%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : KLE026+2 : 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 : n004.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 07:43:27 AM UTC 2026
% Result : Theorem 39.25s 10.13s
% Output : CNFRefutation 39.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 45 ( 34 unt; 0 def)
% Number of atoms : 62 ( 40 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 25 ( 8 ~; 6 |; 4 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 59 ( 0 sgn 25 !; 1 ?)
% 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_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(order,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ) ).
fof(test_1,axiom,
! [X0] :
( test(X0)
<=> ? [X1] : complement(X1,X0) ) ).
fof(test_2,axiom,
! [X0,X1] :
( complement(X1,X0)
<=> ( addition(X0,X1) = one
& multiplication(X1,X0) = zero
& multiplication(X0,X1) = zero ) ) ).
fof(goals,conjecture,
! [X0,X1,X2] :
( ( test(X2)
& test(X1) )
=> ( multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2)
=> leq(multiplication(X1,X0),multiplication(X0,X2)) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( ( test(X2)
& test(X1) )
=> ( multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2)
=> leq(multiplication(X1,X0),multiplication(X0,X2)) ) ),
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(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(clausification,[status(esa)],[additive_associativity]) ).
cnf(c3,plain,
addition(X0,X0) = X0,
inference(clausification,[status(esa)],[additive_idempotence]) ).
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(c12,plain,
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(clausification,[status(esa)],[order]) ).
cnf(c13,plain,
( complement(sK23(X0),X0)
| ~ test(X0) ),
inference(clausification,[status(esa)],[test_1]) ).
cnf(c16,plain,
( addition(X1,X0) = one
| ~ complement(X0,X1) ),
inference(clausification,[status(esa)],[test_2]) ).
cnf(c25,plain,
test(sK35),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c26,plain,
~ leq(multiplication(sK35,sK34),multiplication(sK34,sK36)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c27,plain,
multiplication(multiplication(sK35,sK34),sK36) = multiplication(sK35,sK34),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( leq(X0,X1)
| addition(X1,X0) != X1 ),
inference(superposition,[status(thm)],[c0,c12]) ).
cnf(d1,plain,
addition(X0,multiplication(X1,X0)) = multiplication(addition(one,X1),X0),
inference(superposition,[status(thm)],[c6,c8]) ).
cnf(d2,plain,
( ~ test(X0)
| addition(X0,sK23(X0)) = one ),
inference(resolution,[status(thm)],[c16,c13]) ).
cnf(d3,plain,
addition(sK35,sK23(sK35)) = one,
inference(resolution,[status(thm)],[d2,c25]) ).
cnf(d4,plain,
addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(superposition,[status(thm)],[c3,c1]) ).
cnf(d5,plain,
addition(sK35,sK23(sK35)) = addition(sK35,one),
inference(superposition,[status(thm)],[d3,d4]) ).
cnf(d6,plain,
one = addition(sK35,one),
inference(demodulation,[status(thm)],[d5,d3]) ).
cnf(d7,plain,
one = addition(one,sK35),
inference(demodulation,[status(thm)],[d6,c0]) ).
cnf(d8,plain,
addition(X0,multiplication(sK35,X0)) = multiplication(one,X0),
inference(superposition,[status(thm)],[d7,d1]) ).
cnf(d9,plain,
addition(X0,multiplication(sK35,X0)) = X0,
inference(demodulation,[status(thm)],[d8,c6]) ).
cnf(d10,plain,
( leq(multiplication(sK35,X0),X0)
| X0 != X0 ),
inference(superposition,[status(thm)],[d9,d0]) ).
cnf(d11,plain,
leq(multiplication(sK35,X0),X0),
inference(equality_resolution,[status(thm)],[d10]) ).
cnf(d12,plain,
multiplication(sK35,multiplication(sK34,sK36)) = multiplication(sK35,sK34),
inference(demodulation,[status(thm)],[c27,c4]) ).
cnf(d13,plain,
multiplication(multiplication(sK35,sK34),X0) = multiplication(sK35,multiplication(multiplication(sK34,sK36),X0)),
inference(superposition,[status(thm)],[d12,c4]) ).
cnf(d14,plain,
multiplication(sK35,multiplication(sK34,X0)) = multiplication(sK35,multiplication(multiplication(sK34,sK36),X0)),
inference(demodulation,[status(thm)],[d13,c4]) ).
cnf(d15,plain,
multiplication(sK35,multiplication(sK34,X0)) = multiplication(sK35,multiplication(sK34,multiplication(sK36,X0))),
inference(demodulation,[status(thm)],[d14,c4]) ).
cnf(d16,plain,
multiplication(sK35,multiplication(sK34,one)) = multiplication(sK35,multiplication(sK34,sK36)),
inference(superposition,[status(thm)],[c5,d15]) ).
cnf(d17,plain,
multiplication(sK35,sK34) = multiplication(sK35,multiplication(sK34,sK36)),
inference(demodulation,[status(thm)],[d16,c5]) ).
cnf(d18,plain,
leq(multiplication(sK35,sK34),multiplication(sK34,sK36)),
inference(superposition,[status(thm)],[d17,d11]) ).
cnf(d19,plain,
$false,
inference(resolution,[status(thm)],[c26,d18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : KLE026+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.41 % Computer : n004.cluster.edu
% 0.08/0.41 % Model : x86_64 x86_64
% 0.08/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.41 % Memory : 8046.5625MB
% 0.08/0.41 % OS : Linux 6.8.0-71-generic
% 0.08/0.41 % CPULimit : 300
% 0.08/0.41 % WCLimit : 300
% 0.08/0.41 % DateTime : Fri Sep 25 19:14:53 UTC 2026
% 0.08/0.42 % CPUTime :
% 0.08/0.42 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 39.25/10.13 % SZS status Theorem for theBenchmark.p
% 39.25/10.13 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------