%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : HEN007-3 : 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 : n002.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 31.74s 9.69s
% Output : CNFRefutation 31.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 8
% Syntax : Number of clauses : 70 ( 52 unt; 0 nHn; 21 RR)
% Number of literals : 90 ( 42 equ; 22 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 111 ( 14 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a_LE_b,hypothesis,
'less$uequal'(a,b) ).
cnf(prove_c_divide_b_LE_c_divide_a,negated_conjecture,
~ 'less$uequal'(divide(c,b),divide(c,a)) ).
cnf(quotient_less_equal1,axiom,
( divide(X0,X1) = zero
| ~ 'less$uequal'(X0,X1) ) ).
cnf(quotient_less_equal2,axiom,
( 'less$uequal'(X0,X1)
| divide(X0,X1) != zero ) ).
cnf(quotient_smaller_than_numerator,axiom,
'less$uequal'(divide(X0,X1),X0) ).
cnf(quotient_property,axiom,
'less$uequal'(divide(divide(X0,X1),divide(X2,X1)),divide(divide(X0,X2),X1)) ).
cnf(zero_is_smallest,axiom,
'less$uequal'(zero,X0) ).
cnf(less_equal_and_equal,axiom,
( X0 = X1
| ~ 'less$uequal'(X1,X0)
| ~ 'less$uequal'(X0,X1) ) ).
cnf(c0,plain,
'less$uequal'(a,b),
inference(clausification,[status(esa)],[a_LE_b]) ).
cnf(c1,plain,
~ 'less$uequal'(divide(c,b),divide(c,a)),
inference(clausification,[status(esa)],[prove_c_divide_b_LE_c_divide_a]) ).
cnf(c2,plain,
( divide(X0,X1) = zero
| ~ 'less$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[quotient_less_equal1]) ).
cnf(c3,plain,
( 'less$uequal'(X0,X1)
| divide(X0,X1) != zero ),
inference(clausification,[status(esa)],[quotient_less_equal2]) ).
cnf(c4,plain,
'less$uequal'(divide(X0,X1),X0),
inference(clausification,[status(esa)],[quotient_smaller_than_numerator]) ).
cnf(c5,plain,
'less$uequal'(divide(divide(X0,X1),divide(X2,X1)),divide(divide(X0,X2),X1)),
inference(clausification,[status(esa)],[quotient_property]) ).
cnf(c6,plain,
'less$uequal'(zero,X0),
inference(clausification,[status(esa)],[zero_is_smallest]) ).
cnf(c7,plain,
( X0 = X1
| ~ 'less$uequal'(X1,X0)
| ~ 'less$uequal'(X0,X1) ),
inference(clausification,[status(esa)],[less_equal_and_equal]) ).
cnf(d0,plain,
( ~ 'less$uequal'(X0,divide(X0,X1))
| divide(X0,X1) = X0 ),
inference(resolution,[status(thm)],[c7,c4]) ).
cnf(d1,plain,
( ~ 'less$uequal'(X0,zero)
| zero = X0 ),
inference(resolution,[status(thm)],[c7,c6]) ).
cnf(d2,plain,
divide(zero,X0) = zero,
inference(resolution,[status(thm)],[c2,c6]) ).
cnf(d3,plain,
'less$uequal'(divide(divide(X1,X0),zero),divide(divide(X1,zero),X0)),
inference(superposition,[status(thm)],[d2,c5]) ).
cnf(d4,plain,
divide(divide(X0,X1),X0) = zero,
inference(resolution,[status(thm)],[c2,c4]) ).
cnf(d5,plain,
'less$uequal'(divide(divide(X0,X0),divide(X1,X0)),zero),
inference(superposition,[status(thm)],[d4,c5]) ).
cnf(d6,plain,
'less$uequal'(divide(divide(X0,X0),zero),zero),
inference(superposition,[status(thm)],[d2,d5]) ).
cnf(d7,plain,
zero = divide(divide(X0,X0),zero),
inference(resolution,[status(thm)],[d6,d1]) ).
cnf(d8,plain,
( 'less$uequal'(divide(X0,X0),zero)
| zero != zero ),
inference(superposition,[status(thm)],[d7,c3]) ).
cnf(d9,plain,
divide(a,b) = zero,
inference(resolution,[status(thm)],[c2,c0]) ).
cnf(d10,plain,
divide(zero,a) = zero,
inference(superposition,[status(thm)],[d9,d4]) ).
cnf(d11,plain,
zero = zero,
inference(demodulation,[status(thm)],[d10,d2]) ).
cnf(d12,plain,
'less$uequal'(divide(X0,X0),zero),
inference(resolution,[status(thm)],[d11,d8]) ).
cnf(d13,plain,
zero = divide(X0,X0),
inference(resolution,[status(thm)],[d12,d1]) ).
cnf(d14,plain,
'less$uequal'(divide(divide(X0,divide(X0,zero)),zero),zero),
inference(superposition,[status(thm)],[d13,d3]) ).
cnf(d15,plain,
zero = divide(divide(X0,divide(X0,zero)),zero),
inference(resolution,[status(thm)],[d14,d1]) ).
cnf(d16,plain,
( 'less$uequal'(divide(X0,divide(X0,zero)),zero)
| zero != zero ),
inference(superposition,[status(thm)],[d15,c3]) ).
cnf(d17,plain,
'less$uequal'(divide(X0,divide(X0,zero)),zero),
inference(resolution,[status(thm)],[d11,d16]) ).
cnf(d18,plain,
zero = divide(X0,divide(X0,zero)),
inference(resolution,[status(thm)],[d17,d1]) ).
cnf(d19,plain,
( 'less$uequal'(X0,divide(X0,zero))
| zero != zero ),
inference(superposition,[status(thm)],[d18,c3]) ).
cnf(d20,plain,
'less$uequal'(X0,divide(X0,zero)),
inference(resolution,[status(thm)],[d11,d19]) ).
cnf(d21,plain,
divide(X0,zero) = X0,
inference(resolution,[status(thm)],[d20,d0]) ).
cnf(d22,plain,
'less$uequal'(divide(divide(X2,X0),zero),divide(divide(X2,divide(X0,X1)),X0)),
inference(superposition,[status(thm)],[d4,c5]) ).
cnf(d23,plain,
'less$uequal'(divide(X0,X1),divide(divide(X0,divide(X1,X2)),X1)),
inference(demodulation,[status(thm)],[d22,d21]) ).
cnf(d24,plain,
( ~ 'less$uequal'(divide(divide(X0,X2),X1),divide(divide(X0,X1),divide(X2,X1)))
| divide(divide(X0,X1),divide(X2,X1)) = divide(divide(X0,X2),X1) ),
inference(resolution,[status(thm)],[c7,c5]) ).
cnf(d25,plain,
( divide(divide(X0,divide(X0,X1)),divide(X1,divide(X0,X1))) = divide(divide(X0,X1),divide(X0,X1))
| ~ 'less$uequal'(zero,divide(divide(X0,divide(X0,X1)),divide(X1,divide(X0,X1)))) ),
inference(superposition,[status(thm)],[d13,d24]) ).
cnf(d26,plain,
( ~ 'less$uequal'(zero,divide(divide(X0,divide(X0,X1)),divide(X1,divide(X0,X1))))
| divide(divide(X0,divide(X0,X1)),divide(X1,divide(X0,X1))) = zero ),
inference(demodulation,[status(thm)],[d25,d13]) ).
cnf(d27,plain,
divide(divide(X0,divide(X0,X1)),divide(X1,divide(X0,X1))) = zero,
inference(resolution,[status(thm)],[c6,d26]) ).
cnf(d28,plain,
'less$uequal'(divide(divide(X0,divide(X0,X1)),X1),divide(zero,X1)),
inference(superposition,[status(thm)],[d27,d23]) ).
cnf(d29,plain,
'less$uequal'(divide(divide(X1,divide(X1,X0)),X0),zero),
inference(demodulation,[status(thm)],[d28,d2]) ).
cnf(d30,plain,
zero = divide(divide(X0,divide(X0,X1)),X1),
inference(resolution,[status(thm)],[d29,d1]) ).
cnf(d31,plain,
( 'less$uequal'(divide(X0,divide(X0,X1)),X1)
| zero != zero ),
inference(superposition,[status(thm)],[d30,c3]) ).
cnf(d32,plain,
( divide(X0,zero) = X0
| ~ 'less$uequal'(X0,X0) ),
inference(superposition,[status(thm)],[d21,d0]) ).
cnf(d33,plain,
( ~ 'less$uequal'(X0,X0)
| X0 = X0 ),
inference(demodulation,[status(thm)],[d32,d21]) ).
cnf(d34,plain,
( 'less$uequal'(X0,X0)
| zero != zero ),
inference(superposition,[status(thm)],[d13,c3]) ).
cnf(d35,plain,
'less$uequal'(X0,X0),
inference(resolution,[status(thm)],[d11,d34]) ).
cnf(d36,plain,
X0 = X0,
inference(resolution,[status(thm)],[d35,d33]) ).
cnf(d37,plain,
'less$uequal'(divide(X0,divide(X0,X1)),X1),
inference(resolution,[status(thm)],[d36,d31]) ).
cnf(d38,plain,
divide(divide(divide(X0,X1),divide(X2,X1)),divide(divide(X0,X2),X1)) = zero,
inference(resolution,[status(thm)],[c5,c2]) ).
cnf(d39,plain,
divide(divide(divide(divide(divide(X0,X1),divide(X2,X1)),X3),divide(divide(divide(X0,X2),X1),X3)),divide(zero,X3)) = zero,
inference(superposition,[status(thm)],[d38,d38]) ).
cnf(d40,plain,
divide(divide(divide(divide(divide(X1,X2),divide(X3,X2)),X0),divide(divide(divide(X1,X3),X2),X0)),zero) = zero,
inference(demodulation,[status(thm)],[d39,d2]) ).
cnf(d41,plain,
divide(divide(divide(divide(divide(X0,b),zero),X1),divide(divide(divide(X0,a),b),X1)),zero) = zero,
inference(superposition,[status(thm)],[d9,d40]) ).
cnf(d42,plain,
divide(divide(divide(divide(X0,b),zero),X1),divide(divide(divide(X0,a),b),X1)) = zero,
inference(demodulation,[status(thm)],[d41,d21]) ).
cnf(d43,plain,
divide(divide(divide(X0,b),X1),divide(divide(divide(X0,a),b),X1)) = zero,
inference(demodulation,[status(thm)],[d42,d21]) ).
cnf(d44,plain,
'less$uequal'(divide(divide(divide(X0,X1),X2),divide(X0,X2)),divide(zero,X2)),
inference(superposition,[status(thm)],[d4,c5]) ).
cnf(d45,plain,
'less$uequal'(divide(divide(divide(X1,X2),X0),divide(X1,X0)),zero),
inference(demodulation,[status(thm)],[d44,d2]) ).
cnf(d46,plain,
zero = divide(divide(divide(X0,X1),X2),divide(X0,X2)),
inference(resolution,[status(thm)],[d45,d1]) ).
cnf(d47,plain,
zero = divide(divide(divide(X0,X1),zero),X0),
inference(superposition,[status(thm)],[d21,d46]) ).
cnf(d48,plain,
zero = divide(divide(X0,X1),X0),
inference(demodulation,[status(thm)],[d47,d21]) ).
cnf(d49,plain,
divide(divide(divide(X0,b),divide(X0,a)),zero) = zero,
inference(superposition,[status(thm)],[d48,d43]) ).
cnf(d50,plain,
divide(divide(X0,b),divide(X0,a)) = zero,
inference(demodulation,[status(thm)],[d49,d21]) ).
cnf(d51,plain,
'less$uequal'(divide(divide(X0,b),zero),divide(X0,a)),
inference(superposition,[status(thm)],[d50,d37]) ).
cnf(d52,plain,
'less$uequal'(divide(X0,b),divide(X0,a)),
inference(demodulation,[status(thm)],[d51,d21]) ).
cnf(d53,plain,
$false,
inference(resolution,[status(thm)],[d52,c1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN007-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n002.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Fri Sep 25 15:59:36 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 31.74/9.69 % SZS status Unsatisfiable for theBenchmark.p
% 31.74/9.69 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------