%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : HEN010-5 : 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 : n004.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 07:31:50 AM UTC 2026
% Result : Unsatisfiable 101.95s 15.11s
% Output : CNFRefutation 101.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 8
% Syntax : Number of clauses : 70 ( 42 unt; 0 nHn; 20 RR)
% Number of literals : 104 ( 103 equ; 38 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 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 : 127 ( 26 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(property_of_divide1,axiom,
( divide(divide(X0,X2),X1) = zero
| divide(divide(X0,X1),X2) != zero ) ).
cnf(property_of_divide3,axiom,
( divide(divide(X0,X2),divide(X1,X2)) = zero
| divide(X0,X1) != zero ) ).
cnf(prove_this,negated_conjecture,
divide(identity,a) != divide(divide(identity,a),divide(identity,divide(identity,a))) ).
cnf(quotient_smaller_than_numerator,axiom,
divide(divide(X0,X1),X0) = zero ).
cnf(quotient_property,axiom,
divide(divide(divide(X0,X1),divide(X2,X1)),divide(divide(X0,X2),X1)) = 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(identity_is_largest,axiom,
divide(X0,identity) = 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(X0,X2),divide(X1,X2)) = zero
| divide(X0,X1) != zero ),
inference(clausification,[status(esa)],[property_of_divide3]) ).
cnf(c3,plain,
divide(identity,a) != divide(divide(identity,a),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(c5,plain,
divide(divide(divide(X0,X1),divide(X2,X1)),divide(divide(X0,X2),X1)) = zero,
inference(clausification,[status(esa)],[quotient_property]) ).
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(c8,plain,
divide(X0,identity) = zero,
inference(clausification,[status(esa)],[identity_is_largest]) ).
cnf(d0,plain,
( divide(divide(X0,X1),divide(identity,X1)) = zero
| zero != zero ),
inference(superposition,[status(thm)],[c8,c2]) ).
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,
divide(divide(X0,X1),divide(identity,X1)) = zero,
inference(resolution,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
( divide(divide(identity,X1),divide(X0,X1)) != zero
| divide(X0,X1) = divide(identity,X1)
| zero != zero ),
inference(superposition,[status(thm)],[d3,c7]) ).
cnf(d5,plain,
( divide(divide(identity,X1),divide(X0,X1)) != zero
| divide(X0,X1) = divide(identity,X1) ),
inference(resolution,[status(thm)],[d2,d4]) ).
cnf(d6,plain,
( divide(X0,divide(X0,X1)) != zero
| divide(X0,X1) = X0
| zero != zero ),
inference(superposition,[status(thm)],[c4,c7]) ).
cnf(d7,plain,
( divide(X0,divide(X0,X1)) != zero
| divide(X0,X1) = X0 ),
inference(resolution,[status(thm)],[d2,d6]) ).
cnf(d8,plain,
( divide(X0,zero) != zero
| zero = X0
| zero != zero ),
inference(superposition,[status(thm)],[c6,c7]) ).
cnf(d9,plain,
( zero = X0
| divide(X0,zero) != zero ),
inference(resolution,[status(thm)],[d2,d8]) ).
cnf(d10,plain,
( divide(divide(X0,X0),X1) = zero
| zero != zero ),
inference(superposition,[status(thm)],[c4,c1]) ).
cnf(d11,plain,
divide(divide(X0,X0),X1) = zero,
inference(resolution,[status(thm)],[d2,d10]) ).
cnf(d12,plain,
( zero = divide(X0,X0)
| zero != zero ),
inference(superposition,[status(thm)],[d11,d9]) ).
cnf(d13,plain,
zero = divide(X0,X0),
inference(resolution,[status(thm)],[d2,d12]) ).
cnf(d14,plain,
( divide(divide(X0,divide(X0,X1)),X1) = zero
| zero != zero ),
inference(superposition,[status(thm)],[d13,c1]) ).
cnf(d15,plain,
divide(divide(X0,divide(X0,X1)),X1) = zero,
inference(resolution,[status(thm)],[d2,d14]) ).
cnf(d16,plain,
( zero = divide(X0,divide(X0,zero))
| zero != zero ),
inference(superposition,[status(thm)],[d15,d9]) ).
cnf(d17,plain,
zero = divide(X0,divide(X0,zero)),
inference(resolution,[status(thm)],[d2,d16]) ).
cnf(d18,plain,
( divide(X0,zero) = X0
| zero != zero ),
inference(superposition,[status(thm)],[d17,d7]) ).
cnf(d19,plain,
divide(X0,zero) = X0,
inference(resolution,[status(thm)],[d2,d18]) ).
cnf(d20,plain,
divide(divide(divide(X0,divide(identity,X1)),divide(X1,divide(identity,X1))),zero) = zero,
inference(superposition,[status(thm)],[d3,c5]) ).
cnf(d21,plain,
divide(divide(X0,divide(identity,X1)),divide(X1,divide(identity,X1))) = zero,
inference(demodulation,[status(thm)],[d20,d19]) ).
cnf(d22,plain,
( divide(X0,divide(identity,X0)) = divide(identity,divide(identity,X0))
| zero != zero ),
inference(superposition,[status(thm)],[d21,d5]) ).
cnf(d23,plain,
( divide(X0,zero) = X0
| divide(X0,X0) != zero ),
inference(superposition,[status(thm)],[d19,d7]) ).
cnf(d24,plain,
( divide(X0,zero) = X0
| zero != zero ),
inference(demodulation,[status(thm)],[d23,d13]) ).
cnf(d25,plain,
( X0 = X0
| zero != zero ),
inference(demodulation,[status(thm)],[d24,d19]) ).
cnf(d26,plain,
X0 = X0,
inference(resolution,[status(thm)],[d2,d25]) ).
cnf(d27,plain,
divide(X0,divide(identity,X0)) = divide(identity,divide(identity,X0)),
inference(resolution,[status(thm)],[d26,d22]) ).
cnf(d28,plain,
( divide(divide(divide(X0,X1),X2),divide(identity,X1)) = zero
| divide(zero,X2) != zero ),
inference(superposition,[status(thm)],[d3,c1]) ).
cnf(d29,plain,
( zero != zero
| divide(divide(divide(X1,X2),X0),divide(identity,X2)) = zero ),
inference(demodulation,[status(thm)],[d28,c6]) ).
cnf(d30,plain,
divide(divide(divide(X0,X1),X2),divide(identity,X1)) = zero,
inference(resolution,[status(thm)],[d2,d29]) ).
cnf(d31,plain,
( divide(divide(identity,X1),divide(divide(X0,X1),X2)) != zero
| divide(divide(X0,X1),X2) = divide(identity,X1)
| zero != zero ),
inference(superposition,[status(thm)],[d30,c7]) ).
cnf(d32,plain,
( divide(divide(identity,X1),divide(divide(X0,X1),X2)) != zero
| divide(divide(X0,X1),X2) = divide(identity,X1) ),
inference(resolution,[status(thm)],[d26,d31]) ).
cnf(d33,plain,
divide(divide(divide(divide(X0,divide(X0,X1)),X2),divide(X1,X2)),divide(zero,X2)) = zero,
inference(superposition,[status(thm)],[d15,c5]) ).
cnf(d34,plain,
divide(divide(divide(divide(X1,divide(X1,X2)),X0),divide(X2,X0)),zero) = zero,
inference(demodulation,[status(thm)],[d33,c6]) ).
cnf(d35,plain,
divide(divide(divide(X0,divide(X0,X1)),X2),divide(X1,X2)) = zero,
inference(demodulation,[status(thm)],[d34,d19]) ).
cnf(d36,plain,
divide(divide(divide(X2,divide(X2,divide(X0,X1))),X0),zero) = zero,
inference(superposition,[status(thm)],[c4,d35]) ).
cnf(d37,plain,
divide(divide(X0,divide(X0,divide(X1,X2))),X1) = zero,
inference(demodulation,[status(thm)],[d36,d19]) ).
cnf(d38,plain,
divide(divide(divide(X2,X0),zero),divide(divide(X2,divide(X0,X1)),X0)) = zero,
inference(superposition,[status(thm)],[c4,c5]) ).
cnf(d39,plain,
divide(divide(X0,X1),divide(divide(X0,divide(X1,X2)),X1)) = zero,
inference(demodulation,[status(thm)],[d38,d19]) ).
cnf(d40,plain,
divide(divide(divide(X0,X1),zero),divide(X0,divide(X1,X2))) = zero,
inference(superposition,[status(thm)],[d39,d37]) ).
cnf(d41,plain,
divide(divide(X0,X1),divide(X0,divide(X1,X2))) = zero,
inference(demodulation,[status(thm)],[d40,d19]) ).
cnf(d42,plain,
divide(divide(divide(X1,X0),zero),divide(divide(X1,X0),X0)) = zero,
inference(superposition,[status(thm)],[d13,c5]) ).
cnf(d43,plain,
divide(divide(X0,X1),divide(divide(X0,X1),X1)) = zero,
inference(demodulation,[status(thm)],[d42,d19]) ).
cnf(d44,plain,
( divide(divide(X0,X1),X1) = divide(X0,X1)
| zero != zero ),
inference(superposition,[status(thm)],[d43,d7]) ).
cnf(d45,plain,
divide(divide(X0,X1),X1) = divide(X0,X1),
inference(resolution,[status(thm)],[d26,d44]) ).
cnf(d46,plain,
divide(divide(X0,X1),divide(divide(X0,X1),divide(X1,X2))) = zero,
inference(superposition,[status(thm)],[d45,d41]) ).
cnf(d47,plain,
( divide(divide(identity,X0),divide(X0,X1)) = divide(identity,X0)
| zero != zero ),
inference(superposition,[status(thm)],[d46,d32]) ).
cnf(d48,plain,
divide(divide(identity,X0),divide(X0,X1)) = divide(identity,X0),
inference(resolution,[status(thm)],[d26,d47]) ).
cnf(d49,plain,
divide(divide(identity,X0),divide(identity,divide(identity,X0))) = divide(identity,X0),
inference(superposition,[status(thm)],[d27,d48]) ).
cnf(d50,plain,
divide(identity,divide(identity,divide(identity,X0))) = divide(identity,X0),
inference(demodulation,[status(thm)],[d49,d27]) ).
cnf(d51,plain,
divide(identity,a) != divide(identity,divide(identity,divide(identity,a))),
inference(demodulation,[status(thm)],[c3,d27]) ).
cnf(d52,plain,
divide(identity,a) != divide(identity,a),
inference(demodulation,[status(thm)],[d51,d50]) ).
cnf(d53,plain,
$false,
inference(resolution,[status(thm)],[d26,d52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : HEN010-5 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n004.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Fri Sep 25 15:57:50 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 101.95/15.11 % SZS status Unsatisfiable for theBenchmark.p
% 101.95/15.11 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------