%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : KLE146+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/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 : Sun Sep 27 07:43:40 AM UTC 2026
% Result : Theorem 23.37s 3.23s
% Output : CNFRefutation 23.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 24 ( 21 unt; 0 def)
% Number of atoms : 27 ( 18 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 4 ~; 2 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 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 : 35 ( 2 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0) ).
fof(additive_associativity,axiom,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0) ).
fof(additive_identity,axiom,
! [X0] : addition(X0,zero) = X0 ).
fof(idempotence,axiom,
! [X0] : addition(X0,X0) = X0 ).
fof(infty_unfold1,axiom,
! [X0] : 'strong$uiteration'(X0) = addition(multiplication(X0,'strong$uiteration'(X0)),one) ).
fof(order,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ) ).
fof(goals,conjecture,
! [X0] : leq(one,'strong$uiteration'(X0)) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] : leq(one,'strong$uiteration'(X0)),
inference(negate_conjecture,[status(cth)],[goals]) ).
cnf(c0,plain,
addition(X0,X1) = addition(X1,X0),
inference(clausification,[status(esa)],[additive_commutativity]) ).
cnf(c1,plain,
addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
inference(clausification,[status(esa)],[additive_associativity]) ).
cnf(c2,plain,
addition(X0,zero) = X0,
inference(clausification,[status(esa)],[additive_identity]) ).
cnf(c3,plain,
addition(X0,X0) = X0,
inference(clausification,[status(esa)],[idempotence]) ).
cnf(c14,plain,
'strong$uiteration'(X0) = addition(multiplication(X0,'strong$uiteration'(X0)),one),
inference(clausification,[status(esa)],[infty_unfold1]) ).
cnf(c18,plain,
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(clausification,[status(esa)],[order]) ).
cnf(c19,plain,
~ leq(one,'strong$uiteration'(sK34)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c3,c1]) ).
cnf(d1,plain,
( leq(X0,addition(X0,X1))
| addition(X0,X1) != addition(X0,X1) ),
inference(superposition,[status(thm)],[d0,c18]) ).
cnf(d2,plain,
addition(X0,addition(X1,zero)) = addition(X0,X1),
inference(superposition,[status(thm)],[c1,c2]) ).
cnf(d3,plain,
addition(X1,X0) = addition(X1,X0),
inference(demodulation,[status(thm)],[d2,c2]) ).
cnf(d4,plain,
leq(X0,addition(X0,X1)),
inference(resolution,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
'strong$uiteration'(X0) = addition(one,multiplication(X0,'strong$uiteration'(X0))),
inference(demodulation,[status(thm)],[c14,c0]) ).
cnf(d6,plain,
addition(one,multiplication(X0,'strong$uiteration'(X0))) = 'strong$uiteration'(X0),
inference(superposition,[status(thm)],[d5,d3]) ).
cnf(d7,plain,
leq(one,'strong$uiteration'(X0)),
inference(superposition,[status(thm)],[d6,d4]) ).
cnf(d8,plain,
$false,
inference(resolution,[status(thm)],[d7,c19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE146+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n020.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 : Fri Sep 25 19:27:48 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 23.37/3.23 % SZS status Theorem for theBenchmark.p
% 23.37/3.23 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------