%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : KLE142+1 : 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 : n006.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 43.33s 7.74s
% Output : CNFRefutation 43.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 50 ( 33 unt; 0 def)
% Number of atoms : 68 ( 36 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 36 ( 18 ~; 16 |; 0 &)
% ( 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 : 86 ( 14 sgn 19 !; 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_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$uiteration'(X0),X1)) ) ).
fof(order,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ) ).
fof(goals,conjecture,
! [X0] : 'strong$uiteration'('strong$uiteration'(X0)) = 'strong$uiteration'(one) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] : 'strong$uiteration'('strong$uiteration'(X0)) = 'strong$uiteration'(one),
inference(negate_conjecture,[status(cth)],[goals]) ).
cnf(c0,plain,
addition(X0,X1) = addition(X1,X0),
inference(clausification,[status(esa)],[additive_commutativity]) ).
cnf(c1,plain,
addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
inference(clausification,[status(esa)],[additive_associativity]) ).
cnf(c3,plain,
addition(X0,X0) = X0,
inference(clausification,[status(esa)],[idempotence]) ).
cnf(c5,plain,
multiplication(X0,one) = X0,
inference(clausification,[status(esa)],[multiplicative_right_identity]) ).
cnf(c6,plain,
multiplication(one,X0) = X0,
inference(clausification,[status(esa)],[multiplicative_left_identity]) ).
cnf(c8,plain,
multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(clausification,[status(esa)],[distributivity2]) ).
cnf(c14,plain,
'strong$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,
'strong$uiteration'('strong$uiteration'(sK34)) != 'strong$uiteration'(one),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ leq(X0,X1)
| addition(X1,X0) = X1 ),
inference(superposition,[status(thm)],[c17,c0]) ).
cnf(d1,plain,
( ~ leq(X1,X0)
| ~ leq(X0,X1)
| X0 = X1 ),
inference(superposition,[status(thm)],[d0,c17]) ).
cnf(d2,plain,
( leq(X0,multiplication('strong$uiteration'(one),X1))
| ~ leq(X0,addition(X0,X1)) ),
inference(superposition,[status(thm)],[c6,c15]) ).
cnf(d3,plain,
( ~ leq(X0,addition(X0,one))
| leq(X0,'strong$uiteration'(one)) ),
inference(superposition,[status(thm)],[c5,d2]) ).
cnf(d4,plain,
X0 = addition(X0,X0),
inference(superposition,[status(thm)],[c3,c0]) ).
cnf(d5,plain,
addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[d4,c1]) ).
cnf(d6,plain,
( leq(X0,addition(X0,X1))
| addition(X0,X1) != addition(X0,X1) ),
inference(superposition,[status(thm)],[d5,c18]) ).
cnf(d7,plain,
( ~ leq(X0,X1)
| X1 = addition(X1,X0) ),
inference(superposition,[status(thm)],[c17,c0]) ).
cnf(d8,plain,
( ~ leq(addition(X0,X1),X0)
| X0 = addition(X0,X1) ),
inference(superposition,[status(thm)],[d5,d7]) ).
cnf(d9,plain,
( X0 = addition(X0,X0)
| ~ leq(X0,X0) ),
inference(superposition,[status(thm)],[d4,d8]) ).
cnf(d10,plain,
( ~ leq(X0,X0)
| X0 = X0 ),
inference(demodulation,[status(thm)],[d9,c3]) ).
cnf(d11,plain,
( leq(X0,X0)
| X0 != X0 ),
inference(superposition,[status(thm)],[d4,c18]) ).
cnf(d12,plain,
leq(X0,X0),
inference(equality_resolution,[status(thm)],[d11]) ).
cnf(d13,plain,
X0 = X0,
inference(resolution,[status(thm)],[d12,d10]) ).
cnf(d14,plain,
leq(X0,addition(X0,X1)),
inference(resolution,[status(thm)],[d13,d6]) ).
cnf(d15,plain,
leq(X0,'strong$uiteration'(one)),
inference(resolution,[status(thm)],[d14,d3]) ).
cnf(d16,plain,
( ~ leq('strong$uiteration'(one),X0)
| X0 = 'strong$uiteration'(one) ),
inference(resolution,[status(thm)],[d15,d1]) ).
cnf(d17,plain,
( leq(X1,multiplication('strong$uiteration'(X0),X2))
| ~ leq(X1,addition(X2,multiplication(X0,X1))) ),
inference(superposition,[status(thm)],[c0,c15]) ).
cnf(d18,plain,
addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(superposition,[status(thm)],[c1,c0]) ).
cnf(d19,plain,
leq(X0,addition(X2,addition(X0,X1))),
inference(superposition,[status(thm)],[d18,d14]) ).
cnf(d20,plain,
multiplication(addition(one,X1),X0) = addition(X0,multiplication(X1,X0)),
inference(superposition,[status(thm)],[c6,c8]) ).
cnf(d21,plain,
leq(X0,addition(X2,multiplication(addition(one,X1),X0))),
inference(superposition,[status(thm)],[d20,d19]) ).
cnf(d22,plain,
leq(X0,multiplication('strong$uiteration'(addition(one,X1)),X2)),
inference(resolution,[status(thm)],[d21,d17]) ).
cnf(d23,plain,
leq(X1,'strong$uiteration'(addition(one,X0))),
inference(superposition,[status(thm)],[c5,d22]) ).
cnf(d24,plain,
'strong$uiteration'(X0) = addition(one,multiplication(X0,'strong$uiteration'(X0))),
inference(demodulation,[status(thm)],[c14,c0]) ).
cnf(d25,plain,
leq(X1,'strong$uiteration'('strong$uiteration'(X0))),
inference(superposition,[status(thm)],[d24,d23]) ).
cnf(d26,plain,
'strong$uiteration'('strong$uiteration'(X0)) = 'strong$uiteration'(one),
inference(resolution,[status(thm)],[d25,d16]) ).
cnf(d27,plain,
$false,
inference(resolution,[status(thm)],[d26,c19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE142+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.43 % Computer : n006.cluster.edu
% 0.10/0.43 % Model : x86_64 x86_64
% 0.10/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.43 % Memory : 8046.5625MB
% 0.10/0.43 % OS : Linux 6.8.0-71-generic
% 0.10/0.43 % CPULimit : 300
% 0.10/0.43 % WCLimit : 300
% 0.10/0.43 % DateTime : Fri Sep 25 19:26:11 UTC 2026
% 0.10/0.44 % CPUTime :
% 0.10/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 43.33/7.74 % SZS status Theorem for theBenchmark.p
% 43.33/7.74 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------