%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : KLE142+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 07:43:39 AM UTC 2026
% Result : Theorem 8.61s 14.37s
% Output : CNFRefutation 8.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 58 ( 35 unt; 0 def)
% Number of atoms : 82 ( 34 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 48 ( 24 ~; 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 : 97 ( 13 sgn 22 !; 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(idempotence,axiom,
! [X0] : addition(X0,X0) = X0 ).
fof(multiplicative_associativity,axiom,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2) ).
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(infty_unfold1,axiom,
! [X0] : 'strong$uiteration'(X0) = addition(multiplication(X0,'strong$uiteration'(X0)),one) ).
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$uiteration'('strong$uiteration'(X0)))
& leq('strong$uiteration'('strong$uiteration'(X0)),'strong$uiteration'(one)) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( leq('strong$uiteration'(one),'strong$uiteration'('strong$uiteration'(X0)))
& leq('strong$uiteration'('strong$uiteration'(X0)),'strong$uiteration'(one)) ),
inference(negate_conjecture,[status(cth)],[goals]) ).
cnf(c0,plain,
addition(X0,X1) = addition(X1,X0),
inference(clausification,[status(esa)],[additive_commutativity]) ).
cnf(c1,plain,
addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
inference(clausification,[status(esa)],[additive_associativity]) ).
cnf(c3,plain,
addition(X0,X0) = X0,
inference(clausification,[status(esa)],[idempotence]) ).
cnf(c4,plain,
multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(clausification,[status(esa)],[multiplicative_associativity]) ).
cnf(c5,plain,
multiplication(X0,one) = X0,
inference(clausification,[status(esa)],[multiplicative_right_identity]) ).
cnf(c6,plain,
multiplication(one,X0) = X0,
inference(clausification,[status(esa)],[multiplicative_left_identity]) ).
cnf(c8,plain,
multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(clausification,[status(esa)],[distributivity2]) ).
cnf(c14,plain,
'strong$uiteration'(X0) = addition(multiplication(X0,'strong$uiteration'(X0)),one),
inference(clausification,[status(esa)],[infty_unfold1]) ).
cnf(c15,plain,
( leq(X0,multiplication('strong$uiteration'(X1),X2))
| ~ leq(X0,addition(multiplication(X1,X0),X2)) ),
inference(clausification,[status(esa)],[infty_coinduction]) ).
cnf(c17,plain,
( addition(X0,X1) = X1
| ~ leq(X0,X1) ),
inference(clausification,[status(esa)],[order]) ).
cnf(c18,plain,
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(clausification,[status(esa)],[order]) ).
cnf(c19,plain,
( ~ leq('strong$uiteration'(one),'strong$uiteration'('strong$uiteration'(sK34)))
| ~ leq('strong$uiteration'('strong$uiteration'(sK34)),'strong$uiteration'(one)) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( leq(X0,multiplication('strong$uiteration'(one),X1))
| ~ leq(X0,addition(X0,X1)) ),
inference(superposition,[status(thm)],[c6,c15]) ).
cnf(d1,plain,
multiplication(X0,multiplication(X1,one)) = multiplication(X0,X1),
inference(superposition,[status(thm)],[c4,c5]) ).
cnf(d2,plain,
multiplication(X1,X0) = multiplication(X1,X0),
inference(demodulation,[status(thm)],[d1,c5]) ).
cnf(d3,plain,
X0 = multiplication(X0,one),
inference(superposition,[status(thm)],[c5,d2]) ).
cnf(d4,plain,
( ~ leq(X0,addition(X0,one))
| leq(X0,'strong$uiteration'(one)) ),
inference(superposition,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
( ~ leq(X0,X1)
| X1 = addition(X1,X0) ),
inference(superposition,[status(thm)],[c17,c0]) ).
cnf(d6,plain,
( ~ leq(one,X0)
| leq(X0,'strong$uiteration'(one))
| ~ leq(X0,X0) ),
inference(superposition,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
( leq(X0,X0)
| X0 != X0 ),
inference(superposition,[status(thm)],[c3,c18]) ).
cnf(d8,plain,
leq(X0,X0),
inference(equality_resolution,[status(thm)],[d7]) ).
cnf(d9,plain,
( ~ leq(one,X0)
| leq(X0,'strong$uiteration'(one)) ),
inference(resolution,[status(thm)],[d8,d6]) ).
cnf(d10,plain,
( ~ leq('strong$uiteration'(one),'strong$uiteration'('strong$uiteration'(sK34)))
| ~ leq(one,'strong$uiteration'('strong$uiteration'(sK34))) ),
inference(resolution,[status(thm)],[d9,c19]) ).
cnf(d11,plain,
( leq(one,multiplication('strong$uiteration'(X0),X1))
| ~ leq(one,addition(X0,X1)) ),
inference(superposition,[status(thm)],[c5,c15]) ).
cnf(d12,plain,
( ~ leq(one,addition(X0,one))
| leq(one,'strong$uiteration'(X0)) ),
inference(superposition,[status(thm)],[d3,d11]) ).
cnf(d13,plain,
( leq(one,'strong$uiteration'(X0))
| ~ leq(one,addition(one,X0)) ),
inference(superposition,[status(thm)],[c0,d12]) ).
cnf(d14,plain,
addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c3,c1]) ).
cnf(d15,plain,
( leq(X0,addition(X0,X1))
| addition(X0,X1) != addition(X0,X1) ),
inference(superposition,[status(thm)],[d14,c18]) ).
cnf(d16,plain,
( ~ leq(addition(X0,X1),X0)
| X0 = addition(X0,X1) ),
inference(superposition,[status(thm)],[d14,d5]) ).
cnf(d17,plain,
X0 = addition(X0,X0),
inference(superposition,[status(thm)],[c3,c0]) ).
cnf(d18,plain,
( X0 = addition(X0,X0)
| ~ leq(X0,X0) ),
inference(superposition,[status(thm)],[d17,d16]) ).
cnf(d19,plain,
( ~ leq(X0,X0)
| X0 = X0 ),
inference(demodulation,[status(thm)],[d18,c3]) ).
cnf(d20,plain,
X0 = X0,
inference(resolution,[status(thm)],[d8,d19]) ).
cnf(d21,plain,
leq(X0,addition(X0,X1)),
inference(resolution,[status(thm)],[d20,d15]) ).
cnf(d22,plain,
leq(one,'strong$uiteration'(X0)),
inference(resolution,[status(thm)],[d21,d13]) ).
cnf(d23,plain,
~ leq('strong$uiteration'(one),'strong$uiteration'('strong$uiteration'(sK34))),
inference(resolution,[status(thm)],[d22,d10]) ).
cnf(d24,plain,
( leq(X1,multiplication('strong$uiteration'(X0),X2))
| ~ leq(X1,addition(X2,multiplication(X0,X1))) ),
inference(superposition,[status(thm)],[c0,c15]) ).
cnf(d25,plain,
addition(X2,addition(X0,X1)) = addition(X0,addition(X1,X2)),
inference(superposition,[status(thm)],[c1,c0]) ).
cnf(d26,plain,
leq(X0,addition(X2,addition(X0,X1))),
inference(superposition,[status(thm)],[d25,d21]) ).
cnf(d27,plain,
multiplication(addition(one,X1),X0) = addition(X0,multiplication(X1,X0)),
inference(superposition,[status(thm)],[c6,c8]) ).
cnf(d28,plain,
leq(X0,addition(X2,multiplication(addition(one,X1),X0))),
inference(superposition,[status(thm)],[d27,d26]) ).
cnf(d29,plain,
leq(X0,multiplication('strong$uiteration'(addition(one,X1)),X2)),
inference(resolution,[status(thm)],[d28,d24]) ).
cnf(d30,plain,
leq(X1,'strong$uiteration'(addition(one,X0))),
inference(superposition,[status(thm)],[d3,d29]) ).
cnf(d31,plain,
'strong$uiteration'(X0) = addition(one,multiplication(X0,'strong$uiteration'(X0))),
inference(demodulation,[status(thm)],[c14,c0]) ).
cnf(d32,plain,
leq(X1,'strong$uiteration'('strong$uiteration'(X0))),
inference(superposition,[status(thm)],[d31,d30]) ).
cnf(d33,plain,
$false,
inference(resolution,[status(thm)],[d32,d23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : KLE142+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.44 % Computer : n018.cluster.edu
% 0.12/0.44 % Model : x86_64 x86_64
% 0.12/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.44 % Memory : 8046.5625MB
% 0.12/0.44 % OS : Linux 6.8.0-71-generic
% 0.12/0.44 % CPULimit : 300
% 0.12/0.44 % WCLimit : 300
% 0.12/0.44 % DateTime : Fri Sep 25 19:28:21 UTC 2026
% 0.12/0.44 % CPUTime :
% 0.12/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.61/14.37 % SZS status Theorem for theBenchmark.p
% 8.61/14.37 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------