%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : KLE002+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 : 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 07:43:22 AM UTC 2026
% Result : Theorem 6.24s 11.08s
% Output : CNFRefutation 6.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 26 ( 19 unt; 0 def)
% Number of atoms : 33 ( 19 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 13 ( 6 ~; 4 |; 0 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 50 ( 1 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_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(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(goals,conjecture,
! [X0,X1,X2] :
( leq(X0,X1)
=> leq(multiplication(X0,X2),multiplication(X1,X2)) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( leq(X0,X1)
=> leq(multiplication(X0,X2),multiplication(X1,X2)) ),
inference(negate_conjecture,[status(cth)],[goals]) ).
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(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(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(sK22,sK23),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c14,plain,
~ leq(multiplication(sK22,sK24),multiplication(sK23,sK24)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( leq(multiplication(X0,X1),multiplication(X2,X1))
| multiplication(addition(X0,X2),X1) != multiplication(X2,X1) ),
inference(superposition,[status(thm)],[c8,c12]) ).
cnf(d1,plain,
addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c3,c1]) ).
cnf(d2,plain,
( leq(multiplication(X0,X2),multiplication(addition(X0,X1),X2))
| multiplication(addition(X0,X1),X2) != multiplication(addition(X0,X1),X2) ),
inference(superposition,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
multiplication(X0,multiplication(X1,one)) = multiplication(X0,X1),
inference(superposition,[status(thm)],[c4,c5]) ).
cnf(d4,plain,
multiplication(X1,X0) = multiplication(X1,X0),
inference(demodulation,[status(thm)],[d3,c5]) ).
cnf(d5,plain,
leq(multiplication(X0,X1),multiplication(addition(X0,X2),X1)),
inference(resolution,[status(thm)],[d4,d2]) ).
cnf(d6,plain,
addition(sK22,sK23) = sK23,
inference(resolution,[status(thm)],[c11,c13]) ).
cnf(d7,plain,
leq(multiplication(sK22,X0),multiplication(sK23,X0)),
inference(superposition,[status(thm)],[d6,d5]) ).
cnf(d8,plain,
$false,
inference(resolution,[status(thm)],[d7,c14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE002+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
% 0.10/5.36 % Computer : n009.cluster.edu
% 0.10/5.36 % Model : x86_64 x86_64
% 0.10/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.36 % Memory : 8046.5625MB
% 0.10/5.36 % OS : Linux 6.8.0-71-generic
% 0.10/5.36 % CPULimit : 300
% 0.10/5.36 % WCLimit : 300
% 0.10/5.36 % DateTime : Fri Sep 25 19:12:05 UTC 2026
% 0.10/5.36 % CPUTime :
% 0.10/5.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.24/11.08 % SZS status Theorem for theBenchmark.p
% 6.24/11.08 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------