%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : HEN009-1 : 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 : n015.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 07:31:48 AM UTC 2026
% Result : Unsatisfiable 26.93s 7.21s
% Output : CNFRefutation 26.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 13
% Syntax : Number of clauses : 117 ( 70 unt; 0 nHn; 82 RR)
% Number of literals : 209 ( 40 equ; 95 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 : 181 ( 22 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(identity_divide_a,hypothesis,
quotient(identity,a,idQa) ).
cnf(identity_divide_idQa,hypothesis,
quotient(identity,idQa,'idQ$uidQa') ).
cnf(identity_divide_idQ_idQa,hypothesis,
quotient(identity,'idQ$uidQa','idQ$u$uidQ$uidQa') ).
cnf(prove_one_inversion_equals_three,negated_conjecture,
idQa != 'idQ$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$uidQa'),
inference(clausification,[status(esa)],[identity_divide_idQa]) ).
cnf(c2,plain,
quotient(identity,'idQ$uidQa','idQ$u$uidQ$uidQa'),
inference(clausification,[status(esa)],[identity_divide_idQ_idQa]) ).
cnf(c3,plain,
idQa != 'idQ$u$uidQ$uidQa',
inference(clausification,[status(esa)],[prove_one_inversion_equals_three]) ).
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$uequal'(divide(divide(X0,X2),X4),X3)
| ~ quotient(X1,X2,X4)
| ~ quotient(divide(X0,X1),X2,X3) ),
inference(resolution,[status(thm)],[d3,c11]) ).
cnf(d19,plain,
( 'less$uequal'(divide(divide(X3,X1),X2),divide(divide(X3,X0),X1))
| ~ quotient(X0,X1,X2) ),
inference(resolution,[status(thm)],[d18,c11]) ).
cnf(d20,plain,
divide(divide(X0,X1),X0) = zero,
inference(resolution,[status(thm)],[d5,d0]) ).
cnf(d21,plain,
quotient(divide(X0,X1),X0,zero),
inference(superposition,[status(thm)],[d20,c11]) ).
cnf(d22,plain,
( 'less$uequal'(divide(divide(X1,X1),X2),zero)
| ~ quotient(X0,X1,X2) ),
inference(resolution,[status(thm)],[d21,d18]) ).
cnf(d23,plain,
'less$uequal'(divide(divide(X0,X0),zero),zero),
inference(resolution,[status(thm)],[d22,d11]) ).
cnf(d24,plain,
divide(divide(X0,X0),zero) = zero,
inference(resolution,[status(thm)],[d23,d1]) ).
cnf(d25,plain,
quotient(divide(X0,X0),zero,zero),
inference(superposition,[status(thm)],[d24,c11]) ).
cnf(d26,plain,
'less$uequal'(divide(X0,X0),zero),
inference(resolution,[status(thm)],[d25,c5]) ).
cnf(d27,plain,
divide(X0,X0) = zero,
inference(resolution,[status(thm)],[d26,d1]) ).
cnf(d28,plain,
( ~ quotient(X1,divide(X0,X1),X2)
| 'less$uequal'(divide(divide(X0,divide(X0,X1)),X2),zero) ),
inference(superposition,[status(thm)],[d27,d19]) ).
cnf(d29,plain,
'less$uequal'(divide(divide(X0,divide(X0,zero)),zero),zero),
inference(resolution,[status(thm)],[d28,d11]) ).
cnf(d30,plain,
divide(divide(X0,divide(X0,zero)),zero) = zero,
inference(resolution,[status(thm)],[d29,d1]) ).
cnf(d31,plain,
quotient(divide(X0,divide(X0,zero)),zero,zero),
inference(superposition,[status(thm)],[d30,c11]) ).
cnf(d32,plain,
'less$uequal'(divide(X0,divide(X0,zero)),zero),
inference(resolution,[status(thm)],[d31,c5]) ).
cnf(d33,plain,
divide(X0,divide(X0,zero)) = zero,
inference(resolution,[status(thm)],[d32,d1]) ).
cnf(d34,plain,
quotient(X0,divide(X0,zero),zero),
inference(superposition,[status(thm)],[d33,c11]) ).
cnf(d35,plain,
'less$uequal'(X0,divide(X0,zero)),
inference(resolution,[status(thm)],[d34,c5]) ).
cnf(d36,plain,
X0 = divide(X0,zero),
inference(resolution,[status(thm)],[d35,d17]) ).
cnf(d37,plain,
( ~ 'less$uequal'(X4,X2)
| 'less$uequal'(divide(divide(X4,X0),X3),X1)
| ~ quotient(X2,X0,X3)
| ~ quotient(zero,X0,X1) ),
inference(resolution,[status(thm)],[d3,c4]) ).
cnf(d38,plain,
( 'less$uequal'(divide(divide(X3,X1),X2),zero)
| ~ 'less$uequal'(X3,X0)
| ~ quotient(X0,X1,X2) ),
inference(resolution,[status(thm)],[d37,d11]) ).
cnf(d39,plain,
( 'less$uequal'(divide(divide(X0,X1),zero),zero)
| ~ 'less$uequal'(X0,divide(X1,X2)) ),
inference(resolution,[status(thm)],[d38,d21]) ).
cnf(d40,plain,
( 'less$uequal'(X4,X3)
| ~ quotient(identity,X0,X2)
| ~ quotient('idQ$uidQa',X1,X4)
| ~ quotient(X2,idQa,X3)
| ~ quotient(X0,idQa,X1) ),
inference(resolution,[status(thm)],[c7,c1]) ).
cnf(d41,plain,
( 'less$uequal'(divide('idQ$uidQa',X3),X1)
| ~ quotient(identity,X2,X0)
| ~ quotient(X2,idQa,X3)
| ~ quotient(X0,idQa,X1) ),
inference(resolution,[status(thm)],[d40,c11]) ).
cnf(d42,plain,
( 'less$uequal'(divide('idQ$uidQa',X0),X1)
| ~ quotient(idQa,idQa,X1)
| ~ quotient(a,idQa,X0) ),
inference(resolution,[status(thm)],[d41,c0]) ).
cnf(d43,plain,
( divide('idQ$uidQa',X0) = zero
| ~ quotient(idQa,idQa,zero)
| ~ quotient(a,idQa,X0) ),
inference(resolution,[status(thm)],[d42,d1]) ).
cnf(d44,plain,
quotient(X0,X0,zero),
inference(superposition,[status(thm)],[d27,c11]) ).
cnf(d45,plain,
( ~ quotient(a,idQa,X0)
| divide('idQ$uidQa',X0) = zero ),
inference(resolution,[status(thm)],[d44,d43]) ).
cnf(d46,plain,
divide('idQ$uidQa',divide(a,idQa)) = zero,
inference(resolution,[status(thm)],[d45,c11]) ).
cnf(d47,plain,
quotient('idQ$uidQa',divide(a,idQa),zero),
inference(superposition,[status(thm)],[d46,c11]) ).
cnf(d48,plain,
'less$uequal'('idQ$uidQa',divide(a,idQa)),
inference(resolution,[status(thm)],[d47,c5]) ).
cnf(d49,plain,
'less$uequal'(divide(divide('idQ$uidQa',a),zero),zero),
inference(resolution,[status(thm)],[d48,d39]) ).
cnf(d50,plain,
divide(divide('idQ$uidQa',a),zero) = zero,
inference(resolution,[status(thm)],[d49,d1]) ).
cnf(d51,plain,
quotient(divide('idQ$uidQa',a),zero,zero),
inference(superposition,[status(thm)],[d50,c11]) ).
cnf(d52,plain,
'less$uequal'(divide('idQ$uidQa',a),zero),
inference(resolution,[status(thm)],[d51,c5]) ).
cnf(d53,plain,
divide('idQ$uidQa',a) = zero,
inference(resolution,[status(thm)],[d52,d1]) ).
cnf(d54,plain,
quotient('idQ$uidQa',a,zero),
inference(superposition,[status(thm)],[d53,c11]) ).
cnf(d55,plain,
( 'less$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(d56,plain,
( 'less$uequal'(divide(idQa,X3),X1)
| ~ quotient(identity,X2,X0)
| ~ quotient(X2,a,X3)
| ~ quotient(X0,a,X1) ),
inference(resolution,[status(thm)],[d55,c11]) ).
cnf(d57,plain,
( 'less$uequal'(divide(idQa,X0),X1)
| ~ quotient('idQ$u$uidQ$uidQa',a,X1)
| ~ quotient('idQ$uidQa',a,X0) ),
inference(resolution,[status(thm)],[d56,c2]) ).
cnf(d58,plain,
( divide(divide(idQa,X0),X1) = zero
| ~ quotient('idQ$u$uidQ$uidQa',a,X1)
| ~ quotient('idQ$uidQa',a,X0) ),
inference(resolution,[status(thm)],[d57,d5]) ).
cnf(d59,plain,
( ~ quotient('idQ$uidQa',a,X0)
| divide(divide(idQa,X0),divide('idQ$u$uidQ$uidQa',a)) = zero ),
inference(resolution,[status(thm)],[d58,c11]) ).
cnf(d60,plain,
divide(divide(idQa,zero),divide('idQ$u$uidQ$uidQa',a)) = zero,
inference(resolution,[status(thm)],[d59,d54]) ).
cnf(d61,plain,
quotient(divide(idQa,zero),divide('idQ$u$uidQ$uidQa',a),zero),
inference(superposition,[status(thm)],[d60,c11]) ).
cnf(d62,plain,
'less$uequal'(divide(idQa,zero),divide('idQ$u$uidQ$uidQa',a)),
inference(resolution,[status(thm)],[d61,c5]) ).
cnf(d63,plain,
'less$uequal'(idQa,divide('idQ$u$uidQ$uidQa',a)),
inference(demodulation,[status(thm)],[d62,d36]) ).
cnf(d64,plain,
idQa = divide('idQ$u$uidQ$uidQa',a),
inference(resolution,[status(thm)],[d63,d16]) ).
cnf(d65,plain,
'less$uequal'(idQa,'idQ$u$uidQ$uidQa'),
inference(superposition,[status(thm)],[d64,d0]) ).
cnf(d66,plain,
( 'less$uequal'(X4,X3)
| ~ quotient(identity,X0,X2)
| ~ quotient('idQ$u$uidQ$uidQa',X1,X4)
| ~ quotient(X2,'idQ$uidQa',X3)
| ~ quotient(X0,'idQ$uidQa',X1) ),
inference(resolution,[status(thm)],[c7,c2]) ).
cnf(d67,plain,
( 'less$uequal'(divide('idQ$u$uidQ$uidQa',X3),X1)
| ~ quotient(identity,X2,X0)
| ~ quotient(X2,'idQ$uidQa',X3)
| ~ quotient(X0,'idQ$uidQa',X1) ),
inference(resolution,[status(thm)],[d66,c11]) ).
cnf(d68,plain,
( 'less$uequal'(divide('idQ$u$uidQ$uidQa',X0),X1)
| ~ quotient('idQ$uidQa','idQ$uidQa',X1)
| ~ quotient(idQa,'idQ$uidQa',X0) ),
inference(resolution,[status(thm)],[d67,c1]) ).
cnf(d69,plain,
( divide('idQ$u$uidQ$uidQa',X0) = zero
| ~ quotient('idQ$uidQa','idQ$uidQa',zero)
| ~ quotient(idQa,'idQ$uidQa',X0) ),
inference(resolution,[status(thm)],[d68,d1]) ).
cnf(d70,plain,
( 'less$uequal'(divide(divide(X0,idQa),'idQ$uidQa'),zero)
| ~ 'less$uequal'(X0,identity) ),
inference(resolution,[status(thm)],[d38,c1]) ).
cnf(d71,plain,
'less$uequal'(divide(divide(X0,idQa),'idQ$uidQa'),zero),
inference(resolution,[status(thm)],[c10,d70]) ).
cnf(d72,plain,
( ~ quotient(X1,X2,X0)
| X0 = divide(X1,X2) ),
inference(resolution,[status(thm)],[c12,c11]) ).
cnf(d73,plain,
'idQ$uidQa' = divide(identity,idQa),
inference(resolution,[status(thm)],[d72,c1]) ).
cnf(d74,plain,
'less$uequal'(divide('idQ$uidQa','idQ$uidQa'),zero),
inference(superposition,[status(thm)],[d73,d71]) ).
cnf(d75,plain,
divide('idQ$uidQa','idQ$uidQa') = zero,
inference(resolution,[status(thm)],[d74,d1]) ).
cnf(d76,plain,
quotient('idQ$uidQa','idQ$uidQa',zero),
inference(superposition,[status(thm)],[d75,c11]) ).
cnf(d77,plain,
( ~ quotient(idQa,'idQ$uidQa',X0)
| divide('idQ$u$uidQ$uidQa',X0) = zero ),
inference(resolution,[status(thm)],[d76,d69]) ).
cnf(d78,plain,
divide('idQ$u$uidQ$uidQa',divide(idQa,'idQ$uidQa')) = zero,
inference(resolution,[status(thm)],[d77,c11]) ).
cnf(d79,plain,
quotient('idQ$u$uidQ$uidQa',divide(idQa,'idQ$uidQa'),zero),
inference(superposition,[status(thm)],[d78,c11]) ).
cnf(d80,plain,
'less$uequal'('idQ$u$uidQ$uidQa',divide(idQa,'idQ$uidQa')),
inference(resolution,[status(thm)],[d79,c5]) ).
cnf(d81,plain,
'less$uequal'(divide(divide('idQ$u$uidQ$uidQa',idQa),zero),zero),
inference(resolution,[status(thm)],[d39,d80]) ).
cnf(d82,plain,
divide(divide('idQ$u$uidQ$uidQa',idQa),zero) = zero,
inference(resolution,[status(thm)],[d81,d1]) ).
cnf(d83,plain,
quotient(divide('idQ$u$uidQ$uidQa',idQa),zero,zero),
inference(superposition,[status(thm)],[d82,c11]) ).
cnf(d84,plain,
'less$uequal'(divide('idQ$u$uidQ$uidQa',idQa),zero),
inference(resolution,[status(thm)],[d83,c5]) ).
cnf(d85,plain,
divide('idQ$u$uidQ$uidQa',idQa) = zero,
inference(resolution,[status(thm)],[d84,d1]) ).
cnf(d86,plain,
quotient('idQ$u$uidQ$uidQa',idQa,zero),
inference(superposition,[status(thm)],[d85,c11]) ).
cnf(d87,plain,
'less$uequal'('idQ$u$uidQ$uidQa',idQa),
inference(resolution,[status(thm)],[d86,c5]) ).
cnf(d88,plain,
( ~ 'less$uequal'(idQa,'idQ$u$uidQ$uidQa')
| idQa = 'idQ$u$uidQ$uidQa' ),
inference(resolution,[status(thm)],[d87,c9]) ).
cnf(d89,plain,
~ 'less$uequal'(idQa,'idQ$u$uidQ$uidQa'),
inference(resolution,[status(thm)],[c3,d88]) ).
cnf(d90,plain,
$false,
inference(resolution,[status(thm)],[d89,d65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : HEN009-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.44 % Computer : n015.cluster.edu
% 0.16/0.44 % Model : x86_64 x86_64
% 0.16/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.44 % Memory : 8046.5625MB
% 0.16/0.44 % OS : Linux 6.8.0-71-generic
% 0.16/0.44 % CPULimit : 300
% 0.16/0.44 % WCLimit : 300
% 0.16/0.44 % DateTime : Fri Sep 25 16:00:44 UTC 2026
% 0.16/0.45 % CPUTime :
% 0.16/0.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 26.93/7.21 % SZS status Unsatisfiable for theBenchmark.p
% 26.93/7.21 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------