%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : KLE150+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 : Sun Sep 27 07:43:41 AM UTC 2026
% Result : Theorem 32.10s 5.05s
% Output : CNFRefutation 32.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 26 ( 26 unt; 0 def)
% Number of atoms : 26 ( 25 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 33 ( 2 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0) ).
fof(multiplicative_associativity,axiom,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2) ).
fof(multiplicative_right_identity,axiom,
! [X0] : multiplication(X0,one) = X0 ).
fof(left_annihilation,axiom,
! [X0] : multiplication(zero,X0) = zero ).
fof(star_unfold1,axiom,
! [X0] : addition(one,multiplication(X0,star(X0))) = star(X0) ).
fof(infty_unfold1,axiom,
! [X0] : 'strong$uiteration'(X0) = addition(multiplication(X0,'strong$uiteration'(X0)),one) ).
fof(goals,conjecture,
! [X0] : 'strong$uiteration'(multiplication(X0,zero)) = addition(one,multiplication(X0,zero)) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] : 'strong$uiteration'(multiplication(X0,zero)) = addition(one,multiplication(X0,zero)),
inference(negate_conjecture,[status(cth)],[goals]) ).
cnf(c0,plain,
addition(X0,X1) = addition(X1,X0),
inference(clausification,[status(esa)],[additive_commutativity]) ).
cnf(c4,plain,
multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(clausification,[status(esa)],[multiplicative_associativity]) ).
cnf(c5,plain,
multiplication(X0,one) = X0,
inference(clausification,[status(esa)],[multiplicative_right_identity]) ).
cnf(c9,plain,
multiplication(zero,X0) = zero,
inference(clausification,[status(esa)],[left_annihilation]) ).
cnf(c10,plain,
addition(one,multiplication(X0,star(X0))) = star(X0),
inference(clausification,[status(esa)],[star_unfold1]) ).
cnf(c14,plain,
'strong$uiteration'(X0) = addition(multiplication(X0,'strong$uiteration'(X0)),one),
inference(clausification,[status(esa)],[infty_unfold1]) ).
cnf(c19,plain,
'strong$uiteration'(multiplication(sK34,zero)) != addition(one,multiplication(sK34,zero)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
addition(one,multiplication(X0,multiplication(X1,star(multiplication(X0,X1))))) = star(multiplication(X0,X1)),
inference(superposition,[status(thm)],[c4,c10]) ).
cnf(d1,plain,
multiplication(X0,multiplication(X1,one)) = multiplication(X0,X1),
inference(superposition,[status(thm)],[c4,c5]) ).
cnf(d2,plain,
multiplication(X1,X0) = multiplication(X1,X0),
inference(demodulation,[status(thm)],[d1,c5]) ).
cnf(d3,plain,
zero = multiplication(zero,X0),
inference(superposition,[status(thm)],[c9,d2]) ).
cnf(d4,plain,
addition(one,multiplication(X0,zero)) = star(multiplication(X0,zero)),
inference(superposition,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
'strong$uiteration'(multiplication(sK34,zero)) != star(multiplication(sK34,zero)),
inference(demodulation,[status(thm)],[c19,d4]) ).
cnf(d6,plain,
'strong$uiteration'(X0) = addition(one,multiplication(X0,'strong$uiteration'(X0))),
inference(demodulation,[status(thm)],[c14,c0]) ).
cnf(d7,plain,
'strong$uiteration'(multiplication(X0,X1)) = addition(one,multiplication(X0,multiplication(X1,'strong$uiteration'(multiplication(X0,X1))))),
inference(superposition,[status(thm)],[c4,d6]) ).
cnf(d8,plain,
'strong$uiteration'(multiplication(X0,zero)) = addition(one,multiplication(X0,zero)),
inference(superposition,[status(thm)],[d3,d7]) ).
cnf(d9,plain,
'strong$uiteration'(multiplication(X0,zero)) = star(multiplication(X0,zero)),
inference(demodulation,[status(thm)],[d8,d4]) ).
cnf(d10,plain,
$false,
inference(resolution,[status(thm)],[d9,d5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE150+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 19:33:25 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 32.10/5.05 % SZS status Theorem for theBenchmark.p
% 32.10/5.05 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------