%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : KLE066+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 : n007.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 4.95s 3.97s
% Output : CNFRefutation 4.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 33 ( 31 unt; 0 def)
% Number of atoms : 35 ( 34 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 4 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 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; 4 con; 0-2 aty)
% Number of variables : 34 ( 1 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_identity,axiom,
! [X0] : addition(X0,zero) = 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(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(domain4,axiom,
domain(zero) = zero ).
fof(goals,conjecture,
! [X0,X1] :
( multiplication(X0,domain(X1)) = zero
=> multiplication(X0,X1) = zero ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( multiplication(X0,domain(X1)) = zero
=> multiplication(X0,X1) = zero ),
inference(negate_conjecture,[status(cth)],[goals]) ).
cnf(c2,plain,
addition(X0,zero) = X0,
inference(clausification,[status(esa)],[additive_identity]) ).
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(c10,plain,
multiplication(zero,X0) = zero,
inference(clausification,[status(esa)],[left_annihilation]) ).
cnf(c13,plain,
addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(clausification,[status(esa)],[domain1]) ).
cnf(c14,plain,
domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(clausification,[status(esa)],[domain2]) ).
cnf(c16,plain,
domain(zero) = zero,
inference(clausification,[status(esa)],[domain4]) ).
cnf(c18,plain,
multiplication(sK28,domain(sK29)) = zero,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c19,plain,
multiplication(sK28,sK29) != zero,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
domain(multiplication(sK28,sK29)) = domain(zero),
inference(superposition,[status(thm)],[c18,c14]) ).
cnf(d1,plain,
domain(multiplication(sK28,sK29)) = zero,
inference(demodulation,[status(thm)],[d0,c16]) ).
cnf(d2,plain,
multiplication(addition(one,X1),X0) = addition(X0,multiplication(X1,X0)),
inference(superposition,[status(thm)],[c6,c8]) ).
cnf(d3,plain,
multiplication(addition(X3,multiplication(X0,X1)),X2) = addition(multiplication(X3,X2),multiplication(X0,multiplication(X1,X2))),
inference(superposition,[status(thm)],[c4,c8]) ).
cnf(d4,plain,
addition(multiplication(sK28,sK29),multiplication(zero,multiplication(sK28,sK29))) = multiplication(domain(multiplication(sK28,sK29)),multiplication(sK28,sK29)),
inference(superposition,[status(thm)],[d1,c13]) ).
cnf(d5,plain,
multiplication(addition(sK28,multiplication(zero,sK28)),sK29) = multiplication(domain(multiplication(sK28,sK29)),multiplication(sK28,sK29)),
inference(demodulation,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
multiplication(multiplication(addition(one,zero),sK28),sK29) = multiplication(domain(multiplication(sK28,sK29)),multiplication(sK28,sK29)),
inference(demodulation,[status(thm)],[d5,d2]) ).
cnf(d7,plain,
multiplication(addition(one,zero),multiplication(sK28,sK29)) = multiplication(domain(multiplication(sK28,sK29)),multiplication(sK28,sK29)),
inference(demodulation,[status(thm)],[d6,c4]) ).
cnf(d8,plain,
multiplication(one,multiplication(sK28,sK29)) = multiplication(domain(multiplication(sK28,sK29)),multiplication(sK28,sK29)),
inference(demodulation,[status(thm)],[d7,c2]) ).
cnf(d9,plain,
multiplication(sK28,sK29) = multiplication(domain(multiplication(sK28,sK29)),multiplication(sK28,sK29)),
inference(demodulation,[status(thm)],[d8,c6]) ).
cnf(d10,plain,
multiplication(sK28,sK29) = multiplication(zero,multiplication(sK28,sK29)),
inference(demodulation,[status(thm)],[d9,d1]) ).
cnf(d11,plain,
multiplication(sK28,sK29) = zero,
inference(demodulation,[status(thm)],[d10,c10]) ).
cnf(d12,plain,
$false,
inference(resolution,[status(thm)],[c19,d11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE066+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
% 0.11/0.37 % Computer : n007.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 25 19:17:08 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.95/3.97 % SZS status Theorem for theBenchmark.p
% 4.95/3.97 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------