%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : KLE144+2 : 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 : n018.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 24.19s 12.02s
% Output : CNFRefutation 24.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 38 ( 27 unt; 0 def)
% Number of atoms : 49 ( 22 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 21 ( 10 ~; 7 |; 2 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 65 ( 11 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(multiplicative_right_identity,axiom,
! [X0] : multiplication(X0,one) = X0 ).
fof(multiplicative_left_identity,axiom,
! [X0] : multiplication(one,X0) = X0 ).
fof(distributivity2,axiom,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)) ).
fof(star_unfold1,axiom,
! [X0] : addition(one,multiplication(X0,star(X0))) = star(X0) ).
fof(infty_coinduction,axiom,
! [X0,X1,X2] :
( leq(X2,addition(multiplication(X0,X2),X1))
=> leq(X2,multiplication('strong$uiteration'(X0),X1)) ) ).
fof(order,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ) ).
fof(goals,conjecture,
! [X0] :
( leq('strong$uiteration'(one),'strong$uiteration'(star(X0)))
& leq('strong$uiteration'(star(X0)),'strong$uiteration'(one)) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( leq('strong$uiteration'(one),'strong$uiteration'(star(X0)))
& leq('strong$uiteration'(star(X0)),'strong$uiteration'(one)) ),
inference(negate_conjecture,[status(cth)],[goals]) ).
cnf(c1,plain,
addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
inference(clausification,[status(esa)],[additive_associativity]) ).
cnf(c2,plain,
addition(X0,zero) = X0,
inference(clausification,[status(esa)],[additive_identity]) ).
cnf(c3,plain,
addition(X0,X0) = X0,
inference(clausification,[status(esa)],[idempotence]) ).
cnf(c5,plain,
multiplication(X0,one) = X0,
inference(clausification,[status(esa)],[multiplicative_right_identity]) ).
cnf(c6,plain,
multiplication(one,X0) = X0,
inference(clausification,[status(esa)],[multiplicative_left_identity]) ).
cnf(c8,plain,
multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(clausification,[status(esa)],[distributivity2]) ).
cnf(c10,plain,
addition(one,multiplication(X0,star(X0))) = star(X0),
inference(clausification,[status(esa)],[star_unfold1]) ).
cnf(c15,plain,
( leq(X0,multiplication('strong$uiteration'(X1),X2))
| ~ leq(X0,addition(multiplication(X1,X0),X2)) ),
inference(clausification,[status(esa)],[infty_coinduction]) ).
cnf(c18,plain,
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(clausification,[status(esa)],[order]) ).
cnf(c19,plain,
( ~ leq('strong$uiteration'(one),'strong$uiteration'(star(sK34)))
| ~ leq('strong$uiteration'(star(sK34)),'strong$uiteration'(one)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( leq(X0,multiplication('strong$uiteration'(one),X1))
| ~ leq(X0,addition(X0,X1)) ),
inference(superposition,[status(thm)],[c6,c15]) ).
cnf(d1,plain,
addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c3,c1]) ).
cnf(d2,plain,
( leq(X0,addition(X0,X1))
| addition(X0,X1) != addition(X0,X1) ),
inference(superposition,[status(thm)],[d1,c18]) ).
cnf(d3,plain,
addition(X0,addition(X1,zero)) = addition(X0,X1),
inference(superposition,[status(thm)],[c1,c2]) ).
cnf(d4,plain,
addition(X1,X0) = addition(X1,X0),
inference(demodulation,[status(thm)],[d3,c2]) ).
cnf(d5,plain,
leq(X0,addition(X0,X1)),
inference(resolution,[status(thm)],[d4,d2]) ).
cnf(d6,plain,
leq(X0,multiplication('strong$uiteration'(one),X1)),
inference(resolution,[status(thm)],[d5,d0]) ).
cnf(d7,plain,
leq(X0,'strong$uiteration'(one)),
inference(superposition,[status(thm)],[c5,d6]) ).
cnf(d8,plain,
~ leq('strong$uiteration'(one),'strong$uiteration'(star(sK34))),
inference(resolution,[status(thm)],[d7,c19]) ).
cnf(d9,plain,
multiplication(addition(one,X1),X0) = addition(X0,multiplication(X1,X0)),
inference(superposition,[status(thm)],[c6,c8]) ).
cnf(d10,plain,
( leq(X1,multiplication('strong$uiteration'(addition(one,X0)),X2))
| ~ leq(X1,addition(addition(X1,multiplication(X0,X1)),X2)) ),
inference(superposition,[status(thm)],[d9,c15]) ).
cnf(d11,plain,
( leq(X0,multiplication('strong$uiteration'(addition(one,X1)),X2))
| ~ leq(X0,addition(X0,addition(multiplication(X1,X0),X2))) ),
inference(demodulation,[status(thm)],[d10,c1]) ).
cnf(d12,plain,
leq(X0,multiplication('strong$uiteration'(addition(one,X1)),X2)),
inference(resolution,[status(thm)],[d5,d11]) ).
cnf(d13,plain,
leq(X1,'strong$uiteration'(addition(one,X0))),
inference(superposition,[status(thm)],[c5,d12]) ).
cnf(d14,plain,
star(X0) = addition(one,multiplication(X0,star(X0))),
inference(superposition,[status(thm)],[c10,d4]) ).
cnf(d15,plain,
leq(X1,'strong$uiteration'(star(X0))),
inference(superposition,[status(thm)],[d14,d13]) ).
cnf(d16,plain,
$false,
inference(resolution,[status(thm)],[d15,d8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE144+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n018.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 19:28:50 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 24.19/12.02 % SZS status Theorem for theBenchmark.p
% 24.19/12.02 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------