%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : HEN006-4 : 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 : n026.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 07:31:46 AM UTC 2026
% Result : Unsatisfiable 15.23s 7.48s
% Output : CNFRefutation 15.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of clauses : 60 ( 37 unt; 0 nHn; 35 RR)
% Number of literals : 88 ( 39 equ; 31 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 68 ( 8 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(x_divide_zero_is_x,axiom,
divide(a,zero) = a ).
cnf(transitivity_of_less_equal,axiom,
( 'less$uequal'(X0,X2)
| ~ 'less$uequal'(X1,X2)
| ~ 'less$uequal'(X0,X1) ) ).
cnf(a_divide_b_LE_d,hypothesis,
'less$uequal'(divide(a,b),d) ).
cnf(prove_a_divide_d_LE_b,negated_conjecture,
~ 'less$uequal'(divide(a,d),b) ).
cnf(quotient_less_equal1,axiom,
( divide(X0,X1) = zero
| ~ 'less$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(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,
divide(a,zero) = a,
inference(clausification,[status(esa)],[x_divide_zero_is_x]) ).
cnf(c4,plain,
( 'less$uequal'(X2,X1)
| ~ 'less$uequal'(X2,X0)
| ~ 'less$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[transitivity_of_less_equal]) ).
cnf(c5,plain,
'less$uequal'(divide(a,b),d),
inference(clausification,[status(esa)],[a_divide_b_LE_d]) ).
cnf(c6,plain,
~ 'less$uequal'(divide(a,d),b),
inference(clausification,[status(esa)],[prove_a_divide_d_LE_b]) ).
cnf(c7,plain,
( divide(X0,X1) = zero
| ~ 'less$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[quotient_less_equal1]) ).
cnf(c8,plain,
( 'less$uequal'(X0,X1)
| divide(X0,X1) != zero ),
inference(clausification,[status(esa)],[quotient_less_equal2]) ).
cnf(c9,plain,
'less$uequal'(divide(X0,X1),X0),
inference(clausification,[status(esa)],[quotient_smaller_than_numerator]) ).
cnf(c10,plain,
'less$uequal'(divide(divide(X0,X1),divide(X2,X1)),divide(divide(X0,X2),X1)),
inference(clausification,[status(esa)],[quotient_property]) ).
cnf(c11,plain,
'less$uequal'(zero,X0),
inference(clausification,[status(esa)],[zero_is_smallest]) ).
cnf(c12,plain,
( X0 = X1
| ~ 'less$uequal'(X1,X0)
| ~ 'less$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[less_equal_and_equal]) ).
cnf(d0,plain,
( ~ 'less$uequal'(X0,divide(X0,X1))
| divide(X0,X1) = X0 ),
inference(resolution,[status(thm)],[c12,c9]) ).
cnf(d1,plain,
( ~ 'less$uequal'(X0,zero)
| zero = X0 ),
inference(resolution,[status(thm)],[c12,c11]) ).
cnf(d2,plain,
'less$uequal'(divide(divide(X1,X0),zero),divide(divide(X1,zero),X0)),
inference(superposition,[status(thm)],[c1,c10]) ).
cnf(d3,plain,
'less$uequal'(divide(divide(X0,divide(X0,zero)),zero),zero),
inference(superposition,[status(thm)],[c2,d2]) ).
cnf(d4,plain,
zero = divide(divide(X0,divide(X0,zero)),zero),
inference(resolution,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
( 'less$uequal'(divide(X0,divide(X0,zero)),zero)
| zero != zero ),
inference(superposition,[status(thm)],[d4,c8]) ).
cnf(d6,plain,
'less$uequal'(a,a),
inference(superposition,[status(thm)],[c3,c9]) ).
cnf(d7,plain,
divide(a,a) = zero,
inference(resolution,[status(thm)],[d6,c7]) ).
cnf(d8,plain,
zero = zero,
inference(demodulation,[status(thm)],[d7,c2]) ).
cnf(d9,plain,
'less$uequal'(divide(X0,divide(X0,zero)),zero),
inference(resolution,[status(thm)],[d8,d5]) ).
cnf(d10,plain,
zero = divide(X0,divide(X0,zero)),
inference(resolution,[status(thm)],[d9,d1]) ).
cnf(d11,plain,
( 'less$uequal'(X0,divide(X0,zero))
| zero != zero ),
inference(superposition,[status(thm)],[d10,c8]) ).
cnf(d12,plain,
'less$uequal'(X0,divide(X0,zero)),
inference(resolution,[status(thm)],[d8,d11]) ).
cnf(d13,plain,
divide(X0,zero) = X0,
inference(resolution,[status(thm)],[d12,d0]) ).
cnf(d14,plain,
divide(divide(a,b),d) = zero,
inference(resolution,[status(thm)],[c7,c5]) ).
cnf(d15,plain,
'less$uequal'(divide(divide(a,d),divide(b,d)),zero),
inference(superposition,[status(thm)],[d14,c10]) ).
cnf(d16,plain,
zero = divide(divide(a,d),divide(b,d)),
inference(resolution,[status(thm)],[d15,d1]) ).
cnf(d17,plain,
( ~ 'less$uequal'(divide(divide(X0,X2),X1),divide(divide(X0,X1),divide(X2,X1)))
| divide(divide(X0,X1),divide(X2,X1)) = divide(divide(X0,X2),X1) ),
inference(resolution,[status(thm)],[c12,c10]) ).
cnf(d18,plain,
( divide(divide(divide(a,d),X0),divide(divide(b,d),X0)) = divide(divide(divide(a,d),divide(b,d)),X0)
| ~ 'less$uequal'(divide(zero,X0),divide(divide(divide(a,d),X0),divide(divide(b,d),X0))) ),
inference(superposition,[status(thm)],[d16,d17]) ).
cnf(d19,plain,
( ~ 'less$uequal'(divide(zero,X0),divide(divide(divide(a,d),X0),divide(divide(b,d),X0)))
| divide(divide(divide(a,d),X0),divide(divide(b,d),X0)) = divide(zero,X0) ),
inference(demodulation,[status(thm)],[d18,d16]) ).
cnf(d20,plain,
( ~ 'less$uequal'(divide(zero,X0),divide(divide(divide(a,d),X0),divide(divide(b,d),X0)))
| divide(divide(divide(a,d),X0),divide(divide(b,d),X0)) = zero ),
inference(demodulation,[status(thm)],[d19,c1]) ).
cnf(d21,plain,
( ~ 'less$uequal'(zero,divide(divide(divide(a,d),X0),divide(divide(b,d),X0)))
| divide(divide(divide(a,d),X0),divide(divide(b,d),X0)) = zero ),
inference(demodulation,[status(thm)],[d20,c1]) ).
cnf(d22,plain,
divide(divide(divide(a,d),X0),divide(divide(b,d),X0)) = zero,
inference(resolution,[status(thm)],[c11,d21]) ).
cnf(d23,plain,
divide(divide(X0,X1),X0) = zero,
inference(resolution,[status(thm)],[c7,c9]) ).
cnf(d24,plain,
divide(divide(divide(a,d),b),zero) = zero,
inference(superposition,[status(thm)],[d23,d22]) ).
cnf(d25,plain,
divide(divide(a,d),b) = zero,
inference(demodulation,[status(thm)],[d24,d13]) ).
cnf(d26,plain,
( 'less$uequal'(divide(a,d),b)
| zero != zero ),
inference(superposition,[status(thm)],[d25,c8]) ).
cnf(d27,plain,
zero != zero,
inference(resolution,[status(thm)],[c6,d26]) ).
cnf(d28,plain,
( 'less$uequal'(divide(X0,X2),X1)
| ~ 'less$uequal'(X0,X1) ),
inference(resolution,[status(thm)],[c9,c4]) ).
cnf(d29,plain,
( ~ 'less$uequal'(X1,divide(X0,X2))
| divide(X0,X2) = X1
| ~ 'less$uequal'(X0,X1) ),
inference(resolution,[status(thm)],[d28,c12]) ).
cnf(d30,plain,
( ~ 'less$uequal'(X0,X0)
| divide(X0,zero) = X0 ),
inference(resolution,[status(thm)],[d12,d29]) ).
cnf(d31,plain,
( ~ 'less$uequal'(X0,X0)
| X0 = X0 ),
inference(demodulation,[status(thm)],[d30,d13]) ).
cnf(d32,plain,
( 'less$uequal'(X0,X0)
| zero != zero ),
inference(superposition,[status(thm)],[c2,c8]) ).
cnf(d33,plain,
'less$uequal'(X0,X0),
inference(resolution,[status(thm)],[d8,d32]) ).
cnf(d34,plain,
X0 = X0,
inference(resolution,[status(thm)],[d33,d31]) ).
cnf(d35,plain,
$false,
inference(resolution,[status(thm)],[d34,d27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : HEN006-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n026.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Fri Sep 25 15:59:25 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.23/7.48 % SZS status Unsatisfiable for theBenchmark.p
% 15.23/7.48 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------