%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : KLE054+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 : n018.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 07:43:31 AM UTC 2026
% Result : Theorem 34.48s 15.79s
% Output : CNFRefutation 34.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 47 ( 39 unt; 0 def)
% Number of atoms : 55 ( 45 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 20 ( 12 ~; 7 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 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 : 74 ( 6 sgn 22 !; 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_right_identity,axiom,
! [X0] : multiplication(X0,one) = X0 ).
fof(right_distributivity,axiom,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)) ).
fof(order,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ) ).
fof(domain2,axiom,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))) ).
fof(domain3,axiom,
! [X0] : addition(domain(X0),one) = one ).
fof(domain5,axiom,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)) ).
fof(goals,conjecture,
! [X0,X1] : addition(domain(multiplication(X0,X1)),domain(X0)) = domain(X0) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] : addition(domain(multiplication(X0,X1)),domain(X0)) = domain(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(c5,plain,
multiplication(X0,one) = X0,
inference(clausification,[status(esa)],[multiplicative_right_identity]) ).
cnf(c7,plain,
multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(clausification,[status(esa)],[right_distributivity]) ).
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(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(c17,plain,
domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(clausification,[status(esa)],[domain5]) ).
cnf(c18,plain,
addition(domain(multiplication(sK28,sK29)),domain(sK28)) != domain(sK28),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
domain(addition(X2,multiplication(X0,domain(X1)))) = addition(domain(X2),domain(multiplication(X0,X1))),
inference(superposition,[status(thm)],[c14,c17]) ).
cnf(d1,plain,
domain(addition(X0,multiplication(X1,domain(X2)))) = domain(addition(X0,multiplication(X1,X2))),
inference(demodulation,[status(thm)],[d0,c17]) ).
cnf(d2,plain,
multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(superposition,[status(thm)],[c5,c7]) ).
cnf(d3,plain,
addition(X0,addition(X1,zero)) = addition(X0,X1),
inference(superposition,[status(thm)],[c1,c2]) ).
cnf(d4,plain,
addition(X1,X0) = addition(X1,X0),
inference(demodulation,[status(thm)],[d3,c2]) ).
cnf(d5,plain,
addition(one,domain(X0)) = one,
inference(demodulation,[status(thm)],[c15,c0]) ).
cnf(d6,plain,
one = addition(one,domain(X0)),
inference(superposition,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
multiplication(X1,one) = addition(X1,multiplication(X1,domain(X0))),
inference(superposition,[status(thm)],[d6,d2]) ).
cnf(d8,plain,
X0 = addition(X0,multiplication(X0,domain(X1))),
inference(demodulation,[status(thm)],[d7,c5]) ).
cnf(d9,plain,
domain(X0) = domain(addition(X0,multiplication(X0,X1))),
inference(superposition,[status(thm)],[d8,d1]) ).
cnf(d10,plain,
addition(domain(sK28),domain(multiplication(sK28,sK29))) != domain(sK28),
inference(demodulation,[status(thm)],[c18,c0]) ).
cnf(d11,plain,
domain(addition(sK28,multiplication(sK28,sK29))) != domain(sK28),
inference(demodulation,[status(thm)],[d10,c17]) ).
cnf(d12,plain,
domain(sK28) != domain(sK28),
inference(demodulation,[status(thm)],[d11,d9]) ).
cnf(d13,plain,
( ~ leq(X0,X1)
| X1 = addition(X1,X0) ),
inference(superposition,[status(thm)],[c11,c0]) ).
cnf(d14,plain,
X0 = addition(X0,X0),
inference(superposition,[status(thm)],[c3,c0]) ).
cnf(d15,plain,
addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[d14,c1]) ).
cnf(d16,plain,
( ~ leq(addition(X0,X1),X0)
| X0 = addition(X0,X1) ),
inference(superposition,[status(thm)],[d15,d13]) ).
cnf(d17,plain,
( X0 = addition(X0,X0)
| ~ leq(X0,X0) ),
inference(superposition,[status(thm)],[d14,d16]) ).
cnf(d18,plain,
( ~ leq(X0,X0)
| X0 = X0 ),
inference(demodulation,[status(thm)],[d17,c3]) ).
cnf(d19,plain,
( leq(X0,X0)
| X0 != X0 ),
inference(superposition,[status(thm)],[d14,c12]) ).
cnf(d20,plain,
leq(X0,X0),
inference(equality_resolution,[status(thm)],[d19]) ).
cnf(d21,plain,
X0 = X0,
inference(resolution,[status(thm)],[d20,d18]) ).
cnf(d22,plain,
$false,
inference(resolution,[status(thm)],[d21,d12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE054+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/10.45 % Computer : n018.cluster.edu
% 0.17/10.45 % Model : x86_64 x86_64
% 0.17/10.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/10.45 % Memory : 8046.5625MB
% 0.17/10.45 % OS : Linux 6.8.0-71-generic
% 0.17/10.45 % CPULimit : 300
% 0.17/10.45 % WCLimit : 300
% 0.17/10.45 % DateTime : Fri Sep 25 19:21:02 UTC 2026
% 0.17/10.46 % CPUTime :
% 0.17/10.46 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 34.48/15.79 % SZS status Theorem for theBenchmark.p
% 34.48/15.79 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------