%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : KLE083+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 07:43:34 AM UTC 2026
% Result : Theorem 25.04s 4.68s
% Output : CNFRefutation 25.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 25 ( 25 unt; 0 def)
% Number of atoms : 25 ( 24 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 31 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0) ).
fof(additive_identity,axiom,
! [X0] : addition(X0,zero) = X0 ).
fof(multiplicative_left_identity,axiom,
! [X0] : multiplication(one,X0) = X0 ).
fof(left_distributivity,axiom,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)) ).
fof(domain1,axiom,
! [X0] : multiplication(antidomain(X0),X0) = zero ).
fof(domain3,axiom,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one ).
fof(domain4,axiom,
! [X0] : domain(X0) = antidomain(antidomain(X0)) ).
fof(goals,conjecture,
! [X0] : X0 = multiplication(domain(X0),X0) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] : X0 = multiplication(domain(X0),X0),
inference(negate_conjecture,[status(cth)],[goals]) ).
cnf(c0,plain,
addition(X0,X1) = addition(X1,X0),
inference(clausification,[status(esa)],[additive_commutativity]) ).
cnf(c2,plain,
addition(X0,zero) = X0,
inference(clausification,[status(esa)],[additive_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)],[left_distributivity]) ).
cnf(c13,plain,
multiplication(antidomain(X0),X0) = zero,
inference(clausification,[status(esa)],[domain1]) ).
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,
sK32 != multiplication(domain(sK32),sK32),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
addition(zero,X0) = X0,
inference(superposition,[status(thm)],[c2,c0]) ).
cnf(d1,plain,
multiplication(addition(antidomain(X0),X1),X0) = addition(zero,multiplication(X1,X0)),
inference(superposition,[status(thm)],[c13,c8]) ).
cnf(d2,plain,
multiplication(addition(antidomain(X1),X0),X1) = multiplication(X0,X1),
inference(demodulation,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
addition(antidomain(X0),antidomain(antidomain(X0))) = one,
inference(demodulation,[status(thm)],[c15,c0]) ).
cnf(d4,plain,
addition(antidomain(X0),domain(X0)) = one,
inference(demodulation,[status(thm)],[d3,c16]) ).
cnf(d5,plain,
multiplication(one,X0) = multiplication(domain(X0),X0),
inference(superposition,[status(thm)],[d4,d2]) ).
cnf(d6,plain,
X0 = multiplication(domain(X0),X0),
inference(demodulation,[status(thm)],[d5,c6]) ).
cnf(d7,plain,
$false,
inference(resolution,[status(thm)],[d6,c21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : KLE083+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n009.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Fri Sep 25 19:20:14 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 25.04/4.68 % SZS status Theorem for theBenchmark.p
% 25.04/4.68 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------