%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : HEN010-3 : 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 : n013.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 80.00s 16.38s
% Output : CNFRefutation 80.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 8
% Syntax : Number of clauses : 92 ( 60 unt; 0 nHn; 33 RR)
% Number of literals : 126 ( 58 equ; 38 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 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 : 160 ( 29 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_property_of_inversion,negated_conjecture,
divide(identity,a) != divide(divide(identity,a),divide(identity,divide(identity,a))) ).
cnf(quotient_less_equal1,axiom,
( divide(X0,X1) = zero
| ~ 'less$uequal'(X0,X1) ) ).
cnf(quotient_less_equal2,axiom,
( 'less$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$uequal'(X0,X1) ) ).
cnf(identity_is_largest,axiom,
'less$uequal'(X0,identity) ).
cnf(c0,plain,
divide(divide(identity,a),divide(identity,divide(identity,a))) != divide(identity,a),
inference(clausification,[status(esa)],[prove_property_of_inversion]) ).
cnf(c1,plain,
( divide(X0,X1) = zero
| ~ 'less$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[quotient_less_equal1]) ).
cnf(c2,plain,
( 'less$uequal'(X0,X1)
| divide(X0,X1) != zero ),
inference(clausification,[status(esa)],[quotient_less_equal2]) ).
cnf(c3,plain,
'less$uequal'(divide(X0,X1),X0),
inference(clausification,[status(esa)],[quotient_smaller_than_numerator]) ).
cnf(c4,plain,
'less$uequal'(divide(divide(X0,X1),divide(X2,X1)),divide(divide(X0,X2),X1)),
inference(clausification,[status(esa)],[quotient_property]) ).
cnf(c5,plain,
'less$uequal'(zero,X0),
inference(clausification,[status(esa)],[zero_is_smallest]) ).
cnf(c6,plain,
( X0 = X1
| ~ 'less$uequal'(X1,X0)
| ~ 'less$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[less_equal_and_equal]) ).
cnf(c7,plain,
'less$uequal'(X0,identity),
inference(clausification,[status(esa)],[identity_is_largest]) ).
cnf(d0,plain,
( ~ 'less$uequal'(X0,divide(X0,X1))
| divide(X0,X1) = X0 ),
inference(resolution,[status(thm)],[c6,c3]) ).
cnf(d1,plain,
( ~ 'less$uequal'(X0,zero)
| zero = X0 ),
inference(resolution,[status(thm)],[c6,c5]) ).
cnf(d2,plain,
divide(zero,X0) = zero,
inference(resolution,[status(thm)],[c1,c5]) ).
cnf(d3,plain,
'less$uequal'(divide(divide(X1,X0),zero),divide(divide(X1,zero),X0)),
inference(superposition,[status(thm)],[d2,c4]) ).
cnf(d4,plain,
divide(divide(X0,X1),X0) = zero,
inference(resolution,[status(thm)],[c1,c3]) ).
cnf(d5,plain,
'less$uequal'(divide(divide(X0,X0),divide(X1,X0)),zero),
inference(superposition,[status(thm)],[d4,c4]) ).
cnf(d6,plain,
'less$uequal'(divide(divide(X0,X0),zero),zero),
inference(superposition,[status(thm)],[d4,d5]) ).
cnf(d7,plain,
zero = divide(divide(X0,X0),zero),
inference(resolution,[status(thm)],[d6,d1]) ).
cnf(d8,plain,
( 'less$uequal'(divide(X0,X0),zero)
| zero != zero ),
inference(superposition,[status(thm)],[d7,c2]) ).
cnf(d9,plain,
divide(zero,zero) = zero,
inference(superposition,[status(thm)],[d2,d4]) ).
cnf(d10,plain,
zero = zero,
inference(demodulation,[status(thm)],[d9,d2]) ).
cnf(d11,plain,
'less$uequal'(divide(X0,X0),zero),
inference(resolution,[status(thm)],[d10,d8]) ).
cnf(d12,plain,
zero = divide(X0,X0),
inference(resolution,[status(thm)],[d11,d1]) ).
cnf(d13,plain,
'less$uequal'(divide(divide(X0,divide(X0,zero)),zero),zero),
inference(superposition,[status(thm)],[d12,d3]) ).
cnf(d14,plain,
zero = divide(divide(X0,divide(X0,zero)),zero),
inference(resolution,[status(thm)],[d13,d1]) ).
cnf(d15,plain,
( 'less$uequal'(divide(X0,divide(X0,zero)),zero)
| zero != zero ),
inference(superposition,[status(thm)],[d14,c2]) ).
cnf(d16,plain,
'less$uequal'(divide(X0,divide(X0,zero)),zero),
inference(resolution,[status(thm)],[d10,d15]) ).
cnf(d17,plain,
zero = divide(X0,divide(X0,zero)),
inference(resolution,[status(thm)],[d16,d1]) ).
cnf(d18,plain,
( 'less$uequal'(X0,divide(X0,zero))
| zero != zero ),
inference(superposition,[status(thm)],[d17,c2]) ).
cnf(d19,plain,
'less$uequal'(X0,divide(X0,zero)),
inference(resolution,[status(thm)],[d10,d18]) ).
cnf(d20,plain,
divide(X0,zero) = X0,
inference(resolution,[status(thm)],[d19,d0]) ).
cnf(d21,plain,
'less$uequal'(divide(divide(X2,X0),zero),divide(divide(X2,divide(X0,X1)),X0)),
inference(superposition,[status(thm)],[d4,c4]) ).
cnf(d22,plain,
'less$uequal'(divide(X0,X1),divide(divide(X0,divide(X1,X2)),X1)),
inference(demodulation,[status(thm)],[d21,d20]) ).
cnf(d23,plain,
( ~ 'less$uequal'(divide(divide(X0,X2),X1),divide(divide(X0,X1),divide(X2,X1)))
| divide(divide(X0,X1),divide(X2,X1)) = divide(divide(X0,X2),X1) ),
inference(resolution,[status(thm)],[c6,c4]) ).
cnf(d24,plain,
( divide(divide(X0,divide(X0,X1)),divide(X1,divide(X0,X1))) = divide(divide(X0,X1),divide(X0,X1))
| ~ 'less$uequal'(zero,divide(divide(X0,divide(X0,X1)),divide(X1,divide(X0,X1)))) ),
inference(superposition,[status(thm)],[d12,d23]) ).
cnf(d25,plain,
( ~ 'less$uequal'(zero,divide(divide(X0,divide(X0,X1)),divide(X1,divide(X0,X1))))
| divide(divide(X0,divide(X0,X1)),divide(X1,divide(X0,X1))) = zero ),
inference(demodulation,[status(thm)],[d24,d12]) ).
cnf(d26,plain,
divide(divide(X0,divide(X0,X1)),divide(X1,divide(X0,X1))) = zero,
inference(resolution,[status(thm)],[c5,d25]) ).
cnf(d27,plain,
'less$uequal'(divide(divide(X0,divide(X0,X1)),X1),divide(zero,X1)),
inference(superposition,[status(thm)],[d26,d22]) ).
cnf(d28,plain,
'less$uequal'(divide(divide(X1,divide(X1,X0)),X0),zero),
inference(demodulation,[status(thm)],[d27,d2]) ).
cnf(d29,plain,
zero = divide(divide(X0,divide(X0,X1)),X1),
inference(resolution,[status(thm)],[d28,d1]) ).
cnf(d30,plain,
( 'less$uequal'(divide(X0,divide(X0,X1)),X1)
| zero != zero ),
inference(superposition,[status(thm)],[d29,c2]) ).
cnf(d31,plain,
( divide(X0,zero) = X0
| ~ 'less$uequal'(X0,X0) ),
inference(superposition,[status(thm)],[d20,d0]) ).
cnf(d32,plain,
( ~ 'less$uequal'(X0,X0)
| X0 = X0 ),
inference(demodulation,[status(thm)],[d31,d20]) ).
cnf(d33,plain,
( 'less$uequal'(X0,X0)
| zero != zero ),
inference(superposition,[status(thm)],[d12,c2]) ).
cnf(d34,plain,
'less$uequal'(X0,X0),
inference(resolution,[status(thm)],[d10,d33]) ).
cnf(d35,plain,
X0 = X0,
inference(resolution,[status(thm)],[d34,d32]) ).
cnf(d36,plain,
'less$uequal'(divide(X0,divide(X0,X1)),X1),
inference(resolution,[status(thm)],[d35,d30]) ).
cnf(d37,plain,
( divide(divide(X2,X0),divide(divide(X0,X1),X0)) = divide(divide(X2,divide(X0,X1)),X0)
| ~ 'less$uequal'(divide(divide(X2,divide(X0,X1)),X0),divide(divide(X2,X0),zero)) ),
inference(superposition,[status(thm)],[d4,d23]) ).
cnf(d38,plain,
( ~ 'less$uequal'(divide(divide(X2,divide(X0,X1)),X0),divide(divide(X2,X0),zero))
| divide(divide(X2,X0),zero) = divide(divide(X2,divide(X0,X1)),X0) ),
inference(demodulation,[status(thm)],[d37,d4]) ).
cnf(d39,plain,
( ~ 'less$uequal'(divide(divide(X0,divide(X1,X2)),X1),divide(divide(X0,X1),zero))
| divide(X0,X1) = divide(divide(X0,divide(X1,X2)),X1) ),
inference(demodulation,[status(thm)],[d38,d20]) ).
cnf(d40,plain,
( ~ 'less$uequal'(divide(divide(X0,divide(X1,X2)),X1),divide(X0,X1))
| divide(X0,X1) = divide(divide(X0,divide(X1,X2)),X1) ),
inference(demodulation,[status(thm)],[d39,d20]) ).
cnf(d41,plain,
( divide(divide(divide(X0,X1),X2),divide(X0,X2)) = divide(divide(divide(X0,X1),X0),X2)
| ~ 'less$uequal'(divide(zero,X2),divide(divide(divide(X0,X1),X2),divide(X0,X2))) ),
inference(superposition,[status(thm)],[d4,d23]) ).
cnf(d42,plain,
( ~ 'less$uequal'(divide(zero,X2),divide(divide(divide(X0,X1),X2),divide(X0,X2)))
| divide(divide(divide(X0,X1),X2),divide(X0,X2)) = divide(zero,X2) ),
inference(demodulation,[status(thm)],[d41,d4]) ).
cnf(d43,plain,
( ~ 'less$uequal'(divide(zero,X0),divide(divide(divide(X1,X2),X0),divide(X1,X0)))
| divide(divide(divide(X1,X2),X0),divide(X1,X0)) = zero ),
inference(demodulation,[status(thm)],[d42,d2]) ).
cnf(d44,plain,
( ~ 'less$uequal'(zero,divide(divide(divide(X1,X2),X0),divide(X1,X0)))
| divide(divide(divide(X1,X2),X0),divide(X1,X0)) = zero ),
inference(demodulation,[status(thm)],[d43,d2]) ).
cnf(d45,plain,
divide(divide(divide(X0,X1),X2),divide(X0,X2)) = zero,
inference(resolution,[status(thm)],[c5,d44]) ).
cnf(d46,plain,
'less$uequal'(divide(divide(divide(X0,X1),X2),zero),divide(X0,X2)),
inference(superposition,[status(thm)],[d45,d36]) ).
cnf(d47,plain,
'less$uequal'(divide(divide(X0,X1),X2),divide(X0,X2)),
inference(demodulation,[status(thm)],[d46,d20]) ).
cnf(d48,plain,
divide(X0,X1) = divide(divide(X0,divide(X1,X2)),X1),
inference(resolution,[status(thm)],[d47,d40]) ).
cnf(d49,plain,
'less$uequal'(divide(X0,X1),divide(X0,divide(X1,X2))),
inference(superposition,[status(thm)],[d48,c3]) ).
cnf(d50,plain,
divide(X0,identity) = zero,
inference(resolution,[status(thm)],[c1,c7]) ).
cnf(d51,plain,
'less$uequal'(divide(divide(X0,X1),divide(identity,X1)),divide(zero,X1)),
inference(superposition,[status(thm)],[d50,c4]) ).
cnf(d52,plain,
'less$uequal'(divide(divide(X1,X0),divide(identity,X0)),zero),
inference(demodulation,[status(thm)],[d51,d2]) ).
cnf(d53,plain,
zero = divide(divide(X0,X1),divide(identity,X1)),
inference(resolution,[status(thm)],[d52,d1]) ).
cnf(d54,plain,
( divide(divide(X0,divide(identity,X1)),divide(X1,divide(identity,X1))) = divide(divide(X0,X1),divide(identity,X1))
| ~ 'less$uequal'(zero,divide(divide(X0,divide(identity,X1)),divide(X1,divide(identity,X1)))) ),
inference(superposition,[status(thm)],[d53,d23]) ).
cnf(d55,plain,
( ~ 'less$uequal'(zero,divide(divide(X0,divide(identity,X1)),divide(X1,divide(identity,X1))))
| divide(divide(X0,divide(identity,X1)),divide(X1,divide(identity,X1))) = zero ),
inference(demodulation,[status(thm)],[d54,d53]) ).
cnf(d56,plain,
divide(divide(X0,divide(identity,X1)),divide(X1,divide(identity,X1))) = zero,
inference(resolution,[status(thm)],[c5,d55]) ).
cnf(d57,plain,
'less$uequal'(divide(divide(X0,divide(identity,X1)),X1),zero),
inference(superposition,[status(thm)],[d56,d49]) ).
cnf(d58,plain,
zero = divide(divide(X0,divide(identity,X1)),X1),
inference(resolution,[status(thm)],[d57,d1]) ).
cnf(d59,plain,
'less$uequal'(divide(divide(X0,divide(identity,X1)),zero),X1),
inference(superposition,[status(thm)],[d58,d36]) ).
cnf(d60,plain,
'less$uequal'(divide(X0,divide(identity,X1)),X1),
inference(demodulation,[status(thm)],[d59,d20]) ).
cnf(d61,plain,
( 'less$uequal'(divide(X0,X1),divide(identity,X1))
| zero != zero ),
inference(superposition,[status(thm)],[d53,c2]) ).
cnf(d62,plain,
'less$uequal'(divide(X0,X1),divide(identity,X1)),
inference(resolution,[status(thm)],[d10,d61]) ).
cnf(d63,plain,
( ~ 'less$uequal'(divide(identity,X1),divide(X0,X1))
| divide(X0,X1) = divide(identity,X1) ),
inference(resolution,[status(thm)],[d62,c6]) ).
cnf(d64,plain,
'less$uequal'(divide(divide(X0,divide(X0,X1)),zero),divide(X1,divide(X0,X1))),
inference(superposition,[status(thm)],[d26,d36]) ).
cnf(d65,plain,
'less$uequal'(divide(X0,divide(X0,X1)),divide(X1,divide(X0,X1))),
inference(demodulation,[status(thm)],[d64,d20]) ).
cnf(d66,plain,
divide(X0,divide(identity,X0)) = divide(identity,divide(identity,X0)),
inference(resolution,[status(thm)],[d65,d63]) ).
cnf(d67,plain,
'less$uequal'(divide(X1,divide(X0,divide(identity,X0))),divide(identity,X0)),
inference(superposition,[status(thm)],[d66,d60]) ).
cnf(d68,plain,
divide(identity,X0) = divide(divide(identity,divide(X0,X1)),X0),
inference(resolution,[status(thm)],[d40,d62]) ).
cnf(d69,plain,
( divide(divide(identity,divide(X0,X1)),X0) = divide(identity,divide(X0,X1))
| ~ 'less$uequal'(divide(identity,divide(X0,X1)),divide(identity,X0)) ),
inference(superposition,[status(thm)],[d68,d0]) ).
cnf(d70,plain,
( ~ 'less$uequal'(divide(identity,divide(X0,X1)),divide(identity,X0))
| divide(identity,X0) = divide(identity,divide(X0,X1)) ),
inference(demodulation,[status(thm)],[d69,d48]) ).
cnf(d71,plain,
divide(identity,X0) = divide(identity,divide(X0,divide(identity,X0))),
inference(resolution,[status(thm)],[d70,d67]) ).
cnf(d72,plain,
divide(identity,X0) = divide(identity,divide(identity,divide(identity,X0))),
inference(superposition,[status(thm)],[d66,d71]) ).
cnf(d73,plain,
divide(identity,divide(identity,divide(identity,a))) != divide(identity,a),
inference(demodulation,[status(thm)],[c0,d66]) ).
cnf(d74,plain,
divide(identity,a) != divide(identity,a),
inference(demodulation,[status(thm)],[d73,d72]) ).
cnf(d75,plain,
$false,
inference(resolution,[status(thm)],[d35,d74]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN010-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n013.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 15:57:06 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 80.00/16.38 % SZS status Unsatisfiable for theBenchmark.p
% 80.00/16.38 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------