%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : KLE011+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 07:43:25 AM UTC 2026
% Result : Theorem 139.23s 24.57s
% Output : CNFRefutation 139.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 16
% Syntax : Number of formulae : 163 ( 92 unt; 0 def)
% Number of atoms : 270 ( 148 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 234 ( 127 ~; 94 |; 6 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 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 : 190 ( 3 sgn 31 !; 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_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(multiplicative_left_identity,axiom,
! [X0] : multiplication(one,X0) = X0 ).
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(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(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1))),one)
& leq(one,addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1)))) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( ( test(X0)
& test(X1) )
=> ( leq(addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1))),one)
& leq(one,addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(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(c1,plain,
addition(addition(X0,X1),X2) = addition(X0,addition(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(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(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(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(addition(multiplication(addition(sK31,c(sK31)),sK30),multiplication(addition(sK30,c(sK30)),sK31)),multiplication(c(sK30),c(sK31))),one)
| ~ leq(one,addition(addition(multiplication(addition(sK31,c(sK31)),sK30),multiplication(addition(sK30,c(sK30)),sK31)),multiplication(c(sK30),c(sK31)))) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
X0 = addition(X0,X0),
inference(superposition,[status(thm)],[c3,c0]) ).
cnf(d1,plain,
( leq(X0,X0)
| X0 != X0 ),
inference(superposition,[status(thm)],[d0,c12]) ).
cnf(d2,plain,
leq(X0,X0),
inference(equality_resolution,[status(thm)],[d1]) ).
cnf(d3,plain,
( ~ test(X0)
| addition(X0,sK23(X0)) = one ),
inference(resolution,[status(thm)],[c16,c13]) ).
cnf(d4,plain,
addition(sK31,sK23(sK31)) = one,
inference(resolution,[status(thm)],[d3,c23]) ).
cnf(d5,plain,
addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(superposition,[status(thm)],[c3,c1]) ).
cnf(d6,plain,
addition(sK31,sK23(sK31)) = addition(sK31,one),
inference(superposition,[status(thm)],[d4,d5]) ).
cnf(d7,plain,
one = addition(sK31,one),
inference(demodulation,[status(thm)],[d6,d4]) ).
cnf(d8,plain,
one = addition(one,sK31),
inference(demodulation,[status(thm)],[d7,c0]) ).
cnf(d9,plain,
addition(X2,addition(X0,X1)) = addition(X0,addition(X1,X2)),
inference(superposition,[status(thm)],[c1,c0]) ).
cnf(d10,plain,
addition(X1,addition(X2,X0)) = addition(X2,addition(X1,X0)),
inference(superposition,[status(thm)],[c0,d9]) ).
cnf(d11,plain,
addition(addition(X1,X0),X2) = addition(X0,addition(X1,X2)),
inference(superposition,[status(thm)],[c0,c1]) ).
cnf(d12,plain,
addition(one,X0) = addition(sK31,addition(one,X0)),
inference(superposition,[status(thm)],[d8,d11]) ).
cnf(d13,plain,
addition(one,X0) = addition(one,addition(sK31,X0)),
inference(demodulation,[status(thm)],[d12,d10]) ).
cnf(d14,plain,
addition(X0,multiplication(X1,X0)) = multiplication(addition(one,X1),X0),
inference(superposition,[status(thm)],[c6,c8]) ).
cnf(d15,plain,
addition(sK30,sK23(sK30)) = one,
inference(resolution,[status(thm)],[d3,c22]) ).
cnf(d16,plain,
addition(sK30,sK23(sK30)) = addition(sK30,one),
inference(superposition,[status(thm)],[d15,d5]) ).
cnf(d17,plain,
one = addition(sK30,one),
inference(demodulation,[status(thm)],[d16,d15]) ).
cnf(d18,plain,
one = addition(one,sK30),
inference(demodulation,[status(thm)],[d17,c0]) ).
cnf(d19,plain,
addition(X0,multiplication(sK30,X0)) = multiplication(one,X0),
inference(superposition,[status(thm)],[d18,d14]) ).
cnf(d20,plain,
addition(X0,multiplication(sK30,X0)) = X0,
inference(demodulation,[status(thm)],[d19,c6]) ).
cnf(d21,plain,
addition(one,multiplication(sK30,sK31)) = addition(one,sK31),
inference(superposition,[status(thm)],[d20,d13]) ).
cnf(d22,plain,
addition(one,multiplication(sK30,sK31)) = one,
inference(demodulation,[status(thm)],[d21,d8]) ).
cnf(d23,plain,
addition(X0,one) = addition(sK30,addition(X0,sK23(sK30))),
inference(superposition,[status(thm)],[d15,d10]) ).
cnf(d24,plain,
( ~ test(X0)
| multiplication(X0,sK23(X0)) = zero ),
inference(resolution,[status(thm)],[c15,c13]) ).
cnf(d25,plain,
multiplication(sK31,sK23(sK31)) = zero,
inference(resolution,[status(thm)],[d24,c23]) ).
cnf(d26,plain,
( ~ test(X0)
| multiplication(sK23(X0),X0) = zero ),
inference(resolution,[status(thm)],[c17,c13]) ).
cnf(d27,plain,
multiplication(sK23(sK31),sK31) = zero,
inference(resolution,[status(thm)],[d26,c23]) ).
cnf(d28,plain,
( complement(sK31,sK23(sK31))
| multiplication(sK31,sK23(sK31)) != zero
| addition(sK23(sK31),sK31) != one
| zero != zero ),
inference(superposition,[status(thm)],[d27,c18]) ).
cnf(d29,plain,
( complement(sK31,sK23(sK31))
| multiplication(sK31,sK23(sK31)) != zero
| zero != zero
| addition(sK31,sK23(sK31)) != one ),
inference(demodulation,[status(thm)],[d28,c0]) ).
cnf(d30,plain,
( complement(sK31,sK23(sK31))
| multiplication(sK31,sK23(sK31)) != zero
| zero != zero
| one != one ),
inference(demodulation,[status(thm)],[d29,d4]) ).
cnf(d31,plain,
( complement(sK31,sK23(sK31))
| zero != zero
| zero != zero
| one != one ),
inference(demodulation,[status(thm)],[d30,d25]) ).
cnf(d32,plain,
multiplication(zero,X0) = multiplication(sK31,multiplication(sK23(sK31),X0)),
inference(superposition,[status(thm)],[d25,c4]) ).
cnf(d33,plain,
zero = multiplication(sK31,multiplication(sK23(sK31),X0)),
inference(demodulation,[status(thm)],[d32,c10]) ).
cnf(d34,plain,
zero = multiplication(sK31,zero),
inference(superposition,[status(thm)],[c9,d33]) ).
cnf(d35,plain,
zero = zero,
inference(demodulation,[status(thm)],[d34,c9]) ).
cnf(d36,plain,
( complement(sK31,sK23(sK31))
| zero != zero
| one != one ),
inference(resolution,[status(thm)],[d35,d31]) ).
cnf(d37,plain,
( complement(zero,X0)
| multiplication(zero,X0) != zero
| addition(X0,zero) != one
| zero != zero ),
inference(superposition,[status(thm)],[c9,c18]) ).
cnf(d38,plain,
( complement(zero,X0)
| multiplication(zero,X0) != zero
| zero != zero
| X0 != one ),
inference(demodulation,[status(thm)],[d37,c2]) ).
cnf(d39,plain,
( complement(zero,X0)
| zero != zero
| zero != zero
| X0 != one ),
inference(demodulation,[status(thm)],[d38,c10]) ).
cnf(d40,plain,
( complement(zero,X0)
| zero != zero
| X0 != one ),
inference(resolution,[status(thm)],[d35,d39]) ).
cnf(d41,plain,
( complement(zero,X0)
| X0 != one ),
inference(equality_resolution,[status(thm)],[d40]) ).
cnf(d42,plain,
complement(zero,one),
inference(equality_resolution,[status(thm)],[d41]) ).
cnf(d43,plain,
addition(one,zero) = one,
inference(resolution,[status(thm)],[d42,c16]) ).
cnf(d44,plain,
one = one,
inference(demodulation,[status(thm)],[d43,c2]) ).
cnf(d45,plain,
( complement(sK31,sK23(sK31))
| zero != zero ),
inference(resolution,[status(thm)],[d44,d36]) ).
cnf(d46,plain,
complement(sK31,sK23(sK31)),
inference(equality_resolution,[status(thm)],[d45]) ).
cnf(d47,plain,
( ~ test(sK31)
| c(sK31) = sK23(sK31) ),
inference(resolution,[status(thm)],[d46,c20]) ).
cnf(d48,plain,
c(sK31) = sK23(sK31),
inference(resolution,[status(thm)],[c23,d47]) ).
cnf(d49,plain,
multiplication(sK30,sK23(sK30)) = zero,
inference(resolution,[status(thm)],[d24,c22]) ).
cnf(d50,plain,
multiplication(sK23(sK30),sK30) = zero,
inference(resolution,[status(thm)],[d26,c22]) ).
cnf(d51,plain,
( complement(sK30,sK23(sK30))
| multiplication(sK30,sK23(sK30)) != zero
| addition(sK23(sK30),sK30) != one
| zero != zero ),
inference(superposition,[status(thm)],[d50,c18]) ).
cnf(d52,plain,
( complement(sK30,sK23(sK30))
| multiplication(sK30,sK23(sK30)) != zero
| zero != zero
| addition(sK30,sK23(sK30)) != one ),
inference(demodulation,[status(thm)],[d51,c0]) ).
cnf(d53,plain,
( complement(sK30,sK23(sK30))
| multiplication(sK30,sK23(sK30)) != zero
| zero != zero
| one != one ),
inference(demodulation,[status(thm)],[d52,d15]) ).
cnf(d54,plain,
( complement(sK30,sK23(sK30))
| zero != zero
| zero != zero
| one != one ),
inference(demodulation,[status(thm)],[d53,d49]) ).
cnf(d55,plain,
( complement(sK30,sK23(sK30))
| zero != zero
| one != one ),
inference(resolution,[status(thm)],[d35,d54]) ).
cnf(d56,plain,
( complement(sK30,sK23(sK30))
| zero != zero ),
inference(resolution,[status(thm)],[d44,d55]) ).
cnf(d57,plain,
complement(sK30,sK23(sK30)),
inference(equality_resolution,[status(thm)],[d56]) ).
cnf(d58,plain,
( ~ test(sK30)
| c(sK30) = sK23(sK30) ),
inference(resolution,[status(thm)],[d57,c20]) ).
cnf(d59,plain,
c(sK30) = sK23(sK30),
inference(resolution,[status(thm)],[c22,d58]) ).
cnf(d60,plain,
addition(addition(X0,addition(X1,X2)),X3) = addition(addition(X0,X1),addition(X2,X3)),
inference(superposition,[status(thm)],[c1,c1]) ).
cnf(d61,plain,
addition(X0,addition(addition(X1,X2),X3)) = addition(addition(X0,X1),addition(X2,X3)),
inference(demodulation,[status(thm)],[d60,c1]) ).
cnf(d62,plain,
addition(X3,addition(X0,addition(X1,X2))) = addition(addition(X3,X0),addition(X1,X2)),
inference(demodulation,[status(thm)],[d61,c1]) ).
cnf(d63,plain,
addition(X0,addition(X1,addition(X2,X3))) = addition(X0,addition(X1,addition(X2,X3))),
inference(demodulation,[status(thm)],[d62,c1]) ).
cnf(d64,plain,
addition(X3,addition(X2,addition(X0,X1))) = addition(X3,addition(X0,addition(X1,X2))),
inference(superposition,[status(thm)],[d9,d63]) ).
cnf(d65,plain,
addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(superposition,[status(thm)],[c1,c0]) ).
cnf(d66,plain,
addition(X0,addition(X1,addition(X0,X1))) = addition(X0,X1),
inference(superposition,[status(thm)],[c1,c3]) ).
cnf(d67,plain,
addition(X2,addition(X0,X1)) = addition(addition(X1,addition(X0,X1)),addition(X2,X0)),
inference(superposition,[status(thm)],[d66,d65]) ).
cnf(d68,plain,
addition(X2,addition(X1,X0)) = addition(X0,addition(addition(X1,X0),addition(X2,X1))),
inference(demodulation,[status(thm)],[d67,c1]) ).
cnf(d69,plain,
addition(X2,addition(X1,X0)) = addition(X0,addition(X1,addition(addition(X1,X0),X2))),
inference(demodulation,[status(thm)],[d68,d64]) ).
cnf(d70,plain,
addition(X2,addition(X0,X1)) = addition(X1,addition(X0,addition(X0,addition(X1,X2)))),
inference(demodulation,[status(thm)],[d69,c1]) ).
cnf(d71,plain,
addition(X2,addition(X0,X1)) = addition(X1,addition(X0,addition(X1,X2))),
inference(demodulation,[status(thm)],[d70,d5]) ).
cnf(d72,plain,
addition(X0,addition(addition(X1,addition(X0,X1)),X2)) = addition(X2,addition(X0,X1)),
inference(superposition,[status(thm)],[d66,d65]) ).
cnf(d73,plain,
addition(X1,addition(X0,addition(addition(X1,X0),X2))) = addition(X2,addition(X1,X0)),
inference(demodulation,[status(thm)],[d72,c1]) ).
cnf(d74,plain,
addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(X2,addition(X0,X1)),
inference(demodulation,[status(thm)],[d73,c1]) ).
cnf(d75,plain,
addition(addition(X1,X2),addition(X1,X0)) = addition(X2,addition(X0,X1)),
inference(demodulation,[status(thm)],[d74,d71]) ).
cnf(d76,plain,
addition(X0,addition(X1,addition(X0,X2))) = addition(X1,addition(X2,X0)),
inference(demodulation,[status(thm)],[d75,c1]) ).
cnf(d77,plain,
addition(multiplication(X0,addition(X1,X2)),X3) = addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3)),
inference(superposition,[status(thm)],[c7,c1]) ).
cnf(d78,plain,
addition(X0,X1) = addition(X0,addition(X1,addition(X0,X1))),
inference(superposition,[status(thm)],[c3,c1]) ).
cnf(d79,plain,
addition(multiplication(X0,X1),multiplication(X0,X2)) = addition(multiplication(X0,X1),addition(multiplication(X0,X2),multiplication(X0,addition(X1,X2)))),
inference(superposition,[status(thm)],[c7,d78]) ).
cnf(d80,plain,
multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),addition(multiplication(X0,X2),multiplication(X0,addition(X1,X2)))),
inference(demodulation,[status(thm)],[d79,c7]) ).
cnf(d81,plain,
multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,addition(X1,X2)),multiplication(X0,addition(X1,X2))),
inference(demodulation,[status(thm)],[d80,d77]) ).
cnf(d82,plain,
multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(addition(X1,X2),addition(X1,X2))),
inference(demodulation,[status(thm)],[d81,c7]) ).
cnf(d83,plain,
multiplication(X2,addition(X0,X1)) = multiplication(X2,addition(X0,addition(X1,addition(X0,X1)))),
inference(demodulation,[status(thm)],[d82,c1]) ).
cnf(d84,plain,
multiplication(X2,addition(X0,X1)) = multiplication(X2,addition(X1,addition(X1,X0))),
inference(demodulation,[status(thm)],[d83,d76]) ).
cnf(d85,plain,
multiplication(X2,addition(X1,X0)) = multiplication(X2,addition(X0,X1)),
inference(demodulation,[status(thm)],[d84,d5]) ).
cnf(d86,plain,
addition(multiplication(X2,X1),multiplication(X0,X1)) = multiplication(addition(X0,X2),X1),
inference(superposition,[status(thm)],[c8,c0]) ).
cnf(d87,plain,
addition(multiplication(X0,addition(X3,X1)),multiplication(X2,X1)) = addition(multiplication(X0,X3),multiplication(addition(X2,X0),X1)),
inference(superposition,[status(thm)],[d86,d77]) ).
cnf(d88,plain,
( complement(X0,c(X0))
| ~ test(X0) ),
inference(equality_resolution,[status(thm)],[c19]) ).
cnf(d89,plain,
( addition(c(X0),X0) = one
| ~ test(X0) ),
inference(resolution,[status(thm)],[d88,c16]) ).
cnf(d90,plain,
( ~ test(X0)
| addition(X0,c(X0)) = one ),
inference(demodulation,[status(thm)],[d89,c0]) ).
cnf(d91,plain,
addition(sK31,c(sK31)) = one,
inference(resolution,[status(thm)],[d90,c23]) ).
cnf(d92,plain,
( ~ leq(one,addition(addition(multiplication(addition(sK31,c(sK31)),sK30),multiplication(addition(sK30,c(sK30)),sK31)),multiplication(c(sK30),c(sK31))))
| ~ leq(addition(multiplication(c(sK30),c(sK31)),addition(multiplication(addition(sK31,c(sK31)),sK30),multiplication(addition(sK30,c(sK30)),sK31))),one) ),
inference(demodulation,[status(thm)],[c24,c0]) ).
cnf(d93,plain,
( ~ leq(one,addition(addition(multiplication(addition(sK31,c(sK31)),sK30),multiplication(addition(sK30,c(sK30)),sK31)),multiplication(c(sK30),c(sK31))))
| ~ leq(addition(multiplication(c(sK30),c(sK31)),addition(multiplication(addition(sK30,c(sK30)),sK31),multiplication(addition(sK31,c(sK31)),sK30))),one) ),
inference(demodulation,[status(thm)],[d92,c0]) ).
cnf(d94,plain,
( ~ leq(one,addition(multiplication(c(sK30),c(sK31)),addition(multiplication(addition(sK31,c(sK31)),sK30),multiplication(addition(sK30,c(sK30)),sK31))))
| ~ leq(addition(multiplication(c(sK30),c(sK31)),addition(multiplication(addition(sK30,c(sK30)),sK31),multiplication(addition(sK31,c(sK31)),sK30))),one) ),
inference(demodulation,[status(thm)],[d93,c0]) ).
cnf(d95,plain,
( ~ leq(one,addition(multiplication(c(sK30),c(sK31)),addition(multiplication(addition(sK30,c(sK30)),sK31),multiplication(addition(sK31,c(sK31)),sK30))))
| ~ leq(addition(multiplication(c(sK30),c(sK31)),addition(multiplication(addition(sK30,c(sK30)),sK31),multiplication(addition(sK31,c(sK31)),sK30))),one) ),
inference(demodulation,[status(thm)],[d94,c0]) ).
cnf(d96,plain,
( ~ leq(one,addition(multiplication(c(sK30),c(sK31)),addition(multiplication(addition(sK30,c(sK30)),sK31),multiplication(addition(sK31,c(sK31)),sK30))))
| ~ leq(addition(multiplication(c(sK30),c(sK31)),addition(multiplication(addition(sK30,c(sK30)),sK31),multiplication(one,sK30))),one) ),
inference(demodulation,[status(thm)],[d95,d91]) ).
cnf(d97,plain,
( ~ leq(one,addition(multiplication(c(sK30),c(sK31)),addition(multiplication(addition(sK30,c(sK30)),sK31),multiplication(one,sK30))))
| ~ leq(addition(multiplication(c(sK30),c(sK31)),addition(multiplication(addition(sK30,c(sK30)),sK31),multiplication(one,sK30))),one) ),
inference(demodulation,[status(thm)],[d96,d91]) ).
cnf(d98,plain,
( ~ leq(one,addition(multiplication(c(sK30),c(sK31)),addition(multiplication(addition(sK30,c(sK30)),sK31),multiplication(one,sK30))))
| ~ leq(addition(multiplication(one,sK30),addition(multiplication(c(sK30),c(sK31)),multiplication(addition(sK30,c(sK30)),sK31))),one) ),
inference(demodulation,[status(thm)],[d97,d9]) ).
cnf(d99,plain,
( ~ leq(one,addition(multiplication(c(sK30),c(sK31)),addition(multiplication(addition(sK30,c(sK30)),sK31),multiplication(one,sK30))))
| ~ leq(addition(sK30,addition(multiplication(c(sK30),c(sK31)),multiplication(addition(sK30,c(sK30)),sK31))),one) ),
inference(demodulation,[status(thm)],[d98,c6]) ).
cnf(d100,plain,
( ~ leq(one,addition(multiplication(c(sK30),c(sK31)),addition(multiplication(addition(sK30,c(sK30)),sK31),multiplication(one,sK30))))
| ~ leq(addition(sK30,addition(multiplication(c(sK30),addition(c(sK31),sK31)),multiplication(sK30,sK31))),one) ),
inference(demodulation,[status(thm)],[d99,d87]) ).
cnf(d101,plain,
( ~ leq(one,addition(multiplication(c(sK30),c(sK31)),addition(multiplication(addition(sK30,c(sK30)),sK31),multiplication(one,sK30))))
| ~ leq(addition(sK30,addition(multiplication(sK30,sK31),multiplication(c(sK30),addition(c(sK31),sK31)))),one) ),
inference(demodulation,[status(thm)],[d100,c0]) ).
cnf(d102,plain,
( ~ leq(one,addition(multiplication(c(sK30),c(sK31)),addition(multiplication(addition(sK30,c(sK30)),sK31),multiplication(one,sK30))))
| ~ leq(addition(sK30,addition(multiplication(sK30,sK31),multiplication(c(sK30),addition(sK31,c(sK31))))),one) ),
inference(demodulation,[status(thm)],[d101,d85]) ).
cnf(d103,plain,
( ~ leq(one,addition(multiplication(c(sK30),c(sK31)),addition(multiplication(addition(sK30,c(sK30)),sK31),multiplication(one,sK30))))
| ~ leq(addition(sK30,addition(multiplication(sK30,sK31),multiplication(sK23(sK30),addition(sK31,c(sK31))))),one) ),
inference(demodulation,[status(thm)],[d102,d59]) ).
cnf(d104,plain,
( ~ leq(one,addition(multiplication(c(sK30),c(sK31)),addition(multiplication(addition(sK30,c(sK30)),sK31),multiplication(one,sK30))))
| ~ leq(addition(sK30,addition(multiplication(sK30,sK31),multiplication(sK23(sK30),addition(sK31,sK23(sK31))))),one) ),
inference(demodulation,[status(thm)],[d103,d48]) ).
cnf(d105,plain,
( ~ leq(one,addition(multiplication(c(sK30),c(sK31)),addition(multiplication(addition(sK30,c(sK30)),sK31),multiplication(one,sK30))))
| ~ leq(addition(sK30,addition(multiplication(sK30,sK31),multiplication(sK23(sK30),one))),one) ),
inference(demodulation,[status(thm)],[d104,d4]) ).
cnf(d106,plain,
( ~ leq(one,addition(multiplication(c(sK30),c(sK31)),addition(multiplication(addition(sK30,c(sK30)),sK31),multiplication(one,sK30))))
| ~ leq(addition(sK30,addition(multiplication(sK30,sK31),sK23(sK30))),one) ),
inference(demodulation,[status(thm)],[d105,c5]) ).
cnf(d107,plain,
( ~ leq(one,addition(multiplication(c(sK30),c(sK31)),addition(multiplication(addition(sK30,c(sK30)),sK31),multiplication(one,sK30))))
| ~ leq(addition(multiplication(sK30,sK31),one),one) ),
inference(demodulation,[status(thm)],[d106,d23]) ).
cnf(d108,plain,
( ~ leq(one,addition(multiplication(c(sK30),c(sK31)),addition(multiplication(addition(sK30,c(sK30)),sK31),multiplication(one,sK30))))
| ~ leq(addition(one,multiplication(sK30,sK31)),one) ),
inference(demodulation,[status(thm)],[d107,c0]) ).
cnf(d109,plain,
( ~ leq(one,addition(multiplication(c(sK30),c(sK31)),addition(multiplication(addition(sK30,c(sK30)),sK31),multiplication(one,sK30))))
| ~ leq(one,one) ),
inference(demodulation,[status(thm)],[d108,d22]) ).
cnf(d110,plain,
( ~ leq(one,addition(multiplication(one,sK30),addition(multiplication(c(sK30),c(sK31)),multiplication(addition(sK30,c(sK30)),sK31))))
| ~ leq(one,one) ),
inference(demodulation,[status(thm)],[d109,d9]) ).
cnf(d111,plain,
( ~ leq(one,addition(sK30,addition(multiplication(c(sK30),c(sK31)),multiplication(addition(sK30,c(sK30)),sK31))))
| ~ leq(one,one) ),
inference(demodulation,[status(thm)],[d110,c6]) ).
cnf(d112,plain,
( ~ leq(one,addition(sK30,addition(multiplication(c(sK30),addition(c(sK31),sK31)),multiplication(sK30,sK31))))
| ~ leq(one,one) ),
inference(demodulation,[status(thm)],[d111,d87]) ).
cnf(d113,plain,
( ~ leq(one,addition(sK30,addition(multiplication(sK30,sK31),multiplication(c(sK30),addition(c(sK31),sK31)))))
| ~ leq(one,one) ),
inference(demodulation,[status(thm)],[d112,c0]) ).
cnf(d114,plain,
( ~ leq(one,addition(sK30,addition(multiplication(sK30,sK31),multiplication(c(sK30),addition(sK31,c(sK31))))))
| ~ leq(one,one) ),
inference(demodulation,[status(thm)],[d113,d85]) ).
cnf(d115,plain,
( ~ leq(one,addition(sK30,addition(multiplication(sK30,sK31),multiplication(sK23(sK30),addition(sK31,c(sK31))))))
| ~ leq(one,one) ),
inference(demodulation,[status(thm)],[d114,d59]) ).
cnf(d116,plain,
( ~ leq(one,addition(sK30,addition(multiplication(sK30,sK31),multiplication(sK23(sK30),addition(sK31,sK23(sK31))))))
| ~ leq(one,one) ),
inference(demodulation,[status(thm)],[d115,d48]) ).
cnf(d117,plain,
( ~ leq(one,addition(sK30,addition(multiplication(sK30,sK31),multiplication(sK23(sK30),one))))
| ~ leq(one,one) ),
inference(demodulation,[status(thm)],[d116,d4]) ).
cnf(d118,plain,
( ~ leq(one,addition(sK30,addition(multiplication(sK30,sK31),sK23(sK30))))
| ~ leq(one,one) ),
inference(demodulation,[status(thm)],[d117,c5]) ).
cnf(d119,plain,
( ~ leq(one,addition(multiplication(sK30,sK31),one))
| ~ leq(one,one) ),
inference(demodulation,[status(thm)],[d118,d23]) ).
cnf(d120,plain,
( ~ leq(one,addition(one,multiplication(sK30,sK31)))
| ~ leq(one,one) ),
inference(demodulation,[status(thm)],[d119,c0]) ).
cnf(d121,plain,
( ~ leq(one,one)
| ~ leq(one,one) ),
inference(demodulation,[status(thm)],[d120,d22]) ).
cnf(d122,plain,
~ leq(one,one),
inference(resolution,[status(thm)],[d2,d121]) ).
cnf(d123,plain,
$false,
inference(resolution,[status(thm)],[d122,d2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE011+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n016.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 19:17:30 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 139.23/24.57 % SZS status Theorem for theBenchmark.p
% 139.23/24.57 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------