%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : HEN006-3 : 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 : n015.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 24.26s 3.92s
% Output : CNFRefutation 24.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 8
% Syntax : Number of clauses : 53 ( 38 unt; 0 nHn; 26 RR)
% Number of literals : 70 ( 29 equ; 20 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 : 55 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
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$uequal'(X0,X1) ) ).
cnf(c0,plain,
'less$uequal'(divide(a,b),d),
inference(clausification,[status(esa)],[a_divide_b_LE_d]) ).
cnf(c1,plain,
~ 'less$uequal'(divide(a,d),b),
inference(clausification,[status(esa)],[prove_a_divide_d_LE_b]) ).
cnf(c2,plain,
( divide(X0,X1) = zero
| ~ 'less$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[quotient_less_equal1]) ).
cnf(c3,plain,
( 'less$uequal'(X0,X1)
| divide(X0,X1) != zero ),
inference(clausification,[status(esa)],[quotient_less_equal2]) ).
cnf(c4,plain,
'less$uequal'(divide(X0,X1),X0),
inference(clausification,[status(esa)],[quotient_smaller_than_numerator]) ).
cnf(c5,plain,
'less$uequal'(divide(divide(X0,X1),divide(X2,X1)),divide(divide(X0,X2),X1)),
inference(clausification,[status(esa)],[quotient_property]) ).
cnf(c6,plain,
'less$uequal'(zero,X0),
inference(clausification,[status(esa)],[zero_is_smallest]) ).
cnf(c7,plain,
( X0 = X1
| ~ 'less$uequal'(X1,X0)
| ~ 'less$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[less_equal_and_equal]) ).
cnf(d0,plain,
( ~ 'less$uequal'(X0,zero)
| zero = X0 ),
inference(resolution,[status(thm)],[c7,c6]) ).
cnf(d1,plain,
divide(zero,X0) = zero,
inference(resolution,[status(thm)],[c2,c6]) ).
cnf(d2,plain,
( ~ 'less$uequal'(X0,divide(X0,X1))
| divide(X0,X1) = X0 ),
inference(resolution,[status(thm)],[c7,c4]) ).
cnf(d3,plain,
'less$uequal'(divide(divide(X1,X0),zero),divide(divide(X1,zero),X0)),
inference(superposition,[status(thm)],[d1,c5]) ).
cnf(d4,plain,
divide(divide(X0,X1),X0) = zero,
inference(resolution,[status(thm)],[c2,c4]) ).
cnf(d5,plain,
'less$uequal'(divide(divide(X0,X0),divide(X1,X0)),zero),
inference(superposition,[status(thm)],[d4,c5]) ).
cnf(d6,plain,
'less$uequal'(divide(divide(X0,X0),zero),zero),
inference(superposition,[status(thm)],[d4,d5]) ).
cnf(d7,plain,
zero = divide(divide(X0,X0),zero),
inference(resolution,[status(thm)],[d6,d0]) ).
cnf(d8,plain,
( 'less$uequal'(divide(X0,X0),zero)
| zero != zero ),
inference(superposition,[status(thm)],[d7,c3]) ).
cnf(d9,plain,
divide(zero,zero) = zero,
inference(superposition,[status(thm)],[d1,d4]) ).
cnf(d10,plain,
zero = zero,
inference(demodulation,[status(thm)],[d9,d1]) ).
cnf(d11,plain,
'less$uequal'(divide(X0,X0),zero),
inference(resolution,[status(thm)],[d10,d8]) ).
cnf(d12,plain,
zero = divide(X0,X0),
inference(resolution,[status(thm)],[d11,d0]) ).
cnf(d13,plain,
'less$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,d0]) ).
cnf(d15,plain,
( 'less$uequal'(divide(X0,divide(X0,zero)),zero)
| zero != zero ),
inference(superposition,[status(thm)],[d14,c3]) ).
cnf(d16,plain,
'less$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,d0]) ).
cnf(d18,plain,
( 'less$uequal'(X0,divide(X0,zero))
| zero != zero ),
inference(superposition,[status(thm)],[d17,c3]) ).
cnf(d19,plain,
'less$uequal'(X0,divide(X0,zero)),
inference(resolution,[status(thm)],[d10,d18]) ).
cnf(d20,plain,
divide(X0,zero) = X0,
inference(resolution,[status(thm)],[d19,d2]) ).
cnf(d21,plain,
'less$uequal'(divide(divide(X2,X0),zero),divide(divide(X2,divide(X0,X1)),X0)),
inference(superposition,[status(thm)],[d4,c5]) ).
cnf(d22,plain,
divide(divide(a,b),d) = zero,
inference(resolution,[status(thm)],[c2,c0]) ).
cnf(d23,plain,
'less$uequal'(divide(divide(a,d),divide(b,d)),zero),
inference(superposition,[status(thm)],[d22,c5]) ).
cnf(d24,plain,
zero = divide(divide(a,d),divide(b,d)),
inference(resolution,[status(thm)],[d23,d0]) ).
cnf(d25,plain,
'less$uequal'(divide(divide(divide(a,d),b),zero),divide(zero,b)),
inference(superposition,[status(thm)],[d24,d21]) ).
cnf(d26,plain,
'less$uequal'(divide(divide(a,d),b),divide(zero,b)),
inference(demodulation,[status(thm)],[d25,d20]) ).
cnf(d27,plain,
'less$uequal'(divide(divide(a,d),b),zero),
inference(demodulation,[status(thm)],[d26,d1]) ).
cnf(d28,plain,
zero = divide(divide(a,d),b),
inference(resolution,[status(thm)],[d27,d0]) ).
cnf(d29,plain,
( 'less$uequal'(divide(a,d),b)
| zero != zero ),
inference(superposition,[status(thm)],[d28,c3]) ).
cnf(d30,plain,
zero != zero,
inference(resolution,[status(thm)],[c1,d29]) ).
cnf(d31,plain,
( divide(X0,zero) = X0
| ~ 'less$uequal'(X0,X0) ),
inference(superposition,[status(thm)],[d20,d2]) ).
cnf(d32,plain,
( ~ 'less$uequal'(X0,X0)
| X0 = X0 ),
inference(demodulation,[status(thm)],[d31,d20]) ).
cnf(d33,plain,
( 'less$uequal'(X0,X0)
| zero != zero ),
inference(superposition,[status(thm)],[d12,c3]) ).
cnf(d34,plain,
'less$uequal'(X0,X0),
inference(resolution,[status(thm)],[d10,d33]) ).
cnf(d35,plain,
X0 = X0,
inference(resolution,[status(thm)],[d34,d32]) ).
cnf(d36,plain,
$false,
inference(resolution,[status(thm)],[d35,d30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN006-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n015.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 15:59:42 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 24.26/3.92 % SZS status Unsatisfiable for theBenchmark.p
% 24.26/3.92 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------