%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : HEN007-6 : 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 : n013.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 14.79s 17.50s
% Output : CNFRefutation 14.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of clauses : 35 ( 17 unt; 0 nHn; 30 RR)
% Number of literals : 72 ( 5 equ; 40 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 71 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(x_divde_zero_is_x,axiom,
quotient(X0,zero,X0) ).
cnf(transitivity_of_less_equal,axiom,
( 'less$uequal'(X0,X2)
| ~ 'less$uequal'(X1,X2)
| ~ 'less$uequal'(X0,X1) ) ).
cnf(xLEy,hypothesis,
'less$uequal'(x,y) ).
cnf(zQy,hypothesis,
quotient(z,y,zQy) ).
cnf(zQx,hypothesis,
quotient(z,x,zQx) ).
cnf(prove_zQyLEzQx,negated_conjecture,
~ 'less$uequal'(zQy,zQx) ).
cnf(quotient_less_equal,axiom,
( quotient(X0,X1,zero)
| ~ 'less$uequal'(X0,X1) ) ).
cnf(divisor_existence,axiom,
( 'less$uequal'(X2,X0)
| ~ quotient(X0,X1,X2) ) ).
cnf(quotient_property,axiom,
( 'less$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(well_defined,axiom,
( X2 = X3
| ~ quotient(X0,X1,X3)
| ~ quotient(X0,X1,X2) ) ).
cnf(c3,plain,
quotient(X0,zero,X0),
inference(clausification,[status(esa)],[x_divde_zero_is_x]) ).
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'(x,y),
inference(clausification,[status(esa)],[xLEy]) ).
cnf(c6,plain,
quotient(z,y,zQy),
inference(clausification,[status(esa)],[zQy]) ).
cnf(c7,plain,
quotient(z,x,zQx),
inference(clausification,[status(esa)],[zQx]) ).
cnf(c8,plain,
~ 'less$uequal'(zQy,zQx),
inference(clausification,[status(esa)],[prove_zQyLEzQx]) ).
cnf(c9,plain,
( quotient(X0,X1,zero)
| ~ 'less$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[quotient_less_equal]) ).
cnf(c11,plain,
( 'less$uequal'(X2,X0)
| ~ quotient(X0,X1,X2) ),
inference(clausification,[status(esa)],[divisor_existence]) ).
cnf(c12,plain,
( ~ quotient(X7,X1,X4)
| ~ quotient(X6,X1,X5)
| ~ quotient(X0,X6,X7)
| ~ quotient(X2,X5,X3)
| 'less$uequal'(X3,X4)
| ~ quotient(X0,X1,X2) ),
inference(clausification,[status(esa)],[quotient_property]) ).
cnf(c16,plain,
quotient(X0,X1,divide(X0,X1)),
inference(clausification,[status(esa)],[closure]) ).
cnf(c17,plain,
( X2 = X3
| ~ quotient(X0,X1,X3)
| ~ quotient(X0,X1,X2) ),
inference(clausification,[status(esa)],[well_defined]) ).
cnf(d0,plain,
'less$uequal'(divide(X0,X1),X0),
inference(resolution,[status(thm)],[c11,c16]) ).
cnf(d1,plain,
( ~ 'less$uequal'(X0,divide(X1,X2))
| 'less$uequal'(X0,X1) ),
inference(resolution,[status(thm)],[d0,c4]) ).
cnf(d2,plain,
( 'less$uequal'(X5,X2)
| ~ quotient(X4,X3,X0)
| ~ quotient(X4,X1,X5)
| ~ quotient(X3,X1,zero)
| ~ quotient(X0,X1,X2) ),
inference(resolution,[status(thm)],[c12,c3]) ).
cnf(d3,plain,
( 'less$uequal'(X4,divide(X2,X3))
| ~ quotient(X1,X3,zero)
| ~ quotient(X0,X3,X4)
| ~ quotient(X0,X1,X2) ),
inference(resolution,[status(thm)],[d2,c16]) ).
cnf(d4,plain,
( 'less$uequal'(X1,divide(zQx,X0))
| ~ quotient(z,X0,X1)
| ~ quotient(x,X0,zero) ),
inference(resolution,[status(thm)],[d3,c7]) ).
cnf(d5,plain,
( 'less$uequal'(X1,zQx)
| ~ quotient(z,X0,X1)
| ~ quotient(x,X0,zero) ),
inference(resolution,[status(thm)],[d4,d1]) ).
cnf(d6,plain,
( 'less$uequal'(zQy,zQx)
| ~ quotient(x,y,zero) ),
inference(resolution,[status(thm)],[d5,c6]) ).
cnf(d7,plain,
~ quotient(x,y,zero),
inference(resolution,[status(thm)],[c8,d6]) ).
cnf(d8,plain,
( ~ quotient(X1,X2,X0)
| X0 = divide(X1,X2) ),
inference(resolution,[status(thm)],[c17,c16]) ).
cnf(d9,plain,
( ~ 'less$uequal'(X0,X1)
| zero = divide(X0,X1) ),
inference(resolution,[status(thm)],[d8,c9]) ).
cnf(d10,plain,
zero = divide(x,y),
inference(resolution,[status(thm)],[d9,c5]) ).
cnf(d11,plain,
quotient(x,y,zero),
inference(superposition,[status(thm)],[d10,c16]) ).
cnf(d12,plain,
$false,
inference(resolution,[status(thm)],[d11,d7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN007-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/15.38 % Computer : n013.cluster.edu
% 0.10/15.38 % Model : x86_64 x86_64
% 0.10/15.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/15.38 % Memory : 8046.5625MB
% 0.10/15.38 % OS : Linux 6.8.0-71-generic
% 0.10/15.38 % CPULimit : 300
% 0.10/15.38 % WCLimit : 300
% 0.10/15.38 % DateTime : Fri Sep 25 15:56:52 UTC 2026
% 0.10/15.39 % CPUTime :
% 0.10/15.39 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.79/17.50 % SZS status Unsatisfiable for theBenchmark.p
% 14.79/17.50 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------