%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : KLE035+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 : n015.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 07:43:28 AM UTC 2026
% Result : Theorem 31.32s 4.41s
% Output : CNFRefutation 31.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 32 ( 28 unt; 0 def)
% Number of atoms : 42 ( 19 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 17 ( 7 ~; 1 |; 6 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 39 ( 0 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0) ).
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(right_distributivity,axiom,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)) ).
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(goals,conjecture,
! [X0,X1,X2,X3] :
( ( leq(multiplication(multiplication(X2,X1),c(X3)),zero)
& leq(multiplication(multiplication(X2,X0),c(X3)),zero)
& test(X2)
& test(X3) )
=> leq(multiplication(multiplication(X2,addition(X0,X1)),c(X3)),zero) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( leq(multiplication(multiplication(X2,X1),c(X3)),zero)
& leq(multiplication(multiplication(X2,X0),c(X3)),zero)
& test(X2)
& test(X3) )
=> leq(multiplication(multiplication(X2,addition(X0,X1)),c(X3)),zero) ),
inference(negate_conjecture,[status(cth)],[goals]) ).
cnf(c0,plain,
addition(X0,X1) = addition(X1,X0),
inference(clausification,[status(esa)],[additive_commutativity]) ).
cnf(c2,plain,
addition(X0,zero) = X0,
inference(clausification,[status(esa)],[additive_identity]) ).
cnf(c4,plain,
multiplication(multiplication(X0,X1),X2) = multiplication(X0,multiplication(X1,X2)),
inference(clausification,[status(esa)],[multiplicative_associativity]) ).
cnf(c7,plain,
addition(multiplication(X0,X1),multiplication(X0,X2)) = multiplication(X0,addition(X1,X2)),
inference(clausification,[status(esa)],[right_distributivity]) ).
cnf(c8,plain,
addition(multiplication(X0,X1),multiplication(X2,X1)) = multiplication(addition(X0,X2),X1),
inference(clausification,[status(esa)],[left_distributivity]) ).
cnf(c11,plain,
( addition(X0,X1) = X1
| ~ leq(X0,X1) ),
inference(clausification,[status(esa)],[order]) ).
cnf(c25,plain,
leq(multiplication(multiplication(sK36,sK35),c(sK37)),zero),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c26,plain,
leq(multiplication(multiplication(sK36,sK34),c(sK37)),zero),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c28,plain,
~ leq(multiplication(multiplication(sK36,addition(sK34,sK35)),c(sK37)),zero),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
leq(multiplication(sK36,multiplication(sK35,c(sK37))),zero),
inference(demodulation,[status(thm)],[c25,c4]) ).
cnf(d1,plain,
addition(multiplication(sK36,multiplication(sK35,c(sK37))),zero) = zero,
inference(resolution,[status(thm)],[c11,d0]) ).
cnf(d2,plain,
multiplication(sK36,multiplication(sK35,c(sK37))) = zero,
inference(demodulation,[status(thm)],[d1,c2]) ).
cnf(d3,plain,
leq(multiplication(sK36,multiplication(sK34,c(sK37))),zero),
inference(demodulation,[status(thm)],[c26,c4]) ).
cnf(d4,plain,
addition(multiplication(sK36,multiplication(sK34,c(sK37))),zero) = zero,
inference(resolution,[status(thm)],[c11,d3]) ).
cnf(d5,plain,
multiplication(sK36,multiplication(sK34,c(sK37))) = zero,
inference(demodulation,[status(thm)],[d4,c2]) ).
cnf(d6,plain,
addition(multiplication(sK36,X0),zero) = multiplication(sK36,addition(X0,multiplication(sK34,c(sK37)))),
inference(superposition,[status(thm)],[d5,c7]) ).
cnf(d7,plain,
multiplication(sK36,X0) = multiplication(sK36,addition(X0,multiplication(sK34,c(sK37)))),
inference(demodulation,[status(thm)],[d6,c2]) ).
cnf(d8,plain,
multiplication(sK36,multiplication(X0,c(sK37))) = multiplication(sK36,multiplication(addition(X0,sK34),c(sK37))),
inference(superposition,[status(thm)],[c8,d7]) ).
cnf(d9,plain,
~ leq(multiplication(multiplication(sK36,addition(sK35,sK34)),c(sK37)),zero),
inference(demodulation,[status(thm)],[c28,c0]) ).
cnf(d10,plain,
~ leq(multiplication(sK36,multiplication(addition(sK35,sK34),c(sK37))),zero),
inference(demodulation,[status(thm)],[d9,c4]) ).
cnf(d11,plain,
~ leq(multiplication(sK36,multiplication(sK35,c(sK37))),zero),
inference(demodulation,[status(thm)],[d10,d8]) ).
cnf(d12,plain,
~ leq(zero,zero),
inference(demodulation,[status(thm)],[d11,d2]) ).
cnf(d13,plain,
leq(zero,zero),
inference(demodulation,[status(thm)],[d3,d5]) ).
cnf(d14,plain,
$false,
inference(resolution,[status(thm)],[d13,d12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE035+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n015.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 19:19:12 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 31.32/4.41 % SZS status Theorem for theBenchmark.p
% 31.32/4.41 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------