%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : KLE007+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 : n016.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 07:43:23 AM UTC 2026
% Result : Theorem 121.15s 22.97s
% Output : CNFRefutation 121.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 13
% Syntax : Number of formulae : 79 ( 35 unt; 0 def)
% Number of atoms : 150 ( 76 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 142 ( 71 ~; 58 |; 6 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 68 ( 3 sgn 24 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [X0,X1] : addition(X0,X1) = addition(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(right_distributivity,axiom,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,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(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(test_3,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ) ).
fof(goals,conjecture,
! [X0,X1] :
( ( test(X0)
& test(X1) )
=> ( leq(addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))),one)
& leq(one,addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1)))) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( ( test(X0)
& test(X1) )
=> ( leq(addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))),one)
& leq(one,addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1)))) ) ),
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(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(c7,plain,
addition(multiplication(X0,X1),multiplication(X0,X2)) = multiplication(X0,addition(X1,X2)),
inference(clausification,[status(esa)],[right_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(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(c15,plain,
( multiplication(X1,X0) = zero
| ~ complement(X0,X1) ),
inference(clausification,[status(esa)],[test_2]) ).
cnf(c16,plain,
( addition(X1,X0) = one
| ~ complement(X0,X1) ),
inference(clausification,[status(esa)],[test_2]) ).
cnf(c17,plain,
( multiplication(X0,X1) = zero
| ~ complement(X0,X1) ),
inference(clausification,[status(esa)],[test_2]) ).
cnf(c18,plain,
( multiplication(X1,X0) != zero
| addition(X1,X0) != one
| multiplication(X0,X1) != zero
| 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(c20,plain,
( ~ complement(X0,X1)
| c(X0) = X1
| ~ test(X0) ),
inference(clausification,[status(esa)],[test_3]) ).
cnf(c22,plain,
test(sK30),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c23,plain,
test(sK31),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c24,plain,
( ~ leq(addition(multiplication(addition(sK30,c(sK30)),sK31),multiplication(addition(sK30,c(sK30)),c(sK31))),one)
| ~ leq(one,addition(multiplication(addition(sK30,c(sK30)),sK31),multiplication(addition(sK30,c(sK30)),c(sK31)))) ),
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,
( ~ test(X0)
| addition(X0,sK23(X0)) = one ),
inference(resolution,[status(thm)],[c16,c13]) ).
cnf(d3,plain,
addition(sK30,sK23(sK30)) = one,
inference(resolution,[status(thm)],[d2,c22]) ).
cnf(d4,plain,
( ~ test(X0)
| multiplication(X0,sK23(X0)) = zero ),
inference(resolution,[status(thm)],[c15,c13]) ).
cnf(d5,plain,
multiplication(sK30,sK23(sK30)) = zero,
inference(resolution,[status(thm)],[d4,c22]) ).
cnf(d6,plain,
( ~ test(X0)
| multiplication(sK23(X0),X0) = zero ),
inference(resolution,[status(thm)],[c17,c13]) ).
cnf(d7,plain,
multiplication(sK23(sK30),sK30) = zero,
inference(resolution,[status(thm)],[d6,c22]) ).
cnf(d8,plain,
( complement(sK30,sK23(sK30))
| multiplication(sK30,sK23(sK30)) != zero
| addition(sK23(sK30),sK30) != one
| zero != zero ),
inference(superposition,[status(thm)],[d7,c18]) ).
cnf(d9,plain,
( complement(sK30,sK23(sK30))
| multiplication(sK30,sK23(sK30)) != zero
| zero != zero
| addition(sK30,sK23(sK30)) != one ),
inference(demodulation,[status(thm)],[d8,c0]) ).
cnf(d10,plain,
( complement(sK30,sK23(sK30))
| multiplication(sK30,sK23(sK30)) != zero
| zero != zero
| one != one ),
inference(demodulation,[status(thm)],[d9,d3]) ).
cnf(d11,plain,
( complement(sK30,sK23(sK30))
| zero != zero
| zero != zero
| one != one ),
inference(demodulation,[status(thm)],[d10,d5]) ).
cnf(d12,plain,
multiplication(sK31,sK23(sK31)) = zero,
inference(resolution,[status(thm)],[d4,c23]) ).
cnf(d13,plain,
multiplication(zero,X0) = multiplication(sK31,multiplication(sK23(sK31),X0)),
inference(superposition,[status(thm)],[d12,c4]) ).
cnf(d14,plain,
zero = multiplication(sK31,multiplication(sK23(sK31),X0)),
inference(demodulation,[status(thm)],[d13,c10]) ).
cnf(d15,plain,
zero = multiplication(sK31,zero),
inference(superposition,[status(thm)],[c9,d14]) ).
cnf(d16,plain,
zero = zero,
inference(demodulation,[status(thm)],[d15,c9]) ).
cnf(d17,plain,
( complement(sK30,sK23(sK30))
| zero != zero
| one != one ),
inference(resolution,[status(thm)],[d16,d11]) ).
cnf(d18,plain,
( complement(zero,X0)
| multiplication(zero,X0) != zero
| addition(X0,zero) != one
| zero != zero ),
inference(superposition,[status(thm)],[c9,c18]) ).
cnf(d19,plain,
( complement(zero,X0)
| multiplication(zero,X0) != zero
| zero != zero
| X0 != one ),
inference(demodulation,[status(thm)],[d18,c2]) ).
cnf(d20,plain,
( complement(zero,X0)
| zero != zero
| zero != zero
| X0 != one ),
inference(demodulation,[status(thm)],[d19,c10]) ).
cnf(d21,plain,
( complement(zero,X0)
| zero != zero
| X0 != one ),
inference(resolution,[status(thm)],[d16,d20]) ).
cnf(d22,plain,
( complement(zero,X0)
| X0 != one ),
inference(equality_resolution,[status(thm)],[d21]) ).
cnf(d23,plain,
complement(zero,one),
inference(equality_resolution,[status(thm)],[d22]) ).
cnf(d24,plain,
addition(one,zero) = one,
inference(resolution,[status(thm)],[d23,c16]) ).
cnf(d25,plain,
one = one,
inference(demodulation,[status(thm)],[d24,c2]) ).
cnf(d26,plain,
( complement(sK30,sK23(sK30))
| zero != zero ),
inference(resolution,[status(thm)],[d25,d17]) ).
cnf(d27,plain,
complement(sK30,sK23(sK30)),
inference(equality_resolution,[status(thm)],[d26]) ).
cnf(d28,plain,
( ~ test(sK30)
| c(sK30) = sK23(sK30) ),
inference(resolution,[status(thm)],[d27,c20]) ).
cnf(d29,plain,
c(sK30) = sK23(sK30),
inference(resolution,[status(thm)],[c22,d28]) ).
cnf(d30,plain,
( complement(X0,c(X0))
| ~ test(X0) ),
inference(equality_resolution,[status(thm)],[c19]) ).
cnf(d31,plain,
( addition(c(X0),X0) = one
| ~ test(X0) ),
inference(resolution,[status(thm)],[d30,c16]) ).
cnf(d32,plain,
( ~ test(X0)
| addition(X0,c(X0)) = one ),
inference(demodulation,[status(thm)],[d31,c0]) ).
cnf(d33,plain,
addition(sK31,c(sK31)) = one,
inference(resolution,[status(thm)],[d32,c23]) ).
cnf(d34,plain,
( ~ leq(one,addition(multiplication(addition(sK30,c(sK30)),sK31),multiplication(addition(sK30,c(sK30)),c(sK31))))
| ~ leq(multiplication(addition(sK30,c(sK30)),addition(sK31,c(sK31))),one) ),
inference(demodulation,[status(thm)],[c24,c7]) ).
cnf(d35,plain,
( ~ leq(one,multiplication(addition(sK30,c(sK30)),addition(sK31,c(sK31))))
| ~ leq(multiplication(addition(sK30,c(sK30)),addition(sK31,c(sK31))),one) ),
inference(demodulation,[status(thm)],[d34,c7]) ).
cnf(d36,plain,
( ~ leq(one,multiplication(addition(sK30,c(sK30)),addition(sK31,c(sK31))))
| ~ leq(multiplication(addition(sK30,c(sK30)),one),one) ),
inference(demodulation,[status(thm)],[d35,d33]) ).
cnf(d37,plain,
( ~ leq(one,multiplication(addition(sK30,c(sK30)),one))
| ~ leq(multiplication(addition(sK30,c(sK30)),one),one) ),
inference(demodulation,[status(thm)],[d36,d33]) ).
cnf(d38,plain,
( ~ leq(one,multiplication(addition(sK30,c(sK30)),one))
| ~ leq(addition(sK30,c(sK30)),one) ),
inference(demodulation,[status(thm)],[d37,c5]) ).
cnf(d39,plain,
( ~ leq(one,multiplication(addition(sK30,c(sK30)),one))
| ~ leq(addition(sK30,sK23(sK30)),one) ),
inference(demodulation,[status(thm)],[d38,d29]) ).
cnf(d40,plain,
( ~ leq(one,multiplication(addition(sK30,c(sK30)),one))
| ~ leq(one,one) ),
inference(demodulation,[status(thm)],[d39,d3]) ).
cnf(d41,plain,
( ~ leq(one,addition(sK30,c(sK30)))
| ~ leq(one,one) ),
inference(demodulation,[status(thm)],[d40,c5]) ).
cnf(d42,plain,
( ~ leq(one,addition(sK30,sK23(sK30)))
| ~ leq(one,one) ),
inference(demodulation,[status(thm)],[d41,d29]) ).
cnf(d43,plain,
( ~ leq(one,one)
| ~ leq(one,one) ),
inference(demodulation,[status(thm)],[d42,d3]) ).
cnf(d44,plain,
~ leq(one,one),
inference(resolution,[status(thm)],[d1,d43]) ).
cnf(d45,plain,
$false,
inference(resolution,[status(thm)],[d44,d1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE007+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n016.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 19:16:14 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 121.15/22.97 % SZS status Theorem for theBenchmark.p
% 121.15/22.97 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------