%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE040+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 : n014.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 12:57:50 PM UTC 2026
% Result : Theorem 1.38s 0.59s
% Output : CNFRefutation 1.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 54 ( 26 unt; 2 def)
% Number of atoms : 86 ( 34 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 60 ( 28 ~; 24 |; 4 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 65 ( 62 !; 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(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(f12,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A] : leq(addition(one,multiplication(A,star(A))),star(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A,B,C] :
( leq(addition(multiplication(A,B),C),B)
=> leq(multiplication(star(A),C),B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,conjecture,
! [X0] :
( leq(star(X0),multiplication(star(X0),star(X0)))
& leq(multiplication(star(X0),star(X0)),star(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [X0] :
( leq(star(X0),multiplication(star(X0),star(X0)))
& leq(multiplication(star(X0),star(X0)),star(X0)) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f20,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f22,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f24,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f26,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,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f12]) ).
fof(f31,plain,
( ! [A,B] :
( addition(A,B) != B
| leq(A,B) )
& ! [A,B] :
( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(miniscoping,[status(thm)],[f30]) ).
fof(f32,plain,
! [X0,X1] :
( addition(X0,X1) = X1
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f33,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f34,plain,
! [X0] : leq(addition(one,multiplication(X0,star(X0))),star(X0)),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f36,plain,
! [A,B,C] :
( leq(multiplication(star(A),C),B)
| ~ leq(addition(multiplication(A,B),C),B) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f37,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),X2),X1)
| ~ leq(addition(multiplication(X0,X1),X2),X1) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f40,plain,
? [X0] :
( ~ leq(star(X0),multiplication(star(X0),star(X0)))
| ~ leq(multiplication(star(X0),star(X0)),star(X0)) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f41,plain,
( ? [X0] : ~ leq(star(X0),multiplication(star(X0),star(X0)))
| ? [X0] : ~ leq(multiplication(star(X0),star(X0)),star(X0)) ),
inference(miniscoping,[status(thm)],[f40]) ).
fof(f42,plain,
( ~ leq(star(sK1_skl),multiplication(star(sK1_skl),star(sK1_skl)))
| ~ leq(multiplication(star(sK0_skl),star(sK0_skl)),star(sK0_skl)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X0,sK0_skl),skolemize(X0,sK1_skl)],[f41]) ).
fof(f43,plain,
( ~ leq(star(sK1_skl),multiplication(star(sK1_skl),star(sK1_skl)))
| ~ leq(multiplication(star(sK0_skl),star(sK0_skl)),star(sK0_skl)) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f44,definition,
( sQ0_spl
<=> leq(multiplication(star(sK0_skl),star(sK0_skl)),star(sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f46,plain,
( sQ0_spl
| ~ leq(multiplication(star(sK0_skl),star(sK0_skl)),star(sK0_skl)) ),
inference(component_clause,[status(thm)],[f44]) ).
fof(f47,definition,
( sQ1_spl
<=> leq(star(sK1_skl),multiplication(star(sK1_skl),star(sK1_skl))) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f49,plain,
( sQ1_spl
| ~ leq(star(sK1_skl),multiplication(star(sK1_skl),star(sK1_skl))) ),
inference(component_clause,[status(thm)],[f47]) ).
fof(f50,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f43,f44,f47]) ).
fof(f56,plain,
( sQ0_spl
| ~ leq(addition(multiplication(sK0_skl,star(sK0_skl)),star(sK0_skl)),star(sK0_skl)) ),
inference(resolution,[status(thm)],[f37,f46]) ).
fof(f61,plain,
( sQ0_spl
| addition(addition(multiplication(sK0_skl,star(sK0_skl)),star(sK0_skl)),star(sK0_skl)) != star(sK0_skl) ),
inference(resolution,[status(thm)],[f56,f33]) ).
fof(f62,plain,
( sQ0_spl
| addition(multiplication(sK0_skl,star(sK0_skl)),addition(star(sK0_skl),star(sK0_skl))) != star(sK0_skl) ),
inference(forward_demodulation,[status(thm)],[f20,f61]) ).
fof(f63,plain,
( sQ0_spl
| addition(multiplication(sK0_skl,star(sK0_skl)),star(sK0_skl)) != star(sK0_skl) ),
inference(forward_demodulation,[status(thm)],[f22,f62]) ).
fof(f100,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f19,f20]) ).
fof(f107,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f22,f20]) ).
fof(f126,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f24,f26]) ).
fof(f358,plain,
! [X0] : addition(addition(one,multiplication(X0,star(X0))),star(X0)) = star(X0),
inference(resolution,[status(thm)],[f34,f32]) ).
fof(f362,plain,
! [X0] : addition(one,addition(multiplication(X0,star(X0)),star(X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f20,f358]) ).
fof(f505,plain,
! [X0] : addition(one,addition(star(X0),multiplication(X0,star(X0)))) = star(X0),
inference(paramodulation,[status(thm)],[f19,f362]) ).
fof(f513,plain,
! [X0] : addition(one,star(X0)) = addition(one,addition(multiplication(X0,star(X0)),star(X0))),
inference(paramodulation,[status(thm)],[f362,f107]) ).
fof(f525,plain,
! [X0] : addition(one,star(X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f362,f513]) ).
fof(f664,plain,
! [X0,X1] : addition(one,addition(star(X0),X1)) = addition(X1,star(X0)),
inference(paramodulation,[status(thm)],[f525,f100]) ).
fof(f669,plain,
! [X0] : addition(multiplication(X0,star(X0)),star(X0)) = star(X0),
inference(backward_demodulation,[status(thm)],[f664,f505]) ).
fof(f674,plain,
( sQ0_spl
| star(sK0_skl) != star(sK0_skl) ),
inference(backward_demodulation,[status(thm)],[f669,f63]) ).
fof(f677,plain,
( sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f674]) ).
fof(f678,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f677]) ).
fof(f681,plain,
( sQ1_spl
| addition(star(sK1_skl),multiplication(star(sK1_skl),star(sK1_skl))) != multiplication(star(sK1_skl),star(sK1_skl)) ),
inference(resolution,[status(thm)],[f49,f33]) ).
fof(f940,plain,
! [X0,X1] : multiplication(X0,star(X1)) = addition(X0,multiplication(X0,star(X1))),
inference(paramodulation,[status(thm)],[f525,f126]) ).
fof(f992,plain,
( sQ1_spl
| multiplication(star(sK1_skl),star(sK1_skl)) != multiplication(star(sK1_skl),star(sK1_skl)) ),
inference(backward_demodulation,[status(thm)],[f940,f681]) ).
fof(f1041,plain,
( sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f992]) ).
fof(f1042,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f1041]) ).
fof(f1043,plain,
$false,
inference(sat_refutation,[status(thm)],[f50,f678,f1042]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE040+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n014.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.02/0.36 % CPULimit : 300
% 0.02/0.36 % WCLimit : 300
% 0.02/0.36 % DateTime : Sun Sep 20 22:40:20 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.37 % Drodi V4.1.1
% 1.38/0.59 % Refutation found
% 1.38/0.59 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.38/0.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.38/0.61 % Elapsed time: 0.232787 seconds
% 1.38/0.61 % CPU time: 1.662280 seconds
% 1.38/0.61 % Total memory used: 91.973 MB
% 1.38/0.61 % Net memory used: 91.135 MB
%------------------------------------------------------------------------------