%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : HEN010-2 : 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 : 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 07:31:49 AM UTC 2026
% Result : Unsatisfiable 43.37s 7.80s
% Output : CNFRefutation 43.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of clauses : 61 ( 30 unt; 0 nHn; 50 RR)
% Number of literals : 118 ( 17 equ; 60 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 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(x_divide_x_is_zero,axiom,
quotient(X0,X0,zero) ).
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$uequal'(X0,X1) ) ).
cnf(xQyLEz_implies_xQzLEy,axiom,
( 'less$uequal'(X4,X1)
| ~ quotient(X0,X3,X4)
| ~ 'less$uequal'(X2,X3)
| ~ quotient(X0,X1,X2) ) ).
cnf(identity_divide_a,hypothesis,
quotient(identity,a,idQa) ).
cnf(identity_divide_idQa,hypothesis,
quotient(identity,idQa,'idQ$uidQa') ).
cnf(identity_divide_idQ_idQa,hypothesis,
quotient(idQa,'idQ$uidQa','idQa$uQ$u$uidQ$uidQa') ).
cnf(prove_idQa_equals_idQa_Q__idQ_idQa,negated_conjecture,
idQa != 'idQa$uQ$u$uidQ$uidQa' ).
cnf(less_equal_quotient,axiom,
( 'less$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(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(c2,plain,
quotient(X0,X0,zero),
inference(clausification,[status(esa)],[x_divide_x_is_zero]) ).
cnf(c3,plain,
quotient(X0,zero,X0),
inference(clausification,[status(esa)],[x_divde_zero_is_x]) ).
cnf(c4,plain,
( 'less$uequal'(X2,X1)
| ~ 'less$uequal'(X2,X0)
| ~ 'less$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[transitivity_of_less_equal]) ).
cnf(c5,plain,
( 'less$uequal'(X2,X3)
| ~ 'less$uequal'(X4,X1)
| ~ quotient(X0,X3,X4)
| ~ quotient(X0,X1,X2) ),
inference(clausification,[status(esa)],[xQyLEz_implies_xQzLEy]) ).
cnf(c9,plain,
quotient(identity,a,idQa),
inference(clausification,[status(esa)],[identity_divide_a]) ).
cnf(c10,plain,
quotient(identity,idQa,'idQ$uidQa'),
inference(clausification,[status(esa)],[identity_divide_idQa]) ).
cnf(c11,plain,
quotient(idQa,'idQ$uidQa','idQa$uQ$u$uidQ$uidQa'),
inference(clausification,[status(esa)],[identity_divide_idQ_idQa]) ).
cnf(c12,plain,
'idQa$uQ$u$uidQ$uidQa' != idQa,
inference(clausification,[status(esa)],[prove_idQa_equals_idQa_Q__idQ_idQa]) ).
cnf(c14,plain,
( 'less$uequal'(X0,X1)
| ~ quotient(X0,X1,zero) ),
inference(clausification,[status(esa)],[less_equal_quotient]) ).
cnf(c15,plain,
( 'less$uequal'(X2,X0)
| ~ quotient(X0,X1,X2) ),
inference(clausification,[status(esa)],[divisor_existence]) ).
cnf(c16,plain,
( ~ quotient(X1,X3,X7)
| ~ quotient(X0,X3,X6)
| ~ quotient(X6,X7,X5)
| 'less$uequal'(X5,X4)
| ~ quotient(X2,X3,X4)
| ~ quotient(X0,X1,X2) ),
inference(clausification,[status(esa)],[quotient_property]) ).
cnf(c18,plain,
( X0 = X1
| ~ 'less$uequal'(X1,X0)
| ~ 'less$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[less_equal_and_equal]) ).
cnf(c20,plain,
quotient(X0,X1,divide(X0,X1)),
inference(clausification,[status(esa)],[closure]) ).
cnf(c21,plain,
( X2 = X3
| ~ quotient(X0,X1,X3)
| ~ quotient(X0,X1,X2) ),
inference(clausification,[status(esa)],[well_defined]) ).
cnf(d0,plain,
'less$uequal'('idQa$uQ$u$uidQ$uidQa',idQa),
inference(resolution,[status(thm)],[c15,c11]) ).
cnf(d1,plain,
( ~ 'less$uequal'(idQa,'idQa$uQ$u$uidQ$uidQa')
| idQa = 'idQa$uQ$u$uidQ$uidQa' ),
inference(resolution,[status(thm)],[c18,d0]) ).
cnf(d2,plain,
( ~ 'less$uequal'(divide(X0,X3),X1)
| 'less$uequal'(X2,X3)
| ~ quotient(X0,X1,X2) ),
inference(resolution,[status(thm)],[c5,c20]) ).
cnf(d3,plain,
( ~ 'less$uequal'(idQa,X0)
| 'less$uequal'(X1,a)
| ~ quotient(identity,X0,X1) ),
inference(resolution,[status(thm)],[c5,c9]) ).
cnf(d4,plain,
( ~ 'less$uequal'(idQa,idQa)
| 'less$uequal'('idQ$uidQa',a) ),
inference(resolution,[status(thm)],[d3,c10]) ).
cnf(d5,plain,
'less$uequal'(X0,X0),
inference(resolution,[status(thm)],[c14,c2]) ).
cnf(d6,plain,
'less$uequal'('idQ$uidQa',a),
inference(resolution,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
( ~ 'less$uequal'(X0,'idQ$uidQa')
| 'less$uequal'(X0,a) ),
inference(resolution,[status(thm)],[d6,c4]) ).
cnf(d8,plain,
( 'less$uequal'(X2,X1)
| ~ quotient(X0,divide(X0,X1),X2) ),
inference(resolution,[status(thm)],[d2,d5]) ).
cnf(d9,plain,
'less$uequal'(divide(X0,divide(X0,X1)),X1),
inference(resolution,[status(thm)],[d8,c20]) ).
cnf(d10,plain,
( ~ quotient(idQa,'idQ$uidQa',X0)
| 'idQa$uQ$u$uidQ$uidQa' = X0 ),
inference(resolution,[status(thm)],[c21,c11]) ).
cnf(d11,plain,
'idQa$uQ$u$uidQ$uidQa' = divide(idQa,'idQ$uidQa'),
inference(resolution,[status(thm)],[d10,c20]) ).
cnf(d12,plain,
'less$uequal'(divide(idQa,'idQa$uQ$u$uidQ$uidQa'),'idQ$uidQa'),
inference(superposition,[status(thm)],[d11,d9]) ).
cnf(d13,plain,
'less$uequal'(divide(idQa,'idQa$uQ$u$uidQ$uidQa'),a),
inference(resolution,[status(thm)],[d12,d7]) ).
cnf(d14,plain,
( 'less$uequal'(X0,'idQa$uQ$u$uidQ$uidQa')
| ~ quotient(idQa,a,X0) ),
inference(resolution,[status(thm)],[d13,d2]) ).
cnf(d15,plain,
'less$uequal'(divide(idQa,a),'idQa$uQ$u$uidQ$uidQa'),
inference(resolution,[status(thm)],[d14,c20]) ).
cnf(d16,plain,
( ~ 'less$uequal'(X0,divide(idQa,a))
| 'less$uequal'(X0,'idQa$uQ$u$uidQ$uidQa') ),
inference(resolution,[status(thm)],[d15,c4]) ).
cnf(d17,plain,
( 'less$uequal'(X4,X5)
| ~ quotient(X3,X1,X5)
| ~ quotient(X2,zero,X4)
| ~ quotient(X0,X1,X3)
| ~ quotient(X0,X1,X2) ),
inference(resolution,[status(thm)],[c16,c2]) ).
cnf(d18,plain,
( 'less$uequal'(X2,X1)
| ~ quotient(identity,a,X0)
| ~ quotient(idQa,zero,X2)
| ~ quotient(X0,a,X1) ),
inference(resolution,[status(thm)],[d17,c9]) ).
cnf(d19,plain,
( 'less$uequal'(idQa,X1)
| ~ quotient(identity,a,X0)
| ~ quotient(X0,a,X1) ),
inference(resolution,[status(thm)],[d18,c3]) ).
cnf(d20,plain,
( 'less$uequal'(idQa,X0)
| ~ quotient(idQa,a,X0) ),
inference(resolution,[status(thm)],[d19,c9]) ).
cnf(d21,plain,
'less$uequal'(idQa,divide(idQa,a)),
inference(resolution,[status(thm)],[d20,c20]) ).
cnf(d22,plain,
'less$uequal'(idQa,'idQa$uQ$u$uidQ$uidQa'),
inference(resolution,[status(thm)],[d21,d16]) ).
cnf(d23,plain,
idQa = 'idQa$uQ$u$uidQ$uidQa',
inference(resolution,[status(thm)],[d22,d1]) ).
cnf(d24,plain,
idQa != idQa,
inference(demodulation,[status(thm)],[c12,d23]) ).
cnf(d25,plain,
( ~ quotient(X0,zero,X1)
| X0 = X1 ),
inference(resolution,[status(thm)],[c21,c3]) ).
cnf(d26,plain,
X0 = divide(X0,zero),
inference(resolution,[status(thm)],[d25,c20]) ).
cnf(d27,plain,
'less$uequal'(divide(X0,X1),X0),
inference(resolution,[status(thm)],[c15,c20]) ).
cnf(d28,plain,
( ~ 'less$uequal'(X0,divide(X0,X1))
| X0 = divide(X0,X1) ),
inference(resolution,[status(thm)],[c18,d27]) ).
cnf(d29,plain,
( X0 = divide(X0,zero)
| ~ 'less$uequal'(X0,X0) ),
inference(superposition,[status(thm)],[d26,d28]) ).
cnf(d30,plain,
( ~ 'less$uequal'(X0,X0)
| X0 = X0 ),
inference(demodulation,[status(thm)],[d29,d26]) ).
cnf(d31,plain,
X0 = X0,
inference(resolution,[status(thm)],[d5,d30]) ).
cnf(d32,plain,
$false,
inference(resolution,[status(thm)],[d31,d24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : HEN010-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.41 % Computer : n009.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Fri Sep 25 15:57:43 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 43.37/7.80 % SZS status Unsatisfiable for theBenchmark.p
% 43.37/7.80 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------