%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : KLE093+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 : n014.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 07:43:35 AM UTC 2026
% Result : Theorem 27.87s 8.98s
% Output : CNFRefutation 27.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 29 ( 25 unt; 0 def)
% Number of atoms : 33 ( 26 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 5 ~; 3 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 37 ( 5 sgn 15 !; 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(multiplicative_right_identity,axiom,
! [X0] : multiplication(X0,one) = X0 ).
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(domain1,axiom,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0) ).
fof(domain3,axiom,
! [X0] : addition(domain(X0),one) = one ).
fof(domain5,axiom,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)) ).
fof(goals,conjecture,
! [X0] : domain(star(X0)) = one ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] : domain(star(X0)) = 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(c5,plain,
multiplication(X0,one) = X0,
inference(clausification,[status(esa)],[multiplicative_right_identity]) ).
cnf(c11,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(c17,plain,
addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(clausification,[status(esa)],[domain1]) ).
cnf(c19,plain,
addition(domain(X0),one) = one,
inference(clausification,[status(esa)],[domain3]) ).
cnf(c21,plain,
domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(clausification,[status(esa)],[domain5]) ).
cnf(c22,plain,
domain(star(sK36)) != one,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
addition(one,domain(X0)) = one,
inference(demodulation,[status(thm)],[c19,c0]) ).
cnf(d1,plain,
addition(one,domain(one)) = multiplication(domain(one),one),
inference(superposition,[status(thm)],[c5,c17]) ).
cnf(d2,plain,
one = multiplication(domain(one),one),
inference(demodulation,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
one = domain(one),
inference(demodulation,[status(thm)],[d2,c5]) ).
cnf(d4,plain,
domain(addition(one,X0)) = addition(one,domain(X0)),
inference(superposition,[status(thm)],[d3,c21]) ).
cnf(d5,plain,
domain(addition(one,X0)) = one,
inference(demodulation,[status(thm)],[d4,d0]) ).
cnf(d6,plain,
( ~ leq(addition(X0,X1),X2)
| addition(X0,addition(X1,X2)) = X2 ),
inference(superposition,[status(thm)],[c11,c1]) ).
cnf(d7,plain,
( ~ leq(addition(one,X0),X1)
| domain(X1) = one ),
inference(superposition,[status(thm)],[d6,d5]) ).
cnf(d8,plain,
domain(star(X0)) = one,
inference(resolution,[status(thm)],[d7,c13]) ).
cnf(d9,plain,
$false,
inference(resolution,[status(thm)],[d8,c22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE093+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
% 0.09/5.36 % Computer : n014.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Fri Sep 25 19:20:53 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 27.87/8.98 % SZS status Theorem for theBenchmark.p
% 27.87/8.98 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------