%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : HEN010-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 33.63s 11.37s
% Output : CNFRefutation 33.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of clauses : 42 ( 28 unt; 0 nHn; 15 RR)
% Number of literals : 58 ( 26 equ; 18 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 63 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(zero_divide_anything_is_zero,axiom,
divide(zero,X0) = zero ).
cnf(x_divide_x_is_zero,axiom,
divide(X0,X0) = zero ).
cnf(property_of_divide1,axiom,
( 'less$uequal'(divide(X0,X2),X1)
| ~ 'less$uequal'(divide(X0,X1),X2) ) ).
cnf(property_of_divide2,axiom,
( 'less$uequal'(divide(X2,X1),divide(X2,X0))
| ~ 'less$uequal'(X0,X1) ) ).
cnf(one_inversion_equals_three,axiom,
divide(identity,divide(identity,divide(identity,X0))) = divide(identity,X0) ).
cnf(prove_property_of_inversion,negated_conjecture,
divide(identity,a) != divide(divide(identity,a),divide(identity,divide(identity,a))) ).
cnf(quotient_less_equal2,axiom,
( 'less$uequal'(X0,X1)
| divide(X0,X1) != zero ) ).
cnf(quotient_smaller_than_numerator,axiom,
'less$uequal'(divide(X0,X1),X0) ).
cnf(quotient_property,axiom,
'less$uequal'(divide(divide(X0,X1),divide(X2,X1)),divide(divide(X0,X2),X1)) ).
cnf(zero_is_smallest,axiom,
'less$uequal'(zero,X0) ).
cnf(less_equal_and_equal,axiom,
( X0 = X1
| ~ 'less$uequal'(X1,X0)
| ~ 'less$uequal'(X0,X1) ) ).
cnf(c1,plain,
divide(zero,X0) = zero,
inference(clausification,[status(esa)],[zero_divide_anything_is_zero]) ).
cnf(c2,plain,
divide(X0,X0) = zero,
inference(clausification,[status(esa)],[x_divide_x_is_zero]) ).
cnf(c5,plain,
( 'less$uequal'(divide(X0,X2),X1)
| ~ 'less$uequal'(divide(X0,X1),X2) ),
inference(clausification,[status(esa)],[property_of_divide1]) ).
cnf(c6,plain,
( 'less$uequal'(divide(X2,X1),divide(X2,X0))
| ~ 'less$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[property_of_divide2]) ).
cnf(c8,plain,
divide(identity,divide(identity,divide(identity,X0))) = divide(identity,X0),
inference(clausification,[status(esa)],[one_inversion_equals_three]) ).
cnf(c9,plain,
divide(identity,a) != divide(divide(identity,a),divide(identity,divide(identity,a))),
inference(clausification,[status(esa)],[prove_property_of_inversion]) ).
cnf(c11,plain,
( 'less$uequal'(X0,X1)
| divide(X0,X1) != zero ),
inference(clausification,[status(esa)],[quotient_less_equal2]) ).
cnf(c12,plain,
'less$uequal'(divide(X0,X1),X0),
inference(clausification,[status(esa)],[quotient_smaller_than_numerator]) ).
cnf(c13,plain,
'less$uequal'(divide(divide(X0,X1),divide(X2,X1)),divide(divide(X0,X2),X1)),
inference(clausification,[status(esa)],[quotient_property]) ).
cnf(c14,plain,
'less$uequal'(zero,X0),
inference(clausification,[status(esa)],[zero_is_smallest]) ).
cnf(c15,plain,
( X0 = X1
| ~ 'less$uequal'(X1,X0)
| ~ 'less$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[less_equal_and_equal]) ).
cnf(d0,plain,
( 'less$uequal'(X0,X0)
| zero != zero ),
inference(superposition,[status(thm)],[c2,c11]) ).
cnf(d1,plain,
'less$uequal'(X0,X0),
inference(equality_resolution,[status(thm)],[d0]) ).
cnf(d2,plain,
'less$uequal'(divide(X0,divide(X0,X1)),X1),
inference(resolution,[status(thm)],[c5,d1]) ).
cnf(d3,plain,
( ~ 'less$uequal'(X0,divide(X1,divide(X1,X0)))
| X0 = divide(X1,divide(X1,X0)) ),
inference(resolution,[status(thm)],[d2,c15]) ).
cnf(d4,plain,
( ~ 'less$uequal'(divide(X0,divide(X0,X1)),X1)
| divide(X0,X1) = divide(X0,divide(X0,divide(X0,X1))) ),
inference(resolution,[status(thm)],[d3,c6]) ).
cnf(d5,plain,
divide(X0,X1) = divide(X0,divide(X0,divide(X0,X1))),
inference(resolution,[status(thm)],[d2,d4]) ).
cnf(d6,plain,
( ~ 'less$uequal'(X0,divide(X0,X1))
| X0 = divide(X0,X1) ),
inference(resolution,[status(thm)],[c15,c12]) ).
cnf(d7,plain,
( ~ 'less$uequal'(X0,zero)
| X0 = zero ),
inference(resolution,[status(thm)],[c15,c14]) ).
cnf(d8,plain,
divide(X0,divide(X0,zero)) = zero,
inference(resolution,[status(thm)],[d2,d7]) ).
cnf(d9,plain,
( 'less$uequal'(X0,divide(X0,zero))
| zero != zero ),
inference(superposition,[status(thm)],[d8,c11]) ).
cnf(d10,plain,
divide(zero,zero) = zero,
inference(superposition,[status(thm)],[c2,d8]) ).
cnf(d11,plain,
zero = zero,
inference(demodulation,[status(thm)],[d10,c1]) ).
cnf(d12,plain,
'less$uequal'(X0,divide(X0,zero)),
inference(resolution,[status(thm)],[d11,d9]) ).
cnf(d13,plain,
X0 = divide(X0,zero),
inference(resolution,[status(thm)],[d6,d12]) ).
cnf(d14,plain,
'less$uequal'(divide(divide(X1,X0),zero),divide(divide(X1,X0),X0)),
inference(superposition,[status(thm)],[c2,c13]) ).
cnf(d15,plain,
'less$uequal'(divide(X0,X1),divide(divide(X0,X1),X1)),
inference(demodulation,[status(thm)],[d14,d13]) ).
cnf(d16,plain,
divide(X0,X1) = divide(divide(X0,X1),X1),
inference(resolution,[status(thm)],[d15,d6]) ).
cnf(d17,plain,
divide(identity,divide(identity,divide(identity,X0))) = divide(divide(identity,X0),divide(identity,divide(identity,X0))),
inference(superposition,[status(thm)],[c8,d16]) ).
cnf(d18,plain,
divide(identity,X0) = divide(divide(identity,X0),divide(identity,divide(identity,X0))),
inference(demodulation,[status(thm)],[d17,d5]) ).
cnf(d19,plain,
$false,
inference(resolution,[status(thm)],[d18,c9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN010-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n007.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Fri Sep 25 15:55:53 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.34 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 33.63/11.37 % SZS status Unsatisfiable for theBenchmark.p
% 33.63/11.37 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------