%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : HEN006-1 : 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 : n009.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 16.01s 4.47s
% Output : CNFRefutation 16.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 12
% Syntax : Number of clauses : 55 ( 30 unt; 0 nHn; 46 RR)
% Number of literals : 108 ( 15 equ; 55 neg)
% Maximal clause size : 6 ( 1 avg)
% Maximal term depth : 3 ( 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 : 100 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(xQy,hypothesis,
quotient(x,y,xQy) ).
cnf(xQyLEz,hypothesis,
'less$uequal'(xQy,z) ).
cnf(xQz,hypothesis,
quotient(x,z,xQz) ).
cnf(prove_xQzLEy,negated_conjecture,
~ 'less$uequal'(xQz,y) ).
cnf(quotient_less_equal,axiom,
( quotient(X0,X1,zero)
| ~ 'less$uequal'(X0,X1) ) ).
cnf(less_equal_quotient,axiom,
( 'less$uequal'(X0,X1)
| ~ quotient(X0,X1,zero) ) ).
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(zero_is_smallest,axiom,
'less$uequal'(zero,X0) ).
cnf(less_equal_and_equal,axiom,
( X0 = X1
| ~ 'less$uequal'(X1,X0)
| ~ 'less$uequal'(X0,X1) ) ).
cnf(closure,axiom,
quotient(X0,X1,divide(X0,X1)) ).
cnf(well_defined,axiom,
( X2 = X3
| ~ quotient(X0,X1,X3)
| ~ quotient(X0,X1,X2) ) ).
cnf(c0,plain,
quotient(x,y,xQy),
inference(clausification,[status(esa)],[xQy]) ).
cnf(c1,plain,
'less$uequal'(xQy,z),
inference(clausification,[status(esa)],[xQyLEz]) ).
cnf(c2,plain,
quotient(x,z,xQz),
inference(clausification,[status(esa)],[xQz]) ).
cnf(c3,plain,
~ 'less$uequal'(xQz,y),
inference(clausification,[status(esa)],[prove_xQzLEy]) ).
cnf(c4,plain,
( quotient(X0,X1,zero)
| ~ 'less$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[quotient_less_equal]) ).
cnf(c5,plain,
( 'less$uequal'(X0,X1)
| ~ quotient(X0,X1,zero) ),
inference(clausification,[status(esa)],[less_equal_quotient]) ).
cnf(c6,plain,
( 'less$uequal'(X2,X0)
| ~ quotient(X0,X1,X2) ),
inference(clausification,[status(esa)],[divisor_existence]) ).
cnf(c7,plain,
( ~ quotient(X7,X5,X3)
| ~ quotient(X6,X5,X2)
| ~ quotient(X6,X7,X4)
| ~ quotient(X4,X5,X1)
| ~ quotient(X2,X3,X0)
| 'less$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[quotient_property]) ).
cnf(c8,plain,
'less$uequal'(zero,X0),
inference(clausification,[status(esa)],[zero_is_smallest]) ).
cnf(c9,plain,
( X0 = X1
| ~ 'less$uequal'(X1,X0)
| ~ 'less$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[less_equal_and_equal]) ).
cnf(c11,plain,
quotient(X0,X1,divide(X0,X1)),
inference(clausification,[status(esa)],[closure]) ).
cnf(c12,plain,
( X2 = X3
| ~ quotient(X0,X1,X3)
| ~ quotient(X0,X1,X2) ),
inference(clausification,[status(esa)],[well_defined]) ).
cnf(d0,plain,
( ~ 'less$uequal'(X0,zero)
| X0 = zero ),
inference(resolution,[status(thm)],[c9,c8]) ).
cnf(d1,plain,
( 'less$uequal'(X4,X3)
| ~ quotient(x,X0,X2)
| ~ quotient(xQz,X1,X4)
| ~ quotient(X2,z,X3)
| ~ quotient(X0,z,X1) ),
inference(resolution,[status(thm)],[c7,c2]) ).
cnf(d2,plain,
( 'less$uequal'(divide(xQz,X3),X1)
| ~ quotient(x,X2,X0)
| ~ quotient(X2,z,X3)
| ~ quotient(X0,z,X1) ),
inference(resolution,[status(thm)],[d1,c11]) ).
cnf(d3,plain,
( 'less$uequal'(divide(xQz,X0),X1)
| ~ quotient(xQy,z,X1)
| ~ quotient(y,z,X0) ),
inference(resolution,[status(thm)],[d2,c0]) ).
cnf(d4,plain,
( divide(xQz,X0) = zero
| ~ quotient(xQy,z,zero)
| ~ quotient(y,z,X0) ),
inference(resolution,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
( ~ 'less$uequal'(X1,X2)
| ~ quotient(X1,X2,X0)
| X0 = zero ),
inference(resolution,[status(thm)],[c12,c4]) ).
cnf(d6,plain,
( ~ 'less$uequal'(X0,X1)
| divide(X0,X1) = zero ),
inference(resolution,[status(thm)],[d5,c11]) ).
cnf(d7,plain,
divide(xQy,z) = zero,
inference(resolution,[status(thm)],[d6,c1]) ).
cnf(d8,plain,
quotient(xQy,z,zero),
inference(superposition,[status(thm)],[d7,c11]) ).
cnf(d9,plain,
( ~ quotient(y,z,X0)
| divide(xQz,X0) = zero ),
inference(resolution,[status(thm)],[d8,d4]) ).
cnf(d10,plain,
divide(xQz,divide(y,z)) = zero,
inference(resolution,[status(thm)],[d9,c11]) ).
cnf(d11,plain,
quotient(xQz,divide(y,z),zero),
inference(superposition,[status(thm)],[d10,c11]) ).
cnf(d12,plain,
'less$uequal'(xQz,divide(y,z)),
inference(resolution,[status(thm)],[d11,c5]) ).
cnf(d13,plain,
'less$uequal'(divide(X0,X1),X0),
inference(resolution,[status(thm)],[c6,c11]) ).
cnf(d14,plain,
divide(zero,X0) = zero,
inference(resolution,[status(thm)],[d0,d13]) ).
cnf(d15,plain,
quotient(zero,X0,zero),
inference(superposition,[status(thm)],[d14,c11]) ).
cnf(d16,plain,
( 'less$uequal'(X6,X4)
| ~ quotient(X5,X0,X3)
| ~ quotient(divide(X5,X1),X2,X6)
| ~ quotient(X3,X1,X4)
| ~ quotient(X0,X1,X2) ),
inference(resolution,[status(thm)],[c7,c11]) ).
cnf(d17,plain,
( 'less$uequal'(divide(divide(X0,X3),X5),X4)
| ~ quotient(X1,X3,X5)
| ~ quotient(X2,X3,X4)
| ~ quotient(X0,X1,X2) ),
inference(resolution,[status(thm)],[d16,c11]) ).
cnf(d18,plain,
( ~ 'less$uequal'(X4,X2)
| 'less$uequal'(divide(divide(X4,X0),X3),X1)
| ~ quotient(X2,X0,X3)
| ~ quotient(zero,X0,X1) ),
inference(resolution,[status(thm)],[d17,c4]) ).
cnf(d19,plain,
( 'less$uequal'(divide(divide(X3,X1),X2),zero)
| ~ 'less$uequal'(X3,X0)
| ~ quotient(X0,X1,X2) ),
inference(resolution,[status(thm)],[d18,d15]) ).
cnf(d20,plain,
divide(divide(X0,X1),X0) = zero,
inference(resolution,[status(thm)],[d6,d13]) ).
cnf(d21,plain,
quotient(divide(X0,X1),X0,zero),
inference(superposition,[status(thm)],[d20,c11]) ).
cnf(d22,plain,
( 'less$uequal'(divide(divide(X0,X1),zero),zero)
| ~ 'less$uequal'(X0,divide(X1,X2)) ),
inference(resolution,[status(thm)],[d21,d19]) ).
cnf(d23,plain,
'less$uequal'(divide(divide(xQz,y),zero),zero),
inference(resolution,[status(thm)],[d22,d12]) ).
cnf(d24,plain,
divide(divide(xQz,y),zero) = zero,
inference(resolution,[status(thm)],[d23,d0]) ).
cnf(d25,plain,
quotient(divide(xQz,y),zero,zero),
inference(superposition,[status(thm)],[d24,c11]) ).
cnf(d26,plain,
'less$uequal'(divide(xQz,y),zero),
inference(resolution,[status(thm)],[d25,c5]) ).
cnf(d27,plain,
divide(xQz,y) = zero,
inference(resolution,[status(thm)],[d26,d0]) ).
cnf(d28,plain,
quotient(xQz,y,zero),
inference(superposition,[status(thm)],[d27,c11]) ).
cnf(d29,plain,
'less$uequal'(xQz,y),
inference(resolution,[status(thm)],[d28,c5]) ).
cnf(d30,plain,
$false,
inference(resolution,[status(thm)],[c3,d29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : HEN006-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n009.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Fri Sep 25 15:56:44 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.01/4.47 % SZS status Unsatisfiable for theBenchmark.p
% 16.01/4.47 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------