%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : HEN009-5 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 07:31:49 AM UTC 2026
% Result : Unsatisfiable 84.83s 14.71s
% Output : CNFRefutation 84.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 6
% Syntax : Number of clauses : 44 ( 20 unt; 0 nHn; 17 RR)
% Number of literals : 73 ( 72 equ; 32 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 68 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(property_of_divide1,axiom,
( divide(divide(X0,X2),X1) = zero
| divide(divide(X0,X1),X2) != zero ) ).
cnf(property_of_divide2,axiom,
( divide(divide(X2,X1),divide(X2,X0)) = zero
| divide(X0,X1) != zero ) ).
cnf(prove_this,negated_conjecture,
divide(identity,a) != divide(identity,divide(identity,divide(identity,a))) ).
cnf(quotient_smaller_than_numerator,axiom,
divide(divide(X0,X1),X0) = zero ).
cnf(zero_is_smallest,axiom,
divide(zero,X0) = zero ).
cnf(divide_and_equal,axiom,
( X0 = X1
| divide(X1,X0) != zero
| divide(X0,X1) != zero ) ).
cnf(c1,plain,
( divide(divide(X0,X2),X1) = zero
| divide(divide(X0,X1),X2) != zero ),
inference(clausification,[status(esa)],[property_of_divide1]) ).
cnf(c2,plain,
( divide(divide(X2,X1),divide(X2,X0)) = zero
| divide(X0,X1) != zero ),
inference(clausification,[status(esa)],[property_of_divide2]) ).
cnf(c3,plain,
divide(identity,a) != divide(identity,divide(identity,divide(identity,a))),
inference(clausification,[status(esa)],[prove_this]) ).
cnf(c4,plain,
divide(divide(X0,X1),X0) = zero,
inference(clausification,[status(esa)],[quotient_smaller_than_numerator]) ).
cnf(c6,plain,
divide(zero,X0) = zero,
inference(clausification,[status(esa)],[zero_is_smallest]) ).
cnf(c7,plain,
( X0 = X1
| divide(X1,X0) != zero
| divide(X0,X1) != zero ),
inference(clausification,[status(esa)],[divide_and_equal]) ).
cnf(d0,plain,
( divide(X0,zero) != zero
| zero = X0
| zero != zero ),
inference(superposition,[status(thm)],[c6,c7]) ).
cnf(d1,plain,
divide(zero,zero) = zero,
inference(superposition,[status(thm)],[c6,c4]) ).
cnf(d2,plain,
zero = zero,
inference(demodulation,[status(thm)],[d1,c6]) ).
cnf(d3,plain,
( zero = X0
| divide(X0,zero) != zero ),
inference(resolution,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
( divide(divide(X0,X0),X1) = zero
| zero != zero ),
inference(superposition,[status(thm)],[c4,c1]) ).
cnf(d5,plain,
divide(divide(X0,X0),X1) = zero,
inference(resolution,[status(thm)],[d2,d4]) ).
cnf(d6,plain,
( zero = divide(X0,X0)
| zero != zero ),
inference(superposition,[status(thm)],[d5,d3]) ).
cnf(d7,plain,
zero = divide(X0,X0),
inference(resolution,[status(thm)],[d2,d6]) ).
cnf(d8,plain,
( divide(divide(X0,divide(X0,X1)),X1) = zero
| zero != zero ),
inference(superposition,[status(thm)],[d7,c1]) ).
cnf(d9,plain,
( divide(X0,divide(X0,X1)) != zero
| divide(X0,X1) = X0
| zero != zero ),
inference(superposition,[status(thm)],[c4,c7]) ).
cnf(d10,plain,
( divide(X0,divide(X0,X1)) != zero
| divide(X0,X1) = X0 ),
inference(resolution,[status(thm)],[d2,d9]) ).
cnf(d11,plain,
( divide(divide(X1,X0),divide(X1,zero)) = zero
| zero != zero ),
inference(superposition,[status(thm)],[c6,c2]) ).
cnf(d12,plain,
divide(divide(X0,X1),divide(X0,zero)) = zero,
inference(resolution,[status(thm)],[d2,d11]) ).
cnf(d13,plain,
( divide(divide(X0,divide(X0,zero)),X1) = zero
| zero != zero ),
inference(superposition,[status(thm)],[d12,c1]) ).
cnf(d14,plain,
divide(divide(X0,divide(X0,zero)),X1) = zero,
inference(resolution,[status(thm)],[d2,d13]) ).
cnf(d15,plain,
( zero = divide(X0,divide(X0,zero))
| zero != zero ),
inference(superposition,[status(thm)],[d14,d3]) ).
cnf(d16,plain,
zero = divide(X0,divide(X0,zero)),
inference(resolution,[status(thm)],[d2,d15]) ).
cnf(d17,plain,
( divide(X0,zero) = X0
| zero != zero ),
inference(superposition,[status(thm)],[d16,d10]) ).
cnf(d18,plain,
divide(X0,zero) = X0,
inference(resolution,[status(thm)],[d2,d17]) ).
cnf(d19,plain,
( divide(X0,zero) = X0
| divide(X0,X0) != zero ),
inference(superposition,[status(thm)],[d18,d10]) ).
cnf(d20,plain,
( divide(X0,zero) = X0
| zero != zero ),
inference(demodulation,[status(thm)],[d19,d7]) ).
cnf(d21,plain,
( X0 = X0
| zero != zero ),
inference(demodulation,[status(thm)],[d20,d18]) ).
cnf(d22,plain,
X0 = X0,
inference(resolution,[status(thm)],[d2,d21]) ).
cnf(d23,plain,
divide(divide(X0,divide(X0,X1)),X1) = zero,
inference(resolution,[status(thm)],[d22,d8]) ).
cnf(d24,plain,
( divide(X1,divide(X0,divide(X0,X1))) != zero
| divide(X0,divide(X0,X1)) = X1
| zero != zero ),
inference(superposition,[status(thm)],[d23,c7]) ).
cnf(d25,plain,
( divide(X1,divide(X1,X0)) = X0
| divide(X0,divide(X1,divide(X1,X0))) != zero ),
inference(resolution,[status(thm)],[d22,d24]) ).
cnf(d26,plain,
( divide(divide(X2,X1),divide(X2,divide(X0,divide(X0,X1)))) = zero
| zero != zero ),
inference(superposition,[status(thm)],[d23,c2]) ).
cnf(d27,plain,
divide(divide(X0,X1),divide(X0,divide(X2,divide(X2,X1)))) = zero,
inference(resolution,[status(thm)],[d22,d26]) ).
cnf(d28,plain,
( divide(X0,divide(X0,divide(X0,X1))) = divide(X0,X1)
| zero != zero ),
inference(superposition,[status(thm)],[d27,d25]) ).
cnf(d29,plain,
divide(X0,divide(X0,divide(X0,X1))) = divide(X0,X1),
inference(resolution,[status(thm)],[d22,d28]) ).
cnf(d30,plain,
divide(identity,a) != divide(identity,a),
inference(demodulation,[status(thm)],[c3,d29]) ).
cnf(d31,plain,
$false,
inference(resolution,[status(thm)],[d22,d30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN009-5 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n008.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 15:58:39 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 84.83/14.71 % SZS status Unsatisfiable for theBenchmark.p
% 84.83/14.71 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------