%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : KLE085+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/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 07:43:34 AM UTC 2026
% Result : Theorem 24.79s 3.46s
% Output : CNFRefutation 24.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 33 ( 29 unt; 0 def)
% Number of atoms : 37 ( 29 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 6 ~; 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; 3 con; 0-2 aty)
% Number of variables : 44 ( 5 sgn 13 !; 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(additive_identity,axiom,
! [X0] : addition(X0,zero) = X0 ).
fof(additive_idempotence,axiom,
! [X0] : addition(X0,X0) = X0 ).
fof(order,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ) ).
fof(domain3,axiom,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one ).
fof(domain4,axiom,
! [X0] : domain(X0) = antidomain(antidomain(X0)) ).
fof(goals,conjecture,
! [X0] : addition(domain(X0),one) = one ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] : addition(domain(X0),one) = 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(c2,plain,
addition(X0,zero) = X0,
inference(clausification,[status(esa)],[additive_identity]) ).
cnf(c3,plain,
addition(X0,X0) = X0,
inference(clausification,[status(esa)],[additive_idempotence]) ).
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(c15,plain,
addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
inference(clausification,[status(esa)],[domain3]) ).
cnf(c16,plain,
domain(X0) = antidomain(antidomain(X0)),
inference(clausification,[status(esa)],[domain4]) ).
cnf(c21,plain,
addition(domain(sK32),one) != one,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
addition(one,domain(sK32)) != one,
inference(demodulation,[status(thm)],[c21,c0]) ).
cnf(d1,plain,
addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c3,c1]) ).
cnf(d2,plain,
( leq(X0,addition(X0,X1))
| addition(X0,X1) != addition(X0,X1) ),
inference(superposition,[status(thm)],[d1,c12]) ).
cnf(d3,plain,
addition(zero,X0) = X0,
inference(superposition,[status(thm)],[c2,c0]) ).
cnf(d4,plain,
addition(X0,addition(zero,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c2,c1]) ).
cnf(d5,plain,
addition(X1,X0) = addition(X1,X0),
inference(demodulation,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
leq(X0,addition(X0,X1)),
inference(resolution,[status(thm)],[d5,d2]) ).
cnf(d7,plain,
addition(antidomain(X0),antidomain(antidomain(X0))) = one,
inference(demodulation,[status(thm)],[c15,c0]) ).
cnf(d8,plain,
addition(antidomain(X0),domain(X0)) = one,
inference(demodulation,[status(thm)],[d7,c16]) ).
cnf(d9,plain,
one = addition(antidomain(X0),domain(X0)),
inference(superposition,[status(thm)],[d8,d5]) ).
cnf(d10,plain,
leq(antidomain(X0),one),
inference(superposition,[status(thm)],[d9,d6]) ).
cnf(d11,plain,
leq(domain(X0),one),
inference(superposition,[status(thm)],[c16,d10]) ).
cnf(d12,plain,
addition(domain(X0),one) = one,
inference(resolution,[status(thm)],[d11,c11]) ).
cnf(d13,plain,
addition(one,domain(X0)) = one,
inference(demodulation,[status(thm)],[d12,c0]) ).
cnf(d14,plain,
$false,
inference(resolution,[status(thm)],[d13,d0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE085+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n009.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 19:20:29 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.79/3.46 % SZS status Theorem for theBenchmark.p
% 24.79/3.46 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------