%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : HEN008-3 : 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 : n004.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 28.07s 4.63s
% Output : CNFRefutation 28.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of clauses : 28 ( 20 unt; 0 nHn; 15 RR)
% Number of literals : 38 ( 14 equ; 12 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 33 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a_LE_b,hypothesis,
'less$uequal'(a,b) ).
cnf(prove_a_divide_c_LE_b_divide_c,negated_conjecture,
~ 'less$uequal'(divide(a,c),divide(b,c)) ).
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'(a,b),
inference(clausification,[status(esa)],[a_LE_b]) ).
cnf(c1,plain,
~ 'less$uequal'(divide(a,c),divide(b,c)),
inference(clausification,[status(esa)],[prove_a_divide_c_LE_b_divide_c]) ).
cnf(c2,plain,
( divide(X0,X1) = zero
| ~ 'less$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$uequal'(X0,zero)
| zero = X0 ),
inference(resolution,[status(thm)],[c7,c6]) ).
cnf(d1,plain,
divide(zero,X0) = zero,
inference(resolution,[status(thm)],[c2,c6]) ).
cnf(d2,plain,
divide(a,b) = zero,
inference(resolution,[status(thm)],[c2,c0]) ).
cnf(d3,plain,
'less$uequal'(divide(divide(a,X0),divide(b,X0)),divide(zero,X0)),
inference(superposition,[status(thm)],[d2,c5]) ).
cnf(d4,plain,
'less$uequal'(divide(divide(a,X0),divide(b,X0)),zero),
inference(demodulation,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
zero = divide(divide(a,X0),divide(b,X0)),
inference(resolution,[status(thm)],[d4,d0]) ).
cnf(d6,plain,
( 'less$uequal'(divide(a,X0),divide(b,X0))
| zero != zero ),
inference(superposition,[status(thm)],[d5,c3]) ).
cnf(d7,plain,
divide(divide(X0,X1),X0) = zero,
inference(resolution,[status(thm)],[c2,c4]) ).
cnf(d8,plain,
divide(zero,a) = zero,
inference(superposition,[status(thm)],[d2,d7]) ).
cnf(d9,plain,
zero = zero,
inference(demodulation,[status(thm)],[d8,d1]) ).
cnf(d10,plain,
'less$uequal'(divide(a,X0),divide(b,X0)),
inference(resolution,[status(thm)],[d9,d6]) ).
cnf(d11,plain,
$false,
inference(resolution,[status(thm)],[d10,c1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN008-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.54 % Computer : n004.cluster.edu
% 0.09/0.54 % Model : x86_64 x86_64
% 0.09/0.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.54 % Memory : 8046.5625MB
% 0.09/0.54 % OS : Linux 6.8.0-71-generic
% 0.09/0.54 % CPULimit : 300
% 0.09/0.54 % WCLimit : 300
% 0.09/0.54 % DateTime : Fri Sep 25 15:57:21 UTC 2026
% 0.09/0.54 % CPUTime :
% 0.09/0.54 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 28.07/4.63 % SZS status Unsatisfiable for theBenchmark.p
% 28.07/4.63 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------