%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : KLE089+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 17.50s 4.65s
% Output : CNFRefutation 17.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 13
% Syntax : Number of formulae : 54 ( 52 unt; 0 def)
% Number of atoms : 56 ( 55 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 5 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 63 ( 3 sgn 23 !; 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(multiplicative_associativity,axiom,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2) ).
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(right_annihilation,axiom,
! [X0] : multiplication(X0,zero) = zero ).
fof(left_annihilation,axiom,
! [X0] : multiplication(zero,X0) = zero ).
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,X1] :
( addition(domain(X0),antidomain(X1)) = antidomain(X1)
=> multiplication(domain(X0),X1) = zero ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( addition(domain(X0),antidomain(X1)) = antidomain(X1)
=> multiplication(domain(X0),X1) = zero ),
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(c4,plain,
multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(clausification,[status(esa)],[multiplicative_associativity]) ).
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(c9,plain,
multiplication(X0,zero) = zero,
inference(clausification,[status(esa)],[right_annihilation]) ).
cnf(c10,plain,
multiplication(zero,X0) = zero,
inference(clausification,[status(esa)],[left_annihilation]) ).
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,
addition(domain(sK32),antidomain(sK33)) = antidomain(sK33),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c22,plain,
multiplication(domain(sK32),sK33) != zero,
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(sK33),domain(sK32)) = antidomain(sK33),
inference(demodulation,[status(thm)],[c21,c0]) ).
cnf(d4,plain,
multiplication(antidomain(sK33),sK33) = multiplication(domain(sK32),sK33),
inference(superposition,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
zero = multiplication(domain(sK32),sK33),
inference(demodulation,[status(thm)],[d4,c13]) ).
cnf(d6,plain,
zero != zero,
inference(demodulation,[status(thm)],[c22,d5]) ).
cnf(d7,plain,
multiplication(antidomain(X0),multiplication(X0,X1)) = multiplication(zero,X1),
inference(superposition,[status(thm)],[c13,c4]) ).
cnf(d8,plain,
multiplication(antidomain(X1),multiplication(X1,X0)) = zero,
inference(demodulation,[status(thm)],[d7,c10]) ).
cnf(d9,plain,
addition(antidomain(sK33),addition(domain(sK32),X0)) = addition(antidomain(sK33),X0),
inference(superposition,[status(thm)],[d3,c1]) ).
cnf(d10,plain,
addition(antidomain(sK33),addition(addition(domain(sK32),X0),X1)) = addition(addition(antidomain(sK33),X0),X1),
inference(superposition,[status(thm)],[d9,c1]) ).
cnf(d11,plain,
addition(antidomain(sK33),addition(domain(sK32),addition(X0,X1))) = addition(addition(antidomain(sK33),X0),X1),
inference(demodulation,[status(thm)],[d10,c1]) ).
cnf(d12,plain,
addition(antidomain(sK33),addition(X0,X1)) = addition(addition(antidomain(sK33),X0),X1),
inference(demodulation,[status(thm)],[d11,d9]) ).
cnf(d13,plain,
addition(antidomain(sK33),addition(X0,X1)) = addition(antidomain(sK33),addition(X0,X1)),
inference(demodulation,[status(thm)],[d12,c1]) ).
cnf(d14,plain,
addition(antidomain(sK33),X0) = addition(antidomain(sK33),addition(X0,X0)),
inference(superposition,[status(thm)],[c3,d13]) ).
cnf(d15,plain,
addition(antidomain(sK33),X0) = addition(antidomain(sK33),X0),
inference(demodulation,[status(thm)],[d14,c3]) ).
cnf(d16,plain,
addition(antidomain(X0),antidomain(antidomain(X0))) = one,
inference(demodulation,[status(thm)],[c15,c0]) ).
cnf(d17,plain,
addition(antidomain(sK33),antidomain(antidomain(sK33))) = one,
inference(superposition,[status(thm)],[d16,d15]) ).
cnf(d18,plain,
addition(antidomain(sK33),domain(sK33)) = one,
inference(demodulation,[status(thm)],[d17,c16]) ).
cnf(d19,plain,
one = addition(antidomain(sK33),domain(sK33)),
inference(superposition,[status(thm)],[d18,d15]) ).
cnf(d20,plain,
multiplication(one,sK33) = multiplication(domain(sK33),sK33),
inference(superposition,[status(thm)],[d19,d2]) ).
cnf(d21,plain,
sK33 = multiplication(domain(sK33),sK33),
inference(demodulation,[status(thm)],[d20,c6]) ).
cnf(d22,plain,
multiplication(antidomain(domain(sK33)),sK33) = zero,
inference(superposition,[status(thm)],[d21,d8]) ).
cnf(d23,plain,
multiplication(antidomain(antidomain(domain(sK33))),zero) = zero,
inference(superposition,[status(thm)],[d22,d8]) ).
cnf(d24,plain,
zero = zero,
inference(demodulation,[status(thm)],[d23,c9]) ).
cnf(d25,plain,
$false,
inference(resolution,[status(thm)],[d24,d6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE089+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
% 0.16/0.41 % Computer : n009.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Fri Sep 25 19:20:45 UTC 2026
% 0.16/0.41 % CPUTime :
% 0.16/0.41 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.50/4.65 % SZS status Theorem for theBenchmark.p
% 17.50/4.65 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------