%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : KLE048+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 : 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 07:43:30 AM UTC 2026
% Result : Theorem 40.99s 25.20s
% Output : CNFRefutation 40.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 13
% Syntax : Number of formulae : 65 ( 50 unt; 0 def)
% Number of atoms : 82 ( 54 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 29 ( 12 ~; 9 |; 2 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 75 ( 0 sgn 23 !; 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_right_identity,axiom,
! [X0] : multiplication(X0,one) = X0 ).
fof(multiplicative_left_identity,axiom,
! [X0] : multiplication(one,X0) = X0 ).
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(star_unfold_right,axiom,
! [X0] : leq(addition(one,multiplication(X0,star(X0))),star(X0)) ).
fof(star_induction_left,axiom,
! [X0,X1,X2] :
( leq(addition(multiplication(X0,X1),X2),X1)
=> leq(multiplication(star(X0),X2),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(goals,conjecture,
! [X0] :
( test(X0)
=> star(X0) = one ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( test(X0)
=> star(X0) = one ),
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(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(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(c8,plain,
multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
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,
leq(addition(one,multiplication(X0,star(X0))),star(X0)),
inference(clausification,[status(esa)],[star_unfold_right]) ).
cnf(c15,plain,
( leq(multiplication(star(X0),X2),X1)
| ~ leq(addition(multiplication(X0,X1),X2),X1) ),
inference(clausification,[status(esa)],[star_induction_left]) ).
cnf(c17,plain,
( complement(sK31(X0),X0)
| ~ test(X0) ),
inference(clausification,[status(esa)],[test_1]) ).
cnf(c21,plain,
( addition(X1,X0) = one
| ~ complement(X0,X1) ),
inference(clausification,[status(esa)],[test_2]) ).
cnf(c26,plain,
test(sK38),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c27,plain,
star(sK38) != one,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( leq(multiplication(star(X0),X2),X1)
| ~ leq(addition(X2,multiplication(X0,X1)),X1) ),
inference(superposition,[status(thm)],[c0,c15]) ).
cnf(d1,plain,
multiplication(addition(one,X1),X0) = addition(X0,multiplication(X1,X0)),
inference(superposition,[status(thm)],[c6,c8]) ).
cnf(d2,plain,
( ~ test(X0)
| addition(X0,sK31(X0)) = one ),
inference(resolution,[status(thm)],[c21,c17]) ).
cnf(d3,plain,
addition(sK38,sK31(sK38)) = one,
inference(resolution,[status(thm)],[d2,c26]) ).
cnf(d4,plain,
addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c3,c1]) ).
cnf(d5,plain,
addition(sK38,one) = addition(sK38,sK31(sK38)),
inference(superposition,[status(thm)],[d3,d4]) ).
cnf(d6,plain,
addition(one,sK38) = addition(sK38,sK31(sK38)),
inference(demodulation,[status(thm)],[d5,c0]) ).
cnf(d7,plain,
addition(one,sK38) = one,
inference(demodulation,[status(thm)],[d6,d3]) ).
cnf(d8,plain,
multiplication(one,X0) = addition(X0,multiplication(sK38,X0)),
inference(superposition,[status(thm)],[d7,d1]) ).
cnf(d9,plain,
X0 = addition(X0,multiplication(sK38,X0)),
inference(demodulation,[status(thm)],[d8,c6]) ).
cnf(d10,plain,
( leq(multiplication(star(sK38),X0),X0)
| ~ leq(X0,X0) ),
inference(superposition,[status(thm)],[d9,d0]) ).
cnf(d11,plain,
( leq(X0,X0)
| X0 != X0 ),
inference(superposition,[status(thm)],[c3,c12]) ).
cnf(d12,plain,
leq(X0,X0),
inference(equality_resolution,[status(thm)],[d11]) ).
cnf(d13,plain,
leq(multiplication(star(sK38),X0),X0),
inference(resolution,[status(thm)],[d12,d10]) ).
cnf(d14,plain,
leq(star(sK38),one),
inference(superposition,[status(thm)],[c5,d13]) ).
cnf(d15,plain,
addition(star(sK38),one) = one,
inference(resolution,[status(thm)],[d14,c11]) ).
cnf(d16,plain,
addition(one,star(sK38)) = one,
inference(demodulation,[status(thm)],[d15,c0]) ).
cnf(d17,plain,
addition(addition(one,multiplication(X0,star(X0))),star(X0)) = star(X0),
inference(resolution,[status(thm)],[c13,c11]) ).
cnf(d18,plain,
addition(one,addition(multiplication(X0,star(X0)),star(X0))) = star(X0),
inference(demodulation,[status(thm)],[d17,c1]) ).
cnf(d19,plain,
addition(one,addition(star(X0),multiplication(X0,star(X0)))) = star(X0),
inference(demodulation,[status(thm)],[d18,c0]) ).
cnf(d20,plain,
addition(one,multiplication(addition(one,X0),star(X0))) = star(X0),
inference(demodulation,[status(thm)],[d19,d1]) ).
cnf(d21,plain,
addition(one,multiplication(one,star(sK38))) = star(sK38),
inference(superposition,[status(thm)],[d7,d20]) ).
cnf(d22,plain,
addition(one,star(sK38)) = star(sK38),
inference(demodulation,[status(thm)],[d21,c6]) ).
cnf(d23,plain,
one = star(sK38),
inference(demodulation,[status(thm)],[d22,d16]) ).
cnf(d24,plain,
one != one,
inference(demodulation,[status(thm)],[c27,d23]) ).
cnf(d25,plain,
addition(X2,addition(X0,X1)) = addition(X0,addition(X1,X2)),
inference(superposition,[status(thm)],[c1,c0]) ).
cnf(d26,plain,
addition(X1,X0) = addition(X0,addition(X0,X1)),
inference(superposition,[status(thm)],[c3,d25]) ).
cnf(d27,plain,
addition(zero,X0) = X0,
inference(superposition,[status(thm)],[c2,c0]) ).
cnf(d28,plain,
addition(X0,addition(zero,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c2,c1]) ).
cnf(d29,plain,
addition(X1,X0) = addition(X1,X0),
inference(demodulation,[status(thm)],[d28,d27]) ).
cnf(d30,plain,
one = addition(one,sK38),
inference(superposition,[status(thm)],[d7,d29]) ).
cnf(d31,plain,
addition(sK38,one) = addition(one,one),
inference(superposition,[status(thm)],[d30,d26]) ).
cnf(d32,plain,
addition(one,sK38) = addition(one,one),
inference(demodulation,[status(thm)],[d31,c0]) ).
cnf(d33,plain,
one = addition(one,one),
inference(demodulation,[status(thm)],[d32,d7]) ).
cnf(d34,plain,
one = one,
inference(demodulation,[status(thm)],[d33,c3]) ).
cnf(d35,plain,
$false,
inference(resolution,[status(thm)],[d34,d24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE048+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.38 % Computer : n016.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.15/15.66 % CPULimit : 300
% 0.15/15.66 % WCLimit : 300
% 0.15/15.66 % DateTime : Fri Sep 25 19:21:29 UTC 2026
% 0.15/15.66 % CPUTime :
% 0.15/15.66 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 40.99/25.20 % SZS status Theorem for theBenchmark.p
% 40.99/25.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------