%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : KLE040+2 : 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 : n011.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 07:43:29 AM UTC 2026
% Result : Theorem 35.41s 9.17s
% Output : CNFRefutation 35.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 51 ( 28 unt; 0 def)
% Number of atoms : 75 ( 29 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 50 ( 26 ~; 20 |; 2 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 87 ( 7 sgn 18 !; 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_idempotence,axiom,
! [X0] : addition(X0,X0) = X0 ).
fof(multiplicative_left_identity,axiom,
! [X0] : multiplication(one,X0) = X0 ).
fof(left_distributivity,axiom,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)) ).
fof(order,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ) ).
fof(star_unfold_right,axiom,
! [X0] : leq(addition(one,multiplication(X0,star(X0))),star(X0)) ).
fof(star_induction_left,axiom,
! [X0,X1,X2] :
( leq(addition(multiplication(X0,X1),X2),X1)
=> leq(multiplication(star(X0),X2),X1) ) ).
fof(goals,conjecture,
! [X0] :
( leq(star(X0),multiplication(star(X0),star(X0)))
& leq(multiplication(star(X0),star(X0)),star(X0)) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( leq(star(X0),multiplication(star(X0),star(X0)))
& leq(multiplication(star(X0),star(X0)),star(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(c3,plain,
addition(X0,X0) = X0,
inference(clausification,[status(esa)],[additive_idempotence]) ).
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)],[left_distributivity]) ).
cnf(c11,plain,
( addition(X0,X1) = X1
| ~ leq(X0,X1) ),
inference(clausification,[status(esa)],[order]) ).
cnf(c12,plain,
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(clausification,[status(esa)],[order]) ).
cnf(c13,plain,
leq(addition(one,multiplication(X0,star(X0))),star(X0)),
inference(clausification,[status(esa)],[star_unfold_right]) ).
cnf(c15,plain,
( leq(multiplication(star(X0),X2),X1)
| ~ leq(addition(multiplication(X0,X1),X2),X1) ),
inference(clausification,[status(esa)],[star_induction_left]) ).
cnf(c17,plain,
( ~ leq(star(sK30),multiplication(star(sK30),star(sK30)))
| ~ leq(multiplication(star(sK30),star(sK30)),star(sK30)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ leq(multiplication(X0,X1),X2)
| leq(multiplication(star(X0),X2),X1)
| ~ leq(X2,X1) ),
inference(superposition,[status(thm)],[c11,c15]) ).
cnf(d1,plain,
X0 = addition(X0,X0),
inference(superposition,[status(thm)],[c3,c0]) ).
cnf(d2,plain,
addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[d1,c1]) ).
cnf(d3,plain,
( leq(X0,addition(X0,X1))
| addition(X0,X1) != addition(X0,X1) ),
inference(superposition,[status(thm)],[d2,c12]) ).
cnf(d4,plain,
( ~ leq(X0,X1)
| X1 = addition(X1,X0) ),
inference(superposition,[status(thm)],[c11,c0]) ).
cnf(d5,plain,
( ~ leq(addition(X0,X1),X0)
| X0 = addition(X0,X1) ),
inference(superposition,[status(thm)],[d2,d4]) ).
cnf(d6,plain,
( X0 = addition(X0,X0)
| ~ leq(X0,X0) ),
inference(superposition,[status(thm)],[d1,d5]) ).
cnf(d7,plain,
( ~ leq(X0,X0)
| X0 = X0 ),
inference(demodulation,[status(thm)],[d6,c3]) ).
cnf(d8,plain,
( leq(X0,X0)
| X0 != X0 ),
inference(superposition,[status(thm)],[d1,c12]) ).
cnf(d9,plain,
leq(X0,X0),
inference(equality_resolution,[status(thm)],[d8]) ).
cnf(d10,plain,
X0 = X0,
inference(resolution,[status(thm)],[d9,d7]) ).
cnf(d11,plain,
leq(X0,addition(X0,X1)),
inference(resolution,[status(thm)],[d10,d3]) ).
cnf(d12,plain,
multiplication(addition(X1,one),X0) = addition(multiplication(X1,X0),X0),
inference(superposition,[status(thm)],[c6,c8]) ).
cnf(d13,plain,
multiplication(addition(X0,one),X1) = addition(X1,multiplication(X0,X1)),
inference(demodulation,[status(thm)],[d12,c0]) ).
cnf(d14,plain,
leq(X0,multiplication(addition(X1,one),X0)),
inference(superposition,[status(thm)],[d13,d11]) ).
cnf(d15,plain,
( ~ leq(one,X0)
| leq(X1,multiplication(X0,X1)) ),
inference(superposition,[status(thm)],[d4,d14]) ).
cnf(d16,plain,
( ~ leq(multiplication(star(sK30),star(sK30)),star(sK30))
| ~ leq(one,star(sK30)) ),
inference(resolution,[status(thm)],[d15,c17]) ).
cnf(d17,plain,
( ~ leq(X0,X1)
| addition(X1,X0) = X1 ),
inference(superposition,[status(thm)],[c11,c0]) ).
cnf(d18,plain,
( ~ leq(X1,X0)
| X0 = addition(X1,X0) ),
inference(superposition,[status(thm)],[d17,c0]) ).
cnf(d19,plain,
( ~ leq(addition(X0,X1),X2)
| X2 = addition(X0,addition(X1,X2)) ),
inference(superposition,[status(thm)],[c1,d18]) ).
cnf(d20,plain,
( ~ leq(addition(X0,X1),X2)
| leq(X0,X2) ),
inference(superposition,[status(thm)],[d19,d11]) ).
cnf(d21,plain,
leq(one,star(X0)),
inference(resolution,[status(thm)],[d20,c13]) ).
cnf(d22,plain,
~ leq(multiplication(star(sK30),star(sK30)),star(sK30)),
inference(resolution,[status(thm)],[d21,d16]) ).
cnf(d23,plain,
( ~ leq(multiplication(sK30,star(sK30)),star(sK30))
| ~ leq(star(sK30),star(sK30)) ),
inference(resolution,[status(thm)],[d22,d0]) ).
cnf(d24,plain,
~ leq(multiplication(sK30,star(sK30)),star(sK30)),
inference(resolution,[status(thm)],[d9,d23]) ).
cnf(d25,plain,
addition(X2,addition(X0,X1)) = addition(X0,addition(X1,X2)),
inference(superposition,[status(thm)],[c1,c0]) ).
cnf(d26,plain,
addition(X1,addition(X2,X0)) = addition(X2,addition(X1,X0)),
inference(superposition,[status(thm)],[c0,d25]) ).
cnf(d27,plain,
leq(X0,addition(X1,addition(X0,X2))),
inference(superposition,[status(thm)],[d26,d11]) ).
cnf(d28,plain,
( ~ leq(addition(X0,X1),X2)
| leq(X1,X2) ),
inference(superposition,[status(thm)],[d19,d27]) ).
cnf(d29,plain,
leq(multiplication(X0,star(X0)),star(X0)),
inference(resolution,[status(thm)],[d28,c13]) ).
cnf(d30,plain,
$false,
inference(resolution,[status(thm)],[d29,d24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE040+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n011.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 19:16:58 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 35.41/9.17 % SZS status Theorem for theBenchmark.p
% 35.41/9.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------