%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : HEN009-3 : TPTP v9.3.1. Released v1.0.0.
% 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 07:31:48 AM UTC 2026
% Result : Unsatisfiable 31.14s 4.60s
% Output : CNFRefutation 31.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 11
% Syntax : Number of clauses : 99 ( 66 unt; 0 nHn; 69 RR)
% Number of literals : 134 ( 46 equ; 38 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 : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 60 ( 19 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(id_divide_a_is_b,hypothesis,
divide(identity,a) = b ).
cnf(id_divide_b_is_c,hypothesis,
divide(identity,b) = c ).
cnf(id_divide_c_is_d,hypothesis,
divide(identity,c) = d ).
cnf(prove_b_equals_d,negated_conjecture,
b != d ).
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(c1,plain,
divide(identity,a) = b,
inference(clausification,[status(esa)],[id_divide_a_is_b]) ).
cnf(c2,plain,
divide(identity,b) = c,
inference(clausification,[status(esa)],[id_divide_b_is_c]) ).
cnf(c3,plain,
divide(identity,c) = d,
inference(clausification,[status(esa)],[id_divide_c_is_d]) ).
cnf(c4,plain,
b != d,
inference(clausification,[status(esa)],[prove_b_equals_d]) ).
cnf(c5,plain,
( divide(X0,X1) = zero
| ~ 'less$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[quotient_less_equal1]) ).
cnf(c6,plain,
( 'less$uequal'(X0,X1)
| divide(X0,X1) != zero ),
inference(clausification,[status(esa)],[quotient_less_equal2]) ).
cnf(c7,plain,
'less$uequal'(divide(X0,X1),X0),
inference(clausification,[status(esa)],[quotient_smaller_than_numerator]) ).
cnf(c8,plain,
'less$uequal'(divide(divide(X0,X1),divide(X2,X1)),divide(divide(X0,X2),X1)),
inference(clausification,[status(esa)],[quotient_property]) ).
cnf(c9,plain,
'less$uequal'(zero,X0),
inference(clausification,[status(esa)],[zero_is_smallest]) ).
cnf(c10,plain,
( X0 = X1
| ~ 'less$uequal'(X1,X0)
| ~ 'less$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[less_equal_and_equal]) ).
cnf(c11,plain,
'less$uequal'(X0,identity),
inference(clausification,[status(esa)],[identity_is_largest]) ).
cnf(d0,plain,
( ~ 'less$uequal'(X0,zero)
| X0 = zero ),
inference(resolution,[status(thm)],[c10,c9]) ).
cnf(d1,plain,
divide(zero,X0) = zero,
inference(resolution,[status(thm)],[d0,c7]) ).
cnf(d2,plain,
( ~ 'less$uequal'(X0,X1)
| 'less$uequal'(divide(divide(X0,X2),divide(X1,X2)),divide(zero,X2)) ),
inference(superposition,[status(thm)],[c5,c8]) ).
cnf(d3,plain,
( 'less$uequal'(divide(divide(X1,X0),divide(X2,X0)),zero)
| ~ 'less$uequal'(X1,X2) ),
inference(demodulation,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
( ~ 'less$uequal'(X0,identity)
| 'less$uequal'(divide(divide(X0,a),b),zero) ),
inference(superposition,[status(thm)],[c1,d3]) ).
cnf(d5,plain,
'less$uequal'(divide(divide(X0,a),b),zero),
inference(resolution,[status(thm)],[c11,d4]) ).
cnf(d6,plain,
divide(divide(X0,a),b) = zero,
inference(resolution,[status(thm)],[d5,d0]) ).
cnf(d7,plain,
( 'less$uequal'(divide(X0,a),b)
| zero != zero ),
inference(superposition,[status(thm)],[d6,c6]) ).
cnf(d8,plain,
'less$uequal'(divide(b,divide(X0,a)),divide(divide(identity,X0),a)),
inference(superposition,[status(thm)],[c1,c8]) ).
cnf(d9,plain,
'less$uequal'(divide(b,b),divide(divide(identity,identity),a)),
inference(superposition,[status(thm)],[c1,d8]) ).
cnf(d10,plain,
( ~ 'less$uequal'(identity,identity)
| 'less$uequal'(divide(b,b),divide(zero,a)) ),
inference(superposition,[status(thm)],[c5,d9]) ).
cnf(d11,plain,
( ~ 'less$uequal'(identity,identity)
| 'less$uequal'(divide(b,b),zero) ),
inference(demodulation,[status(thm)],[d10,d1]) ).
cnf(d12,plain,
'less$uequal'(divide(b,b),zero),
inference(resolution,[status(thm)],[c11,d11]) ).
cnf(d13,plain,
divide(b,b) = zero,
inference(resolution,[status(thm)],[d12,d0]) ).
cnf(d14,plain,
'less$uequal'(divide(c,divide(X0,b)),divide(divide(identity,X0),b)),
inference(superposition,[status(thm)],[c2,c8]) ).
cnf(d15,plain,
'less$uequal'(divide(c,divide(a,b)),divide(b,b)),
inference(superposition,[status(thm)],[c1,d14]) ).
cnf(d16,plain,
'less$uequal'(divide(c,divide(a,b)),zero),
inference(demodulation,[status(thm)],[d15,d13]) ).
cnf(d17,plain,
divide(c,divide(a,b)) = zero,
inference(resolution,[status(thm)],[d16,d0]) ).
cnf(d18,plain,
( ~ 'less$uequal'(b,b)
| 'less$uequal'(divide(c,divide(a,b)),zero) ),
inference(superposition,[status(thm)],[c5,d15]) ).
cnf(d19,plain,
( divide(c,divide(a,b)) = zero
| ~ 'less$uequal'(b,b) ),
inference(resolution,[status(thm)],[d18,d0]) ).
cnf(d20,plain,
( ~ 'less$uequal'(b,b)
| zero = zero ),
inference(demodulation,[status(thm)],[d19,d17]) ).
cnf(d21,plain,
( 'less$uequal'(b,b)
| zero != zero ),
inference(superposition,[status(thm)],[d13,c6]) ).
cnf(d22,plain,
'less$uequal'(b,b),
inference(equality_resolution,[status(thm)],[d21]) ).
cnf(d23,plain,
zero = zero,
inference(resolution,[status(thm)],[d22,d20]) ).
cnf(d24,plain,
'less$uequal'(divide(X0,a),b),
inference(resolution,[status(thm)],[d23,d7]) ).
cnf(d25,plain,
( ~ 'less$uequal'(b,divide(X0,a))
| b = divide(X0,a) ),
inference(resolution,[status(thm)],[d24,c10]) ).
cnf(d26,plain,
( ~ 'less$uequal'(X0,divide(X0,X1))
| X0 = divide(X0,X1) ),
inference(resolution,[status(thm)],[c10,c7]) ).
cnf(d27,plain,
'less$uequal'(divide(divide(X1,X0),zero),divide(divide(X1,zero),X0)),
inference(superposition,[status(thm)],[d1,c8]) ).
cnf(d28,plain,
'less$uequal'(divide(divide(b,X0),divide(b,X0)),divide(zero,X0)),
inference(superposition,[status(thm)],[d13,c8]) ).
cnf(d29,plain,
'less$uequal'(divide(divide(b,X0),divide(b,X0)),zero),
inference(demodulation,[status(thm)],[d28,d1]) ).
cnf(d30,plain,
divide(divide(b,X0),divide(b,X0)) = zero,
inference(resolution,[status(thm)],[d29,d0]) ).
cnf(d31,plain,
'less$uequal'(divide(divide(b,divide(b,zero)),zero),zero),
inference(superposition,[status(thm)],[d30,d27]) ).
cnf(d32,plain,
divide(divide(b,divide(b,zero)),zero) = zero,
inference(resolution,[status(thm)],[d31,d0]) ).
cnf(d33,plain,
( 'less$uequal'(divide(b,divide(b,zero)),zero)
| zero != zero ),
inference(superposition,[status(thm)],[d32,c6]) ).
cnf(d34,plain,
'less$uequal'(divide(b,divide(b,zero)),zero),
inference(resolution,[status(thm)],[d23,d33]) ).
cnf(d35,plain,
divide(b,divide(b,zero)) = zero,
inference(resolution,[status(thm)],[d34,d0]) ).
cnf(d36,plain,
( 'less$uequal'(b,divide(b,zero))
| zero != zero ),
inference(superposition,[status(thm)],[d35,c6]) ).
cnf(d37,plain,
'less$uequal'(b,divide(b,zero)),
inference(resolution,[status(thm)],[d23,d36]) ).
cnf(d38,plain,
b = divide(b,zero),
inference(resolution,[status(thm)],[d37,d26]) ).
cnf(d39,plain,
'less$uequal'(divide(b,divide(c,a)),divide(d,a)),
inference(superposition,[status(thm)],[c3,d8]) ).
cnf(d40,plain,
( ~ 'less$uequal'(c,a)
| 'less$uequal'(divide(b,zero),divide(d,a)) ),
inference(superposition,[status(thm)],[c5,d39]) ).
cnf(d41,plain,
( 'less$uequal'(c,divide(a,b))
| zero != zero ),
inference(superposition,[status(thm)],[d17,c6]) ).
cnf(d42,plain,
'less$uequal'(c,divide(a,b)),
inference(equality_resolution,[status(thm)],[d41]) ).
cnf(d43,plain,
( ~ 'less$uequal'(divide(a,b),c)
| divide(a,b) = c ),
inference(resolution,[status(thm)],[d42,c10]) ).
cnf(d44,plain,
( ~ 'less$uequal'(X0,identity)
| 'less$uequal'(divide(divide(X0,b),c),zero) ),
inference(superposition,[status(thm)],[c2,d3]) ).
cnf(d45,plain,
'less$uequal'(divide(divide(X0,b),c),zero),
inference(resolution,[status(thm)],[c11,d44]) ).
cnf(d46,plain,
divide(divide(X0,b),c) = zero,
inference(resolution,[status(thm)],[d45,d0]) ).
cnf(d47,plain,
( 'less$uequal'(divide(X0,b),c)
| zero != zero ),
inference(superposition,[status(thm)],[d46,c6]) ).
cnf(d48,plain,
'less$uequal'(divide(X0,b),c),
inference(resolution,[status(thm)],[d23,d47]) ).
cnf(d49,plain,
divide(a,b) = c,
inference(resolution,[status(thm)],[d48,d43]) ).
cnf(d50,plain,
'less$uequal'(c,a),
inference(superposition,[status(thm)],[d49,c7]) ).
cnf(d51,plain,
'less$uequal'(divide(b,zero),divide(d,a)),
inference(resolution,[status(thm)],[d50,d40]) ).
cnf(d52,plain,
'less$uequal'(b,divide(d,a)),
inference(demodulation,[status(thm)],[d51,d38]) ).
cnf(d53,plain,
b = divide(d,a),
inference(resolution,[status(thm)],[d52,d25]) ).
cnf(d54,plain,
'less$uequal'(b,d),
inference(superposition,[status(thm)],[d53,c7]) ).
cnf(d55,plain,
'less$uequal'(divide(c,c),divide(divide(identity,identity),b)),
inference(superposition,[status(thm)],[c2,d14]) ).
cnf(d56,plain,
( ~ 'less$uequal'(identity,identity)
| 'less$uequal'(divide(c,c),divide(zero,b)) ),
inference(superposition,[status(thm)],[c5,d55]) ).
cnf(d57,plain,
( ~ 'less$uequal'(identity,identity)
| 'less$uequal'(divide(c,c),zero) ),
inference(demodulation,[status(thm)],[d56,d1]) ).
cnf(d58,plain,
'less$uequal'(divide(c,c),zero),
inference(resolution,[status(thm)],[c11,d57]) ).
cnf(d59,plain,
divide(c,c) = zero,
inference(resolution,[status(thm)],[d58,d0]) ).
cnf(d60,plain,
'less$uequal'(divide(d,divide(X0,c)),divide(divide(identity,X0),c)),
inference(superposition,[status(thm)],[c3,c8]) ).
cnf(d61,plain,
'less$uequal'(divide(d,divide(b,c)),divide(c,c)),
inference(superposition,[status(thm)],[c2,d60]) ).
cnf(d62,plain,
'less$uequal'(divide(d,divide(b,c)),zero),
inference(demodulation,[status(thm)],[d61,d59]) ).
cnf(d63,plain,
divide(d,divide(b,c)) = zero,
inference(resolution,[status(thm)],[d62,d0]) ).
cnf(d64,plain,
( 'less$uequal'(d,divide(b,c))
| zero != zero ),
inference(superposition,[status(thm)],[d63,c6]) ).
cnf(d65,plain,
'less$uequal'(d,divide(b,c)),
inference(equality_resolution,[status(thm)],[d64]) ).
cnf(d66,plain,
( ~ 'less$uequal'(divide(b,c),d)
| divide(b,c) = d ),
inference(resolution,[status(thm)],[d65,c10]) ).
cnf(d67,plain,
( ~ 'less$uequal'(X0,identity)
| 'less$uequal'(divide(divide(X0,c),d),zero) ),
inference(superposition,[status(thm)],[c3,d3]) ).
cnf(d68,plain,
'less$uequal'(divide(divide(X0,c),d),zero),
inference(resolution,[status(thm)],[c11,d67]) ).
cnf(d69,plain,
divide(divide(X0,c),d) = zero,
inference(resolution,[status(thm)],[d68,d0]) ).
cnf(d70,plain,
( 'less$uequal'(divide(X0,c),d)
| zero != zero ),
inference(superposition,[status(thm)],[d69,c6]) ).
cnf(d71,plain,
'less$uequal'(divide(X0,c),d),
inference(resolution,[status(thm)],[d23,d70]) ).
cnf(d72,plain,
divide(b,c) = d,
inference(resolution,[status(thm)],[d71,d66]) ).
cnf(d73,plain,
'less$uequal'(d,b),
inference(superposition,[status(thm)],[d72,c7]) ).
cnf(d74,plain,
( ~ 'less$uequal'(b,d)
| b = d ),
inference(resolution,[status(thm)],[d73,c10]) ).
cnf(d75,plain,
~ 'less$uequal'(b,d),
inference(resolution,[status(thm)],[c4,d74]) ).
cnf(d76,plain,
$false,
inference(resolution,[status(thm)],[d75,d54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN009-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n016.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Fri Sep 25 16:02:14 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 31.14/4.60 % SZS status Unsatisfiable for theBenchmark.p
% 31.14/4.60 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------