%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : HEN008-2 : 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 : n016.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 29.14s 4.04s
% Output : CNFRefutation 29.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of clauses : 30 ( 18 unt; 0 nHn; 24 RR)
% Number of literals : 61 ( 0 equ; 33 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 54 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(zero_divide_anything_is_zero,axiom,
quotient(zero,X0,zero) ).
cnf(x_divde_zero_is_x,axiom,
quotient(X0,zero,X0) ).
cnf(xQyLEz_implies_xQzLEy,axiom,
( 'less$uequal'(X4,X1)
| ~ quotient(X0,X3,X4)
| ~ 'less$uequal'(X2,X3)
| ~ quotient(X0,X1,X2) ) ).
cnf(aLEb,hypothesis,
'less$uequal'(a,b) ).
cnf(aQc,hypothesis,
quotient(a,c,aQc) ).
cnf(bQc,hypothesis,
quotient(b,c,bQc) ).
cnf(prove_aQcLEbQc,negated_conjecture,
~ 'less$uequal'(aQc,bQc) ).
cnf(quotient_less_equal,axiom,
( quotient(X0,X1,zero)
| ~ 'less$uequal'(X0,X1) ) ).
cnf(quotient_property,axiom,
( 'less$uequal'(X6,X7)
| ~ quotient(X2,X3,X7)
| ~ quotient(X5,X4,X6)
| ~ quotient(X0,X3,X5)
| ~ quotient(X1,X3,X4)
| ~ quotient(X0,X1,X2) ) ).
cnf(closure,axiom,
quotient(X0,X1,divide(X0,X1)) ).
cnf(c1,plain,
quotient(zero,X0,zero),
inference(clausification,[status(esa)],[zero_divide_anything_is_zero]) ).
cnf(c3,plain,
quotient(X0,zero,X0),
inference(clausification,[status(esa)],[x_divde_zero_is_x]) ).
cnf(c5,plain,
( 'less$uequal'(X2,X3)
| ~ 'less$uequal'(X4,X1)
| ~ quotient(X0,X3,X4)
| ~ quotient(X0,X1,X2) ),
inference(clausification,[status(esa)],[xQyLEz_implies_xQzLEy]) ).
cnf(c7,plain,
'less$uequal'(a,b),
inference(clausification,[status(esa)],[aLEb]) ).
cnf(c8,plain,
quotient(a,c,aQc),
inference(clausification,[status(esa)],[aQc]) ).
cnf(c9,plain,
quotient(b,c,bQc),
inference(clausification,[status(esa)],[bQc]) ).
cnf(c10,plain,
~ 'less$uequal'(aQc,bQc),
inference(clausification,[status(esa)],[prove_aQcLEbQc]) ).
cnf(c11,plain,
( quotient(X0,X1,zero)
| ~ 'less$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[quotient_less_equal]) ).
cnf(c14,plain,
( ~ quotient(X2,X7,X5)
| ~ quotient(X4,X1,X6)
| ~ quotient(X3,X1,X7)
| 'less$uequal'(X5,X6)
| ~ quotient(X0,X3,X4)
| ~ quotient(X0,X1,X2) ),
inference(clausification,[status(esa)],[quotient_property]) ).
cnf(c18,plain,
quotient(X0,X1,divide(X0,X1)),
inference(clausification,[status(esa)],[closure]) ).
cnf(d0,plain,
( ~ 'less$uequal'(X2,zero)
| 'less$uequal'(X0,X1)
| ~ quotient(X0,X1,X2) ),
inference(resolution,[status(thm)],[c5,c3]) ).
cnf(d1,plain,
( 'less$uequal'(X0,X1)
| ~ 'less$uequal'(divide(X0,X1),zero) ),
inference(resolution,[status(thm)],[d0,c18]) ).
cnf(d2,plain,
( 'less$uequal'(X4,zero)
| ~ quotient(X5,X1,X3)
| ~ quotient(X5,X0,zero)
| ~ quotient(X3,X2,X4)
| ~ quotient(X0,X1,X2) ),
inference(resolution,[status(thm)],[c14,c1]) ).
cnf(d3,plain,
( 'less$uequal'(X2,zero)
| ~ quotient(X0,c,X1)
| ~ quotient(aQc,X1,X2)
| ~ quotient(a,X0,zero) ),
inference(resolution,[status(thm)],[d2,c8]) ).
cnf(d4,plain,
( 'less$uequal'(X0,zero)
| ~ quotient(aQc,bQc,X0)
| ~ quotient(a,b,zero) ),
inference(resolution,[status(thm)],[d3,c9]) ).
cnf(d5,plain,
quotient(a,b,zero),
inference(resolution,[status(thm)],[c11,c7]) ).
cnf(d6,plain,
( 'less$uequal'(X0,zero)
| ~ quotient(aQc,bQc,X0) ),
inference(resolution,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
'less$uequal'(divide(aQc,bQc),zero),
inference(resolution,[status(thm)],[d6,c18]) ).
cnf(d8,plain,
'less$uequal'(aQc,bQc),
inference(resolution,[status(thm)],[d7,d1]) ).
cnf(d9,plain,
$false,
inference(resolution,[status(thm)],[c10,d8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN008-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n016.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Fri Sep 25 16:02:00 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 29.14/4.04 % SZS status Unsatisfiable for theBenchmark.p
% 29.14/4.04 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------