%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : KLE167+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 : n009.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 07:43:42 AM UTC 2026
% Result : Theorem 38.76s 7.80s
% Output : CNFRefutation 38.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 44 ( 30 unt; 0 def)
% Number of atoms : 60 ( 32 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 30 ( 14 ~; 10 |; 2 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 69 ( 3 sgn 21 !; 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(multiplicative_right_identity,axiom,
! [X0] : multiplication(X0,one) = X0 ).
fof(distributivity1,axiom,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)) ).
fof(star_unfold1,axiom,
! [X0] : addition(one,multiplication(X0,star(X0))) = star(X0) ).
fof(star_induction2,axiom,
! [X0,X1,X2] :
( leq(addition(multiplication(X2,X0),X1),X2)
=> leq(multiplication(X1,star(X0)),X2) ) ).
fof(order,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ) ).
fof(goals,conjecture,
! [X0,X1] :
( leq(X0,multiplication(X0,star(X1)))
& ( multiplication(X0,X1) = zero
=> leq(multiplication(X0,star(X1)),X0) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( leq(X0,multiplication(X0,star(X1)))
& ( multiplication(X0,X1) = zero
=> leq(multiplication(X0,star(X1)),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(addition(X0,X1),X2) = addition(X0,addition(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(c7,plain,
addition(multiplication(X0,X1),multiplication(X0,X2)) = multiplication(X0,addition(X1,X2)),
inference(clausification,[status(esa)],[distributivity1]) ).
cnf(c10,plain,
star(X0) = addition(one,multiplication(X0,star(X0))),
inference(clausification,[status(esa)],[star_unfold1]) ).
cnf(c13,plain,
( leq(multiplication(X2,star(X1)),X0)
| ~ leq(addition(multiplication(X0,X1),X2),X0) ),
inference(clausification,[status(esa)],[star_induction2]) ).
cnf(c18,plain,
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(clausification,[status(esa)],[order]) ).
cnf(c19,plain,
( ~ leq(sK34,multiplication(sK34,star(sK35)))
| multiplication(sK34,sK35) = zero ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c20,plain,
( ~ leq(sK34,multiplication(sK34,star(sK35)))
| ~ leq(multiplication(sK34,star(sK35)),sK34) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
addition(X2,addition(X0,X1)) = addition(X0,addition(X1,X2)),
inference(superposition,[status(thm)],[c1,c0]) ).
cnf(d1,plain,
addition(X0,addition(X1,X0)) = addition(X1,X0),
inference(superposition,[status(thm)],[c3,d0]) ).
cnf(d2,plain,
addition(X0,addition(X1,addition(X0,X1))) = addition(X0,X1),
inference(superposition,[status(thm)],[c1,c3]) ).
cnf(d3,plain,
( leq(X0,addition(X1,addition(X0,X1)))
| addition(X0,X1) != addition(X1,addition(X0,X1)) ),
inference(superposition,[status(thm)],[d2,c18]) ).
cnf(d4,plain,
( leq(X1,addition(X0,addition(X1,X0)))
| addition(X1,X0) != addition(X1,X0) ),
inference(demodulation,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
( leq(X1,addition(X1,X0))
| addition(X1,X0) != addition(X1,X0) ),
inference(demodulation,[status(thm)],[d4,d1]) ).
cnf(d6,plain,
addition(X0,addition(X1,zero)) = addition(X0,X1),
inference(superposition,[status(thm)],[c1,c2]) ).
cnf(d7,plain,
addition(X1,X0) = addition(X1,X0),
inference(demodulation,[status(thm)],[d6,c2]) ).
cnf(d8,plain,
leq(X0,addition(X0,X1)),
inference(resolution,[status(thm)],[d7,d5]) ).
cnf(d9,plain,
addition(X0,multiplication(X0,X1)) = multiplication(X0,addition(one,X1)),
inference(superposition,[status(thm)],[c5,c7]) ).
cnf(d10,plain,
leq(X0,multiplication(X0,addition(one,X1))),
inference(superposition,[status(thm)],[d9,d8]) ).
cnf(d11,plain,
addition(one,multiplication(X0,star(X0))) = star(X0),
inference(superposition,[status(thm)],[c10,d7]) ).
cnf(d12,plain,
leq(X1,multiplication(X1,star(X0))),
inference(superposition,[status(thm)],[d11,d10]) ).
cnf(d13,plain,
~ leq(multiplication(sK34,star(sK35)),sK34),
inference(resolution,[status(thm)],[d12,c20]) ).
cnf(d14,plain,
addition(zero,X0) = X0,
inference(superposition,[status(thm)],[c2,c0]) ).
cnf(d15,plain,
multiplication(sK34,sK35) = zero,
inference(resolution,[status(thm)],[d12,c19]) ).
cnf(d16,plain,
( leq(multiplication(X0,star(sK35)),sK34)
| ~ leq(addition(zero,X0),sK34) ),
inference(superposition,[status(thm)],[d15,c13]) ).
cnf(d17,plain,
( leq(multiplication(X0,star(sK35)),sK34)
| ~ leq(X0,sK34) ),
inference(demodulation,[status(thm)],[d16,d14]) ).
cnf(d18,plain,
~ leq(sK34,sK34),
inference(resolution,[status(thm)],[d17,d13]) ).
cnf(d19,plain,
( leq(X0,X0)
| X0 != X0 ),
inference(superposition,[status(thm)],[c3,c18]) ).
cnf(d20,plain,
leq(X0,X0),
inference(equality_resolution,[status(thm)],[d19]) ).
cnf(d21,plain,
$false,
inference(resolution,[status(thm)],[d20,d18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE167+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
% 0.07/0.34 % Computer : n009.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Fri Sep 25 19:29:43 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 38.76/7.80 % SZS status Theorem for theBenchmark.p
% 38.76/7.80 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------