%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : KLE065+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 : n013.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 07:43:32 AM UTC 2026
% Result : Theorem 44.16s 5.79s
% Output : CNFRefutation 44.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of formulae : 47 ( 45 unt; 0 def)
% Number of atoms : 49 ( 48 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 : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 58 ( 4 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,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(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] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0) ).
fof(domain2,axiom,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))) ).
fof(domain3,axiom,
! [X0] : addition(domain(X0),one) = one ).
fof(domain4,axiom,
domain(zero) = zero ).
fof(goals,conjecture,
! [X0,X1] :
( multiplication(X0,X1) = zero
=> multiplication(X0,domain(X1)) = zero ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( multiplication(X0,X1) = zero
=> multiplication(X0,domain(X1)) = zero ),
inference(negate_conjecture,[status(cth)],[goals]) ).
cnf(c0,plain,
addition(X0,X1) = addition(X1,X0),
inference(clausification,[status(esa)],[additive_commutativity]) ).
cnf(c4,plain,
multiplication(multiplication(X0,X1),X2) = multiplication(X0,multiplication(X1,X2)),
inference(clausification,[status(esa)],[multiplicative_associativity]) ).
cnf(c5,plain,
multiplication(X0,one) = X0,
inference(clausification,[status(esa)],[multiplicative_right_identity]) ).
cnf(c6,plain,
multiplication(one,X0) = X0,
inference(clausification,[status(esa)],[multiplicative_left_identity]) ).
cnf(c8,plain,
addition(multiplication(X0,X1),multiplication(X2,X1)) = multiplication(addition(X0,X2),X1),
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(domain(X0),X0) = addition(X0,multiplication(domain(X0),X0)),
inference(clausification,[status(esa)],[domain1]) ).
cnf(c14,plain,
domain(multiplication(X0,domain(X1))) = domain(multiplication(X0,X1)),
inference(clausification,[status(esa)],[domain2]) ).
cnf(c15,plain,
addition(domain(X0),one) = one,
inference(clausification,[status(esa)],[domain3]) ).
cnf(c16,plain,
domain(zero) = zero,
inference(clausification,[status(esa)],[domain4]) ).
cnf(c18,plain,
multiplication(sK28,sK29) = zero,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c19,plain,
multiplication(sK28,domain(sK29)) != zero,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
addition(one,domain(X0)) = one,
inference(demodulation,[status(thm)],[c15,c0]) ).
cnf(d1,plain,
addition(X0,multiplication(X1,X0)) = multiplication(addition(one,X1),X0),
inference(superposition,[status(thm)],[c6,c8]) ).
cnf(d2,plain,
addition(multiplication(X3,X2),multiplication(X0,multiplication(X1,X2))) = multiplication(addition(X3,multiplication(X0,X1)),X2),
inference(superposition,[status(thm)],[c4,c8]) ).
cnf(d3,plain,
multiplication(domain(multiplication(X0,domain(X1))),multiplication(X0,domain(X1))) = addition(multiplication(X0,domain(X1)),multiplication(domain(multiplication(X0,X1)),multiplication(X0,domain(X1)))),
inference(superposition,[status(thm)],[c14,c13]) ).
cnf(d4,plain,
multiplication(domain(multiplication(X0,X1)),multiplication(X0,domain(X1))) = addition(multiplication(X0,domain(X1)),multiplication(domain(multiplication(X0,X1)),multiplication(X0,domain(X1)))),
inference(demodulation,[status(thm)],[d3,c14]) ).
cnf(d5,plain,
multiplication(domain(multiplication(X0,X1)),multiplication(X0,domain(X1))) = multiplication(addition(X0,multiplication(domain(multiplication(X0,X1)),X0)),domain(X1)),
inference(demodulation,[status(thm)],[d4,d2]) ).
cnf(d6,plain,
multiplication(domain(multiplication(X0,X1)),multiplication(X0,domain(X1))) = multiplication(multiplication(addition(one,domain(multiplication(X0,X1))),X0),domain(X1)),
inference(demodulation,[status(thm)],[d5,d1]) ).
cnf(d7,plain,
multiplication(domain(multiplication(X0,X1)),multiplication(X0,domain(X1))) = multiplication(addition(one,domain(multiplication(X0,X1))),multiplication(X0,domain(X1))),
inference(demodulation,[status(thm)],[d6,c4]) ).
cnf(d8,plain,
multiplication(domain(multiplication(X0,X1)),multiplication(X0,domain(X1))) = multiplication(one,multiplication(X0,domain(X1))),
inference(demodulation,[status(thm)],[d7,d0]) ).
cnf(d9,plain,
multiplication(domain(multiplication(X0,X1)),multiplication(X0,domain(X1))) = multiplication(X0,domain(X1)),
inference(demodulation,[status(thm)],[d8,c6]) ).
cnf(d10,plain,
multiplication(zero,X0) = multiplication(sK28,multiplication(sK29,X0)),
inference(superposition,[status(thm)],[c18,c4]) ).
cnf(d11,plain,
multiplication(zero,one) = multiplication(sK28,sK29),
inference(superposition,[status(thm)],[c5,d10]) ).
cnf(d12,plain,
zero = multiplication(sK28,sK29),
inference(demodulation,[status(thm)],[d11,c5]) ).
cnf(d13,plain,
multiplication(domain(zero),multiplication(sK28,domain(sK29))) = multiplication(sK28,domain(sK29)),
inference(superposition,[status(thm)],[d12,d9]) ).
cnf(d14,plain,
multiplication(zero,multiplication(sK28,domain(sK29))) = multiplication(sK28,domain(sK29)),
inference(demodulation,[status(thm)],[d13,c16]) ).
cnf(d15,plain,
zero = multiplication(sK28,domain(sK29)),
inference(demodulation,[status(thm)],[d14,c10]) ).
cnf(d16,plain,
zero != zero,
inference(demodulation,[status(thm)],[c19,d15]) ).
cnf(d17,plain,
multiplication(zero,zero) = multiplication(sK28,zero),
inference(superposition,[status(thm)],[c9,d10]) ).
cnf(d18,plain,
zero = multiplication(sK28,zero),
inference(demodulation,[status(thm)],[d17,c9]) ).
cnf(d19,plain,
zero = zero,
inference(demodulation,[status(thm)],[d18,c9]) ).
cnf(d20,plain,
$false,
inference(resolution,[status(thm)],[d19,d16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE065+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
% 0.10/0.35 % Computer : n013.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Fri Sep 25 19:18:52 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 44.16/5.79 % SZS status Theorem for theBenchmark.p
% 44.16/5.79 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------