%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : HEN007-4 : 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 : n012.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 07:31:47 AM UTC 2026
% Result : Unsatisfiable 13.23s 2.19s
% Output : CNFRefutation 13.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of clauses : 19 ( 10 unt; 0 nHn; 12 RR)
% Number of literals : 30 ( 5 equ; 14 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 : 28 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(x_divide_x_is_zero,axiom,
divide(X0,X0) = zero ).
cnf(transitivity_of_less_equal,axiom,
( 'less$uequal'(X0,X2)
| ~ 'less$uequal'(X1,X2)
| ~ 'less$uequal'(X0,X1) ) ).
cnf(property_of_divide1,axiom,
( 'less$uequal'(divide(X0,X2),X1)
| ~ 'less$uequal'(divide(X0,X1),X2) ) ).
cnf(a_LE_b,hypothesis,
'less$uequal'(a,b) ).
cnf(prove_c_divide_b_LE_c_divide_a,negated_conjecture,
~ 'less$uequal'(divide(c,b),divide(c,a)) ).
cnf(quotient_less_equal2,axiom,
( 'less$uequal'(X0,X1)
| divide(X0,X1) != zero ) ).
cnf(c2,plain,
divide(X0,X0) = zero,
inference(clausification,[status(esa)],[x_divide_x_is_zero]) ).
cnf(c4,plain,
( 'less$uequal'(X0,X2)
| ~ 'less$uequal'(X1,X2)
| ~ 'less$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[transitivity_of_less_equal]) ).
cnf(c5,plain,
( 'less$uequal'(divide(X0,X2),X1)
| ~ 'less$uequal'(divide(X0,X1),X2) ),
inference(clausification,[status(esa)],[property_of_divide1]) ).
cnf(c6,plain,
'less$uequal'(a,b),
inference(clausification,[status(esa)],[a_LE_b]) ).
cnf(c7,plain,
~ 'less$uequal'(divide(c,b),divide(c,a)),
inference(clausification,[status(esa)],[prove_c_divide_b_LE_c_divide_a]) ).
cnf(c9,plain,
( 'less$uequal'(X0,X1)
| divide(X0,X1) != zero ),
inference(clausification,[status(esa)],[quotient_less_equal2]) ).
cnf(d0,plain,
( 'less$uequal'(X0,X0)
| zero != zero ),
inference(superposition,[status(thm)],[c2,c9]) ).
cnf(d1,plain,
'less$uequal'(X0,X0),
inference(equality_resolution,[status(thm)],[d0]) ).
cnf(d2,plain,
'less$uequal'(divide(X0,divide(X0,X1)),X1),
inference(resolution,[status(thm)],[c5,d1]) ).
cnf(d3,plain,
( 'less$uequal'(divide(X2,divide(X2,X0)),X1)
| ~ 'less$uequal'(X0,X1) ),
inference(resolution,[status(thm)],[d2,c4]) ).
cnf(d4,plain,
( 'less$uequal'(divide(X2,X1),divide(X2,X0))
| ~ 'less$uequal'(X0,X1) ),
inference(resolution,[status(thm)],[d3,c5]) ).
cnf(d5,plain,
~ 'less$uequal'(a,b),
inference(resolution,[status(thm)],[d4,c7]) ).
cnf(d6,plain,
$false,
inference(resolution,[status(thm)],[c6,d5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : HEN007-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Fri Sep 25 15:56:35 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.23/2.19 % SZS status Unsatisfiable for theBenchmark.p
% 13.23/2.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------