%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : KLE009+1 : 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 : n020.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 37.59s 5.07s
% Output : CNFRefutation 37.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 8
% Syntax : Number of formulae : 45 ( 26 unt; 0 def)
% Number of atoms : 79 ( 39 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 82 ( 48 ~; 25 |; 4 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 63 ( 9 sgn 20 !; 0 ?)
% 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(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(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(multiplication(X0,X1),multiplication(X0,c(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(multiplication(X0,X1),multiplication(X0,c(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(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
inference(clausification,[status(esa)],[additive_associativity]) ).
cnf(c6,plain,
multiplication(one,X0) = X0,
inference(clausification,[status(esa)],[multiplicative_left_identity]) ).
cnf(c7,plain,
multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(clausification,[status(esa)],[right_distributivity]) ).
cnf(c8,plain,
multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(clausification,[status(esa)],[left_distributivity]) ).
cnf(c17,plain,
( addition(X1,X0) = one
| ~ 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(sK31),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c23,plain,
test(sK30),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c24,plain,
one != addition(addition(addition(multiplication(sK30,sK31),multiplication(sK30,c(sK31))),multiplication(c(sK30),sK31)),multiplication(c(sK30),c(sK31))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( complement(X0,c(X0))
| ~ test(X0) ),
inference(equality_resolution,[status(thm)],[c19]) ).
cnf(d1,plain,
addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3)) = addition(multiplication(X0,addition(X1,X2)),X3),
inference(superposition,[status(thm)],[c7,c1]) ).
cnf(d2,plain,
addition(X2,addition(X0,X1)) = addition(X0,addition(X1,X2)),
inference(superposition,[status(thm)],[c1,c0]) ).
cnf(d3,plain,
one != addition(multiplication(c(sK30),c(sK31)),addition(addition(multiplication(sK30,sK31),multiplication(sK30,c(sK31))),multiplication(c(sK30),sK31))),
inference(demodulation,[status(thm)],[c24,c0]) ).
cnf(d4,plain,
one != addition(multiplication(c(sK30),c(sK31)),addition(multiplication(c(sK30),sK31),addition(multiplication(sK30,sK31),multiplication(sK30,c(sK31))))),
inference(demodulation,[status(thm)],[d3,c0]) ).
cnf(d5,plain,
one != addition(multiplication(c(sK30),c(sK31)),addition(multiplication(c(sK30),sK31),multiplication(sK30,addition(sK31,c(sK31))))),
inference(demodulation,[status(thm)],[d4,c7]) ).
cnf(d6,plain,
one != addition(multiplication(c(sK30),sK31),addition(multiplication(sK30,addition(sK31,c(sK31))),multiplication(c(sK30),c(sK31)))),
inference(demodulation,[status(thm)],[d5,d2]) ).
cnf(d7,plain,
one != addition(multiplication(c(sK30),sK31),addition(multiplication(c(sK30),c(sK31)),multiplication(sK30,addition(sK31,c(sK31))))),
inference(demodulation,[status(thm)],[d6,c0]) ).
cnf(d8,plain,
one != addition(multiplication(c(sK30),addition(sK31,c(sK31))),multiplication(sK30,addition(sK31,c(sK31)))),
inference(demodulation,[status(thm)],[d7,d1]) ).
cnf(d9,plain,
one != multiplication(addition(c(sK30),sK30),addition(sK31,c(sK31))),
inference(demodulation,[status(thm)],[d8,c8]) ).
cnf(d10,plain,
one != multiplication(addition(sK30,c(sK30)),addition(sK31,c(sK31))),
inference(demodulation,[status(thm)],[d9,c0]) ).
cnf(d11,plain,
( ~ complement(sK30,X0)
| ~ test(sK30)
| one != multiplication(addition(sK30,X0),addition(sK31,c(sK31))) ),
inference(superposition,[status(thm)],[c20,d10]) ).
cnf(d12,plain,
( ~ complement(sK30,X0)
| one != multiplication(addition(sK30,X0),addition(sK31,c(sK31))) ),
inference(resolution,[status(thm)],[c23,d11]) ).
cnf(d13,plain,
( ~ complement(sK30,X0)
| one != multiplication(addition(X0,sK30),addition(sK31,c(sK31))) ),
inference(superposition,[status(thm)],[c0,d12]) ).
cnf(d14,plain,
( ~ complement(sK30,X0)
| ~ complement(sK30,X0)
| one != multiplication(one,addition(sK31,c(sK31))) ),
inference(superposition,[status(thm)],[c17,d13]) ).
cnf(d15,plain,
( ~ complement(sK30,X0)
| one != addition(sK31,c(sK31)) ),
inference(demodulation,[status(thm)],[d14,c6]) ).
cnf(d16,plain,
( ~ complement(sK31,X0)
| ~ test(sK31)
| ~ complement(sK30,X1)
| one != addition(sK31,X0) ),
inference(superposition,[status(thm)],[c20,d15]) ).
cnf(d17,plain,
( ~ complement(sK30,X1)
| ~ complement(sK31,X0)
| one != addition(sK31,X0) ),
inference(resolution,[status(thm)],[c22,d16]) ).
cnf(d18,plain,
( ~ complement(sK30,X1)
| ~ complement(sK31,X0)
| one != addition(X0,sK31) ),
inference(superposition,[status(thm)],[c0,d17]) ).
cnf(d19,plain,
( ~ complement(sK31,X0)
| ~ complement(sK30,X1)
| ~ complement(sK31,X0)
| one != one ),
inference(superposition,[status(thm)],[c17,d18]) ).
cnf(d20,plain,
( ~ complement(sK30,X1)
| ~ complement(sK31,X0) ),
inference(equality_resolution,[status(thm)],[d19]) ).
cnf(d21,plain,
( ~ complement(sK31,X0)
| ~ test(sK30) ),
inference(resolution,[status(thm)],[d0,d20]) ).
cnf(d22,plain,
~ complement(sK31,X0),
inference(resolution,[status(thm)],[c23,d21]) ).
cnf(d23,plain,
~ test(sK31),
inference(resolution,[status(thm)],[d22,d0]) ).
cnf(d24,plain,
$false,
inference(resolution,[status(thm)],[c22,d23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE009+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n020.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 19:12:21 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 37.59/5.07 % SZS status Theorem for theBenchmark.p
% 37.59/5.07 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------