%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : KLE064+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 : n019.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 77.50s 15.21s
% Output : CNFRefutation 77.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 17
% Syntax : Number of formulae : 91 ( 82 unt; 0 def)
% Number of atoms : 100 ( 86 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 19 ( 10 ~; 6 |; 0 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 124 ( 18 sgn 29 !; 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_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(order,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ) ).
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(domain5,axiom,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)) ).
fof(goals,conjecture,
! [X0,X1] :
( addition(domain(X0),domain(X1)) = domain(X1)
=> addition(X0,multiplication(domain(X1),X0)) = multiplication(domain(X1),X0) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( addition(domain(X0),domain(X1)) = domain(X1)
=> addition(X0,multiplication(domain(X1),X0)) = multiplication(domain(X1),X0) ),
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(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,
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(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(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(c15,plain,
addition(domain(X0),one) = one,
inference(clausification,[status(esa)],[domain3]) ).
cnf(c16,plain,
domain(zero) = zero,
inference(clausification,[status(esa)],[domain4]) ).
cnf(c17,plain,
domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(clausification,[status(esa)],[domain5]) ).
cnf(c18,plain,
addition(domain(sK28),domain(sK29)) = domain(sK29),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c19,plain,
addition(sK28,multiplication(domain(sK29),sK28)) != multiplication(domain(sK29),sK28),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
addition(X2,addition(X0,X1)) = addition(X0,addition(X1,X2)),
inference(superposition,[status(thm)],[c1,c0]) ).
cnf(d1,plain,
X0 = addition(X0,X0),
inference(superposition,[status(thm)],[c3,c0]) ).
cnf(d2,plain,
addition(X0,addition(X1,X0)) = addition(X1,X0),
inference(superposition,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
addition(X0,addition(X1,addition(X0,X1))) = addition(X0,X1),
inference(superposition,[status(thm)],[c1,c3]) ).
cnf(d4,plain,
( leq(X0,addition(X1,addition(X0,X1)))
| addition(X0,X1) != addition(X1,addition(X0,X1)) ),
inference(superposition,[status(thm)],[d3,c12]) ).
cnf(d5,plain,
( leq(X1,addition(X0,addition(X1,X0)))
| addition(X1,X0) != addition(X1,X0) ),
inference(demodulation,[status(thm)],[d4,d2]) ).
cnf(d6,plain,
( leq(X1,addition(X1,X0))
| addition(X1,X0) != addition(X1,X0) ),
inference(demodulation,[status(thm)],[d5,d2]) ).
cnf(d7,plain,
multiplication(addition(one,X1),X0) = addition(X0,multiplication(X1,X0)),
inference(superposition,[status(thm)],[c6,c8]) ).
cnf(d8,plain,
addition(one,domain(X0)) = one,
inference(demodulation,[status(thm)],[c15,c0]) ).
cnf(d9,plain,
addition(one,domain(one)) = multiplication(domain(one),one),
inference(superposition,[status(thm)],[c5,c13]) ).
cnf(d10,plain,
one = multiplication(domain(one),one),
inference(demodulation,[status(thm)],[d9,d8]) ).
cnf(d11,plain,
one = domain(one),
inference(demodulation,[status(thm)],[d10,c5]) ).
cnf(d12,plain,
addition(zero,X0) = X0,
inference(superposition,[status(thm)],[c2,c0]) ).
cnf(d13,plain,
domain(addition(sK28,sK29)) = domain(sK29),
inference(demodulation,[status(thm)],[c18,c17]) ).
cnf(d14,plain,
domain(multiplication(X0,addition(sK28,sK29))) = domain(multiplication(X0,domain(sK29))),
inference(superposition,[status(thm)],[d13,c14]) ).
cnf(d15,plain,
domain(multiplication(X0,addition(sK28,sK29))) = domain(multiplication(X0,sK29)),
inference(demodulation,[status(thm)],[d14,c14]) ).
cnf(d16,plain,
multiplication(X0,multiplication(zero,X1)) = multiplication(zero,X1),
inference(superposition,[status(thm)],[c9,c4]) ).
cnf(d17,plain,
multiplication(X1,zero) = multiplication(zero,X0),
inference(demodulation,[status(thm)],[d16,c10]) ).
cnf(d18,plain,
zero = multiplication(zero,X1),
inference(demodulation,[status(thm)],[d17,c9]) ).
cnf(d19,plain,
domain(zero) = domain(multiplication(zero,sK29)),
inference(superposition,[status(thm)],[d18,d15]) ).
cnf(d20,plain,
zero = domain(multiplication(zero,sK29)),
inference(demodulation,[status(thm)],[d19,c16]) ).
cnf(d21,plain,
zero = domain(zero),
inference(demodulation,[status(thm)],[d20,c10]) ).
cnf(d22,plain,
domain(addition(zero,X0)) = addition(zero,domain(X0)),
inference(superposition,[status(thm)],[d21,c17]) ).
cnf(d23,plain,
domain(X0) = addition(zero,domain(X0)),
inference(demodulation,[status(thm)],[d22,d12]) ).
cnf(d24,plain,
domain(X0) = domain(X0),
inference(demodulation,[status(thm)],[d23,d12]) ).
cnf(d25,plain,
domain(multiplication(X0,domain(X1))) = domain(multiplication(X0,X1)),
inference(superposition,[status(thm)],[c14,d24]) ).
cnf(d26,plain,
domain(domain(X0)) = domain(multiplication(one,X0)),
inference(superposition,[status(thm)],[c6,d25]) ).
cnf(d27,plain,
domain(domain(X0)) = domain(X0),
inference(demodulation,[status(thm)],[d26,c6]) ).
cnf(d28,plain,
domain(addition(domain(X0),X1)) = addition(domain(X0),domain(X1)),
inference(superposition,[status(thm)],[d27,c17]) ).
cnf(d29,plain,
domain(addition(domain(X0),X1)) = domain(addition(X0,X1)),
inference(demodulation,[status(thm)],[d28,c17]) ).
cnf(d30,plain,
domain(addition(X1,domain(X0))) = domain(addition(X0,X1)),
inference(superposition,[status(thm)],[c0,d29]) ).
cnf(d31,plain,
domain(one) = domain(addition(X0,one)),
inference(superposition,[status(thm)],[d8,d30]) ).
cnf(d32,plain,
domain(one) = domain(addition(one,X0)),
inference(superposition,[status(thm)],[c0,d31]) ).
cnf(d33,plain,
one = domain(addition(one,X0)),
inference(demodulation,[status(thm)],[d32,d11]) ).
cnf(d34,plain,
domain(one) = one,
inference(superposition,[status(thm)],[d11,d24]) ).
cnf(d35,plain,
domain(addition(one,X0)) = addition(one,domain(X0)),
inference(superposition,[status(thm)],[d34,c17]) ).
cnf(d36,plain,
one = addition(one,domain(X0)),
inference(demodulation,[status(thm)],[d35,d33]) ).
cnf(d37,plain,
multiplication(one,X1) = addition(X1,multiplication(domain(X0),X1)),
inference(superposition,[status(thm)],[d36,d7]) ).
cnf(d38,plain,
X0 = addition(X0,multiplication(domain(X1),X0)),
inference(demodulation,[status(thm)],[d37,c6]) ).
cnf(d39,plain,
X0 = addition(X0,multiplication(domain(sK29),X0)),
inference(superposition,[status(thm)],[d13,d38]) ).
cnf(d40,plain,
X0 = X0,
inference(demodulation,[status(thm)],[d39,d38]) ).
cnf(d41,plain,
leq(X0,addition(X0,X1)),
inference(resolution,[status(thm)],[d40,d6]) ).
cnf(d42,plain,
multiplication(addition(X0,X2),X1) = addition(multiplication(X2,X1),multiplication(X0,X1)),
inference(superposition,[status(thm)],[c8,c0]) ).
cnf(d43,plain,
leq(multiplication(X0,X1),multiplication(addition(X2,X0),X1)),
inference(superposition,[status(thm)],[d42,d41]) ).
cnf(d44,plain,
X0 = multiplication(domain(X0),X0),
inference(demodulation,[status(thm)],[c13,d38]) ).
cnf(d45,plain,
leq(X0,multiplication(addition(X1,domain(X0)),X0)),
inference(superposition,[status(thm)],[d44,d43]) ).
cnf(d46,plain,
addition(domain(X1),domain(X0)) = domain(addition(X0,X1)),
inference(superposition,[status(thm)],[c17,c0]) ).
cnf(d47,plain,
leq(X1,multiplication(domain(addition(X1,X0)),X1)),
inference(superposition,[status(thm)],[d46,d45]) ).
cnf(d48,plain,
leq(sK28,multiplication(domain(sK29),sK28)),
inference(superposition,[status(thm)],[d13,d47]) ).
cnf(d49,plain,
( ~ leq(sK28,multiplication(domain(sK29),sK28))
| multiplication(domain(sK29),sK28) != multiplication(domain(sK29),sK28) ),
inference(superposition,[status(thm)],[c11,c19]) ).
cnf(d50,plain,
multiplication(X0,multiplication(X1,one)) = multiplication(X0,X1),
inference(superposition,[status(thm)],[c4,c5]) ).
cnf(d51,plain,
multiplication(X1,X0) = multiplication(X1,X0),
inference(demodulation,[status(thm)],[d50,c5]) ).
cnf(d52,plain,
~ leq(sK28,multiplication(domain(sK29),sK28)),
inference(resolution,[status(thm)],[d51,d49]) ).
cnf(d53,plain,
$false,
inference(resolution,[status(thm)],[d52,d48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE064+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 : n019.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 19:19:33 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 77.50/15.21 % SZS status Theorem for theBenchmark.p
% 77.50/15.21 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------