inference(paramodulation,[status(thm)],[f24,f100]) ).
fof(f479,plain,
! [X0] : strong_iteration(X0) = addition(strong_iteration(X0),one),
inference(forward_demodulation,[status(thm)],[f37,f454]) ).
fof(f2644,plain,
! [X0,X1] : addition(one,multiplication(strong_iteration(X0),strong_iteration(X1))) = multiplication(strong_iteration(X0),strong_iteration(X1)),
inference(resolution,[status(thm)],[f158,f365]) ).
fof(f2687,plain,
( ~ leq(strong_iteration(strong_iteration(sK0_skl)),strong_iteration(one))
| ~ leq(strong_iteration(one),addition(multiplication(strong_iteration(sK1_skl),strong_iteration(one)),one)) ),
inference(resolution,[status(thm)],[f159,f48]) ).
fof(f2691,plain,
( ~ leq(strong_iteration(strong_iteration(sK0_skl)),strong_iteration(one))
| ~ leq(strong_iteration(one),addition(one,multiplication(strong_iteration(sK1_skl),strong_iteration(one)))) ),
inference(paramodulation,[status(thm)],[f21,f2687]) ).
fof(f2693,plain,
( ~ leq(strong_iteration(strong_iteration(sK0_skl)),strong_iteration(one))
| ~ leq(strong_iteration(one),multiplication(strong_iteration(sK1_skl),strong_iteration(one))) ),
inference(forward_demodulation,[status(thm)],[f2644,f2691]) ).
fof(f2695,plain,
( ~ leq(strong_iteration(one),addition(multiplication(sK1_skl,strong_iteration(one)),strong_iteration(one)))
| ~ leq(strong_iteration(strong_iteration(sK0_skl)),strong_iteration(one)) ),
inference(resolution,[status(thm)],[f2693,f39]) ).
fof(f2696,plain,
( ~ leq(strong_iteration(one),multiplication(addition(sK1_skl,one),strong_iteration(one)))
| ~ leq(strong_iteration(strong_iteration(sK0_skl)),strong_iteration(one)) ),
inference(forward_demodulation,[status(thm)],[f303,f2695]) ).
fof(f3070,plain,
! [X0,X1] : leq(X0,multiplication(addition(X1,one),X0)),
inference(paramodulation,[status(thm)],[f303,f275]) ).
fof(f3113,plain,
~ leq(strong_iteration(strong_iteration(sK0_skl)),strong_iteration(one)),
inference(backward_subsumption_resolution,[status(thm)],[f2696,f3070]) ).
fof(f3183,plain,
~ leq(strong_iteration(strong_iteration(sK0_skl)),addition(multiplication(one,strong_iteration(strong_iteration(sK0_skl))),one)),
inference(resolution,[status(thm)],[f3113,f159]) ).
fof(f3184,plain,
~ leq(strong_iteration(strong_iteration(sK0_skl)),multiplication(one,addition(strong_iteration(strong_iteration(sK0_skl)),one))),
inference(forward_demodulation,[status(thm)],[f136,f3183]) ).
fof(f3185,plain,
~ leq(strong_iteration(strong_iteration(sK0_skl)),addition(strong_iteration(strong_iteration(sK0_skl)),one)),
inference(forward_demodulation,[status(thm)],[f27,f3184]) ).
fof(f3186,plain,
~ leq(strong_iteration(strong_iteration(sK0_skl)),strong_iteration(strong_iteration(sK0_skl))),
inference(forward_demodulation,[status(thm)],[f479,f3185]) ).
fof(f3187,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f3186,f60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE142+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n004.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 22:46:06 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.39 % Drodi V4.1.1
% 1.36/0.64 % Refutation found
% 1.36/0.64 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.36/0.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.36/0.65 % Elapsed time: 0.265138 seconds
% 1.36/0.65 % CPU time: 1.808408 seconds
% 1.36/0.65 % Total memory used: 95.346 MB
% 1.36/0.65 % Net memory used: 94.508 MB
%------------------------------------------------------------------------------