%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : KLE150+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 0.08s 0.58s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 53 ( 28 unt; 2 def)
% Number of atoms : 82 ( 37 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 55 ( 26 ~; 22 |; 4 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 54 ( 51 !; 3 ?)
% 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(f5,axiom,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A] : multiplication(zero,A) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A] : addition(one,multiplication(A,star(A))) = star(A),
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(f17,axiom,
! [A] : strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero)),
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] :
( leq(addition(one,multiplication(X0,zero)),strong_iteration(multiplication(X0,zero)))
& leq(strong_iteration(multiplication(X0,zero)),addition(one,multiplication(X0,zero))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ ! [X0] :
( leq(addition(one,multiplication(X0,zero)),strong_iteration(multiplication(X0,zero)))
& leq(strong_iteration(multiplication(X0,zero)),addition(one,multiplication(X0,zero))) ),
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(f25,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f30,plain,
! [X0] : multiplication(zero,X0) = zero,
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f31,plain,
! [X0] : addition(one,multiplication(X0,star(X0))) = star(X0),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f37,plain,
! [X0] : strong_iteration(X0) = addition(multiplication(X0,strong_iteration(X0)),one),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f40,plain,
! [X0] : strong_iteration(X0) = addition(star(X0),multiplication(strong_iteration(X0),zero)),
inference(cnf_transformation,[status(thm)],[f17]) ).
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] :
( ~ leq(addition(one,multiplication(X0,zero)),strong_iteration(multiplication(X0,zero)))
| ~ leq(strong_iteration(multiplication(X0,zero)),addition(one,multiplication(X0,zero))) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f46,plain,
( ? [X0] : ~ leq(addition(one,multiplication(X0,zero)),strong_iteration(multiplication(X0,zero)))
| ? [X0] : ~ leq(strong_iteration(multiplication(X0,zero)),addition(one,multiplication(X0,zero))) ),
inference(miniscoping,[status(thm)],[f45]) ).
fof(f47,plain,
( ~ leq(addition(one,multiplication(sK1_skl,zero)),strong_iteration(multiplication(sK1_skl,zero)))
| ~ leq(strong_iteration(multiplication(sK0_skl,zero)),addition(one,multiplication(sK0_skl,zero))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X0,sK0_skl),skolemize(X0,sK1_skl)],[f46]) ).
fof(f48,plain,
( ~ leq(addition(one,multiplication(sK1_skl,zero)),strong_iteration(multiplication(sK1_skl,zero)))
| ~ leq(strong_iteration(multiplication(sK0_skl,zero)),addition(one,multiplication(sK0_skl,zero))) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f49,definition,
( sQ0_spl
<=> leq(strong_iteration(multiplication(sK0_skl,zero)),addition(one,multiplication(sK0_skl,zero))) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f51,plain,
( sQ0_spl
| ~ leq(strong_iteration(multiplication(sK0_skl,zero)),addition(one,multiplication(sK0_skl,zero))) ),
inference(component_clause,[status(thm)],[f49]) ).
fof(f52,definition,
( sQ1_spl
<=> leq(addition(one,multiplication(sK1_skl,zero)),strong_iteration(multiplication(sK1_skl,zero))) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f54,plain,
( sQ1_spl
| ~ leq(addition(one,multiplication(sK1_skl,zero)),strong_iteration(multiplication(sK1_skl,zero))) ),
inference(component_clause,[status(thm)],[f52]) ).
fof(f55,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f48,f49,f52]) ).
fof(f60,plain,
( sQ0_spl
| ~ leq(strong_iteration(multiplication(sK0_skl,zero)),addition(multiplication(sK0_skl,zero),one)) ),
inference(paramodulation,[status(thm)],[f21,f51]) ).
fof(f90,plain,
! [X0,X1] : addition(X0,X1) = addition(addition(X0,X1),X1),
inference(paramodulation,[status(thm)],[f24,f22]) ).
fof(f129,plain,
! [X0,X1] : multiplication(X0,zero) = multiplication(multiplication(X0,zero),X1),
inference(paramodulation,[status(thm)],[f30,f25]) ).
fof(f136,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f21,f90]) ).
fof(f194,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f21,f136]) ).
fof(f309,plain,
( sQ0_spl
| addition(strong_iteration(multiplication(sK0_skl,zero)),addition(multiplication(sK0_skl,zero),one)) != addition(multiplication(sK0_skl,zero),one) ),
inference(resolution,[status(thm)],[f60,f44]) ).
fof(f869,plain,
! [X0] : strong_iteration(X0) = addition(multiplication(strong_iteration(X0),zero),star(X0)),
inference(paramodulation,[status(thm)],[f21,f40]) ).
fof(f874,plain,
! [X0] : addition(multiplication(strong_iteration(X0),zero),star(X0)) = addition(star(X0),strong_iteration(X0)),
inference(paramodulation,[status(thm)],[f40,f194]) ).
fof(f891,plain,
! [X0] : strong_iteration(X0) = addition(star(X0),strong_iteration(X0)),
inference(forward_demodulation,[status(thm)],[f869,f874]) ).
fof(f1212,plain,
! [X0] : strong_iteration(multiplication(X0,zero)) = addition(multiplication(X0,zero),one),
inference(paramodulation,[status(thm)],[f129,f37]) ).
fof(f1213,plain,
! [X0] : addition(one,multiplication(X0,zero)) = star(multiplication(X0,zero)),
inference(paramodulation,[status(thm)],[f129,f31]) ).
fof(f1230,plain,
( sQ0_spl
| addition(strong_iteration(multiplication(sK0_skl,zero)),addition(multiplication(sK0_skl,zero),one)) != strong_iteration(multiplication(sK0_skl,zero)) ),
inference(backward_demodulation,[status(thm)],[f1212,f309]) ).
fof(f1247,plain,
( sQ0_spl
| addition(strong_iteration(multiplication(sK0_skl,zero)),strong_iteration(multiplication(sK0_skl,zero))) != strong_iteration(multiplication(sK0_skl,zero)) ),
inference(forward_demodulation,[status(thm)],[f1212,f1230]) ).
fof(f1248,plain,
( sQ0_spl
| strong_iteration(multiplication(sK0_skl,zero)) != strong_iteration(multiplication(sK0_skl,zero)) ),
inference(forward_demodulation,[status(thm)],[f24,f1247]) ).
fof(f1249,plain,
( sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1248]) ).
fof(f1250,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f1249]) ).
fof(f1251,plain,
( sQ1_spl
| ~ leq(star(multiplication(sK1_skl,zero)),strong_iteration(multiplication(sK1_skl,zero))) ),
inference(forward_demodulation,[status(thm)],[f1213,f54]) ).
fof(f1253,plain,
( sQ1_spl
| addition(star(multiplication(sK1_skl,zero)),strong_iteration(multiplication(sK1_skl,zero))) != strong_iteration(multiplication(sK1_skl,zero)) ),
inference(resolution,[status(thm)],[f1251,f44]) ).
fof(f1254,plain,
( sQ1_spl
| strong_iteration(multiplication(sK1_skl,zero)) != strong_iteration(multiplication(sK1_skl,zero)) ),
inference(forward_demodulation,[status(thm)],[f891,f1253]) ).
fof(f1255,plain,
( sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1254]) ).
fof(f1256,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f1255]) ).
fof(f1257,plain,
$false,
inference(sat_refutation,[status(thm)],[f55,f1250,f1256]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE150+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n020.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 20 22:47:33 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.08/0.58 % Refutation found
% 0.08/0.58 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.29/0.60 % Elapsed time: 0.221242 seconds
% 1.29/0.60 % CPU time: 1.502893 seconds
% 1.29/0.60 % Total memory used: 89.957 MB
% 1.29/0.60 % Net memory used: 89.245 MB
%------------------------------------------------------------------------------