%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : HEN010-1 : 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 : n010.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 45.35s 6.96s
% Output : CNFRefutation 45.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 13
% Syntax : Number of clauses : 115 ( 64 unt; 0 nHn; 81 RR)
% Number of literals : 214 ( 46 equ; 102 neg)
% Maximal clause size : 6 ( 1 avg)
% Maximal term depth : 4 ( 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 : 190 ( 21 sgn)
% Comments :
%------------------------------------------------------------------------------
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(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$uequal'(X0,X1) ) ).
cnf(identity_is_largest,axiom,
'less$uequal'(X0,identity) ).
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(identity,a,idQa),
inference(clausification,[status(esa)],[identity_divide_a]) ).
cnf(c1,plain,
quotient(identity,idQa,'idQ$uidQa'),
inference(clausification,[status(esa)],[identity_divide_idQa]) ).
cnf(c2,plain,
quotient(idQa,'idQ$uidQa','idQa$uQ$u$uidQ$uidQa'),
inference(clausification,[status(esa)],[identity_divide_idQ_idQa]) ).
cnf(c3,plain,
idQa != 'idQa$uQ$u$uidQ$uidQa',
inference(clausification,[status(esa)],[prove_idQa_equals_idQa_Q__idQ_idQa]) ).
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$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[less_equal_and_equal]) ).
cnf(c10,plain,
'less$uequal'(X0,identity),
inference(clausification,[status(esa)],[identity_is_largest]) ).
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$uequal'(divide(X0,X1),X0),
inference(resolution,[status(thm)],[c6,c11]) ).
cnf(d1,plain,
( ~ 'less$uequal'(X0,zero)
| X0 = zero ),
inference(resolution,[status(thm)],[c9,c8]) ).
cnf(d2,plain,
( 'less$uequal'(X6,X4)
| ~ quotient(X5,X0,X3)
| ~ quotient(divide(X5,X1),X2,X6)
| ~ quotient(X3,X1,X4)
| ~ quotient(X0,X1,X2) ),
inference(resolution,[status(thm)],[c7,c11]) ).
cnf(d3,plain,
( 'less$uequal'(divide(divide(X0,X3),X5),X4)
| ~ quotient(X1,X3,X5)
| ~ quotient(X2,X3,X4)
| ~ quotient(X0,X1,X2) ),
inference(resolution,[status(thm)],[d2,c11]) ).
cnf(d4,plain,
( ~ 'less$uequal'(X1,X2)
| ~ quotient(X1,X2,X0)
| X0 = zero ),
inference(resolution,[status(thm)],[c12,c4]) ).
cnf(d5,plain,
( ~ 'less$uequal'(X0,X1)
| divide(X0,X1) = zero ),
inference(resolution,[status(thm)],[d4,c11]) ).
cnf(d6,plain,
divide(X0,identity) = zero,
inference(resolution,[status(thm)],[d5,c10]) ).
cnf(d7,plain,
quotient(X0,identity,zero),
inference(superposition,[status(thm)],[d6,c11]) ).
cnf(d8,plain,
( 'less$uequal'(divide(divide(X3,X0),X2),X1)
| ~ quotient(identity,X0,X2)
| ~ quotient(zero,X0,X1) ),
inference(resolution,[status(thm)],[d7,d3]) ).
cnf(d9,plain,
( divide(divide(X2,X0),X1) = zero
| ~ quotient(zero,X0,zero)
| ~ quotient(identity,X0,X1) ),
inference(resolution,[status(thm)],[d8,d1]) ).
cnf(d10,plain,
divide(zero,X0) = zero,
inference(resolution,[status(thm)],[d1,d0]) ).
cnf(d11,plain,
quotient(zero,X0,zero),
inference(superposition,[status(thm)],[d10,c11]) ).
cnf(d12,plain,
( ~ quotient(identity,X1,X2)
| divide(divide(X0,X1),X2) = zero ),
inference(resolution,[status(thm)],[d11,d9]) ).
cnf(d13,plain,
divide(divide(X0,a),idQa) = zero,
inference(resolution,[status(thm)],[d12,c0]) ).
cnf(d14,plain,
quotient(divide(X0,a),idQa,zero),
inference(superposition,[status(thm)],[d13,c11]) ).
cnf(d15,plain,
'less$uequal'(divide(X0,a),idQa),
inference(resolution,[status(thm)],[d14,c5]) ).
cnf(d16,plain,
( ~ 'less$uequal'(idQa,divide(X0,a))
| idQa = divide(X0,a) ),
inference(resolution,[status(thm)],[d15,c9]) ).
cnf(d17,plain,
( ~ 'less$uequal'(X0,divide(X0,X1))
| X0 = divide(X0,X1) ),
inference(resolution,[status(thm)],[d0,c9]) ).
cnf(d18,plain,
( 'less$uequal'(X4,X3)
| ~ quotient(identity,X0,X2)
| ~ quotient(idQa,X1,X4)
| ~ quotient(X2,a,X3)
| ~ quotient(X0,a,X1) ),
inference(resolution,[status(thm)],[c7,c0]) ).
cnf(d19,plain,
( 'less$uequal'(divide(idQa,X3),X1)
| ~ quotient(identity,X2,X0)
| ~ quotient(X2,a,X3)
| ~ quotient(X0,a,X1) ),
inference(resolution,[status(thm)],[d18,c11]) ).
cnf(d20,plain,
( 'less$uequal'(divide(idQa,X0),X1)
| ~ quotient('idQ$uidQa',a,X1)
| ~ quotient(idQa,a,X0) ),
inference(resolution,[status(thm)],[d19,c1]) ).
cnf(d21,plain,
( ~ 'less$uequal'(X1,divide(idQa,X0))
| X1 = divide(idQa,X0)
| ~ quotient('idQ$uidQa',a,X1)
| ~ quotient(idQa,a,X0) ),
inference(resolution,[status(thm)],[d20,c9]) ).
cnf(d22,plain,
( ~ quotient('idQ$uidQa',a,zero)
| ~ quotient(idQa,a,X0)
| zero = divide(idQa,X0) ),
inference(resolution,[status(thm)],[d21,c8]) ).
cnf(d23,plain,
divide(divide(X0,X1),X0) = zero,
inference(resolution,[status(thm)],[d5,d0]) ).
cnf(d24,plain,
quotient(divide(X0,X1),X0,zero),
inference(superposition,[status(thm)],[d23,c11]) ).
cnf(d25,plain,
( ~ 'less$uequal'(X4,X2)
| 'less$uequal'(divide(divide(X4,X0),X3),X1)
| ~ quotient(X2,X0,X3)
| ~ quotient(zero,X0,X1) ),
inference(resolution,[status(thm)],[d3,c4]) ).
cnf(d26,plain,
( 'less$uequal'(divide(divide(X3,X1),X2),zero)
| ~ 'less$uequal'(X3,X0)
| ~ quotient(X0,X1,X2) ),
inference(resolution,[status(thm)],[d25,d11]) ).
cnf(d27,plain,
( 'less$uequal'(divide(divide(X0,X1),zero),zero)
| ~ 'less$uequal'(X0,divide(X1,X2)) ),
inference(resolution,[status(thm)],[d26,d24]) ).
cnf(d28,plain,
( 'less$uequal'(X4,X3)
| ~ quotient(identity,X0,X2)
| ~ quotient('idQ$uidQa',X1,X4)
| ~ quotient(X2,idQa,X3)
| ~ quotient(X0,idQa,X1) ),
inference(resolution,[status(thm)],[c7,c1]) ).
cnf(d29,plain,
( 'less$uequal'(divide('idQ$uidQa',X3),X1)
| ~ quotient(identity,X2,X0)
| ~ quotient(X2,idQa,X3)
| ~ quotient(X0,idQa,X1) ),
inference(resolution,[status(thm)],[d28,c11]) ).
cnf(d30,plain,
( 'less$uequal'(divide('idQ$uidQa',X0),X1)
| ~ quotient(idQa,idQa,X1)
| ~ quotient(a,idQa,X0) ),
inference(resolution,[status(thm)],[d29,c0]) ).
cnf(d31,plain,
( divide('idQ$uidQa',X0) = zero
| ~ quotient(idQa,idQa,zero)
| ~ quotient(a,idQa,X0) ),
inference(resolution,[status(thm)],[d30,d1]) ).
cnf(d32,plain,
( ~ 'less$uequal'(identity,X0)
| 'less$uequal'(divide(idQa,X1),X2)
| ~ quotient(zero,a,X2)
| ~ quotient(X0,a,X1) ),
inference(resolution,[status(thm)],[d19,c4]) ).
cnf(d33,plain,
( 'less$uequal'(divide(idQa,X1),zero)
| ~ 'less$uequal'(identity,X0)
| ~ quotient(X0,a,X1) ),
inference(resolution,[status(thm)],[d32,d11]) ).
cnf(d34,plain,
( 'less$uequal'(divide(idQa,idQa),zero)
| ~ 'less$uequal'(identity,identity) ),
inference(resolution,[status(thm)],[d33,c0]) ).
cnf(d35,plain,
'less$uequal'(divide(idQa,idQa),zero),
inference(resolution,[status(thm)],[c10,d34]) ).
cnf(d36,plain,
divide(idQa,idQa) = zero,
inference(resolution,[status(thm)],[d35,d1]) ).
cnf(d37,plain,
quotient(idQa,idQa,zero),
inference(superposition,[status(thm)],[d36,c11]) ).
cnf(d38,plain,
( ~ quotient(a,idQa,X0)
| divide('idQ$uidQa',X0) = zero ),
inference(resolution,[status(thm)],[d37,d31]) ).
cnf(d39,plain,
divide('idQ$uidQa',divide(a,idQa)) = zero,
inference(resolution,[status(thm)],[d38,c11]) ).
cnf(d40,plain,
quotient('idQ$uidQa',divide(a,idQa),zero),
inference(superposition,[status(thm)],[d39,c11]) ).
cnf(d41,plain,
'less$uequal'('idQ$uidQa',divide(a,idQa)),
inference(resolution,[status(thm)],[d40,c5]) ).
cnf(d42,plain,
'less$uequal'(divide(divide('idQ$uidQa',a),zero),zero),
inference(resolution,[status(thm)],[d41,d27]) ).
cnf(d43,plain,
divide(divide('idQ$uidQa',a),zero) = zero,
inference(resolution,[status(thm)],[d42,d1]) ).
cnf(d44,plain,
quotient(divide('idQ$uidQa',a),zero,zero),
inference(superposition,[status(thm)],[d43,c11]) ).
cnf(d45,plain,
'less$uequal'(divide('idQ$uidQa',a),zero),
inference(resolution,[status(thm)],[d44,c5]) ).
cnf(d46,plain,
divide('idQ$uidQa',a) = zero,
inference(resolution,[status(thm)],[d45,d1]) ).
cnf(d47,plain,
quotient('idQ$uidQa',a,zero),
inference(superposition,[status(thm)],[d46,c11]) ).
cnf(d48,plain,
( ~ quotient(idQa,a,X0)
| zero = divide(idQa,X0) ),
inference(resolution,[status(thm)],[d47,d22]) ).
cnf(d49,plain,
zero = divide(idQa,divide(idQa,a)),
inference(resolution,[status(thm)],[d48,c11]) ).
cnf(d50,plain,
quotient(idQa,divide(idQa,a),zero),
inference(superposition,[status(thm)],[d49,c11]) ).
cnf(d51,plain,
'less$uequal'(idQa,divide(idQa,a)),
inference(resolution,[status(thm)],[d50,c5]) ).
cnf(d52,plain,
idQa = divide(idQa,a),
inference(resolution,[status(thm)],[d51,d17]) ).
cnf(d53,plain,
( 'less$uequal'(divide(divide(X0,X2),X4),X3)
| ~ quotient(X1,X2,X4)
| ~ quotient(divide(X0,X1),X2,X3) ),
inference(resolution,[status(thm)],[d3,c11]) ).
cnf(d54,plain,
( 'less$uequal'(divide(divide(X1,X1),X2),zero)
| ~ quotient(X0,X1,X2) ),
inference(resolution,[status(thm)],[d24,d53]) ).
cnf(d55,plain,
'less$uequal'(divide(divide(X0,X0),zero),zero),
inference(resolution,[status(thm)],[d54,d11]) ).
cnf(d56,plain,
divide(divide(X0,X0),zero) = zero,
inference(resolution,[status(thm)],[d55,d1]) ).
cnf(d57,plain,
quotient(divide(X0,X0),zero,zero),
inference(superposition,[status(thm)],[d56,c11]) ).
cnf(d58,plain,
'less$uequal'(divide(X0,X0),zero),
inference(resolution,[status(thm)],[d57,c5]) ).
cnf(d59,plain,
divide(X0,X0) = zero,
inference(resolution,[status(thm)],[d58,d1]) ).
cnf(d60,plain,
( 'less$uequal'(divide(divide(X3,X1),X2),divide(divide(X3,X0),X1))
| ~ quotient(X0,X1,X2) ),
inference(resolution,[status(thm)],[d53,c11]) ).
cnf(d61,plain,
( ~ 'less$uequal'(divide(divide(X3,X0),X1),divide(divide(X3,X1),X2))
| divide(divide(X3,X0),X1) = divide(divide(X3,X1),X2)
| ~ quotient(X0,X1,X2) ),
inference(resolution,[status(thm)],[d60,c9]) ).
cnf(d62,plain,
( ~ quotient(X1,X2,X0)
| X0 = divide(X1,X2) ),
inference(resolution,[status(thm)],[c12,c11]) ).
cnf(d63,plain,
quotient(X0,X0,zero),
inference(superposition,[status(thm)],[d59,c11]) ).
cnf(d64,plain,
zero = divide(X0,X0),
inference(resolution,[status(thm)],[d63,d62]) ).
cnf(d65,plain,
( ~ quotient(X1,divide(X0,X1),X2)
| divide(divide(X0,X1),divide(X0,X1)) = divide(divide(X0,divide(X0,X1)),X2)
| ~ 'less$uequal'(zero,divide(divide(X0,divide(X0,X1)),X2)) ),
inference(superposition,[status(thm)],[d64,d61]) ).
cnf(d66,plain,
( ~ 'less$uequal'(zero,divide(divide(X0,divide(X0,X1)),X2))
| ~ quotient(X1,divide(X0,X1),X2)
| zero = divide(divide(X0,divide(X0,X1)),X2) ),
inference(demodulation,[status(thm)],[d65,d59]) ).
cnf(d67,plain,
( ~ quotient(X1,divide(X0,X1),X2)
| zero = divide(divide(X0,divide(X0,X1)),X2) ),
inference(resolution,[status(thm)],[c8,d66]) ).
cnf(d68,plain,
zero = divide(divide(X0,divide(X0,zero)),zero),
inference(resolution,[status(thm)],[d67,d11]) ).
cnf(d69,plain,
quotient(divide(X0,divide(X0,zero)),zero,zero),
inference(superposition,[status(thm)],[d68,c11]) ).
cnf(d70,plain,
'less$uequal'(divide(X0,divide(X0,zero)),zero),
inference(resolution,[status(thm)],[d69,c5]) ).
cnf(d71,plain,
divide(X0,divide(X0,zero)) = zero,
inference(resolution,[status(thm)],[d70,d1]) ).
cnf(d72,plain,
quotient(X0,divide(X0,zero),zero),
inference(superposition,[status(thm)],[d71,c11]) ).
cnf(d73,plain,
'less$uequal'(X0,divide(X0,zero)),
inference(resolution,[status(thm)],[d72,c5]) ).
cnf(d74,plain,
X0 = divide(X0,zero),
inference(resolution,[status(thm)],[d73,d17]) ).
cnf(d75,plain,
( 'less$uequal'(divide(divide(idQa,X0),X2),X1)
| ~ quotient('idQ$uidQa',X0,X2)
| ~ quotient('idQa$uQ$u$uidQ$uidQa',X0,X1) ),
inference(resolution,[status(thm)],[d3,c2]) ).
cnf(d76,plain,
( divide(divide(divide(idQa,X0),X1),X2) = zero
| ~ quotient('idQa$uQ$u$uidQ$uidQa',X0,X2)
| ~ quotient('idQ$uidQa',X0,X1) ),
inference(resolution,[status(thm)],[d75,d5]) ).
cnf(d77,plain,
( ~ quotient('idQ$uidQa',X0,X1)
| divide(divide(divide(idQa,X0),X1),divide('idQa$uQ$u$uidQ$uidQa',X0)) = zero ),
inference(resolution,[status(thm)],[d76,c11]) ).
cnf(d78,plain,
divide(divide(divide(idQa,a),zero),divide('idQa$uQ$u$uidQ$uidQa',a)) = zero,
inference(resolution,[status(thm)],[d47,d77]) ).
cnf(d79,plain,
divide(divide(idQa,a),divide('idQa$uQ$u$uidQ$uidQa',a)) = zero,
inference(demodulation,[status(thm)],[d78,d74]) ).
cnf(d80,plain,
divide(idQa,divide('idQa$uQ$u$uidQ$uidQa',a)) = zero,
inference(demodulation,[status(thm)],[d79,d52]) ).
cnf(d81,plain,
quotient(idQa,divide('idQa$uQ$u$uidQ$uidQa',a),zero),
inference(superposition,[status(thm)],[d80,c11]) ).
cnf(d82,plain,
'less$uequal'(idQa,divide('idQa$uQ$u$uidQ$uidQa',a)),
inference(resolution,[status(thm)],[d81,c5]) ).
cnf(d83,plain,
idQa = divide('idQa$uQ$u$uidQ$uidQa',a),
inference(resolution,[status(thm)],[d82,d16]) ).
cnf(d84,plain,
'less$uequal'(idQa,'idQa$uQ$u$uidQ$uidQa'),
inference(superposition,[status(thm)],[d83,d0]) ).
cnf(d85,plain,
'less$uequal'('idQa$uQ$u$uidQ$uidQa',idQa),
inference(resolution,[status(thm)],[c6,c2]) ).
cnf(d86,plain,
( ~ 'less$uequal'(idQa,'idQa$uQ$u$uidQ$uidQa')
| idQa = 'idQa$uQ$u$uidQ$uidQa' ),
inference(resolution,[status(thm)],[d85,c9]) ).
cnf(d87,plain,
~ 'less$uequal'(idQa,'idQa$uQ$u$uidQ$uidQa'),
inference(resolution,[status(thm)],[c3,d86]) ).
cnf(d88,plain,
$false,
inference(resolution,[status(thm)],[d87,d84]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : HEN010-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n010.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Fri Sep 25 15:57:59 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 45.35/6.96 % SZS status Unsatisfiable for theBenchmark.p
% 45.35/6.96 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------