%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : KLE021+2 : 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 : 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 07:43:26 AM UTC 2026
% Result : Theorem 53.22s 14.63s
% Output : CNFRefutation 53.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 32 ( 13 unt; 0 def)
% Number of atoms : 57 ( 20 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 49 ( 24 ~; 15 |; 4 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 35 ( 0 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0) ).
fof(additive_idempotence,axiom,
! [X0] : addition(X0,X0) = 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(order,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ) ).
fof(test_2,axiom,
! [X0,X1] :
( complement(X1,X0)
<=> ( addition(X0,X1) = one
& multiplication(X1,X0) = zero
& multiplication(X0,X1) = zero ) ) ).
fof(test_3,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ) ).
fof(goals,conjecture,
! [X0,X1] :
( test(X1)
=> ( leq(addition(multiplication(X1,X0),multiplication(c(X1),X0)),X0)
& leq(X0,addition(multiplication(X1,X0),multiplication(c(X1),X0))) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( test(X1)
=> ( leq(addition(multiplication(X1,X0),multiplication(c(X1),X0)),X0)
& leq(X0,addition(multiplication(X1,X0),multiplication(c(X1),X0))) ) ),
inference(negate_conjecture,[status(cth)],[goals]) ).
cnf(c0,plain,
addition(X0,X1) = addition(X1,X0),
inference(clausification,[status(esa)],[additive_commutativity]) ).
cnf(c3,plain,
addition(X0,X0) = X0,
inference(clausification,[status(esa)],[additive_idempotence]) ).
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(c12,plain,
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(clausification,[status(esa)],[order]) ).
cnf(c16,plain,
( addition(X1,X0) = one
| ~ complement(X0,X1) ),
inference(clausification,[status(esa)],[test_2]) ).
cnf(c19,plain,
( complement(X0,X1)
| c(X0) != X1
| ~ test(X0) ),
inference(clausification,[status(esa)],[test_3]) ).
cnf(c22,plain,
test(sK31),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c23,plain,
( ~ leq(addition(multiplication(sK31,sK30),multiplication(c(sK31),sK30)),sK30)
| ~ leq(sK30,addition(multiplication(sK31,sK30),multiplication(c(sK31),sK30))) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( leq(X0,X0)
| X0 != X0 ),
inference(superposition,[status(thm)],[c3,c12]) ).
cnf(d1,plain,
leq(X0,X0),
inference(equality_resolution,[status(thm)],[d0]) ).
cnf(d2,plain,
( complement(X0,c(X0))
| ~ test(X0) ),
inference(equality_resolution,[status(thm)],[c19]) ).
cnf(d3,plain,
( addition(c(X0),X0) = one
| ~ test(X0) ),
inference(resolution,[status(thm)],[d2,c16]) ).
cnf(d4,plain,
( ~ test(X0)
| addition(X0,c(X0)) = one ),
inference(demodulation,[status(thm)],[d3,c0]) ).
cnf(d5,plain,
addition(sK31,c(sK31)) = one,
inference(resolution,[status(thm)],[d4,c22]) ).
cnf(d6,plain,
( ~ leq(sK30,addition(multiplication(sK31,sK30),multiplication(c(sK31),sK30)))
| ~ leq(multiplication(addition(sK31,c(sK31)),sK30),sK30) ),
inference(demodulation,[status(thm)],[c23,c8]) ).
cnf(d7,plain,
( ~ leq(sK30,multiplication(addition(sK31,c(sK31)),sK30))
| ~ leq(multiplication(addition(sK31,c(sK31)),sK30),sK30) ),
inference(demodulation,[status(thm)],[d6,c8]) ).
cnf(d8,plain,
( ~ leq(sK30,multiplication(addition(sK31,c(sK31)),sK30))
| ~ leq(multiplication(one,sK30),sK30) ),
inference(demodulation,[status(thm)],[d7,d5]) ).
cnf(d9,plain,
( ~ leq(sK30,multiplication(one,sK30))
| ~ leq(multiplication(one,sK30),sK30) ),
inference(demodulation,[status(thm)],[d8,d5]) ).
cnf(d10,plain,
( ~ leq(sK30,multiplication(one,sK30))
| ~ leq(sK30,sK30) ),
inference(demodulation,[status(thm)],[d9,c6]) ).
cnf(d11,plain,
( ~ leq(sK30,sK30)
| ~ leq(sK30,sK30) ),
inference(demodulation,[status(thm)],[d10,c6]) ).
cnf(d12,plain,
~ leq(sK30,sK30),
inference(resolution,[status(thm)],[d1,d11]) ).
cnf(d13,plain,
$false,
inference(resolution,[status(thm)],[d12,d1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE021+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n018.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.45 % DateTime : Fri Sep 25 19:15:35 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 53.22/14.63 % SZS status Theorem for theBenchmark.p
% 53.22/14.63 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------