%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : KLE010+1 : 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 : n014.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 07:43:24 AM UTC 2026
% Result : Theorem 35.00s 27.38s
% Output : CNFRefutation 35.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 15
% Syntax : Number of formulae : 97 ( 77 unt; 0 def)
% Number of atoms : 132 ( 101 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 83 ( 48 ~; 25 |; 4 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 89 ( 3 sgn 29 !; 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(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) )
=> one = addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( ( test(X0)
& test(X1) )
=> one = addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(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(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(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(c22,plain,
test(sK30),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c23,plain,
test(sK31),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c24,plain,
addition(addition(addition(addition(multiplication(sK31,sK30),multiplication(c(sK31),sK30)),multiplication(sK30,sK31)),multiplication(c(sK30),sK31)),multiplication(c(sK30),c(sK31))) != one,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ test(X0)
| addition(X0,sK23(X0)) = one ),
inference(resolution,[status(thm)],[c16,c13]) ).
cnf(d1,plain,
addition(sK31,sK23(sK31)) = one,
inference(resolution,[status(thm)],[d0,c23]) ).
cnf(d2,plain,
addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(superposition,[status(thm)],[c3,c1]) ).
cnf(d3,plain,
addition(sK31,sK23(sK31)) = addition(sK31,one),
inference(superposition,[status(thm)],[d1,d2]) ).
cnf(d4,plain,
one = addition(sK31,one),
inference(demodulation,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
one = addition(one,sK31),
inference(demodulation,[status(thm)],[d4,c0]) ).
cnf(d6,plain,
addition(X2,addition(X0,X1)) = addition(X0,addition(X1,X2)),
inference(superposition,[status(thm)],[c1,c0]) ).
cnf(d7,plain,
addition(X0,one) = addition(one,addition(sK31,X0)),
inference(superposition,[status(thm)],[d5,d6]) ).
cnf(d8,plain,
addition(X0,multiplication(X1,X0)) = multiplication(addition(one,X1),X0),
inference(superposition,[status(thm)],[c6,c8]) ).
cnf(d9,plain,
addition(sK30,sK23(sK30)) = one,
inference(resolution,[status(thm)],[d0,c22]) ).
cnf(d10,plain,
addition(sK30,sK23(sK30)) = addition(sK30,one),
inference(superposition,[status(thm)],[d9,d2]) ).
cnf(d11,plain,
one = addition(sK30,one),
inference(demodulation,[status(thm)],[d10,d9]) ).
cnf(d12,plain,
one = addition(one,sK30),
inference(demodulation,[status(thm)],[d11,c0]) ).
cnf(d13,plain,
addition(X0,multiplication(sK30,X0)) = multiplication(one,X0),
inference(superposition,[status(thm)],[d12,d8]) ).
cnf(d14,plain,
addition(X0,multiplication(sK30,X0)) = X0,
inference(demodulation,[status(thm)],[d13,c6]) ).
cnf(d15,plain,
addition(multiplication(sK30,sK31),one) = addition(one,sK31),
inference(superposition,[status(thm)],[d14,d7]) ).
cnf(d16,plain,
addition(one,multiplication(sK30,sK31)) = addition(one,sK31),
inference(demodulation,[status(thm)],[d15,c0]) ).
cnf(d17,plain,
addition(one,multiplication(sK30,sK31)) = one,
inference(demodulation,[status(thm)],[d16,d5]) ).
cnf(d18,plain,
( complement(X0,c(X0))
| ~ test(X0) ),
inference(equality_resolution,[status(thm)],[c19]) ).
cnf(d19,plain,
( addition(c(X0),X0) = one
| ~ test(X0) ),
inference(resolution,[status(thm)],[d18,c16]) ).
cnf(d20,plain,
( ~ test(X0)
| addition(X0,c(X0)) = one ),
inference(demodulation,[status(thm)],[d19,c0]) ).
cnf(d21,plain,
addition(sK30,c(sK30)) = one,
inference(resolution,[status(thm)],[d20,c22]) ).
cnf(d22,plain,
addition(X0,one) = addition(sK30,addition(c(sK30),X0)),
inference(superposition,[status(thm)],[d21,d6]) ).
cnf(d23,plain,
addition(sK31,c(sK31)) = one,
inference(resolution,[status(thm)],[d20,c23]) ).
cnf(d24,plain,
addition(X1,addition(X2,X0)) = addition(X2,addition(X1,X0)),
inference(superposition,[status(thm)],[c0,d6]) ).
cnf(d25,plain,
addition(multiplication(X0,addition(X1,X2)),X3) = addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3)),
inference(superposition,[status(thm)],[c7,c1]) ).
cnf(d26,plain,
addition(multiplication(c(sK30),c(sK31)),addition(addition(addition(multiplication(sK31,sK30),multiplication(c(sK31),sK30)),multiplication(sK30,sK31)),multiplication(c(sK30),sK31))) != one,
inference(demodulation,[status(thm)],[c24,c0]) ).
cnf(d27,plain,
addition(multiplication(c(sK30),c(sK31)),addition(multiplication(c(sK30),sK31),addition(addition(multiplication(sK31,sK30),multiplication(c(sK31),sK30)),multiplication(sK30,sK31)))) != one,
inference(demodulation,[status(thm)],[d26,c0]) ).
cnf(d28,plain,
addition(multiplication(c(sK30),c(sK31)),addition(multiplication(c(sK30),sK31),addition(multiplication(sK30,sK31),addition(multiplication(sK31,sK30),multiplication(c(sK31),sK30))))) != one,
inference(demodulation,[status(thm)],[d27,c0]) ).
cnf(d29,plain,
addition(multiplication(c(sK30),c(sK31)),addition(multiplication(c(sK30),sK31),addition(multiplication(sK30,sK31),multiplication(addition(sK31,c(sK31)),sK30)))) != one,
inference(demodulation,[status(thm)],[d28,c8]) ).
cnf(d30,plain,
addition(multiplication(c(sK30),sK31),addition(addition(multiplication(sK30,sK31),multiplication(addition(sK31,c(sK31)),sK30)),multiplication(c(sK30),c(sK31)))) != one,
inference(demodulation,[status(thm)],[d29,d6]) ).
cnf(d31,plain,
addition(multiplication(c(sK30),sK31),addition(multiplication(sK30,sK31),addition(multiplication(addition(sK31,c(sK31)),sK30),multiplication(c(sK30),c(sK31))))) != one,
inference(demodulation,[status(thm)],[d30,c1]) ).
cnf(d32,plain,
addition(multiplication(sK30,sK31),addition(addition(multiplication(addition(sK31,c(sK31)),sK30),multiplication(c(sK30),c(sK31))),multiplication(c(sK30),sK31))) != one,
inference(demodulation,[status(thm)],[d31,d6]) ).
cnf(d33,plain,
addition(multiplication(sK30,sK31),addition(multiplication(addition(sK31,c(sK31)),sK30),addition(multiplication(c(sK30),c(sK31)),multiplication(c(sK30),sK31)))) != one,
inference(demodulation,[status(thm)],[d32,c1]) ).
cnf(d34,plain,
addition(multiplication(sK30,sK31),addition(multiplication(c(sK30),sK31),addition(multiplication(addition(sK31,c(sK31)),sK30),multiplication(c(sK30),c(sK31))))) != one,
inference(demodulation,[status(thm)],[d33,d6]) ).
cnf(d35,plain,
addition(multiplication(sK30,sK31),addition(multiplication(c(sK30),sK31),addition(multiplication(c(sK30),c(sK31)),multiplication(addition(sK31,c(sK31)),sK30)))) != one,
inference(demodulation,[status(thm)],[d34,c0]) ).
cnf(d36,plain,
addition(multiplication(sK30,sK31),addition(multiplication(c(sK30),addition(sK31,c(sK31))),multiplication(addition(sK31,c(sK31)),sK30))) != one,
inference(demodulation,[status(thm)],[d35,d25]) ).
cnf(d37,plain,
addition(multiplication(sK30,sK31),addition(multiplication(addition(sK31,c(sK31)),sK30),multiplication(c(sK30),addition(sK31,c(sK31))))) != one,
inference(demodulation,[status(thm)],[d36,c0]) ).
cnf(d38,plain,
addition(multiplication(sK30,sK31),addition(multiplication(one,sK30),multiplication(c(sK30),addition(sK31,c(sK31))))) != one,
inference(demodulation,[status(thm)],[d37,d23]) ).
cnf(d39,plain,
addition(multiplication(one,sK30),addition(multiplication(sK30,sK31),multiplication(c(sK30),addition(sK31,c(sK31))))) != one,
inference(demodulation,[status(thm)],[d38,d24]) ).
cnf(d40,plain,
addition(sK30,addition(multiplication(sK30,sK31),multiplication(c(sK30),addition(sK31,c(sK31))))) != one,
inference(demodulation,[status(thm)],[d39,c6]) ).
cnf(d41,plain,
addition(sK30,addition(multiplication(sK30,sK31),multiplication(c(sK30),one))) != one,
inference(demodulation,[status(thm)],[d40,d23]) ).
cnf(d42,plain,
addition(sK30,addition(multiplication(sK30,sK31),c(sK30))) != one,
inference(demodulation,[status(thm)],[d41,c5]) ).
cnf(d43,plain,
addition(sK30,addition(c(sK30),multiplication(sK30,sK31))) != one,
inference(demodulation,[status(thm)],[d42,c0]) ).
cnf(d44,plain,
addition(multiplication(sK30,sK31),one) != one,
inference(demodulation,[status(thm)],[d43,d22]) ).
cnf(d45,plain,
addition(one,multiplication(sK30,sK31)) != one,
inference(demodulation,[status(thm)],[d44,c0]) ).
cnf(d46,plain,
one != one,
inference(demodulation,[status(thm)],[d45,d17]) ).
cnf(d47,plain,
( complement(zero,X0)
| multiplication(zero,X0) != zero
| addition(X0,zero) != one
| zero != zero ),
inference(superposition,[status(thm)],[c9,c18]) ).
cnf(d48,plain,
( complement(zero,X0)
| multiplication(zero,X0) != zero
| zero != zero
| X0 != one ),
inference(demodulation,[status(thm)],[d47,c2]) ).
cnf(d49,plain,
( complement(zero,X0)
| zero != zero
| zero != zero
| X0 != one ),
inference(demodulation,[status(thm)],[d48,c10]) ).
cnf(d50,plain,
( ~ test(X0)
| multiplication(X0,sK23(X0)) = zero ),
inference(resolution,[status(thm)],[c15,c13]) ).
cnf(d51,plain,
multiplication(sK31,sK23(sK31)) = zero,
inference(resolution,[status(thm)],[d50,c23]) ).
cnf(d52,plain,
multiplication(zero,X0) = multiplication(sK31,multiplication(sK23(sK31),X0)),
inference(superposition,[status(thm)],[d51,c4]) ).
cnf(d53,plain,
zero = multiplication(sK31,multiplication(sK23(sK31),X0)),
inference(demodulation,[status(thm)],[d52,c10]) ).
cnf(d54,plain,
zero = multiplication(sK31,zero),
inference(superposition,[status(thm)],[c9,d53]) ).
cnf(d55,plain,
zero = zero,
inference(demodulation,[status(thm)],[d54,c9]) ).
cnf(d56,plain,
( complement(zero,X0)
| zero != zero
| X0 != one ),
inference(resolution,[status(thm)],[d55,d49]) ).
cnf(d57,plain,
( complement(zero,X0)
| X0 != one ),
inference(equality_resolution,[status(thm)],[d56]) ).
cnf(d58,plain,
complement(zero,one),
inference(equality_resolution,[status(thm)],[d57]) ).
cnf(d59,plain,
addition(one,zero) = one,
inference(resolution,[status(thm)],[d58,c16]) ).
cnf(d60,plain,
one = one,
inference(demodulation,[status(thm)],[d59,c2]) ).
cnf(d61,plain,
$false,
inference(resolution,[status(thm)],[d60,d46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : KLE010+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/10.63 % Computer : n014.cluster.edu
% 0.15/10.63 % Model : x86_64 x86_64
% 0.15/10.63 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/10.63 % Memory : 8046.5625MB
% 0.15/10.63 % OS : Linux 6.8.0-71-generic
% 0.15/10.63 % CPULimit : 300
% 0.15/10.63 % WCLimit : 300
% 0.15/10.63 % DateTime : Fri Sep 25 19:12:28 UTC 2026
% 0.15/10.63 % CPUTime :
% 0.15/10.63 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 35.00/27.38 % SZS status Theorem for theBenchmark.p
% 35.00/27.38 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------