%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : KLE009+3 : 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 : n009.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 83.27s 11.06s
% Output : CNFRefutation 83.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 12
% Syntax : Number of formulae : 68 ( 37 unt; 0 def)
% Number of atoms : 107 ( 36 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 84 ( 45 ~; 26 |; 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 : 67 ( 2 sgn 25 !; 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_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(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(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one)
& leq(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) )
=> ( leq(addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one)
& leq(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(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(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(c11,plain,
( addition(X0,X1) = X1
| ~ leq(X0,X1) ),
inference(clausification,[status(esa)],[order]) ).
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(c14,plain,
( ~ complement(X1,X0)
| test(X0) ),
inference(clausification,[status(esa)],[test_1]) ).
cnf(c16,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(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(addition(multiplication(sK30,sK31),multiplication(sK30,c(sK31))),multiplication(c(sK30),sK31)),multiplication(c(sK30),c(sK31))),one)
| ~ leq(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,
addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(superposition,[status(thm)],[c3,c1]) ).
cnf(d1,plain,
( leq(X0,addition(X0,X1))
| addition(X0,X1) != addition(X0,X1) ),
inference(superposition,[status(thm)],[d0,c12]) ).
cnf(d2,plain,
addition(zero,X0) = X0,
inference(superposition,[status(thm)],[c2,c0]) ).
cnf(d3,plain,
addition(X0,X1) = addition(X0,addition(zero,X1)),
inference(superposition,[status(thm)],[c2,c1]) ).
cnf(d4,plain,
addition(X1,X0) = addition(X1,X0),
inference(demodulation,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
leq(X0,addition(X0,X1)),
inference(resolution,[status(thm)],[d4,d1]) ).
cnf(d6,plain,
( complement(X0,c(X0))
| ~ test(X0) ),
inference(equality_resolution,[status(thm)],[c19]) ).
cnf(d7,plain,
complement(sK31,c(sK31)),
inference(resolution,[status(thm)],[d6,c23]) ).
cnf(d8,plain,
test(c(sK31)),
inference(resolution,[status(thm)],[d7,c14]) ).
cnf(d9,plain,
complement(sK23(c(sK31)),c(sK31)),
inference(resolution,[status(thm)],[d8,c13]) ).
cnf(d10,plain,
addition(c(sK31),sK23(c(sK31))) = one,
inference(resolution,[status(thm)],[d9,c16]) ).
cnf(d11,plain,
leq(c(sK31),one),
inference(superposition,[status(thm)],[d10,d5]) ).
cnf(d12,plain,
addition(c(sK31),one) = one,
inference(resolution,[status(thm)],[d11,c11]) ).
cnf(d13,plain,
addition(one,c(sK31)) = one,
inference(demodulation,[status(thm)],[d12,c0]) ).
cnf(d14,plain,
leq(one,one),
inference(superposition,[status(thm)],[d13,d5]) ).
cnf(d15,plain,
addition(c(sK31),sK31) = one,
inference(resolution,[status(thm)],[d7,c16]) ).
cnf(d16,plain,
addition(sK31,c(sK31)) = one,
inference(demodulation,[status(thm)],[d15,c0]) ).
cnf(d17,plain,
complement(sK30,c(sK30)),
inference(resolution,[status(thm)],[d6,c22]) ).
cnf(d18,plain,
addition(c(sK30),sK30) = one,
inference(resolution,[status(thm)],[d17,c16]) ).
cnf(d19,plain,
addition(sK30,c(sK30)) = one,
inference(demodulation,[status(thm)],[d18,c0]) ).
cnf(d20,plain,
addition(multiplication(X0,addition(X1,X2)),X3) = addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3)),
inference(superposition,[status(thm)],[c7,c1]) ).
cnf(d21,plain,
( ~ leq(one,addition(addition(addition(multiplication(sK30,sK31),multiplication(sK30,c(sK31))),multiplication(c(sK30),sK31)),multiplication(c(sK30),c(sK31))))
| ~ leq(addition(addition(multiplication(sK30,sK31),multiplication(sK30,c(sK31))),addition(multiplication(c(sK30),sK31),multiplication(c(sK30),c(sK31)))),one) ),
inference(demodulation,[status(thm)],[c24,c1]) ).
cnf(d22,plain,
( ~ leq(one,addition(addition(addition(multiplication(sK30,sK31),multiplication(sK30,c(sK31))),multiplication(c(sK30),sK31)),multiplication(c(sK30),c(sK31))))
| ~ leq(addition(multiplication(sK30,sK31),addition(multiplication(sK30,c(sK31)),addition(multiplication(c(sK30),sK31),multiplication(c(sK30),c(sK31))))),one) ),
inference(demodulation,[status(thm)],[d21,c1]) ).
cnf(d23,plain,
( ~ leq(one,addition(addition(addition(multiplication(sK30,sK31),multiplication(sK30,c(sK31))),multiplication(c(sK30),sK31)),multiplication(c(sK30),c(sK31))))
| ~ leq(addition(multiplication(sK30,sK31),addition(multiplication(sK30,c(sK31)),multiplication(c(sK30),addition(sK31,c(sK31))))),one) ),
inference(demodulation,[status(thm)],[d22,c7]) ).
cnf(d24,plain,
( ~ leq(one,addition(addition(multiplication(sK30,sK31),multiplication(sK30,c(sK31))),addition(multiplication(c(sK30),sK31),multiplication(c(sK30),c(sK31)))))
| ~ leq(addition(multiplication(sK30,sK31),addition(multiplication(sK30,c(sK31)),multiplication(c(sK30),addition(sK31,c(sK31))))),one) ),
inference(demodulation,[status(thm)],[d23,c1]) ).
cnf(d25,plain,
( ~ leq(one,addition(multiplication(sK30,sK31),addition(multiplication(sK30,c(sK31)),addition(multiplication(c(sK30),sK31),multiplication(c(sK30),c(sK31))))))
| ~ leq(addition(multiplication(sK30,sK31),addition(multiplication(sK30,c(sK31)),multiplication(c(sK30),addition(sK31,c(sK31))))),one) ),
inference(demodulation,[status(thm)],[d24,c1]) ).
cnf(d26,plain,
( ~ leq(one,addition(multiplication(sK30,sK31),addition(multiplication(sK30,c(sK31)),multiplication(c(sK30),addition(sK31,c(sK31))))))
| ~ leq(addition(multiplication(sK30,sK31),addition(multiplication(sK30,c(sK31)),multiplication(c(sK30),addition(sK31,c(sK31))))),one) ),
inference(demodulation,[status(thm)],[d25,c7]) ).
cnf(d27,plain,
( ~ leq(one,addition(multiplication(sK30,sK31),addition(multiplication(sK30,c(sK31)),multiplication(c(sK30),addition(sK31,c(sK31))))))
| ~ leq(addition(multiplication(sK30,addition(sK31,c(sK31))),multiplication(c(sK30),addition(sK31,c(sK31)))),one) ),
inference(demodulation,[status(thm)],[d26,d20]) ).
cnf(d28,plain,
( ~ leq(one,addition(multiplication(sK30,addition(sK31,c(sK31))),multiplication(c(sK30),addition(sK31,c(sK31)))))
| ~ leq(addition(multiplication(sK30,addition(sK31,c(sK31))),multiplication(c(sK30),addition(sK31,c(sK31)))),one) ),
inference(demodulation,[status(thm)],[d27,d20]) ).
cnf(d29,plain,
( ~ leq(one,addition(multiplication(sK30,addition(sK31,c(sK31))),multiplication(c(sK30),addition(sK31,c(sK31)))))
| ~ leq(multiplication(addition(sK30,c(sK30)),addition(sK31,c(sK31))),one) ),
inference(demodulation,[status(thm)],[d28,c8]) ).
cnf(d30,plain,
( ~ leq(one,addition(multiplication(sK30,addition(sK31,c(sK31))),multiplication(c(sK30),addition(sK31,c(sK31)))))
| ~ leq(multiplication(one,addition(sK31,c(sK31))),one) ),
inference(demodulation,[status(thm)],[d29,d19]) ).
cnf(d31,plain,
( ~ leq(one,addition(multiplication(sK30,addition(sK31,c(sK31))),multiplication(c(sK30),addition(sK31,c(sK31)))))
| ~ leq(addition(sK31,c(sK31)),one) ),
inference(demodulation,[status(thm)],[d30,c6]) ).
cnf(d32,plain,
( ~ leq(one,addition(multiplication(sK30,addition(sK31,c(sK31))),multiplication(c(sK30),addition(sK31,c(sK31)))))
| ~ leq(one,one) ),
inference(demodulation,[status(thm)],[d31,d16]) ).
cnf(d33,plain,
( ~ leq(one,multiplication(addition(sK30,c(sK30)),addition(sK31,c(sK31))))
| ~ leq(one,one) ),
inference(demodulation,[status(thm)],[d32,c8]) ).
cnf(d34,plain,
( ~ leq(one,multiplication(one,addition(sK31,c(sK31))))
| ~ leq(one,one) ),
inference(demodulation,[status(thm)],[d33,d19]) ).
cnf(d35,plain,
( ~ leq(one,addition(sK31,c(sK31)))
| ~ leq(one,one) ),
inference(demodulation,[status(thm)],[d34,c6]) ).
cnf(d36,plain,
( ~ leq(one,one)
| ~ leq(one,one) ),
inference(demodulation,[status(thm)],[d35,d16]) ).
cnf(d37,plain,
~ leq(one,one),
inference(resolution,[status(thm)],[d14,d36]) ).
cnf(d38,plain,
$false,
inference(resolution,[status(thm)],[d37,d14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE009+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.38 % Computer : n009.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Fri Sep 25 19:11:15 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 83.27/11.06 % SZS status Theorem for theBenchmark.p
% 83.27/11.06 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------