%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : HEN009-6 : 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 : n005.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 16.94s 6.00s
% Output : CNFRefutation 16.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 14
% Syntax : Number of clauses : 60 ( 36 unt; 0 nHn; 35 RR)
% Number of literals : 88 ( 32 equ; 31 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 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 : 66 ( 12 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_divide3,axiom,
( 'less$uequal'(divide(X0,X2),divide(X1,X2))
| ~ 'less$uequal'(X0,X1) ) ).
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$uequal'(divide(X0,X1),X0) ).
cnf(zero_is_smallest,axiom,
'less$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$uequal'(X0,identity) ).
cnf(c1,plain,
divide(zero,X0) = zero,
inference(clausification,[status(esa)],[zero_divide_anything_is_zero]) ).
cnf(c2,plain,
divide(X0,X0) = zero,
inference(clausification,[status(esa)],[x_divide_x_is_zero]) ).
cnf(c3,plain,
( 'less$uequal'(divide(X0,X2),X1)
| ~ 'less$uequal'(divide(X0,X1),X2) ),
inference(clausification,[status(esa)],[property_of_divide1]) ).
cnf(c4,plain,
( 'less$uequal'(divide(X0,X2),divide(X1,X2))
| ~ 'less$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[property_of_divide3]) ).
cnf(c6,plain,
divide(identity,a) = b,
inference(clausification,[status(esa)],[id_divide_a_is_b]) ).
cnf(c7,plain,
divide(identity,b) = c,
inference(clausification,[status(esa)],[id_divide_b_is_c]) ).
cnf(c8,plain,
divide(identity,c) = d,
inference(clausification,[status(esa)],[id_divide_c_is_d]) ).
cnf(c9,plain,
b != d,
inference(clausification,[status(esa)],[prove_b_equals_d]) ).
cnf(c10,plain,
( divide(X0,X1) = zero
| ~ 'less$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[quotient_less_equal1]) ).
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(c14,plain,
'less$uequal'(zero,X0),
inference(clausification,[status(esa)],[zero_is_smallest]) ).
cnf(c15,plain,
( X0 = X1
| ~ 'less$uequal'(X1,X0)
| ~ 'less$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[less_equal_and_equal]) ).
cnf(c16,plain,
'less$uequal'(X0,identity),
inference(clausification,[status(esa)],[identity_is_largest]) ).
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$uequal'(divide(X0,divide(X0,X1)),X1),
inference(resolution,[status(thm)],[d1,c3]) ).
cnf(d3,plain,
'less$uequal'(divide(identity,c),b),
inference(superposition,[status(thm)],[c7,d2]) ).
cnf(d4,plain,
'less$uequal'(d,b),
inference(demodulation,[status(thm)],[d3,c8]) ).
cnf(d5,plain,
( ~ 'less$uequal'(b,d)
| d = b ),
inference(resolution,[status(thm)],[c15,d4]) ).
cnf(d6,plain,
( ~ 'less$uequal'(X0,identity)
| 'less$uequal'(divide(X0,c),d) ),
inference(superposition,[status(thm)],[c8,c4]) ).
cnf(d7,plain,
'less$uequal'(divide(X0,c),d),
inference(resolution,[status(thm)],[c16,d6]) ).
cnf(d8,plain,
'less$uequal'(divide(X0,d),c),
inference(resolution,[status(thm)],[d7,c3]) ).
cnf(d9,plain,
( ~ 'less$uequal'(X0,zero)
| zero = X0 ),
inference(resolution,[status(thm)],[c15,c14]) ).
cnf(d10,plain,
zero = divide(X0,divide(X0,zero)),
inference(resolution,[status(thm)],[d9,d2]) ).
cnf(d11,plain,
( 'less$uequal'(X0,divide(X0,zero))
| zero != zero ),
inference(superposition,[status(thm)],[d10,c11]) ).
cnf(d12,plain,
zero = divide(zero,zero),
inference(superposition,[status(thm)],[c2,d10]) ).
cnf(d13,plain,
zero = zero,
inference(demodulation,[status(thm)],[d12,c1]) ).
cnf(d14,plain,
'less$uequal'(X0,divide(X0,zero)),
inference(resolution,[status(thm)],[d13,d11]) ).
cnf(d15,plain,
( ~ 'less$uequal'(X0,divide(X0,X1))
| divide(X0,X1) = X0 ),
inference(resolution,[status(thm)],[c15,c12]) ).
cnf(d16,plain,
divide(X0,zero) = X0,
inference(resolution,[status(thm)],[d15,d14]) ).
cnf(d17,plain,
( 'less$uequal'(divide(X0,divide(X1,X2)),X2)
| ~ 'less$uequal'(X0,X1) ),
inference(resolution,[status(thm)],[c4,c3]) ).
cnf(d18,plain,
( ~ 'less$uequal'(X0,X1)
| ~ 'less$uequal'(X2,X0)
| 'less$uequal'(divide(X2,zero),X1) ),
inference(superposition,[status(thm)],[c10,d17]) ).
cnf(d19,plain,
( 'less$uequal'(X0,X2)
| ~ 'less$uequal'(X1,X2)
| ~ 'less$uequal'(X0,X1) ),
inference(demodulation,[status(thm)],[d18,d16]) ).
cnf(d20,plain,
( 'less$uequal'(divide(X1,d),X0)
| ~ 'less$uequal'(c,X0) ),
inference(resolution,[status(thm)],[d19,d8]) ).
cnf(d21,plain,
( 'less$uequal'(divide(X1,X0),d)
| ~ 'less$uequal'(c,X0) ),
inference(resolution,[status(thm)],[d20,c3]) ).
cnf(d22,plain,
( ~ 'less$uequal'(c,a)
| 'less$uequal'(b,d) ),
inference(superposition,[status(thm)],[c6,d21]) ).
cnf(d23,plain,
'less$uequal'(divide(identity,b),a),
inference(superposition,[status(thm)],[c6,d2]) ).
cnf(d24,plain,
'less$uequal'(c,a),
inference(demodulation,[status(thm)],[d23,c7]) ).
cnf(d25,plain,
'less$uequal'(b,d),
inference(resolution,[status(thm)],[d24,d22]) ).
cnf(d26,plain,
d = b,
inference(resolution,[status(thm)],[d25,d5]) ).
cnf(d27,plain,
b != b,
inference(demodulation,[status(thm)],[c9,d26]) ).
cnf(d28,plain,
( divide(X0,zero) = X0
| ~ 'less$uequal'(X0,X0) ),
inference(superposition,[status(thm)],[d16,d15]) ).
cnf(d29,plain,
( ~ 'less$uequal'(X0,X0)
| X0 = X0 ),
inference(demodulation,[status(thm)],[d28,d16]) ).
cnf(d30,plain,
X0 = X0,
inference(resolution,[status(thm)],[d1,d29]) ).
cnf(d31,plain,
$false,
inference(resolution,[status(thm)],[d30,d27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : HEN009-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n005.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Fri Sep 25 15:57:32 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.94/6.00 % SZS status Unsatisfiable for theBenchmark.p
% 16.94/6.00 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------