%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : KLE169+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 07:43:43 AM UTC 2026
% Result : Theorem 101.38s 26.57s
% Output : CNFRefutation 101.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 10
% Syntax : Number of formulae : 60 ( 41 unt; 0 def)
% Number of atoms : 81 ( 38 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 45 ( 24 ~; 20 |; 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 102 ( 8 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(an,axiom,
sigma = addition(a,b) ).
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(right_distributivity,axiom,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)) ).
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(a,conjecture,
leq(multiplication(a,multiplication(b,a)),multiplication(star(sigma),multiplication(a,multiplication(sigma,a)))) ).
fof(negated_conjecture,negated_conjecture,
~ leq(multiplication(a,multiplication(b,a)),multiplication(star(sigma),multiplication(a,multiplication(sigma,a)))),
inference(negate_conjecture,[status(cth)],[a]) ).
cnf(c0,plain,
sigma = addition(a,b),
inference(clausification,[status(esa)],[an]) ).
cnf(c1,plain,
addition(X0,X1) = addition(X1,X0),
inference(clausification,[status(esa)],[additive_commutativity]) ).
cnf(c2,plain,
addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
inference(clausification,[status(esa)],[additive_associativity]) ).
cnf(c4,plain,
addition(X0,X0) = X0,
inference(clausification,[status(esa)],[additive_idempotence]) ).
cnf(c7,plain,
multiplication(one,X0) = X0,
inference(clausification,[status(esa)],[multiplicative_left_identity]) ).
cnf(c8,plain,
multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(clausification,[status(esa)],[right_distributivity]) ).
cnf(c9,plain,
multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(clausification,[status(esa)],[left_distributivity]) ).
cnf(c12,plain,
( addition(X0,X1) = X1
| ~ leq(X0,X1) ),
inference(clausification,[status(esa)],[order]) ).
cnf(c13,plain,
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(clausification,[status(esa)],[order]) ).
cnf(c14,plain,
leq(addition(one,multiplication(X0,star(X0))),star(X0)),
inference(clausification,[status(esa)],[star_unfold_right]) ).
cnf(c18,plain,
~ leq(multiplication(a,multiplication(b,a)),multiplication(star(sigma),multiplication(a,multiplication(sigma,a)))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( leq(multiplication(X0,X1),multiplication(X0,X2))
| multiplication(X0,addition(X1,X2)) != multiplication(X0,X2) ),
inference(superposition,[status(thm)],[c8,c13]) ).
cnf(d1,plain,
( ~ leq(X0,X1)
| leq(multiplication(X2,X0),multiplication(X2,X1))
| multiplication(X2,X1) != multiplication(X2,X1) ),
inference(superposition,[status(thm)],[c12,d0]) ).
cnf(d2,plain,
( ~ leq(X0,X1)
| X1 = addition(X1,X0) ),
inference(superposition,[status(thm)],[c12,c1]) ).
cnf(d3,plain,
addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c4,c2]) ).
cnf(d4,plain,
( ~ leq(addition(X0,X1),X0)
| X0 = addition(X0,X1) ),
inference(superposition,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
( X0 = addition(X0,X0)
| ~ leq(X0,X0) ),
inference(superposition,[status(thm)],[c4,d4]) ).
cnf(d6,plain,
( ~ leq(X0,X0)
| X0 = X0 ),
inference(demodulation,[status(thm)],[d5,c4]) ).
cnf(d7,plain,
( leq(X0,X0)
| X0 != X0 ),
inference(superposition,[status(thm)],[c4,c13]) ).
cnf(d8,plain,
leq(X0,X0),
inference(equality_resolution,[status(thm)],[d7]) ).
cnf(d9,plain,
X0 = X0,
inference(resolution,[status(thm)],[d8,d6]) ).
cnf(d10,plain,
( leq(multiplication(X2,X0),multiplication(X2,X1))
| ~ leq(X0,X1) ),
inference(resolution,[status(thm)],[d9,d1]) ).
cnf(d11,plain,
( leq(X0,addition(X0,X1))
| addition(X0,X1) != addition(X0,X1) ),
inference(superposition,[status(thm)],[d3,c13]) ).
cnf(d12,plain,
leq(X0,addition(X0,X1)),
inference(resolution,[status(thm)],[d9,d11]) ).
cnf(d13,plain,
( ~ leq(X0,X1)
| addition(X0,addition(X1,X2)) = addition(X1,X2) ),
inference(superposition,[status(thm)],[c12,c2]) ).
cnf(d14,plain,
( ~ leq(X0,X1)
| leq(X0,addition(X1,X2)) ),
inference(superposition,[status(thm)],[d13,d12]) ).
cnf(d15,plain,
( ~ leq(X0,X1)
| ~ leq(X2,X0)
| leq(X2,X1) ),
inference(superposition,[status(thm)],[c12,d14]) ).
cnf(d16,plain,
multiplication(addition(one,X1),X0) = addition(X0,multiplication(X1,X0)),
inference(superposition,[status(thm)],[c7,c9]) ).
cnf(d17,plain,
leq(X0,multiplication(addition(one,X1),X0)),
inference(superposition,[status(thm)],[d16,d12]) ).
cnf(d18,plain,
addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(superposition,[status(thm)],[c2,c1]) ).
cnf(d19,plain,
addition(X1,X0) = addition(X0,addition(X1,X0)),
inference(superposition,[status(thm)],[c4,d18]) ).
cnf(d20,plain,
( ~ leq(addition(X1,X0),X0)
| X0 = addition(X1,X0) ),
inference(superposition,[status(thm)],[d19,d2]) ).
cnf(d21,plain,
leq(X0,addition(X1,X0)),
inference(superposition,[status(thm)],[c1,d12]) ).
cnf(d22,plain,
( ~ leq(addition(X1,X2),X0)
| X0 = addition(X2,addition(X0,X1)) ),
inference(superposition,[status(thm)],[d18,d2]) ).
cnf(d23,plain,
( ~ leq(addition(X2,X0),X1)
| leq(addition(X1,X2),X1) ),
inference(superposition,[status(thm)],[d22,d21]) ).
cnf(d24,plain,
leq(addition(star(X0),one),star(X0)),
inference(resolution,[status(thm)],[d23,c14]) ).
cnf(d25,plain,
leq(addition(one,star(X0)),star(X0)),
inference(demodulation,[status(thm)],[d24,c1]) ).
cnf(d26,plain,
star(X0) = addition(one,star(X0)),
inference(resolution,[status(thm)],[d25,d20]) ).
cnf(d27,plain,
leq(X1,multiplication(star(X0),X1)),
inference(superposition,[status(thm)],[d26,d17]) ).
cnf(d28,plain,
( ~ leq(X0,X2)
| leq(X0,multiplication(star(X1),X2)) ),
inference(resolution,[status(thm)],[d27,d15]) ).
cnf(d29,plain,
~ leq(multiplication(a,multiplication(b,a)),multiplication(a,multiplication(sigma,a))),
inference(resolution,[status(thm)],[d28,c18]) ).
cnf(d30,plain,
~ leq(multiplication(b,a),multiplication(sigma,a)),
inference(resolution,[status(thm)],[d29,d10]) ).
cnf(d31,plain,
multiplication(addition(X0,X2),X1) = addition(multiplication(X2,X1),multiplication(X0,X1)),
inference(superposition,[status(thm)],[c9,c1]) ).
cnf(d32,plain,
leq(multiplication(X0,X1),multiplication(addition(X2,X0),X1)),
inference(superposition,[status(thm)],[d31,d12]) ).
cnf(d33,plain,
addition(a,addition(b,X0)) = addition(sigma,X0),
inference(superposition,[status(thm)],[c0,c2]) ).
cnf(d34,plain,
addition(a,b) = addition(sigma,b),
inference(superposition,[status(thm)],[c4,d33]) ).
cnf(d35,plain,
sigma = addition(sigma,b),
inference(demodulation,[status(thm)],[d34,c0]) ).
cnf(d36,plain,
leq(multiplication(b,X0),multiplication(sigma,X0)),
inference(superposition,[status(thm)],[d35,d32]) ).
cnf(d37,plain,
$false,
inference(resolution,[status(thm)],[d36,d30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE169+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n010.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 19:30:44 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 101.38/26.57 % SZS status Theorem for theBenchmark.p
% 101.38/26.57 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------